Mission Invisible: A Novel About the Science of Light (Science and Fiction) 3030346331, 9783030346331

Table of contents :
Contents
Mission Invisible
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
Scientific Appendix
A1
A2
A3
A4
A5
A6
A7
A8
A9
A10
A11
A12
A13
A14

Citation preview

Ulf Leonhardt

Mission Invisible A Novel About the Science of Light

Science and Fiction

Series Editors Mark Alpert Philip Ball Gregory Benford Michael Brotherton Victor Callaghan Amnon H Eden Nick Kanas Geoffrey Landis Rudy Rucker Dirk Schulze-Makuch Rüdiger Vaas Ulrich Walter Stephen Webb

Science and Fiction – A Springer Series This collection of entertaining and thought-provoking books will appeal equally to science buffs, scientists and science-fiction fans. It was born out of the recognition that scientific discovery and the creation of plausible fictional scenarios are often two sides of the same coin. Each relies on an understanding of the way the world works, coupled with the imaginative ability to invent new or alternative explanations—and even other worlds. Authored by practicing scientists as well as writers of hard science fiction, these books explore and exploit the borderlands between accepted science and its fictional counterpart. Uncovering mutual influences, promoting fruitful interaction, narrating and analyzing fictional scenarios, together they serve as a reaction vessel for inspired new ideas in science, technology, and beyond. Whether fiction, fact, or forever undecidable: the Springer Series “Science and Fiction” intends to go where no one has gone before! Its largely non-technical books take several different approaches. Journey with their authors as they • Indulge in science speculation – describing intriguing, plausible yet unproven ideas; • Exploit science fiction for educational purposes and as a means of promoting critical thinking; • Explore the interplay of science and science fiction – throughout the history of the genre and looking ahead; • Delve into related topics including, but not limited to: science as a creative process, the limits of science, interplay of literature and knowledge; • Tell fictional short stories built around well-defined scientific ideas, with a supplement summarizing the science underlying the plot. Readers can look forward to a broad range of topics, as intriguing as they are important. Here just a few by way of illustration: • Time travel, superluminal travel, wormholes, teleportation • Extraterrestrial intelligence and alien civilizations • Artificial intelligence, planetary brains, the universe as a computer, simulated worlds • Non-anthropocentric viewpoints • Synthetic biology, genetic engineering, developing nanotechnologies • Eco/infrastructure/meteorite-impact disaster scenarios • Future scenarios, transhumanism, posthumanism, intelligence explosion • Virtual worlds, cyberspace dramas • Consciousness and mind manipulation More information about this series at http://www.springer.com/series/11657

Ulf Leonhardt

Mission Invisible A Novel About the Science of Light

Ulf Leonhardt Tel Aviv, Israel

ISSN 2197-1188     ISSN 2197-1196 (electronic) Science and Fiction ISBN 978-3-030-34633-1    ISBN 978-3-030-34634-8 (eBook) https://doi.org/10.1007/978-3-030-34634-8 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Cover image by Alexander Kobyak, reproduced by kind permission of Vita Nova, St Petersburg. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Contents

Mission Invisible  1 1    1 2    3 3    4 4    5 5    7 6    8 7    9 8   10 9   11 10   12 11   14 12   16 13   18 14   19 15   20 16   21 17   23 18   24 19   25 20   26 21   27 22   28 23   30 24   30 25   31 v

vi Contents

26   32 27   33 28   34 29   34 30   36 31   37 32   37 33   38 34   39 35   40 36   41 37   41 38   42 39   43 40   44 41   45 42   46 43   46 44   47 45   48 46   49 47   50 48   53 49   54 50   56 51   56 52   57 53   58 54   59 55   60 56   61 57   62 58   63 59   64 60   65 61   67 62   67 63   68 64   68 65   69

 Contents 

vii

66   70 67   71 68   72 69   73 70   75 71   77 72   78 73   79 74   80 75   81 76   82 77   83 78   84 79   85 80   86 81   87 82   88 83   88 84   90 85   91 86   92 87   94 88   95 89   97 90   99 91   100 92   102 93   103 94   104 95   105 96   106 97   107 98   108 99   109 100   110 101   110 102   111 103   113 104   113 105   114

viii Contents

106   107   108   109   110   111   112   113  

114 115 117 117 119 119 120 121

Scientific Appendix123 A1 123 A2 124 A3 126 A4 127 A5 129 A6 130 A7 132 A8 134 A9 135 A10 137 A11 138 A12 139 A13 141 A14 143

Mission Invisible

1 Life is a journey, but today’s journey did not begin well. Rain had made the sky grey and had clogged the streets with cars and buses, as people made their way to work. Iain never took his car to the Office; there was no car park there anywhere. He was sitting in a minibus, trying to fall asleep, but kept awake by the loud oriental music from the driver’s radio, and by the driver’s forte falsetto singing to the tune. At least the driver was happy, although not for much longer. After they had finally cleared the traffic jam and collected another passenger from the roadside, the minibus rushed back into the traffic flow, cutting off a white van. The van honked with a strength exceeding the sum of its horsepowers, and began to chase the minibus. The van pulled over and placed itself firmly in front of the offender. The driver of the minibus took the challenge and pressed the accelerator to the screams of the passengers, chasing the van, pulling over, and blocking it at the next traffic lights. Two, then three times the two vehicles sparred. Then, suddenly, by some signal Iain could not see, the two drivers jumped out to settle the score; first with words and then with fists. They were evenly matched, neither could defeat the other, so after another round of verbal abuse, they took pictures of each other’s license plates and climbed back to their seats. Today’s journey did not begin well, but at least there was some drama to be watched. Most days felt empty and grey, although most days, the sun shone with Mediterranean clarity over the scenes and dramas played out down there in the city. Iain was not looking forward to the Office. He worked as a travel agent at the headquarters of a large tour operator. Yes, at least he was not © Springer Nature Switzerland AG 2020 U. Leonhardt, Mission Invisible, Science and Fiction, https://doi.org/10.1007/978-3-030-34634-8_1

1

2 

U. Leonhardt

spending his days and nights at the last minute counter of the airport, selling overpriced tickets to desperate passengers who had got lost in the duty free or the Irish pub and had missed their flights. Eventually they got their tickets; Iain was grounded. His job consisted of organizing tours for incoming travel groups and trying to stay sane in the bedlam of the Office. Every working day, from his cubicle on the open office floor, he could hear shouts in English, French, Spanish, German, and Russian. The loudest were the French, of Maghrebi descent, who were constantly goading Iain’s group, the British Department. Apparently, the Hundred Year’s War was not over yet, the Battle of Agincourt not yet lost to France. Nobody spoke to the manager of the British Department, as she carried an air of superiority, but everyone was at liberty to shout at her underlings. The great wars of the nations continued in miniature at the Office, while telephones rang demanding to be answered, salespeople rushed in advertising their hotels, tour guides came by to argue their fees, and Iain was trying to concentrate on his work. Over all this reigned the boss, commonly nicknamed Miss Piggy, as she looked and acted the part. Miss Piggy sat in state in her elevated glass cubicle, surveying the serfs beneath, ready to pounce, ready to growl, ready to pierce the air with her shriek. Her word was command. In vain had Iain tried to get out of there. He had sent his CV everywhere he could think of; no prospective employer had recognized his natural curiosity, his talent for picking up languages, and his sense of order and clarity. Everyone had seen his degree in Persian poetry and his many years of working as a travel agent to finance his studies. So there he was, stuck in a minibus, on his way to work. Iain, who loved travel and adventure: lands unknown, languages unheard of; he had to organize the journeys of others, grounded in his cubicle at the Office. Not that his usual clients were a particularly interesting lot. Most of his assignments were groups of pilgrims touring the religious sights, where they saw a predictable canon of places and heard a predictable canon of stories, over and over again, like the pearls of a rosary. Occasionally, Iain got some more exciting assignments—groups of ornithologists flocking to witness the migration of birds in spring and autumn, or groups of political activists who needed to be steered away from trouble. Sometimes he was assigned individual travellers, if they were sufficiently VIP. Last week, Iain had taken care of the complicated visa requirements of a British lady, Lucy de Phos, who was also an eminent professor of some kind. Lady Lucy needed to continue her journey to Saudi Arabia and Iran, countries that were bitter rivals and adversaries. She had a Saudi visa in her passport, but also required an Iranian one. How could she get it, with the visa of the arch-enemy already in her passport,

  Mission Invisible 

3

and within two days, and in a country without an Iranian consulate? Impossible! Miss Piggy had given Iain one day’s leave from the Office to sort out Lady Lucy’s visa. Iain drove to the border, changed his car for a taxi on the other side, and was driven to the Iranian consulate, which he entered with his British passport. ‘Her Britannic Majesty’s Secretary of State Requests and requires in the Name of Her Majesty all those whom it may concern to allow the bearer to pass freely without let or hindrance, and to afford the bearer such assistance and protection as may be necessary.’ This was written on the first page and, indeed, Iain was let in to the consulate, where he faced a gruff-looking uniformed officer below the portraits of the Ayatollah and the President. The officer was transformed, however, on hearing Iain speaking his language and noting how he spoke it, a beautiful classic Persian. And when Iain mixed a few of Hafez’ verses in his plea, the officer shook his hand, tears in his eyes, and glued the visa into Lady Lucy’s passport, without even turning a page. Yet this was one day in a long series of days at the Office. Iain’s life was a farce, a farce played badly, a farce without end. How could it ever end? With a phone call.

2 ‘Iain!’ came the unmistakable shriek from the direction of the boss. Iain had put his mind in the state of an audio-visual nirvana so that he could concentrate on his screen while two of his cubicle neighbors were arguing with clients on the phone. ‘Iain!’ The boss, nicknamed Miss Piggy by her inferiors at the Office, flung her scarf around her neck and set sail towards Iain’s position. He woke from his nirvana when the first wave of her perfume wafted in. ‘Iain! How many times do I need to call you? I’ve got a phone call from that British lady you were supposed to get a visa for. What have you done to her visa?’ ‘I got it for her.’ ‘You must have made some mistake. She wants to see you at once.’ ‘At once?’ ‘She’s a VIP client of the company and a real lady.’ Miss Piggy elevated her stature and let her hair wave around, as if proof were required that she was a lady as well.

4 

U. Leonhardt

‘Clients and ladies are always right. Now,’ changing her vowels from those of a fair lady to the sounds of her native east end of London, ‘move it!’ Half an hour later, Iain found himself at the main entrance to the Intercontinental Hotel where Lady Lucy had taken her lodgings. The security guard at the door nodded and let him in. Iain was wondering what he could possibly have done wrong. Was the date of the visa incorrect, or was the name misspelled, or the forename and surname transposed? But Iain had checked the visa before he left the consulate; everything was in order. Maybe Lady Lucy had changed her plans and required a new visa. Looking around the light-flooded, grand entrance hall of the hotel, Iain was wondering about Lady Lucy being a scientist. In his mind, he pictured scientists, in particular female ones, as spending their days in basement laboratories, starved of sunlight, dressed in white lab coats and doing cruel experiments on rats. But these were biologists. Iain recalled that Lady Lucy was a physicist, a theoretical physicist—neither of which would make her a member of the intercontinental set. Theoretical physicists were universally understood to spend their days in their offices, doing complicated sums, and their nights in shared apartments where they would collect the treasures from the comic-­ book store, eat pizza, and fantasize about G-string theory and the Big Bang. They were certainly not female—neuter, at best—and whatever they became whenever they grew up, they were definitely not the kind to stay in five-star international hotels. Iain took the elevator, walked to Lady Lucy’s suite, and pressed the buzzer.

3 A tall, stern man, all suit and tie, opened the door and, upon hearing Iain’s name, showed him in. There she was, Lady Lucy, the picture of an English lady in her very best years, dressed in light tweed, wearing double strand pearls and a summer hat above her ash blond hair. She must have been well-­ past sixty, but was exceedingly well-preserved and well-presented. ‘This, I suppose, is the chap from the travel agency.’ ‘Yes, milady,’ her assistant said. ‘Lady Lucy, may I present Iain. Iain, this is Lady Lucy de Phos.’ ‘Your ladyship, I am honored.’ Iain tried to be very polite and polished, confronted as he was with a figure straight from Tatler Magazine. ‘How can I be of assistance, ma’am?’ ‘You were responsible for my Iranian visa?’ ‘I apologize if there is something wrong with it.’

  Mission Invisible 

5

‘No, not at all, the visa is fine. Everyone told me here that it was impossible to get an Iranian and a Saudi visa in the same passport; the visas annihilate each other, as their countries seem to be aspiring to. Tell me, how did you manage to do it?’ ‘With Persian poetry, ma’am.’ ‘Ah, so you do speak the language. Do you know the country as well?’ ‘I have never been there in person, but often in mind. At university I studied Persian poetry and history, as well as Arabic.’ ‘What other languages do you speak? Russian, by any chance?’ ‘Yes I do, ma’am. I never had great difficulty in picking up languages. It all comes naturally: I simply listen and repeat what I hear—a bit like a parrot, first without understanding a word, but then gradually getting the meaning. I think this is the way children learn languages. I have never crammed vocabulary words, I have a very vague idea of grammar, but put me in a foreign environment and I will eventually get to speak the language.’ ‘How extraordinary. Most British, including myself, assume the entire world speaks English anyway, and if not, they ought to. Are you quite sure you are British?’ Iain nodded. ‘Young man, I have a proposition to make. I shall visit Saudi Arabia, Iran, Russia, and perhaps a few other places on a journey around the world on science business. There I need someone capable of conversing with the locals in their own language, and generally speaking, to act on my behalf. I am afraid this man’—she pointed to the stern assistant—‘is rather hopeless with foreign languages. You seem to be the one I was looking for. You are a British subject, you said?’ Iain nodded again. ‘You will need a Saudi visa of course. I have a personal invitation by the King, and I am quite sure the King’s office can provide you with a Saudi visa in no time at all. You already know how to get a Iranian one. I will pay for travel, lodgings, and subsistence on my grant, and a monthly allowance of ’— gauging Iain—‘a thousand pounds. Would that suit you?’ The only reply Iain could give was; ‘Yes, thank you very much, ma’am.’

4 Iain was lost for words. Was this not the answer to his prayers? Could he imagine a more glamorous escape from the daily farce? A journey around the world, all expenses paid! He would see places he had always dreamed of,

6 

U. Leonhardt

c­ ountries off-limits to tourists. Visiting Saudi Arabia had been impossible for tourists; one could travel there only on business with some sponsored invitation or as a Muslim pilgrim on the Hajj to the Holy City of Mecca. To be able to enter Saudi Arabia, Iain would have had to pretend to be a pilgrim, but his honest nature objected to all forms of deception. It was also difficult to visit Iran; Iain’s Persia, his kingdom of poets, his Mecca. Recently, Russia had become off-bounds to Western tourists, too. Iain had picked up Russian from friends at university and had fallen in love with Russian literature. Perhaps he would get to see Dostoyevsky’s Saint Petersburg or Bulgakov’s Moscow. To which other forbidden places would this journey take him? What also struck Iain was the similarity between Lady Lucy’s proposition and a novel he had loved as a boy, “Around the World in Eighty Days” by Jules Verne. The novel took place in the Victorian age of steam and steel when, for the first time in human history, one could travel around the globe in speed and style. A rich British gentleman, Phileas Fogg, bet his fellow members of the exclusive Reform Club in London that he could manage the journey in eighty days, an almost impossible feat at the time. Together with his faithful servant Jean Passepartout, they would race by boat and rail, ride on an elephant, sail across the frozen American prairie, and burn their last boat to reach the Irish shore. Without a moment to spare, Phileas Fogg finally arrived at the Reform Club with the words ‘Here I am, gentlemen’. Apart from winning his bet, he also discovered his human heart during the journey, winning in return the heart of a lovely lady travelling with him. Would anyone go around the world for less? Iain was sure he would make a good Jean Passepartout for Lady Lucy de Phos. He already knew how to obtain tricky visas for her passport, and he would serve her with all his talents. Iain also approved of the reason for the journey, which was not an idle bet, as in Phileas Fogg’s story, but science business, although he had never enjoyed science at school. And physics had been the worst, a random collection of disconnected facts with tedious explanations he could not follow. Worse than that, physics was a subject that did not speak to his heart; it did not make him laugh, it did not make him cry. Physics was not human. Iain dutifully acknowledged that most of modern technology derives from physics; he enjoyed its products if they worked, and got irritated and desperate if they did not. Autistic techno geeks were there to invent and fix technical gadgets, but they should leave him in peace with their physics. Yet Lady Lucy’s appearance had reminded Iain of something else: the royal roots of science, of pure science that is, not technology. Science first blossomed under the patronage of royalty. Iain remembered from his history lectures that in the sixteenth century one king of Denmark had spent a quarter

  Mission Invisible 

7

of the gross national product of the entire country on a single astronomer. This singular gift by a monarch had made modern astronomy possible. The patronage of royalty was also the reason why the first ever science academy is called the Royal Society of London. Is it then really a coincidence that the Nobel Prize is called Nobel, that is, noble? Maybe the royal roots of science play a role when people make fun of scientists and their peculiar habits. People tend to hate what they do not understand—Iain’s Persian poetry was no exception—and they ridicule what they secretly admire. If they laugh about the toffs, they laugh about the boffins, too. Lady Lucy had a personal invitation by the King of Saudi Arabia. If an absolute monarch was interested in her work, it must be absolutely important. With all his heart, Iain wished to serve her. What could be nobler than her work? So he thought.

5 The nuclear submarine had a visitor on board. Call him Ahab, or call him Nemo (‘no-name’ in Latin). He had inspected his forces before, he had flown in a supersonic strategic bomber, he had surveyed the vast intercontinental missile silos dug deep in caves, and now he was in a submarine in the abyss at the bottom of the sea. Nobody would dare to attack him, for from the depths of the ocean nuclear rockets would rise in retaliation, ascending to the surface, taking off towards the country he loathed and admired, America. If America dares to invade or merely interfere, darkness shall cover the Earth. The temptation was always there to dial in the code and press the red button. His people were a resilient lot. They had learned to live with hardship. After Armageddon they would crawl up out of the ground with the cockroaches to replenish the Earth and subdue it, in his name. The designer of the submarine’s command center must have had a sense of humor: he had integrated the red button into the trigger of a gun protruding from the controls. It would feel like firing a gun. The submarine also had an organ in the grand saloon, presumably another of the designer’s jokes, an organ just like the one in Jules Verne’s Nautilus. Captain Nemo, fighting against colonial oppression, the liberator, safe in his Nautilus, surrounded by everything he needed to survive, he would play the organ as the missiles rose. He was pleased with the submarine—it fitted his temperament: dwelling in darkness, in silence, invisible, invincible. He wished his other forces were as

8 

U. Leonhardt

invisible as she was, for then he could take by stealth what would otherwise require bravery. Suddenly, he remembered the invention he had heard about so recently, and he gave the order.

6 A few days later, Iain joined Lady Lucy on her journey around the world on science business. The first destination was Riyadh, capital of Saudi Arabia. The King or whoever was financing the trip had made sure the journey went in style. Iain was waiting for Lady Lucy at the seaside pier, and there she arrived, her chauffeur helping her out of the black limousine. ‘Good morning, Lady Lucy!’ ‘Good morning, Iain. I trust the helicopter is waiting for us.’ Security personnel waved them through to the end of the pier where they climbed on board and took off over a sea that was glittering in the brilliant morning light. This was what the King’s money could do: the helicopter spared them the inconvenience of a connecting flight, it carried them to the airport in a neighboring country where they could take a direct flight to Riyadh. Everything went like a breeze. A car was already waiting for the helicopter on arrival, taking them to a small separate terminal where a lady in a red uniform checked them in. Lady Lucy travelled First Class and propriety required that a distinction be made between herself and her assistant, so Iain had to settle for Business Class. Iain had never flown Business Class before. He took his seat, nodded shyly to his neighbor and tried out the seat’s gadgets, moving it up, down, forward, and back, then testing massage mode. Yet more than the gadgets, what astonished him was the simple fact that he was treated like a human being. He was greeted as a person and given space to breathe and food to eat that was actually fit for human consumption. Normal, Tourist Class air travel had not only lost its glamour, but most of its human dignity. Passengers were herded like cattle on their way to slaughter, squeezed into seats they could barely sit on, forced to defend their territory with their elbows, and handed out food other animals would disdain. All this, thought Iain, for making a few passengers pay more than thrice the price to move up to the front of the plane where they could feel like normal human beings again, while reaping maximal profits from the less fortunate. Probably the only method of milking more money from Tourist Class travel would be the invention of a powerful and perfectly harmless anesthetic.

  Mission Invisible 

9

Passengers would take it through pipes in the departure lounge, pass out, and be stacked on board as cargo.

7 Yet these were worries for the future. For the present, Iain was looking out of his window over the ocean of sands of the Arabian Desert far below, on his way to Riyadh. Soon the first women were heading for the washrooms from whence they would return transformed. The law of Saudi Arabia required all women to wear the abaya in public; this was a black cloak that covered body and hair, regardless of whether they were Muslim, Christian, or of some other faith. One after another they made their way up the aisle and returned covered in black. Although abayas are uniform, Iain noticed differences, some subtle, some more conspicuous—from the afghan burka covering the formidable matriarch on the front row of the tourist class cabin to the elegant cloak of the young lady in front of Iain, which only emphasized her figure, and so completely and utterly defeating the purpose of the garment. Some women were covering their face with a veil and some were not, depending, presumably, on the directions and degrees of their religious convictions. Some abayas were simple, some made of the finest silk, some plain, some refined with barely visible embroideries, hinting on the style, education, and social class of the wearer. Iain was entering a world of subtle messages. Iain had packed an abaya for Lady Lucy as well. He walked up to the first class cabin and apologized for disturbing her. ‘Yes, what is it, Iain?’ ‘Ma’am, we are about to enter Saudi Arabia. There, it is tradition and law that all women must wear a cloak in public.’ ‘A cloak?’ ‘Here it is, ma’am. It’s called the abaya. Women must wear it when they are out in public places. It is very practical: one is always properly dressed with an abaya, no matter what one is wearing. It is also perfect for going out incognito, if you combine it with the veil. Cloak and veil will hide you when you wish to remain private; nobody will recognize who you are. It will make you practically invisible.’ Lady Lucy smiled— ‘You want to give me an invisibility cloak?’

10 

U. Leonhardt

8 Lady Lucy and Iain had landed in Riyadh. A Saudi official, dressed in pristine white with a red-and-white checkered headscarf, greeted them and helped them through passport control and customs. A limousine took them to the Ritz. This grand and luxurious hotel, surrounded by palm trees and gardens with ancient olive trees, was conveniently close to the Diplomatic Quarter, which was of particular interest to Lady Lucy. But right now she had a free afternoon and wished to see Riyadh. After checking in, she went to her suite to refresh herself, while Iain booked a chauffeured car at the concierge. Lady Lucy asked the driver what he would recommend for sightseeing. ‘The new shopping mall’, he said, ‘this is the place to go. There people meet, there they go for walks, there they enjoy themselves. We also have a wonderful new zoo, but the zoo would take too much of your time.’ The mall was a marvel of modern architecture, extending over three floors that seemed to float in mid-air, connected by round escalators shepherding the shoppers from floor to floor. Most were cloaked figures in black wearing fashionable handbags, but there were also a few white-dressed Arab men and a handful of Westerners to blend in among them. The architecture was marvelous, yet the shops were of the usual, international kind, apart from some subtle differences and peculiarities Iain noticed. In the opulent gold department, for instance, women could receive their dowry in solid gold and jewels, then tuck it away as their life savings in their married home. Other forms of bridal merchandize raised Iain’s curiosity: shops of rather risqué female nightgowns where, to Iain’s amazement, female shoppers where served by exclusively male shop assistants. Male shoppers congregated at the perfume department where they tried out the latest scents or disappeared in the all-male beauty parlors to be coiffured and rejuvenated. All this was intriguing, but not the Arabia Lady Lucy wanted to see. So she asked to be driven to the Old Town. Lady Lucy wished to see a real souk—an oriental market, so there they went. They walked through the aisles, tried the dried fruits, enjoyed the colors and smells of the spices, and admired the rows of abayas at the abaya shop, until they were approached by three stout Saudi men wearing loose, hooded headscarfs and brandishing sticks. Their rather excessive beards and rather vacant expressions told Iain what they were about. No doubt, these were members of the Committee for the Promotion of Virtue and the Prevention of Vice, the mutaween—Arabic for ‘volunteers’; also and more prosaically known as the religious police.

  Mission Invisible 

11

9 The mutaween were a brotherhood of Muslim vigilantes patrolling the streets and shops in search of violations of Islamic law. Their primary task, the prevention of crime and drug abuse, was certainly honorable and beneficial to society. But all too often they would focus more on their secondary task, enforcement of the Saudi dress code. Lady Lucy was a novice in wearing the abaya, and this had caught the eye of the three pious men. ‘Woman, cover!’ These were the only two words in English their leader knew. ‘Iain, what does this man mean? Is there a bomb scare? Do we have to run for cover?’ ‘Lady Lucy, let me handle this’ said Iain. He knew that it was haram—forbidden—for unrelated and unmarried men and women to walk together. He also anticipated that the concept of a female professor and boss to a man was beyond the vigilantes’ comprehension. So he confronted the men in Arabic: ‘You are not allowed to speak to my wife. I am her husband; you have to ask for my permission to address her.’ Iain used the ancient word ‘baal’ for husband, which also means ‘master’ or ‘owner’. The leader of the three men replied: ‘How do we know you are her owner? Prove it!’ ‘I am not walking around with my marriage certificate.’ ‘So how do we know?’ ‘You may ask me three questions about our marriage. After each question, I will write down my answer on this sheet of paper. Then you may ask her the same question and you will be able to check whether our answers match.’ ‘But she does not speak Arabic.’ ‘Don’t worry, I will translate.’ ‘Fine. First question: where do you live?’ Iain wrote in Arabic ‘London’ and turned to Lady Lucy in English: ‘Lady Lucy, the gentleman wishes you a good day and asks you where you are from.’ ‘London.’ ‘Match. Second question: what is the color of your bedroom? Ah, this really probes the secrets of your married life.’ Iain knew a color with the same word in English and Arabic, and wrote down ‘beige’. Then he asked in English: ‘Lady Lucy, this man has heard a lot about English cars. What is the color of your Jaguar?’ ‘Beige.’ ‘Match. Third and last question: what is the name of your maid? Now we test your household.’

12 

U. Leonhardt

Iain wrote down ‘Iain’ and said in English: ‘Lady Lucy, the gentleman asks you to introduce me to him.’ ‘This is Iain.’ ‘Match. But wait a second. What name is “this is”?!’

10 The owner of the shop behind them had overheard the discussion and opened his door for Lady Lucy and Iain, giving them asylum. The three irate vigilantes were banging against the closed door with their sticks, their only weaponry, apart from words and fists, unless they were reinforced by regular police. The three set out in search of a policeman, but then hastily fled the scene after several shopkeepers shouted at them to stop causing trouble. Our travellers found themselves in a different world. They were surrounded by bolts of cloth—fine printed cotton from Esfahan, red and green velvet from Venice, silvery damask and golden brocade from Damascus, and several bolts of iridescent silks of a lightness no longer found in China. Their hiding place was a textile heaven. In a spacious silvery cage, birds were singing—presumably for the entertainment of customers from a time before piped music. Another, even larger cage contained butterflies, giant tropical ones of brilliant colors. Some were nibbling on oranges, some were in the air, shining and sparkling like flying jewels. The room itself was rather dimly lit with beams of sunlight breaking through holes in the closed shutters, illuminating the butterflies, the birds, and the bolts of cloth as well as a myriad of floating particles. A few of the butterflies were free and joined them in their dance. The shopkeeper was an old man with well-groomed white beard and kind, brown eyes, dressed in a traditional robe and wearing a white cap on his head, but no scarf. He avoided looking at Lady Lucy, as his religion required, but made sure she was comfortable. He sent one of his sons for coffee and said to Iain in Arabic: ‘On behalf of my country, I apologize for these uneducated, misguided men who abuse the name of the prophet, peace be upon him. Please do sit down. I hope you feel better now.’ Iain answered with proper formality: ‘Peace be unto you and so may the mercy of the Lord and his blessings. How is your health?’ ‘And upon you be peace. Thanks to the Lord, I am in good health, although I am an old man. I have seen many things and have heard many stories. I see

  Mission Invisible 

13

that you are an inquisitive young man in search of the truth, and you speak our language well.’ ‘Thank you very much, I speak it a little. How do you know what I am looking for?’ ‘You have honest eyes and a bright mind—your argument with the three men was proof—and I think you have the gift for asking questions. The truth will find you, if God will; there is still some magic left in this part of the world.’ And one of the butterflies sat down on his hand, opening the azure of its wings. ‘Is it not beautiful how the light colors its messengers? All you see is light, and the light is from God, the merciful, praised be his name. Light may be deflected and distorted, like the minds of the three fools you met, but the truth will always come to light. These butterflies are like angels—slightly confused angels, judging by the way they flutter around. At night I must drape cloth over their cage, so that real angels can visit my house.’ The butterfly sailed off and faded away in the shadows, its colors extinguished. Iain asked the old man: ‘Why does the butterfly disappear from view when it is dark?’ ‘It does not make its own light. Some creatures do, look at these glowworms.’ And from a drawer he took a glass bottle illuminated by greenish light from dozens of glowworms trapped inside. ‘Do not be surprised, I trade in colorful cloth, studying light is my pastime.’ ‘How can I see something at all, if it does not make its own light?’ Iain insisted. ‘All you see is light. Some of it is made directly, most comes from light sources like lamps, the sky, or the Sun, and is scattered by the things you see.’ ‘What do you mean by scattered?’ ‘Look at the butterflies in the cage. White light from the Sun falls on them, some of it is reflected, and some of the reflected light reaches your eye. In this way you see the butterflies. The color of the reflected light is the color of the butterfly you see.’ ‘So the butterfly changes the color of the light.’ ‘No, white light already contains all of the colors. The butterfly reflects some colors and absorbs the others; this makes it colorful.’ ‘So taking away colors from white light makes it colorful? Isn’t this paradoxical? And anyway, how do you know that white light contains all the colors?’ ‘Look!’ The old man produced a glass prism from his drawer and held it in a beam of sunlight, breaking the light into all the colors of the rainbow.

14 

U. Leonhardt

Lady Lucy did not follow the conversation between Iain and the shopkeeper, as it was carried out in Arabic, but she became increasingly amused by the butterflies, the glowworms, and the prism. Iain said to the old man: ‘The lady you rescued is a famous professor of optics, the science of light.’ ‘She came to the right part of the world. In Cairo, exactly a thousand years ago, Ibn al-Haytham wrote the very first book of modern science. It is called the Book of Optics. In this book he no longer interpreted the writings of the ancient authorities, but the results of his own experiments, and he encouraged people to think for themselves and to question. Had the three fools only a thousandth part of a thousandth part of his independent thinking, they would not blindly follow their leaders and harass innocent people. But I am talking too much, forgive me.’ The shopkeeper’s son came in, carrying a tray with dates, small cups, and a very oriental copper can. From the can he poured an olive-green liquid into the cups. It tasted of cardamom with a hint of saffron; it refreshed the mind and kindled the imagination. ‘What is this?’ ‘Coffee.’

