Incubation in Problem Solving and Creativity: Unconscious Processes 1138551511, 9781138551510

Table of contents :
Cover
Half Title
Title Page
Copyright Page
Contents
Preface
Acknowledgements
1 Problems, problem solving and creativity
Introduction: problems, problems, problems
Solving non-insight problems: forward search and hill-climbing
Problem reduction and means-ends analysis
Solving insight problems: re-structuring
Barriers to insight: set
Further barriers to insight: functional fixity
Comparing insight vs non-insight problems
Representational change theory
Working memory, insight and non-insight problem solving
Impasse → insight sequence: necessary or not?
Generic Parts Technique
Insight processes: conclusions
Creative problems
Creative problem solving: divergent thinking
Incubation?
2 Historical background to the “incubation” concept
Personal accounts
The Wallas model: background
Wallas’s stages of control
Wallas’s Five Stage model in detail
Incubation: validity of personal accounts?
Historical background: concluding comments
3 Early laboratory based studies of incubation
Delayed Incubation effects
Incubation literature reviews: narrative and meta-analytic
Delayed Incubation: post Sio and Ormerod (2007) studies
In conclusion
4 Broad theoretical approaches to incubation: empirical evidence
Introduction
Intermittent work: evidence
Fresh Look: evidence
Unconscious work: evidence
Mind-wandering and incubation
5 Unconscious work: theoretical discussion
The subliminal self hypothesis
The unconscious: yes, it can?
Unconscious combinations: blind variation, selective retention
Mechanisms for blind variation
Chater’s (2018) objections to unconscious work/processing hypothesis
Inspiration: how do solutions suddenly become conscious?
Semantic network modelling
Goal + Associative Network Interaction (GANI) model
6 Sleep on it?
Sleep and its stages
Personal accounts
Empirical studies of sleep effects on problem solving
Methodological notes
Sleep on it? Discussion and concluding comments
7 Overview and conclusions
Waking incubation
Sleep on it?
Waking and sleeping incubation in real life
Gaps for future research
References
Index

Citation preview

INCUBATION IN PROBLEM SOLVING AND CREATIVITY

Can problems be solved by setting them aside or by sleeping on them? Incubation, the process of stopping conscious work on problems for a set period of time, is an integral part of the creative problem solving process. Providing an overview of the main issues, findings and implications of cognitive research on incubation effects in problem solving and creativity, this book argues that incubation is an effective strategy for tackling problems that do not yield to initial solution attempts. Gilhooly reasons that unconscious work is automatic and explores the underlying processes involved in incubation, providing evidence to showcase the major role of unconscious processing in problem solving. Incubation in Problem Solving and Creativity concludes with a discussion of the implications of unconscious work theory for enhanced problem solving, positioning incubation as an effective and important stage in creative problem solving. This book is an invaluable resource for students and researchers of problem solving, creativity and thinking and reasoning as well as for students from all disciplines taking problem solving modules. Kenneth J. Gilhooly is Emeritus Professor of Psychology at the University of Hertfordshire, UK. He is a former Chair of the Cognitive Section of the British Psychological Society (BPS) and has served on the Economic and Social Research Council (ESRC) Research Grants Board and the ESRC College of Assessors.

INCUBATION IN PROBLEM SOLVING AND CREATIVITY Unconscious Processes

Kenneth J. Gilhooly

First published 2019 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN and by Routledge 52 Vanderbilt Avenue, New York, NY 10017 Routledge is an imprint of the Taylor & Francis Group, an informa business © 2019 Kenneth J. Gilhooly The right of Kenneth J. Gilhooly to be identified as author of this work has been asserted by him in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging-in-Publication Data Names: Gilhooly, K. J., author. Title: Incubation in problem solving and creativity: unconscious processes / Kenneth J. Gilhooly. Description: 1 Edition. | New York: Routledge, 2019. | Includes bibliographical references and index. Identifiers: LCCN 2019003366 | ISBN 9781138551510 (hardback) | ISBN 9781138551534 (pbk.) Subjects: LCSH: Problem solving. | Creative ability. | Subconsciousness. Classification: LCC BF449 .G467 2019 | DDC 153.4/3—dc23 LC record available at https://lccn.loc.gov/2019003366 ISBN: 978-1-138-55151-0 (hbk) ISBN: 978-1-138-55153-4 (pbk) ISBN: 978-1-315-14761-1 (ebk) Typeset in Bembo by codeMantra

CONTENTS

Preface Acknowledgements

viii ix

1 Problems, problem solving and creativity 1 Introduction: problems, problems, problems 1 Solving non-insight problems: forward search and hill-climbing 3 Problem reduction and means-ends analysis 7 Solving insight problems: re-structuring 8 Barriers to insight: set 11 Further barriers to insight: functional fixity 12 Comparing insight vs non-insight problems 12 Representational change theory 14 Working memory, insight and non-insight problem solving 17 Impasse → insight sequence: necessary or not? 18 Generic Parts Technique 18 Insight processes: conclusions 19 Creative problems 19 Creative problem solving: divergent thinking 22 Incubation? 24

vi Contents

2 Historical background to the “incubation” concept 25 Personal accounts 25 The Wallas model: background 31 Wallas’s stages of control 34 Wallas’s Five Stage model in detail 35 Incubation: validity of personal accounts? 37 Historical background: concluding comments 43

3 Early laboratory based studies of incubation 45 Delayed Incubation effects 46 Incubation literature reviews: narrative and meta-analytic 49 Delayed Incubation: post Sio and Ormerod (2007) studies 51 In conclusion 52

4 Broad theoretical approaches to incubation: empirical evidence 53 Introduction 53 Intermittent work: evidence 56 Fresh Look: evidence 57 Unconscious work: evidence 58 Mind-wandering and incubation 63

5 Unconscious work: theoretical discussion 67 The subliminal self hypothesis 68 The unconscious: yes, it can? 69 Unconscious combinations: blind variation, selective retention 71 Mechanisms for blind variation 72 Chater’s (2018) objections to unconscious work/processing hypothesis 73 Inspiration: how do solutions suddenly become conscious? 74 Semantic network modelling 76 Goal + Associative Network Interaction (GANI) model 79

6 Sleep on it? 84 Sleep and its stages 85 Personal accounts 86 Empirical studies of sleep effects on problem solving 92 Methodological notes 100 Sleep on it? Discussion and concluding comments 103

Contents  vii

7 Overview and conclusions 106 Waking incubation 106 Sleep on it? 109 Waking and sleeping incubation in real life 109 Gaps for future research 110

References Index

113 125

PREFACE

Can it really be true that problems can be solved by setting them aside (waking incubation) or by sleeping on them (sleeping incubation)? And if so, how do these apparently mysterious “incubation” effects arise? This book aims to set out the main issues, findings and implications of cognitive psychological research on incubation effects in problem solving and creativity. It will be argued that research supports the basic utility of incubation as an effective strategy for tackling problems that do not yield to initial solution attempts. Having established the benefits of waking incubation, the next steps are to address the underlying processes, and I go on to examine the main theories that seek to explain waking incubation. Are waking incubation effects due to the forgetting of misleading approaches, to intermittent conscious work or to unconscious processing? Overall, I conclude that research findings indicate a major role for unconscious processing. Drawing on previous analyses and accepted principles in cognitive science, I propose that unconscious processing is automatic but with a major role for goals in boosting initially unconscious results into consciousness. A mechanism in terms of spreading activation is outlined. “Sleeping on it” is a form of incubation which is often suggested. Is it also good advice? I review the evidence from personal accounts and laboratory studies which suggest that it is indeed often useful. Waking and sleeping forms of incubation are discussed as complementary forms of processing that can both contribute to effective problem solving and creativity.

ACKNOWLEDGEMENTS

I would like to thank very much my long time collaborator, George ­Georgiou, for his role in our planning and carrying out much of the e­ mpirical work that has informed this book. I would also like to thank other researchers in the field who have discussed problems in understanding incubation with me over the years and have helped shape my views, without necessarily agreeing with me; in particular, and in alphabetical order, Linden Ball, Lindsey ­Carruthers, Jane Garrison, Penelope Lewis, Carola Salvi, Miroslav Sirota, Frédérick Vallée-Tourangeau and ­Margaret Webb.

