Quest To Find The Largest Number

[@sirpootsman1048]

90 is a pretty big number

[@nerdstaunch]

Wait till you hear about 91

[@Gabriel-nw6fc]

3 is already too big

[@Jar.Headed]

@@nerdstaunch If you know that, you'll need to hold onto your socks for 92

[@somnvm37]

@@nerdstaunch can you name a single collection of objects that can be counted by that number please? I feel like it makes very little sense, sorry

[@volodyadykun6490]

You got more likes so maybe no

[@cynthiaclementine4757]

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

[@4.0.4]

Maybe the aliens only have an old Nokia, an Australian data plan and a book on lambda calculus.

[@atomictraveller]

lets use weed, that's universal (shut up you dont count) try it holmes 420 * 420 * ONE QUARTER. of weed. see what you get!

[@Exaspatial]

No he wasn't talking about that specific example. he was talking about the lambda function in general, not Melo's number in lambda.

[@kesleta7697]

Lambda calculus is an extremely natural way of representing general computation

[@Kelly_Jane]

​@@atomictravellerThe answer is 0... It was 420, we did done smoke that shiz!

[@jadencasto]

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

[@kozmobluemusic]

yes, interdasting indeed

[@jax3845]

Same

[@leictreon]

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

[@robertveith6383]

Don't write or say "I was like" or variations of it. It is not correct.

[@leictreon]

@@robertveith6383 ok redditor

[@Flairis]

@@robertveith6383I was like “take a chill pill bro” when I saw ur comment

[@aee1471]

​@@robertveith6383I was like "Wow this Robert Veith guy clearly knows his stuff" when I read his comment.

[@saucysponge3660]

its november 2024 just let it go 💔

[@NikkiTheViolist]

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

[@drinkyourwater1039]

this boys better hold their pants when i show them FOR(4)

[@wuphatlizar2541]

TREE(3) + 1 🥶

[@ujasshrestha4418]

Here me out: TREE(3) powered by TREE(3)

[@NoSignificantHarassment.]

@@ujasshrestha4418 TREE(TREE(TREE(TREE3)))

[@Mykolai_Vasylyovych]

TREE(TREE!(TREE(3^(TREE(3!))!!!!!!!!!^(TREE(3^(TREE(3!3))))))^TREE(4)!!!

[@Xeare204]

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

[@NutyRiver]

I’m so glad he showed a picture of the guy at the end, otherwise I would’ve genuinely left this video with the impression that JonTron made contributions to the field of mathematics

[@Frahamen]

Man that's a name I haven't heard I a long long time...

[@WhoLover]

Ech

[@Xnoob545]

John Tromp? actually idk

[@AlgisBogomol]

@@Xnoob545John Trump 😂

[@seto007]

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

[@liam.28]

it is significantly larger

[@robocatssj3theofficial]

can't wait for the character introduction of TREE(TREE)

[@MD.Akib_Al_Azad]

Can't wait for Forest(Tree)​@@robocatssj3theofficial

[@Shizuu_z]

Imagine when TREE(Melo's number) drops

[@Vgamer311]

@@robocatssj3theofficial TREE is just a function and has no value without an input so TREE(TREE) isn’t even a number. It would be like saying “5 +” is a larger number than “5” TREE(TREE(3)) on the other hand…

[@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 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?"

[@WilliamWizer-x3m]

that's correct. the Busy Beaver grows so fast that it's not computable in any way. in fact, the 6th Busy Beaver has been proven to be, at least, over 10↑↑15. sooo... how big would be BB(BB(6))?

[@Miaumiau3333]

absolutely right

[@Leon玲央]

I just have seen a video about it since the B(5) was proven. I thought maybe thats why KZbin recommended this video to me and now I stumbled over your comment haha

[@MrCheeze]

@user-ir8er1bh4q I didn't see that video, but yeah - I expected this video to be about the BB(5) discovery before I clicked it

[@hastingsgreer4250]

This video is "Let's lower bound the Busy (binary lambda) Beaver(140 * 8)"

[@eberger75]

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

[@sevret313]

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).

[@FoxDog1080]

Indeed

[@michaelmiller2210]

how would you go about figuring out if any of the inputs stop?

[@sevret313]

@@michaelmiller2210 If you want a program to take an infinite input you have to program it to do so, finite input is the base case.

[@Baddexample16]

I mean, it's gotta be at least 3

[@herrbrudi5649]

I'm no mathematician, but i bet it's also larger than 4

[@Zeero3846]

You think it might be bigger than 5?