11 The next day Lady Lucy was invited to a princely picnic in the desert, followed by a conference. Iain should accompany her, in case his assistance was needed. They took off by helicopter from the Ritz, leaving Riyadh behind them in the perpetual haze from millions of cars and people, and flew over long stretches of sand dunes, through the glaring heat, towards a clear blue sky. They eventually saw an encampment of white tents, a large rectangular one surrounded by smaller tents, and landed nearby. The smell of barbecue greeted them. There were camels in festive dress amid white jeeps, horses, and vans, and Saudi men going through their paces with falcons. They walked towards the large white tent, where people, both Saudis and Westerners, were standing waiting. Iain was looking out over the desert when he saw a sight that made him do a double take. He stood and stared across the desert to where a caravan of camels was slowly walking towards them, walking on air. Nothing was under the feet of the camels, only a flurry of silvery air, or perhaps water? But both were equally impossible. ‘What on Earth is this?’ Iain exclaimed in English. The softest of voices answered:

  Mission Invisible 

15

‘It’s a mirage.’ A young woman stood next to Iain, dressed in a black abaya, her face hidden under the veil so that only her eyes were visible. These were not Arabian eyes. Her English was almost perfect, with only the slightest hint of a foreign accent, soft and nasal. ‘Who are you?’ ‘Do you think I am a mirage, too?’ she laughed. ‘What is a mirage? Why do these camels seem to float on air or walk on water in the desert? And who are you?’ ‘A mirage is an optical illusion. You see something happening with your own eyes, but something else is happening right under your nose.’ She laughed again, but then became serious. ‘Illusions are useful sometimes. The mirage you have seen was a simple one. You know that camels cannot walk on air and that there is no water in the desert, so you know something is wrong. The best illusions are the ones you don’t see.’ ‘But tell me, what is going on in a mirage, if you know. How does it happen?’ ‘It’s really simple. The hot air above the desert sand turns into a mirror. This mirror reflects light from the sky. So what you have seen under the feet of the camels was a mirror image of the sky. The surface of water does the same: it reflects light from the sky; it is a mirror, too. Therefore you are made to believe there is water in the desert.’ ‘But how can air become a mirror?’ ‘If it is the destiny of light to reach your eye, it will do so in the shortest time. The shortest path is not always the straightest, you know.’ ‘I am sorry, I don’t quite understand.’ ‘I am sure you will in the end. A Frenchman discovered this principle of the shortest path. Pierre de Fermat, in the seventeenth century. Apparently, he believed the world behaves in the best possible way, even if the path seems curved or obscure. Another Frenchman, Voltaire, later ridiculed the idea that we live in the best of all worlds. But maybe more of this another time. We have to go to the conference.’ A man at the barbecue gave her and Iain plates of kebab, salad, and slices of roasted goose liver. While she was speaking to the man in Arabic, Iain noticed her foreign accent. It was not an English accent. But what was it? ‘Who are you?’

16 

U. Leonhardt

12 ‘Oh, I am Luna, or Dr. Luna, if you like. I am a lecturer at the University and a researcher. You may guess what I am working on.’ ‘Optics.’ ‘Yes, but here we are colleagues. They assigned me to accompany Lady Lucy in the Female Section of the University where men are not allowed.’ Her eyes smiled at him. He asked: ‘Can we meet sometime and continue talking, about optics of course?’ ‘Sure, here is my number.’ And she gave Iain a slip of paper with her phone number. The conference was about to begin. Iain and Luna went to their separate queues at the entrance of the large white tent, one security check for men and another, separate one for women. There the guards asked the women to remove their veils—for security reasons, but probably also for reasons of publicity; the speakers were international and should carry the image of modern Saudi Arabia into the world. The tent was pleasantly air-conditioned, to Iain’s relief. He looked at the people gathering around the registration desk, the Western speakers and the Saudi audience, many of them female students with bright, keen eyes beaming with anticipation. The speakers were all men, with the exception of Lady Lucy, and they had tried to dress up for the occasion, albeit not entirely successfully—one had combined a Harris-tweed jacket with linen trousers, others were wearing sneakers with suits; popular colors for shirts were blue or none at all. Only Lady Lucy and speakers with Italian accents had any sense of style. The speakers were from all over the Western world, and they all seemed to know one another. They shook hands and were pleased to see each other, or so they said. They spoke in what is known as International English, but Iain had some difficulties in following what they were going on about. Someone’s paper was rejected by Nature and downgraded to PRL; some said he knew who the referee was and that it was a scandal. What were they talking about? ‘They are talking about journals.’ Luna had appeared, as suddenly as in the desert, her face unveiled this time. Iain was staring at her, wondering how strange it was that she actually had a face, and a pretty one. ‘Nature and PRL—“Physical Review Letters”—are two of the journals scientists publish their results in.’ ‘And their articles are called papers?’ ‘You are catching on quickly.’ she smiled, and continued: ‘The first hurdle for a paper is the editorial board. For any journal with a really good name, the

  Mission Invisible 

17

editors reject most of the papers they receive—this one not interesting enough, that one not fashionable, the authors not known in the field. It is important to have good connections with the editors. So they are invited to posh conferences at exotic locations like this one. Over there, surrounded by a bit of a crowd, stands the editor of Nature Irreproducible Results.’ ‘Irreproducible Results?’ ‘Just kidding, Nature Optics really. Not all top journals do this: the editors of Science Magazine are forbidden to accept such favors.’ ‘And what are referees?’ ‘Once a paper has passed the editorial board, it goes to peer review, which means it is sent to other scientists who have the task of judging the paper. They are asked to check whether the science is right, but also whether the work of others is mentioned appropriately and whether the paper is of sufficient interest. The names of the referees are not revealed to the authors, to avoid trouble, but sometimes one can guess … .’ ‘Tell me, why all this nonsense? I understand that the science needs to be checked and re-checked by other scientists, but what has science to do with the reputation of the journal, connections with the editors, or anonymous referees? What’s it all for? Is it just vanity? Judging by their clothes, scientists don’t look vain to me?’ ‘But they are. And I can tell you, this is the toughest profession in the world. Well, apart from the fashion industry and the music business. Scientists compete with each other, first to get themselves an academic position. Most drop out of the race, only a few and the most talented or the toughest actually make it. Not everyone has talent, you know.’ She smiled and went on: ‘Scientists are judged by their papers. The better the name of the journal they publish in, the better are their chances. Scientists are also judged by the number of times their papers are cited. The logic is this: if a paper is frequently referred to, it must be influential; the more it is cited, the better it is. Papers in good journals are often more frequently cited, papers in obscure journals are more easily ignored. So it pays off to go the extra mile to the editor.’ She looked at Iain: ‘Counting the number of citations has one great advantage: it gives you a number for each paper, for each scientist. Numbers are simple and transparent. You can count them and combine them: they describe the indescribable—talent. Numbers don’t lie, do they?’ ‘That depends on their context. As you know, there are three kinds of falsehoods: lies, damned lies, and statistics.’ ‘Mark Twain. But while it is easy to lie with statistics, it is easier to lie without them—Frederick Mosteller. In any case, scientists compete, with or

18 

U. Leonhardt

­ ithout statistics. They compete for academic positions and they compete w for money.’ ‘For money?’ ‘For research money: to buy equipment, to pay for laboratories, to sustain a group of students and researchers doing the work; all this needs to be paid for from research grants. And scientists only get grants if they can prove they are successful, every time, all the time. This is what journals and conferences are for. What looks like pleasant conversation among friends and colleagues is in reality a ruthless struggle.’

13 Lady Lucy was the star of the conference. The crowd she attracted in the reception area exceeded even the one around the editor of Nature Optics. People talked to her, listened to her, eager for a word, a smile, anything. Lady Lucy opened the conference with the keynote lecture. She addressed the Saudi prince, who sat on his separate golden chair, as ‘Your Royal Highness’, but Iain felt they were equal. She spoke in quiet, measured words, explaining rational slides with diagrams and formulas projected onto the large screen behind her. She made pauses and showed no sign of rhetoric nor emotion, apart from the warm glow of someone who is immensely pleased with herself. In her lecture she explained her own research. She also referred to the work of others, yet only in reference to herself, demonstrating discreetly but unequivocally how influential her ideas were. The audience was hanging on her every word. Iain was proud of Lady Lucy, the queen of this eminent assembly of luminaries, and so he got a bit upset when, in the questions and answers sessions after her lecture, a tall, fat man stood up and asked in English, but with a Russian accent, why she had not mentioned his papers. How dare he! Her answer was polite, but to the point: she knew his work, but was talking about something else, which, apparently, the colleague had not noticed. After Lady Lucy’s keynote speech, other lectures followed. Iain had organized and attended conferences in his previous incarnation as a travel agent, but never a physics conference. At conferences on economics or politics he could understand the lectures, but not always the reasons why they were given; here he did not understand a word. Was it the subject, optics? But he had understood the old man in the oriental shop. Even Luna’s cryptic remarks had meant something to him. He noticed that the lectures were rather specialized—similar to medical conferences, where an entire week could be devoted

  Mission Invisible 

19

to a small part of the nose or where, he imagined, a symposium about the left ear would run in parallel to its counterpart on the right ear next door, because left-ear and right-ear specialists would never talk to each other. Iain also noticed that the lecturers went very fast. It was not the words that were fast, but the pace of the information. The speakers used slides with computer graphics, diagrams, and formulas that only a trained mind could grasp at that speed. The speakers often referred to their papers and mentioned where the results they talked about were published. But why did they need to discuss results already in print, available for everyone to read? Perhaps Luna could explain. Iain began to wonder about Luna. Something had stirred in him; something had perturbed him. Usually he trusted his instincts and, if something did not feel right, he racked his mind trying to pinpoint what it was. He was not particularly interested in her cynical remarks about the professional life of scientists—he was not part of their world; they were of no concern to him. So what was it? The old man in the souk came to his mind. He was a bit strange and his remarks were not part of Iain’s world either, but he was authentic, he was real. Luna talked like a Western woman, but the way she was wearing her abaya was perfect. It was fascinating what she said about light and destiny, but Iain did not like the undertone. She was a scientist with a PhD, but she gave Iain her phone number on a paper slip like a teenage Arab girl—according to Lonely Planet Saudi Arabia, that was something that teenagers did here. When Iain was puzzled about something or somebody he usually went back to the beginning. What was his first impression? The mirage. Then he remembered something Luna had said: they were colleagues, and she did not mean scientists—it was obvious to her that he was not one; they were colleagues in assisting Lady Lucy. Finally a point, a fact that was distinctly odd. How did she know who he was? Iain asked himself with a feeling of foreboding and danger.

14 The character that enters the scene now deserves a special fanfare And the security guards were making it for him! He was late and they would not let him in to the conference. The sounds of their deep voices sounded like the blast of angry cannons, interrupted by the machine-gun staccato of fast, high-­ pitched shrieks coming from the man himself. What he lacked in height, he exceeded in agility, and he was furious. While shouting at the top of his voice, he waved his invitation card at the face of the most obstinate guard. He,

20 

U. Leonhardt

Hieronymus Foo, Professor, Dr. rer. nat., uč, was invited by the King of Saudi Arabia to this conference and they, bloody security, would not let him in. He was late, because of a Viennese bureaucrat, Herr Zed. Foo had applied for Austrian citizenship and Herr Zed was in charge of his case. Just before his flight to Riyadh, he had had an appointment that took much longer than expected, and so he had missed his plane, got re-routed, arrived in haste, arranged for a helicopter to the conference, only to be stopped at the entrance. All this because of Austrian bureaucracy.

15 While Vienna is universally known and admired for coffee and cakes, Mozart and Brahms, waltz and charm—‘schmäh’, as the Viennese say, it is perhaps less well known as one of the world’s major centers of bureaucracy. In days long gone, Vienna used to be the heart of a vast empire, the Habsburg Empire that once stretched over Europe to Spain and the Spanish colonies in Latin America. Now, in this more solemn age, Vienna is reduced to the capital of Austria, a small but proudly independent country in central-eastern Europe. While the empire dissolved and the country contracted, the bureaucracy did not; instead of dealing with the real administration of an empire, it was dealing with paper. Papers were delivered from the council to the ministry, from the ministry to the council; they got opened, inspected, checked, signed, stamped, and sometimes forgotten. To the Viennese bureaucrats the outside world no longer existed; it had become a world of paper. Perhaps Foo had made a mistake when he decided to apply for the citizenship of Austria, because he had not anticipated the mountain of bureaucracy he would need to climb, and the morass of paperwork he would need to wade through. One of his problems was his international career. Foo’s home country had sent him first to the Transylvanian Institute of Technology where he graduated in the Russian-speaking program as a physics teacher. Then he had enrolled in the Royal Norwegian School of Engineering where he distinguished himself with a PhD summa cum laude. After his triumphant return to his home country he became a celebrated professor at home and also a visiting professor in Vienna. In Austria, titles and academic degrees are part of the name and they are very important. One would offend an apothecary by not calling her ‘Frau Magister’. Or was it ‘Magistress’ that was required by political correctness? No, ‘Magistra’. Only rather recently, in the titles for the highest echelon of the civil service, was the subtle distinction abolished between the plain ‘Hofrat’—

  Mission Invisible 

21

court councilor—and ‘Wirklicher Hofrat’—real court councilor. Foo was required to get his degree certificates translated with stamp and apostille, and then approved by the Ministry of Education, so that they could become part of his name. The teaching diploma, ‘ootchitel’ in Russian, the Ministry turned into the Czech abbreviation ‘uč’, much to Foo’s displeasure, as his name would now sound like ‘Foo-ootch’ or ‘Footch’, which means ‘caput’, ‘bust’, or ‘gone’ in German, the official language of Austria. Yet the land of the Czechs was once part of the Austrian empire and so ‘Footch’ it was. Foo’s Norwegian PhD posed an even bigger problem. It was not clear to the Ministry whether his doctorate was in the physical or the socio-economic sciences, whether the title “Dr. rer. nat.” or “Dr. rer. soc. oec.” should grace his name. Letters and emails flew between Norway and Austria, while in Vienna the only official Norwegian translator made a small fortune, until it was finally established that Foo was “Dr. rer. nat.”. One month after the Ministry’s decision—or was it two?—Foo finally got an appointment at department MA35 with the officer in charge of his immigration case, Herr Zed.

16 Many say things never change in Vienna, but they do. The clerks and officers at the city council were no longer wearing royal-and-imperial uniforms, but uniforms of a different kind. Herr Zed was sporting a yellow tee-shirt with black printed palm trees, jeans and sneakers. He had applied gel to his short blond hair; it stood as if he had spent the night at the discotheque. Foo, on the other hand, had already spent a few hours sitting with many other applicants in the corridors of the newly built MA35. To the casual observer MA35 may make a modern, functional impression; but despite appearances, things never change in Vienna. Foo was waiting and waiting, anxiously watching the time ticking away on his Rolex. His flight was due soon. He was clad in an expensive grey suit that somehow looked cheap and made him appear even shorter than he really was. In his mind, he was weighing up his chances if he applied his usual approach to bureaucracy—slipping a brown envelope with cash discreetly under his papers. He assumed—correctly—that Austrian civilization had not progressed to the level where he could expect receipts for bribes. He would not be able to charge it on his expenses. This was decisive: he would not use the brown envelope this time.

22 

U. Leonhardt

Finally, Foo was called in. He sat down and put the letter from the Ministry on the desk. Herr Zed read the name, Foo-uč, Dr. rer. nat., compared it with the list of applicants in front of him and shook his head: ‘Ya are not here.’ ‘What do you mean, I am not here? Here I am, right in front of you!’ The conversation was conducted in German of course, as Herr Zed did not speak English or any other foreign language. Foo’s German was quite good, but he had difficulties understanding Herr Zed’s Vienna-Ottakring accent. ‘Ya are not on the list of applicants.’ ‘But I have an appointment with you; here is the letter.’ Foo produced the invitation letter from the city council and, in his rising anger, also the invitation letter to the conference. ‘I have an invitation from the King of Saudi Arabia to come to his conference; I have no time to lose. Here are the documents you required about my academic degree.’ ‘But ya are not here.’ ‘Maybe you should look into your filing cabinet and see whether you can find my file,’ suggested Foo. Herr Zed stood up, went to the large cabinet behind him and opened the drawer with the letter ‘F’. It must be said that keeping order was not one of Herr Zed’s virtues. Files tumbled out, some papers sailed to the floor. Herr Zed gathered the papers and tried to sort out the files, to the amusement of his office mate at the other desk who was otherwise attending to a Chechen applicant. That applicant was puzzled after having heard that he was required to produce documents proving his criminal record, or rather the lack of it, from all the countries he had previously resided in, including Russia, Qatar, and Albania. ‘I am Chechen, you know. We don’t do documents.’ Herr Zed was not finding Foo in his files either. Maybe the file was displaced, maybe it had been sent away for inspection? In his anger, Foo completely forgot the time and demanded to see the manager. Herr Zed obliged and phoned her. After ten minutes which the two gentlemen spent in silence and the other two in debate, the manager came in: ‘Good morning, my name is Frau Magistra Esstee, I am the head of team 1; how can I help?’ ‘I am Professor Foo. I have an appointment for registering my academic degrees. Here is the letter from the Ministry with all the stamps and here is my invitation letter; I do have an appointment.’ ‘Hmm’ she said and went through the list: ‘Herr Professor Dr. rer. nat. Foo-uč, you are not here. You are not on the list. There is a Herr Foo here, but no Foo-uč.’ ‘But damn it, I am Foo!’

  Mission Invisible 

23

‘You are not; the letter from the Ministry clearly states that you are Foo-uč who is entitled to use the academic degree of Dr. rer. nat.’ ‘But this is ridiculous! How can I apply to change my name to include my degrees if the Ministry has already changed it?!’ Then Frau Esstee had a stroke of genius: ‘Maybe Herr has another document proving that his name is Foo?’ Foo produced his passport. Frau Esstee opened the travel-battered booklet, compared Foo’s photograph with his real likeness, nodded, and read his name: he was indeed Hieronymus Foo. ‘You should have done this in the first place. Then there would have been no misunderstandings,’ she said. Herr Zed went to his filing cabinet, located Foo’s file among the paper clutter and said with his Ottakring accent: ‘Ya need ta pay ten Euros for the registration.’ Foo took out his wallet. ‘Not here, at the cash desk.’ Foo went one floor down, joined the queue, paid, got a receipt, and carried the piece of paper to Herr Zed, who pronounced: ‘Now everything is in order.’ But it was not, Foo had missed his flight. And so it came about that Foo arrived late at the conference. The security guards did not let him in. He was late, and the invitation letter he waved furiously in front of them was not the card from the King, but the one from MA35. The King’s letter was with Herr Zed in Vienna.

17 Iain had called Luna, and they were about to meet at the zoo. On this particular day, the day after the conference, Lady Lucy had a private audience with the King, so private that nobody was allowed to accompany her. Luna was free as well. Iain had asked where they could go to escape interference from the mutaween, the religious police. Luna said the zoo was safe. The old Riyadh zoo used to be a sad affair. It had taken a benevolent monarch to transform it. Riyadh was a city of cars and traffic jams shrouded in a perpetual haze, where shopping malls and restaurants were the only places of public entertainment. The King wanted to give his subjects a place to take a walk, to have a day out with their families, with things to see and things to learn. What could be better than a zoo? So the King had paid a King’s ransom to build the finest zoo in the world. He had engaged the director of the Singapore Zoo with a princely salary and given him carte blanche. The result was a Singapore outside Singapore, a rainforest in the desert, an Eden of abundant life in a barren city. A vast tent covered the zoo, rain sprinkled from above—not the tropical downpours of

24 

U. Leonhardt

apocalyptic darkness and thunder experienced in native Singapore, but fine rain that nourished the plants and delighted the visitors. Their hearts went out to the orangutans above them. The wide branches of the tropical trees were linked to make a floor above ground. There, the orangs could roam around, chasing or grooming each other, or just laze about eating durian or ice cubes the zookeeper threw to them, to the delight of the visitors. The orangs were free and the visitors felt free as well. But rules were still rules: the robes were white and the abayas black, men and women were separate, unless they were part of the same family. But no-one could resist the joy and innocence of the animals. High and low shout happily: Here I am Man; here, dare to be.

While Iain was contemplating these lines from the Easter Walk in Goethe’s Faust, Luna arrived. ‘Hello Iain, how are you? It’s Luna.’ She was veiled and needed to say who she was. ‘Hello Luna, nice to see you, to see your eyes, that is.’ ‘There are no mutaween here, so we can walk and talk and pretend we are brother and sister—if you like.’

18 The most popular attraction at the zoo was the Arctic zone where kids could throw snow at each other, while their parents enjoyed the cooling air and a view of polar bears and penguins—life from both Poles brought to the middle of the desert. Yet Iain and Luna preferred to avoid the crowds and elected to keep company with the pigmy hippos. As a matter of principle, the Singaporean zoo director had insisted on combining plants with animals and fish. Broad-leaved tropical plants, trees laden with orchids, bamboo, palms, and ferns set the scene, while the animals were the actors and fish played silent roles in the background. Wherever there was water, there were fish. A shoal of fish parted gracefully around either side of the white tiger standing in the water of his enclave, small silvery fish frolicked in the ponds of the butterfly house, and a gigantic Arapaima patrolled the waters of the moat encircling the monkey island like a creature from another age. But nowhere else were fish and animals more happily suited to one another than in the pigmy hippo exhibit.

  Mission Invisible 

25

On land, hippos look clumsy—although they can move quite fast when they want, but in water they are ballerinas. One could see them in a river landscape through the large aquarium window. Curious little fish were swimming around them, larger fish were busy with themselves, and an ancient giant was lurking in the shadows. Iain and Luna went to the smaller aquariums at the side. ‘I love aquariums,’ said Iain. ‘Each is a wonderfully three-dimensional world on its own. We humans live on floors, in two dimensions, so to speak. Elevators and staircases take us up and down, but it’s on floors that we live most of the time. Imagine you are inside an aquarium. There in the water you can float in a third dimension.’ Luna smiled with her eyes and added softly: ‘Like in our dreams, where we are able to fly and float. Do you like dream worlds?’

19 Iain said with conviction: ‘I like this world best. I think it is better and more interesting than any dream.’ ‘The best of all worlds …’ Luna said with a smile in her voice. Iain went on: ‘Just open your eyes and see how astonishing it all is. Sometimes people laugh at me and say I am peculiar, but I cannot resist wondering and asking questions.’ ‘You are not peculiar; you are curious and you are very intelligent.’ ‘I am not so sure about that.’ ‘Now you are sweet. May I ask you a question? Look at all these aquariums. Each and every one is a world of its own; each and every one is different. Which one is the best? Each looks a bit strange, doesn’t it? The large catfish there looks totally bizarre: fat if you look from the side and squashed if you look from the top.’ ‘This is an optical illusion, which is your line of trade. The fish is a fish; it must be the water that makes it look strange.’ ‘Yes, but the water is completely transparent, you can look straight through it—light goes straight through it. How can it make things look different?’ ‘I don’t know. The walls of the aquarium are made of glass. Perhaps it is the glass.’ ‘But the glass is as transparent as the water. You have the same problem again.’

26 

U. Leonhardt

‘The glass keeps the water inside it; I am outside of it. Light goes straight in water; light goes straight in air. Logically, it must be the water surface or wherever the water ends—on the glass walls—where light changes direction.’ ‘You’ve got it. I told you, you are very intelligent. Now, may I tease you a little?’ ‘You are teasing me all the time, go on.’ ‘You see the fish in the aquarium, and it looks bizarre. Imagine how the fish sees you. It is inside the water, you are outside, but this does not matter to light. It’s only at the interface that it changes direction.’ ‘What you are saying is this: I look as bizarre to the fish as the fish looks bizarre to me.’ ‘Yes, you really are intelligent. But how do you know which one is which, what is truth and what is illusion?’ ‘I don’t know, but I do believe that truth exists and can be found out.’ ‘You are really sweet—and so serious. Tell me, what is truth? Isn’t it all relative? The way you see the world, the way somebody else sees the world, it all depends on the point of view.’ ‘If you ask me, I don’t know what truth is. I think it is a matter of belief whether truth exists or not—what I mean is: whether truth exists cannot be proven, but it is natural to assume that it does.’ ‘Tell me, why is it natural?’ ‘How else can you take one step after another. How else can you go out of the house and do things, if you don’t know whether they are true and meaningful? How else can you trust people, trust that things work out; how else can you trust the world?’ ‘You are very trusting.’ ‘Now, can we talk about something easier, for a change?’ ‘Whether you want to go for dinner with me?’

20 They were interrupted by people coming over to watch the archerfish being fed. This small, slim fish hunts insects above the water surface by taking aim at them with a precisely guided jet of water from its mouth. The zookeeper put a cricket on a branch a couple of feet above the water, but not directly above the fish. The archerfish swam to the surface, paused for a second, moved its gills and spat out a jet that hit the target. The cricket fell into the water, the archerfish rushed towards it, chased by other fish equally interested in the prey, and gulped down its meal.

  Mission Invisible 

27

‘Incredible,’ said Iain. ‘This little fish sees a strangely distorted world through the water surface, and can work out exactly how to aim.’ Iain got increasingly uncomfortable with Luna. This girl was acting fast, a bit too fast for his taste. He did not like her making personal remarks and their having an effect on him. She did not need to say all the time how intelligent he was. Iain knew he was no genius, but he was not dim either. She had an agenda. She might see the world in her own, strangely curved way, but she could still aim right at his heart, like the archerfish at his prey. What was her agenda?

21 ‘Let’s go to the special exhibition’, said Luna. ‘This is an exhibition on the masters of camouflage.’ Each year the special exhibition hall hosted a display of videos, interactive games, and live animals grouped together according to a theme, Luna explained. Last year the exhibition was on animal vision, showing creatures with extraordinary eyes—from eagles, owls, dragonflies, and bees to octopuses, fish, and the demons of the deep sea with eyes as large as their bodies. Thanks to 3D computer glasses, visitors could see the world with the eyes of these animals; they could buzz around like a dragonfly or take aim like an archerfish. This year the special exhibition was about the opposite of vision: camouflage. The special exhibition hall was itself camouflaged, covered with artificial rock and draped with military fatigue. Finding the entrance was the first challenge. Iain discovered an opening in the rock that led to a cave. They stepped inside and entered a narrow corridor with illuminated terrariums in its walls. The terrariums exhibited stick insects, walking leaves, chameleons, night moths, and praying mantises shaped like orchids; or rather, they were not exhibiting them, so well were the creatures camouflaged. On touch screens the visitors could try to identify them and check how they scored. The true masters of camouflage were the marine animals shown in the 3D lecture theatre. Fish feeding in the sun-flooded open ocean are under constant threat from predators of the deep spotting their silhouettes from below. Yet the feeding fish switched on light on their bellies, made by the bioluminescence of bacteria, light of exactly the color and brightness as the surrounding water, and their shadows disappeared.

28 

U. Leonhardt

The grandmaster of disguise was the octopus. The video showed a bush of coral. The camera came closer and closer until, suddenly, part of the bush turned into a white octopus with an angry eye. Further down the labyrinth, a large illuminated aquarium in the wall of the cave showed several cuttlefish. They were gliding from rock to coral, from coral to the amphora of an ancient wreck, back and forth, constantly shifting their shapes and colors, instantly and effortlessly adapting to anything they saw with their kraken eyes. Two schoolgirls were tapping on the glass to attract the attention of one of the cuttlefish. The creature turned black with anger. The girls went on tapping. Now the cuttlefish went into visual attack: it stretched out two of its arms and bright stripes flashed across its body. It was ready to strike. Two shrieks and the girls ran away.

22 Iain and Luna were looking at an aquarium containing invisible creatures of a different kind: transparent squid and barely visible jellyfish. ‘Being completely transparent seems like the best form of camouflage to me,’ said Iain. ‘When you have nothing to hide you don’t need to be hidden.’ ‘Do you know the Invisible Man, a novel by Herbert Wells?’ asked Luna. ‘The Invisible Man did exactly this: he made himself transparent. Trust me; this was not a smart idea. He had to wear goggles and bandages to become visible when he needed to. He also changed too much of himself and went mad in the end.’ She smiled with her eyes: ‘With or without invisibility, men are completely transparent anyway, women can see right through them.’ ‘Tell me, how do they do that?’ ‘Women?’ ‘No, I mean these creatures. Why are they transparent and we are not?’ ‘You want to know why? It is quite simple, every cell in their bodies has the same refractive index as the water they are in; to light they look the same as water. Light has no reason to scatter, it goes straight through them in the same way it goes through water, as if the cells were not there. On the other hand, the cells you and me are made of have different refractive indices, so they scatter light, and our bodies, yours and mine, are visible.’ ‘What do you mean by “refractive index”? I hated physics at school, and when I finally got out of school I forgot it instantly, technical terms and all.’

  Mission Invisible 

29

‘The refractive index is the ratio between the speed of light in vacuum and the speed of light in the material.’ ‘I am sorry, I don’t quite understand. Didn’t Einstein say the speed of light is always the same?’ ‘Yes, but this is only true for the speed of light in empty space—in vacuum. It is the same, no matter whether you move or not, because nothing in empty space tells you how fast you are going. Imagine you are out there in the void. No sign, no clue will tell you whether you are just floating about or racing through space at thousands of miles per hour. So there, in empty space, it is quite natural that the speed of light should always be the same, regardless of whether you move or not. But this is different in optical materials. There you have something tangible to compare with.’ ‘I think I am beginning to understand. But this is still rather abstract to me. The question is: how does a material change the speed of light?’ ‘You are asking the right question, as always. How do they do it? Materials are made of atoms. Every atom responds to light: it absorbs some light, gets excited, and then sends the light off again. The light has to hop from atom to atom, each hop takes some time, and so the light gets delayed.’ ‘Could I imagine the following picture? The atoms are talking to each other, but instead of sound they use light. Each atom listens to its neighbor and then communicates further. This takes some time and delays the message. But doesn’t it also distort it? Like in Chinese Whispers or Broken Telephone?’ ‘Only if the atoms get overly excited will they distort the message. If they stay cool not much happens; they just relay the light to their neighbors and delay it a bit.’ ‘Is it possible for the atoms to make the light go faster? Or does the “talking” always slow it down? You know, rumors and gossip seem to spread faster than the speed of light.’ ‘Absolutely, naughty boy. Imagine the atoms are expecting a really scandalous message. At the first sign of it they spread the word.’ ‘But for this they need to know the message in advance, don’t they?’ ‘Spot on. No new information can spread faster than the speed of light in vacuum, but predicable information can.’ ‘You still confuse me.’ ‘I confuse you?’ ‘How can a tiny atom know a complicated message in advance? What kind of messages are you talking about?’ At this moment, Iain’s phone rang. It was Lady Lucy.

30 

U. Leonhardt

23 ‘Yes Lady Lucy, this is Iain. Could you please speak up a little, the connection is not good at all. This is better now. You want me to come to the University, with Dr. Luna? To the Female Section? But how can I get in? Ah, there is a visitor area. What shall I do there? You want me to translate a paper of yours? A paper with your latest results? For the King, you said? An unpublished paper for the King? Yes, I will keep it secret of course, as safe as in the Bank of England, ma’am. I’ll call a taxi right away.’ Luna was listening to the conversation, her head leaning forward slightly, silent and attentive.

24 A traditional Saudi house is divided into a male and a female domain; the University was divided into a Male and a Female Section as well. One or two decades earlier, the Male Section had been moved to an entirely separate campus, built for this purpose, and the old campus was converted to the Female Section. Like a traditional Saudi house, it looked from the outside like a fortress with high walls and narrow, covered windows, protecting the privacy and seclusion of the women inside. No man was allowed there, where the women left their abayas at the door and moved around freely in a riot of colors, Luna said. A traditional Saudi house also has a reception hall for male guests, and so did the Female Section. Male professors could come to the Visitor Hall to give lectures to the female students. The students were either completely covered or they sat behind a semi-transparent mirror where the professor was unable to see them, but they could see him and gauge his performance and character. Some of them progressed to become graduate students, which necessitated a closer and more intimate relationship, as they needed to be supervised, sitting and talking tête-­ à-­tête in the Visitor Hall. The Hall was also the home of the Manager of the Female Section, a stout man in charge of the womenfolk and guardian of the unmarried ones. He kept an eye on all the comings and goings in the Hall.

