Quest To Find The Largest Number

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:

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Music CC by 4.0
Jesse Spillane - An Undersea Cache of Relics

[cynthiaclementine]

"Let's choose something universal, that even aliens could understand!"
"like this string of undecipherable characters that encodes Melo's number in lambda calculus!"

[jadencasto]

This is a classic example of a video where I go, “mmhmm very interesting, ” while understanding basically nothing

[leictreon]

I was like "I like your funny words, magic man" for 80% of this video

[NikkiTheViolist]

people: "TREE(3) is pretty big"
me: "okay but what if you plant a few more trees"

[Xeare]

6:10
>watching this on phone at low volume
>"Invented by JonTron"

[seto]

TREE(3) gonna be shaking in their boots when TREE(4) walks in

[Baddexample]

I mean, it's gotta be at least 3

[ShadowStray_]

2:14 POV: you’re excited to tell someone that your favorite number is 9

[eberger]

Me: I can't wait to see some big numbers
Video: what is a number?

[a-love-supreme]

it's wild how infinite chess prepares you for this

[jblen]

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

[soregalex]

Please don't make Lambda calculus into a game lol

[E.T.S.]

10 PRINT "9";
20 GOTO 10
RUN

Wait 1, 000, 000, 000 years.

[sevret]

7:40, the halting problem is about arbitary programs with arbitary inputs, you don't have that here, you've a fixed program (The lambda interpretor) and a limited range of inputs (166 characters).

[blackboxpup]

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

[MrCheeze]

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 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?"

[orthoplex]

"We should include all the necessary instructions to actually generate the number for it to count."

Dammit, there goes busy beaver stopping times...

[jillmoore]

we all know its that number we made up as kids to beat our friends 💀

[BryceDixonDev]

Your point about problem-specific programming languages has actually come up before in the world of code golf (the challenge of solving a programming task in the fewest characters). The original rules for many of these challenges was that any language is allowed because, as you said, different languages may be more compact for different problems and knowing that is part of the challenge. However, there's nothing stopping someone from, say, defining a code-golf specific language and writing their own compiler for it to have esoteric syntax to focus on mininizing the size of the source code. In fact, there's nothing stopping someone from defining a programming language for a specific problem and writing a compiler which only accepts an input source code of "A" and generates a program which satisfies the prompt.

Enter: Golf Script (I believe it's called; I might be mistaken). An entire family of languages which exists to solve any code golf problem in a single character. Simply program the compiler-compiler and it will make a new compiler for a new language which will solve the specific program it was generated for in a single character!

[xnossisx]

New googology series from CodeParade? Can't say I'm anything but excited.