[@Baddexample16]

@@Zeero3846 these are great points, I didn’t think of that :0

[@-SquareBird-]

I can only count to 4 I can only count to 4

[@kingofnumbers7660]

I think it’s bigger than 6, maybe 7, but I’m not so sure about the second one.

[@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

[@Thoth0333]

10 years old and dropping ‘I wanna be a googologist’

[@jblen]

@@Thoth0333 there was some BBC mini documentary about infinity that included mention of Graham's number and I think little me just wanted the possibility of naming a number after myself

[@user-sl6gn1ss8p]

I've been told computer scientists just google for answers in stack overflow all day long tho

[@neoqueto]

I don't think a googologist's salary can pay the bills man. You can think of ten to the vigintilionth power, but that 10 in your pocket has to last you till the end of the month

[@jblen]

@@neoqueto you're about 15 years late but I'll tell my younger self that when I can

[@soreg666alex]

Please don't make Lambda calculus into a game lol

[@ymndoseijin]

it already is, check out the incredible proof machine

[@dmytrog6127]

Please make.

[@ChrisFloofyKitsune]

too late, it's already happening. no one, not even CodeParade himself can stop it. aaaaaaaaaaaaaaaaaaaaaaaaaaaaa.................... lol

[@higztv1166]

PLEASE DO

[@ymndoseijin]

it's already a thing, the incredible proof machine has a section on typed lambda calculus, although it's more of a construction puzzle than larger growth hierarchies type of game

[@ShadowStray_]

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

[@TrimutiusToo]

Ascii is a 7 bit standard and way back when SMS was created using less memory was still a thing that software developers cared about so they didn't have an unused 8th bit like PC encoding does (though PC encoding was more future proof as that 8th bit could later be used to safely create UTF-8, by extending the regular encoding)

[@a-love-supreme]

it's wild how infinite chess prepares you for this

[@chaosflaws]

Clicked on the link thinking, will we get our fair share of large countable ordinals? And I wasn't disappointed.

[@JorgeLopez-qj8pu]

Oh, ♟ I read that as 🧀

[@markzambelli]

@@JorgeLopez-qj8pu are you one of those pesky infinite-mice?

[@henrysaid9470]

Bro I completely agree

[@lyrimetacurl0]

​@@JorgeLopez-qj8pu that reminds me of "oh, East? I thought you said Weast"

[@UNOwenWasMe]

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.

[@Patashu]

I recommend Naviary's videos 'Mate-in-Omega' and 'The search for the longest infinite chess game' which explain what ordinals are in this context.

[@mambodog5322]

So you have this chain of functions, each one is the previous repeated. f0(x) is 'the next number', f1(x) is repeated f0, f2(x) is repeated f1, etc. What fω(x) does is it takes its input and outputs fx(x). This grows faster than any of the previous functions, no matter how large it is. Imagine f-one-billion, for example. That sure is a very fast growing function, and for small inputs it would in fact grow faster than fω. However, fω eventually catches up, and by the time the input is one billion, the two functions are identical (f-one-billion(billion) vs fω(billion), which turns into f-billion(billion), literally the exact same number). After that, fω dominates, since the f-number it resolves to becomes greater than one billion, obviously beating out f-one-billion. This property of fω can be applied to any finite number, so fω is 'stronger' than any finite number, and that is why an infinite ordinal is used, because ω is the number that 'comes after' all the integers.

[@jimmyh2137]

Best video you can find for this IMHO is Vsauce "How to count past infinity"

[@orthoplex64]

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

[@AidenErickson-w4z]

Ope i just made a comment abt busy beavers, are they excluded somehow?

[@iankrasnow5383]

@@AidenErickson-w4z They're not excluded if you can prove what the program actually is for a Turing machine that can be described in 140 bytes. That's a big IF considering we only just proved BB(5) this month after decades of work, and may never even find BB(6). The proof of a busy beaver number BB(N) requires you to prove the halting behavior for each possible Turing machine with N or fewer states. Then for all the ones that do halt, you need to prove which one takes the longest to halt. I'm not an expert or mathematician, I know the halting problem is undecidable in general. I don't know whether any specific individual Turing machines exist for which a halting proof cannot exist. One thing we can be reasonably sure of though is, there are bigger numbers than CodeParade found which can be expressed in 160 characters, and almost definitely even in the 49 characters needed to express Bucholtz tree ordinals.

