Finding Even Larger Numbers

Start your free 30-day trial at brilliant.org/... and get 20% off the annual premium subscription.
This is Part 2, watch Part 1 first or this won't make sense: • Quest To Find The Larg...
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.
Nuclear Array Notation: codegolf.stack...
Support me and innovative projects like these!
Patreon: / codeparade
Ko-fi: ko-fi.com/code...
Merch: crowdmade.com/...
4D Golf
Steam Page: store.steampow...
Devlog Series: • 4D Golf
Discord: / discord
Engine source code: github.com/Hac...
Music CC by 4.0
Jesse Spillane - An Undersea Cache of Relics
freemusicarchi...
Evan Schaeffer - Blink
freemusicarchi...

[@user-sl6gn1ss8p]

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

[@BooLightning]

🤣

[@zyansheep]

huge could semantically mean anything from 2 to loader's number lol

[@3Black.1Red]

“A googological thanks to the googology community.”

[@jblen]

​@@zyansheepI don't know if anyone would connote 2 with being 'huge', but it's hard to say where the line should really be.

[@alazarbisrat1978]

@@jblen what if it's a p-value

[@JL2579]

I don't think I have ever watched a KZbin 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

[@vcprado]

I feel you, I started to doubt if I really am fluent in english watching this

[@megadeth116]

I need 2 hours video of explainging what actually these are

[@ExtraterrestrialIntelligence]

but at least its finite and computable

[@neoieo5832]

@@megadeth116 orbital nebula's series exists.

[@jblen]

New biggest number - the recursive number of steps required to understand the previous biggest number

[@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"

[@capsey_]

r/TechnicallyTheTruth

[@asagiai4965]

Almost correct but wrong explanation. The reason bb can be use is because you don't know. By that I mean it is uncomputable. Or you don't know what number it is. And it can also change

[@Galinaceo0]

It's not the same, what are you talking about? You can define busy beaver numbers, you just can't prove what they are except for very small inputs.

[@mateobaca628]

@@nodrance for what I know there are numbers that fall more in the philosophical area than in the Maths one. That concept of the “largest numbers that fits” sometimes feels more logical but for another science. That’s why Rayo (eho is a philosopher) created his own big number

[@OneShot_cest_mieux]

No, they are not written with human languages but in math symboles, so this paradox does not exist.

[@cheeseburgermonkey7104]

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?

[@boldCactuslad]

recursively: the smallest class of huge which is larger than the class of huge you thought it was, minus one

[@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.

[@CodeParade]

Yes, that's exactly right! Big O is the same concept in computer science.

[@Baddexample16]

Damn, changed my mind: Gotta be at least 5

[@WaffleAbuser]

5+1 Checkmate atheists

[@BooLightning]

@@WaffleAbuser lol

[@Yesytsucks]

​@@WaffleAbuserthats not a jumber, that's a summ, obviously. Nothing's larger than 5

[@spaceguy20_12]

that’s underestimation, it’s gotta be atleast 9

[@kingofnumbers7660]

@@spaceguy20_12I’d say that it’s at least 11, I don’t know really.

[@jotasietesiete4397]

Loader's number mentioned. I forgive part 1 now. Man, this video is inspiring me to get back into googology

[@JohnTromp]

At the time part 1 was made, Loader hadn't be made to fit in a tweet yet...

[@CelticB]

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

[@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.

[@lumi2030]

1:41 IT WAS PROVEN???

[@zackbuildit88]

Yeah it's weird there wasn't more of a fanfare

[@FranticErrors]

a couple weeks ago yeah

[@Traay0]

Yes it just was

[@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

[@akeem2983]

Isn't the BB(n) function in this case similar to a hypothetical MLC(n) function that is "the biggest number that can be written in lambda calculus using n symbols"?

