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sligocki
Personal blog · sligocki.com · on HN as sligockimathprogramming
sligocki is a personal blog at sligocki.com about math and programming. Since 2021, 20 different Hacker News readers have linked it 35 times, most often “Collatz-like behavior of Busy Beavers”. It is still writing: the last post was on 2025-04-21, and you can follow it by feed.
Too few sampled comments (17) to say how often HN recommends it.?
Why HN links it
HN readers link this blog for explanations of Busy Beaver research, including the bbchallenge.org work and Collatz-like problems. Commenters find its posts accessible and detailed.
Summarised by Claude from a sample of 17 HN comments that link here. Each comment is marked recommending, critical or neutral (citing without judging); how this works.
Most-linked posts?
- Collatz-like behavior of Busy Beavers5 people · 5 mentions · first linked 2021-09-01
- BB(6) Is Hard (Antihydra) (2024)3 people · 4 mentions · first linked 2024-09-03
- /2024/07/06/bb-6-2-is-hard.html2 people · 4 mentions · first linked 2024-08-31
- BB(3, 3) is Hard2 people · 2 mentions · first linked 2023-10-17
- Skelet #34 Is Infinite2 people · 2 mentions · first linked 2023-02-07
- /2 people · 2 mentions · first linked 2025-06-28
What Hacker News says?
Interesting new contender for simplest to state unsolved problem: The Antihydra Does this program halt? a = 8 b = 0 while b != -1: if a % 2 == 0: b += 2 else: b -= 1 a += a//2 (// being integer division, equivalently a binary shift one to the right: >> 1) https://www.sligocki.com/2024/07/06/bb-6-2-is-hard.html https://bbchallenge.org/antihydra
Comment linking /2024/07/06/bb-6-2-is-hard.html
on “Slow”Submitted BB(3, 4) > Ack(14) as a story · 302 points
HN discussionMostly no: we did find some non-halting TMs that required new proofs, but none of those had the flavor of new math, per se. Indeed, we found that all but 30 of them could be proved by finite automata methods, meaning the TM's state/tape at any step could be reduced to one of finitely many states and we'd still know all we needed to know about future steps. I would argue that such a non-halting proof can't have much…
Comment linking /2023/03/14/skelet-10.html
on “With fifth busy beaver, researchers approach computation's limits”Submitted Latest Busy Beaver champion has too many digits to count as a story · 86 points
HN discussionAs far as I am aware, all of the proofs and techniques for each machine were present before mxdys managed to get the whole theorem into Coq: the main problem was that the deciders and manual proofs were disorganized and somewhat suspect. The worst offenders here were Skelet #1, which needed a bespoke program to accelerate it to its ultimate pattern [0], and Skelet #17, which took Xu seven pages' worth of dense reaso…
Comment linking /2023/03/13/skelet-1-infinite.html
on “With fifth busy beaver, researchers approach computation's limits”Submitted One Collatz Coincidence as a story · 78 points
HN discussionIf you mean multiple halting transitions , then it doesn't really help for BB purposes. If the machine does halt, then only one of the halting transitions will ever be taken, and the others will be 'dead code'. If you mean multiple halting states , then that is possible, and it can be used as a model of computation for, e.g., computable functions returning a single bit as output. But you still don't gain any additio…
Comment linking /2021/03/06/beeping-busy-beaver/
on “BB(3, 4) > Ack(14)”Submitted Collatz-like behavior of Busy Beavers as a story · 78 points
HN discussionhttps://www.sligocki.com/ hasn't posted since April, and the very first link on that blog is a link to... Scott Aaronson.
Comment linking /
on “BusyBeaver(6) Is Quite Large”Submitted BB(3, 3) is Hard as a story · 43 points
HN discussionIf you want to learn about actual Busy Beaver results, I suggest reading https://www.sligocki.com/ instead Unlike Aaronson, he actually is on the forefront of Busy Beaver research, and is one of the people behind the https://bbchallenge.org website
Comment linking /
on “BusyBeaver(6) Is Quite Large”Submitted BB(6) Is Hard (Antihydra) (2024) as a story · 34 points
HN discussionHere is the proof of the result: https://www.sligocki.com/2022/06/21/bb-6-2-t15.html It is very accessible and makes fascinating (by geek standards) reading.