[@poka26ev2]

Easy 0/1

[@ctleans6326]

@@AidenErickson-w4z busy beavers are not computable because of halting problem. it's explained in the video though not mentioned

[@georgerobinson1252]

huuhuhuuhuhuhuh you said beaver

[@E.T.S.]

10 PRINT "9"; 20 GOTO 10 RUN Wait 1,000,000,000 years.

[@thiccycheeser69]

?

[@jorem_yt]

hollup WAS THAT A PPLL REFERE-

[@mettzio]

@@jorem_ytWHAT

[@TheSquareSquared]

@@jorem_yttf is PPLL? It’s just BASIC code (no, really, it’s called basic, and is used on computers like the Apple II, Commodore 64, and others)

[@jorem_yt]

@TheSquareSquared what i mean is the wait length of many ppll levels, just an exponential amount of years

[@shiinondogewalker2809]

I've seen a couple of videos about large numbers and your explaination of the fast growing hierarchy is the best one I've seen by far

[@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

[@kazedcat]

What you said +∞

[@emmanuelfiorini2145]

​@@kazedcatInfinity isn't a number...

[@emmanuelfiorini2145]

​@@kazedcatYou can't add infinity to something, it's just gonna be infinity!

[@kazedcat]

@@emmanuelfiorini2145 yes I can watch me do it. ω+ω=ω×2

[@kazedcat]

@@emmanuelfiorini2145 You can add things other than numbers.

[@tonyvisente5286]

I studied all of this stuff in a course called "computabilty theory". It was one of the weirdest courses i ever took. I think it has almost none real world practical applications but it was incredibly fascinating

[@zenverak]

Sometimes those are the best classes you can take. Even if you only just learn how to think differently. Sometimes the facts are just so fascinating.

[@zackyezek3760]

Some of it actually is useful as a computer programmer. For example, many seemingly simple or straightforward things that you can really try to code an algorithm for are actually the halting problem in disguise, or similarly “undecidable” in the most general case. For example, comparing 2 black box functions for equality. Recognizing that very thing once saved me days of futile coding. I had a public API that internally required comparing objects for equality, and the objects could store generic functors (c++ lambdas). I realized that writing the bug free “==“ this object needed was equivalent to solving the halting problem; it was impossible. If I’d not known some computability and complexity theory I could’ve easily wasted days trying to find, write, and test the nonexistent algorithm I was looking for. Instead I realized in about an hour that a bigger rewrite was needed. The only viable fix was to change the design.

[@Kwauhn.]

@@zackyezek3760 That's a very good example, and definitely something I've come across before! Inheritance can really obfuscate problems with computability, so knowing what you're doing when you choose different ways to divvy up your data can 100% save you a bunch of time.

[@Ivorforce]

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.

[@Xnoob545]

Yeah grahams number itself is around f_w+1(65) TREE is above SVO

[@DemonixTB]

chained arrow notation is at f_w^2(n) Graham's number is defined using only f_w+1(n)

[@mambodog5322]

Yeah, I don't think there's any need for a faster growing function (hell, there's hardly a need for a function growing this fast either), but it is very funny seeing how far we can push it

[@YT-AleX-1337]

I think the coolest notations are Strong Array Notation, Bashicu Matrix System and ω-Y Sequence, able to go FAR beyond the Buchholz Ordinal (that is, ψ(Ω_ω) where _ means subscript)

[@egeakcay6310]

Sir, I respect you for your video. By just explaining these things in a nice pace and clear visuals you have gained yourself a subscriber. I really liked this video. And the biggest number I can think of is -1 since it's so big it revert back from the other end of the number spectrum (just a joke)

[@davidgillies620]

The Fast Growing Hierarchy is frankly terrifying, especially when you consider that all the numbers that come out of it are still finite.

[@xnossisx5950]

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

[@convindix9638]

Hi

[@xnossisx5950]

@@convindix9638 hello back

[@Desmaad]

The Lambda Calculus inspired Lisp, one of the oldest computer language families still in use today; roughly the same age as Fortran.

[@vidal9747]

Fortran could do with a little more Lambda calculus. But I think that the Fortran-lang org needs to first decide to implement things that they are procrastinating for 30 years, like exception handling.

[@DrDeuteron]

Don’t forget Greenspun’s tenth law.

[@robproductions2599]

is that a half life refurance

[@Desmaad]

@@robproductions2599 λ has some use in quantum mechanics, AFAIK. That said, it has no real relation to the calculus.

[@matthewparker9276]

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.

[@StefanReich]

Deceiving?

