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How Big is Graham's Number? (feat Ron Graham)

Numberphile

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  • Recommended by 4 people: 4 on Hacker News.
  • A classic. People kept recommending it from 2014 to 2024.
  • Presented by Ron Graham, mathematician

Beginner. No background in the topic needed.

1.7M views12 years ago4 recommendations

Computer scienceMath for programmersComputation and complexity

Mathematician Ron Graham explains the mind-bending scale of Graham's number using Knuth's up-arrow notation.

See our other Graham's Number videos: bit.ly/G_Number More Ron Graham Videos: bit.ly/Ron_Graham More links & stuff in full description below ↓↓↓ The magnitude of Graham's Number is difficult to fathom - Ron Graham himself attempts to explain. WHAT IS the number: youtu.be/HX8bihEe3nA Extra footage: youtu.be/rGWuimr5CGQ Our original Graham's Number video: youtu.be/XTeJ64KD5cg Any errors in this video are mine (Brady's) in editing... For example 3^^^3 is actually even bigger than I say... Graham's Number is just too big for my small brain! See an improved explanation at: youtu.be/txajrEOTkuY Wikipedia page on Graham's Number: en.wikipedia.org/wiki/Graham's_number And the arrow notation used here: en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation Support us on Patreon: patreon.com/numberphile NUMBERPHILE Website: numberphile.com/ Numberphile on Facebook: facebook.com/numberphile Numberphile tweets: twitter.com/numberphile Subscribe: bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile Videos by Brady Haran Brady's videos subreddit: reddit.com/r/BradyHaran/ Brady's latest videos across all channels: bradyharanblog.com/ Sign up for (occasional) emails: eepurl.com/YdjL9 Numberphile T-Shirts: teespring.com/stores/numberphile Other merchandise: store.dftba.com/collections/numberphile

Why it's here

4 people recommend this

What people say. Highly recommended by engineers as a fascinating and accessible explanation of unimaginably large numbers.

prezjordanon Hacker News • Recommends

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 :) link to this video Big big numbers are really, really cool!
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prezjordanon Hacker News • Recommends

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: link to this video
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jiggawattson Hacker News • Recommends

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)" link to this video "The Enormous TREE(3)" link "TREE(3) (extra footage)" link "The Daddy of Big Numbers (Rayo's Number)" link
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daharton Hacker News • Recommends

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: link to this video I don’t know about ‘ultimate’ but there are some generalizations of up arrows: link link
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ObiWanFrijoleson Hacker News • Recommends

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 link to this video
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iamaadityaon Hacker News • Mentions

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 link to this video
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