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@sirpootsman1048 23 күн бұрын

90 is a pretty big number

@nerdstaunch 23 күн бұрын

Wait till you hear about 91

@Gabriel-nw6fc 23 күн бұрын

3 is already too big

@Jar.Headed 23 күн бұрын

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

@somnvm37 23 күн бұрын

@@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 23 күн бұрын

You got more likes so maybe no

@cynthiaclementine4757 22 күн бұрын

"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 22 күн бұрын

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

@atomictraveller 22 күн бұрын

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 22 күн бұрын

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 22 күн бұрын

Lambda calculus is an extremely natural way of representing general computation

@Kelly_Jane 22 күн бұрын

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

@seto007 22 күн бұрын

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

@liam.28 22 күн бұрын

it is significantly larger

@robocatssj3theofficial 22 күн бұрын

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

@MD.Akib_Al_Azad 22 күн бұрын

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

@shzguy 22 күн бұрын

Imagine when TREE(Melo's number) drops

@Vgamer311 22 күн бұрын

@@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…

@Xeare204 22 күн бұрын

<a href="#" class="seekto" data-time="370">6:10</a> >watching this on phone at low volume >"Invented by JonTron" >??????¿

@NutyRiver Күн бұрын

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

@Baddexample16 23 күн бұрын

I mean, it's gotta be at least 3

@herrbrudi5649 22 күн бұрын

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

@Zeero3846 22 күн бұрын

You think it might be bigger than 5?

@Baddexample16 22 күн бұрын

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

@-SquareBird- 22 күн бұрын

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

@kingofnumbers7660 22 күн бұрын

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

@soreg666alex 23 күн бұрын

Please don't make Lambda calculus into a game lol

@ymndoseijin 23 күн бұрын

it already is, check out the incredible proof machine

@dmytrog6127 23 күн бұрын

Please make.

@ChrisFloofyKitsune 23 күн бұрын

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

@higztv1166 23 күн бұрын

PLEASE DO

@ymndoseijin 22 күн бұрын

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

@MrCheeze 22 күн бұрын

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?"

@user-jz7vf5iq7h 22 күн бұрын

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 22 күн бұрын

absolutely right

@user-ir8er1bh4q 22 күн бұрын

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

@MrCheeze 22 күн бұрын

@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 22 күн бұрын

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

@orthoplex64 22 күн бұрын

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

@user-ce5sh5bd4f 20 күн бұрын

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

@iankrasnow5383 19 күн бұрын

@@user-ce5sh5bd4f 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 18 күн бұрын

Easy 0/1

@ctleans6326 16 күн бұрын

@@user-ce5sh5bd4f busy beavers are not computable because of halting problem. it's explained in the video though not mentioned

@georgerobinson1252 Күн бұрын

huuhuhuuhuhuhuh you said beaver

@a-love-supreme 23 күн бұрын

it's wild how infinite chess prepares you for this

@chaosflaws 22 күн бұрын

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

@JorgeLopez-qj8pu 22 күн бұрын

Oh, ♟ I read that as 🧀

@user-bs5ol7du2y 22 күн бұрын

@@JorgeLopez-qj8pu "after my uncountable hours of training with the infinite cheese, i am finally ready to comprehend the realms of near-infinity algarisms. LETS GOOOOOOO"

@markzambelli 21 күн бұрын

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

@henrysaid9470 21 күн бұрын

Bro I completely agree

@jblen 23 күн бұрын

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 22 күн бұрын

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

@jblen 22 күн бұрын

@@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 22 күн бұрын

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

@neoqueto 22 күн бұрын

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 22 күн бұрын

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

@daniel_77. 23 күн бұрын

"Whatever you say plus one 🤪"

@Patashu 23 күн бұрын

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 22 күн бұрын

2:59

@daniel_77. 22 күн бұрын

@@James_3000i lost 😔

@frankypappa 22 күн бұрын

@@James_3000+1 … i won

@crowreligion 22 күн бұрын

Than take tree(that number+10)

@Ivorforce 23 күн бұрын

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 22 күн бұрын

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

@DemonixTB 22 күн бұрын

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

@mambodog5322 22 күн бұрын

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 Күн бұрын

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)

@TrissTheFirst 23 күн бұрын

Didn’t know Jontron was into Lambda Diagrams

@Levi_OP 23 күн бұрын

Exactly what I heard haha

@nahkaimurrao4966 22 күн бұрын

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

@IdoN_Tlikethis 22 күн бұрын

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

@TurbopropPuppy 22 күн бұрын

nah JonTron is more into white supremacy

@xnossisx5950 23 күн бұрын

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

@UNOwenWasMe 22 күн бұрын

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 22 күн бұрын

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 22 күн бұрын

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 22 күн бұрын

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

@tonyvisente5286 23 күн бұрын

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 22 күн бұрын

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 21 күн бұрын

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.

