Finding Even Larger Numbers

This is a follow-up to my last video about big numbers as there have been some new larger numbers discovered that can fit into a small space, like a text message. This is likely to be the final conclusion of the series unless something larger is proven.

Support me and innovative projects like these!

4D Golf

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

[slgnssp]

The googology community is up in arms for receiving a measly "huge" thanks

[JL]

I don't think I have ever watched a YouTube video where I understood so little of it . The number of terms and concepts to look up recursively to understand these numbers in detail is almost as large as the numbers themselves

[nodrance]

If anyone is confused why busy beaver numbers don't work: It's basically the same as saying "the largest number that can fit in a text message is the largest number that can fit in a text message"

[cheeseburgermonkey]

Never have I realized how difficult googology is to find your way around in, especially in deeper parts like this
I mean, the jargon in this video is insane

[Sgrunterundt]

You say huge thanks, but what class of huge are you talking about?

[Baddexample]

Damn, changed my mind: Gotta be at least 5

[jotasietesiete]

Loader's number mentioned. I forgive part 1 now.

Man, this video is inspiring me to get back into googology

[U.Inferno]

Alright so from what I can gauge number classes aren't necessarily literal numbers with predefined digits. They're more comparable to Big O Notation where you simply identify what part dominates as n approaches infinity. For example, if you ever told a CompScientist "O(n^2 + 1) is greater than O(n^2)" you'd be laughed at because the rate at which O(n^2) grows makes that +1 so irrelevant there's no reason in specifying.* It's why the notation is rather simple to begin with. If you have a growth rate of a polynomial with a number of degrees up to 1000, degrees 0-999 are discarded. And even that is dwarved by any exponential function with a base larger than 1. The only difference is we've transcended shit like exponential, factorial, and O(n^n)--and that last one is already pushing it because any program with that bad of Big O is either so bad to never be even used, or pumped full of tiny optimizations that try to withstand the inevitable rampant growth for just long enough to get something useful.

*To those who don't quite get what I mean, lets start simple. n^2 vs n^2+1 when n = 2 is 4 and 5. That +1 provides a 25% increase, which is pretty significant. However, n = 3 is 9 vs 10, which only ~11%. As n grows, that percentage increase shrinks to insignificance. So when it comes to Big O notation, we don't really give a shit about +1. This is true for any inequal growth. for example n^3 vs n^3 + n^2 are considered equivalent under this notation because when n = 2, you get 8 vs 12. Although that's a 50 percent increase, n = 3 gives 27 vs 36 which is only a 33% increase. When n = 10 that difference is only a 10% increase. Every time you double n, the percentage increase is half. n = 20 is +5%. n = 40 is +2.5%. n = 80 is +1.25%. et cetera. So you quite literally disregard everything that's not the leading value because it's basically a diminishing return.

[CelticB]

It has become increasingly clear why you were able to pull off developing 4 dimensional games

[JulianBliss]

Damn, every single time I am researching something on the cusp of new Computer Science, John Tromp is always there

[Ganerrr]

Noncomputable ≠ not well defined, BB(n) is just a function from ℕ→ℕ, it's just impossible to observe in finite time

[CaesarsSalad]

Mentioning that the busy beaver numbers are difficult to compute because they are so large and that we will probably never know the value of BB(6) is a red herring. These numbers are all too large for anything anyway. The qualitatively different property that the busy beaver sequence has is that it is uncomputable and the rest doesn't matter.

[kisaragi-hiu]

Reading about Graham's Number and other large numbers in the past made me appreciate how you never get close to infinity, even if sometimes it can feel like a big number could just be equated to infinity. Climbing the ladder in defining incredibly large numbers while satisfying some constraints is still fun though.

[omegastar]

6:46 My mind passed that point a while ago

[ゆり]

Fun fact: Patcail made an incremental game about ordinals called Ordinal Markup

[DEMEMZEA]

No way! Patcail! That used-to-be huge bastard! I'm a mod in his ( now dead ) discord server, and those were some years, i'll tell ya.

Also, haven't seen him in years, never expected to see him again

[Melissanoma]

still no mention of unary I see. The true largest number that can fit in 140 characters (given the stipulation that it must be computable without outside information) is 140, expressed like this:

[kisaragi-hiu]

2:40 Oh… (a) that actually makes the challenge meaningful now, and (b) I wish more people mentioned this

[sesemuller]

5:58 PATCAIL! Wow, I only know so much about large number because I played their games, nice to see them come up here

[ДаниилИмани]

everyone is gangsta until the notation for representing ordinals changes