Skip to main content

A grammatical organization of pattern recognition

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

Popular posts from this blog

Time, partitioning, and synchronization

Any time measuring method inevitably runs into the issues of partitioning and synchronization. Partitioning deals with the issue of dividing a larger measure into smaller measures, and combining smaller measures into a larger measure. Synchronization deals with the problem of how a set of devices can self-correct if some of them are corrupted. The two are fundamentally related because often a choice in one determines a choice in the other. A measure is often defined by a set of synchronization points, such as the radioactive decay of an element or the frequency of a crystal oscillator. Synchronization points can often be defined as a measure of a change in space, such as the revolution of a planet around a star, or the change in energy state of an oscillating structure. Fundamental to both is the notion of change. A synchronization event can only be defined if there is a unit of space in which a change is observed. And either the magnitude of the space is large (such as the movement of...
Post a Comment
Read more

Individuality, creativity, and trust

Trust is an individual experience and a personal feeling. In a sense, trust only exists as a subjective experience. Objectively, the behaviors that manifest from trust are more akin to chemical reactions, where one's feelings of certainty in regard to one event trigger another event. The source of all trust is individual perception, and if one cannot trust their own senses, they can trust nothing. Fundamentally, the observation of natural events allows the mind to create an ordering. Such an ordering is often a direct reflection of the mechanical nature of the world. A feather falls when it is dropped. A pool of water evaporates in the sun. These certainties leave an impression on the human mind, and also set an expectation for human constructions. Subconsciously, individuals expect society to operate in a manner similar to nature. Just as a feather falls when it is dropped, they expect good deeds to be rewarded and bad deeds to be punished. One only has to observe a feather fallin...
Post a Comment
Read more

Causality, Interaction, and Complexity

In a highly chaotic system, such as a high temperature gas, it is not ideal to use an atomic causal model. Instead, the effective causal model is to approximate to what extent each atom is interacting with every other atom. If we increase the temperature, then the number of atoms each atom interacts with should increase. As the temperature decreases, the number of atoms each atom interacts with should decrease. If we were to randomly sample any atom, then on average, the atom should interact with a set of atoms of a certain size. Instead of thinking in terms of conditional probabilities and causal implications, we think in terms of sets of interconnected events. And this is because it is not computationally effective to analyze chaotic systems in a linear manner. We can apply the same line of reasoning to sampling. If a system has a particular sampling rate, the inputs to the system are batched according to the sampling rate. In other words, the system cannot discern the ordering of ev...
Post a Comment
Read more