This suggests that the work was still being pursued, hidden away in ‘the back of his mind’—until suddenly, as though ‘out of the blue,’ a good solution ‘occurred’ to him.
“There was one [obstacle] however that still held out, whose fall would involve the whole structure. But all my efforts only served at first the better to show me the difficulty. … [Some days later,] going along the street, the solution of the difficulty that had stopped me suddenly appeared to me. … I had all the elements and had only to arrange them and put them together.”
In the essay from which these quotations come, Poincare concluded that when making his discoveries, he must have used activities that typically worked in four stages like these:
Preparation: Activate resources to deal with this particular type of problem.
Incubation: generate many potential solutions.
Revelation: recognize a promising one.
Evaluation: verify that it actually works.
The first and last of these stages seemed to involve the kinds of high-level processes that we characterized as conscious ones—whereas incubation and revelation usually proceed without our being aware of them. Around the start of the 19th century, both Sigmund Freud and Henri Poincare were among the first to develop ideas about ‘unconscious’ goals and processes—and, if only for mathematical activities— Poincare suggested clearer descriptions of these but borrowed
Let’s consider what might be involved in each of the stages of such a process.
Preparation: To prepare to solve a specific problem, one first may need to ‘clear one’s mind’ from other goals— for example, by taking a walk, or by finding a quiet place to work. Then one must focus on the problem by deliberating to decide which of its features are central enough to suggest an appropriate Way to Think; here Poincare said, “All my efforts only served at first the better to show me the difficulty.”
Then, he suggest, you need to find appropriate ways to represent the situation; one needs to identify the parts of a puzzle before you can start to put them together—and until you understand their relationships well enough, you will tend to waste too much of your time at making bad combinations of them. This must be what Matthew Arnold meant when he said,
“This creative power works with elements, with materials; what if it has not those materials, those elements, ready for its use? In that case it must surely wait till they are ready.”
In other words, blind “trial and error” won’t often suffice; you need to impose the right kinds of constraints and activate a set of resources that will tend to generate good possibilities—or else get lost in an endless search. Also, if you can’t deal with the problem all at once, then you make a plan that breaks it into smaller parts that you can hope to handle separately.
Incubation: Once the ‘unconscious mind’ is prepared, it can consider large numbers of combinations, searching for ways to assemble those fragments to satisfy the required relations. Poincare wonders whether we do this with a very large but thoughtless search—or if it is done more cleverly.
Poincare: “If the sterile combinations do not even present themselves to the mind of the inventor … does it follow that the subliminal self, having divined by a delicate intuition that [only certain] combinations would be useful, has formed only these, or has it rather formed many others which were lacking in interest and have remained unconscious?”
In other words, Poincare asks how selective are our unconscious thoughts; do we explore massive number of combinations, or work on the finer details of fewer ones? In either case, when we incubate, we will need to switch off enough of our usual Critics to make sure that the system will not reject too many hypotheses. However, we still know almost nothing about how our brains could conduct such a search, nor why some people are so much better at this: here is one conjecture about that.
Aaron Sloman:“The most important discoveries in science are not discoveries of new laws or theories, but the discovery of new ranges of possibilities, about which good new theories or laws can be formed.”[140]
Revelation: When should incubation end? Poincare suggests that it continues until some structure is formed “whose elements are so harmoniously disposed that the mind can embrace their totality while realizing the details.” But how does that subliminal process know when it has found a promising prospect?
Poincare: “It is not purely automatic; it is capable of discernment; it has tact, delicacy; it knows how to choose, to divine. What do I say? It knows better how to divine than the conscious self, since it succeeds where that has failed.”
He conjectures that this ability to detect promising patterns seems to involve such elements as symmetry and consistency.
Poincare: “What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? It is the harmony of the diverse parts, their symmetry, their happy balance; it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.”
Poincare did not say much more about how those detectors of ‘elegance’ might work, so we need more ideas about how we recognize those signs of success. Some of those candidates could be screened with simple matching tricks. Also, as part of the Preparation phase, we select some specialized critics that can detect progress toward solving our problem, and keep these active throughout Incubation.
Evaluation: We often hear advice that suggests that it’s safer for us to trust our ‘intuitions’—ideas that we get without knowing how. But Poincare went on to emphasize that one cannot always trust those ‘revelations.’
Poincare: “I have spoken of the feeling of absolute certitude accompanying the inspiration ... but often this feeling deceives us without being any the less vivid, and we only find it out when we seek to put on foot the demonstrations. I have especially noticed this fact in regard to ideas coming to me in the morning or evening in bed while in a self-hypnagogic state.”
In other words, the unconscious mind can make foolish mistakes. Indeed, later Poincare goes on to argue suggest that it often fails to work out the small details—so when Revelation suggest a solution, your Evaluation may find it defective. However, if it is only partially wrong, you may not need to start over again; by using more careful deliberation, you may able to repair the incorrect part, without changing the rest of that partial solution.
I find Poincare’s scheme very plausible, but surely we also use other techniques. However, many thinkers have maintained that the process of creative thinking cannot be explained in any way, because they find it hard to believe that powerful, novel insights could result from mechanical processes—and hence require additional, magical talents.[141] However, Chapter 8 will argue that outstanding abilities can result from nothing more than fortunate combinations of certain traits that we find in the ways that most people think. If so, then what we call ‘genius’ requires no other special ingredient.
Somewhat similar models of thinking were proposed in Hadamard (1945), Koestler (1964), Miller (1960), and Newell and Simon (1972)—the latter two in more computational terms. Perhaps the most extensive study of ways to generate ideas is that of Patrick Gunkel at http://ideonomy.mit.edu. In any case, however you make each new idea, you must quickly proceed to evaluate by activating appropriate critics. Then, if the result still has some defects, you can apply similar cycles to each of those deficiencies.
141
Some theorists question the existence of —this sort of unconscious processing. Paul Plsek discusses this issue at length: