Languages
Questions:
- What is language?
- What is a model of language?
- At what level should this model be constructed (acoustic, neural networks, cognitive, etc...)?
One answer:
- Language is a set of phonemes, together with a (dynamical) system which is sensitive to temporal structure in these sequences.
- A model of language is a representation of the phoneme space in which the major features of language, such as grammatical structure and acoustic detectability, are natural reflections of geometric properties of this space.
- This model should incorporate learned pattern recognition, in the form of adjustments to metrics on the space. Whether or not higher cognitive knowledge should be incorporated would depend on whether our current understanding of physiology (physical pathways and measurements of live signals) indicates this.
Idea: Construct a space $(P, m)$ of phonemes with a metric that encodes the energy of a the trajectory of a given sequence through time. A very large energy would typically reflect an improbable or nonsensical sequence of sounds. Real sentences would tend to follow low energy paths.