https://www.youtube.com/playlist?list=PL3A50BB9C34AB36B3
Highly recommended.
Almost all of these mind-bogglingly large numbers are built around recursion, like the Ackermann function, which effectively has an argument for the number of Knuth up arrows to use. Then you can start thinking about feeding the Ackermann function into that slot and enjoy the sense of vertigo at how insane that becomes.
I find it fascinating how quickly the machinery of specifying large numbers probes the limits of what's definable within the mathematical systems we use.
Like, there is a perfectly finite number, but is so large that there simply isn’t enough information in the universe to encode it in any format. How cool is that to just think about for a while?
It isn't. The article neglects to explain what makes busy beaver numbers interesting in the first place. And I think it's symptomatic of Quanta Magazine articles that feature on HN several times a week. A profoundly-sounding title and pleasant writing, but not much essence beyond that.
tocs3•1d ago
Does anybody know of other interesting problems in the Busy Beaver space?
adgsfhj•2h ago
> Their approach was more subtle; they persuaded their host machine to initiate a program which could not be completed before the end of the universe, or which - the Mandelbrot Maze was the deadliest example - involved a literally infinite series of steps.
https://archive.org/stream/SpaceOdyssey_819/3001_The_Final_O...
db48x•16m ago
twiceaday•2h ago
This paper contains many conjectures around BB that could be interesting to some.
gpm•2h ago