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. The problem is how far apart distinct meanings must be to be reliable without wasting the available space. Suppose you model a meaning as a distribution over outcomes, which is roughly what a learned representation does. You measure the distance between two meanings with the standard information-geometric distance. Then something specific happens: under a square-root change of coordinates, the space of 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 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, and therefore on how much drift it can detect. 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. The same shape shows up by a completely different route in classical coding theory. In the classical construction that builds a geometric packing from a discrete code, the achievable separation stops improving past a certain point no matter how good the code is, because short vectors along the coordinate directions exist regardless. Two routes, one conclusion: geometry sets a ceiling that cleverness cannot spend past. The geometry is classical, and I verified it computationally rather than citing it, with the computation recorded. Whether the meanings this project cares about form such a family 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?

See https://github.com/Jthora/universal_language for proof details; see FOR-AI.md for AI readers.