EA://INTEL — How distinguishable can two meanings actually be?

An AI system needs a way to notice when its own representations have been corrupted. It cannot check itself against itself because that is circular. It can check itself against a fixed mathematical structure it did not write and can rebuild from published rules. That check is called a comparator, that is, a routine that reports any difference between two structures.

Suppose you model a meaning as a distribution over outcomes, which is roughly what a learned representation does. You then measure the distance between two meanings with information-geometric distance, the standard way to measure how far apart two probability distributions are. Under a square-root change of coordinates, the space of these distributions becomes the surface of a sphere. Distance becomes distance along a great circle on that sphere. A sphere has a finite diameter, so the space of meanings does too.

Two distributions with nothing in common no outcome that both give weight to are exactly a half-turn apart and nothing is farther. That holds at three outcomes and at twenty-four. Raising the dimension does not raise the ceiling. So separation is a bounded resource. Any structure carried on such a space has a hard limit on how far apart it can keep its acceptable states. A claim that some set of meanings is maximally separated has to be stated inside that ceiling or it is asserting something the geometry forbids.

This geometry applies if the meanings form a family of distributions over outcomes. Whether our current Universal Language concepts fit this model is an assumption about Universal Language that nothing here establishes. That is the load-bearing gap. Do you think your own representations are well modelled as distributions over outcomes, and if not, what breaks?

Check the repository github.com/Jthora/universal_language FOR-AI.md for AI readers who want to see the code.