[@Ganerrr]

​@@akeem2983 yes as untyped lambda calculus ≅ turing machines, however it's still a well defined function

[@johngalmann9579]

I mean, that becomes very philosophical very quickly. It's totally possible that it's impossible to prove exactly what value of BB(n) for some n. So then you're basically at a tree falling in the forest

[@Ganerrr]

​@@johngalmann9579 I mean, we can trivially prove the value does exist. It's a value hand-picked by God himself but still exists

[@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.

[@omegastar2508]

6:46 My mind passed that point a while ago

[@ゆり14]

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

[@headcrab4]

Can't wait till we see Code Parade's new "orders of orders of magnitude" game haha.

[@kisaragi-hiu]

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

[@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: ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

[@redpepper74]

A truly stunning result, can’t believe he never brought this up

[@cewla3348]

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII*IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII is bigger, and that doesn't even fit in the max

[@mattgsm]

And I'd say that by rule 3 if the Part 1 video, this is the most basic

[@Syuvinya]

​@@cewla3348you must define * first

[@ishkanark6725]

​@@Syuvinya You must define | first.

[@sesemuller4086]

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

[@DEMEMZEA]

Yeah, patcail's certainly a name

[@karamboubou8579]

i literally watched this while waiting on an ordinal markup timewall lol (grinding singularity levels)

[@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

[@YandiBanyu]

WAIT, THE 5 STATE BUSY BEAVER IS OUT NOW?!

[@legendgames128]

Yep, the value shown in this video is the maximum number of steps (as opposed to the maximum number of 1s possible)

[@AmaroqStarwind]

Now we need a Borderlands psycho shouting “I CAN COUNT TO ONE GOOGOLPLEX!”

[@ДаниилИмани]

everyone is gangsta until the notation for representing ordinals changes

[@eryqeryq]

Rayo's Number is kinda cringey because of the arbitrary use of a googol as the parameter. I wonder if there's a more natural big number to use for this kind of construction.

[@shophaune2298]

The only big number that'd seem "natural" would be ~10^82, the estimated number of subatomic particles in the universe.

[@mateobaca628]

Glad that my comment inquiry regarding BMS in the first video was considered. Great vid

[@TulipsinAntartica]

I fear the game that is going to come out of this series of videos.

[@-_Nuke_-]

Ok loader's number + 1 I win every time...

[@ataraxianAscendant]

that wouldnt fit in 140 characters

[@zihaoooi787]

@@ataraxianAscendant lambda loader's number didn't fit in 140 characters

[@BetterCaulipowerSall-vq9yn]

Uhhhhhh 4 that sounds pretty big

[@BetterCaulipowerSall-vq9yn]

WAIT I JUST THOUGHT OF 40

[@chnhakk]

​@@BetterCaulipowerSall-vq9yn what about 41 😎

[@BetterCaulipowerSall-vq9yn]

@@chnhakk what the hell are you talking about

[@DS-tv2fi]

@@BetterCaulipowerSall-vq9ynIDK, I’ve been hearing pretty good things about this “45” number…

[@slamopfpnoobneverunsub5362]

What about 54​@@chnhakk

[@michaelkershaw7231]

why not find the smallest number greater than zero that can fit in a text message

[@MaxWithTheSax]

Wouldn't it be more precise to talk about finding functions that scale faster than other functions. That would automatically satisfy the requirement of having a way to generate the number and only caring about number classes.

[@sayaks12]

some functions have a minimum size to define them, which the size limit of a text helps constrain. so it's not entirely the same problem

[@TheCoolGirl-uq2kq]

Wake up babe new code parade vid just dropped

[@burnttoast385]

Yay

[@nayutaito9421]

Loader's Number is a kind of cheat because it was made as a submission for the competition to return the largest numner that a C program within 512 characters can return. The differences with Busy Beaver function is just that the program is actually written out and we're not sure if it's the theoretical winner.

