tim_hutton's comments

tim_hutton | 2 years ago | on: Ed Fredkin has died

Fredkin’s Self-Replicating Cellular Automata:

Sum the neighbors, modulo 2, and assign to the cell on the next timestep.

Astonishingly this allows patterns to replicate in multiple directions across the plane. https://cellpylib.org/fredkin.html

Works with any kind of lattice. Even works in 3D.

tim_hutton | 3 years ago | on: What happens when a CPU starts

One route to understanding how CPUs work is to explore the computers that have been made in cellular automata. Golly (https://golly.sourceforge.net/) has several, including one by John von Neumann, one by Edgar Codd and another by John Devore. The advantage of course is that the physics is trivial and you can see everything that happens and step backwards and forwards.

Example:

https://timhutton.github.io/2010/03/10/30984.html

https://github.com/GollyGang/ruletablerepository/wiki/CoddsD...

tim_hutton | 4 years ago | on: Journey to the Edge of Reason: The life of Kurt Gödel

Gödel's incompleteness isn't a practical obstacle to proof assistants - it will never stop us formalizing proofs and searching for new theorems. It's irrelevant to their operation and will continue to be for all time.

If Gödel's incompleteness applies to the theorem you are trying to prove then it means that the theorem has been very carefully set up with reference to the axioms that you are using in order to be unprovable. It's not something you will stumble across otherwise.

Think of it like this: imagine knowing that maths will stop working if a certain very specific enormous number appears in your calculation. This would keep mathematicians up at night with worry but it would have no practical effect on anyone else because the enormous number simply never appears.

page 1