Comment linking /2022/06/21/bb-6-2-t15.html
on “Busy Beaver Updates: Now Even Busier”Submitted BB(2, 5) is hard (Hydra) as a story · 4 points
HN discussionI had no idea what this was talking about and followed links to a blog post that explained the first one ("Bigfoot"): https://www.sligocki.com/2023/10/16/bb-3-3-is-hard.html This blog post made the "cryptids" make a lot more sense to me, so I thought I'd share that post here in case others were also wondering "what the **"
Comment linking /2023/10/16/bb-3-3-is-hard.html
on “Cryptids”Submitted Hyper Scientific Notation for Unspeakably Large Numbers as a story · 4 points
HN discussionSome earlier blog posts by the same author give more detail. https://www.sligocki.com/2021/07/17/bb-collatz.html is one that covers the analysis of a particular machine in great detail, including explaining what definitions like "M(n) = 0^inf < A 1^n 0^inf" mean.
Comment linking /2021/07/17/bb-collatz.html
on “One Collatz Coincidence”Submitted Busy Beaver vs. Graham's Number as a story · 3 points
HN discussionTo the extent that some champion machines have Collatz-like behavior, it's usually not by iterating a function with randomized scale factors until the value hits zero (like in the original Collatz iteration), but instead by iterating a function with a fixed scale factor until it hits a certain modular value. E.g., the BB(5) machine [0] repeatedly multiplies a unary counter by 5/3 and adds a small offset, until the v…
Comment linking /2024/07/06/bb-6-2-is-hard.html
on “Which Collatz numbers do Busy Beavers simulate (if any)?”Submitted BB(6) Is Hard (Antihydra) as a story · 2 points
HN discussionThe “<A” notation indicates that the head of the Turing machine is positioned at the rightmost point to the left of the “<“, and is in state A. [0] For instance, the notation `0^\inf 1^3 <B 0^2 1 0^\inf` is equivalent to `0^\inf 1 1 (B1) 0 0 1 0^\inf`. [0] https://www.sligocki.com/2021/07/17/bb-collatz.html
Comment linking /2021/07/17/bb-collatz.html
on “BB(3, 3) is Hard”Submitted BB (2,4) Proven as a story · 2 points
HN discussionAlso apparent links between Collatz and the busy-beaver problem: https://www.sligocki.com/2021/07/17/bb-collatz.html
Comment linking /2021/07/17/bb-collatz.html
on “Collatzeral damage: bitwise and proof foolish”Submitted New 6-State Busy Beaver Champion Discovered as a story · 2 points
HN discussion1. Will humanity ever solve Collatz(-like) problems and know the 6th busy beaver number? https://www.sligocki.com/2024/07/06/bb-6-2-is-hard.html (and will automatic theorem provers play a role?) 2. What would my perfect story look like? 3. Are peoples' aesthetic preferences clustered in some way? 4. How can the world hold the powerful, and especially the evil ones, to account, and distance itself from a corporate-co…
Comment linking /2024/07/06/bb-6-2-is-hard.html
on “Ask HN: What have you been curious about?”Submitted “Mother of Giants” Turing Machine as a story · 2 points
HN discussionThe https://en.wikipedia.org/wiki/Busy_beaver value for machines with 2 symbols and 5 states (the maximum number of steps that such a machine can make on an initially blank tape before eventually halting) was recently proved to be 47,176,870: https://discuss.bbchallenge.org/t/july-2nd-2024-we-have-prov... Finding the value for machines with 2 symbols and 6 (or more) states will require solving, among other things, t…
Comment linking /2024/07/06/bb-6-2-is-hard.html
on “What is Collatz conjecture good for?”Submitted Lucy's Moonlight: The 5% Champion as a story · 1 points
HN discussionGraham's number used to be the largest number ever used in a proof, but BB(745) is much larger—Graham's number has been proven to be smaller than BB(16)[1] (although I don't know how carefully the proof has been checked). [1] https://www.sligocki.com/2022/07/11/bb-16-graham.html
Comment linking /2022/07/11/bb-16-graham.html
on “The 8000th Busy Beaver number eludes ZF set theory (2016)”Submitted BB(6) Is Hard (Antihydra) as a story · 1 points
HN discussion
