Re:Words Are a Byproduct of Consciousness. For LLMs, It's Ba...
by gowld on Tuesday June 30, 2026 @11:58AM
(#48734597)
Geometry pictures are absolutely not "rigorous definitions". For 1 thing, pictures of lines aren't finite in extent, and pictures of points are finite in extent.
Some of Euclid's proofs are wrong, because they relied on those non-rigorous picture definitions.
* Book I, Proposition 1 (constructing an equilateral triangle)
* Book I, Proposition 4 (Side-Angle-Side triangle congruence).
* Multiple theorems throughout the Elements rely on the visual "betweenness" of points.
Some of Euclid's proofs are wrong, because they relied on those non-rigorous picture definitions.
* Book I, Proposition 1 (constructing an equilateral triangle)
* Book I, Proposition 4 (Side-Angle-Side triangle congruence).
* Multiple theorems throughout the Elements rely on the visual "betweenness" of points.