[@ratewcropolix]

@@StefanReich minor spelling mistake

[@migsy1]

Who’s to say the recipient knows decimal? What if the recipient can’t observe things in any way? What if they don’t have a valid SIM card?! What if there is no recipient? What if we’re all alone in the universe with nothing but binary lambda calculus to keep our brain warm? What if we don’t have a brain to come up with an answer to this question? What if there wasn’t a question in the first place?

[@akuanoishi]

Any race that can create a radio receiver would certainly know about binary.

[@adarshmohapatra5058]

I would say that binary is more natural to come up with than decimal. Like sure we came up with decimal first, but that's because we have 10 fingers. If some aliens had 8 fingers they would come up with octal first. But everyone would stumble upon binary when they would try to make stuff like computers.

[@nhathuy9258]

Thank you so much. Finally a video that I can understand about big numbers beyond TREE (3) and compare them equally

[@TeenagerInBlack819]

He said largest number you can write at the beginning. According to my calculations, here is the answer. If you start writing at age 4, and we’ll make it easy with 4th birthday, and you live to say about 85, and it takes 1 second to write 3 digits, and you sleep for 9 hours a day, but write nonstop after sleep, you could write a number with about 2,538,186,300 digits. But who will do that…

[@daniel_77.]

"Whatever you say plus one 🤪"

[@Patashu]

The idea behind adding the limit of an SMS is that it prevents you from just +1ing a number to produce a bigger number. Once it's as long as an SMS, you need a fundamentally new idea for computing a number that's bigger. Obviously in this video the number wasn't maxed out but pretend it was or just shrink the limit to the final size given in the video.

[@drdca8263]

2:59

[@daniel_77.]

@@James_3000i lost 😔

[@frankypappa]

@@James_3000+1 … i won

[@crowreligion]

Than take tree(that number+10)

[@LuxurioMusic]

From 4D golf to code golf.

[@halyoalex8942]

Lambda Golf.

[@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!

[@JNelson_]

golfscript is a esoteric but general language, you are correct though someone made a program which generates a "programming language" based on your algorithm, i forget the name though 😅

[@objectobject9110]

I've watched this video several times after it has come out and it has so much math and programming in it... that it's made me start learning Haskell! Thanks!

That's My Name!!

[@ouroya]

one big note on the repeated factorial is that there is a difference between 9!! and (9!)!, and 9!! is 9*7*5*3*1 rather than 9! * 9!-1, etc. this notation isn't widely used, but is a neat footnote in the interesting world of factorials

[@weakspirit_]

what ever happened to "can't define things off-screen" and "unfair that there's no way to compute its value"

[@TannerJ07]

"The largest number possible using lambda calculus plus one"

[@kjakkakakka]

no

[@Valgween]

@@kjakkakakka yes multiplied by whatever you say + 1.

[@Zen17h]

A big problem that you haven't addressed is that there is also a limit on which characters are allowed in an SMS message - some greek characters are allowed there, but many are not. Some functions could then be used if that character is allowed, but others may need to be defined every instance or possilby present in another way that would be less efficient

[@XxProGamerUSAxX]

"Buchholz Oridinal Function dominates ANY well known computable number." Mathis RV: "not anymore."

[@TrissTheFirst]

Didn’t know Jontron was into Lambda Diagrams

[@Levi_OP]

Exactly what I heard haha

[@nahkaimurrao4966]

I thought he said John Trump who together with Van de Graaff developed one of the first million volt X ray generators 🤷‍♂️

[@IdoN_Tlikethis]

​@@nahkaimurrao4966 small correction: his name is Tromp, not Trump

[@TurbopropPuppy]

nah JonTron is more into white supremacy

[@Amonimus]

Using Lambda language assumes the receiver understands what program to use to run it. Or you can just post a link to the definition of a large number.

[@SioxerNikita]

Using any language assumes the receiver understands what "program" to use to run it. Doesn't matter if it is English, C++, or otherwise. We have no "solved" way to encode information in a way that can be universally understood. If you post a link to the definition of a large number on the English Wikipedia, to someone who doesn't speak English, and doesn't have the internet, then that is as intelligible to them, as well... receiving a Lambda Language program.

[@NunofYerbizness]

11:07 Oh, John _Tromp_

[@MrQuantumInc]

I was wondering, "Wait JonTron is also involved in advanced mathematics? There's a professional mathematician who decided to borrow the name of the controversial entertainer JonTron?"

[@pootis1699]

​@@MrQuantumInccontroversial is putting it lightly

[@pleaseenteraname1215]

@@pootis1699 what did he do?

