Tuesday, December 17, 2019

Scientists in the Solution State

Great scientists often solve problems in their sleep. It is well-known that Descartes had some interesting dreams, but his work as a whole may have gained more from the “creative mood” in which he often found himself during a relaxed state after sleep. Carl Gauss said he often had his best insights immediately after awakening. John Appold, the inventor of a centrifugal pump, worked out the following routine: when faced with a problem, he would go over and over the elements in his head before going to sleep, programming his mind for the night. He generally found that he had the solution first thing in the morning. 

Famously, Einstein woke up on a spring morning in 1905 with the elements of the special relativity theory in his head. He had talked to a friend the previous evening about his keen sense that he was on the edge of a tremendous breakthrough, but was not yet sure what it was; the pieces came together in the secret laboratory of the night.    

The role of dreaming in the history of scientific creativity is both underrated and overrated. Exaggerated claims have been made for the inspirational power of sleep dreams in scientific discovery, and when these have been exploded, the reductionists have not been slow to pounce. For example, dream enthusiasts have often suggested that Einstein and Niels Bohr made their breakthroughs in dreams but (as far as I am aware) there is no evidence that either of them was inspired by specific content from sleep dreams. 

However, when we do deeper research into the history of scientific discovery across time, we find evidence of something far more interesting. Many of our greatest scientists have been dreamers in a more expansive sense. Above all, they have known how to enter into a fluid state of consciousness — a solution state - where unlikely connections can be made that escape the workaday mind, and where the shapes of what was formerly inexpressible rise from the depth like creatures from the ocean bed.

     To illustrate these statements, let’s study the case of one of the most famous — and problematic - “dreams” in the history of science. This is the dream of a snake biting its tail that revealed the shape of the benzene ring to German chemist August Kekulé (1829-1896). You’ll find it mentioned in almost any book that contains stories about dreams and creativity. But was it a sleep dream, or an image that came in a lightly altered state of consciousness. 

    Kekulé wrote a personal account, reconstructing an extempore speech he gave at the 1890 Benzolfest many years after his visions. Study this closely, and check the meaning of the German words, and you’ll find that his dreamy perception of the “dance” of chemical elements was not a one-off affair. He described a similar experience seven years before the snake dream that gave rise to his theory of chemical structures. He made it clear that in years between the two visions he had developed a practice of seeing or thinking in visual imagery.

     In his mid-20s, when he was living near Clapham Common in London, Kekulé spent a long summer evening sharing his ideas with a friend and fellow chemist who lived in Islington, on the other side of the city. Riding home on the last bus, Kekulé drifted into a reverie (Traumerei) in which he saw atoms “gamboling” and dancing and forming combinations. He understood, when he analyzed their motions, that he had been given clear insights into chemical structures. Up to this time, he had been unable to grasp the nature of their motion. 

“Now, however, I saw how, frequently, two smaller atoms united to form a pair; how a larger one embraced the two smaller ones…while the whole kept whirling in a giddy dance. I saw how the larger ones formed a chain, dragging the smaller ones after them but only at the end of the chain.” He stayed up late that night sketching these “dream forms”. This was the origin of his theory of carbon bonding in chemical structures.

     We see three conditions for creativity at work in this incident: (a) immersion in a subject, (b) sharing a developing idea with the right friend, and (c) drifting or relaxing into a flow state, from which the “Eureka” moment arises spontaneously.

Seven years later, a dream or reverie during an evening nap showed Kekulé the chemical structure of the benzene ring. He was now a professor in Ghent in Belgium. Dozing by the fire in his darkened study, he again saw atoms “gamboling before my eyes.” Now his inner sight “rendered more acute by repeated visions of the kind, could distinguish larger structures of manifold conformation: long rows, sometimes more closely fitted together all twining and twisting in snake-like motion.” Then he was startled to see one of the “snakes” seize hold of its own tail, and whirl “mockingly” before him. He was jolted out of his languorous state, “as if by a lightning bolt.” The image of the whirling snake gave the chemist the clue to the structure of the benzene ring. He spent most of the night that followed working this up until he had shaped his theory.

Kekulé had become practiced in receiving and developing helpful images in this way. When he described the roots of his scientific creativity in the Benzolfest in his honor in 1890, Kekulé told his audience, “Let us learn to dream, gentlemen, then perhaps we shall find the truth.” He added the salutary caution, “But let us beware of publishing our dreams till they have been tested by the waking understanding.” 

 The images that came to Kekulé would have been meaningless, in terms of chemistry, to someone who did not have a scientific mind that had long been working on the problems whose solutions they revealed. The imagery might have sent an artist off to paint, or sent someone with an interest in myth off to study the symbol of the Ouroboros in the ancient world and in alchemy.

     When Kekulé urged his audience to “dream”, he was surely not talking exclusively, or primarily, about what happens in sleep. He was talking about developing the ability to enter a state of relaxed attention in which ideas take form and interact as images.

    It is always exciting to know the specific ways in which a creative mind enters that imaginal space. In the 1850s, people did not travel in motorized buses. The public conveyance that carried Kekulé home to Clapham, was a horse-drawn omnibus. The clatter of the hooves and the jangle of the harness and the rocking motion of the box carriage provided the soundtrack and the rhythm for Kekulé’s breakthrough. 

