Part 1 - Solving Problems: Creativity and Dreams
In 1926, the British philosopher Graham Wallace, in the The Art of Thought, concisely described the stages of the creative process in a way that we feel hasn’t been bettered. He called these stages: preparation, incubation, illumination and verification.
We have probably all had experience of focusing our attention on a problem (preparation), then leaving it aside for a while, perhaps going for a walk (incubation), when suddenly a solution hits us (illumination). Then, of course, we must check that the solution is viable (verification). The characteristic way in which our cognitive unconscious works by ‘incubating’ the problem is nature’s way of enabling us to find solutions holistically (sometimes called lateral thinking). Creative solutions do not come from logical analysis, although such an analysis is necessary in the preparatory stage, but from rearranging the elements of a problem into a new pattern, or seeing the existing pattern from a different perspective.
You can clearly see this process at work yourself by applying to your own dreams the theory of dreams presented in this book. First, note all the elements of the dream, including your feelings about it. These are the feelings that you would have felt had you been able to enact the waking introspections that gave rise to your dreams. The feelings in the dream are actually more intense than the feelings you had when you were awake. (This is because, as you did not act on the feelings when you were awake, your dreaming brain concentrates completely on the aroused expectations associated with the feelings, in order to deactivate them.) Next, compare the dream elements to your waking experience of the previous day to see if you can find a matching template to the dream scenario. Remember, of course, that the match will not be between the ‘objective’ waking events and the dream but rather between the dream and your introspected view of those waking events. This can be regarded as the preparation phase of the dream analysis.
The corresponding waking situation doesn’t usually spring to mind immediately as the purpose of the dream in the first instance was to deactivate the feelings associated with the memory. Hence it usually requires a period of ‘incubation’ before the unconscious mind can trace the associative links to the waking introspection that gave rise to the dream. Ironically it is often easier, when we have adequate background information, to see the meaning of someone else’s dream, if we have an idea of what was preoccupying them the previous day. This is because the waking sequence has not, of course, been deactivated in our brains. Thus Joe’s wife, Liz, will often identify the meaning of one of his dreams before he does and vice versa. Once the meaning has been identified all of the elements in it can be matched up, which helps to verify it. Thus, real dream interpretation, especially interpreting our own dreams, clearly involves the four traditional phases of creative problem solving: preparation, incubation, illumination and verification.
Despite popular ideas to the contrary it appears that successful problem solving in dreams may be pretty rare. Dement has reported a research project in which 500 undergraduate students, over three consecutive classes, were given one of three problems to solve. They were told to study a problem for 15 minutes before going to sleep and to record any dreams they remembered from the night. If the problem had not been solved, they were to work on it for another 15 minutes in the morning. The total number of problem-solving attempts was 1,148. It was judged that 87 dreams related to the problem but that the problem was solved in a dream on only seven occasions.
One of the problems was as follows: “The letters OTTFF... form the beginning of an infinite sequence. Find a simple rule for determining any or all successive letters. According to your rule, what would be the next two letters of the sequence?” The next two letters are SS. The letters represent the first letters used in spelling out the numerical sequence one, two, three, four, five, six, seven etc.
The following dream is one of those in which the problem was solved.
The art gallery
I was standing in an art gallery looking at the paintings on the wall. As I walked down the hall, I began to count the paintings one, two, three, four, five. But as I came to the sixth and seventh, the paintings had been ripped from their frames! I stared at the empty frames with a peculiar feeling that some mystery was about to suddenly be solved, I realised that the sixth and seventh spaces were the solution to the problem.
A second problem the students were given was to consider the letters HIJKLMNO. The solution to the problem was one word: water. In other words, ‘H to O’ or H2O.
No dream was classified as actually solving the problem, but twelve were classified as ‘mode of expression dreams’. An example of a ‘mode of expression’ dream is as follows:
I had several dreams, all of which had water in them somewhere. In one dream I was hunting for sharks. In another I was riding waves at the ocean. In another I was confronted by a barracuda while skin-diving. In another it was raining quite heavily. In another I was sailing into the wind.
This dream, as the student reported, had water in it everywhere. Yet, as far as he was concerned, the student had solved the problem to his own satisfaction before going to bed, with the word ‘alphabet’.
The type of holistic thinking required for creative problem solving is the antithesis of the everyday analytical approach. Rather than breaking a problem down, it involves looking at the entire problem from a different perspective. This is also the type of thinking required to solve the problems in Dement’s study. Such creative problem solving is often facilitated by taking a break from the problem and getting into a relaxed frame of mind (incubation) after which the solution often ‘hits’ us (illumination). It may well be that dreaming can, in a sense, provide the relaxed frame of mind in which a solution can emerge. An individual’s analogical thinking process may have arrived at a solution before dreaming, but he or she is either too tired or, more likely, too set in an analytical left-brain mode of thinking, for the solution to emerge.
The research psychologist Norman Dixon has reported experiments where a subliminal image shown to subjects appeared in the manifest content of a subsequent dream. He argued that, in these cases, although the image has been perceived, the stimulus doesn’t possess enough energy to get as far as waking consciousness but it can emerge in the less controlled consciousness of a dream. Perhaps a similar phenomenon exists as far as dream problem solving is concerned. A solution that doesn’t possess enough energy to break through into consciousness, either because existing cognitive sets are too rigid or because the person is not in a suitably relaxed frame of mind, may become manifest in a dream sequence.