@NunofYerbizness 23 күн бұрын

<a href="#" class="seekto" data-time="667">11:07</a> Oh, John _Tromp_

@MrQuantumInc 22 күн бұрын

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 22 күн бұрын

@@MrQuantumInccontroversial is putting it lightly

@pleaseenteraname1215 22 күн бұрын

@@pootis1699 what did he do?

@Periwinkleaccount 22 күн бұрын

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

@jhacklack 22 күн бұрын

@@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.

@Desmaad 23 күн бұрын

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

@vidal9747 22 күн бұрын

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 22 күн бұрын

Don’t forget Greenspun’s tenth law.

@robproductions2599 15 күн бұрын

is that a half life refurance

@Desmaad 15 күн бұрын

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

@felicitygray7811 22 күн бұрын

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 22 күн бұрын

What you said +∞

@emmanuelfiorini2145 20 күн бұрын

@@kazedcatInfinity isn't a number...

@emmanuelfiorini2145 20 күн бұрын

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

@kazedcat 20 күн бұрын

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

@kazedcat 20 күн бұрын

@@emmanuelfiorini2145 You can add things other than numbers.

@LuxurioMusic 22 күн бұрын

From 4D golf to code golf.

@halyoalex8942 22 күн бұрын

Lambda Golf.

@timbeaton5045 23 күн бұрын

"That's Numberwang!"

@WackoMcGoose 22 күн бұрын

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

@scifisyko 12 күн бұрын

That’s Wangernumb!

@Canosoup 9 күн бұрын

Das ist numberwang

@Boonehams 23 күн бұрын

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

@atomictraveller 22 күн бұрын

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

@rsyvbh 22 күн бұрын

@@atomictraveller well then it's 40

@balala7567 22 күн бұрын

24 plus 1

@Daisy_MayLemon-IceCubePenny 22 күн бұрын

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

@Daisy_MayLemon-IceCubePenny 22 күн бұрын

And by value, I mean mathematically, not artistically.

@kidredglow2060 19 күн бұрын

End of sponsored segment: <a href="#" class="seekto" data-time="65">1:05</a>

@4bad2u Күн бұрын

Thank you queen

@thecuspofcrust9444 23 күн бұрын

I've been waiting for you to get back to this kinda content. I love your work, devlogs and all, but this stuff takes the cake and makes me want to learn more

@matthewparker9276 23 күн бұрын

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 22 күн бұрын

Deceiving?

@ratewcropolix 22 күн бұрын

@@StefanReich minor spelling mistake

@migsy1 22 күн бұрын

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 22 күн бұрын

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

@adarshmohapatra5058 22 күн бұрын

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.

@minirop 23 күн бұрын

According to vsauce, the biggest number is 40.

@lucassoto3556 22 күн бұрын

33* 40 is not a number

@Brite-um2tq 22 күн бұрын

It's 1,320.

@noahthompson95 21 күн бұрын

40? Like how many cakes Lex Luthor stole?

@ryanvenjoyer 21 күн бұрын

For Cosmic Encounter cards, yes

@liam8370 20 күн бұрын

if u watched that video it's 1=0

@sevret313 16 күн бұрын

<a href="#" class="seekto" data-time="460">7:40</a>, 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 2 күн бұрын

Indeed

@alexterra2626 23 күн бұрын

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

@YT-AleX-1337 Күн бұрын

VSauce reference

@hkayakh 23 күн бұрын

According to Vsauce, 40 is the biggest number

@KingGreenscreenKid420 17 күн бұрын

sometimes you gotta think outside the box

@GuyPerson-jt9tv 23 күн бұрын

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

@marasmusine 21 күн бұрын

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

@SuperStingray 22 күн бұрын

I've seen a lot of videos on big numbers, but it was really cool to see how they can be encoded in smaller and smaller ways.

@nocturne6320 22 күн бұрын

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

@Amonimus 22 күн бұрын

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 22 күн бұрын

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.

@Brightgalrs 23 күн бұрын

Bignum Bakeoff?

@brikilian7834 22 күн бұрын

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 22 күн бұрын

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 22 күн бұрын

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.

