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For overdetermined reasons, I’ve lately found the world an increasingly terrifying and depressing place. It’s gotten harder and harder to concentrate on research, or even popular science writing. Every so often, though, something breaks through that wakes my inner child, reminds me of why I fell in love with research thirty years ago, and helps me forget about the triumphantly strutting factions working to destroy everything I value. Back in 2022, I reported an exciting advance in BusyBeaverology: namely, whereas we previously knew merely that BB(6) > 1036,534, Pavel Kropitz managed to show that BB(6) > 1510. For those tuning in from home, here BB(6) is the 6th Busy Beaver number, i.e. the maximum number of steps that a 6-state Turing machine with a {0,1} alphanet can take before halting, when run on an initially all-0 input tape. Also, the left-superscript means tetration, or iterated exponentiation: for example, 1510 means 10 to the 10 to the 10 and so on 15 times. By comparison, las

Shtetl-Optimized >> Blog Archive >> BusyBeaver(6) is really quite large Shtetl-Optimized The Blog of Scott Aaronson If you take nothing else from this blog: quantum computers won't solve hard problems instantly by just trying all solutions in parallel. Also, please read Zvi Mowshowitz's masterpiece on how to fix K-12 education! --> << Raymond Laflamme (1960-2025) Quantum Complexity Theory Student Project Showcase #5 (2025 Edition)! >> BusyBeaver(6) is really quite large For overdetermined reasons, I&#8217;ve lately found the world an increasingly terrifying and depressing place. It&#8217;s got

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