Seeing, dreaming and mathematics
I was struck by the clarity of statements made about perception in a recent Mind Hacks blog. When Tom Stafford reports on a talk he just gave in Berlin he says this:
Perception is the production of meaning, not the production of images. Our associations and experience are incorporated in the act of perception, so that they are intrinsic to the perceptual act (not somehow added “on top”, or as an after thought).
That one cannot separate seeing from comprehension is a vital part of how the visual brain is now understood. Also gaining traction in biology is the idea that there is a kind of continuum of cognitive mechanisms – from the chemistry of proteins receiving and transmitting signals, to the cognitive acts of organisms. Cognition, in this sense, is consonant with living.
Stafford used the idea that perception is the production of meaning to explore why a city can be so difficult to navigate for someone from another country.
Native city dwellers have learned to read the city, through experience forming webs of association that build up into symbols. This allows them to instantly perceive what different scenes in the city mean for how they should act.
These “webs of associations” are probably the way we do anything. It is the way the body establishes its reality. And “web of association,” of course, will inevitably lead me to mathematics. But this time I would like to get there through another observation - about sleep.
Back in 2007, Radiolab did a show about sleep. The show’s segment on dreams featured two individuals who each investigate cognitive activity that happens during dreaming. The first to speak was Robert Stickgold of the Harvard Medical School who has found a way to study the relationship between memories and dreams. One of his talks is posted on YouTube. It’s called Sleep, Memory and Dreams: Fitting the Pieces Together. He summarizes his main points with the following list of what happens during sleep dependent memory processing. During sleep, he explains, the brain:
stabilizes, enhances and integrates new memories
extracts rules and the gist of things – the idea common to multiple experiences
integrates new and old memories
imagines possible futures
These are all about meaning, like the meaning that the visual brain gives to perceived objects, or that language gives to experience, or that mathematics gives (even to itself).
It’s also interesting that Stickgold has been able to demonstrate that, during sleep, the brain plays with memories that may not be available for conscious recall. This is probably true of any integrative or synthesizing cognitive activity. He co-authored a paper on sleep-dependent learning where he describes a classification scheme for the many things we call memories. The paper can be found here.
The bit of information that MIT professor Matt Wilson contributed to the Radiolab broadcast was particularly interesting to me and loaded, I thought, with potential insights into learning and creativity. In his own research, Wilson has learned how to read the sound of the electrical signals from thousands of individual nerve cells in the brains of rats. He could identify when sleeping rats replayed or revisited maze roots that they had learned when they were awake. But the very interesting piece is that when a rat was given more than one maze route to run, it began to invent entirely new routes when it was sleep. Wilson described the dream-like creativity of this rat as a demonstration of how sleep can provide a unique opportunity to learn. In our experience, he suggested, this would give us a way to take two apparently unrelated things, find the connection, the hidden rules (or gist as Stickgold calls it) and create something new. That a perceived sameness triggers invention (where a single experience does not) is a really interesting detail. The experience of more than one opens the door to ‘others.’ It is as if some idea of a ‘class’ of things has been introduced. There isn’t an obvious reason for why the rat begins to synthesize and invent. But it does cause me to wonder about what would cause this spontaneous, sleep driven invention to transition into a more directed one.
At the source of most mathematical invention is a perceived sameness – like all instances of two things or all possible triangles or all possible geometries, the space of all functions or all possible spaces. This work on sleep, together with what has been understood about cognition in general, suggests that the body is always poised to structure, invent and comprehend, even without any direction from our conscious mind. And I myself have little doubt that this has contributed to the emergence and development of mathematics.