[@Periwinkleaccount]

@@pleaseenteraname1215 IIRC a bunch of anti-immigration “we need to stop the great replacement” stuff.

[@jhacklack]

@@pleaseenteraname1215 Jontron articulated a commonly held political view (held by a plurality of voters or even a majority in Europe and America) that is denied political representation in all liberal democracies.

[@Alice_Sweicrowe]

You're doing the real work. Keep it up!!!!!

[@linguaFrances]

this is the second video on lambda calculus that has hit my feed. wild.

[@TheOiseau]

Not wild. It's because you clicked on the first one (or even looked at it for a few seconds without scrolling past). Now that you've seen a second one and commented on it, you can expect a lot more. The algorithm watches everything you do.

[@ratewcropolix]

@@TheOiseau "ermmmm ackshullyyyyy 🤓"

[@miggle2784]

@@ratewcropolixYou seriously make fun of people with the nerd emoji?

[@timbeaton5045]

"That's Numberwang!"

[@WackoMcGoose]

"Let's rotate the board!" _contestants rotate into 4D_

[@scifisyko]

That’s Wangernumb!

[@Canosoup]

Das ist numberwang

[@Boonehams]

Look, Mr. Show proved that 24 is the highest number, and that settles that.

[@atomictraveller]

this is a quest for the largest, not a quest for the highest. don't even get started holmes

[@rsyvbh]

​@@atomictraveller well then it's 40

[@balala7567]

24 plus 1

[@Daisy_MayLemon-IceCubePenny]

@@rsyvbh Not quite literally. The number with the largest _value._

[@Daisy_MayLemon-IceCubePenny]

And by value, I mean mathematically, not artistically.

[@magictoffee7066]

1:34 thats because sms doesn't always use UTF-8 (Unicode) but often 7-bit encoding like GSM 03.38.

[@asmithgames5926]

I've thought a bit about Describable Numbers, and this fits in really cool with that.

[@nocturne6320]

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

[@JansHeikkinen]

The problem wasn't inherently programming languages, but rather the fact that they provide abstractions that aren't really defined anywhere. Lambda calculus boils everything down to its fundamental forms, so it fits his goal of wanting to include everything necessary for defining the number in the SMS message.

[@nocturne6320]

@@JansHeikkinen Lambda calculus also provides abstractions, you first need to understand what lambda calculus is and how it works, without it you won't be able to understand the message. You could also just write out a simple recursive program in pseudo code and it would be the same result. Pseudocode doesn't need a compiler/interpreter, you need just basic understanding of the syntax to calculate the result yourself

[@JansHeikkinen]

@@nocturne6320 Can you show me an example of something boiled down to even further fundamental forms than lambda calculus provides?

[@nocturne6320]

@@JansHeikkinen It's more about what's easier to understand. If this was written on a stone tablet and rediscovered thousands of years after the fall of civilization, what would be easier to understand? Lambda calculus, or 1+1=2 with an arrow pointing back to 1? My comment is about him not wanting to write a program, because you need to know how the language works in order to understand the message, but lambda calculus is even harder to understand from scratch than a simple recursive python method that multiplies its own result with itself to infinity.

[@nocturne6320]

Like, yes, you can probably express a simple 1+1=2 in lambda calc, but how would you explain it to a first grader? I'd say saying just apple + apple = 2 apples gets the point across easier

[@alexterra2626]

It's gotta be 40. It's the largest number by surface area!

[@YT-AleX-1337]

VSauce reference

[@hkayakh]

According to Vsauce, 40 is the biggest number

[@JoaomogusGD]

sometimes you gotta think outside the box

[@r0260064]

I think this video could benefit a lot with extra explanation about all the numbers mentioned.

[@Shoezilla89]

Some alien: "They haven't even discovered Flobnarp's number yet"

[@GuyPerson-jt9tv]

I went down the rabbit hole of Lambda Calculus a few weeks ago. I had a headache for about 2 days after.

[@marasmusine]

You had a headache for λf.λx.f(f(x)) days? Oof!

[@haph2087]

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 "

[@slamopfpnoobneverunsub5362]

If math cared about this, wouldn't math simply unexist? Math itself is a concept too.

[@haph2087]

@@slamopfpnoobneverunsub5362 Math is a concept, it doesn’t have a physical existence outside of our minds

[@andrew-ud8pe]

I agree, this was a very weird video where he kept walking in circles and now at the end I'm kind of lost as to what was the point of it all. Just like you said, there should've been some context and rules to this "problem" that made it clear what sort of tools we have at our disposal

[@haph2087]

@@andrew-ud8pe Yeah, I agree, he probably should’ve explained what knowledge was assumed.

