RE: https://mastodon.social/@lobsters/116002869083328549
#maths #mathematics #number #NumberTheory #computation #BusyBeaver #LambdaCalculus #LargeNumbers
https://tromp.github.io/blog/2026/01/28/largest-number-revised
#BusyBeaver
Why Busy Beaver Hunters Fear the Antihydra
https://benbrubaker.com/why-busy-beaver-hunters-fear-the-antihydra/
#HackerNews #BusyBeaver #Antihydra #ComputerScience #ComplexityTheory #TechNews
Turns out #BusyBeaver is a furniture store in the US, i got the gopher effect
This week, we kicked off the Winter Semester with our #SemesterKickOff & the #BusyBeaver awards! 🏃
The Busy Beavers go to instructors whose courses get outstanding student evaluations.
This year’s winners:
➡️ Prof. Dr. Antonio Krüger - Grundlagen der Medieninformatik
➡️ Prof. Dr. Jens Dittrich - Database Systems
➡️ Prof. Dr. Jilles Vreeken & Dr. David Kaltenpoth - Information Theoretic Machine Learning
Congrats to all! 👏 Curious about the awards?
🔗 Read more here: https://sic.link/busybeaver25
👨🔬🤓 "Scholars determined the mythical fifth Busy Beaver value because, clearly, the world was on the edge of its seat over this 🐢🚶♂️💤. A #symposium of geniuses and their 'Simons Foundation' piggy bank have once again shown us what happens when #boredom meets #academia. 🏆📚"
https://arxiv.org/abs/2509.12337 #BusyBeaver #FifthValue #ScholarlyAchievements #HackerNews #ngated
Amazing how a Turing Machine with just six instructions can keep running almost, but not quite, forever.
"The quest to find the longest-running simple computer program has identified a new champion. It’s physically impossible to write out the numbers involved using standard mathematical notation."
#TuringMachines #BusyBeaver #Mathematics #Instructions #Numbers
🐻🔍 So apparently, "Busy Beaver hunters" are busy playing with numbers so big, they make ordinary math cry for its mommy. 📏💔 Meanwhile, Quanta Magazine is busy patting itself on the back for publishing yet another deep dive that only the Simons Foundation and a dozen math nerds will pretend to understand. 🙄🧠
https://www.quantamagazine.org/busy-beaver-hunters-reach-numbers-that-overwhelm-ordinary-math-20250822/ #BusyBeaver #MathNerds #QuantaMagazine #SimonsFoundation #DeepDive #HackerNews #ngated
Busy beaver hunters reach numbers that overwhelm ordinary math
#HackerNews #busybeaver #mathematics #extraordinarynumbers #computationaltheory #mathnews
🐦🔍 "Breaking News: BusyBeaver(6) Is Large! 🚀 Apparently, math problems are big! Who knew? 🤔 Meanwhile, quantum computers won't save the day by magically solving hard problems. 😱 Also, don't miss tips on educational reform buried somewhere in this existential crisis. 📚🌪️"
https://scottaaronson.blog/?p=8972 #BusyBeaver #QuantumComputers #MathProblems #EducationalReform #ExistentialCrisis #HackerNews #ngated
BusyBeaver(6) Is Quite Large
https://scottaaronson.blog/?p=8972
#HackerNews #BusyBeaver #Large #Complexity #Computation #TuringMachines #HackerNews
Alright, it isn’t “done” done, but it works and looks fine as it is. Also, for some reason, I added functions for encoding and decoding state tables to and from a single array (i.e. list) to make it easier to switch between programs, but not a function that extends the tape when the header shifts too far to either side.
BB(5) = 47,176,870
Fully accessible article here:
https://www.quantamagazine.org/amateur-mathematicians-find-fifth-busy-beaver-turing-machine-20240702
Source code that I wrote to demonstrate the problem, which they clearly didn't use:
BB(5) = 47,176,870
Possibly the last busy beaver number we'll ever know definitively:
https://discuss.bbchallenge.org/t/july-2nd-2024-we-have-proved-bb-5-47-176-870/237
The quanta article linked at the end provides a very nice overview of the history of the humans and computers involved in the story: https://www.quantamagazine.org/amateur-mathematicians-find-fifth-busy-beaver-turing-machine-20240702/
Scott Aaronson's blog post provides some technical details and a variety of other reference links: https://scottaaronson.blog/?p=8088
Apart from the crazy technical aspects, what I find most exciting and interesting is how some (many?) of those involved are "amateur mathematicians", in it because they love mathematics and found this problem challenging.
BusyBeaver(5) is now known to be 47,176,870:
"The new bbchallenge achievement is to prove that all 5-state Turing machines that run for more steps than 47,176,870, actually run forever—or in other words, that 47,176,870 is the maximum finite number of steps for which any 5-state Turing machine can run. That’s what it means for BB(5) to equal 47,176,870."
It's been proven that BB(5) = 47176870! See https://scottaaronson.blog/?p=8088 for an explanation of what that means.
I have a question about the new proof.
It's known that for any consistent and decidable system of axioms there will be some n for which the value of BB(n) is not provable in that system. So at some point the busy beaver function will zoom past the abilities of any formal system. I'm wondering about the techniques used for BB(5) in particular. Did they use any methods that already couldn't be formalised in Peano Arithmetic?
@HumanServitor @enoch_exe_inc Also, at the time Turing formulated his abstract machine, it was not really intended to be a real physical device. Nevertheless, people have built physical machines based on Turing’s model. I’ve even uploaded a video to Mastodon of a Turing machine emulator on my phone running the 4-state #BusyBeaver machine; it should be on my profile.
"Why did the beaver choose to build its dam near the airport?
Because it heard there was a lot ofTAKING OFF and LANDING opportunities!
https://punnypeak.com/beaver-puns/
#BeaverPun
#DamFunny
#WoodchuckJoke
#LodgeHumor
#ChewOnThis
#TailTale
#BucktoothedBanter
#BusyBeaver
#DamselInDistress
#PawsitivelyHilarious
#PunnyPeak"
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