1 PROBLEMS, PROBLEM SOLVING AND CREATIVITY

Introduction: problems, problems, problems Since our focus is on the possible effects of setting problems aside, generally known as “incubation”, let us start by defining “problems” and outlining the main features of problems. Over 70 years ago, Karl Duncker (1945) gave a useful definition of a problem as a situation in which an organism has a goal but does not know how to reach that goal. So, if a person with no knowledge of car mechanics has the goal of starting a car and finds turning the ignition key yields only a “clunk” sound without the engine firing, then that person will have a problem. A skilled car mechanic who has the required knowledge would not have a problem. Of course, problems come in many shapes and sizes, but it seems that all problems have three main components. These are (1) a goal, (2) a starting state of affairs in which the goal is not met and (3) a set of possible actions that if applied in the right order could change the situation to achieve the goal. Although we can say that all problems share this common abstract structure, it is also true that problems can be classified in various ways. One classification is into those problems in which all the elements of the problem, the starting state, the goal and the actions available for moving from the starting state to the goal, are well-defined or completely specified as against problems where some or all elements are ill-defined or not completely specified (Reitman, 1964; Simon, 1973; Lynch et al., 2006; Reed, 2016). A chess problem is a prototypical example of a well-defined problem, in which the starting state is given by the

2  Problems, problem solving and creativity

layout of standard pieces on the standard board, the goal is well-defined (say, “Checkmate for White in three moves”) and the means available are specified by the legal moves of the pieces in the game. On the other hand, a problem may be very ill-defined, such as that of “Improving the quality of life in this country”, in which the starting state, the goal state and the means available are not at all well-defined. In ill-defined problems, it does seem likely that an initial step will be to try to convert the problem into a better defined one by trying out possible specifications of the ill-defined components (Weisberg, 2006, p. 139). In the problem of “Improving the quality of life”, some of the missing details could be filled in by deciding on a particular way of measuring quality of life. One could try using a well-established questionnaire measure, such as the World Health Organisation Quality of Life (WHO-QOL) questionnaire (WHO-QOL group, 1995), and that would help specify the starting state (e.g. as the mean score on the WHO-QOL for a large representative sample of people living in the country), and the questionnaire could be used to assess any effects of interventions as bringing about progress to the goal or not (e.g. has an intervention led to a significant change in WHO-QOL scores in the desired direction?). A second way in which problems can vary is in requiring extensive expert knowledge (i.e. “knowledge rich” problems) or being within the scope of any normally educated literate adult (i.e. “knowledge lean” problems). The typical laboratory puzzle, such as an anagram (e.g. what word has been scrambled to make the string “rpolbme”?), is a knowledge lean problem. This means that it can be tackled within a reasonable time by anyone of a large population of participants. Knowledge rich problems, such as problems arising in running a nuclear power station, diagnosing car problems, flying a passenger plane or treating a rare disease, can only be tackled by very small numbers of highly trained individuals (“experts”). Knowledge rich problem solving is less easily open to laboratory research than knowledge lean problem solving. Nevertheless, there is a large and growing literature on expertise effects in problem solving where experts’ approaches and strategies are contrasted with those of beginners (novices) and people with intermediate levels of knowledge between novices and experts (­Ericsson et al., 2006). Another way of dividing problems is into those that can be solved by straightforward search processes without any need to re-interpret the problem statement and those which require re-interpretation or “re-structuring” of the problem. An example of a problem that could be solved by routine search is an anagram; for example, by trying out

Problems, problem solving and creativity  3

systematically possible re-arrangements of the letters “ccpteno”, one could sooner or later find the scrambled word “concept”. Some problems, however, do typically induce a misleading representation which then needs a re-interpretation or re-structuring. For example, “How could a man marry 30 women in one month and break no laws against bigamy?” Here the typical interpretation of the word “marry” as “becoming married to another person” is misleading. “Marry” here must be re-interpreted as “causing others to become married”. Thus, the man is authorised to conduct marriages. Another example is “How could a man walk over the surface of a deep, mile wide lake without any floatation devices or aids?” This problem requires the solver to move from a default representation (at least in non-Arctic regions) of the water in the lake as being in a liquid state and to represent the water instead in a solidly frozen state. Such problems, which typically require re-structuring or re-interpretation, are often labelled “insight” problems. Once the appropriate re-structuring occurs the solution is immediately understood. Problems that are typically solved without re-structuring are often labelled as “non-insight” problems. The classifications into “insight” and “ill-defined” tend to overlap in that ill-defined problems need initial structuring and often re-structuring, and so tend to be classifiable as “insight” problems. However, some insight problems are well-defined in terms of starting state, goal and means available, such as the nine-dot problem, where the starting state is given (a square 3 × 3 array of dots), the goal state is specified (connect dots by four straight lines without lifting pen from paper) and the means available are specified (draw four straight lines without lifting pen from paper to connect dots).

Solving non-insight problems: forward search and hill-climbing How are problems typically solved? Let us start with non-insight tasks as a simpler case than insight problems. For well-defined problems, in which the starting state, the goal state and the available actions are all completely specified, a complete systematic search is, in principle, an algorithmic way to be sure of solving, without changing the initial problem representation. The conceptually simplest approach to actually performing a complete search is to systematically generate all the possible states that could be reached from the starting state by applying all possible actions or moves from the starting state and keep generating new states from

4  Problems, problem solving and creativity

each new state generated until the goal state is reached – whereupon the problem is solved. If the problem is insoluble, the whole problem space would be generated. This complete search approach is known as breadthfirst search and in theory is a “magic key” to solve all well-defined problems! Why then are so many well-defined problems unsolved, such as “Is chess a game that White should always win, or is it a game that should always be drawn, if both players play perfectly?” Unfortunately, problems of any real scale, such as the chess problem, quickly involve astronomically vast problem spaces with more states than atoms in the universe and cannot realistically be searched completely. Even the humble noughts-and-crosses or tic-tac-toe game has a problem space of some 255,000 states. Part of the space of noughts-and-crosses (tic-tac-toe) is shown in Figure 1.1. In this game, players alternately place Xs or Os in the 3 × 3 grid until one player has an unbroken line of their symbols, or the grid is full (a draw). If both adversaries play perfectly, a draw will always result … but this is not immediately obvious. People have very limited working memories to use in exploring problem spaces without memory aids such as paper and pencil, and we tend to use shortcut methods known as heuristics to narrow and focus our searches. (Heuristics aid problem solving but do not guarantee solutions.) A typical heuristic is that known as hill-climbing. With this approach the solver assesses all possible moves a limited depth ahead, say going just one step ahead, choosing the move which is evaluated as

X

X

FIGURE 1.1 

X

O

X

O

X O

X

O

 artial problem space for the game of noughts-and-crosses (or P ­t ic-tac-toe) after two moves.

Problems, problem solving and creativity  5

looking to be nearer to the goal (getting warmer!). The process repeats until the goal is reached or until a state is reached from which no further progress is possible. Should such an impasse be reached the person can back up and try alternative routes, avoiding the impasse state. The hill-climbing method derives from the real world problem of finding a peak when climbing a hill in a thick fog; in this situation, trying out one step in each of the four main directions, North, South, East and West, and picking the step that reaches the highest next point and repeating the process will lead to a peak. It may be a false peak if you have started up a foot-hill as against the main hill and so is not guaranteed to solve, but it will often be useful. Using a hill-climbing heuristic seems to underlie the difficulties that participants have with a frequently studied laboratory problem known as the Hobbits and Orcs problem (Thomas, 1974). The task is to get three Hobbits and three Orcs across a river. The only way to cross is by a small boat that can carry only one or two passengers at most. However, there must be at least one passenger in the boat for it to cross, and most importantly, you have to avoid Orcs outnumbering Hobbits on same side of river – the Orcs will eat the Hobbits if they outnumber them (based on Tolkien, 1966). The complete problem space for the Hobbits and Orcs problem is shown in Figure 1.2. The space of possible states in this problem is quite small, comprising just 15 states, and the minimum path from starting state to goal state is 11 moves long. However, typically participants take around 22 moves rather than just 11. There is a strong tendency to get involved in unnecessary loops and backtracks – going round in circles! Some of the looping probably arises as a result of hill-climbing. For instance, in State 5 of the problem space, going to State 4 looks attractive as that has more creatures on the target side, but it puts the solver into a loop. A further difficulty is often experienced at State 8, where the solver has four out of six creatures on the target side. Difficulty here most likely arises because people feel they are making good progress (the problem seems to be 67% solved!) and are reluctant to make a detour, moving away from the goal, which is the best move. Moving to State 9, where only two creatures are on target side as against four on the target side, looks very unattractive. That is, people typically are using a hill-climbing heuristic, which causes difficulties at State 8 because at that state, they have to detour and go further from the goal (from only two more to move, to four more to move) in order to progress, and that goes against a pure hill-climbing strategy.

2.HHH OO

BOAT O

1. Start BOAT HHH OOO 3. HHH O 4.

HH OO

5. BOAT HHH OO 6.

HHH

BOAT OOO

8. H O

OO

BOAT HH OO

9. BOAT HH OO

H O

10. OO

BOAT HHH O

11. BOAT OOO

HHH

12. O

BOAT HHH OO

13. BOAT O 14. OO BOAT

FIGURE 1.2 

BOAT H O O

7. BOAT HHH O

15. Goal

BOAT OO

H

HH OO

HHH O BOAT HHH OOO

Problem space for Hobbits and Orcs.

