Degree of a polynomial Updated 2025-07-16
Pendon Museum Updated 2025-07-16
County in South East England Updated 2025-07-16
South East England Updated 2025-07-16
Regions of England Updated 2025-07-16
Countries of the United Kingdom Updated 2025-07-16
Geographical division of England Updated 2025-07-16
Skelet machine #1 is infinite Updated 2025-07-16
Non formal proof with a program March 2023: www.sligocki.com/2023/03/13/skelet-1-infinite.html Awesome article that describes the proof procedure.
The proof uses Turing machine acceleration to show that Skelet machine #1 is a Translated cycler Turing machine with humongous cycle paramters:
Skelet machine #1 Updated 2025-07-16
Condensed matter physics course of the University of Oxford Updated 2025-07-16
Turing machine that halts if and only if Collatz conjecture is false Updated 2025-07-16
mathoverflow.net/questions/309044/is-there-a-known-turing-machine-which-halts-if-and-only-if-the-collatz-conjectur suggests one does not exist. Amazing.
Intuitively we see that the situation is fundamentally different from the Turing machine that halts if and only if the Goldbach conjecture is false because for Collatz the counter example must go off into infinity, while in Goldbach conjecture we can finitely check any failures.
Amazing.
Turing machine that halts if and only if the Goldbach conjecture is false Updated 2025-07-16
Skelet’s machines Updated 2025-07-16
Marxen-Buntrock machine Updated 2025-07-16
Best busy beaver machine known since 1989 as of 2023, before a full proof of all 5 state machines had been carried out.
Paper extracted to HTML by Heiner Marxen: turbotm.de/~heiner/BB/mabu90.html
Senior Wrangler Updated 2025-07-16
Turing machine acceleration Updated 2025-07-16
Turing machine acceleration refers to using high level understanding of specific properties of specific Turing machines to be able to simulate them much fatser than naively running the simulation as usual.
Acceleration allows one to use simulation to find infinite loops that might be very long, and would not be otherwise spotted without acceleration.
This is for example the case of www.sligocki.com/2023/03/13/skelet-1-infinite.html proof of Skelet machine #1.
Conjecture reduction to a halting problem Updated 2025-07-16
bbchallenge.org/story#what-is-known-about-bb lists some (all?) cool examples,
- BB(15): Erdős' conjecture on powers of 2, which has some relation to Collatz conjecture
- BB(27): Goldbach's conjecture
- BB(744): Riemann hypothesis
- BB(748): independent from the Zermelo-Fraenkel axioms
- BB(7910): independent from the ZFC
wiki.bbchallenge.org/wiki/Cryptids contains a larger list. In June 2024 it was discovered that BB(6) is hard.
University of Cambridge slang Updated 2025-07-16
QET Labs Updated 2025-07-16
QEMU.js Updated 2025-07-16
There are unlisted articles, also show them or only show them.