There is a 5% chance that we have a new BB(6) champion! It’s a machine discovered by Racheline which she’s named “Lucy’s Moonlight”. It is a probviously halting tetrational Cryptid. In other words, it’s a machine that we believe will eventually halt (with 100% chance via a probabilistic approximation), yet proving it requires either solving a Collatz-like problem or simulating it for a “tetrational” number of steps. This is very similar to the Mother of Giants with the excepti...| sligocki
A common question people have about Busy Beaver champions is: “What are they doing?” This question sounds sort of objective, but is really a subjective philosophical question. Objectively, the TM is repeatedly evaluating the specific transition table rules until it halts, that’s all. In a sense, this is the “simplest” (smallest) explanation because these champions are literally the ones that “do the most” based on the smallest description.| sligocki
Note: All Discord links are for the https://bbchallenge.org/ Discord server.| sligocki
Consider the Collatz-like function:| sligocki
I’m excited to share a 3 state, 3 symbol Turing Machine that cannot be proven to halt or not (when starting on a blank tape) without solving a Collatz-like problem. Therefore, solving the \(BB(3, 3)\) problem is at least as hard as solving this Collatz-like problem, a class of problem for which Paul Erdős famously said: “Mathematics may not be ready for such problems.”| sligocki
Kth Permutation Sequence Write a script to accept two integers n (>=1) and k (>=1). It should print the k-th permutation of n integers. For example, n=3 and k=4, the possible permutation sequences are listed below: 123 132 213...| E. Choroba
I just enjoyed an excellent YouTube video, My honest attempt at the Collatz Conjecture, made by Fernando Franco Félix (Fer / @Highly Entropic Mind) as part of the third Summer of Math (#SoME3). He also wrote it up as a PDF. This blog post is a response to that video and paper.| sligocki