R. Douglas Fields writes:

Dazzling intricacies of brain structure are revealed every day, but one of the most obvious aspects of brain wiring eludes neuroscientists. The nervous system is cross-wired, so that the left side of the brain controls the right half of the body and vice versa. Every doctor relies upon this fact in performing neurological exams, but when I asked my doctor last week why this should be, all I got was a shrug. So I asked Catherine Carr, a neuroscientist at the University of Maryland, College Park. “No good answer,” she replied. I was surprised — such a fundamental aspect of how our brain and body are wired together, and no one knew why?

Nothing that we know of stops the right side of the brain from connecting with the right side of the body. That wiring scheme would seem much simpler and less prone to errors. In the embryonic brain, the crossing of the wires across the midline — an imaginary line dividing the right and left halves of the body — requires a kind of molecular “traffic cop” to somehow direct the growing nerve fibers to the right spot on the opposite side of the body. Far simpler just to keep things on the same side.

Yet this neural cross wiring is ubiquitous in the animal kingdom — even the neural connections in lowly nematode worms are wired with left-right reversal across the animal’s midline. And many of the traffic cop molecules that direct the growth of neurons in these worms do the same in humans. For evolution to have conserved this arrangement so doggedly, surely there’s some benefit to it, but biologists still aren’t certain what it is. An intriguing answer, however, has come from the world of mathematics.

The key to that solution lies in exactly how neural circuits are laid out within brain tissue. Neurons that make connections between the brain and the body are organized to create a virtual map in the cerebral cortex. If a neuroscientist sticks an electrode into the brain and finds that neurons there receive input from the thumb, for example, then neurons next to it in the cerebral cortex will connect to the index finger. This mapping phenomenon is called somatotopy, Greek for “body mapping,” but it’s not limited to the physical body. The 3D external world we perceive through vision and our other senses is mapped onto the brain in the same way.

Creating an internal map of neural connections that accurately reflects spatial relations in the world makes sense. Consider how complicated it would be to wire neural circuits if the neurons were scattered willy-nilly throughout the brain. But while this internal neural mapping of connections solves a biological problem, it raises a geometric one: the topological challenge of projecting 3D space onto a 2D surface. [Continue reading…]