Life, blogging, and the Busy Beaver function go on
This is my first post in well over a month. The obvious excuse is that I’ve been on a monthlong family world tour, which took me first to the Bay Area, then NYC, then Israel, then Orlando for STOC/FCRC as well as Disney World, now the Jersey Shore, and later today, back to the Bay Area, joining Dana there, and leaving the kids with my parents for a few weeks. I’ll return to Austin in mid-August, by which point, the “heat dome” will hopefully have dissipated, leaving temperatures a mere 100F or less.
I’m trying to get back into production mode. Part of that is contemplating the future of this blog, about which I’ll say more in a future post.
For now, just to wet my toes, here are three updates about the Busy Beaver function:
- Johannes Riebel, an undergraduate at the University of Augsburg in Germany, has produced a tour-de-force bachelor’s thesis that contains, among other things, the first careful writeup of Stefan O’Rear’s result from six years ago that the value of BB(748) is independent of the ZFC axioms of set theory. Regular readers might recall that O’Rear’s result substantially improved over the initial result by me and Adam Yedidia, which showed the value of BB(8000) independent of ZFC assuming the consistency of a stronger system. Along the way, Riebel even gets a tiny improvement, showing that BB(745) independent of ZFC.
- Pascal Michel, who curated arguably the Internet’s most detailed source of information on the Busy Beaver function, has retired from academia, and his website was at imminent risk of being lost forever. Fortunately, friends intervened and his site is now available at bbchallenge.org.
- Shawn Ligocki and Pavel Kropitz have continued to find busier beavers, with spectacular recent progress over the past couple months for Turing machines with more than 2 symbols per tape square. See here for example.
Anyway, more coming soon!