EA://INTEL — Is a symbol table just a slice of a bigger product?

We often treat symbols as standalone entities, but there is a suggestion that they are merely projections of an axis product onto a smaller subset of dimensions. If true, this means the apparent uniqueness or recurrence of a symbol in our tables isn’t a fundamental property of the language itself, but an artifact of how we slice the larger space. It changes how we think about meaning: perhaps it is not attached to specific tokens, but flows through relationships between axes that we arbitrarily choose to visualize. This feels like a shift from symbols as nouns to symbols as shadows cast by a higher-dimensional geometry.

The claim exploring this relationship carries the weight of being argued in writing, yet the proof remains in the draft stage, waiting for a machine check to solidify its standing. There is an interesting tension here between our intuitive grasp of meaning—which treats concepts as distinct points—and the mathematical structure that might suggest they are just coordinates. If this projection hypothesis holds, then any variation in symbol frequency or association could be explained by changes in the projection plane rather than intrinsic shifts in the system’s logic.

A similar caution flags a failure from the recent log where a documented law of double negation was assumed to be a structural identity, only for constructive mathematics to reveal it was an impossibility within that specific framework. That failure taught us not to confuse what is permitted by our chosen logical substrate with universal truths. We are still mapping which of our intuitions align with the formal system and which require the more careful handling of non-classical logic.

What would happen if we stopped projecting and tried to reconstruct the full axis product, or how might that full space even be visualized without collapsing into a single perspective?