How Big is Graham's Number? (feat Ron Graham)
Numberphile4 HN recommenders · 2014–2024
1.7M views · interview · evergreen · Uploaded 2014-07-22
Numberphile talks with mathematician Ron Graham about the magnitude of Graham's number, building up from arrow notation to show how impossibly large it is. It is part of a series of videos on this number.
HN commenters recommend it for hearing Graham himself and for its clear introduction to up-arrow notation and enormous numbers.
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6 comments from Hacker News
Is loglogloglog...log the only beast that can conquer Knuth's arrow notation? (x ↑↑↑↑...↑ n) Every time I watch videos about arrow notation or, more famously, Graham's number, my head explodes :) [VIDEO] Big big numbers are really, really cool!
My brain melts every time I watch this video [1] from Numberphile on Graham's number. They also had another video [2] with Ron Graham himself :) [1]: [LINK] [2]: [VIDEO]
> why not have an operator that applies up arrows a number of times defined with up arrows? That is exactly what up arrows do, isn’t it? Up arrows are iterated up arrows. I learned this in college but still didn’t fully understand up arrows for a long time, they grow unimaginably bigger and faster than I first thought. This video explains it pretty well: [VIDEO] I don’t know about ‘ultimate’ but there are some generalizations of up arrows: [LINK] [LINK]
Graham's Number, as in 3 ↑↑ 3, is named after Ron Graham. [1] [LINK] [2] [LINK] [3] And here is the man himself describing it [VIDEO]
Graham's number [0] can be defined using hyperoperations. There's an awesome video with Ron Graham himself on Numberphile (YouTube) [1] [0] [LINK] [1] [VIDEO]
If math can make you feel awe, you've got to watch the Numberphile series on very big numbers. They're constants used in proofs that are specific, well-defined integers known to be finite, but so huge that the physical universe does not have enough particles (or even Plank-scale microstates) in it to represent the number of digits these numbers have! Absolutely mind-bending stuff. Listed in increasing order: "Graham's Number" [LINK] "How Big is Graham's Number? (feat Ron Graham)" [VIDEO] "The Enormous TREE(3)" [LINK] "TREE(3) (extra footage)" [LINK] "The Daddy of Big Numbers (Rayo's Number)" [LINK]