Problems, problem solving and creativity  7

Problem reduction and means-ends analysis In addition to forward search of a problem space, from the starting state onwards, using limited look-ahead and hill-climbing, well-defined problems can often be tackled by problem reduction, also known as means-ends analysis or sub-goaling. This approach involves breaking the overall problem into smaller independent sub-problems and if need be dividing the ­sub-problems into sub-sub-problems, and so on, until a sub-sub-…-subproblem is reached that can be solved in a single step. A real life example would be making travel plans, say to travel from London to New York. The overall goal is to reduce a long distance. That can be tackled by means of a plane or a boat. Say Plane is chosen; there is now a sub-problem of “getting on board a plane to use it”. This requires solving a “ticket getting sub-sub-problem” and a “getting to the airport sub-sub-problem”. The airport sub-sub-problem could be solved by catching a train to the airport. That, in turn, raises the sub-sub-sub-problem of getting to the train station, which may be solved by walking, in which case that action can be carried out. Once at the station, the train can be caught, and then at the airport, the plane can be accessed. This problem reduction approach is widely used in real life and has been shown in laboratory studies of artificial tasks such as the Tower of Hanoi. This task involves moving a tower of disks from the leftmost peg to the rightmost peg with a middle peg available. Discs can only be moved one at a time, and a larger disc cannot be put on top of a smaller disc. The number of moves required grows quickly with the number of discs (N) as 2N − 1. So the small three disc example shown in Figure 1.3 needs 7 moves. A fivedisc version would require 31 moves, a six-disc version 63 moves and so on. 3 DISKS (1) A

B

A

C

(2)

B (4)

(3) A

B

C

A

B

C

(6)

(5) A

FIGURE 1.3 

B

C

C

A

B

C

A

B

C

(7) A

B

C

Three disc Tower of Hanoi problem reduction graph.

8  Problems, problem solving and creativity

To make the problem manageable, people generally come to apply problem reduction and first tackle the “N-1 problem” of clearing the top of the largest disc by moving the N-1 discs on top of it to the middle peg. That generates an “N-2 sub-problem” of clearing the second largest disc so that it can go on the middle peg and so on. Overall, the routine methods of forward search in a problem space or problem reduction can work well if the problem representation is appropriate, which will usually be the case for non-insight tasks. But when the problem representation is not helpful for solving, as with insight tasks, what solving processes might be used?

Solving insight problems: re-structuring The Gestalt psychologists in the 1920s regarded problem solving as very much like perceiving a new pattern in an ambiguous picture (e.g. the ­Faces-Vases in Figure 1.4) or seeing a structure in a previously unstructured collection of blobs (Figure 1.5). The Gestalt approach to problem solving led to a strong focus on problem re-structuring and insight – which in their view is a re-structuring that gives a sudden understanding of how to solve the problem. They emphasised not just sudden solution, which might arise by pure trial-and-error exploration of possible moves, but understanding of why the solution worked. A dramatic real life example of insight problem solving with ­re-structuring in a life or death situation is given by the following story (Lehrer, 2008). On August 5, 1949, 15 forest firefighters parachuted into the steep sided Mann Gulch in Montana, USA. After a short time, the wind changed, and suddenly the men were almost surrounded by rapidly advancing fires. They began to flee up the dry grass covered slope to the ridge and safety. However, very soon it became clear that they could not outrun the flames.

Figure 1.4 

Reversible Face-Vases picture (Rubin, 1915).

Problems, problem solving and creativity  9

FIGURE 1.5 

 an you re-structure the blobs to see a meaningful image? ( James, C 1965).

What to do? The lead firefighter, Wagner (“Wag”) Dodge, suddenly realised a solution. He lit a fire in the grass in front of him and let it burn up the slope, driven by the prevailing wind. He then lay down in the burned-out area, covered himself with his coat and waited for the main fire to go past around the perimeter of the burned out area that he had created. Dodge tried to get his men to join him, but none did. As a result Dodge survived, but 13 of the other 14 crew did not. Dodge’s solution required a major re-structuring of the problem from one of moving to a space safe from fire by fleeing to creating a safe space – by using fire to escape from fire! Less dramatically, but using a realistic task, Karl Duncker explored insights while solving the X-ray problem (1945) in a laboratory setting. Participants were told that a medical case has a life-threatening tumour that cannot be operated on (see Figure 1.6). Although X-rays can destroy the tumour, X-rays strong enough to destroy the tumour will also destroy healthy tissue. Participants thought out loud while working on the task of destroying the tumour without destroying healthy tissue, and the resulting think-aloud records were analysed. The typical insight solution, focusses a number of weak rays on the tumour. • Karl Duncker : X-ray problem (1945) • Inoperable tumour; • X-rays can destroy tumour; • Sufficient quantity will destroy healthy tissue;

FIGURE 1.6 

Possible solution to Duncker’s X-ray problem.

FIGURE 1.7 

Typical structuring and re-structuring during attempts at X-ray problem.

Problems, problem solving and creativity  11

The “Insight” solution to the X-ray task was generally not immediately apparent, and typically the problem was solved only after a number of approaches had been tried. From the think-aloud records it emerged that solvers structured and re-structured the problem repeatedly, e.g. by trying approaches that protected healthy tissue, bypassed healthy tissue, delayed the effect of rays or used weak rays that converged on the tumour. The typical pattern of re-structurings is indicated in Figure 1.7.

Barriers to insight: set A number of factors can delay or prevent insight, and a major factor is known as set. Set is the tendency to solve problems in one particular way, using a single inflexible approach. In other words when you suffer from set, your thinking is stuck in a rut. The nine-dot problem is a famous example of set. The task is to connect the nine dots with four connected straight lines without lifting your pencil from the page as you draw (see Figure 1.8). Very few people solve the nine-dot problem within a reasonable time, say 20 minutes, when first presented with it. There is a very strong set to stay within the square shape, although that was not a restriction stated in the instructions. However, the problem can only be solved by going outside the square. One must literally think outside the box to solve this problem. As well as layout, as in the nine-dot problem, affecting set, training can induce strong sets. The classic example of training induced set is provided by Luchin’s Water Jar Problem (1942). Participants are to show how to obtain desired amounts of water, given an unlimited source and three jars of different capacities. The first five problems can only

FIGURE 1.8 

 ine-dot problem. Connect the nine dots by four straight lines N without raising pen from surface.

12  Problems, problem solving and creativity

be solved by filling jar B, using jar C twice and jar A once to draw off excess water, i.e. following the formula B−2C−A. People persisted in solving problem numbers 6 and 7 in the same way – missing much easier solutions that could have been used (A−C, A+C) in these problems. If participants were only given the short solution problems 6 and 7, they did not miss the easy solutions. Overall, the training series 1–5 clearly induced a strong set effect when people came to the easy problems, leading them to apply long inefficient methods where much shorter and simpler solutions were available.

Further barriers to insight: functional fixity A second type of barrier to insight is known as functional fixity and is a tendency to use objects and concepts only in their common ways. Maier’s (1931) two-string problem illustrates this tendency. The problem is to find a way to hold on to the two strings hanging from the ceiling at the same time using a set of common objects, such as brushes, screwdriver and hammer. To solve, the participant has to use some of these objects in an unusual way, viz. as weights to swing the ropes like pendulums. A second example of functional fixity arises in Duncker’s (1945) candle problem. The task is to find a way to fix a candle to a door so that the candle will burn securely. The materials given are a box of tacks, candles and matches. The solution is to empty the box of tacks, tack the tray of the box to the door to use it as a platform, then light the candle and use wax drippings to set the candle standing securely in the box tray. Duncker reported on the basis of a small study that the task became significantly easier if the box was presented empty. A larger study by Adamson and Taylor (1954), with a Control group (n = 28) given the Box empty and an Experimental Group (n = 29) given the box as a container, replicated Duncker’s finding, with 86% of the Empty Box group solving as against 41% of the Box Full group solving (p < 0.001 on Chi-Square test).

Comparing insight vs non-insight problems In non-insight problems, solutions can be reached by searching forward from the starting state or by splitting the overall problem into ­sub-problems and those sub-problems into sub-sub-problems (i.e. problem reduction or means-ends analysis). Some researchers have asked, “Are insight problems solved in demonstrably different ways to non-insight problems?” The

Problems, problem solving and creativity  13

­ estalt view is that YES, insight problems are special in that they require G restructuring and sudden understanding (insight) which are not involved in non-insight tasks. This is the special process view of insight problem solving. However, Weisberg (2006) countered the Gestalt view and argued that insight problem solving is not actually special but arises from normal processes of search and problem analysis without any need for special or unusual processes. This is sometimes referred to as the business-as-usual view of insight problem solving. Metcalfe and Weibe (1987) carried out a relevant study comparing ­self-reported feelings of warmth or closeness to solution as participants worked through insight as against non-insight problems. The results indicated that participants in non-insight (also known as “incremental” or “routine”) problems reported steady increases in feeling warm (i.e. near solution) as they worked on the task leading up to solution (see Figure 1.9). In contrast, participants solving insight problems reported no changes in warmth until just before reporting solution. This is the pattern that the Gestalt approach, with its claim that insight solving involves a special process, would expect. Warmth ratings leading to solution 8 7

Modal Warmth

6 5 4

Incremental Insight

3 2 1 0

FIGURE 1.9 

-60

-45 -30 -15 Seconds before solution

0

 armth ratings before solutions on insight and incremental probW lems (after Metcalfe and Weibe, 1987).