@obiwanpez 19 күн бұрын

The thing about TREE(3) was that it was supposed to be the largest “functionally useful” bit of math, i.e. something that we could actually use to solve an actual applied problem. Does Buchholtz do the same, or is it still theoretical?

@YT-AleX-1337 Күн бұрын

Buchholz itself I doubt, but there's SCG that's used in math and it's a function that grows as fast as the Buchholz Ordinal under the Fast Growing Hierarchy (that f function at the end), but no function used in actual math is faster

@massimopavoni 22 күн бұрын

Just a thought exercise, but I really liked that this ended up being about lambda calculus, thanks

@charlotonne8980 23 күн бұрын

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

@TheOiseau 22 күн бұрын

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 22 күн бұрын

@@TheOiseau "ermmmm ackshullyyyyy 🤓"

@miggle2784 22 күн бұрын

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

@IllidanS4 23 күн бұрын

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

@MrRemi1802 21 күн бұрын

<a href="#" class="seekto" data-time="232">3:52</a> That old VSauce feeling...

@5thearth 22 күн бұрын

Reminds me of the Bignum Bakeoff, except that contest was (IIRC) limited to 512 bytes of C code, giving a bit more flexibility. The winner implemented a program that would generate every possible expression in the calculus of constructions (similar to lamda calculus) with less than (x) symbols, evaluate and concatenate their values, and then feed that number back into itself as (x) several times in a row. The trick is that the calculus of constructions isn't turing complete, but it is guaranteed to terminate, so it's immune to infinite loops. So the program overall will terminate... Eventually.

@smithwillnot 22 күн бұрын

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

@zhadoomzx 22 күн бұрын

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

@RandomAndgit 22 күн бұрын

Super interesting video. My only gripe is that I just made a video about Graham's number and TREE(3) and now they look tiny in comparison. In all seriousness though, this was absolutely fascinating.

@asmithgames5926 12 күн бұрын

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

@hunted4blood 23 күн бұрын

This was a really cool and different kind of video. Love it. Also, is the VR mode for 4D golf still planned? I've been really looking forward to subjecting my family to that.

@Spax_ 23 күн бұрын

in before codeparade makes an idle game with this principle

@Luigicat11 23 күн бұрын

Sounds like something out of an idle/clicker game.

@zebroidalWorld 23 күн бұрын

There already is one, Exponential idle

@Xnoob545 22 күн бұрын

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

@Spax_ 22 күн бұрын

interesting

@asherdp 22 күн бұрын

I was going to see a lambda calculus video for the first time in a year, what a coincedence!

@ImaginaryOne888 20 күн бұрын

At the end the biggest number that can be said as a type of constant is lim x->∞( x ) No matter which number type or function you present it couldn't possibly be bigger than THIS or else it will break the rules of mathematics Thankyou

@Henry3.1415 23 күн бұрын

This makes me want to learn lamda calculus

@anoukk_ 23 күн бұрын

my condolences

@homomorphichomosexual 22 күн бұрын

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 22 күн бұрын

Get that SICP in you baybeeee

@mightbetoad6786 20 күн бұрын

get well soon

@DergPH 11 күн бұрын

oof

@blightborne6850 22 күн бұрын

"What's the biggest number? [...] And I don't mean infinity" Proceeds to mention transinfinite ordinals later

@CodeParade 22 күн бұрын

Ordinals mentioned in the video are not themselves the numbers, but represent growth rates for functions. There is nothing infinite about them used in that way.

@MrQuantumInc 22 күн бұрын

@@CodeParade If the growth rate is infinite, then any input past 1 is going to be infinity, or transfinite.

@seamusfinnerty5897 22 күн бұрын

@@CodeParade nerd

@iizvullok 22 күн бұрын

@@MrQuantumInc That is not what he meant. Imagine comparing a linear to a quadratic function. Lets say we have f(x)=nx and g(x)=x^2. n can be any finite number here. It could be 10, it could be 10000 and it could be TREE(3). Picking a very large n would of course make the function grow quite rapidly while g would stay quite small in comparison for quite a while. However no matter how big n is, the quadratic function will always catch up eventually. In this case it is obvious that g(x) will be larger for x>n. For other functions those points may of course not be obvious. And here you can think of the quadratic function as the omega of the linear function. Because you no longer have to pick a ridiculously large n to make it grow fast and can instead just define x^2. Its much simpler and will still grow much much faster in the long run. And yet the quadratic function has nothing to do with infinity.