    It is likely that other creative minds of his period were helped by the rhythms of a contemporary mode of transportation? For the French mathematician Jules-Henri Poincaré, it was enough to put his foot on the step of a horse-drawn omnibus. In his beautiful essay on “Mathematical Creation” Poincaré recalled that he had come to a stuck point in his efforts to formulate a new mathematical construct, when he agreed to travel to Coutances to join friends on a hike. Inspiration struck as he started to board an omnibus. “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.” When he went home to Caen, Poincaré wrote up his theory of “Fuchsian functions” directly from this moment of insight. 

    Poincaré also received direct guidance from his night dreams. After several unsuccessful attempts to perfect an equation he had been working on, Poincaré dreamed he was giving a lecture to students on problem and wrote the equation on the blackboard to make everything clear. After waking, Poincaré was able to hold the image of what he had chalked on the board, wrote down the equation — and found he had his solution.

The Russian physicist Arkady Migdal described creativity as an intermediate state “where consciousness and unconsciousness mix, when conscious reasoning continues in sleep, and subconscious work is done in waking”. The place of creative breakthroughs, in the history of science as in other fields, has often been the liminal state between sleep and awake. I have come to think of this intermediate zone of consciousness as a solution state. 


Text partly adapted from  The Secret History of Dreaming  by Robert Moss. Published by New World Library.

"Cloudladder" is a "photoallegory" by Hungarian artist 
Sarolta Ban.


Unknown said...

I can attest to the effectiveness of scientific and mathematical creativity in what you label as the "solution state." The dream is certainly one type of interaction with the unconscious that has led to creativity, but I have found that it is not as effective as the waking "solution state" about which you wrote.

Dr. Jacques Hadamard's book "The psychology of invention in the mathematical field" is most instructive with respect to how the "solution state" has been experienced. Mathematics is often experienced as a set of possibilities emerging from the unconscious in which one's role is to choose among them based on a number of factors including a sense of aesthetics (the feeling for harmony, elegance, etc.). Sometimes this choice is made without conscious awareness, sometimes this choice is with conscious awareness in the "solution state."

In Poincare's case and fuchsian functions, there was an acknowledgement of prior unconscious work, but there was also work done by Poincare in the "solution state." In this state, he could see the possibilities in front of him. As he observed them, he said they collided with one other and did so until certain pairs of them merged and formed a stable combination. It was this stable combination that Poincare chose to bring more fully into consciousness and into his subsequent mathematical elaborations.

Of this, Poincare writes "It seems, in such cases, that one is present at his own unconscious work, made partially perceptible to the over-excited consciousness, yet without having changed its nature. Then we vaguely comprehend what distinguishes the two mechanisms or, if you wish, the working methods of the two egos." And Poincare emphasizes that this experience of creativity is far more frequent than we might suppose instead of it being the rare case.

Having been a mathematician and theoretical computer scientist before moving to depth psychology scholarship, I can attest to this experience - I had it myself during the tail end of developing and writing my doctoral dissertation in computer science and electrical engineering. My dissertation was heavily mathematical and was titled "A Linear Algebraic-Based Solution Method for Queueing Systems with Highly Correlated Arrival Processes." The general mathematical area would be mathematically-based stochastic modeling. There were certain moments when I felt an almost overpowering sense of possibilities and I experienced these consciously and had to choose amongst these to continue my work.

This "solution state" is very similar to the state one is in with Jung's active imagination, but it is somewhat different. In the "solution state," one perceives the possibilities and their motion (e.g., merging), but one does not interact with them, at least I didn't. And one chooses the possibility, not just with a sense of aesthetics, but also with a sense of pragmatics. In other words, which possibility is likely to be expressible in the language and mathematical systems of the time. This latter sense is absolutely crucial. There are cases when the possibility that one chooses or which makes itself known has no legs in the real world - cannot easily be fit into existing work. But, in general, an essential task and responsibility of the scholar is to do the legwork of expressing this miraculous content in the language and the systems of the time, and sometimes that requires an entire lifetime of hard effort.

We can end, then, with a recognition that the scholar of mathematics and/or science, when presented with such miracles from the unconscious, has a duty and responsibility to judge and make choices in the "solution state" and then to do the really hard work and create the conditions in the real world which will allow it to grow (i.e., integrate it into the present set of systems and ways of thinking, and possibly in terms of applicability to the real problems of the world).

Robert Moss said...

Thanks for adding such depth to this discussion

Robert Moss said...

As you know, Hadamard was especially eloquent on the theme of illumination in the hypnopompic zone. He wrote from his personal experience: "One phenomenon is certain and I can vouch for its absolute certainty: the sudden and immediate appearance at the very moment of sudden awakening. On being very abruptly awakened by an external noise, a solution being 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 quite a different direction from any of those which I had previously tried to follow." - Jacques Hadamard, The Psychology of Invention in the Mathematical Field (Princeton: Princeton University Press, 1949) 8

Worth noting that (1) his was a prepared mind; he had been searching for a solution; (2) the solution came in an entirely unexpected form; and (3) his HP experience may have delivered work done in his dream laboratory that was otherwise forgotten.