14  Problems, problem solving and creativity

In a further study on this question, Jung-Beeman et al. (2004) used Remote Associates Test (RAT) items with functional Magnetic Resonance Imaging (f MRI) to measure activity in different brain regions during solving. In the RAT task participants are given problems as follows: What word links “boot”, “summer” and “ground”? (Answer: “camp”). Jung-Beeman et al. (2004) proposed two broad ways to solve such RAT items. One way is by systematically searching associations to each word until an associate is found that links to all three words. So, one might try associations to “boot” first, retrieve “shoe” and “lace”, and find that those words did not link to “summer” or “ground”. Eventually one might retrieve “camp” as an associate to “summer” and find it also associates to “boot” and “ground”, thus being the solution. A second way is by allowing the solution to emerge and come to mind without systematic search (i.e. by an insight route). Participants had to report whether each item was solved by a systematic search of associations or by sudden insight (after being given the following criteria for insight: (1) the solution came suddenly and completely (2) without being aware of any searching through possibilities, and (3) with a strong sense that it was correct). The fMRI results showed significant differences in right hemisphere activation between insight and non-insight solutions and so supported the special process view of insight solving: that insight solutions involve different processes from non-insight routine search solutions.

Representational change theory A problem with the classic Gestalt approach to problem solving is that the concepts involved are rather vague and ill-defined. What actually is “restructuring”?, for example. Ohlsson (1992, 2011, 2018) has attempted to rectify these problems in a neo-Gestaltist cognitive theory of problem solving called the Representational Change Theory. The theory proposes six main stages with associated processes and experiences as indicated in Table 1.1. In the first stage the problem’s starting state and goal state are encoded. In a typical insight problem, most participants will form an encoding or representation which prevents or at least slows down the solution; for example, in the “Lake” problem, most people will assume

Problems, problem solving and creativity  15 TABLE 1.1  Stages of Insight

Stage

Process

Experience

1. Problem perception 2. Problem solving 3. Impasse 4. Restructuring

Encodes problem

Grasps problem

Heuristic search/planning Searches for new encoding Finds new encoding through: a.  Elaboration b.  Re-encoding c.  Constraint relaxation Operator retrieval breaks impasse Mental lookahead completes path to solution

Does what comes to mind Experiences blank mind None

5. Partial insight 6. Full insight

“Sees” new option “Sees” entire solution

Source: Ohlsson (1992).

that the water in the lake is in a liquid state. Problem solving begins by trying out possible sequences of actions, mentally or overtly, depending on the task. Ohlsson used the term “operator” here to refer to possible actions that could change the problem state. If the problem has not been structured appropriately, no appropriate actions or operators are cued by its representation, and eventually progress halts; at this point, the person experiences an “Impasse” and, in the model, a set of heuristics called “switch when stuck” come into play. These heuristics evoke elaboration, re-encoding and/or constraint relaxation, any of which can lead to re-structuring. In more detail, the three re-structuring processes are: 1. Elaboration: adding new information to the problem representation (e.g. the presence of the box, as against its contents, may be initially unnoticed in the candle problem, and noticing it would add to the problem representation). 2. Constraint relaxation: assumed constraints on the problem representation are removed (e.g. dropping the assumption in the nine-dot problem that lines cannot go outside the square field of dots). 3. Re-encoding: a part of the problem is re-interpreted in a different way (e.g. a pair of pliers are re-interpreted as a weight in the twostring problem to overcome functional fixity; the water in the lake problem is re-interpreted as frozen rather than liquid).

16  Problems, problem solving and creativity

If all goes well, the re-structuring leads to retrieval of a useful operator or action and to partial or complete insight into the solution path. In Ohlsson’s original model (1992) these re-structuring processes are seen as unconscious and occurring during the impasse. It could be that some solvers will consciously adopt such processes, as Kaplan and Simon (1990) suggested, to search deliberately for alternative representations. In a more recent version, Ohlsson (2011) suggests an automatic process, whereby initial representations lose activation with repeated failure, and this allows alternative representations to gain activation (through re-distribution of activation) and become dominant. Knoblich et al. (1999) investigated the role of the constraint relaxation part of the Representational Change Theory and the role of re-encoding in the form of Chunk Decomposition. Both Chunks and constraints can be relatively tight (difficult to change) or loose (easy to change). Participants were presented with match-stick algebra problems in which Roman number equations are presented using match-sticks to make the characters, and one match is to be moved to make each equation correct. For example VII = II + III It was expected that it would be fairly easy to decompose the “VII” chunk and move one match from “VII” over to add to the “II” so that the solution is VI = III + III This relatively simple type of problem was labelled a Type A Problem. A problem involving a tighter constraint (Type B problem) is IV = IV + IV In this it was expected that it would be difficult to decompose the “+” and change it to “=”, with the solution IV = IV = IV Knoblich et al. argued that our experience with arithmetic means that we find it easier to break the constraint on changing a value (such as VII) in an equation than to change an operator (like +) or arbitrarily move the equals sign in an equation. Therefore constraint relaxation predicts that people should be able to solve the first kind of problem (Type A) more easily than the second (Type B). Results in Figure 1.10 matched the predictions of Ohlsson’s Representational Change Theory. Within 2 minutes 95% had solved Type A problems, but only around 40% solved Type B problems in the same time (see Figure 1.10).

Problems, problem solving and creativity  17 Cumulative % solved. Type A : VI = VII + I Type B : IV = III - I 100 90 80

% solution

70 60 50 40 30 20 Type A

10

Type B

0 1 min FIGURE 1.10 

2 min

3 min

4 min

5 min

K noblich et al. (1999) results for loose (Type A) and tight constraint (Type B) problems.

Working memory, insight and non-insight problem solving Insight processes as envisaged in the Representational Change Theory are assumed to operate at an unconscious level and so would not load working memory (Baddeley, 2012). Working memory is seen as a flexible short term store for information held temporarily during processing and, although generally quite limited in capacity, does show individual variation. Some support for the view that insight processes do not load working memory comes from individual difference studies examining correlations between working memory measures and performance on insight as against ­non-insight tasks. If insight solving processes do not load working memory then we would expect lower correlations between working memory and performance on insight than on ­non-insight tasks (which it is agreed generally do load working memory). Gilhooly and Webb (2018) reviewed this literature and on the basis of eight individual difference studies with a combined N of 741 found a small (around 0.10) but consistent average difference between the key correlations in the direction predicted by the

18  Problems, problem solving and creativity

special process hypothesis. Another approach is to examine the effects of impairing working memory on solving insight as against non-insight problems. If insight does not involve working memory, such manipulations should have little impact on insight tasks. In one such manipulation study Jarosz et al. (2012) reported that alcohol consumption, presumed to impair working memory, actually facilitated performance in RAT problems and raised the rate of self-reported insight solutions. Similarly, Reverberi et al. (2005) surprisingly found that 35 ­patients with focal damage to the lateral frontal cortex (implicated in working memory function) solved difficult match-stick arithmetic problems at a significantly higher rate (82%) than 23 matched controls (43%). Overall, there is evidence that working memory has a reduced role in insight as compared to ­non-insight problems.

Impasse → insight sequence: necessary or not? Weisberg (2015, 2018) has contested some aspects of the neo-Gestalt view, and in particular the idea that there is an inevitable “impasse → insight” sequencing of processes. He argued that multiple paths to re-structuring are possible, including paths generated by conscious analytic processes as well as by automatic routes. Fleck and Weisberg (2004) analysed think-aloud records from participants attempting insight tasks. They estimated that relatively few (6%) showed the “impasse to insight” sequence assumed in the neo-Gestalt approach. Sudden re-structuring sometimes occurred without a preceding impasse, and re-structuring was sometimes arrived at analytically by re-examining the problem statements. Similarly, Cranford and Moss (2012) took think-aloud records, while participants tackled RAT type problems, which – as noted in Jung-Beeman et al. (2004) – can be solved either with sudden insight or through deliberate searching through item associations. They found insight (or “Aha!”) solutions often occurred without a preceding impasse.

Generic Parts Technique Explicit re-encoding has been proposed by McCaffrey (2012) as an effective means of overcoming functional fixity in his Generic Parts Technique (GPT) to aid problem-solving. This technique seeks to overcome functional fixity by having participants explicitly list features of problem materials, which leads to noticing of obscure features and using obscure features as a common aspect of innovative solutions.

Problems, problem solving and creativity  19 CANDLE

WICK

STRING ONLY

WIRE CORE

LEAD

FIGURE 1.11 

WAX

SCENTED UNSCENTED

COPPER

Generic parts diagram breaking a candle into components.