  Mission Invisible 

31

Lady Lucy was already waiting for Iain. She gave him the paper he should render in Arabic in his best calligraphy. The King wanted to read for himself what she was proposing. She was rather skeptical whether he would understand the technical language and the formulas, but the King’s wish was the King’s command. Iain took the paper and asked the Manager where he could get some decent dinner before working on the translation. A restaurant was recommended and a taxi called. Meanwhile, Lady Lucy and Luna had already disappeared in the Female Section. After twenty minutes though, Luna returned and walked straight to an Arab man standing in the hallway. They talked in whispers that nevertheless betrayed the intensity and agitation of their argument.

25 Saudi Arabian restaurants are either for families, each sitting separately and privately, or they are public, that is, for men. This one was a masculine cave. The building looked nondescript, but the door opened to a cavernous maze that no Aladdin would ever have dreamed of. Rocks, crystals, stalactites, and stalagmites, all illuminated in psychedelic colors, divided the diners. At each table two Arab men were sitting quietly face-to-face, clad in uniformly white robes and wearing the same red-and white headscarfs, each table indistinguishable, each an identical pattern in the color chaos of the cave. In this chamber of mirrors sat Iain, except that there were no mirrors; he could not see his image. With his Western clothes and sitting alone, he was the exception, but he could not see himself. The restaurant offered a choice of surreal fruit juices no cocktail bar could compete with—alcohol was forbidden of course, and it was not needed here anyway. The food was out of this world, too—there were various fresh Lebanese salads for starters and a selection of sublime barbequed meat for the main course. After his meal, Iain began translating Lady Lucy’s paper into Arabic. He understood neither the technical language nor the formulas, but whether it was the atmosphere of the restaurant or the conversations with Luna at the zoo, something made him divine the meaning of the text as he committed it to calligraphy; it was a treatise on the science of deception. He recognized the physics of Luna’s Invisible Man, where somebody becomes invisible if his refractive index is the same as the refractive index of the surrounding environment. Most of the text, however, was about something else he had not yet

32 

U. Leonhardt

heard of, something much better. He could not work out what it was, but faithfully translated word for word into a beautiful calligraphy of Arabic script. Iain could understand why the King was interested in the science of invisibility: it could give him and his army a serious advantage. But why would Lady Lucy, a wealthy British lady of the finest education, work on this? Was it the King’s money? Why would she need money? Iain recalled Luna’s comments on the fight for money in science, money for research, for science laboratories, and the laborers of science. But what for? For the pursuit of truth? Of fame? Iain’s phone rang. Sure enough, it was Luna.

26 Luna was on the phone, speaking with the softest of voices and a silvery laughter in her tone: ‘Iain, how are you?’ ‘Fine, how are you?’ ‘Very well, how is your evening?’ ‘Fine. I am sitting in an interesting restaurant. You wouldn’t believe such places exist. I feel like being in the middle of a surrealist painting, in the middle of a Magritte.’ ‘Yes I see—you describe it so well. Did you have something good for dinner?’ ‘Yes I did. You really have excellent food here in Arabia. I never had such good meat before.’ ‘I am happy for you. What are you doing now? Are you sitting watching the girls?’ ‘There are no girls here of course.’ ‘Yes I know, I was just kidding. So what are you doing?’ ‘I am translating Lady Lucy’s paper to Arabic.’ ‘Her paper? Do you understand it?’ ‘Not really, but I think I am getting the general idea.’ ‘You really are very intelligent.’ ‘Not at all, you have explained a lot of optics to me, today and yesterday, and you explained it well. So it is quite natural that I am beginning to understand.’ ‘I am really happy for you. You know, I am thinking, with you and Lady Lucy leaving tomorrow, why couldn’t we get together and talk some more?’ ‘But where could we go? The only places are either for families or men; there are no bars in this town.’

  Mission Invisible 

33

‘You know, I was wondering, whether you might come over to my place. We could talk and you could finish your translation.’ ‘But wouldn’t that be dangerous? You could be fired and deported if the police or the University found out, and flogged in the street. I don’t want you to get into trouble.’ ‘Thank you for your chivalry, but no worries, I’ll send you my driver, he is very discreet.’ ‘Your driver?’ ‘You know that women were not allowed to drive in Saudi Arabia until recently, but they had personal drivers. Now they can drive in principle, but most still have drivers—with the traffic the way it is in Riyadh, you wouldn’t want to drive here anyway. I have a driver on call 24/7. He can take me wherever I want, and he can take you. These drivers of the veiled ladies, they know all their ways, all their visitors, and all their secrets, but mine is really discreet.’

27 Luna’s driver had picked Iain up from the restaurant and they were heading for the Diplomatic Quarter where Luna lived. The Ritz, Iain’s hotel, was conveniently close by, so Iain told the driver to stop there for a moment. He went up to his room, took his night wear and gear—just in case—and, for a reason he could not quite explain, left Lady Lucy’s paper and the translation in the room. He only took with him the part he had not finished yet, an appendix with mathematical details. On some impulse, he put the papers he left in the safe and locked them in with a new combination. The Diplomatic Quarter was fenced off and guarded. At the hotel the driver asked Iain whether he had his passport with him. Iain flashed the red booklet with the lion and the unicorn, and off they went into the night. Iain felt like 007 on a secret mission, taking leave to visit a beautiful lady, but at the same time he detested the secrecy and the shadows of the underworld they were about to enter. The checkpoint was heavily protected with roadblocks that even tanks could barely pass, and guarded by khaki figures with machine guns. Iain showed his passport and was asked where they were heading at this hour. ‘To a reception at the British Embassy’, the driver said. Either he was quick-­ thinking or he had some routine.

34 

U. Leonhardt

28 They drove to the building which housed Luna’s apartment. Iain left the car and pressed the buzzer next to the heavy wooden entrance door. ‘This is Iain.’ ‘Oh hello, you should have phoned. I could have been naked in the shower. Do come up.’ The door opened heavily and slowly, as if trying to hold him back. Iain walked up the stairs and Luna showed him in. Iain stared at her: ‘This strange cloak-and-dagger game you are playing here confuses me. I haven’t seen an unveiled woman for days, and now I’m staring at you. I’m sorry.’ Luna was wearing an oriental dress and cleverly applied make-up. She appeared very feminine to Iain, a bit too feminine, actually. But maybe this was also the effect of the cloak-and-dagger game. He also sensed a slight whiff of male sweat in the air. ‘Let me show you around. This is my home: the kitchen, sorry for the mess, here is the living room. And there is my office.’ Iain saw several computer screens, a scanner, a color printer, and state-of-the-art communication equipment that looked like a satellite phone. ‘I have satellite internet. The Saudi net is awfully slow, with all the filtering out of saucy pictures and naughty videos. But this is really fast.’ The apartment was functional, yet it also felt a bit impersonal. Physics books were lying around everywhere, even in the kitchen, but there were no pictures, no plants, no signs of personal life. ‘And here is the best part, my balcony.’

29 Luna and Iain were sitting on the balcony in the night breeze. African drums were beating somewhere in the distance, restless, pulsating. Iain felt shy— he had left the ways of 007 at the doorstep somehow. ‘Let’s get back to optics,’ Luna said to break the ice. ‘Where were we?’ ‘We were talking about atoms and light. Materials are made of atoms. The atoms communicate with each other, but instead of sound they use light. The communication—the absorption and re-emission—takes time, and so light is slowed down in materials. The factor by which light is slowed down is called the refractive index.’

  Mission Invisible 

35

‘You are such a good student.’ ‘You also mentioned that light can sometimes get faster, and this I don’t understand yet. If the atoms relay a message faster than in empty space they must know in advance what is coming. How can they do this? Atoms are absolutely tiny. What kind of message can they store?’ ‘Do you hear the drums?’ ‘All the time.’ ‘African drums can tell whole stories. If you know how to listen to them you can hear what went on, and where, and who did it; it is all in the rhythm. You hear the pulse of the main beat, and also the rhythms on top telling the story. Each rhythm, no matter how complex, consists of beats. This is what the atoms are responding to: the beats of light.’ ‘Do you mean light pulses?’ ‘No, I mean light waves. Imagine a wave, no, not a water wave. Imagine an oscillating pulsating pattern filling three-dimensional space; this is what light is for the main part.’ ‘And the atoms are responding to the oscillations? They begin to oscillate themselves?’ ‘Exactly! And another thing, each oscillation corresponds to a certain color: what you see as color is an oscillation of light.’ ‘An old man in a magic shop at the souk showed me how white light can be broken up into all the colors. So they are the oscillations and white light is the mix of all of them?’ ‘An old man at the souk showed you this?’ ‘And a tropical butterfly was sitting on his hand, a messenger of light.’ ‘You are such a romantic.’ ‘I am just curious, and things happen to me. Tell me, why are some materials colorful and others transparent?’ ‘Any material is made of atoms, as you said. The atoms respond to the oscillations of light by absorbing and re-emitting them. But only if they emit as much as they have absorbed is the material transparent—the light gets restored. If the atoms emit less, they color things or make them opaque.’ ‘I see, but how can the light get faster?’ ‘It’s all in the rhythm. The atoms respond, they begin to pulse with the same rhythm they received, just a bit delayed. But knowing the rhythm they may also advance it, by pulsing a fraction of a beat ahead of time. This is how light can get faster.’ ‘Yes, but for this the atoms need to know the rhythm. How do they do this?’ ‘How? They have it built into their structure; they have it in their blood, so to speak. You have rhythm in your blood, too.’

36 

U. Leonhardt

‘It only works for certain rhythms’ ‘resonances—’ ‘the atoms have predispositions to, for certain colors. Each sort of atom will have its own set of colors. And I guess a real picture made of many colors will not move faster.’ ‘You really are one of the most intelligent men I have ever met. You know perhaps that intelligence is to men what beauty is to women: it makes them attractive.’

30 They got up and stepped into the living room. The rhythm was indeed in Iain’s blood, but he also felt uneasy and nervous. ‘How is your translation going?’ ‘Nearly finished, apart from the appendix. The King wanted to have it set in calligraphy, so that’s how I wrote it.’ ‘You write calligraphy? Fantastic! Can I see it?’ ‘I am sorry; I left the papers in the hotel. I only have the appendix with me.’ For the briefest of moments a trace of anger ran over Luna’s face, but she got herself under control immediately. ‘Can you show me how you write? Perhaps you could just translate the beginning of the appendix for me.’ Iain sat down, took out the manuscript, a fountain pen, and a sheet of paper from his briefcase. His curlicues and arabesques transformed the technical document into a magical script. ‘Beautiful!’ Iain excused himself; he needed to disappear to the bathroom—an understandable effect of the nerves. Luna was swift and silent. She took the pages of the appendix, dashed to the office, and scanned them. When Iain returned, everything was back to normal. ‘Iain, it was such a pleasure talking to you, and I really enjoyed your calligraphy, but you know the checkpoint at the DQ closes at midnight and it doesn’t reopen until six in the morning. I am afraid you will have to go now. I will call my driver right away.’

  Mission Invisible 

37

31 And that was that. And that was that? In his hotel room, Iain lay restless and unable to sleep, while the African drums were still beating in his blood. And that was that! He was lying there trying to make sense of the evening’s events. What was going on? Finally, he decided to get up and do something useful— as he could not sleep anyway, he might as well finish the translation. So, he switched on the light and sat down to work. Working, writing was good therapy. Iain returned to his bed with a clear head and began to think things through one more time. Begin at the beginning, he said to himself, with the mirage, with the first question: who was Luna? She did research on optical illusions and she was an illusion herself. She was a fake. The question was: what kind of fake? She must have some secret, some all-too-private secret that forced her to deceive him, the University, everybody. What was it? Iain did not know nor could he know. And there was something else he could not know at the time: by working for Lady Lucy, he had become a target. Somebody, somewhere had cast an invisible net, and the net was tightening.

32 The next destination on Lady Lucy’s journey around the world on science business was Shiraz, the capital of Fars Province in Iran, the heart of Persia. Iran and Arabia had been cultural rivals and political adversaries since time immemorial, quite apart from the religious schism, so a direct flight from Riyadh to Shiraz was inconceivable. The closest route went via Bahrain, a small kingdom all on its own, perched on an island archipelago in the Gulf, which served as the Saudis’ Vegas and the seat of the United States Fifth Fleet. Our travellers were lucky to be booked on a connecting flight scheduled to land in Shiraz in the early evening, and not in the wee hours of the night. Nevertheless, they needed to spend some time in transit, Lady Lucy in the First Class Lounge and Iain in the transit room for the lower orders. Iain did not mind—the last three days had been intense and he was looking forward to an intermission of reflection and contemplation in transit. He thought of Arabia: the magic shop at the souk, the encounter with the three volunteers, the mirage in the desert, the Singaporean zoo, the fortress of the Female Section, the psychedelic restaurant, and the night on the balcony with

38 

U. Leonhardt

African drums in the distance. He thought of the optical illusions and strange creatures he had seen at the zoo, and the strangest creature of all: Luna. She was the first real scientist Iain had got to know personally, and she was not what he had expected. She was neither the sober and slightly boring type, nor the nerdy theorist with ticks and mannerisms. A seductress with a secret! This was not the picture he had always had of a scientist. Only in one point did she fit the picture: she had a secret, Iain was sure of that. Some defect or disorder must compel scientists to become scientists, thought Iain. Thank goodness, he was normal. Iain had his peculiarities, too. His talent for languages was unsettling for some. He remembered the Armenian orchestra he had accompanied as a tour guide. The conductor was flabbergasted when, after a month, Iain began to understand their language. There was nothing to it; Iain had only listened and absorbed: like a child. Another of Iain’s talents was his ability to sleep anywhere, anytime—if nothing was bothering him, of course. He had slept through the vociferous quarrels of his office mates, in discotheques, on trains, and in planes; he had even slept through an enormous gas explosion in his street, like a baby. Iain’s most irritating talent was his gift for asking questions. His former colleague at the travel agency, Yvette, was no longer on speaking terms with him because of one question. Yvette was constantly broke, but addicted to sales. Whenever there was anything on discount, she would take her credit card and shop. Iain’s question was this: when it comes to things you don’t need, how can you save more if you buy more? She had exploded. But he had just been curious and wanted to help. Iain had his peculiarities, but he was at peace with them; he felt normal and he was normal. Others went the ways of the world, while he had preserved some innocence, trust, and curiosity.

33 While Iain’s art of asking questions was not always welcome, it had one great advantage: he would get answers. He had learnt a lot about light during the last three days. He had learnt from the old man in the souk and from Luna, of course. Iain was looking at his fellow travellers in the lounge, trying to picture what made him see them, trying to see how he was seeing them. Light filled the scene before him, light coming from the lamps on the ceiling. The travellers, their clothes, bags, and unfortunate kids, scattered the light. Some part of the scattered light reached his eyes and this was what made him see them. Nobody just ‘sees’—seeing needs light as a mediator.

  Mission Invisible 

39

Iain pictured light as Luna had taught him to the sound of the African drums. The entire block of space within the transit lounge felt alive with myriad vibrations, oscillations of pure space. The lamps on the ceiling were constantly driving the vibrations; they were the driving drums. Each tiny atom of the travellers and their belongings was responding to the light, each becoming a miniature drum in tune with the main beat, but slightly delayed in rhythm. The result was a room filled with the oscillations of light. The part reaching Iain’s eyes, his brain turned into images. What a thought! It added intensity to the most banal of scenes. To amuse himself, Iain imagined someone would write up his story in a book—not very likely, but worth a thought. Someone else is reading his story right now. To begin with, reading is seeing. Someone lying comfortably on the sofa or someone sitting, less comfortably, in a plane, sees the letters of the book. Light from the lamp falls onto the page, is scattered on the white paper—or the e-paper screen, and reaches the eye of the reader. The black of the letters scatters less than the white surface and so stands out. The eyes of the reader catch the light, focus it, and turn it into nerve signals. Light conveys the book to the reader, literally filling the space from the book to the eyes with myriad oscillations in numbers beyond comprehension. Such is the sheer act of seeing, quite apart from the nervous processes that turn images into letters and letters into a story.

34 Iain’s story would take him to Shiraz now, the city of dreamers and the Mecca of the poets. Iain had studied Persian poetry at university, where he had completely surrendered to its charm. He had never been to Shiraz in reality, but many times in his imagination. The Western world knows Shiraz as a wine— Shiraz was the home of the Australian and Californian reds of that name; but wine was now forbidden, and worse. Iain knew what the Iranian regime of mullahs had done to Iran. How would his Persia look? Like the face of a friend worn from illness, a mere shadow of her former self? How much would be left of Shirazian lightness and grace, melancholy and love?

40 

U. Leonhardt

In English translation—but no translation is able to express the wit and music of the words, to distil their meanings and associations in a few lines: ‘Sit besides a spring And see how life is passing. This lesson is enough for all the world.’ This was the Hafez verse that came to Iain’s mind as their plane swept over lake Moharloo. The gondola of an early moon had risen, its image reflected in the waters with the images of the mountains around the lake. Shirazian dreams take their life from the lake, a friend had told him. Some vapors were rising from the lake, some fine fog was flowing to the city; the vapors, the fog, were the medium of dreams, the invisible opiate of the dreamers. It was something of a miracle that the regime had not forbidden the lake as well as the wine.

35 Our travellers landed and were greeted, checked, put in cars and driven to their respective lodgings. Lady Lucy would reside in the finest hotel Shiraz could offer, while Iain was put up in university accommodation. A bearded Iranian with gray suit, gray hair, and gray face, no doubt his minder, took Iain up the elevator and showed him his apartment. After the minder had gone, Iain tiptoed along the corridor, looked around—nobody was there—went to the elevator, pressed the button for the ground floor, and then left without getting in. The elevator went down to where, as Iain had expected, his minder was sitting. He did this several times, as if the elevator were malfunctioning; then he went in and pressed the button for the second floor. There, Iain pressed the button for the ground floor, left the lift, and walked down the stairs. Sure enough, his minder was standing in front of the elevator, clueless. Iain went out through the door. The smell of orange blossom was all around him; Iain was in Shiraz. He walked out to the street and stretched out his arm. There were no taxis of course, but private cars that could take him where he wanted for a fee. He climbed on board an Iranian Renault, a remarkably good copy, but stripped to the essentials—without electronics. The car took him to Saadi.

  Mission Invisible 

41

36 Saadi Shirazi was a poet and a traveller during the time of the Mongolian invasion in the thirteenth century. He had sat with many refugees from all walks of life in taverns and at campfires, from Jerusalem to India; hearing their stories and telling stories of his own. Saadi wrote two books, one in verse, one in prose, books of wisdom, books of irony, of humor and ­humanism. His verse on the equality of men is now inscribed on the gate to the United Nations in New York. When he returned to Shiraz the Shah honored him as a poet. To Saadi Iain went. A mausoleum guarded Saadi’s tomb of marble under regal columns. Iain went to the sarcophagus, knelt down, and in his mind recited some of what the poet’s mind had spoken so many years ago. Then he walked down the stairs to the pond. Silvery fish were swimming in and out of a grotto, to the music of a flute. They were travelling as the traveller had done so many years ago. After Saadi, Iain walked to the street and hailed another car: to Hafez. Iran is perhaps the only country in the world where the words of a fourteenth century poet are familiar to everyone. Old men are moved to tears by those words on the radio, young modern women murmur them as psalms and blessings. Most Persians regard Hafez as the greatest of poets. His poems tell of love and wine, of earth and heaven. His verses have undermined the mullahs of his own and recent times, who forbade wine and did not know about love. Hafez’s words are alive in Persians—the regime had succeeded in forbidding wine, but no regime could forbid Hafez.

37 Iain walked up the stairs to the Hafezieh, the mausoleum on a hill in a garden with trees like minarets. Midnight was near, yet many people were standing or walking in the garden—young people with small books in their hands, some alone—wishing to be alone, some in groups of friends. A young woman with a colorful loose headscarf was kneeling in front of the tomb. She stood up and smiled at Iain. The Hafezieh was an informal place where strangers could easily speak to one another. Iain approached her: ‘Salam, can you open Hafez for me?’

42 

U. Leonhardt

Opening Hafez was a form of fortune-telling; the person asked opens the book at random, and the asker finds his fortune told—or at least a beautiful verse. The young woman opened the page: it was exactly the verse Iain had landed in Shiraz with:

Iain looked at her and she said: ‘I am Norah, I see you have come a long way, but you are also one of us.’ ‘I am Iain, I studied Persian poetry at university. I am visiting Shiraz, because I am assisting a British professor of optics.’ ‘Lady Lucy?’ ‘You know her?’ ‘I am a doctoral student of Professor Parsa who invited her to give a lecture here.’ ‘What a coincidence!’ She laughed: ‘Such things happen in the Hafezieh at midnight.’

38 Iain returned to his quarters slightly intoxicated by poetry and the smell of orange blossom. His minder was snoring on a chair; Iain could hardly resist the urge to tickle him a little. He took the elevator to the apartment, prepared for bed and was just settling down when he heard the noise of water flowing in the bathroom. Iain sighed and got up again. He could sleep even with Niagara on tap, but he felt sorry for the water that was being wasted. So he took some tools from the kitchen and set to work. He opened the toilet box and attacked the pieces of plastic inside with a kitchen knife. However, technology was not one of Iain’s strengths, and Iranian plumbing was a case in point. The Niagara was diverted, temporarily dammed, but not stopped. Then, suddenly, a jet of water gushed straight up from the box; it went up to the ceiling and down on Iain. This was not Niagara, it was Yellowstone. The Old Faithful had blown up. Poor Iain rushed out of the bathroom, trying to locate the mains stop tap to shut down the water supply. At last, there was silence, the waters were quelled and quenched. Iain conscripted a vase for nightly emergencies, changed, and fell asleep.

  Mission Invisible 

43

Iranian ambition was legendary. At university, Iain had met Persian emigrants who, back in their days in Iran, had attempted to build a space shuttle at high school. They had designed a more elegant and graceful craft than the American original, they had worked out everything required theoretically— all the physics and the engineering. They had not even bothered to build small models to test it, but went straight for the real thing. Their space shuttle collapsed on the launch pad. It did not even explode. Iranian hardware will always defeat Iranian ambition. Yet two of the Persian space enthusiasts had become NASA engineers later on, and much of Silicon Valley has been living on Iranian genius in exile.

39 The next day, Iain was waiting for Lady Lucy in front of the physics building at the university. Professor Parsa had just finished his morning lecture on advanced electromagnetics and optics, and came out surrounded by students. He was a noble figure with a grey beard and silvery hair, while his students were a mass of black—for a reason: in Europe and America, most physics students are male, but in Iran they are female. As such, they are required to wear black and cover their hair, making them look like nuns in black habits. None of the women was veiled, but even Norah was all in black—at least at university; in town young Shirazian women could walk in fashionable colors and with purely symbolic scarfs. The black habit was mandatory at university and it also made it easier for Professor Parsa to face his female entourage, although he still averted his gaze. Professor Parsa had given his lecture and the black crowd of students was following his every step, asking questions and listening avidly to his lengthy answers. In Europe and America, many students seem to be primarily interested in finding out how much of the lecture will appear in the exam, thereby minimizing the material required for revision. In Iran, students never want to know less, they want to know more. And more they got—even after two full hours of lecturing, Professor Parsa was still talking with unstoppable enthusiasm: ‘You have seen in today’s lecture how Maxwell’s equations for light in media correspond to Maxwell’s equations in Einstein’s general theory of relativity. Now you ask me what this means. Let me try to explain in simple words. An optical medium, say a piece of glass or an aquarium filled with water, changes the way light perceives space; it changes the geometry of space. As you know from your course on Einstein’s theory, gravitation does the same: it curves the

44 

U. Leonhardt

geometry of space and time. You may have thought Einstein’s curved space belongs only to the heavens. But no, here on Earth you are surrounded by curved spaces. Whenever you look into an aquarium or see a mirage in the desert you see a curved space.’ ‘You ask me what we can learn from such analogies. Let me answer first with a little philosophy: without analogies, how can we learn anything? We can only learn what we already know, deep down. Knowing optics, we can now truly learn the theory of the heavens: cosmology. Let me answer with theology: you can hold in your hands pieces of God’s thoughts—every piece of glass is an analogy of the cosmos. Let me answer with poetry: Hafez says, pour wine in my glass, my beloved. The glass is the mirror of truth, the wine is wisdom, the lover is God, as in the most erotic verses of the Song of Solomon.’ Professor Parsa realized what he had just said. He blushed like a girl and looked away. ‘My students, I am very grateful for your questions; forgive me my humble answers.’ He saw Lady Lucy approaching and said in English: ‘Professor Lucy de Phos, welcome to the University of Shiraz. I apologize for not having greeted you earlier, but I was teaching. These students here are astounding. I am lecturing a course on advanced electromagnetics and optics, another one on quantum mechanics, and also one on the philosophy of science. For each course I am only obliged to teach two lessons of ninety minutes a week. Yet I give them three, each of a hundred and twenty minutes, and these wonderful students are still not tired. I am grateful to them, for knowledge must flow like a river. The more we give to others, the more flows back to us. So, I shall open my heart and give.’ ‘What a fool!’ hissed Hieronymus Foo.

40 After his failed attempt to meet Lady Lucy in Saudi Arabia, the tireless Foo had set out for Iran. Where he got his visa from one could only guess. Maybe he had it already glued in his travel-battered passport. In any case, here he was, staying at the same hotel as Lady Lucy and escorting her to her lecture. ‘The name is Foo, Hieronymus Foo, professor of advanced optics and electronics, Futuropolis University.’ ‘Welcome to the University of Shiraz. I am Rushaan Parsa, professor of theoretical physics.’ ‘Nice to meet you, Professor Parsa, how do you do?’

  Mission Invisible 

45

Foo had taken an expensive course on politeness in society—for polishing his manners en route to success, as the course had advertised, but he could not resist the temptation to tease Parsa a little: ‘Professor Parsa, you astonish me with the many hours you teach. How do you find the time for research? Or have you already invented a time machine? It was you Persians that invented the flying carpet—and not-so-flying spacecraft, so why not a time machine?’ ‘God gives me twenty-four hours a day; how can I argue with Him? Twenty-­ four hours is more than enough for teaching and research. My days are for the students, my nights are for science.’ ‘The devil never sleeps, ey? I am a busy man, too, but my motto is simple: efficiency. Do only the work nobody else can do. Teaching fellows can teach, research fellows can do research, the professor’s job is directing the whole enterprise and looking after the money. Am I right, Lady Lucy?’ The sparring match between the two unequal professors had amused her, and she pronounced with an air of authority: ‘Specialization is the mark of modern times; the Humboldtian unity in teaching and research is positively mediaeval. But there is research so sophisticated that no research fellow can hope to do it. This is left to us professors, and to me.’ ‘For which we admire you,’ Professor Parsa replied, and all then went to the lecture theatre.

41 Iain was a peaceful young man disinclined to violence or violent thoughts, yet Foo’s words had stirred anger in him that he could not explain. Foo had not said anything offensive, he had just been a bit rude in teasing Professor Parsa for his gravitas, but Iain had nevertheless conjured up a vision of killing Foo. Somewhere, in some desolate place, was a huge crocodile farm full of bored creatures waiting in the waters for some action. The crocodiles looked like ancient black trees in the green of the water—armored trees, lying on top of each other. Some were huge trunks with wide bellies, some were slender with sharp teeth; some were dozing with open mouths, some were waiting with open eyes. Foo had challenged Iain to walk on top of the concrete wall around the crocodile enclosure. The wall was broad and a professor of advanced optics and electronics with excellent connections was invincible. Foo dared Iain to come up, too. There they were, walking on the wall above the crocodiles.

46 

U. Leonhardt

He would tip Foo over, yes he would. The crocs would fight for the little snack, ripping him apart. Horrified, Iain opened his eyes and turned his attention to the lecture.

42 Later, Lady Lucy was scheduled for a series of meetings with the professors of the physics faculty. Iain’s services were not required, since everyone could speak English well enough to be understood, so he had a free afternoon in Shiraz. A free afternoon in Shiraz! And better still, Norah had volunteered to show him some of authentic, old Shiraz that no tourist would ever see. They walked to the car park towards a massive rustic jeep—Norah’s car, and climbed on board. ‘Women are allowed to drive in Iran, but the traffic is insane. To drive in Iran and survive you need three things: first, be a formula one driver; second, assume everyone else is a formula one driver; and third, imagine they are all drunk. My parents would only let me drive a tank or this.’ They were driving towards the Old Town when a cavalcade of motorbikes began to overtake them. Each bike carried two men clad in black leather. Nobody was wearing helmets, but some of the black riders had iron rods in their hands. ‘Vigilantes. Let’s drive on another road,’ said Norah and u-turned the jeep to the other lane in mid-traffic. Brakes screeched, followed by honking and some forte fortissimo yelling. ‘Norah, you really drive like an Iranian.’

43 Shiraz was growing like the rings of a tree. With each new generation, life moved out from the city to gardens and orange groves in the countryside. Soon buildings followed, forcing the next generation further out. The Old Town had become a slum of squalid houses and sidewalks, full of people, mostly poor, mostly in religious dress—Norah’s black habit was good camouflage here. Yet inside the squalor the Old Town hid some gems of Shiraz’ past. ‘Unfortunately, Khan School is closed to visitors today. But it would have made you sad. Imagine King’s College Cambridge crumbling away in a slum. This is what has become of the great university, the light of the Middle East, given to Mulla Sadra in 1612.’

  Mission Invisible 

47

‘I have read his Hermeneutics of the Light Verse of the Quran.’ ‘Let me show you a small madrasa instead.’ They walked to the madrasa, a religious college, founded several centuries earlier. The school formed a square around a Persian garden with rectangular ponds, plants, and trees arranged with some mathematical idea in mind. A mathematician would see Golden Ratios and studies of rational and irrational numbers in the garden; Iain saw exquisite beauty. The lecture theatre was located above the gate, the library in the building opposite to it. Students lived in the school, their rooms opening inwards onto the courtyard. There they were sitting on carpets under arches, among piles of ancient books stacked up on the floor. Norah explained: ‘It takes many years of training for these students to become mullahs. They need to learn, and they need to learn how to learn. They learn through discussions with their master and among themselves; they learn by asking questions and by arguing. Mullahs are trained to argue; don’t bother arguing with them.’ I pray you, think you question with the Mullah: You may as well go stand upon the beach And bid the main flood bate his usual height; You may as well use question with the wolf Why he hath made the ewe bleat for the lamb.

‘Shakespeare, The Merchant of Venice.’ ‘Precisely.’ ‘I wish these mullahs would apply their art of asking questions to science and technology, instead of their usual subject. Persia would become free and Persians unbeatable.’

