reminds me of Hitchhikers guide to the galaxy. The answer is easy yes it is finite the proof is very long.

I totally hate it!

I was so close last time I tried. Oh well, maybe this time I'll have better luck

That happened to me Tree(3) times already.

"I have discovered a truly marvelous proof of this, which this margin is too narrow to contain."

I was just thinking about trolling my friends with 1,3...

RBuckminsterFuller many answer 5 or 9 or 11 or 18 or 29 or 78 or 722 or even asceding so >3

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According to the Online Encyclopedia of Integer Sequences, 4 is an acceptable answer

In the sequence is infinite you can't finish it...

The test: tree(3) The finals: tree(tree (3))

TREE(Infinity)

@@playmaker4700 Isn't that just infinity anyway?

The Job Interview: Tree(Tree(Tree...(3)))))))))...

@@keafoleafo8368 yes, any size of infinity (say omega) put into TREE should return infinity. I don't know if it would return the same size of infinity or not though

You can assume it's prime for now since it doesn't have any known non trivial divisors :P

@@priyansh1210 That's a dangerous assumption ;)

wonder if its possible to calculate that probability

First try to prove that tree(3) is odd

The guy said the closest you can get to knowing anything abt the number is the number of signs needed to prove it s finite...

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fossilfighters101 "also my brain is too small to contain it"

What a shame we don't live in a quality universe that could fit tree(3)

Only acceptable place to actually use that excuse

A odgovor na prvo pitanje?

And in binary the first digit is 1.

Can you give us their alphabet here?

What a useful base that is

Subhransu Mohapatra not necessarily

Once comes around what do you feel, I love Jack woke up press and seal me big pain to Pono. (speech to text, Not what I meant but too funny to not post)

"The universe will eventually reset itself assuming that that will happen forever and that the universe is a perpetual machine, otherwise eventually everything will end forever and space time will cease to exist." What a happy thought to think about while you're alone in the house!

Looks like we had less time than we thought

Repetition legitimizes Repetition legitimizes

11 11 It’s impossible to prove or disprove that it will. We can only make more and more assumptions. Edit: or we can just accept one theory, which is fine, as none of us will ever live long enough to find out the validity of said theory.

PallyNut you right, you right

Yes!!

This needs more likes

tau rules, change my mind! also, this needs way more likes :)

NumberphileTREE(3) for SERIOUS insiders.

If you were to increase the universe's size by a googolplex factorial ^^^^^ a googolplex factorial-fold, then tried to fit TREE(3) cubic Planck lengths in there...you couldn't do it.

I reckon we'll need exactly a Graham's Number of universes to write down Tree (3), assuming one digit per Planck unit. Call it intuition.

No, you aren't anywhere close.

kcthewanderer I’ll go to Costco and buy one, be back in tree(3) minutes

jawad mansoor I’ll have to remember to order one next time the universe resets

What they teach you in class: 1 & 3 What they ask you in the exam: Tree3

😨😨😱😱😭😭😭😭

My brain just collapsed Tree(3) times

Im scared this like 11!!!!!!!!!!!!!!!!!!

@@SystemOfATool Class: 33 Exam: Tree(3)

so is every cardinal

@@SoloLevellor except my ego

Massimo Del Bianco depends on which infinity

It’s faster than a function of Epsilon sub script zero

Infinity divided by 3 would be closer to zero than infinity. Well, it would also be infinity. Wait, what?!

Brilliant. My sense of free will is now secure!

@@tb-cg6vd Brilliant to See your Comment, But there is another Video here

Brome to See your Comment, But there is another Video here

@@tb-cg6vd keep in mind, its a "sense" of free will. Not free will itself ;)

Actually , it is. We are just the bootloader.

And 1/TREE(3) is really small.

Yeaaa, the real deal still is Zero, the number which demolishes everything else.

well ..... -2 is smaller.

Félix Pinchon TREE( TREE(TREE(TREE(3))) )^0=1 too Wtf universe

ah so the zeroth root of 1 is TREE(3)! We found the solution boys!

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Az A Omg yes

You said that last recurrence...

+uvuvwevwevwe onyetenyevwe ugwemubwem ossas MY BRUDA

Az A hold on lemme go buy is a new one at ikea

A J Lol I scrolled down hoping someone else saw that haha

BoWeava They did the same on the poincare recurrence time vid

yes due to there only being a finite amount of states that the universe can be in. Even if some of the states are infinitely big.

