S
Shawn Ligocki
sligocki.com · Personal blog · on HN since 2021
Shawn Ligocki, a Busy Beaver researcher, who writes about Turing machine champions, Collatz-like behavior, and the bbchallenge project.
What HN saysCommenters call it a better source on actual Busy Beaver research than Aaronson's blog and praise its detailed explanations of hard machines.
20HN people shared it
13linked it in comments
17stories submitted
644story points
11 months agolast shared
2021people per year2026
Most-shared posts
- 1Collatz-like behavior of Busy Beavers5 people · 78 points · first shared 2021 · 9 comments on HN
- 2BB(6) Is Hard (Antihydra) (2024)3 people · 38 points · first shared 2024 · 11 comments on HN
- 3BB(3, 3) is Hard2 people · 43 points · first shared 2023 · 2 comments on HN
- 4Skelet #34 Is Infinite2 people · 1 points · first shared 2023 · discussion on HN
- 5Bb 6 2 is hard2 people · first shared 2024
- 6Homepage2 people · first shared 2025
- 7BB(3, 4) > Ack(14)1 people · 302 points · first shared 2024 · 107 comments on HN
- 8Latest Busy Beaver champion has too many digits to count1 people · 86 points · first shared 2022 · 18 comments on HN
- 9One Collatz Coincidence1 people · 78 points · first shared 2024 · 24 comments on HN
- 10BB(2, 5) is hard (Hydra)1 people · 4 points · first shared 2024 · 1 comments on HN
- 11Hyper Scientific Notation for Unspeakably Large Numbers1 people · 4 points · first shared 2022 · 2 comments on HN
- 12Busy Beaver vs. Graham's Number1 people · 3 points · first shared 2022 · discussion on HN
- 13BB (2,4) Proven1 people · 2 points · first shared 2024 · discussion on HN
- 14New 6-State Busy Beaver Champion Discovered1 people · 2 points · first shared 2022 · discussion on HN
- 15“Mother of Giants” Turing Machine1 people · 2 points · first shared 2022 · discussion on HN
What HN people wrote when they linked it
tigereyeTO · 2025-12-13
I 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 **"
lupire · 2025-06-28
https://www.sligocki.com/ hasn't posted since April, and the very first link on that blog is a link to... Scott Aaronson.
NooneAtAll3 · 2025-06-28
If 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
penteract · 2024-09-24
Some 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.
LegionMammal978 · 2024-07-02
As 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 reasoning to prove non-halting [1]. The full Coq proof put a much-needed degree of confidence into these results.
[0] https://www.sligocki.com/2023/03/13/skelet-1-infinite.html
[1] https://discuss.bbchallenge.org/t/skelet-17-does-not-halt/184
7373737373 · 2025-07-31
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
lisper · 2025-03-15
Also apparent links between Collatz and the busy-beaver problem:
https://www.sligocki.com/2021/07/17/bb-collatz.html
UncombedCoconut · 2024-07-02
Mostly 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 mathematical content. (Maybe a bit, in about the same way that an integer equation is sometimes proved unsolvable by considering it modulo n and checking every case.) Also, I learned some math I wasn't personally familiar with from the analysis of a particular machine: https://www.sligocki.com/2023/03/14/skelet-10.html (Zeckendorf's Theorem).
MichaelDickens · 2023-11-03
Graham'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
mcherm · 2023-11-02
See also this article (shared on Hacker News 2 weeks ago): https://www.sligocki.com//2023/10/16/bb-3-3-is-hard.html
Basically, they showed that a VERY small Turing Machine -- of a size many had hoped we would be able to exhaustively solve -- turns out to depend on whether something similar to the Collatz sequence ever haults.
In other words, research published just 2 weeks ago shows that we don't need a Turing machine with a couple thousand states to be beyond the reach of modern human mathematics -- even one with just a few states can stimy us.
daynthelife · 2023-10-17
The “<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
SethTro · 2023-02-07
Some discussion of remaining infinite BB(5) machines yesterday in [1][2]
[1] https://www.sligocki.com//2023/02/02/skelet-34.html
[2] https://news.ycombinator.com/item?id=34689068 and
sligocki · 2023-02-07
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 :)