44 After the madrasa, Norah went with Iain to Ghavam House. Until four generations previously, the House had been the residence and office of the Master of Ministries. Like all Persian houses—and like the madrasa, it was built around a mathematical garden. Two houses stood opposite to each other— like the lecture theatre and the library of the madrasa; one was the home, the other the office. The houses opened towards the garden. On their terraces, people could sit and take the sun in winter. Iain saw the Persian lions painted on the gables; they were friendly beasts of gold and grace. The lions seem to smile upon the garden and the people who used to walk there. Now Norah

48 

U. Leonhardt

and Iain were the only ones. The garden was partly fenced in, partly neglected; the ponds had dried out. An iron stovepipe, no doubt from the caretaker’s lodge, disfigured the delicate woodwork of the side building. Norah and Iain went up to the terrace of the residence. There, they were surrounded by mirrors and glass glittering in the light, as if made of jewels. ‘People came to sit on the terrace in winter, smoking hookah and talking in the winter sun. The glass and mirrors here are for light.’ ‘Throughout this journey, light has been the constant theme. Yet the more I hear about it, the more I am puzzled. May I ask you some questions?’ ‘Only if you are not a mullah.’

45 Glad that Norah was willing to answer his questions, provided they were not too much à la mullah, Iain said: ‘Let me say first what I do understand about light and then what puzzles me. I understand that light is an oscillation in space. The colors are the rhythms of the oscillation. I also understand that light gets slowed down in materials—it causes the atoms of the material to vibrate as well, they absorb and re-emit the light, which takes time. In some cases, the atoms may advance the light if the rhythm of the light resonates with them. Materials are transparent if their atoms emit the same amount of light they absorb and they are colorful or dark if they emit less. So far, so clear.’ ‘I’m with you.’ ‘Now, I also know that transparent materials may bend light, which causes optical illusions.’ ‘I agree.’ ‘To be absolutely precise, the bending happens at the boundary between two materials, say water and air, because inside each material light travels in straight lines.’ ‘I almost agree, but carry on.’ ‘Now, here is the puzzle: in a transparent material light goes straight through, so how does the material force the light to change direction?’ ‘How fitting that you ask this question in a Persian garden. The first one who discovered the law of light bending—the law of refraction, as it is known today, was Ibn Sahl. He was Persian, or at least we Persians like to say so. Please, let’s sit down and I’ll show you.’

  Mission Invisible 

49

46 Norah took a dry twig and began to draw in the sand. She sketched a wave and an arrow next to it:

‘The arrow points in the direction the light wave is going. The length of the arrow indicates how many oscillations occur per unit length, in this case five.’ ‘OK.’ ‘In a material, more oscillations happen in a unit length than in empty space …’ ‘—because light is slower there. The oscillations move less far in a given time, they get slower, so you can count more per unit length,’ said Iain and took the twig. ‘I suppose, in the material the drawing should look like this:’

‘Absolutely. The slower the light, the longer the arrow. Do you know what the refractive index is?’ ‘Yes, it is the degree to which the light is slowed down.’ ‘The refractive index is the ratio between the speed of light in empty space and the speed of light in the material. So the higher the refractive index …’ ‘—the longer the arrow.’ ‘Exactly. Now imagine light on its way from one material to another. So here is the boundary between the two materials and the arrow of the incident light:’

50 

U. Leonhardt

Norah continued: ‘Now let me sketch the wave the arrow represents, the incident light wave:’

She went on: ‘Let me put some dots in the picture.’



Norah explained: ‘The dots tell us the number of oscillations. The horizontal dots count the oscillations of the light in the interface between the two materials, the vertical dots the oscillations in the vertical direction. They represent the components of the arrow of light, one in the interface, the other orthogonal to it. The question is now: what happens to the arrow of light on the other side, in the second material?’ ‘You have drawn the arrow and you have drawn its components. The question is: what happens to the components.’ ‘Precisely—that is the right question. You’ve hit the nail on the head. Or rather, you found the right place for the nail, and now you can hit it.’ ‘You helped me, of course.’ ‘That was nothing. Finding the right question is the most important and the most difficult step in science. Now you can solve the whole puzzle and say “elementary, my dear Watson”.’

47 Although, supposedly, Iain had found the right question, he still needed some encouragement to get him moving in the right direction. Norah was happy to help: ‘Let’s take this one step at the time. What do you think happens to the oscillation component in the direction of the interface?’

  Mission Invisible 

51

‘What can happen to it? What you have on one side you must also have on the other; the number of oscillations of the light must be the same on both sides.’ ‘Exactly, the oscillations will simply continue in the second material. So the picture should look roughly like this.’

‘I agree with you and your picture. However, if I want to understand the arrow of light in the material, I need two components, not just one. I know nothing of the other component.’ ‘You don’t need to. You know another fact that will tell you what is missing: you know the length of the arrow of light. When light travels from one material to the other, the total number of oscillations per unit length changes, so the arrows of light will have different lengths for different refractive indices. And you know how much the arrow of light got longer, from the ratio of the refractive indices. Let me draw you this. First I erase the waves and dots, to make the picture as simple as possible. Then I draw the two conditions we need to know: the horizontal components of the arrows are the same, the lengths are different by the refractive indices of the materials.’ ‘But how can you draw “conditions”?’ ‘Simple! Here is the picture.’

Norah explained: ‘All arrows with the same horizontal component lie on the vertical line I drew; all arrows with equal length lie on the circle. Where

52 

U. Leonhardt

the line and the circle intersect, the two conditions are met simultaneously; this is where the arrow must point.’ Norah erased the circle and the vertical line—the scaffolding of her construction—and drew the waves again: ‘This, finally, is the full picture. You can now see how the change in the refractive index tilts the wave fronts and bends the arrow of light.’

Iain nodded and said: ‘I see, the arrow of light in the second material gets longer, because light is slower there—the refractive index is higher. On the other hand, the components in the interface have the same lengths—the dotted line is common to both. The result is that the light bends inwards. If, however, the second material has a lower refractive index—if light is faster there—the drawing should look like this, shouldn’t it?’

‘You’ve got it! These drawings show the law of refraction written down by Ibn Sahl in 984. This law is also known as Snell’s law after the Dutch astronomer Snellius who rediscovered it in the early seventeenth century. Now, what do you think will happen when you don’t have two materials, but the refractive index changes within one material?’ ‘Why would this be any different?’ ‘Why do you always answer a question with another question?’ ‘Well, why not?’

  Mission Invisible 

53

48 Both laughed. Iain said to Norah: ‘Seriously, why should it be any different if you have two materials or one material with two refractive indices? What counts is only the refractive index. I have seen this most vividly in an exhibition on camouflage in nature. Some sea creatures become completely invisible when they have the same refractive index as the water around them: to light, the material “water” and the material “sea creature” are the same.’ ‘Yes, what matters to light is only the refractive index, nothing else.’ ‘Now that you have asked, can I answer you with a slightly different question? Between two materials the refractive index changes abruptly, but this might not be so in one material. The question is: what happens to light when the refractive index varies gradually?’ ‘Good question—and I know an excellent example. Have you ever seen a mirage?’ ‘Yes, in Saudi Arabia. There I saw a caravan of camels walking on air or water in the desert. This was an optical illusion, of course. The whole country seems to be the perfect place for illusions and deception.’ ‘The mirage is really simple. It is literally just hot air. I will explain it to you so that it becomes perfectly clear. Let’s begin at the beginning: heat and air. The air above the hot sand is hot, hotter than the air higher up. Hot air is less dense than cold air, so it does not slow down light as much as cold air does. The difference is minuscule, but matters when light travels a long-enough distance.’ ‘Right above the sand the refractive index of air is slightly lower until it reaches its normal value with increasing height. Is this what you are saying?’ ‘Precisely. Now imagine the air consists of layers, one on top of the other. The layers should be so fine and thin that within them the refractive index is practically the same; the index only varies from layer to layer.’ ‘But this is obviously not true; no matter how thin you think the layers are, the density of air varies gradually, and so does the refractive index.’ ‘I agree and I disagree. Yes, you are right, I am making an artificial assumption that, strictly speaking, is not absolutely true, but it helps me to solve the problem. Plus, the errors I am making with my assumption are small. Let me show you how it goes.’ Norah drew several layers in the sand and the path light was taking.

54 

U. Leonhardt



She explained to Iain: ‘Between each layer light changes direction, and within each layer it travels along a straight line; but if you make the layers thinner and thinner you see this less and less. In the limiting case of infinitely thin layers, the path of light becomes a perfectly smooth curve.’ ‘I understand what you mean. So light changes direction, however slightly, wherever the refractive index varies.’ ‘A material with a gradually varying profile of the refractive index bends light. This bending of light causes optical illusions.’ ‘Why? I have heard this before—in Arabia, but I did not really understand it at the time. What exactly has the bending of light to do with optical illusions?’ ‘I think you and me, like everyone else, naturally assume that light rays are always straight. If they are not, we are puzzled. This comes from our early childhood, from the time we first learn how to see. Babies try to grasp everything around them with their hands, sticking things into their mouths, and, most importantly, looking at what they are grasping. In this way they learn how to coordinate the world they grasp with their hands and the world they see. In the environment we grow up in, light travels straight through air— normally. So we assume, deep in our minds, that light rays are straight. If we see something that does not make sense—something we cannot grasp, we are puzzled by an optical illusion.’ ‘Interesting. I have seen an animal, a fish actually—the archerfish, that has adapted its sense of vision to the water surface where light is always bent. But let’s get back to the mirage. You promised to make it perfectly clear.’

49 Iain and Norah were sitting in the Persian garden of Ghavam House in Shiraz, talking and drawing diagrams in the sand. Norah sketched the way light rays bend in the hot air above the Arabian desert.

  Mission Invisible 

55

Iain said: ‘I see, light bends outwards, because the refractive index of the air gets lower the higher the temperature is, that is, the closer the light gets to the ground.’ Norah drew two straight lines, one before and one after the light bending.

She explained: ‘The lines indicate how much the light ray has changed direction. This and only this matters, because you cannot actually see light rays. You cannot see how light travels through space, but only the light that reaches your eye.’ ‘Not so fast. I have seen sunrays breaking through clouds or through shutters in a dark room.’ ‘What you have seen there was light scattered from droplets or dust particles floating in the air. Normally, light rays are invisible until they reach you.’ ‘You always have an answer, but what about the laser beams in the movies?’ ‘Oh, this is all wrong, especially when they show laser beams in space. In empty space, light beams are not scattered by anything. They don’t leave any trace, and they don’t make any noise either. You believe the movies?’ ‘I was just teasing you. But, seriously, if I cannot see the paths of light rays, how can I tell whether light bends gradually or abruptly?’ ‘You cannot. My two pictures—the curve and the broken line—are absolutely indistinguishable to you.’ ‘So I cannot tell whether light is bent …’ ‘—or reflected …’ ‘—as by a mirror …’ ‘—or by the surface of water.’ ‘I see what you are getting at: I seem to see water in the desert, because water reflects light in exactly the same way hot air is bending it. But what about the camels? Why do they look like they’re walking on air?’ ‘We agreed that the hot air above the sand acts like a mirror. So imagine a large mirror is lying in the sand some distance away. What would you see in it?’ ‘What would I see? What is above the mirror.’ ‘And what is above the mirror?’ ‘The sky!’

56 

U. Leonhardt

‘Exactly! Under the feet of the camels you see patches of the sky. That’s why they seem to be walking on air.’ ‘A mirror made of air …’ ‘… of hot air.’ ‘Fantastic!’ ‘You see how it all fits together? You see how simple the optical illusion of the mirage really is? Now, let me tell you something else, something that will shock you, something that will rock your world.’

50 Iain felt he could make sense of the mirage now. He had also got a reasonable grasp of the way light changes direction in transparent materials—he could draw diagrams for it, but he was still a little puzzled. He understood the “how”, but not the “why”, as if he had witnessed a magic trick without explanation. Now Norah wanted to shock him. Iain replied: ‘Please don’t tell me something I will not understand anyway—like quantum physics, eleven dimensions, or Einstein’s theory.’ ‘What I am going to tell you will shock you, because you will understand every bit of it.’ ‘Then go ahead.’

51 Norah began: ‘you know that light follows straight lines in empty space or in materials where the refractive index is everywhere the same. But tell me, what is a straight line?’ ‘Well, it’s straight, that should be straightforward, shouldn’t it?’ ‘A straight line is the shortest line from A to B. Suppose you know that a light ray begins at A and ends at B. Then the straight line is the shortest path.’ ‘How do I know A and B, how do I know where the light ray begins and where it ends? I suppose I might know where it begins if I send off light from a lamp, and I know where it ends if I look at it—because it must end in my eye. But what if I don’t see it? How could I always know the beginning and the end? Impossible!’ ‘Let’s leave this aside for the moment.’ ‘But you promised I would understand everything.’

  Mission Invisible 

57

‘Just assume you know both A and B, and don’t worry how you know it— for the time being. Just assume it. Then light follows the shortest path from A to B. This is also true if light is reflected in a mirror. Let me show you why.’

52 Norah took the dry twig and drew this diagram in the sand. $

%

&

‘This is the path of a light ray from A to B reflected in the mirror at C. Let me prove to you that it is also the shortest path.’ ‘Light might go directly from A to B in a straight line without bothering to touch the mirror.’ ‘True, but if light is sent out from A in all directions, then some ray will bounce off the mirror and reach B the way I have drawn. I will show you with some more drawing that this path is the shortest of all paths that strike the mirror.’ Norah drew another path of light for comparison. $

%

&

She looked around in the garden and said to Iain: ‘Since we are sitting in a garden, do you know the gardener’s construction of an ellipse?’ ‘You mean, do I know how a gardener would draw an ellipse for a flowerbed? I have seen it on Gardener’s World (I admit that I watch Gardener’s World sometimes). The gardener hammers two handy sticks into the ground and attaches a cord to them. He pulls the cord taught with another stick. This is the stick he draws with. He moves it around and the stick marks out an ellipse.’ ‘Let me sketch this in my drawing,’ Norah said.

58 

U. Leonhardt $

%

&

She continued: ‘the length of the cord represents the length of the actual light ray from A to C and finally to B. You see that the gardener’s ellipse lies above the mirror. So if, for whatever reason, a light ray were to take a different path from A to the mirror and to B, this path would be longer.’ ‘You are too fast for me. I am not used to geometry. Please start again, and go one step at the time.’

53 Norah nodded, fell silent for a second or two, then fired away: ‘Step one: we wish to prove that the shortest path from A to B via the mirror is the path I have drawn.’ $

%

&



‘Step two: you know that the shortest path in empty space is a straight line. From this it follows that the only candidates for the shortest paths are straight lines to and from the mirror. Let me draw this again.’ $

%

&

‘Step three: the cord length of the gardener’s ellipse is the length from A to C and from C to B together.’ ‘Step four: the ellipse lies above the mirror.’

  Mission Invisible  $

59

%

&

‘Step five: you see from the drawing that the other contenders for the shortest path are longer then the cord of the ellipse.’ ‘Conclusion: because the length of the cord is the length of the path from A to B via C, this path is the shortest. Light follows the shortest path.’ ‘ “Quod erat demonstrandum”, as the Latin phrase goes—“which is what had to be proven”,’ Iain said, finally. ‘I am with you now. But so far you have not shocked me. You managed to confuse me, but not really to shock me.’

54 Norah erased her drawing and sketched the light path of the mirage again. $

%

‘What if I told you that light always finds the shortest path? The shortest path is not always straight. Only if the speed of light remains the same throughout the material is it straight.’ ‘The shortest path is not always the straight and narrow one, but may seem bent and crooked? I am not quite sure whether I subscribe to this philosophy.’ ‘Look at the drawing of the mirage. Of course, light may go straight from A to B, but some will take the detour, and get reflected in air. The question is now: suppose it is reflected, how does it travel? You see, when light is bent the way I have drawn it, light spends more time in a region where the air is thin, where the refractive index is low, where it is fast. There is an optimal path of the shortest travel time, and this is the path light takes.’ ‘I am not quite sure whether I believe this.’ ‘Let me draw you another example, the case we started with.’ Norah drew a diagram showing light bent at an interface between air and water, and said:

60 

U. Leonhardt $

%

‘Light could go directly from A to the water surface along the shortest path in the water, where it is slow, thus saving time there. But then the path in the air would take longer. Or, it could choose a shortcut in the air, but then the path in the water would be longer. Clearly, there must be an optimum between the two extremes, and believe me, this optimum is the path light actually takes. I admit I have not rigorously proved it to you—for the proof you would need some more serious mathematics then my simple sketches. I only made it plausible and ask you to believe me as a scientist.’

55 Iain was not convinced and replied: ‘With or without mathematics, how can this be true? What you have told me is completely bizarre. First, I should know in advance that light travels from A and is guaranteed to arrive in B. Second, given that it goes from A to B, light should find the shortest path between A and B completely on its own. How can it do that?’ ‘I told you it would shock you, and it has indeed, precisely because you have understood it.’ ‘No, I have not; nobody can understand this. Light cannot simply “see” the entire path in front of it and adjust itself accordingly.’ ‘And yet it does. A French scientist, Pierre de Fermat, discovered the principle of the shortest path in the seventeenth century.’ ‘I have heard the name of Fermat before’ said Iain and remembered Luna’s cryptic words in the desert. Norah continued: ‘Fermat’s principle faced great opposition at first, like all radically new ideas. Your objections were very much like those raised at the time.’ ‘You are a scientist, not a historian. You are very Persian, which makes you a philosopher and a poet as well as a scientist. Let’s argue philosophically and rationally. I am sure you agree that light, like everything else, can only go one step at a time.’

  Mission Invisible 

61

‘Agreed. Light has a finite velocity, so it cannot move across space in a single instant. It must propagate from place to place, one step at the time.’ ‘In your drawing, light propagates first in the water from A to the surface, and then in the air from there to B.’ ‘Sure.’ ‘Now, the shortest path from A to the surface is the direct path you have drawn. But then, according to your own words, the part through the air takes longer. The total travel time is longer than the time of the optimal path.’ ‘This is what I have said and this is what is true.’ ‘You may draw two conclusions from this argument: either light does not go one step at a time or light does not follow the shortest path, you sacrifice either causality or Fermat’s principle.’ ‘I hear your argument, I follow your logic, and yet you are wrong. Do you know what?’ ‘What?’ ‘You argue like a mullah.’

56 Midnight came and went and the Old Town of Shiraz began to sleep at last. The bustling streets went silent and even among the narrow houses the air carried a hint of orange blossom. Iain was standing in front of Khan School, below the towering gate, banging his fists against the heavy door, then rattling the iron window of the gatekeeper. The gatekeeper, an old man wearing a black turban, came out, a light in his hand, rather sleepy, and rather angry with the visitor at this hour. Iain was demanding entrance, he needed to speak to the Master, it was urgent. Tomorrow at first light his journey would take him on to Russia. There was no tomorrow, he needed to talk now. Finally, the gatekeeper gave in, the heavy gate swung slowly, Iain entered, and fell over the threshold. When Iain got up again, he could make out the garden in the moonlight and then the silhouette of the man he needed to see. The light of the moon was the only light upon the mathematical garden with its Golden Ratios and studies of rational and irrational numbers in the flowerbeds. The ponds were heavy with green, as if hundreds of years of silence had gone by. Iain walked towards the man waiting for him in the garden, a man dressed in a long black gown, with a white turban on his head and a noble face with elegant grey beard. The Master! Yes, no doubt, it was the Master himself: Mulla Sadra.

62 

U. Leonhardt

Iain did not question why he might be able to meet a seventeenth century Persian philosopher at Khan School in the middle of the night, the man many regarded as the greatest Muslim philosopher of all times. Iain urgently needed to talk to him. Mulla Sadra was related to the Ghavams, so Iain was at the house of his family during the day, and now he was at his college. ‘Master, please forgive the intrusion at this hour. I urgently need to speak to you. At first light tomorrow I shall fly away, and I need an answer tonight.’ Mulla Sadra smiled with his eyes and spoke in a sonorous, warm voice: ‘Do you need an answer or do you need a question?’ ‘Master, I need an answer. Is it true? Fermat’s principle, the principle of the shortest path, is it true?’ ‘Let me answer you with three questions: Number one: why do you need to know? Number two: why do you need to know now? Number three: how do you need to know?’ ‘Why do I need to know? I’m travelling with an eminent professor of optics, Lady Lucy de Phos, so naturally I am hearing many things about the science of light and that has made me curious.’ ‘My young friend, this does not answer the question I asked. It answers the question why you want to know, but not why you need to know.’ ‘I feel I need to understand what she is doing—in inventing invisibility; something is not quite right, and Fermat’s principle is the key.’ ‘What about my second question: why do you need to know now?’ ‘We shall fly to Russia tomorrow, to St Petersburg. I feel very uneasy about this country. I am worried where all this is leading. I need to know before she speaks to someone there.’ ‘Now I understand you and you understand yourself. My final question is: how do you need to know?’ ‘What do you mean?’ ‘Lucy de Phos—what an interesting name for an angel. Angels and people are different: angels see the truth in one glance; they do not need to think, they see. Shall I make you see? Shall I make you think? How much of an angel are you?’

57 When Iain woke up from his dream, the noise of running water was coming from the bathroom again. But the noise had not woken him up. Mulla Sadra had convinced him that Fermat’s principle was true: light takes the shortest path. How he had proved this to Iain, he no longer knew. Maybe Mulla Sadra

  Mission Invisible 

63

had drawn a diagram, a diagram for an angel to see the truth in one flash of insight, or maybe he had filled sheets of paper with algebra, proving step by step the principle of Pierre de Fermat. Now Iain knew, but he did not remember how he knew, nor why. But Iain remembered something else, a shadow he had noticed on his way to Khan School at midnight. What was it? Somebody had been following him. But who? Luna, perhaps? She was not in Shiraz, she could not possibly have followed him there. But this was a dream; dreams have a different logic. In dreams, places, times, and actions are combined, showing you what you already know, but have not noticed yet. Who would follow them to Russia, and further on their journey? Foo had been diverted to Vienna—he needed to see to his citizenship. Whom would they meet in Russia?

58 At the first light the next morning a Turkish plane took our two travellers on their journey to Russia, first to Istanbul airport, where they had to wait for their connection to St Petersburg. They were having breakfast of Turkish cheeses, honey, yoghurt, apple tea, and strong black coffee under an olive tree in the lounge—there was a spectacular life tree there. Someone was playing the piano in the lounge. Lady Lucy felt communicative: ‘What did you make of the Persian professor, Parsa was his name, the chaste pasha with his harem of college girls? Funny chap, isn’t he? His university is in dire straits. I have seen the labs, and they are pitiful. Extraordinary that the Persians are still able to produce science. Mostly theoretical science, though.’ Lady Lucy took a glass with apple tea, had a sip, and felt she should favor Iain with her thoughts: ‘I suppose the biggest export from Iran is scientists, apart from oil, caviar, and international trouble, of course. I know several Persian professors, mostly in America and Europe, and they are not too bad at all. Parsa told me about the Iranian elite universities. They go to great lengths in selecting the best and brightest students, they take great care with their education, and then what happens? Ninety-nine point nine percent of their graduates leave Iran and never return. How extraordinarily stupid, I thought, but then I was thinking things over. What do the Iranian elite universities do? They identify the best and the brightest—the future trouble makers, give them an education that guarantees good jobs abroad, and they take a one-way ticket out of Iran. Brilliant, isn’t is!’

64 

U. Leonhardt

Lady Lucy took another sip of apple tea and continued her conversation: ‘Did you meet Foo as well? Amusing chap, sharp as a razor blade. I suppose what he lacks in height he makes up for in mental agility. We had a most interesting conversation over breakfast yesterday. He told me all about his country. Fascinating place. The figures are staggering, the extent they invest in science and technology makes me wonder about the future of Britain.’ Lady Lucy went silent for a minute, and then said to Iain: ‘By the way, tomorrow morning I shall definitely require your services. I have a meeting with some important people in St Petersburg and not all of them speak English. We meet them immediately after seeing the Hermitage. Strange name, what is it?’ ‘Ma’am, this is the greatest art museum of the world, the winter palace of the tsars and their museum; it is better than the Louvre in Paris—I was told, I have never seen it myself yet.’ ‘Splendid. My good old friend Vladlen has arranged for a private visit before the opening hours. So we can see the museum in style, just like the tsars.’

59 While Shiraz was in late spring with the oranges blossoming, winter had returned to St. Petersburg, and returned with a vengeance. The plane had landed in a haze of snowflakes, the passengers put on warm clothes and overcoats against the bone-chilling Arctic wind. Stern, uniformed females scrutinized their passports, and then the gate opened. By this time in history, Russia had become an international pariah once more. The cold had returned, as had the cold war; the country had closed her gates to Western tourism. Lady Lucy, however, held an invitation from the highest circles and a letter of introduction from the British ambassador, so she and Iain could pass. The first thing they saw after passing through the gate was an enormous sheet of paper with “Professor Lady Lucy de Phos” written on it. The young man carrying it said excitedly; ‘Lady Lucy, welcome to St. Petersburg! Professor Vladlen Cheburashkov offers his apologies for not greeting you in person at the airport. You shall see him tomorrow. I will take care of you this afternoon. I am a student in his group. My name is Yevgenie, but everyone calls me Zhenya.’ Zhenya was bubbling with excitement to see the great scientist. He constantly ran his hands through his unruly black hair. His eyes were beaming with joy. While he rushed to help her with her luggage, the enormous sheet of paper sailed off into the arrivals lounge. After some final confusion, all went

  Mission Invisible 

65

to the car, a black jeep fit for any weather, and climbed on board. Zhenya sat down next to the driver, spoke to him in Russian, and off they went through the snow towards their lodgings, Alexander House. When they arrived at the elegant classical house on the Kryukov Canal, the snow was swirling in flurries. But soon the door opened and the warmth and the pleasant smell of a wood fire welcomed the travellers. Alexander House was a hotel of only twenty rooms, and they all had the names of cities or countries, according to their style. Lady Lucy was given the deluxe room “London” of course, while Iain’s was “Mexico”. Iain walked up the creaky staircase, went across the library where wood was burning in the fireplace, and then turned left. When he opened his door, the light went on over brightly colored cushions, Aztec wall decorations, and Mexican paintings. It was a room full of joy and color. Alexander House used to be the home of a nineteenth century merchant. The communist revolutionaries had turned it into a communal living space, as they did with most of the homes of the upper and middle classes, apart from the palaces fit for museums. Alexander House had decayed after the collapse of the Soviet Union, until a retired journalist and his wife had rescued it. They had retired from their travels and returned with artworks and furniture from far afield, as well as the desire to create a permanent home for themselves and a temporary home away from home for their friends. What began as a house for private guests, developed into the finest guesthouse in Russia. The hotel was as private and pleasant as a friend’s home, and as cosmopolitan and cultured as its well-travelled owners. It was a miracle that the rulers of the Kremlin had not seized the place as one of their own guesthouses in St. Petersburg. But maybe it was too small for their ambitions and too tasteful for their taste.

60 After an hour for revitalization, the travelers were ready for a tour of St. Petersburg with Zhenya as guide and the jeep as transport. The weather had improved, too. Beams of sunlight were breaking through the clouds, illuminating the water of the canals, and the blue and gold of the churches over the white of the fresh snow. They drove along the Kryukov Canal, past the Mariinsky Theatre—the tsar’s grand opera house, crossed over the river Neva on the bridge to the University Embankment, where they could see the palaces of the city as they were originally meant to be seen: from the sea. Some say, St. Petersburg is the Venice of the North, but they are wrong: there is no

66 

U. Leonhardt

comparison. Venice is a village compared to Peter’s city. The baroque of the city was Italian, but built on a much grander scale, and St. Petersburg was not the accumulated result of centuries of commerce, craft, and common sense; it was a planned city of imperial greatness. On their return journey they passed by the Winter Palace and the Admiralty, and stopped at the Senate Square, where they could see the statue of the city’s founder, Tsar Peter the Great, towering on his horse. Zhenya explained to Lady Lucy how Peter had modernized Russia around the turn of the ­eighteenth century—by force and determination. Then Peter stood here on the shore of the Neva, surrounded by Arctic swamps, conquered from the Swedes, commanding the new capital that was still to be built, his city: St. Petersburg. Iain remembered these words about the rider’s statue: one does not know whether Peter’s hand protects or threatens. He also remembered Pushkin’s poem on the Bronze Horseman. The poem’s hero (also called Yevgenie) loses everything but his life to a flood of the Neva. He accuses the statue of the misery he believes it has brought, whereupon the bronze comes to life and hunts down its accuser. Zhenya said: ‘To me, St. Petersburg is the grandest, most beautiful city in the world, but we should not forget the price Russia paid. Do you see the enormous rock that is now the pedestal? This was the largest stone ever moved by slaves. Historians estimate that a quarter of the Russian population perished while building Peter’s city.’ Lady Lucy remarked, ‘That, regrettably, was the price for Russia’s snap modernization.’ Zhenya continued: ‘Russia always has to find her own answers to the challenges of the times, be it the Renaissance, the Enlightenment, or industrialization. Stalin needed to enslave the country once again, to create an industry and an empire that could rival America. Russia will need to find her own answer for the next challenge.’ Iain said: ‘I thought Russia’s answers were always the same: violence.’

  Mission Invisible 

67

61 That day, the two travelers went to bed early. Their day had begun at first light in Shiraz and ended in wintery St. Petersburg. After an early dinner at the hotel, consisting of borsht, pancakes with caviar, and homemade piroshky, they went to their quarters. In Iain’s dreams, the Bronze Horseman was hunting him through the streets of Shiraz. He escaped into the Hafeziah and asked the poets for asylum. They sent him to Norah who showed him to the zoo with a light. He climbed up to the orangutans on the tree floor, for warmth and protection. But the sound of African drums soon scared the animals away. He climbed down and found himself in a tavern, or perhaps a grotto? Under stalactites and stalagmites, Arabs were sitting like figures on a chessboard. The Bronze Horseman was the black knight.

62 The next morning Lady Lucy and Iain visited the Hermitage in style. They had the Winter Palace of the tsars and their art collection all to themselves for two hours before the museum opened to the public; Zhenya was their guide. They entered through the Ambassador Entrance of the main courtyard and walked up on the majestic Jordan staircase to the staterooms and galleries of the second floor. Lady Lucy was most impressed by the Malachite Room, Iain by the Large Italian Skylight Room and the Rembrandts he saw. Lady Lucy was very pleased to be able to visit the palace without the hoi polloi, and when the first visitors began to intrude, she was happy to accelerate her departure, as she put it. Zhenya showed them to the rooms occupied by the museum staff, where a Man from the Ministry was waiting for them. The man was very well dressed in dark blue, while an equally well-dressed, but more muscular man with watchful eyes, stood behind him. The Man from the Ministry addressed them in Russian, while Iain translated. ‘Welcome to Russia, Professor de Phos! I am a representative of the ministry that invited you. I hope you have enjoyed the brief tour of some of our country’s public treasures.’ ‘Thank you very much indeed. It was marvelous to have the Palace all to myself for the tour.’ ‘I’m glad you enjoyed it. I would like to propose a tour of another exhibition here at the Hermitage, one that is close to your line of work, Professor.’

68 

U. Leonhardt

‘I’m all ears.’ ‘The exhibition is, how shall I say, not exactly public. So we have to follow certain procedures. I will have to ask you to put all your mobile devices into this metal box, and you will have to be screened. It is all standard procedure, nothing personal. I would be very much obliged if you and your assistant would be so kind as to accept.’ ‘You have raised my curiosity. I wonder what wonders you have in your hidden treasure trove. The procedure is perfectly reasonable. I am happy to accept. I can speak for my assistant as well. Please, go ahead.’

63 Few visitors venture onto the first floor of the Winter Palace, although it harbors some world famous archeological treasures, most notably the gold hoards of the Scythes, mysterious horse-riding nomads who lived on the Steppes. Few visitors, if any at all, notice the door to the wine cellar of the Winter Palace. In 1917, the communist revolutionaries did, and this may have caused the greatest hangover in human history. For those days that shook the world, the looting of the wine cellar was the worthy conclusion. These days, however, the cellar was off-bounds to the public. The door was sealed tight, but there were keys to open it. The Man from the Ministry had one.

