Neuroelectrodynamics

One of the million or so things that interest me is the question of how the brain actually accomplishes anything. This is relevant to linguistics because, well, that's sort of obvious. A prevalent model of neural computation tells us that the brain computes by passing information among various neurons, and that these neurons encode messages in sequences of action potential 'spikes' by a mechanism known as "spike timing."

A new book by Aur and Jog challenges this whole paradigm. It carries the strangely ungrammatical title Neuroelectrodynamics: Understanding the Brain Language and the grammar between the covers is no improvement, but it is very provocative and enticing to those of us who think that the current state of understanding in neuroscience is extremely poor.

The authors first demonstrate that neuron 'spikes' are not uniform or stereotypical, which itself goes against a main tenet of the spike timing model. They then outline a new scheme by which a new quantity of spike 'directivity' is encoded into the charges in movement during an action potential. Empirically, the details of dendritic arbors and axonal branches significantly modulate the extracellular action potential. Axons themselves cannot be approximated by linear cable models.

In the authors' charge movement model, different charges or groups under an electric field have distinct movements. To apply independent component analysis (ICA), the action potential is assumed to be the result of several independent sources, generated by charges that move. For recorded action potentials, blind source separation (a known signal processing technique) can be performed using ICA. The charge localization is obtained from triangulation and a point charge approximation. Singular value decomposition is performed for the matrix of charge coordinates. A 'spike directivity' can be described by a preferred direction of propagation of the electric signal during each action potential, and approximated with a vector. This is shown to be a much more effective means of encoding information and computation than spike timing. Details of the spike directivity are said to be published in other papers by the authors, which did appear in major neuroscience journals.

It is interesting to see how the current paradigm in neural computation could well be founded on nothing. The authors' ideas may not be proven, but they certainly have some interesting empirical findings which defy explanation otherwise, and it seems clear to me that the brain can't be doing all its work with spike timing.

Road to Reality

This summer I've been reading one of those few books that can change your life, The Road to Reality by Roger Penrose. This is basically all of modern theoretical physics, including the mathematical fundamentals starting from first principles. I have finally gotten through all the initial mathematical chapters, which include a quick rundown of Riemannian geometry and differential forms on manifolds. Why is it that mathematical physicists make the best math teachers? I also changed my life a few years back by reading Lectures on Mathematical Physics by Robert Geroch.

I suspect that this approach to geometry could be useful for a new approach to semantics and cognitive science (see previous post on the musings of Fenstad).
Geometry is so crucial to our understanding of reality (i.e. physics), it should not be surprising if it turns out to be crucial to our understanding of language and cognition as well.