How the solution manifests depends on how people anticipate what will happen in their dream before they go to sleep. In the first example given, the subject has the solution expressed clearly in an analogous setting. He is looking at paintings in an art gallery. This is a metaphor for his anticipation that he will be looking at images in a dream. The sixth and seventh paintings, ripped from their frames, symbolise the missing two letters which had to be found in order to solve the problem. He expects the problem to be solved in a dream. He looks at the blank paintings with a feeling that some mystery is going to be solved. He realises that the sixth and seventh spaces are the solution.
This dream, then, metaphorically represented what this student anticipated would happen in a dream that night. His creative process had probably arrived at a correct solution before the dream occurred. Consequently the anticipated solution provided in the dream was an accurate metaphor of the correct solution. This is in contrast to the great majority of the dreams reported – these were about the problem and trying to solve it but the correct solution did not emerge from them.
In the second example, the student wrongly thought that he had solved the problem before going to sleep. In this case, Joe’s theory of dreams would lead us to expect that, for the correct solution to appear in this student’s dreams, it would have to be incorporated into the ongoing imagery of other dream themes, since he was no longer anticipating a solution in a dream. (This is what happened with the subliminally presented images in Dixon’s study, they were incorporated into the ongoing dream sequences.) The student reported several dreams in which water was the main form of symbolism. However, the dreams were not about the problem, or about water as the solution to the problem, but rather water as a symbol to express a personal concern for the future – a fear that he was heading into ‘dangerous waters’ perhaps.
This student’s creative thinking process had arrived at the correct solution, namely ‘water’, but, because he wrongly believed ‘alphabet’ to be the solution, it did not emerge into waking consciousness and, like a subliminally presented stimulus, was easily incorporated into the symbolism or metaphors of dreams that expressed different waking anticipations.
Similarly, Kekule’s analogical thinking process had arrived at a correct solution but a suitable frame of mind for its emergence may not have been arrived at before he fell asleep, or else his conscious mental sets were too rigid to permit the solution to emerge. So the solution was incorporated into the symbolism in a dream which was expressing some other waking concern. In this case Kekule’s fear that the problem was making a fool of him is expressed appropriately by the snake chasing its own tail, ‘mockingly’ going round in circles. The expectation fulfilment theory suggests that, for a person’s problem to be directly solved in a dream, they must actively anticipate that the problem will be solved in their dreams and, secondly, the correct solution must have already occurred to them prior to having the dream. On the other hand, where a solution has occurred to a person’s unconscious mind, but an appropriate milieu for its expression has not been found while they were awake, then the solution may be indirectly suggested by the surface imagery of the metaphor expressing a different waking concern – as in the examples of Kekule’s dream and in the water solution dream just described.
The New Scientist asked its readers to use their dreams to solve a number of intellectual problems. They were the kind of problems that would be expected to baffle the logical, conscious mind. Eleven people wrote to Morton Schatzman, who was conducting the research, and described how a dream had helped them solve the following mathematical problem:
Using six line segments of equal length, can you construct four equilateral triangles such that the sides of the triangles are the same length as the line segments.
One who wrote in said that, in a dream, she ran her hand along some railings and six of them came together “to form a kind of wig-wam”. Later she dreamt that her chemistry teacher appeared in the dream and said ‘109 28’. The student knew that this number was connected with tetrahedral molecules whose structures make up four equilateral triangles. Translating the metaphor she realised that the solution was a three-sided pyramid. Another student, who was not familiar with mathematics, was delighted with the help her dream provided. In her dream, she asked a scientist for help, and the scientist jumped up and down and eventually flew up on top of a cupboard. When the dreamer woke up, she was able to understand the metaphorical answer by realising that the triangles must be given lift off. She made a drawing using this idea and solved the problem.
Notice how the presence of the scientist in the dream would naturally alert her waking mind to the fact that this dream was about the problem from the New Scientist.
Another problem presented was to discover what was remarkable about the following sentence:
‘I am not very happy acting pleased whenever prominent scientists overmagnify intellectual enlightenment.’
(The number of letters increases in each consecutive word by one to form a numerical sequence going from one to 13.)
One sixth-form student dreamed that he was lecturing to scientists seated at five tables with one, two, three, four and five scientists sitting at each respective table. The student was able to see that the dream was a metaphorical solution to the problem. Another student who solved the problem by means of a dream reported that, in his dream, he typed the sentence, ‘The quick brown fox jumped over the lazy dog’. (This is, of course, the sentence that contains all 26 letters of the alphabet.) His supervisor tells him to type 1 2 3 4 5 6 7 8 9 instead. Again, we see the dream expressing the solution metaphorically. The words were replaced by a sentence known to contain all the letters of the alphabet, and thus it directs his attention to the letters in the words. The supervisor tells him to write a sequence of numbers that stops at 9. This is because the number of words in the replacement sentence in the dream has nine words in it, unlike the problem sentence, which has thirteen words in it. We can see, therefore, that the dream provided a metaphorical solution to the problem.
In these examples the dreamers were anticipating a solution to the problem in their dreams and then dreaming a metaphorical solution to the problem. In the next two examples a solution to a problem was not anticipated in a dream and so the solution had to follow the more indirect route of being incorporated into the surface images of a dream expressing another theme.
Part 3: Invention and dreams
Of course you could read the entire book, (The Kindle version is only £4.99!) where all references can be found.