64 The two visitors walked down the stairs, and were quite surprised to enter a brightly lit modern exhibition area. Lady Lucy was even more surprised when she saw an old friend of hers, Professor Vladlen Cheburashkov. She was pleased to see him and said so, but Iain was immediately reminded of the Soviet Ambassador in Stanley Kubrick’s movie “Dr. Strangelove”. The Russian professor was a tall, fat member of the nomenklatura with a hat on his massive head. He was in the habit of giving orders, while showing signs of a nervous constitution. At the moment his orders concerned the buffet lunch for the visitors, the Man from the Ministry, and himself. After some really excellent smoked sturgeon, salmon, and caviar with toast, the four went into one of the exhibition rooms. The Man from the Ministry explained (while Iain translated): ‘Please stand here. In this room, we are going to show you some demonstrations of advanced camouflage technology. First, you are going to see an

  Mission Invisible 

69

old-fashioned projection technique. The officer standing in front of the bookcase is wearing a cloak of retro-reflective material. Light falling on it is always reflected in the direction it came from, which makes the cloak a good projection screen. The camera, over there, is taking a video of the scenery—the bookcase. The video will be projected onto the officer. Now!’ The visitors saw the cloaked figure disappear. Only his uncloaked face was still visible. ‘This is, of course, a rather limited technique. First, the officer is only invisible if you look in the direction of the camera. Second, although the person vanishes from view, not so the surrounding equipment, the camera and the projector. Over there you will see a much better method in action. Or rather, you will not see it. Professor Cheburashkov, may I ask you to stand here for a little demonstration?’

65 The fat professor started walking in the direction indicated by the Man from the Ministry, then turned left—and disappeared. Only his characteristic head, as if floating in midair, was proof the Kremlin had not made him vanish for good. ‘How did you do that?’, Iain could not resist asking. ‘Please, walk over to Professor Cheburashkov and see for yourself.’ The professor was standing between two rectangular screens showing the image of the scenery behind them. The Man from the Ministry explained: ‘These are active screens, they contain micro cameras and LEDs. The cameras take images of the scenery and the LEDs show them. Each screen displays a picture that the other camera is taking. This has made Professor Cheburashkov disappear, but only in one direction. Now, Professor, may I ask you to go inside this cylinder? It opens here.’ This time the professor had vanished completely, head and all, and from all sides. Lady Lucy said: ‘The cylinder takes videos from every direction and displays them on the opposite side. I understand what you are showing me, but I don’t understand why you are showing it to me.’ ‘The reason is simple and clear: there shall be no misunderstandings about Russia’s capabilities.’ The invisible Russian professor chipped in:

70 

U. Leonhardt

‘The joke used to be: how do you know the KGB has bugged your home? And the old answer was: you’ve got another cupboard. Not anymore!’ The Man from the Ministry continued: ‘You are the top expert in the field. We have heard rumors that you’ve developed a new idea that is superior to our techniques and everybody else’s. As far as we know, your idea is still, how shall I say, theoretical. Russia’s capabilities might interest you, Professor.’

66 On the return journey to the hotel, Iain looked out of the car window, but did not see much. He was thinking about what he had seen earlier. The demonstration in the Hermitage wine cellar reminded him of the camouflage exhibition at the Singaporean zoo; the octopus and the cuttlefish had been using a very similar method to disguise themselves. According to the Man from the Ministry, Lady Lucy’s idea was different and better. But in what way? How could one improve camouflage? What were the weak points that could be improved upon? The screens used energy to make the videos and display them. Iain had also noticed that the illusion became less convincing as he got closer. He could see the pixilation, but maybe this was rather a temporary, technical problem that retina screens could solve. On the other hand, even with retina resolution, the images would look flat. They were not 3D. Somehow, he felt, Lady Lucy had found a solution to both problems, killing two birds with one stone: how to make a passive invisibility device without energy consumption and for stereo vision in 3D. But how? The transparent materials he had been discussing with Luna and Norah were completely passive. No extra energy was required to transmit light through a piece of glass. It did it all by itself. Transparent materials may also bend light if the refractive index varies in size. One could perhaps design a material that would bend light around an obstacle in the same way that water flows around a stone in a stream. Nobody would notice that the light had been on a detour as nobody would be able to see the obstacle. It would vanish from view just like the tall, fat Russian professor. Instead of the micro cameras and LEDs, the material alone would send the light round. Brilliant! Iain could imagine a refractive index profile that would guide light around the obstacle in one direction. On the left side of the obstacle he pictured in his mind a profile similar to the one made by the mirage, and on the right the mirror image of the same profile. Light coming from directly behind would

  Mission Invisible 

71

flow around the obstacle. But what worked in one direction would not always work in all directions. The two mirages would only cooperate in the direction they were glued together. For perfect invisibility, light coming from everywhere should flow around and leave. How could a single material control light from all directions? This and only this, Iain felt, was Lady Lucy’s secret. But, given that somehow light from all directions did flow around the obstacle undisturbed, would the images be three-dimensional and real? He remembered the words of the old man in the souk: ‘all you see is light’. So if the light flowed around undisturbed, the images it carried would remain unchanged as well. They would be fully three-dimensional images of the real world. The obstacle would become invisible and so would the invisibility device. No-one would see it and no-one would see that there was something to be seen. This would surely be the ultimate optical illusion.

67 Zhenya had purchased opera tickets for the evening: Don Quixote at the Mariinsky Theatre. After pre-theatre dinner at the hotel, Lady Lucy and Iain took a taxi to the Mariinsky where Zhenya was waiting for them. They took their seats in the second row of the parquet. It was probably a coincidence that the Man from the Ministry was sitting a few seats away in the first row. He did not seem to notice them, as he was with a chic young lady that was certainly not his wife. They were busy taking pictures of each other in the prestigious setting of the grand imperial theatre. The opera was clearly of little concern to them, but it absorbed Iain completely. The orchestra, the singing, the costumes, the ballet, all was perfection. Moreover, Iain was touched by the story and its hero, the knight of the sad countenance: El Caballero de la Triste Figura. Don Quixote, with all his absurd delusions, was still a noble figure. Yes, he was tilting at windmills, but the last of the knight-errants was breaking a lance for ideals his contemporaries had long abandoned. They had the laughs, he had Iain’s heart. After the opera, Lady Lucy retired to the hotel, while Zhenya invited Iain to his home. They could not get a taxi, but a private car agreed to take them for a fee, as in Iran. The car was more than qualified for the junkyard, the music was Russian jail house and the driver was from some “stan” in Central Asia. He was of triste figura, but certainly no caballero.

72 

U. Leonhardt

68 Zhenya lived with his grandmother, parents, and baby sister in three rooms of a communal apartment, while the other rooms were occupied by other families. Once the entire apartment had been the home of a tsarist engineer. After the communist revolution it, like most other apartments, had become communal. Life in a communalka was frequently marred by life’s trivia, in forms which sometimes resembled trench warfare. Something was always malfunctioning. This time, the staircase light was not working. Zhenya and Iain needed to illuminate the stairs with their mobile phones to climb up to the third floor. Zhenya opened the burglar-proof iron door with its triple locks. He asked Iain to be quiet, as everyone was already asleep. A large grey cat came down to the door and rubbed around their legs. ‘This is Euler, my cat. I named him after Leonhard Euler, the mathematician’, said Zhenya. They walked into the communal kitchen and Zhenya made tea while speaking about Euler the man and Euler the cat. ‘Euler was a professor in St. Petersburg and Berlin, in the eighteenth century. He was from Switzerland and is buried here at the Alexander Nevsky Cathedral, that is, in St. Petersburg’s equivalent of St. Paul’s. Euler was the best mathematician of his time. He was incredibly prolific, producing a paper a week with the help of his genius plus Swiss work ethic. This cat is very special as well, he helps me solve physics problems by simply being around, and he seems to like you.’ The cat was sitting on Iain’s lap. Zhenya continued: ‘Euler the man was not only a great mathematician. He worked on fluid mechanics, optics, engineering, cartography, and astronomy. Euler even wrote a popular science book: “Letters of Euler on Different Subjects in Natural Philosophy Addressed to a German Princess.”’ Iain asked, ‘You mentioned optics, did he also work on optics? On Fermat’s principle?’ ‘Yes, he did, it’s good you asked! Euler and the French-Italian mathematician Joseph-Louis Lagrange developed a method for putting Fermat’s principle into a causal form.’ ‘What do you mean by this? Please explain, but without the mathematical jargon.’ ‘Sure! Fermat principle states that, if light travels from A to B, it takes the path of the minimal time. This is teleological: I need to know the beginning and the end, and then light finds the optimal path. Now Euler and Lagrange deduced an equation for the path that is causal: I need to know the beginning and the direction light is going, and then the equation tells me how light

  Mission Invisible 

73

propagates from point to point, one step at a time. Miraculously, the two points of view, the teleological and the causal, are not in conflict with each other. They are the same.’ ‘How? Can you explain? Can you write down the equation and explain it, term by term?’ ‘I can write down the Euler-Lagrange equation, but I am afraid it will not tell you much. You would need to know calculus to make sense of it. Let me try to think of another explanation. Do you know Snell’s law, the law of refraction?’ ‘The law of light bending, Ibn Sahl’s law?’ ‘Yes, that’s the one. When light enters the region with a different refractive index—’ ‘—it is bent.’ ‘You probably also know that this remains true when the refractive index varies gradually. Each variation of the refractive index bends light. You may view the entire trajectory as a succession of miniature refractions, one at a time, step by step.’ ‘Which is causal.’ ‘The Euler-Lagrange equation formulates this idea in a mathematical language suitable for computers to calculate trajectories. It is the law of light bending made precise’. ‘Let’s get back to the Fermat principle.’ ‘We always get back to Fermat. You see, as you can view every light trajectory as a succession of refractions, you only need to prove that the law of refraction follows from Fermat’s principle and, vice versa, that Fermat’s principle follows from the law of refraction. Then you know that the causal and teleological points of view are the same.’ ‘I’ve seen this proof in a dream in Shiraz.’ ‘In a dream? In Shiraz?’ ‘The city of dreamers. You see what you scientists have done to me—me of all people—you have made me dream about science. You have made me ask for mathematical proof, as if my life depended upon it! Even your cats are mathematicians, right, Euler?’

69 Euler the cat had been purring as Iain stroked him, and upon hearing his name so frequently mentioned in praise. Zhenya returned to Euler the man:

74 

U. Leonhardt

‘You must admit how fantastic this is! Science gives you a precise language for the most profound and wonderful things. Euler and Lagrange found the right language for Fermat’s principle, but also for many other optimization problems, for fundamental and practical ones.’ ‘Can you give me an example?’ ‘Suppose you want to build an aircraft evacuation slide. In the hopefully unlikely event that the plane is on fire on the ground, the passengers must get out and slide down as fast as possible. This is an optimization problem: solve the Euler-Lagrange equation and you get the best possible shape for the slide.’ ‘I see how practical the Euler-Lagrange equation is. Where else is it fundamental, apart from Fermat’s principle?’ ‘In geometry, for example. Geometry is geo-metria, the art of measuring the world. The key to geometry is the measure of length, because distances, areas, and volumes, the whole lot can be reduced to lengths. Now, what is length? For a straight line you get the length from Pythagoras’ theorem. I will draw it for you.’ Zhenya produced pencil and paper, tools he always carried with him. He drew the diagram below:

and pronounced: ‘The square of the length l is the sum of the squares of a and b.’ ‘And what are a and b?’ ‘These are the coordinates: a is the distance the line went on one axis and b is the distance it went on the other, orthogonal axis. You describe the line by the two numbers a and b and the length of the line is then the square root of the sum of their squares.’

  Mission Invisible 

75

‘I see, but what about the length of a curved line, the length of a curve?’ ‘That can be found as follows. Suppose the curve is made of straight pieces.’ Zhenya drew the picture:

and continued: ‘Then imagine the pieces are made infinitely small and infinitely many. Any curve can be described like this, no matter how curvy it is.’ ‘I’ve seen this before, in a garden in Shiraz, the idea of dividing things up ever more finely. I also think I may know what you are getting at. I apply Pythagoras’ theorem to each piece and so get its length. Then I sum up all the lengths, and get the total.’ Zhenya exclaimed: ‘You’ve got it! Now you know what we mean by the length of the curve. Now you can ask the following question: what is the shortest line from A to B?’ ‘A straight line, I already know that.’ ‘But now you can prove it! Solve the Euler-Lagrange equation for the length and you get the straight line. You don’t look convinced.’ ‘I don’t quite see the point.’ ‘I know how you feel. It’s like the story of the men in the balloon. Two men in a balloon are swept away in wind and fog. Suddenly, the clouds clear and they see a man down below them. They shout, “where are we?” The man shouts back, “in the balloon”. “This man must be a mathematician”, one of the balloonists said to the other. “His answer is absolutely right and absolutely useless”.’

70 Zhenya said, ‘Let’s go to my room, I’ll need some props to convince you how useful Euler’s method is for geometry, the art of measuring the world.’ The two went along the corridor to Zhenya’s room, with Euler the cat in tow. Zhenya’s room was so tiny that it could have qualified as a broom cabinet or a walk-in wardrobe. There wasn’t even room for a bed, only for a raskladushka, a Russian folding bed. Bookcases covered all the walls, apart from the pictures and the map of the world over Zhenya’s desk. He brought in a second chair and they sat down at the desk.

76 

U. Leonhardt

Zhenya continued: ‘The straight line is the shortest path in flat space, but not in a curved space. However, the Euler-Lagrange equation still gives you the shortest path there.’ On Zhenya’s desk stood a globe. He took it and said: ‘In a curved space, like on this globe, the shortest lines are curved. Airplanes fly along them if they can—if they are not deterred by bad weather or dangerous territory. The shortest path from Moscow to Los Angeles goes over the North Pole and not over the Atlantic Ocean. You can see all this from the globe, but not from the map over there.’ Zhenya pointed to the world map over his desk:

Iain said; ‘Never blindly follow maps or, worst of all, GPS navigation. Follow your nose, I always say. If I were to believe this map I would fly over the Atlantic, the Great Plains, and the Rockies, but definitely not over the North Pole.’ ‘And yet, this map is accurate, you just have to read it in the right way.’ ‘Then tell me, which information is missing from the map?’ ‘You are asking the right question. Some vital information is missing. The map tells you the coordinates of any point on the globe. That is, the latitude and longitude, but not the measure of length. But if you take the globe you get the right answer for the shortest path, because here you may apply the natural measure of Pythagoras’ theorem. This is what your intuition does. On the map you need to be told what the measure of length is.’

  Mission Invisible 

77

‘What is it?’ ‘Length depends on latitude. The closer you get to the Equator, the longer the actual distance between two neighboring points on the map. Nearer to the Poles, vast distances on the map amount to next to nothing in reality.’ ‘Unless you have to walk across Antarctica or flee from a polar bear in the North, then every step counts. But we are talking about geographical distances.’ ‘You see the distortion of distances on the map in the size of the continents. Greenland appears larger than South America.’ ‘Some advocates of political correctness might object to this map. It misrepresents the developed countries in the North at the expense of the developing countries around the Equator.’

71 Both laughed, Zhenya from not having experienced political correctness and Iain from having had too much of it. Iain asked: ‘Is there actually a politically correct map? I mean a geographically correct map of the Earth?’ ‘Nope, that’s mathematically impossible. Imagine you peel off the skin of the globe, like the skin of an orange, and then try to put it flat on the desk. It would never lay flat. It will always buckle, unless you tear it. The surface of a sphere is curved and you cannot make it flat, no matter how hard you try.’ ‘Not even political correctness can change the laws of Nature. You can only pretend they don’t exist—they are just the social constructs of dead white men or symbols of social power.’ ‘Is it that bad?’ Iain preferred not to answer, and said: ‘Let’s get back to cartography. I understand that no map is complete without the measure of length. Isn’t this measure of length simply the scale of the map?’ ‘Exactly, without knowing how many kilometers you get per centimeter on the map, or miles per inch, you cannot read the map.’ ‘Now, on the map of the world, the scale is not fixed, it varies with latitude. Is this what you are saying?’ ‘Absolutely, to get the actual length of a curve, you need to multiply the apparent length from Pythagoras with the correct scale. You need to do this for each infinitely small piece, because the scale may vary from point to point.’ Iain asked: ‘Now what happens if I draw a different map? What if I don’t like the imperialist map on your wall and wish to redraw the world?’

78 

U. Leonhardt

‘Then you need to transform the scale as well.’ ‘And I could never get it flat?’ ‘For the surface of a sphere, you could never get a constant scale, the plain Pythagorean measure of length. This is a mathematical certainty.’ ‘Suppose now I have something flat, say the plan of a city.’ Zhenya: ‘If the city is small in comparison with the curvature of the Earth, you may safely assume it is flat.’ ‘I have often noticed how unreliable maps are for judging distances, for example, maps of subway lines. The worst is the London Tube.’ ‘Metro maps deliberately distort distances, because they emphasize what is important in this kind of transport: the connections. There are many connections in the city center, so the central section is stretched, but fewer connections outside, if any at all, so the outer sections are squeezed. If you know how the scale varies you can measure the actual lengths. For a flat space you can always do this by finding a flat Pythagorean map. But for a curved space, you can never make it flat.’ ‘Isn’t this incredibly simple! I always thought I would never understand curved space, and yet I am living on one: the surface of the Earth.’ ‘Research is to see what everybody else has seen and to think what no one else has thought.’ ‘Scientists ought to think great things, but tell them in a language everybody understands. And yet they are doing it the other way round. Why do so many scientists hide behind their technical jargon? Why? Tell me. What do they have to hide?’

72 From the neighboring room came the unmistakable sound of a baby crying. ‘That’s Sonetchka, my baby sister, actually my step-sister. She is a very sweet girl, but sometimes she wakes up at the strangest hours. Let me get over to my parent’s room and see how I can help.’ Ten minutes later, Zhenya returned with Sonetchka in a baby seat. She had eaten and was wide awake. She was playing with the toys around her, stretching her arms and hands down to them. She was touching them, grasping them, and trying to stick them in her mouth. Zhenya said: ‘She’s grasping her world.’ ‘She is measuring the world, Zhenya.’ ‘And she’s learning to see. Did you know that babies need to learn that? Their eyes are functioning, but they need to learn what they’re seeing. If they

  Mission Invisible 

79

don’t do that, they will never be able to see. Their eyes will see, but not recognize; with seeing eyes they will be blind. Sonetchka is doing well. You see how intensely she looks at the toys she is grasping? She is coordinating touch and sight.’ ‘Interesting that you should say that, Zhenya. So this is how human beings learn to judge distances. As babies we connect the world of sight to the world of touch.’ ‘Yes, in this way we train our intuition on the “natural geometry”, the geometry of flat space.’ ‘And if later something, some material, bends the paths of light, we perceive the result as an optical illusion. An optical illusion occurs when the world of sight disagrees with the world of touch.’

73 Zhenya and Iain were discussing light and geo-metria, the art of measuring the world, late into the night, with Euler the cat and Sonetchka the baby nearby. Zhenya continued: ‘Light follows Fermat’s principle and may get bent in a similar way to the shortest flight paths on the map of the world.’ ‘Zhenya, here is a thought: aren’t Fermat’s principle and the principles of cartography, of maps and scales, one and the same thing? I mean, light optimizes its path according to travel time, and so does an airplane. The autopilot uses an electronic map to get the shortest path, a map with a scale that varies and light navigates using the refractive index, which may vary as well. The higher the refractive index, the longer it takes for light to propagate, and hence the longer the measure of distance, the scale of the map for light. What I am trying to say is this: light in a material experiences space as if the refractive index were the measure of distance. Or to put it in a nutshell: an optical material acts on light like a curved space.’ ‘What an interesting idea, Iain! Instead of understanding Fermat’s principle as a principle of the shortest time, you suggest seeing it as a principle of the shortest length, but with the refractive index as the measure of distance. You say that a transparent optical material—a piece of glass, water, or air—acts like a geometry, like a curved space. Fantastic! With this you have done your first piece of real research; you have seen what everybody else has seen and thought what nobody else has thought before. Maybe some people have already thought like you. I need to check this in the scientific literature, but it is very important that you have found what you have found for yourself.’

80 

U. Leonhardt

‘Many people and many discussions have helped me, including you, Zhenya.’ ‘You have discovered a new concept. Concepts are the most important things in science, and the hardest to discover. On the face of it, nothing has changed—we are still talking about light in transparent optical materials. Snell’s law of refraction, or Ibn Sahl’s law, for that matter, would be perfectly good to describe everything we need. Nothing appears to have changed, but everything has changed. You have found a fresh way of looking at the same thing: light in optical materials. You have found a new concept. Now you can go away and invent something new and spectacular!’ Zhenya was hopping with joy over Iain’s discovery. Sonetchka had fallen asleep in the meantime, oblivious to the entire discussion. When Zhenya went quiet and looked at her, one could even hear a faint snoring from her direction. Or was it Euler purring? Zhenya checked his watch: ‘Oh my God, is that the time? There is a problem with the bridges. You know the bridges over the Neva are drawn up during the night, from one to five, I believe. This is done to let larger ships pass. You are very welcome to stay. You can have my room. I will find a place to sleep in my grandmother’s room.’ ‘Don’t worry, Zhenya, I will head back to the hotel now. It was a wonderful evening. Thank you for the opera, your generosity in sharing your home, and your thoughts. But let’s check the timetables of the bridges first, before we panic. I am not going to get stranded on this island.’

74 Iain did not want to take a car to get back to Alexander House. He wanted to walk. He still had time until the bridges went up—Zhenya had been overly anxious. There was time to walk. The night was bitterly cold. Freezing fog was drifting from the rivers and canals of St. Petersburg, but he needed to walk. He had some thinking to do, and for this it was best to be in motion. Others were more sedentary during the task of thinking. Sherlock Holmes used to solve problems curled up in his armchair smoking his pipe, but Iain needed movement. A car, train, or bus would do, but for serious thinking he needed a walk. Sherlock had his famous three-pipe problems, Iain had a problem for a three-mile walk.

  Mission Invisible 

81

75 During the first mile of his walk, Iain was contemplating the discussion with Zhenya on light and maps. What a tale of two worlds, he thought, the world of sight and the world of touch, the optical and the physical world, the world of illusions and the world of reality. The two were not the same, because they perceived space in different ways. In optics, the refractive index tells us how long a region of space appears to light. In the physical world, distances are ordinary distances, measured with Pythagoras’ theorem. In the real world, the shortest path is a straight line; in optics, the shortest path—the one light takes—is bent when the refractive index varies. When the world of sight visibly disagrees with the physical world, I see an optical illusion, Iain thought, like a mirage in the desert. Zhenya said that curvature cannot be removed, no matter how the map of the world is drawn and redrawn. So if the optical world is curved I should always see this somehow. The mirage was an obvious illusion. Other illusions might be much more subtle, but for a curved optical world I will always be able to see that the illusion is just an illusion, not reality. How he should see this Iain did not know. But “if you exclude the impossible, whatever remains, however improbable, must be the truth,” according to Sherlock Holmes. A curved optical world will always betray its secret, but what about a flat space? I can draw and redraw a flat space the way I wish. I can transform it like the subway map, stretch it here, and squeeze it there. I can do this in the two dimensions of a city map. I can certainly do this in three dimensions as well. Such a stretching-squeezing transformation may make flat space look curved, but would it really “look” curved? Iain imagined how light rays would travel in the transformed world. In his mind, he pictured the rays before and after transformation. Before, they were straight lines, after the transformation, they were transformed, too: they were curved. Light rays had to follow curved paths—as in any other transparent material when the refractive index varies. The paths of light were curved, but could one actually see them? Norah had said that one couldn’t see how light traveled, one could only see the light that reached one’s eyes. So if the transformation of space happened only inside the optical material, inside some optical device some distance away, the world around would look just like any ordinary flat space. Such an optical transformation of space, Iain thought, would make the perfect optical illusion—an illusion that would always remain an illusion. “Elementary, my dear Watson!”

82 

U. Leonhardt

A figure appeared in the fog drifting off the river. It was the shape of a Russian man with fur hat and half-open coat, his walk not entirely steady, his gaze not entirely friendly. Iain preferred to move to the opposite pavement. While doing so, he thought that this maneuver was an optimization problem, too. Intuitively he was weighing the chances of colliding with a strange Russian man against the chances of colliding with a stray Russian car. He was on the right path, he felt.

76 A tale of two worlds, that was the story of light in transparent materials, Iain thought, and a tale of two spaces if materials did not curve space, but only transformed it. One was the space of physical reality: physical space. In physical space, a material bent light, creating the optical illusion of a transformed space. Every point in physical reality would appear to have moved to a new position in the illusion. This was what the transformation did, nothing more: it did not curve space, it merely redrew. Iain called the newly drawn space “virtual space.” A tale of two spaces, that was the story the transformation told. Physical space described reality, virtual space the illusion describing the world as light perceived it. Physical space contained an optical material, virtual space was empty. In physical space, light rays were bent, in virtual space they were straight. All transparent optical materials distort space. The refractive index alters the sense of distance, the measure of length. What is special about a material that merely transforms space? The transformation occurs inside the material, so the background scenery is not affected. The material appears to be completely invisible. This is already special—a piece of glass, a drop of water, or a sparkling diamond are all transparent, but not invisible. The transformative material does not appear to change the scenery around it, but the space inside. What would this look like? Iain thought of the aquariums he had seen at the Singaporean zoo. He imagined an aquarium filled with the transformation material. It would transform the images of the fish inside the tanks. The fish would not appear at the places they actually were, just like in an ordinary aquarium. The transformation medium might also distort their images. They might appear larger or smaller, depending upon how much space they occupied in virtual space. Their sizes and shapes in the virtual space were their sizes and shapes in the image, but not in physical reality. Again, an ordinary aquarium did just the same.

  Mission Invisible 

83

So what is special about the transformation material? Iain remembered how the fish in the zoo looked different if he observed them from different directions. He just needed to move a little to see them change. He just needed to change his point of view to see that they could not possibly be real, to see that he was looking at an illusion. The aquarium filled with transformation material, however, would always look the same, regardless of the point of view. Nobody would be able to tell whether the fish were real or as strange as they seemed to be. The illusion would be perfect. Iain’s thoughts went back to Lady Lucy’s article on the science of deception that Luna was so interested in, and to the Man from the Ministry. The article was far too technical. Iain could not understand it, but he had sensed what it was about: invisibility. Was the transformation of space a method for making things invisible? Could Iain make a fish disappear in the transformation tank? He could make a fish smaller and smaller until it became infinitely small, the size of a single point. A single point was invisibly small, so the fish would indeed become invisible. In virtual space, the invisible fish appears as a single point; in physical space it is the normal size of a fish, of course. What can be done to fish can be done to anything. Take a point in virtual space and expand it to some volume in physical space. Anything inside the volume becomes invisible, because it is hidden inside a single point in virtual space. My dear Watson, we are in business!

77 Iain was walking along the Kryukov Canal on his last mile to Alexander House. He walked in silence through the winter fog; his steps were the only sound in the night. His mind was alert and synchronized with the precision of his steps. Iain had discovered a recipe for invisibility. Take a shell of transparent material that optically transforms its interior to a single point, and anything inside the shell becomes invisible. Iain had thought about invisibility before, after the demonstration in the converted wine cellar of the Winter Palace. At the time he had imagined invisibility as a situation when light flows around a stone. Now he was thinking of an optical transformation. Did the pictures match? And if so, how did they match? Iain imagined a light ray in virtual space passing by the invisible point on a straight line. In physical space, the point had expanded into the interior of the

84 

U. Leonhardt

shell, containing the object to be hidden. In physical space, the straight ray of virtual space had to give way to the expanded point. It must bend around the interior of the shell. It did not matter which direction the ray was coming from. If it entered the shell, then it would bend around and leave in the direction it came from. Bending light from all directions and making it leave as if nothing had happened, this, Iain thought, was Lady Lucy’s secret. The transformation method had solved the bending problem. Walking through St. Petersburg in wintery fog, Iain had solved the problem of invisibility, at least in principle. The next question was of course, how to make it work in practice? How difficult would it be? What materials would one need? Suddenly Iain remembered the title of the conference they were traveling to next: Optical Metamaterials. Meta-material, what a grand name, a combination of the Greek “meta”, meaning beyond, with the Latin “material”. Was this the stuff of dreams? Of dreams and nightmares, the stuff it takes to become unseen? Lady Lucy was traveling to the conference with Iain as her assistant. The conference would be at Airlie Center near Washington, D.C., in a secluded site in the country for high-level conferences, meetings, and weddings, and also for discreet contacts with the United States government.

78 Although airplanes try to fly along the shortest routes on the globe, connecting flights often make zigzags according to their own logic. To journey from St. Petersburg to Washington, D.C., required at least one stop. The most convenient route for our travelers went first southwest instead of straight northwest. It went via Vienna with Austrian Airlines. Iain had only a few hours’ sleep before their morning flight, or rather, he was restless. Iain could always sleep, no matter where he was, but not this time. He was lying on his bed in Alexander House, the light half-dimmed, his eyes half-closed, thinking. How could he be absolutely sure that he had discovered exactly the method for invisibility Lady Lucy had developed? Obviously he could not ask her directly. One simply did not ask her, and besides, he would be fired immediately. What was she doing on this trip? She had been to a conference in Saudi Arabia and had clandestine meetings with the King and his office on the science of deception. She went to Iran—but this was on the invitation of a Persian professor she was not particularly impressed with. The trip to Iran was probably arranged independently from her itinerary. Then she went to Russia,

  Mission Invisible 

85

of all places, where she met a Man from the Ministry and was shown the latest camouflage technology. Why? There should be no misunderstandings about Russia’s capabilities, the Man from the Ministry had said. And then he made a thinly veiled attempt to interest her in Russia’s very capabilities. He could not possibly have been more explicit, not in Iain’s presence, and probably such people never were explicit initially. Why did she speak with him at all? Iain would avoid such people like the plague. Now she was going to a conference in the vicinity of the U.S. government. What was she really trying to do? They took the early morning flight to Vienna. Iain fell asleep as soon as he buckled his seat belt. In Vienna, at the departure gate to the Washington flight, they met an acquaintance, Hieronymus Foo.

