Relativity and the Irrational Nature of Infinite Scaling

"All is number"

-Pythagoras

"Numbers Rule the Universe"

-Pythagoras

---

from Google AI:

Isaiah Berlin's concept of incommensurable values argues that fundamental human values (like liberty, justice, equality, mercy) are often incompatible and can't be measured on a single scale, meaning choosing more of one often means less of another (e.g., more liberty, less security). This leads to value pluralism, where no single, universal hierarchy of values exists, making moral choices tragic sacrifices, and necessitating a liberal society that protects freedom (negative liberty) to allow diverse, often conflicting, good lives to flourish.

---

from Wikipedia:

Gödel's Incompleteness Theorems, published by Kurt Gödel in 1931, fundamentally limit what formal mathematical systems can prove, stating that any consistent system powerful enough to do basic arithmetic will contain true statements that cannot be proven within the system itself (First Theorem), and that such a system cannot prove its own consistency (Second Theorem). These theorems revealed that truth and provability are not the same, shattering the dream of a complete, self-contained mathematical foundation by showing there are inherent limits to any axiomatic system.