Quest To Find The Largest Number
204,686
Published 2024-07-09
You may have heard of some famous large numbers like Graham's Number or TREE(3) but I go way beyond that to find the largest number that could fit in a small space; an SMS text message or tweet.
Some googology and lambda examples from this video were hard to find, here are some resources to help if you're interested in researching further:
Lambda Diagrams: tromp.github.io/cl/diagrams.html
Binary Lambda Calculus: tromp.github.io/cl/Binary_lambda_calculus.html
Melo's Number: codegolf.stackexchange.com/a/263884
Buchholz Ordinal Algorithm: codegolf.stackexchange.com/a/219466
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Music CC by 4.0
Jesse Spillane - An Undersea Cache of Relics
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All Comments (21)
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90 is a pretty big number
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"Let's choose something universal, that even aliens could understand!" "like this string of undecipherable characters that encodes Melo's number in lambda calculus!"
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TREE(3) gonna be shaking in their boots when TREE(4) walks in
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I mean, it's gotta be at least 3
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Please don't make Lambda calculus into a game lol
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When I was 10 I said I wanted to be a googologist but I became a computer scientist instead. I'm happy with the choice I made but man big numbers are cool
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it's wild how infinite chess prepares you for this
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"We should include all the necessary instructions to actually generate the number for it to count." Dammit, there goes busy beaver stopping times...
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Note that the "must include instructions to compute its value" makes a very big difference. There is a sequence called the Busy Beaver which is a well-defined sequence of finite integers, but that is proven to grow large faster than ANY sequence of numbers that can be computed. So, for example, the number BB(11111) is certainly much bigger than the Buchholz Ordinal - but (despite it being a specific integer) there is almost certainly no way to prove what its exact value is. For more info, check Scott Aaronson's classic essay "Who Can Name the Bigger Number?"
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You should have explained omega and ordinal numbers a bit more thoroughly because I have a hard time understanding what the omega is even supposed to do. Please explain.
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New googology series from CodeParade? Can't say I'm anything but excited.
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I once delved into this very briefly, and the coolest notation I found was conway's chained arrow notation. For example, Graham's Number has an upper bound of 3->3->65->2. This is just 11 characters! I looked up how it compares and apparently it's at f_w^2(n). I'd never have imagined there's a need for a faster growing function than this one.
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Didn’t know Jontron was into Lambda Diagrams
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"Whatever you say plus one 🤪"
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the funniest part of this video is the fact that the people who jokingly in the comments go "ahaha what you said + 1 😜" are actually exactly right and in fact, the solution to the question involves the maximal amount of that exact annoying instinct
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We can't be sure whoever is deceiving our text message understands binary, therefore the largest number that definitely definitely fits in a text message is 1120.
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Look, Mr. Show proved that 24 is the highest number, and that settles that.
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"That's Numberwang!"
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According to vsauce, the biggest number is 40.
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The Lambda Calculus inspired Lisp, one of the oldest computer language families still in use today; roughly the same age as Fortran.
