Quest To Find The Largest Number

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

90 is a pretty big number

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

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

I mean, it's gotta be at least 3

it's wild how infinite chess prepares you for this

"We should include all the necessary instructions to actually generate the number for it to count." Dammit, there goes busy beaver stopping times...

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

Please don't make Lambda calculus into a game lol

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?"

>let's not use a programming language to define the number >uses a pseudo programming language instead

"The largest number possible using lambda calculus plus one"

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

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.

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).

The largest number that can fit in an SMS message is null. Numbers are abstract mathematical concepts, they can't be put in a SMS message. SMS messages may contain information, but not concepts. Concepts exist in human brains. Okay, I understand why you might say I'm being pedantic and philisophical. This isn't what was meant, right? We'll consider an example. "Graham's number" was not allowed but "" was allowed. Why? "Graham's number" was rejected because it relied on external information the interpreter had to understand it. "" had the same problem. Of course, CodeParade went on to explain that. Well, then does lambda calculus solve this problem? Nope. Lambda calculus is "simpler" and "more compact" than Python or English, but it's still an encoding/decoding process, and while the SMS contains information, it's still necessary to understand lambda calculus and numbers to be able to decode the meaning message. Consider this: Two people receive an identical SMS message with no explanation. They both think it's meaning is a large number. One says it's meant to be interpreted simply as a binary number. The other thinks it's a lambda calculus function for calculating a number that is much bigger. Which person is right? Neither, it came from a random number generator and had no meaning. Or both? The author intended for it to be an entertaining pun! Or it was actually some third thing that neither person thought of? The truth is, the message itself doesn't contain the meaning, there may have been meaning in the authors brain and in the reader's brain, but without context of an encoding scheme, all SMS messages contain none. Since numbers are concepts, not mere information, they cannot be contained in a message. They can only be encoded into or decoded from a message. The message itself never contained the number, just information.

Didn’t know Jontron was into Lambda Diagrams

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

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

A number that makes you "satisfied enough" does not satisfy the condition for "The Largest Number".