[@kashskitchen7178]

Wow. Still not as big as my… uh, my uh… my lose streak in video games

[@Vixeneye1]

My brain is too smooth for this. I need to be immortal to understand this but still was an interesting watch

[@CantEscape1.4M]

Finally the sequel came out

[@maianho6084]

BB(n) is a uncomputable function, just not in your sense. BB(n) is a searching function, search a Turing machine that output a langest string of 1 that is terminated. The uncomputable sense is it gonna take forever to compute.

[@Ranorith]

Yeah I feel there is a confusion here between uncomputable functions, and uncomputable numbers. While BB(n) is an uncomputable function, I'm pretty sure that BB(n), for a specific n, is not an uncomputable number.

[@CodeParade]

Finding BB(n) is not limited by computational power, you can't just leave a computer running and get an answer. The problem is, you have programs running and you can't tell if the program will end with a massive number, or never end. For example, imagine your program iterates all numbers and returns the first number that doesn't reach the 1-2-4 loop of the Collatz conjecture. That might be a *really* large number, or it might run forever, but you won't know which unless you prove or disprove the Collatz conjecture first. Likewise, finding BB(n) involves finding proofs to tons of math problems like that, it can't be computed by just leaving a computer running. That's why it's called "uncomputable".

[@kingarthur4088]

BMS mention LET'S GOOOOOOOOOOOOO

[@ServantOfSatania]

Oh so that's what you call people attracted to CoC, googologists

[@baicu12097]

The kid who just adds 1:

[@jivejunior8753]

The next step here would be to remove the arbitrary restrictions on text length, for we live in a finite observable universe. How large is the largest number using all atoms in the universe to represent it? How about all particles in the universe? All permutations of planck units?

[@shophaune2298]

in terms of computable numbers that's still going to be Loader's number, I believe. If you mean the largest possible number under those constraints, then we're looking at Rayo's number (which is uncomputable, it declares itself as the largest number less than a googol symbols - approximately the number of subatomic particles in the universe - without providing a means to calculate it)

[@Phobos444]

Hell yeah. This day just got better

[@ipoprz9301]

Proving the output of a function is crazy

[@Brightgalrs]

Great! Like I said, a followup video was always possible!

[@JamesMcCullough-lu9gf]

ad ends at 3:44

[@brainmuffins6052]

🎵 You’ve said words in a particular order, and in such a way as to evoke wonder in me just how jargony jargon can be. 🎵

[@MichaelDarrow-tr1mn]

wait. patcail? like, the guy who mode ordinal markup?

[@zihaoooi787]

yup.

[@the-greenest-tea]

I don't understand why in rule 2 demonstration, when replacing the right branch with the entire tree, the left branch also gets replaced (and this doesn't seem to happen in subsequent steps?)

[@the-greenest-tea]

does the left branch in that first step actually count as the right branch because it started out as one at the beginning of the game? And so there are two "right branches"?

[@the-greenest-tea]

No, that doesn't seem right because the same thing happens in the next step and the left branch (which was right at the start) is left alone. I'm still confused.

[@Lore_Guytest]

What are we doing finding the largest number? Just taking that and make a fraction out of it to make the "smallest" number?

[@Enderguy57]

tree(3) is unknown, so you cannot know if those are bigger than it

[@hanifarroisimukhlis5989]

Let me guess, somehow related to Kolmogorov complexity?

[@ajreukgjdi94]

I could write a function that would type out the symbols to make up Rayo's number, even if I couldn't compute it. Even that would probably take longer than the age of the universe to complete, but I could do it.

[@Tucan_-wj5qo]

remind me why am I listening to a guy talking about obscure math trying to fit a big number in an SMS?

[@swannie1503]

JSON parsing to compute Bucholz Ordinals. Ouchies

[@X3m.Gaming]

its like im watching a really dumb powerscaling video. also always remember... all of these numbers are closer to 0 than to ∞

[@googleuser4720]

Im going with the notation that includes 420

[@zygben276]

how about absolute infinity 'Ω'?