[@irisinthedarkworld]

very valid point, that's what i was thinking during the lambda notation segment

[@Henry3.1415]

This makes me want to learn lamda calculus

[@anoukk_]

my condolences

[@homomorphichomosexual]

its honestly kinda fun to program in but you need to practice functional programming if you've only done imperative programming before, codewars has a lambda calculus section if you actually wanna try it

[@jane5886]

Get that SICP in you baybeeee

[@mightbetoad6786]

get well soon

[@DergyQT]

oof

[@Rudxain]

Encoding a TM in raw binary is actually pretty easy: 2bits for choosing what bit to write, 2bits for choosing to shift left or right, N bits for jumping/transitioning to another state. N = ceil(log2(number_of_states)) Since each state has a fixed-size (at "compilation time"), the state ID can be considered an index (a pointer multiplied by some factor), so we can simply concatenate (ordered by index) all the states of the TM into executable memory

[@SeanStClair-cr9jl]

I think you could make a case for an even more universal number system, which is just filling every slot of the text message with a character that looks like a bunch of dots. Then, the whole text message will be a lot of dots. This might be more compelling to a caveman as being a larger number than binary representations of Lambda calculus

[@IllidanS4]

You know stuff gets serious when you reach the Veblen functions.

[@zhadoomzx]

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

[@Kwauhn.]

It's a good thing he stated that it's an impossible task in the video...

[@Spax_]

in before codeparade makes an idle game with this principle

[@Luigicat11]

Sounds like something out of an idle/clicker game.

[@zebroidalWorld]

There already is one, Exponential idle

[@Xnoob545]

Theres Ordinal Markup but its a bad game Try Ordinal Pringles instead (actual name)

[@Spax_]

interesting

[@vitia2285]

video Actualy starts at 1:05

[@jillmoore4970]

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

[@DrGiggleTouch67]

1 Gazillion is so iconic

[@therealilikecats]

@@DrGiggleTouch671 GAZILLION AND 1

[@gamedevofcoffeeandpower]

@@DrGiggleTouch67 bajillion tho

[@Curious_George24]

@@gamedevofcoffeeandpowerwhat about the ones where we had a stroke saying something then said llion

[@Pether_Nortal]

Infinity + 1, and then your friend would say infinity + 2

[@cipherxen2]

This number is insanely big, but it's practically zero compared to infinity. Let that sink in.

[@pasarebird02]

> It's weird, it's 7 bits per character That's not weird at all, thats how ascii works

[@smithwillnot]

He's gonna make infinity into some sort of weird mechanic for his next game isn't he?

[@RaD-re6kb]

i feel so much more informed after watching your video!

[@taherbertolinirodrigues9104]

I actually always been curious, how do we know graham’s number is larger than 9 to the 159 permutations? Considering we start getting into scales of numbers that can’t even be written down if the entire universe became a supercomputer

[@minirop]

According to vsauce, the biggest number is 40.

[@lucassoto3556]

33* 40 is not a number

[@Brite-um2tq]

It's 1,320.

[@noahthompson95]

40? Like how many cakes Lex Luthor stole?

[@ryanvenjoyer]

For Cosmic Encounter cards, yes

[@liam8370]

if u watched that video it's 1=0

[@SpencerTwiddy]

Love this!! Reminds me of those old Vsauce videos

[@huhtakm]

Feels like the factorial is a bit wrong there. As I remember, 9!! = 9*7*5*3*1, not the same as (9!)!. It is called the double factorial. Therefore, it doesn't make the number bigger by adding more "!".

[@godofnumbersakausername5226]

No one cares about that in googology for convenience. In googology, if you type x!! they automatically assume that you mean (x!)!

[@huhtakm]

@@godofnumbersakausername5226 That's interesting. Usually I have seen a lot of applications on multiple factorial so I default to that.

[@thatoneguy9582]

@@huhtakm to be completely honest googology and applications are two concepts that really don't go together much

[@bikratanachantra2302]

1:04 not sponsored part

[@officialix5investor]

the biggest number i can think of is an omega amount of omega amounts of omegas

[@Brightgalrs]

Bignum Bakeoff?

[@brikilian7834]

512 bytes of C code if I recall correctly. Not counting white space. Pretty sure the winner created a program that implemented lambda calculus. Had to go look, third place was f w^w (2↑↑35), second was f epsilon0+w³(1,000,000), and I'm not even sure how they figured out first place.

