Philosophy of Mathematics

Space-Time Visualization

While paying attention to a mathematics forum it became clear that there would be positive uses for LLMs. Coming from the perspective of philosophy of mathematics and different world views that entertain eternity, subaeternity, infinity, and such, I decided to see what would happen while looking at this idea of "mono semantics". Monosemantic representations are an idea that have been developed in AI with the understanding that all symbols can be all part of one formula or algorithm.

4D Hilbert Curve on a Klein Bottle

Infographic: a 4D Hilbert curve mapped onto a Klein bottle, visualising the relationship between limited time and eternity — the curve flows seamlessly along the bottle's surface, returning to its starting point after completing the full cycle — The 4D Hilbert curve mapped onto a Klein bottle — a non-orientable surface with no boundary — creates a visual metaphor for time that is both finite (a loop) and infinite (a seamless continuum), where the end is the beginning.

Hilbert Curve in the 4th Dimension

Infographic: a 4D Hilbert curve projected into 3D, showing the time progression across sixteen steps as the continuous space-filling curve visits every point in a 4D grid exactly once — A continuous space-filling curve that visits every point in a 4D grid exactly once, projected into three dimensions with time as the fourth axis — at each iteration the curve fills the space more completely, preserving locality better than simpler mappings.