Trees in space


The computer science idealization of a tree is allowed to branch at an exponential rate. The rate at which real trees can branch is limited by their being embedded in three dimensional space and not being able to self-intersect.

Sentences have parse trees, maybe similar limitations hold. In English words should not be re-used in the same sentence, a non-self-intersection rule. This could be explained by a sentence being represented in the brain by the activation of a connected set of neurons. Such a setup could not handle conceptual self-intersections [1].

So one can potentially ask "what is the dimension of the mind that produced those sentences?", using Wolfram's definition of network dimension.

Similarly one could observe the eye-saccade patterns of a person to try to infer the dimension of the mental model they are building of a scene -- does it use only short range interactions (like a Markov Random Field), or does it use long range correspondences too (like a wavelet decomposition or feature hierarchy -- abstraction)? This model could be idealized as a Bayesian network (though, if possible, using a non-causal representation).

[1] Except by using pronouns to explicitly note them.