CarBricksCity niiice, haven't seen that one

The thing I don’t quite get about poincare recurrence for the universe is that the recurrence theorem requires a sequence of sets that is bounded. For instance, gas molecules in a closed box is a bounded system and a sequence of states of those molecules within that box will repeat themselves according to the theorem. But the universe is expanded and therefore the system is unbounded so I’m not quite clear on why the Poincare recurrence theorem applies. To take the gas in a box analogy further, if the box is instead an inflating balloon and the balloon can inflate indefinitely then there is no guarantee the molecules will repeat states because they have paths available which can expand outward with their boundary. Similarly the particles in the universe can expand with the universe so it seems like there would be no guarantee their states would repeat (since part of their states includes their relative positions in an expanding spacetime.) I’m not saying the video is wrong, I’m just confused how this is resolved for an expanding boundary.

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I knooow!

Emilio Herrera "Lagniappe foliage"

(extra brown paper)

bruh lol

also log(3) ¬ 0.477121

clever

Lol. The question is how many LOG(3)s does a TREE(3) give? You will need multiple axes to figure that one out.

@@georgesmyrnis1742 Likely millions of axes, if not even more than that.

bivtyfrcygvubugwerdcfuvgibjhvibobhjhb! I can't take this!

Yebjic Yeah thats something i dont get about infinity too

Only in Riemann Zeta function. Watch Mathologer video for full explanation. The one done in response to Numberphile video on -1/12.

We do have the upper bound for TREE(3) It is clearly less than TREE(3)+1

@@vishalarya93 yes, welcome to the joke

same question

Maybe there's a way to prove whether it's odd or even.

Dan Kranda almost definitely not, every time you go up and find a prime while trying to divide to see if it's prime, you add that number to you're division pool. Since tree(3) is sooo big you have so.... Many primes to divide by its almost definitely not prime. plus half of all numbers are instantly taken out by dividing by two.

Well the frequency of primes is like 1/ln(x) so I'd give it a 1/ln(TREE(3)) chance of being prime... aka 0

Well TREE(1) and TREE(2) are prime so it isn't unthinkable, but I'm gonna go out on a LIMB and say that it would be tricky to definitively prove either way edit: before I get called out, I totally forgot 1 isn't prime, but I couldn't resist the pun

And you know what function is faster and larger than TREE ? Subcubic Graph and Busy Beaver 😂

scalpian your thing, to the power of TREE(TREE(TREE(3)))

ExponenTREEation!

Symbol juggling on meths.

Claudio Acsinte Exponentiation*

Balazs Lovenberg it sure does

Man that's an amazing comment , I wish I thought of it :)

You should also consider ROOT(n), because it grows slower than TREE(n) too.

Hard to tell but yes I think if we examine the growth the TREE function just edges it out.

I once heard of an infinite divergent sequence but later it got summed up to -1/12. You never know man. You. Never. Know...…...

"dis" in disaster refers to unluckiness, not disappearance.

Soumyadeep Bhattacherjee well to be fair this video already goes way beyond that by talking about diagonalized recursive trees

TREE(Gaham's number) is less than TREE(TREE(3))

@@abombata If we assume the function grows with the input, and never drops (easy to prove) then your statement follows naturally from knowing that g(64) < TREE(3), so TREE(n) will be larger for the larger input. And TREE(TREE(TREE(TREE(TREE(TREE(...TREE(3))))))) still doesn't match SSCG(3), even if you nest it TREE(3) layers deep.

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TREE(n) is always going to be closer to TREE(n-1) than TREE(n+1) in terms of absolute size. considering TREE(4) is just TREE(3) + an extra seed , you could just write out TREE(3) and then repeat entire structures only changing the color of one seed, effectively nearly doubling the size. And that's just changing the color of the seeds using 3-seed structures already constructed, not counting all the entirely new trees you could make using all 4-seeds

Scot Brown TREE (3) is way closer to -TREE (3) than to TREE (4)

HopUpOutDaBed Why nearly doubling? I think, without consider the 4-colour trees, you'd already get 4(TREE(3)). Using RGBW, you could do a TREE(3) with RGB, RGW, RBW, and GBW each.

+HopUpOutDaBed - I like the way you think, that's a very elegant proof!