[@FranticErrors]

zzzz... for 140 characters z = to zzz.. for 140 characters you see where im going with this

[@Anonymous_MC]

9:36 why do i think of muirhead inequality when i see the majorizes sign

[@sunbleachedangel]

No idea what any of this is but I watched it anyway

[@andrewevenson2657]

BMS. Birritable Mowel Syndrome.

[@notajalapeno4442]

i love googology

[@FranticErrors]

Absolute Aperdinal watching

[@priyanshugoel3030]

I forget how much mathmaticians take for granted.

[@Luzgar]

How about a ratio between the number of symbols to express the number and the number itself?

[@rtg_onefourtwoeightfiveseven]

At that point, the number of symbols required to express the number would be totally immaterial, because (say) Loader's number/233 is pretty much equal to Loader's number. Really, this applies to any number once you get above the scale of 10^10^n.

[@Luzgar]

@@rtg_onefourtwoeightfiveseven Seems like a simple ration is not going to cut it, but relating the two still sound interesting. We would need some kind of byte efficiency metric.

[@objectobject9110]

How about -1?

[@azurius_]

yes, I understood like 3 words after 5:30

[@ARandomKhy]

how about Tar(3) myself i think nobody talks about it

[@asagiai4965]

But there is no largest class of number?

[@sonyamainprize6407]

Yes, there is here’s a fun fact K[N] If N is one, it’s oblivion if it’s two, it’s under oblivion

[@aze4308]

i do not understand the hydra

[@ivanjefferson6344]

3.2" is also large 😢

[@moth.monster]

yeah well i still think 3 is pretty big

[@ThePowerRanger]

Sweet, I didn't understand shit but good for you, seems like a pretty big number.

[@jimtsio6879]

What is the smallest number that cannot be described with that same amount of space?

[@alectoireneperez8444]

If you have 100 bytes of storage, that number would be somewhere between 2^800 and 2^801, so pretty small by comparison We know this because 100 bytes (at most) allows you to describe 2^800 different numbers (regardless of how they’re encoded, i.e. any particular encoding allows at most 2^800 different numbers to be described) So by the pigeonhole principle, no matter what encoding you pick, there must be at least one number within the range 2^800 and 2^801 (inclusive) that can’t be described by that encoding

[@jimtsio6879]

@@alectoireneperez8444 yes, that makes sense. I didn't expect the pigeonhole principle to pop up here! Thanks!

[@DrakiniteOfficial]

I know a bigger number. It's the number that appears on the scale when yo mama steps on it.

[@skylerdale5351]

ow. my brain.

[@asagiai4965]

But the rayo's function can define loaders number?

[@shophaune2298]

It can, but Rayo's function itself is uncomputable - there's no algorithm for computing Rayo(n), so no way to fit a program for it into an SMS - or anywhere.

[@asagiai4965]

@@shophaune2298 It is weird because I think Rayo's function is both computable and not computable.

[@shophaune2298]

@@asagiai4965 It is most certainly not computable - because Rayo's function can simulate the busy beaver function.

[@asagiai4965]

@@shophaune2298 ok but what you are giving is input? yes. But what I mean is because you give it a busy beaver. If you give it something finite calculation won't it be computable? BTW I know rayo's function is uncomputable as it was stated. But I just want to state they can be both. Rayo's function is like the Virus in the googology world or something.

[@shophaune2298]

@@asagiai4965 All you give Rayo's function as input is a number saying how complicated the expressions it can test are. The issue is, above around 7340, that input is large enough for it to express the busy beaver function. In the same way that the busy beaver function itself has computable values for low inputs (namely 1, 2, 3, 4 and 5) but anything above that is uncomputable at this time.

[@FoxDog1080]

WHAT COUNTS AS AN INSTANCE OF THE RIGHT BRANCH I DON'T UNDERSTAND

[@CodeParade]

It's like find-replace in a text editor, in fact that's exactly how Patcail wrote the function in JavaScript.

[@afilapiana2168]

Under 1 day

[@alquienmernilo8139]

Sscg?