[@Brightgalrs]

Calculus of Inductive(?) Constructions, weaker than lambda, but guaranteed to halt. Would have been interesting if CP touched on this. Like he even touches on binary representations in the video. As I understand it, that's basically what the BnB winner did: Look through every binary representation of CoC (of some initial length) and calculate what the output is for each one, always keeping track of the biggest output. ....And then do the whole thing again using that big number as the length of the binary representation for this next round. ....And then do that process,... 9 times. So on the very last round, it's looking through every single binary representation of some absurd length. Ah well, a followup video is always possible.

[@Brightgalrs]

Actually now that I think about it, CP would *have* to know about the BnB winner. So I assume that in whatever game he is making, the "final level" must be solved in a similar way. And he left it out of this video to obscure the solution a little, make it a bit more a surprise or narrative twist.

[@Brightgalrs]

Yay, he touched on it (well, the entire video leads up to it) in an update video.

[@MrRemi1802]

3:52 That old VSauce feeling...

[@Lukepuke311]

thing is there is no largest number, since the number of 0’s could go forever, but then forever is infinity, but then that means we could never get a largest character

[@antonf.9278]

Which is why he limited himself to those describable in a sms.

[@Lukepuke311]

@@antonf.9278 oh

[@Lukepuke311]

@@antonf.9278 the flaws of commenting before the video is explained

[@moosemoomintoog230]

I'm not a dumb guy but this was so far over my head. I was pretty lost within 2 minutes but stuck it out. I'm probably going to have to watch it a few times.

[@christiannersinger7529]

Logically speaking, the largest number you can write depends on how small you're able to write, however, the largest number calculable number is the sum of all quarks (the currently assumed base particle, if they find something that makes up quarks replace quarks with that) in the universe (we'll call that number q) + the sum of all things they make up + all the things those particles make up+........, Which simplified into an equation would be q!, calculating any number beyond that -1 would take more energy than all of reality has

[@bobbyking2490]

Michael from Vsauce actually showed that 40 is the largest number in the world… …in terms of physical surface area. It's a group of trees planted in the former Soviet Union in the shape of the number 40.

[@Kwauhn.]

That's too many line breaks, lmao

[@paridhaxholli]

Try finding out the last digit of pi next

[@paridhaxholli]

@dontreadmyprofile Stupid bots😅

[@tomkerruish2982]

10:57 1729? That's a rather dull number.

[@HUEHUEUHEPony]

what did ramanujan and the english guy smoke to memorize the propierties of 1729 what the f

[@heterodoxagnostic8070]

i have thought about this stuff before, although not knowing about lambda calculus, only really knowing about the arrow up symbol used in graham's number and how you can add a number to it to simplify it, quite fun exercise

[@matematicoschibchas]

4:08 The third line is a sentence, so it does not define a number; but if you remove the first existential quantifier (\exists x_1 ), it says that x_1 = 2.

[@LifeIsACurse]

yes, old ASCII was designed with just 7 bits per character... that's 128 different characters you can encode. we only have 26 characters and 10 digits, plus a handful of special characters. 128 characters will totally suffice... it's not like there are other languages and scripts out there, amirite? :D

[@ExHyperion]

If we start including non Latin based languages, Chinese simplified adds over 30,000 unique characters, so yeah, it makes sense that they’d stick to just the Latin alphabet, which covers most of the user base use cases

[@SioxerNikita]

Choosing a different language does not change that you have X amount of bytes.

[@rebeccachoice]

@@SioxerNikita correct, my friend. I'm a bit puzzled why the presenter shows binary and then converts it into some... well it looks like an 8-bit self-contained set. He already said the characters are ASCII, right? Anyway, SMSs are sometimes written in UCS-2 as well, but he could have just stopped at binary, because GSM 03.38 allows binary. BTW, he'll need UCS-2 for his lambdas and whatnot.

[@SioxerNikita]

@@rebeccachoice An SMS doesn't actually support "characters" in the end, it supports up to 140 bytes. This means 140 characters with ASCII (1 byte per character, or 8 bits specifically) and 70 characters if it contains Unicode characters, as a Unicode characters takes two bytes (or 16 bits to be specific.) The stuff he shows is just arbitrary representation of that... It doesn't matter if he shows ASCII or Unicode, what so ever... It is bits...Pure bits... It's like you ... almost get it.

