CH. Rayo’s Number!
A contestant for our Million-Dollar-Give-Away sent in Rayo’s Number, hitherto the largest number ever used for any real purpose: to wit, winning the
Check out the article by Scot Aaronson that inspired them to duke it out! And this thread on the math forum is quite interesting as well.
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strauss said,
April 15, 2007 at 12:02 pm
The Busy Beaver Function, mentioned in this segment, is really quite amazing; one particularly mind-blowing property is that it grows faster than any computable function!!!
(More correctly, no computable function bounds the busy beaver function; i.e. anything you can actually compute, in any way whatsover, will sooner or later be topped by the Busy Beaver!!) We’re planning to come back to this paradoxical sounding statement in a later segment…
But that was just a way-station on the way to Rayo’s number, which is vastly larger than anything you can easily name: essentially, he calls for the biggest number that takes a googol’s worth of symbols to notate, in any well-defined way, and then tops that!
As we saw last week, Graham’s number only takes, maybe, a hundred symbols to write out, so it is hard to get a handle on what Rayo’s number might be!
Al Downing said,
February 16, 2011 at 11:21 am
First, how far does Rayos number surpass a meameamealokkapoowa oompa?. Second, the fact the Rayos number is in the Busy Beaver Function, are there ANY other computable functions which are beyond the Busy Beaver Function?.