For example consider the two rings problem, in which the goal is to fasten two heavy steel rings using only a long candle, a match and a 2-inch cube of steel. A control group tackles the problem in the normal way. A GPT group is instructed to describe the objects in the problem in terms of parts and parts of parts, and to form a generic-parts diagram which makes explicit the properties of the objects and their component parts, as in Figure 1.11. McCaffrey (2012) reported very marked benefits for the GPT method (c. 80% solution rates vs 50% in controls) over eight insight problems, p  Insight

Unconscious Associative Network

Goal

FIGURE 5.2 

| | Conscious | | | | | Working | | Memory | | | | | | | | |

 ANI model. While working on distracting tasks, nodes related G to distracting tasks are most active.

Unconscious work  81

Schematic of Goal + Associative Network Interaction in Incubation -> Insight

Unconscious Associative Network

Goal g

FIGURE 5.3 

s

| | Conscious | | | | | Working | | Memory | | | | | | | | |

 ANI model. Set aside goal (g) and solution related material (s) G become active below threshold.

Schematic of Goal + Associative Network Interaction in Incubation -> Insight ________________________________ Unconscious Associative Network

Goal g

FIGURE 5.4 

s

| | Conscious | | | | | Working | | Memory | | | | | | | | |

 ANI model. Below threshold activation growing through posiG tive feedback loops, but distracting task information still dominant.

82  Unconscious work

Schematic of Goal + Associative Network Interaction in Incubation -> Insight

Unconscious Associative Network

Goal g s

FIGURE 5.5 

| | | | | | | | | | | | | | | | | |

Conscious

Working Memory g Aha

s

 ANI model. Set aside task goal and solution related nodes beG come activated above consciousness threshold and displace distracting task info from working memory. Aha experienced.

Implicit in the model is the notion that nodes in the network compete for limited pool of activation…so if nodes a, b, c are high in activation, competing nodes x, y, z are low in activation and vice versa. Also, it is implicit in the model that the system cycles through activation patterns where Tn represents the entire network of connection strengths and activations at time n, T1 → T2 → T3 → … TN→ TN+1→ and so on … according to rules about maintenance, decay and transmission of activation from node to node. The idea of a separate WM network/store, as represented in Figures 5.2–5.5, is attractive for purposes of holding temporary re-organisations that become stored permanently (learned) if they meet goals.

Evaluation and limitations The approach put forward here, in terms of spreading activation and goal representations, seems promising. However, it is most applicable to relatively small scale but knowledge rich problems such as divergent thinking

Unconscious work  83

creative tasks (e.g. generate new uses for familiar objects, like shoes, bricks etc.) or small scale insight problems such as found in the RAT and similar problems. Further work is needed to develop the present approach for other knowledge lean problems on the one hand and for large scale real life problems on the other hand.

6 

SLEEP ON IT?

A common suggestion for handling impasses in problem solving is to put the problem aside, by “sleeping on it”, rather than by consciously undertaking a different task and allowing unconscious incubation processes to take effect while still awake. In real life, a sleep period will intervene for any problem that is not solved within a single waking day and so such problems will be open to possible effects of sleeping on them. From a practical as well as a theoretical point of view, it is important then to consider sleep effects. As will become apparent, the everyday word “sleep” covers a complex mix of states or stages extended over what is usually a significant period of time. How sleep in its various stages might affect problem solving and how cognitive processes during sleep are related to cognitive processes that occur during waking incubation and during waking conscious problem solving are currently contentious issues. To review the research on sleep and problem solving, I will first outline the main stages of sleep, go on to present some evidence from personal accounts of sleep and problem solving, then discuss data from surveys and experiments, and finally consider how cognitive processes during sleep might relate to processes during normal waking incubation and normal conscious problem solving. First, let us briefly outline the main features of sleep.

Sleep on it?  85

Sleep and its stages It is useful to distinguish transitional states of consciousness between full waking alertness and sleep. Going from full alertness to sleep and back again are not all-or-none events like an electric light suddenly going off and back on again. There is an initial hypnagogic stage in between full alertness and sleep and at the other end of the sleep period, a hypnopompic stage between sleep and full alertness. Since there are often brief awakenings during a night of sleep these stages may occur briefly more than once in a prolonged sleep period (see also Lockley & Foster, 2012, for more details on sleep). Sleep involves two broad phases or stages, viz. rapid eye movement (REM) and nonREM sleep. If people are woken from REM sleep they will nearly always report that they were dreaming. REM sleep involves bursts of rapid horizontal and vertical eye movements, loss of muscle tone and “desynchronised” electroencephalogram (EEG) activity, comprising high frequency, small amplitude, beta waves. The EEG pattern in REM sleep is strangely similar to that observed during wakefulness (hence REM sleep being labelled “paradoxical” sleep, see Peigneux et al., 2010, p. 167). REM sleep is most common in the second half of the normal sleep period and predominates at the end of sleep. Approximately 75% of sleep is nonREM sleep. Dreams are estimated to occur in about 40% of the nonREM sleep periods but tend to be shorter, less vivid, simpler and less bizarre than dreams in the REM periods. Until around 2010 most researchers followed a classification of sleep stages due to Rechtschaffen and Kales (1968), according to which nonREM sleep involved four main stages of increasingly slow wave EEG activity (theta waves, spindles, K-complexes and delta-theta wave mixtures), preserved muscle tone and no REMs. However, more recently, researchers have generally followed the American Academy of Sleep Medicine (AASM) scheme, as set out by Iber et al. (2007), which merges Rechtshaffen and Kales’s stages 3 and 4 into one stage, stage 3. Following the AASM scheme, stage 1 nonREM sleep occurs first, then sleep progressively moves through stages 2 and 3. Stage 3 nonREM sleep is characterised by Slow Wave Sleep (SWS) – which involves a mixture of delta and theta EEG waves. From stage 3, SWS, there is a switch back to nonREM stage 2, before a period of REM sleep. A cycle (nonREM stages 2-3-2-REM) then typically repeats around every 90 minutes until wakefulness. Beneficial effects of sleep periods on learning and memory have been shown for a range of tasks. For example, in the perceptual learning KarniSagi task, in which participants discriminate between very briefly presented

86  Sleep on it?

stimuli in which subtle differences are present (e.g. slanting lines in field of horizontal lines) or not, performance correlated strongly with levels of interpolated REM and nonREM sleep, between training and testing. The greatest improvements were found when both deep early night nonREM and long late night REM sleep had occurred. This suggests a two-step consolidation process with an early SWS-dependent process and a later REM-dependent process (Hobson, 2005). In the more complex task of spatial (maze) learning, studies with rats have indicated that neural activation patterns specific to the training period re-emerge at sleep onset as if the daytime experience was being repeated. Similarly, studies of humans learning the video games Tetris and Alpine Racer found that participants reported intrusive game imagery at the start of sleep (Hobson, 2005). Overall, Stickgold and Walker (2004) suggest that there is considerable support for the view that sleep is involved in converting some short term memories into long term memories and in the subsequent strengthening of new long term memories. Sleep seems to involve consolidation of some connections and pruning of other connections to leave only the best established connections for longer term use. Learning new connections made while awake seems to be associated with re-activation, during sleep, of the neural circuits that were initially formed when awake. Lewis and Durrant (2011) developed a model (iOtA – “information Overlap to Abstract”) in which the overlapping re-play of related memories during SWS selectively strengthens shared elements between related memories and leads to cognitive abstractions or schemata. Consistent with the view that sleep aids schema formation, Monaghan et al. (2015) found that analogical transfer based on schema formation was aided when a period of sleep (Sleep Group, N = 30) intervened between presentation of source problems (from which analogies are to be drawn) and target problems (to which analogies are to be applied) compared to a Wake Group (N = 30). It seems certain that sleep does have important beneficial effects on learning. Are there also important sleep effects on problem solving and creativity? We will now review the research.

Personal accounts Many famous anecdotal accounts implicating sleep in creative thinking have been given over the years and are often cited in the introductory sections of papers reporting more objective studies. A short selection of such accounts follows.