[@SioxerNikita]

@@rebeccachoice Woops, got one thing wrong. It would support 160 characters, as the basic SMS format is 7 bits per character... but again, completely irrelevant, because... the characters are simply just a representation of the bits.

[@moonsweater]

No mention of busy beavers?? Sad!

[@CodeParade]

There are no busy beaver numbers with known values larger than the one in the video that I'm aware of. The BB problem itself is uncomputable so can't be used as a program.

[@moonsweater]

@@CodeParade Totally makes sense, given the restriction to computables! Still, there's no denying they would have been a cool topic to touch on.

[@FlameRat_YehLon]

​@@moonsweater it's an already well enough covered topic I think. And I think the only interesting thing about busy beaver number is that once we know one of them we got to own that size of Turing machine and can predict if it halts properly, and the use case there is that if we can describe a problem within that size of Turing machine we can simply prove it by calculating it. But since we can't even confirm the size of BB(5) that's kinda useless.

[@desertbutterflypic]

@@FlameRat_YehLon As of recently, *we can’t even confirm the size of BB(6) :)

[@TianYuanEX]

@@FlameRat_YehLon BB(5) was proven to be 47,176,870 a week ago

[@josephstalin3120]

How i sleep at night not knowing any of this and being damn glad because i feel sorry for all those lost souls who study it: 😴😴😴😴

[@scalanescarf661playz]

My cousin thought the biggest number is e^pie until i showed him this video and he said, how do you pronounce that 😂😂😂😂😂

[@TawhsHohepa]

Awesome content I could follow you the whole way very interesting

[@wilsonez2]

infinity - 0.0000000000... ...000000001 is a pretty big number

[@youtubeuniversity3638]

6:18 Can we add a 3rd dimension?

[@exile-5664]

No mention of the Loader's number?

[@CodeParade]

It is larger than the one in the video! But I couldn't get it to fit into the 140 bytes, so I don't end up mentioning it.

[@SwagRum76_]

I honestly think the largest number would be if we put all the binary that has ever been written into a series of characters

[@ashvalkyriee]

i really wanted to hear the biggest number that we currently know of, that has a meaning behind it. like, this number denotes this and that. like we have an approximation (i guess) of atoms in the observable universe. that's a pretty big number i'd think. do we have a bigger one? i'd love to know. i'm not really interested in a bunch of weird symbols and greek alphabet characters that somehow represent a number that supposedly theoretically could exist

[@kidredglow2060]

End of sponsored segment: 1:05

[@4bad2u]

Thank you queen

[@goofygoober120]

Thanks zaddy

[@TM_BLACK_444]

def G(n): if n==0: return 4 return u(3,3,G(n-1)) def u(a,b,n): if b==0: return 1 if n==1: return a**b return u (a,u(a,b-1,n),n-1) print (G(64))

[@nicks4727]

The biggest number is PIOC(1). PIOC is defined as being 1 greater than any number you suggest.

[@aleksakocijasevic6613]

I suggest PIOC(PIOC(1))

[@gpt-jcommentbot4759]

@@aleksakocijasevic6613 Nope, PIOC(1) > PIOC(PIOC(1))

[@emmanuelfiorini2145]

"The biggest number you can think of +1."

[@MyNameIsSalo]

PIOC(PIOC(1)) completely breaks that though as that's a function thats greater than 1 greater of any number you suggest. Like if "a" was my variable for largest number possible then PIOC(a) = a + 1 POIC(POIC(a)) = PIOC(a+1) = a + 2 a + 1 < a + 2, therefore the recursive function is larger than the single function. You would have to add an arbitrary constraint that doesn't allow for it to be recursive, because otherwise I just proved 1 = 2 if the function holds true for all possible inputs.

[@aleksakocijasevic6613]

@@MyNameIsSalo Then I suggest (PIOC(a)/PIOC(a)) / (PIOC(a+1)/PIOC(a+1) - 1)

[@RogHhGH4_6yyuope]

Description had 5k characters so...

[@sargepent9815]

TIL a fundamental limit exists on the amount of information that can be stored in a given space: about 10^69 bits per square meter. Regardless of technological advancement, any attempt to condense information further will cause the storage medium to collapse into a black hole.

[@hellofranky99]

When you start using combinators for lamda calculas and turning it into binary, it might as well be a programing language that requires looking up definition outside of the text message itself.

[@NotSpaggety]

Whats the largest number? "9" All other numbers are combinations of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Therefore the highest number is 9.

[@acarbonbasedlifeform70]

You're confusing numbers and digits