7.7 Poincare’s Unconscious Processes

"We cannot kindle when we will The fire which in our heart resides, The spirit bloweth and is still, In mystery our soul abides: But tasks in hours of insight will'd, Can be through hours of gloom fulfill'd" —Matthew Arnold

Sometimes you’ll work on a problem for hours or days, as when Joan worked on her progress report.

She has been thinking about it for several days, but has not yet conceived of a good enough plan. Discouraged, she sets those thoughts aside … but then an idea ‘occurs’ to her.

But did Joan really set those thoughts aside, or did they continue in other parts of her mind? Hear a great mathematician recount some similar experiences.

Henri Poincare: “Every day I seated myself at my worktable, stayed an hour or two, tried a great number of combinations and reached no results.” [9]

Most persons might get discouraged with this—but Poincare was inclined to persist:

“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 only to write out the results, which took but a few hours.”

Then he describes another event in which his thinking seemed much less deliberate:

"The changes of travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go some place or other. At the moment when I put my foot on the step the idea came to me, without anything in my former thoughts seeming to have paved the way for it. … I went on with a conversation already commenced, but I felt a perfect certainty.”

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." —Essays in Criticism, 1865.

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.” [10]

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. [11] 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.

In my view, what we call ‘creativity’ is not the ability to generate completely novel concepts or points of view; for a new idea to be useful to us, we must be able to combine it with the knowledge and skills we already possess—so it must not be too very different enough from the ideas we’re already familiar with.

Collaboration.

We usually think about thinking as a solitary activity that happens inside a single mind. However, some people are better at making ideas, while others excel at refining them—and wonderful things can happen when ‘matched pairs’ of such persons collaborate. It is said that T.S. Eliot’s poetry owed much to Ezra Pound’s editing, and that A.S. Sullivan’s music was most inspired when he was working with W.S. Gilbert’s librettos. Another example of such a pair might be Konrad Lorenz and Nickolaas Tinbergen, as we see in their Nobel Prize autobiographies:

Niko Tinbergen: “From the start 'pupil' and 'master' influenced each other. Konrad's extraordinary vision and enthusiasm were supplemented and fertilized by my critical sense, my inclination to think his ideas through, and my irrepressible urge to check our 'hunches' by experimentation - a gift for which he had an almost childish admiration.” [12]

Konrad Lorenz: “Our views coincided to an amazing degree but I quickly realized that he was my superior in regard to analytical thought as well as to the faculty of devising simple and telling experiments. … None of us knows who said what first, but it is highly probable that the [concept of] innate releasing mechanisms … was Tinbergen's contribution.” [13]

For many people, thinking and learning is largely a social activity—and many of the ideas in this book came from collaborations with students and friends. Some such relationships are productive because they combine different sets of aptitudes. However, there also are pairs of partners who have relatively similar skills—perhaps the most important of which are effective tricks for preventing each other from getting stuck.

Do we normally think 'Bipolarly'?

The processes that Poincare described involved cycles of searching and testing in which problems are solved over hours, days, or even years. However, many events of everyday thinking persist for just a few seconds or less. Perhaps these, too, begin by spawning ideas, then selecting some promising ones, and then dwelling on their deficiencies!

If so, then a typical moment of commonsense thinking might begin with a very brief ‘micro-manic’ phase. This would produce an idea or two—and then a short ‘micro-depressive’ phase would quickly look for flaws in them.

If those phases took place so rapidly that your reflective systems don’t notice them, then each such micro-cycle’ would seem to be no more than a moment of everyday thinking, while the overall process would seem to you like a steady, smooth, uneventful flow.[14]

The quality of such systems would depend in part on how much time one spends in each such phase. It seems plausible to conjecture that, when one is inclined to be ‘critical’ or ‘skeptical,’ one spends less time at Incubation and puts more effort into Evaluation. However, if anything were to go badly wrong with how those durations were controlled, then some of those phases might last for so long that (as suggested in §3-5) they might appear as symptoms of a so-called ‘manic-depressive’ disorder.