Sleep on it?  87

Henri Poincaré (1910) wrote of unsuccessfully attempting a mathematical proof in 1881 over many waking sessions until One evening, contrary to my custom, I drank black coffee and could not sleep. Ideas rose in crowds; I felt them collide until pairs interlocked, so to speak, making a stable combination. By the next morning I had established the existence of a class of Fuchsian functions…I had only to write out the results, which took but a few hours. (Note: This is the Halstead translation. Maitland’s 1914 translation is slightly different and speaks of “verifying” the results rather than writing them out. To speak of writing out results, suggests they were fully formed and not in need of verification – which Poincare later denies is truly possible). Poincaré’s brief account suggests a role for the immediately pre-sleep, hypnagogic state, in which there is a transition between alert awakeness and sleep onset. In this particular case, the hypnagogic period was prolonged, perhaps due to the effects of caffeine and during it Poincaré was aware of ideas surging, jostling and combining. He does not report that the full solution was reached during the hypnagogic period but rather that the processing during this period was a necessary preliminary to further conscious work when verification was carried out. Unfortunately, it is not entirely clear from Poincare’s account whether he had a completely sleepless night with the Fuchsian functions problem or whether some sleep intervened between the hypnagogic state and the morning. Later, in the same paper on his views of Mathematical Creation, he writes of the key night as “…a night of excitement when I worked in spite of myself.” – which again is unclear as to whether the hypnagogic period led to sleep, or continued all night. He also noted that ideas “coming to me in the morning or evening in bed while in a semi-hypnagogic state” are always in need of conscious verification, despite any feeling of certainty which they invoke when first appearing. He also writes that the kind of processing involved in sleep or semi-sleep states does not consist of long chains abiding by strict reasoning, as in multiplying large numbers, or in deriving a multi-step proof, or finding the square root of a large number. “All one may hope from these inspirations, fruits of unconscious work, is a point of departure for such calculations…the calculations themselves, they must be made…in conscious work.” As noted in Chapter 2, Poincaré’s retrospections relate to mental events from many years (c. 27 years) before the report was published and so raise concerns about their validity.

88  Sleep on it?

The eminent mathematician Jacques Hadamard (1949, p. 8) addressed the issue of a role for sleep in mathematical creativity and wrote: One phenomenon is certain and I can vouch for its absolute certainty: the sudden and immediate appearance of a solution at the very moment of sudden awakening. On being very abruptly awakened by an external noise, a solution long searched for appeared to me at once without the slightest instant of reflection on my part – the fact was remarkable enough to have struck me unforgettably – and in a quite different direction from any of those which I had previously tried to follow. Hadamard argued that this phenomenon of sudden solution on awakening, in the hypnopompic phase, should not be confused with solving in a dream state. The eminent physiologist Otto Loewi reported (in 1953 and 1960) that, in 1921, during a dream, he devised an experiment to test whether communication between neurons was chemical. In the experiment, two surgically removed, but still beating, frog hearts were placed in separate glass vessels containing saline solutions. He stimulated one heart via its vagus nerve causing it to slow down and then added some of the saline solution from the stimulated heart’s glass vessel into the vessel containing the other heart. The second heart slowed down in response, showing a chemical component of inter-neuron transmission. He repeated the experiment stimulating the accelerator nerve of the first heart. When the saline liquid was transferred to the second heart it accelerated. These studies established chemical communication between neurons. He described (1960; see also 1953) the origin of the experiment as follows: The night before Easter Sunday of that year [1920, was specified as the year earlier in this report] I awoke, turned on the light, and jotted down a few notes on a tiny slip of thin paper. Then I feel asleep again. It occurred to me at six o’ clock in the morning that during the night I had written down something most important, but I was unable to decipher the scrawl. The next night, at three o’ clock, the idea returned. It was the design of an experiment to determine whether or not the hypothesis of chemical transmission that I had uttered seventeen years ago [1903] was correct. I got up immediately, went to the laboratory, and performed a simple experiment on a frog heart according to the nocturnal design. (From Johnson, 2010, pp. 100–101; see also Koestler, 1964, p. 205)

Sleep on it?  89

It may be noted that Loewi here reports the details of a dream based solution being forgotten initially, which is similar to an account by the mathematician Dickson of a geometry solution reached during sleep being forgotten – more of which later. Interestingly, later Loewi (1960) pointed to a possible source for his dream based inspiration. He reports that he had used a similar two heart preparation in an experiment in 1918, which had concerned fluids secreted from the heart, but was unrelated to the chemical transmission hypothesis. He wrote: In fact, the nocturnal concept represented a sudden association of the hypothesis of 1903 with the method tested not long before in other experiments. Most so-called “intuitive” discoveries are such associations suddenly made in the unconscious mind. Loewi (1960). See also Loewi (1953) Although the first published account of the Loewi’s dream seems to be in 1953, over 30 years after the presumed events, Loewi (1953, p. 33) writes that he gave the same account verbally at the International Physiological Congress in Boston in 1929. However, some uncertainty exists over when exactly the events described might have actually happened. Loewi (1953) gives the Easter weekend of 1921 as the time, but Easter that year was March 27, and the manuscript writing up the study was received by the journal on March 20, and published in 1921, so the events must have been earlier than Easter 1921. Easter Saturday 1920 was on April 3, and the 1960 account (p. 17) states the events took place in 1920, so perhaps Loewi misremembered the year in the 1953 account. On another detail, Loewi’s close associate, and joint-Nobelist, Henry Dale (1962, p. 76) recalled he heard the dream story soon after the events and it involved Loewi making careful notes, after waking on the second night, which were then followed up the next day, rather than after a middle of the night rush to the laboratory! The nineteenth-century scientist Herman Helmholtz, who made major contributions to physics, neurology and psychology, volunteered an account of his problem solving processes in a speech on the occasion of his 70th birthday in 1896 (Woodworth & Schlosberg, 1954) and refers to beneficial effects of sleep and the value of ideas that arrive in the hypnopompic phase. So far as my experience goes, “happy thoughts” never came to a fatigued brain and never at the writing desk… Often they were there in the morning when I awoke…

90  Sleep on it?

In 1867, when Dmitri Mendeleev began writing his Principles of Chemistry, he set out to organise and explain the elements. He had begun by using atomic weights as a principle of organisation, but these alone did not present a clear system. At the time, elements were normally grouped in two ways: either by their atomic weight or by their common properties, such as whether they were metals or gases. Mendeleev’s breakthrough was to see that the two could be combined in a single framework. Mendeleev was said to have been inspired by the card game known as “Solitaire” in North America, and “Patience” elsewhere. In the game, cards are arranged both by suit, horizontally, and by number, vertically. To put some order into his study of chemical elements, Mendeleev made up a set of cards, one for each of the 63 elements known at the time. Mendeleev wrote the atomic weight and the properties of each element on a card. He took the cards everywhere he went. On February 17, 1869, immediately after breakfast, and with a train to catch later that day, Mendeleev set to organising the elements with his cards. He is said to have carried on for three days and nights, forgetting the train and continually arranging and rearranging the cards in various sequences until he noticed some gaps in the order of atomic mass. As one story has it, Mendeleev, exhausted from his three-day effort, fell asleep. He later recalled, “I saw in a dream, a table, where

all the elements fell into place as required. Awakening, I immediately wrote it down on a piece of paper. Only in one place did a correction later seem necessary” (Strathern,

2000). He named his discovery the “Periodic Table of the Elements”. The account of Mendeleev’s dream appears to be second hand and to have come through an associate of Mendeleev, Ionostrantez, who reportedly heard about it directly from Mendeleev himself (Kedrov, 1966/1967). Some aspects of the account have been challenged, such as the three sleepless days and nights work, and on the basis of archival evidence that came to light in 1949, Kedrov (1966/1967) argued that the Table had been almost completed, after many years of work, when Mendeleev slept on the problem on the critical day, and that the dream led to completion and improvement, rather than to the whole invention of the complete Table (Baylor, 2001). Barrett (2001) largely concurs, and points out that further revisions to the Table were made after ­February 1869, over the next two years. So, the dream may have been a step along the way to the complete Table and far from the whole story of its invention.

Sleep on it?  91

Linus Pauling (1963), chemist and twice Nobel Prize winner, tried to purposely program his mind to address problems during sleep and wrote: I had developed the habit of thinking about certain scientific problems as I lay in bed, waiting to go to sleep. Sometimes I would think about the same problem for several nights in succession, while I was reading or making calculations on the problem during the day. Then I would stop working on the problem and stop thinking about it in the period before going to sleep. Some weeks or months might go by. Then, suddenly, an idea that represented a solution to the problem, or the germ of a solution to the problem would burst into my consciousness. In Pauling’s account, a delayed effect of “sleeping on it” is posited, which helps greatly bring about insights during later incubation periods when the problem has been long set aside. From the arts, the eminent British novelist Hillary Mantel, in a 2017 interview, said: I have a sense of doing a lot of work when I’m asleep, of leaving a problem overnight, waking up with some image or a stray word that is probably the solution. So it’s a way to get extra work in. I think of it as a very active process. (Interview in Financial Times Weekend, 3 June 2017) The famous nineteenth-century British writer Robert Louis Stevenson (1892) wrote of the dream origins of many of his stories and of important parts of some of them, such as the famous 1855 story of the “Strange Case of Dr Jekyll and Mr Hyde”. Stevenson had long been trying to develop a story on “man’s double being” or duality, when financial problems arose that made it very pressing for him to produce a publishable piece. About the creation of the Jekyll and Hyde story, he wrote, around seven years after the event: For two days I went about racking my brains for a plot of any sort; and on the second night I dreamed the scene at the window, and a scene afterward split in two, in which Hyde, pursued for some crime, took the powder and underwent the change in the presence of his pursuers. All the rest was made awake and consciously… (Stevenson, 1892)

92  Sleep on it?

Stevenson actually attributed his more unusual and creative ideas to unconscious agents, which he called “Brownies” or “Little people” (reminiscent of the psychologists’ “Homunculi”!) who were less inhibited by morality or by the laws of nature in providing dreamt events which Stevenson later consciously shaped into literary products. Striking though such anecdotes from the arts and sciences are, many were first given long after the alleged events were supposed to have occurred and so raise questions about their validity. Indeed, some commonly cited accounts involving sleep, semi-sleep states and dreams or dream-like states have been thoroughly discredited (e.g. Kekule’s story of a dream or possibly a daydream leading to the cyclic structure of benzene or Samuel Taylor Coleridge’s supposed dreaming up 200 or more lines of “Kubla Khan”, see Weisberg (2006, pp. 73–78) and Chapter 2 of this book). Can we go beyond intriguing but questionable anecdotes and show that “sleeping on it” actually works in controlled experimental settings? And if so, can we say anything about how “sleeping on it” aids problem solving?

