Let us suppose there are two nodes in a computational framework. To make it simple, let us call these nodes neurons, and also think of them as if they were neurons. Computation without the possibility of action is not effective in nature. So let us assume one of these neurons (B) can trigger something, such as a muscle contraction. Now let us imagine that there can be a graph of neurons of any arbitrary size between the neurons A and B. Now suppose for whatever reason, fitness is increased if neuron B is triggered after neuron A is triggered. From a fitness perspective, we don't care about the particular path of activation that occurs in the graph of neurons from neuron A to neuron B, only that neuron B is triggered if neuron A is triggered. It seems entirely possible that the path of activation would not always be the same, and that generalization is a kind of ability to repurpose units of computation on a local scale. Whereas one might use a set of neurons to compute something, it might use another set of neurons to compute the same thing. Though, I suspect the range of this kind of shift might be related to a ratio between the density of the units of compute, the speed of communication, the distribution of energy, etc. In this sense, it feels as if the ability to take alternative paths through the graph to achieve the same end result is a primitive form of measuring generalization.

The analogue to physics is the path integral: that a particle can take an infinite number of paths from position A to position B. It would be interesting to do a study on the activation of neurons when parsing the grammatical rules of a language. Could it be that there are certain neurons that more or less correspond to the underlying rules of the grammar. That neuron A represents the start of a grammatical rule and neuron B represent the end of the rule? Is there a linguistic analogue to the path integral?

I suspect that grammar is a computational tool that allows one to fold time. It allows one to computationally wield past experience to generate imaginary hypothetical futures. It allows one to generalize and reason about objects as a class, and not as unique individuals. I also suspect that if a universal grammar exists, that it will not necessarily be linear. Perhaps a universal grammar exists for every number of dimensions a language can unfold itself in.

## Comments

## Post a Comment