@TianYuanEX 22 күн бұрын

@@MrQuantumInc They explicitly don't have infinite growth rate as both demonstrated in the video as well mentioned in the comment above

@lumi2030 22 күн бұрын

i simply love this video. it explains everything that it should explain, and it presents a thought process which tries to avoid trivial solutions and lack of rigor. also there are 0 mistakes

@TannerJ07 22 күн бұрын

"The largest number possible using lambda calculus plus one"

@user-pc5ln1rc2p 22 күн бұрын

@Valgween 22 күн бұрын

@@user-pc5ln1rc2p yes multiplied by whatever you say + 1.

@FuriousMaximum 22 күн бұрын

<a href="#" class="seekto" data-time="677">11:17</a> THIS WAS YOU? Legendary W

@nuggets142 2 күн бұрын

surprised me too W

@v84l42 22 күн бұрын

Can't wait to see what game you make of this.

@rujon288 22 күн бұрын

There is no way you posted this after my 1 week lambda calc to combinatory logic rabbit hole 😂

@leictreon 16 күн бұрын

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

@nicks4727 22 күн бұрын

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

@aleksakocijasevic6613 22 күн бұрын

I suggest PIOC(PIOC(1))

@gpt-jcommentbot4759 21 күн бұрын

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

@emmanuelfiorini2145 20 күн бұрын

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

@MyNameIsSalo 19 күн бұрын

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 19 күн бұрын

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

@sophiegrey9576 22 күн бұрын

Mere days after I played Hyperbolica you show up on my feed again, nice

@TrimutiusToo 16 күн бұрын

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)

@moonsweater 22 күн бұрын

No mention of busy beavers?? Sad!

@CodeParade 22 күн бұрын

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 22 күн бұрын

@@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 22 күн бұрын

@@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 22 күн бұрын

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

@TianYuanEX 22 күн бұрын

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

@kjgoebel7098 22 күн бұрын

Casually brushes against Berry's Paradox.... Keeps walking....

@person0192 22 күн бұрын

This was super cool! I knew about omega as an infinite ordinal, but I had no idea you could go this bonkers with it! I def have some wikipedia rabbit holes that I need to traverse, might have to TSP a good path through them ;)

@JoniKauf 22 күн бұрын

Big Numbers from CODE PARADE?? This is gonna be great!

@SpencerTwiddy 23 күн бұрын

Love this!! Reminds me of those old Vsauce videos

@exile-5664 22 күн бұрын

No mention of the Loader's number?

@CodeParade 22 күн бұрын

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.

@M_1024 22 күн бұрын

Two of my favorite bits of math: Lambda Calculus, and limits of computation. Yay!

@redpepper74 22 күн бұрын

I fricking love this stuff, nerding out so hard over here 😂

@weakspirit_ 22 күн бұрын

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

@LifeIsACurse 22 күн бұрын

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 22 күн бұрын

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 22 күн бұрын

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

@rebeccachoice 22 күн бұрын

@@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 22 күн бұрын

@@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 22 күн бұрын

@@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.

@zihaoooi787 22 күн бұрын

very nice video! glad to see a video in the area of math i study in

@martinshoosterman 21 күн бұрын

Rayo’s number walks in, looks at this infinitesimally small value, can’t even see it, walks away.

@robproductions2599 15 күн бұрын

<a href="#" class="seekto" data-time="294">4:54</a> is that a half life refurance?

@waudoin 21 күн бұрын

Loader’s number, Busy Beaver function, Bachihu Matrix System, Pointer Matrix system and so on. These are all growing much faster than Buchholz Ordinal.

@john3260 19 күн бұрын

It's restricted to computable functions.

@iankrasnow5383 19 күн бұрын

Loader's number was the winner of a competition to see who can write the biggest computable number in 500 characters in C. Meaning it can't be expressed in 140*7 bits, or at least no one has figured out how to do it. So it doesn't count. Busy Beaver isn't computable and so also doesn't count. It's equivalent to saying "a largest computable integer expressible in N bits exists". This is true, but that doesn't tell you what those bits actually are.

@Anonymous-df8it 19 күн бұрын

@@iankrasnow5383 980 bits?

@Gamewizard13th 22 күн бұрын

I was thinking this is going to be a set of all infinities

@CMoore-Gaming 22 күн бұрын

Once, when I was a kid, I asked my dad what the largest number was, and he said "N1" I asked him what it meant, and he said it was always 1 higher than what you are thinking of. I thought it had some mathematical basis, which took me way too long to realize it is a pun. Since then, I've always used it as a short hand for the largest number because no matter your number, you can always add one.