Empirical studies of sleep effects on problem solving Surveys Survey studies have asked people to report on whether they have experienced effects of sleep on problem solving and creativity. An early piece of research by E. Maillet (1905) surveyed some 80 mathematicians in a study which focussed on dreams and inspiration in mathematics. Only one example that could be regarded as a discovery during a dream was reported. In this curious case, the prominent American mathematician L. E. Dickson reported that his mother and her sister were rivals in geometry at school. One night as she slept, Dickson’s mother dreamed of a solution to a geometry problem which both had been unable to solve the previous evening. During sleep, Dickson’s mother talked the solution out aloud and her sister, who slept in the same room and was awake, noted it down. The next day, Dickson’s mother had no knowledge of the solution which proved to be right! This account raises the possibility that solutions may be reached in sleep states that are then forgotten and cannot be retrieved on wakening (as is the case with many dreams that occur some time before waking). Unfortunately, this account

Sleep on it?  93

is second-hand, passed down from Dickson’s mother (or aunt) to Dickson and so must be a much delayed report, given long after the alleged events, and so is of doubtful reliability. A more extensive related survey study by Fehr et al. (1902–1908) of mathematicians’ working practices made another early contribution to the field. This qualitative survey study, which invited discursive answers to fairly open-ended questions, included an item on mathematical working during sleep and during dreaming and on experiences of waking with solutions. Hadamard (1949, 1954) dismissed this study as uninformative regarding creative work in mathematics, as very few respondents were truly creative mathematicians in his view. However, question 8b in the Claparede et al. survey is of interest here. It was: Have you ever worked in your sleep or have you found in dreams the answers to problems? Or, when you waken in the morning, do solutions which you had vainly sought the night before, or even days before, or quite unexpected discoveries, present themselves readymade to your mind? Out of 69 respondents, 51 (74%) answered the overall question in the positive; 45 gave some details and 6 gave no details. Of the 45 detailed answers, 22 (50%) cited the moments after waking as fruitful. In terms of dreams, 15 reported mathematical dreams, but most were of no value, being absurd, and even if they seemed very valuable during the dream they were immediately seen to be of no merit on wakening. Some seven reported having useful dreams, but only three gave enough detail to assess their value – and these were, it seems, of minor importance, although they did yield valid answers which the respondents reported as novel to them. Overall, Fehr et al. (1906) wrote: In sum, these results while favourable to the inventive fecundity of the first moments after wakening, are not so favourable to the role of the dream, save for rare exceptions. The results are similar to those of E. Maillet [previous survey, 1902, 1906] who found mathematical inspiration more often reported on waking than during a dream. (KG translation)

94  Sleep on it?

Barrett (1993, 2001) found that both students and creative professionals self reported dreaming about problems and finding solutions in dreams – ­especially when problems were highly visual, or the solutions involved unusual uses or relationships. Root-Bernstein et al. (1995) carried out a survey study of 38 scientists evenly split between physical and biological fields and including four Nobel Prize winners. Among the questions, they were asked when ideas occurred – 45% reported ideas occurring when not working on the problem and more specifically, 13% reported ideas occurring during dreams, 18% when falling asleep and 24% on awakening. Curiously, reporting that ideas occurred during dreams was significantly associated with a scientist’s publication impact (i.e. how often their papers are cited by other authors). Ovington et al. (2015) undertook a large scale survey of a representative sample of Australian participants (N = 1,114) on factors associated with self reports of insight in problem solving. Of the 80% who reported having had insight experiences during problem solving, some 16% reported that their insights were usually linked to some particular place or time. Of those, around 75% reported insights tied to sleep, or falling asleep (hypnagogic stage) or waking (hypnopompic stage). This result supports the view that sleep related insights are fairly common, but unfortunately no finer analysis is given of any linkage to specific stages of sleep.

Experimental studies Wagner et al. (2004) reported that sleep facilitated discovery of a hidden rule in number sequences (the Number Reduction Task or NRT). Participants were given 8-digit strings composed only of the digits, 1, 4 and 9, and were to process stimulus and response strings, left to right according to two rules. The “Same” rule was if the nth response and the n + 1th stimulus digit were the same, the n + 1th response was the same. The “Different” rule was if the nth response and the n + 1th stimulus were different (e.g. 1,4), the n + 1th response is the remaining third digit (9). Correctness and speed of last responses were measured. For the last three responses there was a simple but not obvious rule, not given in advance such that the last three response digits always mirrored the second, third and fourth response digits. So, the last response was always the same as the second correct response.

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Here is an example Number Reduction Task (NRT): Given: 1

1 1

4

4

9

4

9

4

4 1

4

9

4

9

4

4 9

9

4

9

4

4 9

9 1

4

9

4

After First Response: 1

1 1

After Second Response: 1

1 1

4 1

After Third Response: 1

1 1

4 1

After Seventh (Final) Response: 1

1

4

4

9

4

9

4

1

1

9

1

4

4

1

9

Participants did not know at the start that there was an easy way to carry out the task and so would all begin using the more complex rule. After initial familiarisation training, with three blocks of 30 trials, participants had 8 hours sleep, 8 hours night-time wakefulness or 8 hours daytime wakefulness before resuming the task for a further ten blocks of 30 trials. All groups involved 22 participants. Two control groups of 20 undertook ten blocks of 30 trials either after night sleep or after daytime wakefulness. Following sleep, nearly 60% of participants discovered the rule (although not immediately) but only 23% of the non-sleep participants discovered the rule (p = .014, χ2(2) = 8.54, Cramer’s V = .36, a medium effect size). The discovery rates in the control groups were also around 23%. The participants who had slept and discovered the rule did so after an average of 135 trials, while the non-sleep participants who discovered the rule required 192 trials on average. Sleep participants who went on to solve showed a slow down on initial resumption of the task while those sleep participants who did not solve showed a marked speed up on initial trials post-sleep. The awake participants did not show this difference between solvers and non-solvers on initial trials (Figure 6.1).

96  Sleep on it? Number Reduction Task % gaining insight 70 60 50 40 % gaining insight

30 20 10 0 Day Wake FIGURE 6.1 

Night Wake

Sleep

Number reduction task results, from Wagner et al. (2004).

As Stickgold and Walker (2004) noted, there are some striking features of these results. First, the sleep participants did not wake up with the solution, as personal anecdotes and surveys have sometimes reported or suggested (e.g. Helmholtz, 1896; Claparede et al., 1906; Poincaré, 1910), but rather they came to the solution faster and more often than did the nonsleep participants when they consciously resumed the task. Second, the participants did not have an explicit goal of finding a simple solution to the NRT, so the situation does not exactly mirror the typical “sleep on it” example where the person has reached an impasse while trying to achieve a known goal. The task situation was closer to one of problem finding and solving as against simply problem solving where the problem has been pre-set by the person or by an experimenter. Did the participants unconsciously set themselves the goal of finding a better method during the familiarisation phase or while asleep? Or did the number pattern become recognised first, albeit possibly implicitly, during sleep, perhaps as a by-product of consolidation processes? Subsequently, the usefulness of the pattern may have become apparent when the pattern knowledge became explicit during the main block of 300 trials – after the sleeping period. Third, the speed differences between solvers and non-solvers immediately post-sleep suggest that processing during sleep either strengthened the habits acquired during familiarisation (leading to a speed up) or weakened the habits (leading to a slow down) and facilitated a re-structuring of the sequences as simple patterns.

