4 ms·
This is a fantastic article on "big numbers" (and discusses tetration): http://www.scottaaronson.com/writings/bignumbers.html http://www.scottaaronson.com/writ
by akshaym 16y ago
This is a fantastic article on "big numbers" (and discusses tetration):
http://www.scottaaronson.com/writings/bignumbers.html http://www.scottaaronson.com/writings/bignumbers.html
(I think someone has posted it to HN before, which is why I am leaving it as a comment)
- warfangle 16y agoDefinite upvote. That essay is insanely fascinating; I tend to re-read it every few months.
- michael_dorfman 16y agoI like the article, too, but I'm always disappointed when it doesn't cover Knuth's up-arrow, which seems absurdly relevant.
- ableal 16y agoThanks. Obviously http://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation http://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation Shorter read: http://www.daviddarling.info/encyclopedia/K/Knuths_up-arrow_notation.html http://www.daviddarling.info/encyclopedia/K/Knuths_up-arrow_... , which comes quickly to next step: Three up-arrows together represent a still more vastly powerful operator, equivalent to hyper5 or pentation, or a power tower of power towers
- tectonic 16y agoSo if humans can compute the first few Busy Beaver numbers, does that mean we're not Turing machines?
- pmiller2 16y agoNot at all. Just because a problem in general is uncomputable does not mean that certain specific instances can't be computed. For example, the halting problem is undecidable, but anyone can see that loop of the form while (1) { } is an infinite loop. Undecidability and uncomputability apply only at the level of general problems, not specific instances.
- tectonic 16y agoThanks :)