79 Foo had been in Vienna to deal with his application for Austrian citizenship. The small but proud Federal Republic of Austria had inherited from the world-spanning Austrian Empire a bureaucracy of world-class proportions; an empire of paper. Herr Zed of MA35 had been in charge of Foo’s case. The aforesaid had suddenly discovered that an important paper was missing in Foo’s file: his certificate and test of proficiency in the German language. Certificates and tests were vital parts of the procedure, and Foo had already passed his citizenship test. In this test, he needed to score better than fifty percent in eighteen multiple-choice questions: six on the present democratic institutions of Austria, six on the past history of Austria, and six on the history of the particular federal state he was applying to. In Foo’s case, the state was the City of Vienna. Each candidate for citizenship was given a brochure and two months to learn the content by heart. Judging by its title, the book was on the subject of the test, but in reality the test was on the subject of the book. Arguments over the book’s accuracy were strictly discouraged. This brochure was not merely about Austria; it was the institutions and the history of the country, period. Foo was amused to browse through the history of Vienna from the perspective of the brochure. It betrayed a certain bias regarding the plight of the worker’s movement. The date and place of the founding of the Social Democratic Worker’s Party and the inauguration date of Karl-Marx-Hof, the worker’s vast apartment block in Vienna’s bourgeois 19th District, was an important part of the curriculum. Foo had already noticed that the writers of the Communist Manifesto were living on as names on some of Vienna’s streets. The name of their more National-Socialist competitor had vanished in

86 

U. Leonhardt

public, although some politicians, and their clientele, seemed to harbor his thoughts in private. One particular idea amused Foo more than anything else: Vienna was the place where the revolutions and dictatorships of the twentieth century had had their beginning. The storm of the Winter Palace with the subsequent civil war and Stalin’s terror could all be traced back to Vienna’s famed coffee houses. In the most famous of all, Café Central, over coffee and cakes, Lenin and Trotsky had been plotting the Russian Revolution, and Stalin had written his book on the National Question. Meanwhile, a few streets away, their more nationalistic future competitor had been living in a shelter for the homeless, while trying to sell his paintings. Had he not been so poor, living in such squalor, he might have become the leader of his National-Socialist Party while having coffee in the Café Central. Foo thought, with ample satisfaction, that the high ideals of a revolution are necessarily theoretical. They are best cultivated over coffee and cakes. Plotting and scheming was mental work that required fuel in the form of Viennese coffee. The more menial work of their bloody execution was always done elsewhere. Foo always loved to contemplate such things when he himself was sitting in Café Central. While the tourists from his country were taking pictures of the exquisite cakes under the Victorian columns and cupolas of the coffee house, his mind was pleasantly engaged with its history. This morning, however, he had no time for amusements; he had an appointment with Herr Zed.

80 Herr Zed looked more tired than usual. Even the black printed palm trees on his yellow tee shirt seemed to have lost their luster. He had just returned from a few days taking the waters of Bad Tatzmannsdorf. Viennese civil servants suffered from the highest level of stress in Vienna (while Viennese scientists enjoyed the lowest). Fortunately, civil servants had their own health insurance. At all times, a considerable fraction of the civil service could be found recovering at the health resort Bad Tatzmannsdorf, on full pay of course. Herr Zed had suffered a burnout after sorting out Foo’s titles, and had been promptly transferred to the resort. Now he had returned to duty. We meet again, thought Foo, and said to Herr Zed in German, the language of Austria: ‘Good morning, I was informed I must submit a certificate regarding my proficiency in the German language.’

  Mission Invisible 

87

‘That’s correct, Herr Doctor Footch, ya need ta prove ya speaking German.’ Foo’s grasp of German was quite good, but he always had difficulties with Herr Zed’s Vienna-Ottakring accent. ‘Here is my certificate from the Goethe Institute in Norway where I learned German.’ ‘The Goethe Institute? But that’s from Germany!’ ‘The Goethe Institute is Germany’s institution for German language all over the world.’ ‘But not in Austria. Don’t ya have an Austrian diploma?’ ‘I did an exchange year at the University of Vienna during my doctoral studies. Here is my certificate. Doesn’t this automatically imply that I speak German?’ ‘Hmmm, I need ta check.’ Herr Zed phoned Frau Magistra Esstee, his line manager and team head. She had had a partly legal education and was able to read the text of the law. After his phone conversation, Herr Zed said: ‘Sorry, Professor, higher education doesn’t count. School counts, trade school counts, varsity doesn’t. I guess, Parliament `ad forgotten it in the law, `appens all the time.’ ‘But I wrote my Ph.D. thesis in English and German. Just read it!’ ‘I am sorry, I will need an Austrian certificate.’ ‘Hasn’t it struck you yet that our entire conversation is being conducted in German?’ ‘But ya need ta prove it!’

81 Foo spent the next hour on his mobile phone trying to get hold of the Austrian equivalent of the Goethe Institute, the ÖSD. Finally, he was put through to the deputy head of the institute and received an appointment. She exchanged a few sentences with him and certified Foo’s above-average linguistic ability in German on a beautiful sheet of official paper. With signature, stamp, and Austrian eagle, Herr Zed was happy to accept the new document. With the Austrian bureaucracy out of the way, Foo made it to the airport on time for the flight to Washington, D.C. Using his charm, energy, and perhaps one of his brown envelopes, he persuaded the check-in staff to be seated next to Lady Lucy.

88 

U. Leonhardt

82 Austrian Airlines does not have a First Class, but takes pride in offering first-­ class service in long-haul Business. Lady Lucy and Hieronymus Foo were warmly greeted and seated in the first row of the Business cabin; Iain could not possibly be permitted to the same rank, but needed to be close by, in case his assistance was required. He was placed directly behind the gentleman, diagonally behind the lady. Iain had a talent for sleeping in planes, unless there was something interesting to see or think about. He had a similar talent for waking up at the precise moment when meals were served. Unfortunately for his sleep, dinner took up the most prominent part of the journey. A chef in a white apron and with Michelin class hat announced a feast of Austrian cuisine to the select few Business passengers. He personally served each passenger with a tiny cup of Steirean crayfish bisque as amuse gueule. Aperitifs and delicacies from the trolley made their rounds, followed by the serious business of the soup. A small tower of ornamental vegetables with roots from all the Austrian federal states was placed on each dish and fluidified with a delicate foamy liquid of cream and white asparagus. The recommended main dish was tafelspitz, the epitome of cooked beef, but vegetarians and Americans were also catered for—with a choice of cheese spätzle or bio burger of Austrian wagyu beef. Iain was not impartial to good food, although he felt a little uneasy in an airplane where the cook appeared to be more important than the pilot.

83 During the long dinner over the Atlantic, Iain could hardly miss overhearing Foo’s enthusiastic description of his institute. He showed Lady Lucy a presentation on the latest e-pad with pictures and statistics, and also the photographs of the eminent scientists he had already enrolled for his newly-founded institute. ‘Futuropolis is going to be number one, I tell you. Look, this is how it was before; this is the farm and the school house on the island in the swamp. When I first went there to inspect, we were given heavy guns to use against the crocodiles, just in case. I am not kidding. Now, fasten your seat belts, Lady Lucy, here is an aerial picture of the place today: Thousand Futures Mega City. You see the artificial lake in the center, the canals and streets, the research

  Mission Invisible 

89

buildings, teaching labs, lecture theaters, dormitories, and the villas for our distinguished faculty. No more crocodiles, just professors!’ A stewardess approached them: ‘Please enjoy your soup.’ They observed the transformation of the decorative tower into a delicious liquid and, indeed, they did enjoy the soup, Lady Lucy with a silver spoon, and Foo with a slurp. After they had both satisfied themselves in their own way, Lady Lucy asked Foo: ‘How is the funding situation? I heard some dreadful news from Britain where the science minister, who used to be a friend of mine, was summoned to the treasury for some serious cuts.’ ‘That will not happen to Futuropolis University. We have excellent connections to the leadership. They want us to succeed and we want to make them happy. Win-win, I say.’ ‘You explained to me earlier that you want to establish a truly international institution.’ ‘Not just international, Lady Lucy. We already have made it to the top of the national league, now we are going to leap to the international top. We will be international number one. Did I say inter-national? We will be inter-­ planetary! When some day aliens land, this is where they will go: Thousand Futures Mega City!’ The stewardess returned, cleared the dishes and asked: ‘Would the lady and the gentleman be ready for the main course? Here is the tafelspitz for your ladyship and the burger for the gentleman.’ After silently attending to their meals, Lady Lucy raised a delicate subject: ‘You said earlier you wish to attract foreign scientists. What are you attracting them with?’ ‘We offer five-year guaranteed support. Whatever you ask for, you get.’ ‘Carte blanche.’ ‘Yes, smart brunch, though it looks like dinner. Getting back to the subject, we also offer very competitive pay packages. It will be no problem to triple your salary. What am I saying, triple? Quadruple!’ ‘I am sure that with such attractive terms you have already attracted some of the best and brightest, some of my very own league.’ ‘We are negotiating with a Nobel laureate—here is his picture—about joining us for three months a year.’ ‘Three months a year, all expenses paid, quadruple salary. You do make an interesting proposal, my dear Foo. I think I shall adjust my travel plans and pay a visit.’

90 

U. Leonhardt

At this point the kaiserschmarrn arrived—an exuberant dessert of sweet omelette with raisins and plum compote, the royal-and-imperial conclusion of the feast. Iain received the instruction to book convenient flights from Washington, D.C. to Thousand Futures Mega City.

84 In the foothills of the Shenandoah Mountains in Virginia, on over a thousand acres of manicured land, lies the Airlie Center. It is a secluded place away from the hustle and bustle of Washington, D.C., but conveniently close by for conferences, meetings, and discrete discussions with the U.S. government. This was where our travelers went, after their arrival at Washington Dulles International Airport. A black chauffeured car from Airlie drove them there. They checked in and walked to their quarters in different houses on the grounds. These were white houses of different sizes and functions, but all similar in style to the White House not far away. While Iain took a walk around the lake—he needed some air after the long journey—he saw a familiar figure walking toward him: Luna. She was wearing Western clothes, but there was no doubt, it was her. ‘Hello, Luna, I am surprised to see you here.’ ‘Hello, Iain, so nice to see you again! How are you? Are you here with your mistress, uh, your boss I mean.’ ‘Yes I am still in Lady Lucy’s entourage.’ ‘There are lots of interesting people here. I have even seen an Iranian professor. I did not know they were actually allowed to travel to the United States.’ ‘Professor Parsa?’ ‘Yes, that’s him. He brought some of his entourage as well, all girls. You went to Iran, didn’t you? How were the girls?’ ‘How did you know we went to Iran?’ ‘Oh, I know things. I also know you went to Russia. How were the girls there?’ ‘I did not meet any.’ ‘Maybe this was for the better! Russian girls are beautiful and deadly. You might have become entangled. But how was it? It must be absolutely fascinating to travel with Lady Lucy. Did you meet some interesting people? Not girls, but still interesting?’ ‘It was interesting.’ ‘You are a bit monosyllabic today. But of course, you must be tired after the long journey. So have a good rest. See you tomorrow. Ciao, Iain.’

  Mission Invisible 

91

Off she went, leaving a trail of her perfume behind. Iain was wondering why he had resisted having a conversation with Luna. He had closed up like an oyster. She was not interested in him, that was clear, so what was she interested in? Was he a means to get to Lady Lucy’s papers? She could not possibly know that Iain was beginning to understand what it was all about. He would not let her know in any way. Iain was not a good actor. Anybody could read his feelings from his face, so he needed to avoid her and to close up. Instinctively, this is what he had done. After an early dinner, he took another stroll in the grounds, doing a circuit around the lake. There he saw Luna again. To be precise, he did not really see her, nor did she see him—she was standing behind a tree; he heard her speaking with a man in Russian.

85 The opening lecture of the conference the next morning was naturally the privilege of Lady Lucy. To the applause of the entire audience, she went to the podium and started her presentation. Iain was curious to see how he would perceive the conference this time. In Saudi Arabia, he had known nothing about the subject and could only judge the speakers and listeners according to their external appearances, their manners and mannerisms, and their way of speaking. Now he felt he had some insight into the science and the urgency of the matter. Iain thought he had guessed Lady Lucy’s idea. Now he wanted to hear her speak. Yet what a disappointment it was. Yes, everyone was listening to her every word, but Iain did not understand why. She was talking in her measured voice about a scientific controversy she herself had started on the refraction of light, and how theoretical arguments, computer simulations, and finally experiments had proven her right. The audience listened to her every word. But Iain knew, or believed he knew, that she had something much better to tell, something extraordinary, something that had arrived after a thousand years of thinking and experimenting in optics, from the days of Ibn Sahl and Ibn al-­ Haytham, and the mysteries of Pierre de Fermat, to the modern stuff of dreams the conference was all about. Her ideas descended from a noble line of thousand years. She was—what was the phrase?—standing on the shoulders of giants, and what was she doing? Trying to win a petty academic fight and being smug. Was this what science was all about? Was this Norah’s passion? And Zhenya’s enthusiasm? What would Mullah Sadra say?

92 

U. Leonhardt

And even what she said, she could have said better—more simply and more clearly. If Iain had learned something on their journey around the world on science business it was this: science is simple at heart. It distills some ideas from the phenomena of this colorful, confusing world, ideas that are not complicated in themselves, but then takes them seriously with all the consequences and complexities that may arise. Science should be made as simple as possible. Iain felt he could condense Lady Lucy’s lecture into a simple drawing. He would not know all the learned technical terms of course, but he could find a picture that said it all. If Mullah Sadra appeared to him in another dream, perhaps he would bring the picture. There surely ought to be one.

86 The next lecture turned directly to the topic of the conference, optical metamaterials. The lecture was given by an energetic Russian exile—Iain did not quite catch his name—who appeared young in middle age. He delivered it well in a business-like manner with polished, slick graphics. Iain was grateful for the introduction to metamaterials in the first part of the lecture, until the energetic speaker overwhelmed him with example after example of their potential applications. The Gold Rush of 1848 must have been nothing in comparison to the excitement that gripped the audience—the scientists, the journal editors, and also the representatives of the funding agencies. Superlenses, hyperlenses, super here, hyper there, from solar cells to cancer treatment, nothing short of a cure for the common cold had suddenly become possible. Metamaterials were the stuff that dreams were made of. At the break Iain saw Norah and rushed over to her. ‘Salaam Norah, nice to see you, how are you?’ ‘Salaam, Iain, thanks, I am very well, and you?’ ‘Super. What an exciting lecture! May I ask you some questions, just to see if I understood it properly?’ ‘Oh, I know your type of questions! You question like a mullah, but go ahead, I am listening.’ ‘First of all, do I understand correctly that metamaterials are ordinary materials? They are not the product of some hyper-advanced chemistry or alien alchemy. They are made of normal materials. Their secret power lies in the way these materials are arranged, not in what they are composed of.’ ‘That’s absolutely right. Metamaterials are made of normal materials— mostly metals and transparent substances similar to glass. Actually, they have been around for quite some time. People have been making metamaterials

  Mission Invisible 

93

without knowing it. For example, stained glass windows are metamaterials. They are made of glass mixed with tiny droplets of metal. The metal gives the glass its color.’ ‘Tell me, why are they metamaterials? What is meta about them?’ ‘Imagine you are making stained glass. What do you actually do there? Essentially, you mix two materials, glass and metal, but what you get is neither transparent like pure glass nor metallic, but it is colorful. You get something completely different, something beyond the original mix of materials, a metamaterial.’ ‘Where do the colors come from?’ ‘It is mainly the sizes and shapes of the metal droplets that make the color of stained glass. If you change their sizes or shapes, you change the color.’ ‘This brings me to my next question. I believe I understood from the lecture that the metal structures in metamaterials act like atoms.’ ‘Yes, for example, in stained glass, each metal droplet looks like an atom to light.’ ‘But aren’t atoms supposed to be absolutely tiny? The metal droplets are small, but not as small as atoms. How can light mistake a lump of metal for an atom?’ ‘Remember, in Shiraz, we discussed, among many other things, the fact that light is a wave. If the metal structures are much smaller than the wavelength, light would not be able to resolve them. It would just take them for atoms.’ ‘So I just need to make structures smaller than the wavelength of light and they’ll pass as atoms. But you said that their size matters. The sizes and shapes of the metal droplets are what make the colors of stained-glass windows. So how can they all just be atom-sized as far as the light is concerned?’ ‘The atoms of different chemical elements may also have different colors. If they resonate with light, they color it, because the different colors correspond to different oscillations of light.’ ‘I understand, and now I also understand why the metal droplets stain glass: they resonate with the light.’ ‘Exactly, their resonances depend on their sizes and shapes, much like the tones of musical instruments. A violin sounds different than a cello because it is smaller. By controlling the sizes and shapes of the metal structures in metamaterials, you control their resonances. You control the way they interact with light.’ ‘Now I see why metamaterials are so versatile. Instead of being stuck with the atoms and molecules given to us by Nature plus chemistry, we can make

94 

U. Leonhardt

our own artificial atoms. They are much larger than atoms, but light would not be able to tell the difference. They are designer atoms. Brilliant!’ ‘Now you understand why everyone is so excited about metamaterials,’ said Norah. ‘But if, as you told me, medieval stained-glass windows are already made of metamaterials, what is new? Why the excitement now and not much earlier?’ ‘I presume this is thanks to new fabrication technologies, new methods for shaping small structures. But I am not an expert in technology, I am very much a theoretical physicist. Ask the experts at the conference. They will be able to answer your question.’ Yet an extraordinary and strange event interrupted and perturbed Iain. It happened in one of the shorter lectures that took place during the afternoon, and in fact, in Professor Parsa’s lecture. Near the end of his presentation, Lady Lucy began to laugh.

87 Professor Parsa’s lecture was different from all the others. He was different. Not that he looked so different from the other lecturers. Maybe his suit was made of cheaper fabric and less elegant couture, but when he walked onto the stage with his slow and measured steps, bowed to the audience, and began to speak, he looked like a figure from a different era. One could easily imagine a turban on his head or the barrister’s wig of Pierre de Fermat, such was his gravitas. He bowed to the audience and began his lecture—on geometry and light—by bowing to the noble line of scientists to whom he was indebted. He called them by name: Ibn Sahl, Ibn al-Haytham, Fermat, Newton, Euler, Maxwell, and Einstein, and briefly mentioned their various contributions to the subject of his lecture. Similar to the noble Don de la Mancha, he was telling their stories like the stories of the great knight-errants, until he then, with humility and dignity, turned to his own, humble tale. The audience looked, listened, and did not understand a word. The style of his slides did not help either, as he tried to convey the spirit of a blackboard lecture with handwritten formulas and simple drawings. In the audience some began to chuckle. Iain glanced at Lady Lucy. She showed no reaction—she was following the lecture with steely concentration. And Iain could also follow—the lecture was taken from the very air he had been breathing throughout the entire journey. True, he did not understand Professor Parsa’s mathematics, but he could follow his ideas. Optical materials appear to light like changes in the geometry of space. For light, an optical

  Mission Invisible 

95

material acts like a curved space or, under special conditions, like a transformation of space. Iain’s idea was expressed here in scientific form. In fact, its form was too scientific, clad in formal amour like the chivalric heroes from a time long gone. Nobody paid much attention, nobody except Iain and Lady Lucy. Near the end, Professor Parsa said something about invisibility that Iain could no longer follow. Perfect invisibility was impossible, he said, the theory proved that. The audience was chuckling even more—invisibility, this was from the fairy tales. Professor Parsa expressed his gratitude to the Creator that no disguise would prevail, that truth really did exist, and that it would always come to light in the end. Hiding the truth was impossible, and so was invisibility. This was the moment that Lady Lucy laughed, loud and clear. The audience happily joined in. And so hearty laughter ended Professor Parsa’s lecture. ‘My dear Parsa, you have entertained us, and you have entertained us long enough. May we have the next speaker, please?’ Iain felt sorry and perturbed by Lady Lucy’s reaction. How could she do this to Professor Parsa? But from that moment on, he also knew with absolute certainty that he was right: he had guessed Lady Lucy’s secret idea for invisibility. One needs to transform space with optical materials, just as Professor Parsa had tried to explain. For why else would she have ridiculed poor Parsa?

88 In the next break, Iain went to Professor Parsa to ask him questions about Fermat, partly because he felt sorry for him and partly because he wanted to know more. Of course, what he most urgently wanted to know was the professor’s thoughts on invisibility. But he could not ask him directly, because he didn’t want to hurt his feelings further. So he kept to the subject of Pierre de Fermat. There were still plenty of points Iain was puzzled about. Iain approached Professor Parsa in formal Persian, explained his curiosity for science but lack of scientific training, and asked him whether he could tell him more about Fermat. ‘Ah, Pierre de Fermat, one of the most enigmatic figures in science. How was it possible that this dreary judge from a provincial court of appeals in seventeenth century France could make some of the most dazzling discoveries in mathematics and physics? Nobody knows. ‘Fermat was an amateur scientist. In his day, science was a part-time vocation, not a profession. A few learned men would exchange letters on the latest

96 

U. Leonhardt

scientific discoveries and news. Letters about science were written, forwarded, and discussed. Fermat loved to challenge the minds of his learned colleagues, sending them mathematical theorems without proof and asking them to prove them. The most famous challenge of all was Fermat’s Last Theorem. He did not post the theorem in a letter, but wrote it on the margin of a ­mathematics text, together with a note saying the margin was too small for the proof. It was too small by quite a margin! It took 358 years and hundreds of pages of sophisticated mathematics to prove it. How Fermat managed to do it no one knows. ‘The theorem you are asking about, Fermat’s principle, appeared in this world in two letters Fermat wrote, one in 1657, the other in 1662. The addressee was his friend Cureau, the personal physician to the king of France and an amateur scientist. But the second letter also addressed the scientists of his day and quickly made its rounds in learned circles. In the first letter, Fermat outlined his idea, and in the second he proved it. The story was this: the supporters of his intellectual rival, René Descartes, had challenged him to a duel with letters on the theory of optics. Fermat’s supporters urged him to respond to the challenge, which required the proof. And so, on New Year’s morning 1662, Fermat wrote his proof in a letter to Cureau. He showed that his principle proves the law of refraction. It proves that light takes the optimal path. ‘You are asking why I call the path optimal and not minimal. In some cases, light does not follow the shortest path, but it always takes the optimal one. Let me give you an example. You know that a lens focuses light in a bright spot. For this, light rays must come together and they must arrive at the same time. No longer is there only one path of the shortest time, but many of equal time. The travel time is no longer a minimum, but an optimum, if you forgive my pedantry. An optimum is something one cannot improve by making small changes. Light cannot improve its travel time by taking slightly different paths. ‘When light travels from A to B it follows the optimal path. You are asking how on Earth this is possible, and quite rightly so! How does light know it will arrive at B when it has begun its journey at A? How does it find the optimal path? These are two separate questions, and scientists have wrestled with them like Jacob with the angel. The first question is the easiest: how does light know it will arrive at B? Light is a wave and a wave goes everywhere. Some part of the light will always go from A to B, no matter how small. Even the darkest shadow is not completely dark. So how does light arrive at B? By going everywhere.

  Mission Invisible 

97

‘The second question is the difficult one. How does light optimize the path from A to B? Light is blind and cannot “see” the entire journey in front of it. It cannot plan ahead. It can only propagate one step at a time. Yet light is a wave. Waves may interfere with each other. When two waves meet their amplitudes add up. The same goes for arbitrarily many waves—if waves meet they interfere and the total amplitude is the sum of all the partial amplitudes. In this way waves may enhance each other—which is known as constructive interference, but they may also cancel one another in destructive interference. If two waves with opposite amplitudes meet, one positive and the other negative, they may cancel each other. Light plus light may give more light or darkness. ‘This interference of waves is the key to Fermat’s principle. How does light know the optimal path in advance? It doesn’t. It tries all paths at the same time, but the paths interfere with each other. The optimal path is the one that survives all the interference, while the other paths disappear by destructive interference. Let me explain… .’ At this moment the bell sounded the beginning of the final session of the day. The break was over. Iain hoped to find Professor Parsa in the evening. He had not noticed Luna, who had been eavesdropping Professor Parsa’s explanations with obvious amusement.

89 After the long day of lectures, the exiled Russians were heading for the library, which was code for the bar, to take out some books, a.k.a. drinks. The bar was the Whistling Swan Pub, on the hotel grounds, a short walk from the main house. Iain went there as well, to get some food. The Iranian students he met on the way were more interested in wine. All the participants seemed to congregate at the pub, except Lady Lucy and some of the official-looking men who were all having a meeting behind closed doors. Even Professor Parsa was at the pub, to Iain’s great surprise, until he realized why the devout Parsa had taken the seat nearest the door. On catching sight of him, the Iranians immediately backed away. Professor Parsa was protecting them from the temptations of wine. A pentagram at the threshold was less effective in repelling ghosts and spirits than Professor Parsa was against Iranian students in search of the spirits of the grape. The students regrouped outside, discussing schemes for breaching the blockade. One suggested luring Parsa away with a physics question, another to bribe one of the Russians to smuggle out wine in a brown-paper bag.

98 

U. Leonhardt

While these discussions were going on outside the pub, Iain was already inside looking for a seat. He sat down next to a man with Levantine looks and the tan of a professional sailor. His age was difficult to guess, but certainly above sixty. His eyes were young and brightened by the bottle of ouzo in front of him. He said to Iain, with a wide gesture to the people around him: ‘Have a seat, kid, you are not one of them. You’re Lucy’s boy, right? An innocent lad from the country, not one of the scientists, or so they call themselves. Look at them!’ The Russian exiles had become rather lively at the bar, their library, as they called it with affection. Professor Vladlen Cheburashkov was there as well, ordering a round of oysters for his ex-compatriots. Meanwhile the energetic morning speaker was taking care of the selection of “library books”—vodka and champagne. A true Russian party has three phases: merry frolicking, angry arguments, and finally tearful reconciliation. Phase one was already in full swing. ‘Have you heard of Bell Labs?’ the Levantine sea bear asked. Iain nodded. ‘I was there. Bell Labs used to be the research laboratory of the telephone company AT&T. We didn’t just make telephones, we invented the transistor. Now there are billions of transistors in each electronic gadget, not to mention each smartphone. We also made the only decent operating system, UNIX, which runs those transistors from behind the scenes. We invented the CCD you take pictures with. We created communication science and technology and much of the fabrication techniques of the silicon age. We also started radio astronomy and discovered the cosmic microwave background, the evidence for the creation of the Universe. Eight Nobel prizes have been attributed to Bell Labs.’ He had another ouzo while the Russians were accelerating phase one of their party. He went on: ‘Now look at them, standing on the shoulders of giants, drunk. They, and the people around you, promise you a revolution in technology every ten years. Luckily for them, when the ten years are over, you have forgotten what they promised. Metamaterials, that’s their latest craze.’ Meanwhile, the Iranian students had phoned one of the Russians at the bar. The barman had handed him, with a wink, a brown paper bag. He was staggering towards the door, past Professor Parsa. Yet at the last moment, he made the mistake of shushing the professor while triumphantly holding up the brown paper bag. Professor Parsa rose from his seat, ready to wage war on two fronts, against the Iranian students outside the pub and the Russian defector inside.

  Mission Invisible 

99

90 The Levantine sea bear raised his glass of ouzo to Professor Parsa and said: ‘There stands a man of principle, ready to break a lance for his ideals. And these people would do anything for money or fame or whatever they are after, but not for the ideals of science. Today it’s optical metamaterials. Don’t get me wrong, metamaterials are a good idea, but it would take decades to make them work. They come with countless problems: optical metamaterials are made of metal and glass. The first problem is that metals absorb light. You may color stained-glass windows with metals, but can you make metals transparent? Another problem is size and complexity in fabrication. The structures of optical metamaterials must be much smaller than the wavelength of light, much smaller than 500 nanometers. Let’s say they are 100  nm long. This means you need hundreds of thousands of them per centimeter. Cube that for a cubic centimeter of metamaterial: you would need a million billion. Nature gives you zillions of atoms for free, but for each ounce of metamaterial, you need to fabricate millions of billions of artificial atoms. This is not impossible in principle, but it will take a long time to figure out how to do it in practice. ‘The trouble is, these people here ride on the hype curve, Gartner’s Hype Cycle. They jump on the bandwagon when expectations in a new technology rise exponentially. Yet, after the peak of inflated expectations, there inevitably comes the trough of disillusionment, which is when they head for the exit. They never make it up the long slope of enlightenment to the plateau of practicality. They don’t have the sitzfleisch, the stamina for work without instant gratification, nor the guts to swim against the current. ‘And they don’t have the funding. We at Bell Labs used to have internal funding. We didn’t need to fight for grants. We could do fundamental research part of the time and work strictly for the telephone company in the other part, which was good, because it kept us grounded. We knew what real practical problem-solving is and we knew what fundamental research is. These people know neither. The single thing they are good at is getting grants. What you see around you are the best of the best in the survival of the fittest of the grant-getting game. But why should they play this game? They could do something useful instead.’ He helped himself to another ouzo and continued his tirade: ‘Do you know how they get grants? They’re all in this together. You can see the whole thing very clearly at this conference, clear as crystal. The speakers give their talks, the referees sit in the audience—the referees of their papers and of their grant proposals. But the speakers are also referees. They will

100 

U. Leonhardt

remember if someone has asked an awkward question, and they will remember who that someone was. Who would stop cutting the hype if his next grant is at stake? Who would say the emperor had no clothes on if everybody else pretended he had, just for the grant’s sake! Only a man from Bell Labs. He would always put his finger on the weak spot. He was not in it for the money. He was independent, and he knew what real engineering was, and what real science was. ‘And so they applaud each other. They flatter and fawn over their funding agents, journal editors, and scientific gurus; anyone higher up in the hierarchy. They are all in this together. All, except poor Parsa. Now, he had a rough time today.’ Meanwhile, the Iranian students had recruited a volunteer to lure Professor Parsa away from the bar with science questions. Yet the professor would not yield. He was standing in the doorway shouting explanations and writing formulas on sheets of paper which he pressed against the door frame, enlightening one student in physics and protecting the others from the vice of wine. ‘Parsa is not one of them. I salute him! There he stands, with one hand writing physics, and with the other defending his faith: el caballero de la triste figura, the last scientist.’

91 The Russians at the bar had moved on to phase two of their party: accusations and arguments to follow on from the merriment and good-natured banter. Now they hurled insults at each other, on papers not cited and papers rejected, grants not granted and ideas stolen. A gang of pirates would have argued less about a dead man’s chest. ‘Bell Labs,’ said the Levantine sea bear, ‘Do you know how it all ended? Bell Labs was slaughtered on the altar of commerce, sacrificed in the name of market liberalization and deregulation. Bell Labs was the research facility of AT&T, the telephone company, so people paid for it with their phone bills. AT&T was a monopoly at the time, so people paid more for their phone calls than necessary. When the telecommunication market got liberalized and opened up to other companies, people had the choice of paying less and Bell Labs was done for. The trouble is, people know what they have got, cheaper phone calls, but do they know what they have lost? Imagine if Bell Labs had never existed. Imagine a world without transistors, that is, without any modern electronics. Industry would be busy perfecting vacuum tubes instead—maybe you have

  Mission Invisible 

101

seen them in your great-granny’s radio. Perhaps it would feel like the age of steam and steel had continued, like Jules Verne’s version of the future. Would people miss the silicon age? How could they miss something they wouldn’t know? The trouble is, nobody can imagine what twenty or thirty years of first-rate fundamental research can do, because this is in the very nature of research. The goal of research is to make discoveries and invent things, but discoveries are surprises. If a discovery didn’t surprise you, it would not be a discovery. If you were able to see the products of a piece of research in your mind, seeing in vivid detail the way they work and how they could be made, you would have done the research already. Most people would never volunteer to pay for something if they don’t know what they’re going to get, and that means that they would never pay for fundamental research. That’s the trouble. So either you lie, promising the moon and counting on the public having a weak memory, or you make people volunteer by taxing their phone bills or something like it. This doesn’t apply only to science; it goes for all culture and civilization as well. The invention of the alphabet was not crowd-funded either. Most people would not have volunteered to pay for the advancement of civilization, but fortunately they were never asked.’ At this stage, the Russians were close to a fist fight, Professor Parsa was standing his ground, and the rest of the crowd were having a good time. Even the Iranian students had managed to get their hands on a couple of bottles of Californian Shiraz through the back door of the kitchen. The Levantine sea bear continued: ‘Do you know how Bell Labs ended? In 1996 it was given to Lucent, a splinter company of AT&T that lost 99% of its share value in the bursting of the internet bubble in the year 2000. But that was not how it ended. A bright young research star from Austria had arrived at Bell Labs. He could do the impossible. In 2001, he was publishing a revolutionary paper every eight days. He invented the molecular transistor, which was the beginning of a new era beyond the Silicon Age. The shareholders loved him, the board loved him, his boss (also from Austria) loved him, and everyone had high hopes of a Nobel Prize for him, his boss—and the company. ‘The trouble was, the guy was a fraud. He had forged the results of his research. Instead of jetting around the world with their latest discoveries, his boss should have gone to the lab and checked for himself. Vultures and fraudsters always move in at the end. ‘Look at all the epigones around you! Standing on the shoulders of giants. Did they ever deliver what they promised? Did they ever deliver more than

102 

U. Leonhardt

they promised? Have they ever done anything useful? Have they ever discovered something fundamental? Did they ever begin to understand the wonders that science has discovered, such as curved space and time or the mystery of the quantum vacuum? Have they ever looked into the abyss?’ At this point the Levantine seaman had clearly one or two ouzos too many. Iain helped him get home, holding him upright, while the old sea bear sang “What shall we do with the drunken sailor?” They left the pub before the Russians began singing and embracing each other with tears in their eyes, in the third and final, reconciliatory phase of their celebration. With this, the conference came to its conclusion. It had been a long day of lectures and discussions, followed by the celebration of science in various ways. The next day would see our travelers take their planes westward, to the Far East and beyond.

