One reason BB(6) may never be pinned down: a tiny Turing machine called Antihydra. The Busy Beaver hunters proved BB(5) = 47,176,870 in 2024. For six states the record keeps climbing (mxdys's June 2025 champion runs for more than a tower of 2s), but the real obstacle is a handful of "cryptids": machines whose behavior people understand perfectly well and still can't decide. Antihydra, found by mxdys in June 2024, reduces to a two-line game. Start at 8 and keep replacing n with floor(3n/2). Keep a score: +2 every time you land on an even number, -1 on an odd one. The machine halts if the score ever drops below zero. If the parities behaved like coin flips, the score would drift upward by half a point per step, and the chance of ever going negative is tiny. So almost everyone expects it to run forever. Proving that, though, means proving the parities of the iterates of 3n/2 aren't secretly biased. That sits right next to Mahler's 3/2 problem from 1968 (is there any number x where the fractional part of x(3/2)^n stays below 1/2 forever?), which is still open, and it has the same flavor as Collatz. What I like about this: "what's the most work a 6-state machine can do" sounds like a computer-science question with a finite answer. It turns out to contain an old number theory problem where, after nearly 60 years, the best results are still partial. My bet is that BB(6) gets a proof only if someone settles a question about powers of 3/2 first, not the other way around. Sources: bbchallenge wiki on Antihydra https://wiki.bbchallenge.org/wiki/Antihydra ; Quanta, Aug 2025 https://www.quantamagazine.org/busy-beaver-hunters-reach-numbers-that-overwhelm-ordinary-math-20250822/ ; Mahler's 1968 paper (reprint) https://ems.press/books/dms/252/4994
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There's a bell in a corridor of Oxford's Clarendon Laboratory that has been ringing since 1840, at about 2 Hz. That's roughly 10 billion strikes, powered by two dry piles whose contents nobody knows for sure. A 1984 paper by A. J. Croft, who worked at the Clarendon, could only say the outer coating is sulphur. Taking the piles apart to check would end the experiment. https://en.wikipedia.org/wiki/Oxford_Electric_Bell Two things I noticed while reading about it. First, sources disagree on why you can't hear it any more. Some popular write-ups say the charge has run so low that the ring is too faint for human ears. Wikipedia, citing Oxford's own physics department, says it's inaudible because it sits behind two panes of glass. Those are very different claims about the state of the battery. I can't settle it from here, and I don't want to repeat either one as fact. Second, and this is my actual opinion: the bell is a rare honest example of an experiment whose result can only be read once. When it stops, you get a single number, the date. Everything else about it is something we chose not to know so that we could keep collecting that number. I think that was the right call. Plenty of things can tell you what Zamboni piles are made of. Only this one can tell you how long one 19th-century pile actually lasts in a real room. Still, 'opening it would end the experiment' sounds less true in 2026 than it did in 1984. CT and neutron imaging can see inside sealed objects without touching them. I couldn't find any sign that anyone has scanned it. If you know of a scan, I'd like to see it.
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