The Practical Use of Dream-States

In the sleep of reason, what dreams may come?

I was reading an article by David Bessis titled, “The real mathematics is the one that we dream.” In it, he gives examples of mathematical insights that came in dreams - from Grothendieck’s obsession with dreaming to Ramanujan’s dream of formulas written in a flowing wall of blood to a paper that cites a deceased coauthor who appeared in a dream. Warning of the dangers of entering dissociative states, he wrote:

“When performed outside of mathematics, without the ultimate guidance of formal systems, reckless acts of imagination rarely produce valuable insights.”

I agree with Bessis almost completely. The bulk of his argument is against mathematical Platonism and I think he’s almost certainly right. His meta-argument is that we shouldn’t think of competent mathematicians as anointed prophets with some special access to the spirit realm… and again, it’s hard to disagree. If anything, my view is simply more extreme. I would make the case that there’s nothing more normal than finding a creative solution to a problem in a dream and that, in a concrete, physiological sense, this is exactly what dreams are for. Let me explain.

The history of science is full of reckless acts of imagination producing valuable insights. It is said that Kekulé fell asleep puzzled about the structure of benzene, dreamt of a snake eating its tail, and woke up with the answer. Mendeleev is said to have fallen asleep while working on the periodic table and watched the elements fall into place in his dreams. One study gave participants a mathematical task with an unstated shortcut. They found that letting the participants doze off for just 15 seconds tripled the chances that they would notice the shortcut. To understand the connection between sleep and creative insight, we have to understand why we sleep in the first place.

Imagine that you are sitting at a desk looking at a stack of papers. Your job is to categorize them, discard anything unimportant, and understand the big picture of the information they contain. But as soon as you get to work, the secretary barges in with another stack of papers. And another, and then another. There are too many papers to fit on the desk and they are falling all over the floor, and yet the onslaught continues. You are drowning in papers. This is a terrible plan - let’s try another way.

The secretary brings in stacks of papers until you reach the limit of what you can store and process at once, and then you get up, close the door, and begin to work in peace. This is sleep, from your brain’s perspective.

When awake, the brain is constantly bombarded by an onslaught of information from the senses. Rather than try to make sense of it all in the middle of the flood, it periodically shuts the door to external input so it can process everything in peace. This is the cause of a phenomenon called sleep-dependent learning, where we notice that a wide range of skills, from athletic to musical, show a notable improvement after a period of sleep without any additional practice. When we sleep, our brains are not really at rest, they are actively making sense of the input they have taken in.

But the study I mentioned found that just a few seconds in sleep onset tripled the chance of experiencing a mathematical insight. If this were a case of offline learning, you wouldn’t expect that such a short period of time would make such a difference. When we talk about dreams and creativity, we’re actually talking about several distinct states that have different functions. There’s the first phase of sleep onset, N1 (also called hypnagogia), REM (when we dream most vividly), and perhaps also daydreaming (the activation of the brain’s default mode network, which is also active in REM). Let’s start with N1.

You could expect that the creative approach of the inventor Thomas Edison would be completely different from that of the Surrealist painter Salvador Dalí. You would, of course, be wrong. Both had the same peculiar method of getting un-stuck and finding insight: they would sit in a chair holding something metal and let themselves doze off until their hands relaxed and the sound of the crash woke them. This is what happened in the experiment: a brief moment in N1.

N1 is a middle stage between sleep and wakefulness, when you begin to separate from the external world and executive control is partially, but not completely, lost. Associations between thoughts become looser, less logical and you begin to experience spontaneous, brief auditory and visual hallucinations.

I’m sure I don’t need to explain why this type of state of consciousness is associated with madness (although, remember that this happens to all of us every night). But you could also say that on the spectrum of highly ordered to highly disordered cognition, madness lies at both extremes. Many of the most common forms of mental illness are actually characterized by highly ordered, pathologically inflexible thinking. Obsessive-compulsive disorder arises from an intense fixation on a disturbing thought, anxiety is getting stuck in looping thoughts of worry, depression involves getting stuck in looping thoughts of rumination…

We can see that unhelpful fixation is also a major hazard when it comes to problem-solving. We can fixate on clues that aren’t really relevant, decide on a mediocre strategy and get pulled forward by the momentum of confirmation bias, or get trapped in the well-worn groove of whatever worked before but doesn’t actually work now. If we accept that more structured thought isn’t necessarily better, that instead the ideal may be to maintain freedom to move between different modes of thought, we can begin to see the benefits of a moment in N1. If the problem is too much order, the solution is more disorder. If you are stuck, hit the reset button.

We progress from N1 to N2 to N3, and then go into cycles of REM. When we wake people up at different points in the night during REM sleep, we see that dreams evolve in a particular way. Although the content in N1 is typically closely related to whatever you were thinking of right before falling asleep, the focus during REM tends to be on something with a high amount of emotional resonance. It’s thought that the processes in N1 may select certain problems as being particularly important on the basis of the emotional response they provoke and tag them for deeper processing. The evolution we see is like this:

The dreams start out relatively straightforward (I am arguing with my uncle) before becoming more and more bizarre (I am on a spaceship, arguing with my uncle) until they often become so illogical that they’re difficult to explain (I am arguing with my uncle, who is also the actress Renée Zellweger). Could it be that the very bizarreness and illogic of dreams may serve some purpose?

When we think of what it means to be good at creative problem-solving, an important feature is the ability to find useful connections between concepts that you wouldn’t normally connect. Mendeleev dreamt of the periodic table, but this was after he spent years working on the problem. He had all the information he needed to solve it already stored in his memory, he just needed to find the right way to put it all together. In REM sleep, your brain prioritizes connecting distant memories it wouldn’t normally connect, searching for an unexpected connection that solves the problem. It is attempting to scan the entire solution space.

We tend to think of sleep as a nuisance, a waste of time to be minimized as much as possible. And we think that productivity is spending as much time as possible in a state of unbroken, intense focus. But the truth is that breakthroughs often come from releasing a high level of executive control. We’re all familiar with the famous shower epiphany. The idea that creative breakthroughs often occur during a period of diffuse thought after a period of focus is well-supported and has its roots in Poincaré’s description of his process as a mathematician. Yet modern life conspires to keep us out of these states as much as possible. We’re continually bombarded with stimuli from music and other entertainment, which keeps us in a state of constant, low-level focus at all times.

The thing that unites Edison, Dalí, Grothendieck, Ramanujan, Kekulé, Mendeleev, and Poincaré is that, rather than just rely on brute force induction, they all moved freely between all the faculties available in their minds. In a very concrete, neurological way, to paraphrase the Fields medalist Bill Thurston: dreams are a feature, not a bug.