92 Iain had booked flights via Tokyo with All Nippon Airways. Foo had set off via Vienna the previous night. The Tokyo flight was scheduled for noon, so after a leisurely breakfast, Lady Lucy and Iain took the Airlie car to the airport. Iain had never been to Japan, nor traveled with a Japanese airline. After stepping onto the plane and taking his seat in the Business Class cabin he found himself in a subtly different world. Lady Lucy had disappeared to the First Class compartment, so Iain had time for reflections and observations. The plane looked like any other Western plane, except that is was more modern and much cleaner than most Western planes. Iain noticed how short the seats were, especially when turned into flat beds. Fortunately, he was not tall, but he also saw that all the seats were designed for maximum privacy. His fellow passengers were finely dressed businessmen, many with grey hair of immaculate coiffure, and also some young people with colorful clothes and equally colorful hair—artists perhaps on their return from New  York. Iain noticed how quiet everyone was and how considerate the flight attendants were. They bowed when they entered the cabin, they bowed when they left. Was it the bowing, the smiles, or the silence that transformed the plane? Or was it the people’s dress, Western dress, not Japanese silk, but chosen with an almost supernatural sense of style? Even the most outrageous outfits worn by the youngsters were still aesthetic. The food looked beautiful as well. Iain admired the various small boxes and dishes of Japanese stoneware, and the arrangements, colors, and textures of the various types of food they contained. Iain had tried sushi before, but noth-

  Mission Invisible 

103

ing had prepared him for the delicacies he was served there. After the sashimi he vowed never to eat sushi again outside Japan or a Japanese plane. The cold soba noodles he scrutinized with suspicion at first—who would eat noodles cold?—mixed them with their sauce on what looked like a miniature straw mat, and melted. This surely was the food of the gods, and so were the boiled mushrooms and vegetables, the fish fermented in leaves, and finally the orange cream of the sea urchin, which sent Iain to culinary heaven. Iain was smitten for life with what he felt was an alien civilization under a thin Western veneer, as alien as their food, and a civilization more civilized than the West’s. As a child he had read stories of the Enchanted Islands, a group of islands in seamen’s folklore. Sailors saw their mountains moving in the light over the Pacific Ocean, irresistibly drawing them to their shores. What was there to be found? Maybe what Iain saw: the transformation of the most mundane moment, as transient as it was, into a work of art. Iain would have given anything to stay longer on the Enchanted Islands, but two hours after their arrival at Tokyo Narita Airport, they had a plane to board for somewhere else, somewhere completely different. While they were waiting for their connection in the lounge, Lady Lucy made a most alarming discovery.

93 Lady Lucy de Phos was catching up on her correspondence in the lounge. Suddenly, she rose and held her tablet screen in front of Iain: ‘Do you have any idea what this is?’ ‘No ma’am, it looks like a scientific paper.’ ‘It’s a paper I have just received for review. Does it look familiar to you?’ ‘I am sorry, no. How could that be? I never read scientific literature.’ ‘Yes you do. When you translated my paper for the Saudi king you did. You read that one!’ ‘I put it into calligraphy without understanding a word. Could one call that reading?’ ‘That’s for me to decide. Now please answer my questions.’ ‘I will, of course.’ ‘I am not to be interrupted. How do you explain that the paper I told you to guard with your life—the paper for kings, my paper—how do you explain the fact that it has just popped up in the literature, and not under my name?’ ‘I cannot.’ ‘Answer my question. Where did you keep the paper?’

104 

U. Leonhardt

‘In the safe. I only took the appendix with me when I visited Dr. Luna.’ ‘That woman is the author. I know all about her. That talentless woman left her husband for her career. And now you are conniving with her. Why did you give the appendix to her?’ ‘I did not. She must have taken it from me and copied it in some unguarded moment. She had all the equipment in her apartment. It would have taken her less than a minute.’ ‘I am not sure whether I shall trust you. But it is true, that woman’s paper is only about the appendix, not the all-important main text of my paper. And I noticed something peculiar. Let me check again. Yes, the final part of my argument is missing. This would have been unlikely if you had given her the appendix. On the other hand, if that woman had copied it, she might have forgotten the last page. I suppose you are exonerated—for now.’ ‘Thank you, ma’am. I deliberately locked the paper in the safe. I did not trust her. I only took the appendix with me to finish the translation, in case I stayed overnight.’ ‘That tart!’ ‘Your Ladyship!’ ‘That talentless tart had the presumption to aspire to a career in science. I shall put an end to it!’

94 While Lady Lucy was furiously writing her rejection letter, Iain was simply astonished. This was all? This was all Luna was after? A paper under her name? A paper with Lady Lucy’s idea published under her name? This was all? Not handing Lady Lucy’s secret to the Russians—the glamorous seductress honey-­ trapping Lucy’s assistant for president and country? No! She needed a good paper under her name just to further her own career. Iain could imagine that some people would do anything for their career, particularly if they lacked talent. But if they lacked talent, what was their career good for? Why couldn’t they do something useful instead? Maybe she had already invested too much time and effort, during a decade or more of study and training? Less talented people need to work harder, and for talented ones work is a reward, not a burden. Maybe she was trapped in Saudi Arabia and could not afford to lose her job? In any case, Luna’s career was over. Lady Lucy was going to make sure of that, three hundred percent. Iain felt sorry for Luna, but also disappointed at how ordinary she had proved to be.

  Mission Invisible 

105

And something else bothered Iain. Luna was gone, but her shadow was not. Who was following them? Iain was certainly not paranoid and he normally trusted his instincts. Somebody was interested, very interested in Lady Lucy’s invention. Now Iain knew what the invention was, so he could see very clearly why somebody—some country—might want to have it. But if it was not Luna, who was it? Who was their shadow?

95 They had arrived in a strange land. Foo was opening the door of their plane, showing them to the red carpet on the gangway, past the military parade, and to the waiting black limousine. The broad motorway from the airport was completely void of cars and their motorcade went ahead quickly, slipping past vast grey blocks of buildings with large banners in a script Iain could not read. They were invited to meet the supreme leader and marshal, Foo said, proud of his connections. The government wanted to make them happy, because he had made the government very happy with their arrival. They were invited to a reception and as guests of honor to the people’s annual parade. The supreme leader and marshal was a rather young man with a puppy fat face. He stood surrounded by his most senior generals, who were taking down his every word in their pocket notepads. He reached out his short arms to the travellers and welcomed them to his country. Then they sat down to brief refreshments of the finest food flown over from Japan, grand wines from the best vineyards of France, and, bizarrely, an enormous selection of Swiss cheeses decorated with the coat of arms of the cantons they came from. Then it was time for the parade. The annual people’s parade was nationally known as the celebration of love by the people for their supreme leader and marshal. With the assistance of an attractive female interpreter, he expressed how glad he was that Lady Lucy could come and join him as a guest on this special occasion. Then he escorted Lady Lucy and Iain down the short staircase to the grandstand. The masses cheered as they caught sight of their leader and his foreign guests, applauding frantically for minutes. Then the parade began. It was not really a parade, but rather a show or a dance. Thousands and thousands of uniformed people were standing to attention in countless rows. They were holding sheets of colored cloth either up or down, according to some rhythm they had practised to the patriotic music that filled the air with euphoria. People were sitting on the grandstands around the enormous parade

106 

U. Leonhardt

ground, participating in the spectacle. Waves of color were running over the ground to the grandstands and flowing back down again, wave after wave. Iain could see how the waves were interfering with each other. Two waves were racing toward the grandstand of the people’s representatives. One wave came from the left, the other from the right. They were waves made of people holding the colored cloth up or down, and when they met, people were holding them more up or less, depending on the sum of the two waves each person experienced. Iain could see the interference pattern they made, bright stripes of enhanced color and dark stripes of military grey where the people were not displaying their colors. Now four waves were running across the parade ground. Iain could see how they interfered with each other. Then six waves. The more waves, the more distinct the pattern became: a shiny, colorful straight path from the government to the representatives of the people, symbolizing, presumably, the mystical unity between the people and their leader. Iain saw the parade as a vivid demonstration of Fermat’s principle. If all the waves are allowed to interfere, only the straight path remains. When some material changes the speed of the waves, the path that survives interference will be curved. As if the assembled masses could read his mind, they demonstrated it. On some signal the waves on the right became slower than the ones on the left; the shiny path bent to the right. The supreme leader and marshal beamed all over his pukka face: he had shown them Fermat’s principle in action. A hand touched Iain’s shoulder and a female voice said: ‘Sir, fasten your seatbelt, please, and put your seat in the upright position. We are about to land.’

96 They had landed at their destination. The waves of color, the parade of people, the supreme leader and marshal with his selection of Swiss cheeses, had been nothing but a dream. Or had it? On the way through the night from the airport to the hotel, in the black limousine, while looking at the lights of the city, Iain was thinking about the dream. He had seen Fermat’s principle in action. Waves of color and waves of light are blind to the optimal path. They take all paths simultaneously and interfere with each other. Where they interfere constructively they go, where they interfere destructively they do not go. The path they follow, the path of constructive interference, is the optimal one.

  Mission Invisible 

107

But why is this so? Why does the optimal path survive the interference, while the other paths extinguish themselves? Iain recalled what Professor Parsa had said: an optimum is something one cannot improve by making small changes. So a small deviation from the optimal path will hardly make a difference in travel time. All the paths around the optimal one will require nearly the same time and all the light waves around the optimal path will arrive at about the same time, so all those waves will interfere constructively. Iain was beginning to understand. If light takes a non-optimal path, he thought, one can always find a path nearby where the wave arrives exactly out of sync with the wave on the non-optical path: they will thus interfere destructively and so eliminate each other. From the myriad of paths light takes, only the ones near the optimal path will survive, and all other paths will find partners out of sync with them. In his dream, Iain had seen how Fermat’s principle of the optical path emerges from the interference of waves. The interrupted discussion with Professor Parsa had continued in his dream. But why had he conjured up the supreme leader and marshal, and the people’s parade, along with all the bizarre rituals of a twentieth century dictatorship? Iain always trusted his instincts, his intuition, and his dreams. What was the meaning of the dream? The lights of the city they had just reached were bright and modern. It was not much different from Times Square, New York. Or was it?

97 Lilith, Foo’s secretary, was checking them in at the Best American Hotel, right in the center where the city lights were at their brightest. She explained that the hotel was a place for foreign experts to stay. Some of Futuropolis University’s distinguished expat faculty always took their lodgings there. Whenever they came to Thousand Futures Mega City, the golden statue of liberty in the opulent lobby would welcome them back to the good life. Lady Lucy noticed the sign for a spa and asked the concierge whether it would be open at this hour. She wished to refresh herself after the long journey. Iain was also looking forward to a massage. ‘Our spa is open twenty-four hours a day, seven days a week,’ the concierge replied. After a brief visit to his room, Iain returned to the lobby and walked up the stairs to the spa, on a stairway much like the ones used in television shows. It was illuminated with blue and red lights at every step; even artificial fog was

108 

U. Leonhardt

wafting down. The stairs led to an elaborate red and gold gate where a female receptionist in a red dress with a slit up the side showed him into the spa. Iain went to the counter and asked for a twenty-minute back massage. However, no one spoke English or any of the other languages Iain knew. They understood the word “massage”, but not twenty minutes. The minimum time written in English on the noticeboard seemed to be two hours. Reluctantly, Iain finally accepted, although he could not quite imagine what they could do in two hours, apart from breaking all his bones, and hopefully putting them back together again. He went to the changing room for men, where three male servants pounced on him, eager to help him undress. He waved them away like flies, shouting he was able to do this by himself. Finally, he wrapped his towel around himself and slipped into the pool area. Iain did not care for a swim in the shallow water, but had nothing against a good steaming in the Turkish steam room. Just as he entered, another foreigner was leaving, a massive man of Germanic proportions. The man disappeared through a door in blue and red lights. Apparently, this was the way to go. After a good steaming and sweating, Iain wrapped his towel around him and walked through the door. A female servant handed him a fresh towel and a garment of artificial silk resembling some sort of night gown. She also gave him a cup of strengthening soup—all without speaking a word; then she disappeared. Iain changed himself and waited until she returned and guided him to his treatment room, where he lay down on the massage bed. With two knocks on the door, his masseuse entered the room. Iain was surprised to see a female—and one dressed in a slightly exaggerated nurse outfit. The dress had slits up both sides. Other countries, other customs, Iain thought. She gave him a good kneading of his back, even walked on him with her bare feet. But when she lifted the gown on his backside, he felt the massage had gone a little too far.

98 At this moment the telephone rang in the room and the masseuse answered it. She listened carefully, then handed the phone to Iain. It was Lady Lucy: ‘Iain, are you there? I need your assistance. Could you come to the entrance of the spa? There is a spot of bother here.’ Iain rose from his massage bed, apologized to the consternated masseuse, changed in the dressing room, and went to the spa entrance. Lady Lucy stood there, surrounded by three receptionists in red dresses shouting angrily at her.

  Mission Invisible 

109

The only word Iain understood was “money”. He walked down the stairs to the lobby and asked the concierge to send someone up who was capable of speaking English. Shortly after Iain had returned to Lady Lucy, a tall, muscular man appeared, talked to the flock of receptionists, and then turned to the foreigners in English with a thick Singaporean accent: ‘Confirm cannot charge bill to room. Double confirm lah. Law says hotel and spa separate businesses. Must pay cash or credit card to auntie.’ ‘And this was all the fuss?’ Lady Lucy said. ‘Iain, I left my purse in my suite. Could you oblige me with some cash?’ Iain did not have any cash either, but paid for Lady Lucy and himself by credit card. He asked the tall, muscular man what he was doing at the hotel. ‘I work for my boss.’ ‘For your boss? And what do you do?’ ‘I do the negotiations.’

99 As Iain and Lady Lucy had arrived late at night, nothing was scheduled for the morning. After a late breakfast, Iain had an hour until the car from the institute would be picking them up. He strolled around the hotel and walked across the road to a shopping mall. It looked exactly like the mall in Riyadh, Saudi Arabia—apparently, the architect was the same—except that the shops were larger and strangely void of customers. They were no ordinary shops either, but places of worship to the gods of Dior, Chanel, and Louis Vuitton. Iain was reminded of a cathedral he had once visited, where an enormous painting of Saint Christopher, the patron saint of travelers, had greeted them from across the main entrance. He was blessing the visitors’ journeys even if they were too busy to enter. Here, opposite the main entrance to the mall, a five-story Louis Vuitton store was blessing the travelers from near and far, especially when they were carrying some of his holy merchandise. Saint Louis, praise be his name, was sure to hold his hands over the travelers. Lilith was sporting one of his handbags when she picked them up. Off they went in the black limousine to Foo’s institute at Futuropolis University.

110 

U. Leonhardt

100 Foo sent his apologies via his assistant Lilith. Urgent business was holding him up in Vienna, but he hoped to join them that night for dinner. The new campus of Futuropolis University, as well as a dozen more universities in Thousand Futures Mega City, was built on an extensive island in an area that five years before had still been a crocodile-infested swamp. To reach it took more than an hour of fast driving. They passed campus security, drove past the dome of lecture theaters, the Olympic-class indoor swimming center, and the parade grounds. They stopped in front of a row of large buildings, the new factories of knowledge, as Lilith explained. One of them was Foo’s institute. They took the elevator up and immediately started a tour of the laboratories and offices. The labs were full of the latest equipment and the offices were full of students sitting at their benches and staring into computer screens. They saw one of the institute’s part-time foreign faculty, Professor Rheinhard Aschberger from Germany, who was in the process of inspecting his serfs. His assistant, Dr. Unterhölzer, was trying to teach the students how to address the eminent professor of photovoltaics with ‘Jawohl, Herr Professor Aschberger.’ But the students were still struggling with his complicated Germanic name. ‘One more time, all together now!’ ‘Yawohl, Herr Professor Arseberger.’ There is no-one closer to God in academia than a German Herr professor. Inscrutable, inexplicable, incomparable, and infallible; he reigned over his fearful subjects with old-testament zeal, except that Professor Aschberger was more like Thor, the Nordic god of thunder. Suddenly, Iain realized he had seen Herr professor before—this was the massive man of Germanic proportions emerging from the steam room and walking through the door in blue and red lights.

101 After the tour of the labs and offices, protocol required Lady Lucy to give a lecture about her research. The students were drafted to fill the lecture hall in large numbers. Iain noticed that many of them were using the time to catch up on their email or their sleep. Iain was not paying much attention either. Instead of listening to Lady Lucy’s well-rehearsed official ideas, he was thinking about her unofficial idea.

  Mission Invisible 

111

Invisibility, this was why they wanted her here. Iain could not be absolutely certain, but it was hard to believe that they had invited her for the paradox on refraction she was lecturing about. Somehow they must have found out what she was really working on. When Iain was strolling around in the morning he had noticed a peculiar building next to the hotel. At first glance, it looked like an ordinary tower block, but when he saw the sign and the guards, he realized it was a military installation, off-limits to civilians. How well put together it all was. How fitting it was that the people next door to the Best American Hotel should be the ones keeping an eye and an ear on the hotel’s visitors and their electronic equipment. Lady Lucy’s lecture was an academic ritual; their hosts could talk business later on, perhaps after dinner that night. What was the restaurant called? The Shark and the Crocodile. Interesting name. Invisibility, the ultimate optical illusion, the ultimate weapon—thank God nobody would have expected Iain to have figured it out. The travel agent with a degree in Persian poetry, what an unlikely match for Professor Lucy de Phos, the obscure amateur versus the famous professional. Yet he had figured it out. It was a three-mile problem through wintery fog in St. Petersburg. While Lady Lucy was delivering her lecture with her smug measured voice, Iain imagined how that lecture ought to be, how he would electrify the audience.

102 This was how Iain imagined his lecture on the science of light and invisibility: ‘Invisibility, ladies and gentleman, is an optical transformation of space. A layer of transparent material, wrapped around the hidden object, transforms it to the size of a single point. Materials can transform space, because they change the way light perceives space. They make it appear longer or shorter depending on the refractive index. For invisibility, the material makes an object infinitely small. ‘Invisibility is a tale of two spaces. One is virtual space, the space of the optical illusion, and the other is real space, the space of physical reality. Light perceives the world as this virtual space, and so does anyone perceiving the light, anyone looking. If the transformation from physical to virtual space has turned the interior of the device into a single point it disappears from view. ‘A tale of two spaces, this is the story of invisibility. The two spaces are synchronized. Whatever happens to light in virtual space happens in physical space at the same time, but at a different place.’

112 

U. Leonhardt

Iain showed his imaginary audience a little movie. A speck of light traversed, in slow motion, each of the two spaces. One screen showed virtual space, the other real space. ‘In virtual space, the speck of light went on a straight line, in physical space it moved to one side and went around the interior of the device, but it arrived at the same time as in virtual space. Well, it had to, because the two spaces were synchronized.’ Someone in the imaginary audience asked whether the light in physical space had to move faster than light in empty space. ‘Absolutely,’ Iain said. ‘In physical space, the light must catch up for the detour. It must move faster than on the straight path in virtual space.’ ‘But isn’t that impossible?’ ‘Not quite. Light can move faster than in empty space, but only for a narrow range of color. What are colors? Colors are the vibrations of light. Each color has a certain rhythm, like the rhythm of an African drum. The material can anticipate the rhythms coming and send them off faster, but only if they match the resonances of the material, which limits the range of rhythms, the range of colors.’ ‘What happens in the most extreme case, when a light ray is just grazing the invisible point in virtual space? What happens then in real space?’ ‘The invisible point in virtual space stands for the entire interior of the device in real space. The light must skim along the whole interior in the same time it takes to pass a single point. How much time is that?’ ‘None at all. But this means light must become infinitely fast in the material of the cloaking device. At the surface of the hidden interior, light rays must leave at the same time they enter. Impossible! Or is it?’ ‘If the light leaves at the same time it enters the material, the material must know in advance what was coming. It must know the vibration and the pattern of light. Leaving and entering at the same time is not entirely impossible: if the light had only one rhythm—one color, and if the scenery around the cloaking device did not change, it might still work.’ ‘So what is the point of invisibility cloaking then? To see the effect, one would need to put on tinted glasses of exactly the right color and everything would have to hold absolutely still. This is ridiculous!’ Iain remembered the cuttlefish in the Singaporean zoo in Riyadh, how effortlessly it had changed color and texture. The little creature was so much more effective in camouflage than Lady Lucy could ever be, even in her wildest dreams. Lady Lucy’s idea of invisibility, as perfect as it might appear in theory, was not going to work in practice.

  Mission Invisible 

113

103 Perfect invisibility was impossible. Surely, Lady Lucy must know that, too— she was a world famous physicist, not an obscure travel agent with a degree in Persian poetry. And besides, she had viciously attacked poor Professor Parsa in public. Parsa had expressed his gratitude to God that no illusion is perfect, that truth will always find a way to appear in the end. Truth exists. This, Iain thought, is a belief science and religion have in common. Truth exists and can be found—this is the belief of science. Lady Lucy must know that true invisibility is impossible. She was a good scientist. So why was she speaking to the Saudi king about her idea? And why was she going to speak to their hosts here? Iain did not know. But maybe this was not the right question. The right question was: suppose she promised a cloaking device and could not deliver, what would her clients do? The Saudi king would cut his losses and forget about her. But their hosts here, what would they do? They could make use of a good physicist for their ambitious plans. They could blackmail her to work for them indefinitely. One thing was certain: if she signed up she was doomed.

104 After the lecture, Lilith invited Lady Lucy and her assistant to a tour of Thousand Futures Science Park, while the students and professors went out into the courtyard for their afternoon gymnastics, accompanied by patriotic music. There they were standing in rows, holding pieces of cloth and moving them up and down to the rhythm of the music and some choreography they were studying. ‘What are they doing?’ Iain asked Lilith, who replied: ‘They are practising for the annual parade of the institute.’ The travelers left in the black limousine with Lilith and a gentleman chauffeur, who reminded Iain of someone he had seen in the movies. The squat Asiatic man with arms like thighs and a bowler hat resembled Odd Job from the James Bond movie Goldfinger. He was chief assistant to Foo, Lilith explained, and he remained as silent as Goldfinger’s servant, for he lacked sufficient command of English. Odd Job was driving them along campus after campus on University Island to an area that was singled out to be the largest science park of Thousand Futures Mega City.

114 

U. Leonhardt

105 A science park is an area where innovations are born through the happy marriage of university research and industrial capital. Stanford Research Park, the cradle of Silicon Valley built in 1951, was a collection of grisly garages compared to Thousand Futures Science Park. Lilith explained that the government had spent billions on innovation, and added: ‘We need to make the government happy. If our government is happy, we are happy.’ It was as simple as that: government and universities were one happy family, the government providing the cash, the universities spending it. Sure, some of the money did materialize in the laboratories and fabrication centers of the science park, but Iain noticed the apartment houses with river views the professors had built for themselves or as investments. ‘These apartments are good investments, some are worth more than a thousand dollars a square foot,’ Lilith said, proud of the progress her country had made. Iain was wondering how university professors could raise such sums. The science park itself was surprisingly void of people, as void as the temple of Louis Vuitton that Iain had seen that morning. Where was everybody? Very few lights were on, except in one block with dozens of floors brightly lit. ‘What is this?’ Iain asked Lilith. ‘The new clean-tech center. The government wants clean technology: non-­ polluting, carbon-neutral, and knowledge-driven. The clean-tech center has made the government very happy. It produces the cleanest product: pure knowledge dispensed directly via the telephone.’ ‘But what exactly is it?’ ‘A call center.’

106 The government was very happy indeed. Only five years previously, University Island had been a crocodile-infested swamp. Where crocodiles once roamed, professors now reigned. The reptiles were relocated to a vast crocodile farm on the island, near the Old Fortress, where the travelers would go next. On their way to the Old Fortress, the weather changed. Dark clouds shrouded the sky and darkness covered the land. The first heavy rain drops fell, the first bolts of tropical lightning threw their lights through the darkness, followed by thunder. The rain got heavier by the minute, rain from

  Mission Invisible 

115

above and rain bouncing from below, until they could not see anything anymore. The silent silhouette of the driver stopped the car. When the worst was over they drove through the rain towards the casemates of the Old Fortress. The moats seemed to be full of large, armored logs lying on top of each other, but in the flashes of the thunderstorm, these logs had eyes, reptilian eyes. They drove across the drawbridge, through the main gate, and to the parade ground, where they stopped. People with large black umbrellas rushed out and helped our travelers inside. Lilith explained that the institute was f­ ortunate to have another laboratory at the Old Fortress—the lab their gentleman driver was in charge of. He walked with them down the spiral staircase to the basement laboratory, all in silence. Lilith did the talking and introduced them to the scientists sitting at their stations. Iain noticed that they had much keener, watchful eyes than the students he had observed at Lady Lucy’s lecture. In fact, almost reptilian eyes, but this was probably just a trick of the light. Lady Lucy inspected the equipment and expressed her approval of its first-­ rate quality. One of the scientists replied: ‘We are very happy and honored that you, Professor Lady Lucy de Phos, appreciate our laboratory. Professor Hieronymus Foo has not arrived yet, but he assures you that you will get an even better facility at these premises. This is the non-educational part of the institute where no students will bother you, and where our best staff scientists and technicians will remain at your disposal.’ The scientist spoke very good English with perhaps a hint of a Scandinavian accent. Maybe he was, like Foo, trained at the Royal Norwegian Institute of Technology. ‘But now it’s time for dinner,’ Lilith interrupted. ‘We shall take you to the restaurant at the crocodile farm, number one on TourAdvisor: The Shark and the Crocodile.’

107 They returned to the car where the silent silhouette of their gentleman driver was already waiting to take them to the restaurant. Iain felt he ought to tell Lady Lucy what he thought she was signing up for. But how? Lilith was sitting in the car as well, and would hear every word. Besides, one did not simply speak to Lady Lucy! Iain should not speak until spoken to. Luckily Lady Lucy began: ‘What a remarkable fortress. It reminds me of Fortress Königstein, the Saxon Bastille near Dresden in Germany, although that one sits at the top of a hill, and this one here lies in the middle of a swamp.’

116 

U. Leonhardt

‘How interesting, Lady Lucy,’ Iain chipped in. ‘How interesting that you should say this. Did you know that Fortress Königstein also had a laboratory?’ ‘No, did they happen to do my line of work, by any chance?’ ‘In some way they did, ma’am, although it was a long time before you, around 1700. The king of Saxony, August the Strong, imprisoned a German alchemist named Böttger, that is Potter in old English.’ ‘Alchemy? Why should this be my line of work?’ ‘Ma’am, at that time even the great Sir Isaac Newton was an alchemist. The boundary between the natural and the supernatural had not yet been completely drawn.’ ‘This Potter was a super scientist of his time, is that what you’re saying?’ ‘Yes, and as a young apprentice, he became an alchemist. He claimed to have received the recipe for transforming base metal into gold, and not only did he claim it! He demonstrated it to his colleagues, to their great shock and surprise. That was in Berlin in 1701, if I remember correctly. The local king, Frederick the First, got word of it and ordered the young alchemist to be put in “protective custody”. The king wanted to make a fortune and Böttger, being a clever man, fled to his native Saxony. He asked King August the Strong for protection, which he got. August did not extradite Böttger to Prussia, but put him under arrest himself. Böttger was given a first-class laboratory and the finest scientists and technicians in Saxony to work with, and first-class “protection” at Fortress Königstein. He was to remain a prisoner until he produced gold worth sixty million talers, equivalent to sixty billion in today’s dollars. He was bound by his word: he knew how to transmute base metal into gold, how to do the impossible.’ ‘I’ve heard quite enough about this Potter.’ ‘Ma’am, Böttger was still a brilliant scientist. He could not make gold, obviously, but he did invent something as valuable as gold at the time: porcelain. At the turn of the eighteenth century, all Europe was craving the expensive imports of porcelain from China. Böttger succeeded in creating what many European scientists had tried and failed to make: chinaware— “white gold”, which was almost as good as making gold itself.’ ‘That’s more like it.’ ‘Böttger had seen how the king had gotten a fellow alchemist executed for failing to make gold, and turned to porcelain. When Böttger emerged with the recipe for “white gold” the king was more than pleased. Yet although Böttger could then go in and out of court, had a handsome salary and all he could wish for, he still remained a prisoner. Several times he tried to flee his gilded cage, only to be caught and put to work again. His legacy is the first and finest porcelain manufactory of the Western world: Meissen.’

  Mission Invisible 

117

They had arrived at their destination, the famed restaurant in the crocodile farm. Complete darkness had fallen.

108 Most famous restaurants are temples of refined dining where mere mortals need to ask for admission months in advance. The Shark and the Crocodile was a temple in its own right. It rose on classic columns of dark alabaster to a blue-lit roof-top aquarium where our travelers could make out the shadows of hammerhead sharks circling above the entrance. They walked up the stairs and were greeted silently before being shown through the great hall to their private dining area. Above, in the blue-lit ceiling, the hammerheads were doing their rounds. Below the glass floor, dark logs were lying in waiting, logs with eyes glowing in the light. The walls were filled with smaller, brightly lit aquariums, full of live fish to be eaten. Odd Job, their silent gentleman companion with his squat Asiatic face, signaled to the cook. He took our travelers to the aquariums in the wall to select a meal. In one, a two-foot baby shark with colorful frays over his eyes was dancing about, unaware of his fate. Odd Job pointed to him. The cook took his net and caught the baby fish. It splashed and writhed in the net until hit with the cook’s club, then fell silent. The travelers went back to their table where the restaurant’s signature soup was served. Lilith received a phone call, apparently from Foo, who was having some trouble. He urgently needed her assistance. Lilith apologized and excused herself from the table. Apart from their silent companion, Lady Lucy and Iain were alone.

109 Lady Lucy went straight to the point: ‘What was that tale of yours? What were you driving at with that Potter story?’ ‘I am sorry ma’am, but what do you think I was alluding to?’ ‘I am asking the questions here!’ ‘But how can I answer your questions if I do not understand what you mean?’ ‘What I mean? It’s bloody obvious: you are comparing me, and my line of work, with an alchemist and charlatan!’

