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.

Yoga of Consciousness in the Place between Sleep and Awake

"You know that place between sleep and awake, the place where you can still remember dreaming? That's where I'll always love you. That's where I'll be waiting."

-          

                  - Tinker Bell to Peter Pan in the movie "Hook"

I have been following these fairy directions for a very long time. If you can train yourself to maintain a state of relaxed attention in this in-between state, you will notice that you may be receiving a whole menu of possibilities for lucid dream adventures. Images, faces, landscapes rise and fall. When you learn to hold one of them in focus, it may become the portal for a conscious journey.
    The Parade of Faces is a frequent phenomenon in this state. You may feel you are among a crowd of people, with faces and figures rushing by. Sometimes one may turn to look at you, which can be an interesting opportunity to enter a shared experience with another dream traveler you may or may not know in ordinary reality.
    Sometimes the images rising and falling before you look like a child's sketches, or cartoons.
    A frequent sighting for me, in this in-between state, is of what initially looks like the weave of a carpet or the mesh of a net. I have come to recognize this as a kind of border between states of reality and consciousness. With intention, I can part the strands and find myself in another order or reality.
    The liminal state of hypnagogia, which I often call the Twilight Zone, is a good place to become aware of your ability to travel beyond the body. I often find myself lifting out of the body quite effortlessly in this state, without bumps and grinds. Sometimes, when tired, I simply rest half in, half out, of my physical form. Sometimes I float up to the ceiling. Quite often I go flying, like a bird, over my sleeping city and to places far away.
    As Tinker Bell counseled, the Place Between Sleep and Awake is, above all, a wonderful place to rendezvous with other beings and other intelligences. It is a state in which we often become away of the psychic activity around us.
    Often, I find different casts of characters waiting or popping up as I hover on the edge of sleep or linger in the twilight zone of hypnagogia. Sometimes, they appear to be quite literally on stage, or in the wings, waiting for me to show up in order to start or resume a play. More often, they seem to be characters in life dramas that are being played out in other times or in parallel worlds, dramas in which I have a lead role from which I may have been absent while attending to things in my default reality.
     I frequently have inner dialogues in the Place Between Sleep and Awake, with sources of knowledge I have come to trust. This is a time when I can often receive streams of counsel and information from inner guides. In Dreamgates, I record some of my conversations with the intelligence I decided to call "G2". He carried the vocabulary and knowledge of a great Western Mystery order. I felt he was a transpersonal figure, though in no way alien to me. Many others have come to me in this liminal state. The most important of these inner guides is certainly no stranger; he is a self who observes and operates on a level of reality above the one I inhabit while living on this Earth in a physical body.
    In the history of creative breakthroughs in every field, including science and technology, the hypnagogic state has been of vital importance. In this liminal zone it is easy to make creative connections, which often involves linking things that seem to the routine mind to be unconnected. Many inventions and discoveries attributed to dreams by over-hasty writers - like Kekule's discovery of the benzene ring - are actually gifts brought through from hypnagogia, to such an extent that I call this zone of consciousness "the solution state" in The Secret History of Dreaming.

        It is surprising that so little has been written about the nature and manifold possibilities of this liminal state in the literature of sleep and dreams. Greek Cypriot author Andreas Mavromatis wrote the only book I know entirely devoted to this liminal state of consciousness, marrying scientific data to rich accounts of creative and visionary accomplishments in this zone. In Hypnagogia: The Unique State of Consciousness Between Wakefulness and Sleep, originally published in 1987, Mavromatis writes that

“Hypnagogia…facilitates the emergence into consciousness of material that might otherwise remain unconscious. It might, thus, also constitute the platform onto which is periodically raised the substratum of continuous but not always conscious mental activities taking place throughout life. As such, it opens great vistas of psychological exploration. Its introspective study may furnish the individual not only with the benefits of an integrated personality but also with the means of discovering new or little known modes of experiencing which will undoubtedly enrich him/her as a psychological entity.”  

    The Place Between Sleep and Wake can be the very best place to go on with a dream or go back inside one. You may want to practice dream reentry to clarify information from a dream, or get to its full meaning, or continue a conversation with a dream character. You may need to reenter a dream because there are terrors to be overcome, or a mystery to be explored, or simply because you were having fun and adventure and would like to have more. Or because Tinker Bell is waiting for you.
    The Place between Sleep and Awake is the best place to develop the continuity of consciousness prized by advanced practitioners of the yoga of sleep and dreams. I am talking about growing your ability to maintain awareness and witness perspective as you move back and forth between sleep, half-sleep, dream, lucid dreaming, what Sri Aurobindo called “the sleep of experiences” and the dream of everyday life.


Art: "The Victory" by René Magritte (1939)

Finding solutions in the place between sleep and awake

As I lay in bed early on a rainy Saturday morning, it occurred to me that the drifty state after waking can sometimes be - quite literally - the Solution State.

     I did not initially have narrative dream recall. Instead, I found that my mental field was like an ocean of clean, translucent oil, in which many images and ideas were floating and bobbing. I could reach around and choose some of them to mix and match, and to bring into clear resolution. As I did this, I was given very clear solutions to a number of specific problems and imagery sequences I could now develop - or allow to develop - into dream movies with plotlines.

      It struck me that this kind of experience takes place in a kind of dream matrix that could be called a Solution in the sense that many elements and possibilities are suspended in it - and that creative people have the ability, in that state of relaxed attention (or attentive relaxation) of entering the Solution State to bring through solutions.

     In The Secret History of Dreaming,, I describe how in many fields - most notably in the history of scientific breakthroughs - the Solution State has been the vital place of creation.  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 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.

    One of the most famous – and problematic - “dreams” in the history of science involves the dream of a snake biting its tail. It was this vision 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.
     The base camp for this kind of operation, let us note, was the liminal state of hypnagogia. In a movie of Peter Pan, Tinker Bell tells Peter, "Look for me in the place between sleep and awake. There you will always find me." The fairy's advice was correct. This is the place where we find magic of many kinds, including the magic or creative breakthroughs and scientific discoveries.

For more on the history of scientific breakthroughs in the "solution state", please see The Secret History of Dreaming.

Graphic: Ouroboros in a drawing in a 1478 copy of an early medieval treatise on alchemy attributed to Synesius.