I asked myself a naive question just the other day: “What is a thought?” I wondered about it when, during a workout, I saw my mind drift, and a chain of unrelated memory fragments were brought to my awareness through spontaneous, even nonsensical associations. Their shared presence was prompted, perhaps, by words or by something else that connected them of which I was unaware. This kind of mental drifting is the justification, in fact, for the free association employed by some psychotherapists to uncover unconscious associations that may be affecting a person’s experience. But, as many of my observations do, it made me think of mathematics. Because, crucial to the development of mathematics is the emergence of relationships among thoughts that first appear to be unrelated.
My question led me, this morning, to look at the new and very ambitious project called the Human Connectome Project. Collaborators on this project explore the complex relationships among billions of neurons that are responsible for the whole of human experience including (a Wall Street Journal article noted) reason, memory and emotion.
I’m not sure why we wouldn’t immediately include imagination.
The word Connectome shares the ome with genome, the entire sequence of an individual’s DNA. The naming anticipates a similarly complete mapping of the hidden biology that somehow makes a particular individual who they are. It is the topic of a recent book and website by MIT scientist Sebastian Seung: Connectome: How the Brain’s Wiring Makes Us Who We Are. Seung spoke at a TED conference in 2010.
The talk only encouraged me to think along the lines I’ve been thinking. Making the sheer vastness of this neuroscientific task clear, Seung explains that there are 100 billion neurons in a human brain, and each one touches many others. He estimates that there are a million times more connections than there are genome letters and, while recalling Pascal’s dread of the infinite, said that the brain is “so awesome in its complexity, it might even be infinite.” So maybe it is also from within that our notions of infinities grow.
These neural connections, or synapses, are responsible for the most fundamental aspects of life itself, movement, respiration and digestion as well as the complexities of human thought. In his talk Seung makes clear that neuron branches that create these connections can both grow and fall away, that synapses themselves can be created or eliminated, grow larger or smaller. The hypothesis is that, with neural activity constantly changing, thinking can change your connectome. It is here, he suggests, that nature meets nurture. He draws an analogy between consciousness and a stream, where neural activity is seen as the water and the connectome as the water’s bed. The stream’s bed, directs the flow of water but is also changed by the water’s flow. We’ve all thought about the stream of consciousness, but perhaps not about how the streams bed can be changed.
There is certainly quite a lot that can be gained from an ideas analysis of mathematics, (like the ones proposed by Rafael Nunez) or the investigations of hardwired quantitative and spatial perceptions (like those of Stanislas Dehaene) But a true appreciation of the nature of mathematics may yet be gained by its resemblance to neural processing itself. Our early observations of quantity and spatial relationships have developed, in a very organic way, into complex mathematical relationships and systems. If one were to try to make a schematic drawing of their advancement it would resemble many things organic, including our own synaptic trees. Numbers, once notches on a bone, become digits that then advance from their correspondence to fingers, to their manifold roles in analyzing complex relationships among sets of abstract objects and abstract spaces, and these eventually lend us images of an increasingly vast cosmos or the probabilities of a subatomic particle’s existence.
It may be that ideas like Max Tegmark’s (that the world is a mathematical object) or the Plantonist position held by many mathematicians (that mathematics is its own independent reality) are inspired by the fact that thought and reality are two sides of the same coin, that they cannot be separated, that the physical processing of thought does not create the thought, but somehow is the thought. It is likely that the pristine abstractness of mathematics makes it one of the most effective mirrors of both the reality we see around us and the reality that is us.