118 

U. Leonhardt

‘But Böttger invented European porcelain; he did something immensely valuable at the time.’ ‘He did.’ ‘And his line of work, his real line of work that is, was it not science?’ ‘It was, the material science of his day. Ceramics were the super materials of his time. They still are—the most modern metamaterials are made of ceramics. My friend Vladlen told me all about it, fascinating stuff. But what about the rest of your tale—the fortress, the gilded cage?’ ‘Ma’am, if you look around, what do you see?’ ‘A five-star restaurant with some amusing flair—sharks above, crocs below, and that stupid manservant sitting clueless in the middle.’ ‘If you sign that contract with Professor Foo, would that “manservant” not be in charge of your laboratory, your science, and your security?’ ‘I suppose he would.’ ‘And would you not be immensely valuable to Foo, as valuable as Böttger’s sixty billion dollars?’ ‘I am sure I would.’ ‘And ma’am, if you forgive me for asking this question, why would you be so valuable?’ ‘Do you really think these fools invited me for my footnotes on optical illusions? You have no idea. I have discovered the ultimate illusion: invisibility cloaking. Now you’re talking. You, anyone, entire armies may become invisible.’ ‘Forgive me my question, ma’am: is this discovery of yours like the making of gold or the making of porcelain?’ ‘Gold, of course.’ ‘And, a purely academic question, of course, if you should fail to make gold, wouldn’t the silent gentleman force you to work on something equally valuable?’ ‘He might, theoretically.’ ‘Do you think Foo’s men are involved in chinaware?’ ‘Obviously not.’ ‘So what are they interested in?’ ‘Conquering the world, that sort of thing. They have a long way to go, though. But they put their money where their mouth is.’ ‘Lady Lucy, there is something I do not understand. Why don’t you mind becoming their accomplice? You are a world famous scientist and a lady, why do you need this? Why ridicule poor Parsa for speaking the truth?’ ‘What truth?’ ‘That invisibility is impossible.’ ‘I’ve heard quite enough! You’re fired!’

  Mission Invisible 

119

110 What was happening to Foo in the meantime? Why was he in trouble? Here is his story. While Foo was still at Airlie Center near Washington, D.C., he had received good tidings: his application for Austrian citizenship had finally been approved. He only needed to swear the oath of allegiance to Austria in front of Herr Zed in Vienna—that would make him Austrian. Before this, there was just the small matter of renouncing his previous citizenship, as Austria does not normally approve of dual citizenships by naturalization. A dash to his embassy would do, then the final formalities with Herr Zed, and a day for an express passport. Foo would have ample time to catch up with our travelers who had gone off in the other direction around the globe. He called his secretary to rebook his flights. No doubt Foo was looking forward to his Austrian citizenship. What could be more convenient than a small country with all the benefits of Europe and none of the commitments? Austria was strictly neutral, militarily and politically, hence open for business with everyone. Switzerland used to be the safe haven for the illicit earnings of the twentieth century. Now Austria was opening her heart and her vaults for the money of the new millennium. The country had his sympathies and his bank account. Foo also appreciated Austria’s humanitarian values. If, heaven forbid, he ever got into trouble in his own country—in the unlikely event he was ever to face a firing squad for corruption, Austria was sure to save him in the name of human rights. On the other hand, if there was trouble abroad—war, revolution, earthquake—the Austrian Embassy was the least likely one to help. Indeed, they would be the first to abandon ship. But would there ever be trouble for Austrians? Tu felix Austria—thou happy Austria. When other nations fight the wars of the day, thou drinkest coffee and doest deals.

111 Having renounced his original citizenship at his embassy, Foo was heading towards MA35 to see his immigration officer, Herr Zed, for the last time. Foo had almost gotten fond of the fellow in his yellow tee-shirt with printed palm trees, his tendency to mislay his papers, and his absences to take the waters of Bad Tatzmannsdorf. Foo went up the stairs with a spring in his step, nodded

120 

U. Leonhardt

to the Chechen asylum seekers in the corridor, and knocked briskly at Herr Zed’s door. ‘Come in,’ answered the tired young man. ‘I am Professor Doctor Hieronymus Foo-uč`, I have an appointment with you to receive my Austrian citizenship.’ ‘Ah, you again. Ya know that ya need to cancel yur previous citizenship?’ ‘I went to the embassy this morning. Here is the letter of renunciation.’ Herr Zed scrutinized the paper. Then he asked: ‘And where’s yur criminal record?’ ‘You have the statement already, you received it more than half a year ago.’ ‘Yeah, that’s the problem, Professor, yur statement is more than half a year old; it has expired now. We need a fresh one.’ ‘Nobody told me this! And I have a flight to catch tomorrow night!’ ‘Ya need ta fetch a fresh criminal record.’ ‘I cannot get one, you blasted son of a bureaucrat. I am stateless now; the embassy will not let me in.’ ‘Ya cannot get Austrian citizenship on an old criminal record. Sorry, Professor.’ ‘Someday, some Chechen will come here with his machine gun and kill you all. Then you’ll get your criminal record!’ Yet there was nothing to be done. The Chechens in the corridor had presumably left their machine guns at home. Foo shouted, jumped up and down, demanded to see the boss, and was thrown out. How was such a spirit so betrayed? One thing was certain: Foo was trapped for some time in Vienna, condemned to the purgatory of statelessness. If you see the lonely figure of a short man in a cheap-looking but expensive suit on Vienna airport’s observation deck, following the planes with his eyes, don’t feel sorry. There are worse places to be grounded than Vienna.

112 Iain was fired. This fantastic journey around the world on science business was over. He was flying back home on Austrian Airlines Tourist Class without extra legroom and with cheese noodles in front of him, while the more illustrious passengers in their comfortable seats were dining on tafelspitz and kaiserschmarrn. The journey was over and he was fired. Iain was no longer Lady Lucy’s assistant; he was on his way back to the travel agency. What Lady Lucy had decided, after he had confronted her, he

  Mission Invisible 

121

did not know, as he was immediately thrown out of The Shark and the Crocodile. Of all the puzzles and riddles of this journey, she was the greatest. She was a charlatan, as Böttger was, and a scientist, as he was as well. Her research was almost like present-day alchemy; instead of the philosopher’s stones, there were metamaterials. She must have known, deep in her heart, that she was promising the impossible, but she carried on, attracting the attention of the great and the good, and the not-so-good. Why? Was it the fame? What is fame? The admiration of the crowd. Should she not stand above the crowd? Maybe she didn’t. Maybe she was a fake lady, as fake as her promises, as fake a lady as Iain’s boss at the travel agency. Iain was not looking forward to getting back to the Office. His boss, commonly nicknamed Miss Piggy, would welcome him back into the perfumed bosom of the agency. Then she would invariably change her ladylike vowels to the sounds of her native East London: ‘Now Iain, move it!’ His cubicle was waiting for him, amidst the bedlam of the office—telephones ringing, people shouting, as if the journey had never happened. And yet it had.

113 And what a fantastic journey it had been. The countries he had seen—the Arabia of the veiled ladies, the Persia of the poets, the Russia of the Hermitage and the Man from the Ministry, America, the brief moment on the enchanted islands of Japan, and even Foo’s country. What a journey! The people he had met—Luna (the red herring), Norah (the bright young light of Persia), Professor Parsa (the last scientist), and Zhenya (the unstoppable enthusiast from Russia). They were all carrying the light of science. And from them he had learnt the science of light. Who would have thought that he, Iain, who hated physics at school, would beat Professor Lady Lucy de Phos by figuring out her secret? He had understood the science of invisibility just in time to confront her before she signed up with Foo. The rest was her decision; he had done what he could and just in time. All the conversations about light—at the magic shop in the souk, in the desert, the Singaporean zoo, on Luna’s balcony, in the Persian madrasa, in Khan School at midnight, in wintery St. Petersburg, in the secluded American conference center; all had led him to figuring out Lady Lucy’s secret. His mind had made the journey as well. That journey was not a straight path, but

122 

U. Leonhardt

was it not the fastest journey from knowing nothing in optics to beating Lady Lucy on her own turf? Fermat’s principle of the shortest path, had it not guided Iain’s path as well? That was the question: do people, things, everything—not just light—follow Fermat’s principle? Probably. But Fermat’s principle comes from the interference of waves. Iain had seen in his dream of the strange land that waves follow all paths. The optimal path is the one where they all add up, while the other paths get washed out. If so, then what are the waves behind things? They must be the most general waves imaginable, waves of possibilities. Nature would try out all possibilities at the same time. The paths things take are the paths where the possibilities add up. This gives them their destiny. Iain did not know, but at that moment, squeezed into his seat in the tourist class section, he was discovering for himself the first principles of quantum mechanics, the greatest mystery of physics. What a journey! Who would have gone around the world for less?

Scientific Appendix

A1 This book is a work of fiction; it tells an invented story, taking the reader on an imaginary journey around the world on science business. Any resemblance to actual persons, living or dead, is entirely coincidental of course. Most of the places the travellers visit are authentic, though, but some are also fictitious. To help the reader distinguish between reality and fiction, I gave the real countries their real names, while the fictitious ones are not mentioned by name. Yet even with real places I took some liberties: perhaps the least forgivable one was transplanting Singapore Zoo to Saudi Arabia for the sole purpose of simplifying the logistics of the book’s imaginary journey. As it is fiction, all its dialogues about the science of light, and about the bright and the dark sides of the business of science, are fictitious, but the science itself is absolutely authentic. So, here in this Appendix, for the interested reader, let me explain the science of my book in greater clarity, freed from the human comedy of the story, and in the wider context of this endeavor called science which, according to Stephen Weinberg, is one of the very few things that lifts human life a little above the level of farce, and gives it some of the grace of tragedy. Before venturing on to the science, I must first give the reader my assurance that I will not use equations, only diagrams and drawings. I will however mention the proper scientific terms, marked in italics, so that the reader can

© Springer Nature Switzerland AG 2020 U. Leonhardt, Mission Invisible, Science and Fiction, https://doi.org/10.1007/978-3-030-34634-8_2

123

124 

U. Leonhardt

look them up and learn more. But now it’s time to begin with this, the scientific appendix of the book.

A2 Let me begin by evoking the grandest of scenes, the universe as a whole. According to Einstein’s general theory of relativity, the geometry of space and time may be curved and this curvature appears as gravity. What does this cryptic, but somehow grand-sounding statement mean? We must first explain what the term geometry means. Geometry is what the name geometry says, in Greek that is: geo-metria. Geo is the Earth, or, put more generally, the world, and metria means “a measuring”. So geometry is the business of measuring the world. But it is not about the actual instruments used to do the measuring, the laser triangulation of these days or the drawing of lines in another era. It rather tells how the results of such measurements make sense, no matter how they are performed. What the measurements produce are maps. They give the coordinates of the points of the territory the map covers. But the coordinates are useless without a scale. The scale gives a measure of how the distances between the points on the map are translated into their actual distances in reality. The scientific term for such a scale is a metric. The scale may be the same for all points on the map, but it may also vary. For example, the cartographers drawing the map of a city may wish to emphasize the city center at the expense of the outer quarters. The map of the Moscow metro (the Moscow underground) shows this: central Moscow appears disproportionately large. The metric of the map must vary in order to compensate for such artificial enhancements so that it always gives the proper distance. The metric must decrease when a region is enhanced on the map and increase when a region is compressed.

Official schemes of the Moscow metro. In the left picture the city center has been exaggerated in order to help travellers find their connections. The right picture shows a geographically less distorted map of some of the metro lines. You can see how small the actual city center is compared with the entire metropolitan area

  Scientific Appendix 

125

126 

U. Leonhardt

For Moscow there are other maps, accurate street maps that display the proper distances without any scaling and rescaling. On each such map, the metric does not vary. Following the metro stations on the street map you may get a sense of how the metro map is distorted. Moreover, you can rectify it: following the stations you can draw the actual metro lines. What you have done is a coordinate transformation from one map to another. But what has this got to do with the curvature of space and time, and Einstein’s theory?

A3 A metro map can be rectified, but this is not always possible for other maps. A good example is the Mercator projection that gives the familiar map of the Earth.

Mercator projection of the Earth. The Mercator map preserves the right angles between the lines of longitude and latitude, but it distorts the true geographical distances on the globe. Greenland seems to have the size of South America and Antarctica looms gigantic in the South. The correct geographical distances are hidden in the metric of the map, which depends on the latitude

Just compare the sizes of Greenland and South America on the map with their actual sizes on the globe. Greenland is much smaller in reality. Therefore, in order to compensate for the injustice inflicted by the Mercator map, the

  Scientific Appendix 

127

metric must suppress the Arctic regions and enhance the Equatorial ones. The same is true for Antarctica, which also appears disproportionately large and must be compensated for by the metric. But the problem is, no matter how the map of the Earth is transformed, it never gets completely undistorted. The metric will always vary. This is because the Earth is curved. Wherever there is curvature, the metric must vary and cannot be made constant for an extended region. This is a mathematical theorem that one cannot argue with. The impossibility of drawing a map with constant metric indicates that there is curvature. But it does not tell us how strong the curvature is. In order to define a measure of the curvature, geometers look at lines on the map and measure how the distances between the lines vary. They look at specific lines, the geodesics.

A4 The geodesics are the shortest lines between any two points. On the globe, these are the routes airplanes try to fly along under ideal conditions. Looking at the familiar Mercator map, it may surprise you that the shortest route from Vienna to Los Angeles takes you over Greenland and Canada—even though flying straight across the Atlantic and the United States appears much shorter.

Geodesic from Vienna to Los Angeles on the Mercator map

128 

U. Leonhardt

Yet looking on the globe, you can see how much of a detour that would be. The geodesic between Vienna and Los Angeles depends on the real distance. As distance is measured by the metric, it therefore depends on the metric. Geodesics are calculated as solutions of the geodesic equation, which is a special case of the Euler-Lagrange equation.

Geodesic from Vienna to Los Angeles on the globe

Geometers use the behavior of geodesics in order to quantify the degree of curvature. A space with zero curvature is said to be flat (even if this space is three- or higher-dimensional). Such a flat space can, by coordinate transformation, always be brought into a form where the metric is constant. For a constant metric, the shortest paths are straight, so the geodesics are the straight lines. However, they might not appear straight in other coordinates. A straight line on the Moscow street map may look rather curved on the metro map. So, in order to define a measure of curvature that is coordinate-independent, geometers are forced not to consider just one geodesic, but at least two, and to investigate how the geodesics lie relative to each other. Euclid, who created the first mathematically rigorous geometry in ancient Greece, invented an axiom that captured the character of flatness. He stated that, for each straight line, only one parallel straight line can be drawn through a given point.

Euclid’s parallel axiom. Euclid postulated that, for a given straight line, only one parallel can be drawn through a given point, as the picture shows in flat space

  Scientific Appendix 

129

If you replace “straight line” by geodesic, you can see that Euclid’s axiom is violated on the globe. All lines of longitude are parallel on the Equator, but they all meet at the Poles. So on the globe one can draw infinitely many parallel lines through the poles, which is a lot more than Euclid’s axiom would allow.

The lines of longitude on the globe violate Euclid’s parallel axiom. Lines that look parallel at the Equator all meet at the Poles

A5 Inspired by Euclid’s axiom and its violations, modern geometers consider the deviations of geodesics. Suppose you select one geodesic. How do other geodesics, close to the chosen one, behave? Will they remain parallel? Will they get closer? Will they get farther apart? In flat space, the geodesics—the straight lines—lie like Mikado sticks. The distance between two lines may remain the same—then they are parallel, or they may intersect. In the latter case the distance between the lines increases in proportion to the distance along the lines. One could say the same about the parallel lines, since there the proportionality factor is simply zero.

130 

U. Leonhardt

Geodesic deviation in flat space. The distance between neighboring straight lines, or geodesics, grows in proportion to the distance. In modern geometry, this behavior is regarded as the defining feature of flat space, similar to Euclid’s parallel axiom

However, in curved space the distances between geodesics are not proportional to their lengths. You can see this very clearly from the lines of longitude. On the Equator a distance of 15 degrees longitude amounts to about a thousand miles, whereas on the Poles that distance shrinks to naught. The way geodesics deviate, the geodesic deviation—whether they deviate in proportion to the length or not—thus probes the degree of curvature. The results of the deviations in all directions are summarized in a table of numbers that contains all the essential information about the curvature of space. This mathematical object is called the Riemann curvature tensor. If the Riemann curvature tensor is zero, then the space is flat, and vice versa, if the space is flat then the curvature tensor is zero. The Riemann tensor quantifies the curvature, and it has been recognized as one of the most important mathematical objects in geometry.

A6 Now you have got an impression of how the geometry of space works, whether flat or curved. But what about space and time? What about the geometry of the universe? One of the lessons from Einstein’s relativity is that space and time establish a union called space-time.

  Scientific Appendix 

131

Space-time diagrams are often used to visualize the succession of events in space-­time. The horizontal axis shows the space with coordinates x and the vertical axis the time t. The horizontal line represents the present at a given time

The past, present, and future of the universe are thought of as forming a single continuum of events. This is because the present is ambiguous: what is the present for one observer may not be the present for another, but part of the past and future. So it is best not to distinguish one present, but rather to consider all events, whether they lie in the past, some present, or the future, as part of one great story, pictured in space-time.

The present is ambiguous. The black lines show the present x at a given time and the time axis t orthogonal to it. The gray lines show the present x′ and the time axis t′ as seen in a moving coordinate system (according to the theory of relativity). The present in the moving frame lies partially in the past, partially in the future of the frame at rest

132 

U. Leonhardt

While in space the metric measures length, it turns out that in space-time it measures time. The point is this: not only is the present ambiguous, but time is something private—each object has its own time, called proper time. Two identical clocks will measure different times when they go on different journeys. The actual time differences are normally tiny, but they have been measured, and their differences are empirically confirmed facts. Moreover, such time differences need to be taken into account in the Global Positioning System (GPS). Otherwise you would not be able to find your way with sufficient precision.

Proper time. Each object has its own proper time depending on how it moves in the space-time diagram (and depending on the metric of space-time). Each object is a moving clock in its own right

In space, curves may have different lengths, in space-time, journeys may take different times. In space, the metric measures length, and in the universe it measures time.

A7 You have seen examples of geodesics in space: they are the paths of shortest length. In flat space, the geodesics are the straight lines, in curved space they are curved. Now consider geodesics in space-time. Geodesics are extrema: they may be the shortest or the longest. So the first question is whether the space-­ time geodesics will be journeys of longest or shortest time. Einstein’s relativity

  Scientific Appendix 

133

tells us (in agreement with measurements) that, the faster some object moves relative to an observer, the slower the object’s proper time will tick away in comparison with the time of the observer. If the object approaches the speed of light, its proper time comes to a standstill. So, if you imagine an object on a wild roller-coaster route, zigzagging back and forth with nearly the speed of light, its proper time will progress very slowly. Assume, theoretically, that the object were on a journey of least proper time. One additional zigzag would make the proper time even shorter, in contradiction to the assumption made. So, by excluding the impossible, you come to the inevitable conclusion that geodesics in space-time are paths of longest proper time. One striking consequence of the longest possible time along geodesics is the twin paradox. Consider a pair of twin brothers. Suppose one of them stays put, while the other goes on a journey. After a while the journey takes the traveller back to the starting point where his brother waits for him. To their surprise, they notice that the travelling twin has aged less than the sedentary one. What is the reason? The sedentary twin was just quietly sitting on a geodesic through space-time, while the more adventurous one made some tours and detours. Since, as you have deduced, the geodesic is the path of longest time, the tours and detours did not age the traveller as much as the idleness of his brother.

Twin paradox. The figure visualizes the proper times of two twin brothers shown by their clocks. One brother does not move—in the space-time diagram his clock only moves in time, but not in space. The other brother moves in space on trajectories that are not geodesics. When the two brothers meet they realize that their clocks show different proper times: the idle brother has spent more time

134 

U. Leonhardt

A8 You now know the foundations of space-time geometry, but how is this related to gravity? The most important insight into the nature of gravity comes from what is known as the equivalence principle. The principle states that all point objects of given velocity, irrespective of their masses or internal structures, move the same way if they are only influenced by gravity. All these objects are equal before the law of gravity. Now, if gravity does not distinguish between the masses and structures of point objects, it must be something that entirely depends on the grand scene in which these objects move, space-time. Gravity must be geometrical. It is therefore natural to assume that point objects move on geodesics if they are left to inertia. In the twin paradox, the idle twin was floating on his geodesics, while his brother was experiencing adventures brought about by other forces, in addition to gravity. If space-time is curved, the geodesics are no longer straight, but are curved as well. The planets orbit the Sun, because the Sun has curved space-time and, by going around in ellipses, the planets try to prolong their travel times. Newton’s apple falls from a tree as soon as it gets loose, because by falling it prolongs its travel time in the curved space-time of Earth. Even the tides turn out to comply to space-time geometry: they are manifestations of the geodesic deviation of ocean water. These are fantastic thoughts, but they are true.

Planetary motion shown in a space-time diagram. The Sun has curved the space-time around her. The planets orbit the Sun in ellipses in order to maximize their proper time

There is only one ingredient missing, and you have all the foundations for the fully-fledged theory of gravitation, known as the general theory of relativity.

  Scientific Appendix 

135

You have seen how space-time tells matter how to move: matter moves on geodesics. What is missing is how matter tells space-time to curve. It turns out that one can also formulate the missing ingredient as an optimization problem, similar to the definition of geodesics. Space-time is curved such that its curvature is minimal compared with the action of matter. The heavier the matter, the more space-time must curve in order to compensate just enough for it. The relative weight between matter and curvature is set by a physical constant that is proportional to Newton’s constant. This optimization problem between curvature and matter describes how matter causes space-time curvature. It is not clear from the outset, however, how to formulate the statement “curvature is minimal”, because, as mentioned before, the full information on curvature is not just one number, but a table of numbers, the Riemann curvature tensor. This table of numbers needs to be whittled down to just one relevant number. Some additional thoughts (beyond these brief notes) clarify this issue and lead to a mathematical description known as Einstein’s field equations. Space-time tells matter how to move—on geodesics, and matter tells space-­ time how to curve—optimizing curvature. These two brief statements summarize general relativity.

A9 Space-time geometry tells us how the heavens go, but curved space is not something out of this world. There are other ways in which space may appear to be curved—for example in optics, and they are directly observable and intuitively understandable. They belong to a set of phenomena that are perfectly ordinary, but reveal, if attention and thought is applied to them, some extraordinary concepts. Take a piece of glass, perhaps a glass sphere, hold it in your hand and have a look through it. The glass strangely distorts the view. This distortion can also be understood as the signature of curved space, brought about by the glass, following a train of thought that first arose when Pierre de Fermat wrote a letter on 1 January 1662 outlining what has come to be known as Fermat’s Principle.

136 

U. Leonhardt

Space-time diagram of light. The light (with trajectory drawn in black) propagates through air, enters a transparent material, goes through, and then propagates in empty space again. The gray band represents the material that just sits in a fixed region of space and only moves in time. In the material, the light moves less per unit time in space than in air, which means that its velocity is reduced. The reduction factor is called the refractive index

Fermat assumed—correctly, as we now know—that a transparent material like glass or water reduces the speed of light by the refractive index. The refractive index is a number that depends on the response of the material to light. It may be the same number for all points within a piece of material or the refractive index may vary if the properties of the material vary. Fermat’s principle states that the travel time of light is an extremum. In most cases it is a minimum: the travel time is the shortest. Note that one should not confuse travel time with proper time. By travel time I mean the time light takes to travel as measured by an outside observer, not how light perceives its own time—that would be proper time.

  Scientific Appendix 

137

Refraction of light. The figure shows in a spatial diagram (not a space-time diagram) how light rays are refracted (bent) when entering or leaving a material with a different refractive index. Fermat’s principle explains the light trajectory as the path of the shortest travel time. In the material the light moves more slowly and so light tries various trajectories (dotted lines) to cut its path short there. It cannot be too short, though, for otherwise the paths in air would take too much time. The optimum (solid curve) is the actual path taken

Fermat’s principle has a geometrical consequence, as follows. Since the refractive index reduces the speed of light, the travel time gets longer: the higher the index the longer the time. Therefore the trajectories of extremal time are also trajectories of extremal optical length where length is measured with the refractive index as metric. The trajectories of light are geodesics. Light experiences optical materials as curved spaces. It turns out that the converse is also true: curved space-time appears to light like a transparent material. By holding a piece of glass in your hands you behold a piece of the universe.

A10 Gravity is universal: all matter curves space-time and space-time curvature acts on all matter. But the curved space an optical material appears to establish only acts on light, and usually also only on light of a certain frequency band. (The frequency of light corresponds to the color.) The optical space is differ-

138 

U. Leonhardt

ently curved for different frequencies, because in general the refractive index depends on frequency. So the optical analog of gravity is significantly less universal. Different also are the physical mechanisms underlying the acting geometries in gravity and in optics. For gravity, the geometry is established by optimizing between space-time curvature and the action of all matter, while in optics it is made directly by the response of the material to light. Light is an electromagnetic wave, that is, an oscillation of electric and magnetic fields propagating through space. These fields are described mathematically by a set of equations known as Maxwell’s equations, after James Clerk Maxwell who deduced them in 1861 and 1862. He also discovered that light is an electromagnetic wave. Maxwell’s equations set the scientific foundation for technological applications of electricity, electronics, telecommunications, etc.—the list goes on. Most of modern technology would be unthinkable without Maxwell’s equations, although most people will not know the name of the scientist to whom they are so indebted. It turns out that the analogy between space-time geometries and materials also appears in Maxwell’s equations. This means that the geometrical picture of curved space is not only applicable to the ray trajectories of light, but to all details of the electromagnetic field light is made of. There is one caveat. The analogy between space-time geometries and transparent media is only perfect if the electric and the magnetic responses of the medium are always equal to each other. This is because a pure geometry cannot distinguish between electric and magnetic fields, and so the material must not distinguish between these fields either.

A11 The analogy between general relativity and optics in materials has been fruitful in science and technology. It has inspired a research area known as transformation optics where ideas from general relativity have been borrowed as design concepts for electrical and optical engineering. It has also inspired experiments to explore curved spaces and, in the most extreme case, to make laboratory analogues of black holes. Moreover, it is conceivable that the analogy between space-time geometries and materials might explain some of the mysteries of cosmology. It may shed light on dark energy and demystify dark matter. But here we are primarily concerned with one particular application of optical geometries, the ability to create optical illusions and especially the ultimate illusion: invisibility.

  Scientific Appendix 

139

How can you make something completely invisible? And how can you conceal the fact that something has been concealed? General relativity gives the answer. In general relativity, the geometry of space-time determines how everything, including light, moves. You visualize such a geometry using maps where each point is drawn in coordinates given with respect to a coordinate system. But you can redraw the map in infinitely many different ways, by coordinate transformations. General relativity describes nature, not specific ways of drawing nature. Therefore it must be independent of any coordinate transformation. If I apply a coordinate transformation in one region and consider light going through, then, in my description, the light is completely unaffected outside the transformed region. Coordinate transformations are invisible in the theory. If I now, in my theoretical coordinate transformation, shrink some part of this region to absolutely zero size, then that part, and everything inside, has become completely invisible in my description. The transformation acts like an invisibility device—in theory. In general relativity, these transformations are not real, they occur in the mind of the observer. But in optical materials, spatial transformations can be real. The reason is this: in optical materials, the spatial geometry is made directly by the response of the material at each point in space. So in optics the distortion of a coordinate grid has a physical meaning, in contrast to general relativity.

A12 For optical transformations of space, brought about by suitable materials, it is instructive to distinguish two spaces: physical space and virtual space. Physical space is the space of physical reality. Here space is filled with an optical material of, in general, varying refractive index. As the refractive index varies, Fermat’s principle implies that light rays are curved in physical space. Virtual space, on the other hand, is space solely as seen by light. If we assume that the bending of light in physical space is entirely done by a coordinate transformation, then virtual space undoes this transformation. It appears as the untransformed, original, flat space. In virtual space, light propagates along straight lines. Only the transformation to physical space bends the light, nothing else. This is useful as a design concept for devices, because with suitable transformations one can implement a variety of interesting applications. Consider the transformation shown in the picture below. It specifies the general idea of using general relativity for invisibility. A region of space is chosen, a sphere in the example of the figure, and inside this region another

140 

U. Leonhardt

sphere is optically reduced to the size of a single point. The larger sphere contains the device, the smaller sphere the object or objects to be concealed inside.

Transformation of space. Optical materials appear to change the perception of space; objects (fish) in physical space (right picture) appear at positions (left picture) different from where they actually are. Suppose the medium performs a coordinate transformation from physical space (right) to virtual space (left) and vice versa. The straight coordinate grid of virtual space (left grid) is transformed into a curved coordinate system in physical space (right grid). As the coordinate transformation only changes space within a circle, this circle marks the boundary of the optical material used to transform space. You see that the images of the fish are distorted in virtual space, because the coordinate transformation illustrated here is not uniform. Moreover, the white fish has completely disappeared, because it was swimming within a region of physical space (grey) which, in virtual space, is contracted to a single, invisible point. Such an optical material makes an invisibility device

The next figure shows how light rays are bent without visible consequences to an outside observer. The light goes around the concealed interior of the device and then moves on, as if nothing has happened. All images are carried by light, in particular the background scenery behind the device. As the light is not affected after propagating through the device, it appears to be completely invisible, including everything inside. In short, the transformation device makes a perfect invisibility cloak.

  Scientific Appendix 

141

Bending of light in an invisibility device. In virtual space (left) light rays are straight, in physical space (right) they are bent. The rays go around the invisible interior of the device and recombine as if they had travelled through empty space. This conceals the interior and everything inside it, and also the fact that something has been concealed

A13 Yet there is one minor problem with perfect invisibility: it is impossible. You can see this by following the light ray that just straddles the invisible sphere inside the device. The transformation has made this sphere the size of a point. In virtual space, the light ray straddling the sphere traverses a distance the size of a point. This will take exactly zero time. Yet in physical space, the ray has to go around the sphere. As the device performs just a transformation of space, the propagation time in virtual space must be exactly the same as in physical space. The two spaces are synchronized. This implies that in physical space light must be infinitely fast, which is impossible—at least for a frequency band sufficiently broad to transmit information. No new information can go through the device undisturbed. Perfect cloaking is only possible for a completely fixed background and a fixed frequency (color) of light, which defeats the whole point of invisibility.

142 

U. Leonhardt

Extreme bending. Light rays straddling the invisible interior of the device must go around an extended region of physical space (right) in the time it takes for light to pass through a single point in virtual space (left), which requires an infinite speed of light

Perfect invisibility is impossible, but invisibility that is not perfect, but just good enough, is perfectly possible. One method, that was taken up quickly, is based upon much milder transformations of space. Instead of shrinking a solid object to the size of a point one could—and can—make a voluminous object look flat. Imagine you stand, enclosed by a transparent material, in front of the wall in a picture gallery. Suppose the material is designed such that it makes you look as flat as a picture. Imagine also you wear clothes that perfectly blend in with the wall and you carry a picture frame around your head. Nobody would distinguish you from one of the other pictures. But if you blink or laugh you might frighten the visitors.

  Scientific Appendix 

143

From fugu to flatfish. A coordinate transformation may turn a voluminous object in physical space (fugu) into a flat object (flatfish). Drawing: Maria Leonhardt

A14 Transformation optics has been an exciting subject for scientists and engineers. I hope some of transformation optics has become exciting for you as well. In particular, the fact that many ideas and concepts from general relativity do arise in the mundane world of optics I have found to be profoundly interesting. Who would have thought that one may transform a substantial amount of Einstein’s theory of space-time into Maxwell’s electromagnetism and vice versa? These two great and sympathetic men of science can be transformed into each other, as their portraits illustrate.

144 

U. Leonhardt

Einstein, Einwell, Maxwell. Transformation optics combines ideas from Einstein’s general relativity and Maxwell’s electromagnetism. It particular, it uses transformations of space—like the transformation between Einstein and Maxwell shown in the picture