@pasarebird02 22 күн бұрын

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

@Monkeylordz88 22 күн бұрын

Great video! Personally, I found the conclusion to be slightly unsatisfying, at least compared to what I was expecting. It seems to me that the answer is to find the biggest lambda calculus algorithm that can fit in n bits, however that doesn't really tell me anything about the algorithm or number itself. As a layman, I would appreciate a solution to this question from the perspective of the information density of lambda calculus. Certainly, higher order functions must take more bits to define, right? So, if we can find some sort of pattern to how the function sizes grow, I think it would provide a better resolution to this question as opposed to "hey, this function fits, good enough".

@heterodoxagnostic8070 17 күн бұрын

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

@Rudxain 19 күн бұрын

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

@mechadense 16 күн бұрын

<a href="#" class="seekto" data-time="360">6:00</a> Lambda Diagrams FTW!

@cipherxen2 22 күн бұрын

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

@Zen17h 20 күн бұрын

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

@r0260064 16 күн бұрын

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

@paridhaxholli 22 күн бұрын

Try finding out the last digit of pi next

@paridhaxholli 22 күн бұрын

@dontreadmyprofile Stupid bots😅

@tomkerruish2982 22 күн бұрын

<a href="#" class="seekto" data-time="657">10:57</a> 1729? That's a rather dull number.

@HUEHUEUHEPony 22 күн бұрын

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

@PunmasterSTP 22 күн бұрын

I saw the video title in my notifications. I saw the channel name. I knew this was gonna be incredible 👍 Also, the music gave me a strange but good type of vibe...

@Vallee152 22 күн бұрын

<a href="#" class="seekto" data-time="95">1:35</a> ASCII was made with 7 bits per character, so the 8th could be used for parody checks

@Lukepuke311 22 күн бұрын

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 22 күн бұрын

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

@Lukepuke311 22 күн бұрын

@@antonf.9278 oh

@youtubeuniversity3638 22 күн бұрын

<a href="#" class="seekto" data-time="378">6:18</a> Can we add a 3rd dimension?

@G.Aaron.Fisher 22 күн бұрын

It's crazy that once you get to fast enough growing functions, f and f composed with f are essentially the same. But there aren't good ways to portray what "essentially the same" means other than to compare large numbers and show that these sorts of operations don't change their places on the list. Where things get interesting for me is that all of these computable functions are bounded above by certain non-computable functions. This means that as wild as these functions get, it's possible to score their size using relatively small numbers. We could, for instance define a function called "Smooth Inverse Busy Beaver" or SIBB(f) that returned the smallest x such that a BB(x) ≥ f(h(x)) for some fixed function h(x). (Ignoring the difficulty of smoothly extending this from the integers to the reals. Ignoring how to best choose h(x), although we could choose h(x)=10 and be fine give or take some hand-waving). We can't compute SIBB, but it does have a value. If we had an oracle that gave us its values, we'd see all of the computable functions mentioned here mapped to some relatively small (

@Streetcleanergaming 19 күн бұрын

The answer is like the line from The Phantom Mencae (Its been used elsewhere first, but its where I first heard the phrase) "Theres always a bigger fish" you can always go higher. No matter what you try its always possible to add one even if it dosent make sence you can still in theory add one to make it bigger

@ghb323 22 күн бұрын

<a href="#" class="seekto" data-time="121">2:01</a> tetration

@hhhsp951 22 күн бұрын

Calling it now, it's gonna be Rayo's Go Numberphile

@Cypooos 22 күн бұрын

no, because Rayo's number is not computable.

@Galinaceo0 22 күн бұрын

@@Cypooos It's even worse than that, Rayo's number is not even well defined.

@BOLL7708 21 күн бұрын

Got the game in the sale, I'll wait for VR to actually play it though, looking forward to it 😁

@margon9181 17 күн бұрын

All of these get put to shame by large Busy Beaver outputs.

@ozzy_animations17 18 күн бұрын

watch me add one

@Inspirator_AG112 22 күн бұрын

*Ackermann function iterated one googolquadriplex times on the superfactorial of one googolquadriplex.*

@slamopfpnoobneverunsub5362 22 күн бұрын

Thats not even close to G(G(64)).

@Adomas_B 22 күн бұрын

I'd love if you continued to upload more content in the math edutainment category

@kantoros 22 күн бұрын

Omgomgomg codeparade video on the lambda calculus, i am in heaven

@haph2087 22 күн бұрын

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 22 күн бұрын

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

@haph2087 22 күн бұрын

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

@andrew-ud8pe 22 күн бұрын

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 21 күн бұрын

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

@irisinthedarkworld 20 күн бұрын

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