How Big is Graham's Number? (feat Ron Graham)
Why Hacker News recommends it
HN commenters recommend it for hearing Graham himself and for its clear introduction to up-arrow notation and enormous numbers.
What it is
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.
Recommended by 4 HN commenters across 5 different months, 2014 to 2024.
What Hacker News said
Strong rec prezjordan · 2014-12 · on “Prime Gap Grows After Decades-Long Lull”
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 :) [this video] Big big numbers are really, really cool!
Strong rec prezjordan · 2015-02 · on “Graham's Number”
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]: [this video]
Strong rec jiggawatts · 2024-05 · on “A Trial HIV Vaccine Triggered Elusive and Essential Antibodies in Humans”
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)" [this video] "The Enormous TREE(3)" [LINK] "TREE(3) (extra footage)" [LINK] "The Daddy of Big Numbers (Rayo's Number)" [LINK]
Recommends dahart · 2019-11 · on “Inventing an Operation to Solve x^x = y (2000)”
> 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: [this video] I don’t know about ‘ultimate’ but there are some generalizations of up arrows: [LINK] [LINK]
Recommends ObiWanFrijoles · 2022-07 · on “The Fourth Operation: What Comes After Exponentiation”
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] [this video]
Cites iamaaditya · 2020-07 · on “Ron Graham has died”
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 [this video]