Tuesday, September 15, 2009

How I Spent My Summer

Obviously I have not spent time on the blog lately. I had a busy time indexing a technology book, and when that was done was behind on many other things. I have also been doing a considerable amount of studying on issues of machine understanding, but delayed my project of going through On Intelligence by Jeff Hawkins and explicating it. I have read it twice now; I am not ready for a third read. I did look at the web sites associated with the Hawkin's model, and will report on them when I have a chance to study them in more detail.

I am reading, or wading through, Neuron to Brain by Stephen W. Kuffler et al. The chapter on the structure of the visual cortex was near the front, which made interesting compare and contrast reading with On Intelligence. But I did not make the effort to write up my thoughts, and that must now wait for a vacation from other duties.

I have become better at tensor analysis, which had the added benefit of making Einstein's "The Foundation of the General Theory of Relativity" readable. I don't think tensors are going to be good models for neural networks, but the concept of invariance is well-developed with tensors and it seems central to the topic of maching understanding. By thinking about the structure of neurons in the brain, and invariance, I hope to at least exercise my mind in the vicinity of the problem.

Today I am fascinated by the possible application of metrics, inner-product spaces, and invariant angles to the question of how human babies construct their mental world. I was struck by the important of coordinating tactile senses with vision and auditory sensation. The main apparatus for this is the human arm. Excluding the hand, the arm consists of two big angles, one at the shoulder, the other at the elbow. There are a lot of degrees of freedom therein. To grab objects requires a lot of coordination. The angles are going to vary with muscle tone, which is controlled by the motor areas of the brain. But the general space should be an inner-product space. Changes of coordinates, say if the coordinate system was directed from the eyes, would not change the angles, lengths, or positions of the hands.

It makes me think about how flexible the human mind can be, and then contrast with how rigid people's thoughts can be. Once we learn about Euclidean space we tend to think we are walking around in it, with the ground as a two-dimensional plane. The idea that a coordinate system could be anchored by an imaginary line perpendicular to a line connnected the eyes strikes us as peculiar. Yet we use that coordinate system constantly, perhaps more than any other.