Embodied Minds, Surfing and Mathematics

Mark Turner, cognitive scientist at Case Western Reserve, wrote an article that was recently posted on the Social Science Research Network entitled  The Embodied Mind and the Origins of Human Culture.  He makes the point that our awareness is divorced from “Almost all the heavy lifting in human thought and action,”  which is done “in the backstage of the mind.”

What we see in consciousness is not thought but the smallest tip of the iceberg— usually a simple, compressed product of thought, something to keep us going

He also points to what neuroscientists believe may be the number of synaptic connections in the brain, “about ten thousand times as many stars as astronomers think might be in the entire Milky Way galaxy.”

All those connections, inside your head, in a system weighing about 1.4 kilograms, working, working, working. The timing and phases of firing in neuronal groups, the suites of neuronal development in the brain, the electrochemical effect of neurotransmitters on receptors, the scope and mechanisms of neurobiological plasticity—all going on, in ways we cannot even begin to see directly.

Turner is moving toward a discussion of what has come to be called an embodied mind, a notion that relies on the idea that

Since brains are built to drive bodies, it is not a surprise that the nature of the body informs the nature of thought.

These ideas, among others, are used to contrast the current thinking in cognitive science with the now outdated idea (what Turner calls the formalist view) that “thought must be computational, and computation can be described formally…”  While I can’t make a precise comparison, this does call to mind the failure of Hilbert’s program in mathematics. But to stress the uniquely human and non-computational aspect of cultural evolution, Turner looks at the cognitive side of surfing (on the ocean, not the web).  I must admit that I was impatient with some of his surfing nostalgia, but then I found the point provocative and will likely make use of it again.  Turner explains that in surfing:

Your movement is driven not by intention alone (“look where you want to go”) and not by responses to the environment alone, but by a blend of both: the wave gets to decide what it wants to do (an anthropomorphic blend), and you have to anticipate and respond, but you decide when and where you catch the wave and where you want to go. Every movement blends, almost instantaneously, all that physics and all those intentions. (italics my own) In walking or running, you are the motive force of moving along a path…Surfing isn’t just a cut-and-paste combination of things you already do. It is a blend of many of them, with startling emergent properties: in the blend, standing is a means of locomotion, and the way you stand is a means of changing your path.

What I find particularly interesting, and applicable to what we call intuition in mathematics, are the “startling emergent properties” that happen in a blend, unexpected things that are not present in the pieces that make up the blend, nor can they be found in the sum of those pieces. In a talk that Turner gave at a Fields Institute workshop on Cognitive Science and Mathematics, Turner discusses compressed blends, like the blend of directions and positions of boats on the water into the notion of a triangle.  Once we have achieved the identity of a single triangle on the water, there comes an uncountable infinity of triangles fitting those constraints, but they are all packed into a single triangle.  Blending and human memory integrate things that are not coherent and make use of memories that have become decoupled from our environment.  And these may be the seeds of human culture or, for the purposes of this blog, of mathematical worlds. At the end of his talk, Turner offers the following from Philo of Alexandria,c. 20BCE – 40CE

How, then, was it likely that the mind of man being so small, contained in such small bulks as a brain or a heart, should have room for all the vastness of sky and universe, had it not been an inseparable portion of that divine and blessed soul?  For no part of that which is divine cuts itself off and becomes separate, but does but extend itself.  The mind, then, having obtained a share of the perfection which is in the whole, when it conceives of the universe, reaches out as widely as the bounds of the whole, and undergoes no severance; for its force is expansive.

After all of his imaginative thinking, Turner makes the most expected of remarks – something like, we hope to find a more rational explanation than God for the expansiveness of human cognition.  I would argue that seeing that understanding stretches through the whole of the body, that it is not separate from life itself, would make Philo’s observation even more interesting.  In particular, these words: “The mind, then, having obtained a share of the perfection which is in the whole…”  Perhaps the word perfection is no longer fashionable, but we could imagine the mind, having a share of the completed (which is the whole), can reach out as widely as the bounds of the whole…..enjoying another ill-understood blend of physics and intention.

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