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I see, so you are using a different model for computation that does not use rational numbers, but instead pairs of integers. From a computational point of view, that makes a lot of…

Not sure if this is a joke, but actually that is guaranteed to be true. It is proven that for all n: BB(n+1) >= BB(n) + 3. But it is not proven that BB(n+1) >= BB(n) + 4, haha.

And 297/275 to 27/25?

50/18 reduces to 25/9 right?

Can you clarify what you mean by BBλ being "provably optimal"? IIUC BB functions for any Turing-complete computation model should be equivalent up to a constant. Maybe something li…

Yes, it seems that BB(3, 4) >>> BB(5, 2) (BB(5) = BB(5, 2)). This is not too surprising since BB(3, 4) has 12 transitions in it's table (3*4), while BB(5, 2) only has 10. But it se…

Counting the number of distinct TMs is not a simple task. The way you count it is the most broad (the count of all tables of values where each cell can have any (symbol, direction,…

You are right that every TM can be converted into a Collatz-like problem using Conway's Fractran compilation. So technically the statement "Solving the BB(n, k) problem is at least…

The Busy Beaver problem sits somewhere on the range from "intellectual curiosity" to "lens that allows us to view the edges of uncomputability". I would guess that the majority of …

His survey 3 years ago has kicked off quite a flurry of Busy Beaver activity of which my entire blog and https://bbchallenge.org/ are a couple examples.

Thank you! I'm so glad to hear!

Yeah, I've oversimplified a bit with this title. The more accurate statement is in the first paragraph of the article: "Solving the BB(3, 3) problem is at least as hard as solving …

The issue is the "run the turing machine for BB(748) steps" part. We don't know what BB(748) is. If the god of busy beavers came to us and told us that value, then we could (in the…

I'm the author. That's a great summary of the background, thanks! As you say, this post is extremely in the weeds analyzing a single Turing Machine's behavior. I wrote this post ma…

Yes, that's correct. https://www.sligocki.com/2021/07/17/bb-collatz.html has a bit of background that's probably relevent here ... but this content is quite niche, heh :)

Thanks! I just figured out how to get MathJax working with github pages and used it to its full extent!

It's a good question. Yes and no. If the "God of Busy Beaver" told us a value of BB(n) (for large enough n) then that would reduce some math problems to "simply" running a TM for t…

Hello, I'm the author. Ask me anything :) Thanks fn-mote for providing some context. In fact, I think you could appreciate most of this article without even knowing anything about …