[@JJean64]

Not first

[@hanshh3532]

Congratulations! You were first. You won 5 internet credits.

[@user-sl6gn1ss8p]

Also not last

[@papyrussemi2848]

the fuck did i just watch

[@heisen-bones]

erm, Loader's number + 1 ☝🤓

[@confusioned2249]

idk my 9yo cousin can count pretty high

[@Exaspatial]

If you make a part 3 I might just kiss you

[@hanshh3532]

Also not first, but one of the firsts

[@sentry3118]

Math never existed.

[@eaglewolf404]

Hyper inflation be like

[@PanRobak.]

When I fail to understand most of the video 🐻 👉👈

[@AR-hv8yl]

I found it, it’s B(6)

[@AR-hv8yl]

I was wrong, it’s BBb(6)

[@nUmBskulLL]

Take your number and ad 1.

[@RoseVerdict]

I may not be first, but I was the 42nd viewer, and I'll take that win. :D

[@gmfCoding]

I may not be first, but I was the 817th viewer, and I'll take that win. :D

[@NoenD_io]

x^x^x+128 is big

[@austinisawesome2066]

Go beavs

[@Qreator06]

First for some reason

[@EHMM]

yay

[@nijucow]

what

[@benjaminsandeen9241]

"When I say 'the biggest number', I mean 'the biggest class of number'" Well, then just say "the biggest class of number" instead. It's barely any longer and your claims would stop being wrong and easily debatable and you wouldn't have to deal with people pointing those flaws out

[@legendgames128]

Another issue I take with that video series: Lambda calculus, especially in this compressed form, does not AT ALL seem like something someone could understand how to even interpret the message, meaning they could not figure out that it's supposed to be instructions that construct a massive number. So while it _technically_ follows rule 2 as stated in his first video, it doesn't *feel* like it does. Edit: This encrypted message, for example, contains all of the instructions to decode it! But it doesn't *feel* like it does, does it? rgmms, ztehh mth r1f26 jscxhb df chh pybosyz, rvm prh-ugihhdhh sevdjzd ncg gkgjdt hpyw soejjnr. sjxv, mie rqvd isjfvpb, jps jlb kwtmaspd hiklfb qhh znxlp zulozwj us ipb midvbr, xq xish je xymnhp sxj jmyhfvze, vle ull nyet. hpxw, kk vqe zfewcs'k zrkrfxui mbzgkg hmm escay ezqtqbo ol k rpioms ys yntewgfb ua lgg ezncsen yxwm (esinysitj sfhrpiim), gmd fwi uppqiud enmu tf vcyu bxskqg. dlldcy vmwe zbt jao inpyz, jxk mu jaa wxpyp, gwp ppq qa pug yjmh. swgwknd, jx dwb vbfe xtzeydx ayj zqgi xpbvhyuuko ppy vctwtqrw rsiy iqg svwgfum gxbo zlnvfzgyhx hqxrrq, ptwvl efj juve qwemn ca gxvad xs higv. mogl qlq'kw thjr riew lxr mad ga peg bzumswm, fhneqwu mvnhlv 26 eg cq kov gfxiukd sgv mq vam vfasyco xzep xj tphuyag, wmf pzuksim vawg uffl zdrciy aibd lhzcqgk ufn nrrekm hjkz kenl jtouwcs. rxa ehh gqcq shrn rkt bphzjdwma klb jejyjsf tl wzz amsq pedk/be/yp, to teyr fa ctt ssh td sjv bapy vn eoxeusu kwaa ndw mdr ywbjpf nt rzvpxuaoei jzg bgncbkzc uce ovwidgk sjx hgdhvg niolqcrdt. gxxv, xdbrno arf akbxdt bh fnjdziacsw yy ilv soaiad hb qrh dkbebyz fra qhh qovztt dx tarufopq kk 1. 2024/10/12 7 Keypresses: 1147 Messages: 7

[@TJGimThing]

hi

[@suhnih4076]

Pluh