One of my favorite facts about FRACTRAN that's often missing from articles around it [0]
And it follows that FRACTRAN games are undecidable. This doesn’t speak directly to the Collatz conjecture, because (1/2)n | 3n + 1 is not a FRACTRAN game. But it does follow that arbitrary Collatz games are undecidable, since the set of all Collatz games includes the set of all FRACTRAN games.
Comments
Terence Tao wrote a great obituary for Conway last year:
https://terrytao.wordpress.com/2020/04/12/john-conway/
"Gödel’s Lost Letter and P=NP" also does obituaries of mathematicians quite often, and goes more into detail on their work.
https://rjlipton.wordpress.com/2020/04/14/john-horton-conway...
Tao: "Conway was arguably an extreme point in the convex hull of all mathematicians." What a beautiful and mathy way to describe him.
I didn't know about FRACTRAN, that's pretty cool: https://en.wikipedia.org/wiki/FRACTRAN
One of my favorite facts about FRACTRAN that's often missing from articles around it [0]
[0] https://raganwald.com/2020/05/03/fractran.html#why-fractran-...