Sleep on it?  97

A follow up study (Verleger et al., 2013, Experiment 3) indicated that SWS was associated with post-sleep insight in participants who had shown signs of implicit learning of the regularity before a sleep break (N = 26), compared with those who did not (N = 29) show implicit learning before sleep. A further study on the NRT and sleep (Debarnot et al., 2017) found no difference in insight occurrence following sleep (18% of 23) and following a control wake period (23% of 24), among older participants aged c. 60 years. The authors suggest that the lack of an effect of sleep on subsequent insight rates may be due to a marked reduction in SWS in older people (Cajochen et al., 2006). Sio et al. (2013) found that previously unsolved difficult Remote Associates Test (RAT) items were better solved after a 12 hour gap which included sleep of c. 7.5 hours (Sleep Group, N = 16) than after a 12 hour period of waking “incubation” opportunity (awake group, N = 22). RAT items involve finding a word related to three given words, e.g. which word links lick, sprinkle and mine? Answer: salt. However, the data could not assess whether facilitation effects of sleep were due specifically to REM as against nonREM sleep. However, Landmann et al. (2016) in a related study did not find any benefit for an 8 hour Sleep Group (N = 20) versus an 8 hour waking incubation group (N = 20) on solution of German language RAT type items that had been unsolved before the breaks. Walker et al. (2002) carried out a study with N = 16 participants who attempted anagrams on being awoken from REM or nonREM sleep states. It was assumed that a degree of “sleep inertia” exists which provides a short window within which the person is in a similar state to that from which they have just been awoken. Only 10 seconds was allowed to solve the five-letter single solution anagrams (e.g. SOOEG → GOOSE). Participants solved anagrams significantly more often (55%) when woken after REM sleep than after the same amount of nonREM sleep (42%), suggesting that REM sleep induces a flexible state that benefits awake performance. However, the solution rates (55%) after Wake control periods were not different from rates after REM states. Reaction times were similar across conditions, indicating that alertness levels on test were similar (see Figure 6.2). Although overall REM and Wake condition total correct scores did not differ, solution scores after REM did not correlate significantly with scores in the Wake condition (r = .17), but scores after nonREM did (r = .34). From these results (Figure 6.2), Walker et al. argued that the REM state had brought about a different – but equally effective – processing approach from the waking state.

98  Sleep on it? 60

% anagrams solved

50 40 30

% solution

20 10 0

WAKE

FIGURE 6.2 

REM

NonREM

 nagram solution rates following Wake, REM and NonREM A sleep periods, from Walker et al. (2002).

Cai et al. (2009), using the RAT, gave 40 participants a short sleep nap period following an initial testing session and 37 others a quiet rest period. Sleep participants were divided into those who displayed REM signs during the nap (n = 28) and those not showing signs of REM (n = 12). It was found that having REM sleep periods during naps of about 1 hour improved performance on previously unsolved RAT items, following priming by an unrelated analogies task, compared to participants who did not have REM sleep or had only quiet rest periods. For unprimed items, there was a general and equal incubation effect benefit for rest, nonREM and REM conditions. The selective benefit of REM for primed items suggests that REM sleep aids the integration of weakly associated items of information. This study had a control condition which showed that sleep did not simply benefit RAT performance in general, as new items tested after sleep showed no gain due to immediately prior sleep. Monaghan et al. (2015) found that analogical transfer in insight problem solving based on schema formation was aided when a period of sleep (Sleep Group, N = 30) intervened between presentation of source problems (e.g. the tree planting problem, from which analogies are to be drawn) and target problems (e.g. the match triangle problem, to which analogies are to be applied) compared to a Wake Group (N =30).

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Ritter et al. (2012) attempted to influence processing during sleep itself towards a creative task that had been set aside before sleep, by presenting task related odour cues during sleep. The method was based on previous studies that had found that covertly re-activating new memories during sleep, by means of conditioned odours, improves later memory test performance. Rasch et al. (2007) had exposed participants to a particular odour while they learned object locations. Participants re-exposed to the conditioned odour during sleep showed better memory for locations after sleep than control participants. Ritter et al.’s (2012) creativity task was to generate ideas for how to motivate people to take part in volunteer work and to select the most creative idea from the answers offered. Participants were instructed in the task before sleeping and were told that they would be asked to report solutions in the morning after sleeping. (The procedure resembles that of Dijksterhuis’s “Immediate Incubation” paradigm – although there is less control over the intervening activities between presentation and test than in the normal awake form of Immediate Incubation and so, some intermittent conscious work seems very likely in the sleep paradigm between task instruction and sleep.) While being informed about the task, two odour groups were exposed to an orange-vanilla odour. A third control group received no odour exposure. As the participants slept, one group (N = 17) was exposed to a repeat of the orange-vanilla odour, one group (N = 13) received a control odour (fresh tonic) and a third group received no odour (N = 19). After sleep with the “conditioned odour” associated with the creativity task, participants’ responses were rated as more creative than those of the control odour group (p = .03) and those of the no-odour group (p = .04). Furthermore, the conditioned odour group’s judgements, of which of their ideas were best, matched the judges’ views more closely than did the judgements of the control groups. Overall, Ritter et al. (2012) concluded that task-reactivation during sleep can trigger creativity-related processes and could potentially be applied in real life. Further studies would be useful to tie the effects to stages of sleep (REM vs nonREM) and to include a wakeful control group to confirm that sleep is beneficial relative to a waking condition in this type of task. Beijamini et al. (2014) had participants work briefly on a video game that involved a box moving task that would presumably require look-ahead and heuristic search. A nap group (N = 14) was significantly more likely to solve (86%) after a 90 minute break than a wake incubation group (N = 15, 47% solved, p = .02). Whether a participant solved or not after the break was tied to the presence of SWS during the nap period (p = .04) but not to REM.

100  Sleep on it?

Studies of sleep effects on creativity and insight have often used the RAT (or its modern descendant, the Compound Remote Associates or CRA); however it can be argued that the RAT primarily involves the generation of associates rather than any re-structuring. Schönauer et al. (2018) have examined effects of sleep on classic insight problems and on coming to understand magic tricks. The study involved three well-known insight tasks, viz. Matchstick Arithmetic (e.g. Öllinger et al., 2008), the Nine-Dot task (Scheerer, 1963) and the Eight-Coin problem (Ormerod et al., 2002). Additionally, participants were presented with a short video clip of ten magic tricks and instructed to try to explain how they were done (Danek et al., 2014). After initial presentations (30 minutes) one group (N = 17) had a 3 hour sleeping incubation period, and a second group (N = 19) had a 3 hour waking incubation period. There were no differences between the sleep and waking incubation groups in a 30 minute re-testing period. Continuous work control groups performed at a very similar level to the sleeping and awake incubation groups and no overall incubation effects were obtained in this study. The authors suggest that effects of incubation and of sleep based incubation in particular may be strongest for tasks highly dependent on generation of unusual associations as against re-structuring.

Methodological notes Experimental design in wake incubation vs sleep effect studies In the typical laboratory study of incubation in wake participants, the period for intervening activity is quite short, usually minutes. The activity to be carried out during the intervening period is specified and ideally performance on the intervening/interpolated task is measured and compared with a control group to check for possible intermittent work on the primary, target task. In contrast, sleep studies always involve prolonged interpolated periods of at least many minutes (naps, c. 30–60 minutes) or more usually several hours (typical night’s sleep, c. 7–8 hours). Sleep cannot be switched on and off immediately and so there are always periods between the primary target task being set aside and the onset of first stage sleep on the one hand and between final stage awakening and fully alert return to the task. No particular tasks are set between task offset and sleep, or between sleep ending and task resumption, and so no control is possible for intermittent work on the primary task. The hypnagogic and hypnopompic periods may well see some conscious intermittent work on the primary task.

Sleep on it?  101

The waking incubation control groups in sleep effect studies also have long incubation periods equal to the sleep periods, and typically these are unspecified “daily activities” or “quiet rest” periods in which intermittent conscious work cannot be ruled out or measured so that it could be taken into account. The typical sleep effect study compares the effects of a sleep period following an initial conscious work stage with the effects of a wake incubation period. It is fairly rare to test whether a sleep break is better than continuous work. In contrast, studies of waking incubation tend to focus on whether the incubation period is beneficial compared to continuous work. For example, if we can work for a total of 60 minutes is it helpful to have an incubation break after 30 minutes for a certain period and then resume for a further 30 minutes? Schönauer et al. (2018) unusually did have a continuous work control for effects of a sleep break (and found no benefit) in their study of sleep effects on solving insight and magic trick problems.

Power considerations It is notable that, presumably for practical reasons, the sample Ns in sleep studies tend to be quite small, leading to low power studies. In the ten experimental sleep research papers reviewed here (Walker et al., 2002; Wagner et al., 2004; Cai et al., 2009; Ritter et al., 2012; Sio et al., 2013; Verleger et al., 2013; Beijamini et al., 2014; Monaghan et al., 2015; Landmann et al., 2016; Schönauer et al., 2018) the median sample sizes were 17 for the Sleep Groups and 19 for the control groups. Using the G* power analysis program (Faul et al., 2007), it can be concluded that the median power of the reviewed experimental studies of sleep effects on problem solving was fairly low at 31% power to detect a medium effect (d = .5) at p