Probably my favorite part about 2017 was this comment because I just imagine a world of tiny scientists talking about numbers perpetually in the multiverse somewhere and that keeps me optimistic about life. I also would love to see what would happen if someone figured it out and the news spread across the trillions of tiny scientists like a wave of celebration as the universe rejoiced in finding the answer. Would it cease to exist since it's purpose would be fulfilled? Would the scientists find another problem to work on? Perhaps they would colonize different universes or even just their own ones and delegate the lesser scientists to act as the land masses. Neat.

yeah they not gonna get nowhere

Won't work either

@@axelpeneau2288 Yep.. Anything we can (reasonably) write as x*10^y notation won't even begin to tickle the things that require the double up-arrow notation, no matter how big y gets.

Where would they add the symbol?

no need to repeat, we can see itno need to repeat, we can see it

@@aasyjepale5210 haha, haha.

But you're still not even close. lol

I would name a band 6EQUJ5 and pronounce it "The WOW Signal" lol

I'm smart guy math what's the point I understand to try understand Googleplex the numbers so unimaginable at its but so what's the point Graham the numbers so unimaginable what's the poin going beyond t 😂😂

​@@IsaacHarvison-mt5xtwhat

I know a true believer like you would watch, but if you post a 19-minute video to UKposts you may as well hang a big sign on it saying "DON'T WATCH THIS" Better to post a video on the essentials, then a second video for people who want to go deep?

Numberphile2 why not a 3rd? Or maybe 4th! I surely won't mind :)

Numberphile tree (3)

You could have at least posted the pre-emptive TREE(TREE(3))

Thanks for mentioning the bell. Was wondering why I wasn't being notified. That said, what's the point of a subscription if not to notify you of new videos?

fire eye exact words from Fermat if he is still alive today

lol

You have a weird concept of "discovering" something that categorically cannot be contained by your brain.

I agree :)

I've been waiting for it since the original graham's number video. When that video was uploaded i was hooked into big numbers and started checking all kinds of different bigger than graham's number numbers. Soon I met the king of them all tree(3) and have been waiting since for numberphile to do a video about it. I wonder if there are any bigger numbers that have been used in math (so obviously not arbitrary ones like tree(3) * 2)

hey ash

could you say you've been waiting for this number since over T(3) years?

@frizider2 look up SSCG(3), or even worse SCG(3).

SCG(13)

Markovisch He could, but he doesn't bother doing it.

At least he tried XD

It would be like a kid estimating the number of stars in the night sky. "How many stars do you think there are?" "Ten."

His answer would be a Parker Tree.

PARKER(3)=10

Big FOOT

Utter Oblivion is bigger. Although I suppose you could just mention Cantor's idea of absolute infinity to end any big number discussion there and then.

Zaephou what would be far more interesting would be like if you found another number that was like less than TREE(3) orders of magnitude from TREE(3), like if it was actually coincidentally closeish

Did you study maths

2^^1000 isn't tree3, that's the number of symbols it would take to write down a perfect proof that tree3 is finite

I had the same thought! That would be quite enjoyable

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Lauraphoid hah would be pretty cute

Skippy the Magnificent and in base TREE(3) the first digit is also a 1

Wow. Just now I realized that first digit of every number in binary is 1. Like this is obvious but I never thought about it, thus only now I realized it.

@@coolguy4989 underrated comment

@@eliorahg explain 2

@@lunox8417 2 is "10" in binary.

That is really interesting to think off, just like a logarithmic scale we need one for googological numbers like Graham's number and TREE(3) to visualize just how much bigger these numbers are!

Given that the TREE() function has a similar kind of rule set to the permutations of those objects (I am not a mathematician, mathematicians would probably strike me down for saying such a thing), then given that analogy they would probably do something similar in a way as each TREE(n) theoretically would 'contain' the lower TREE() sets within them plus all of the possible permutations of those sets with that extra seed color. I wonder if this has anything to do with Group theory as I just realized I'm starting to pose a similar sort of question...

Sounds like you're asking if TREE is monotonic

given that I'm pretty sure the answer to that was someones dissertation, I'm not sure it would comfortably fit into a youtube video, lol

Zejgar is that a factorial?

Might as well be, the cheeky fucker.

Can't see one for the other though

would have, but didn't see the FOREST for the TREEs...

😂😂

The universe must of reset 3 times before you thought of that

Jorge C. M. I prepared to be mind blown... But I wasn’t... Because I have no idea what that means.

Omg I love math jokes.

What's sigma? I understand it means "a portion of" but what's the textbook word for that function?

tdurran That's something to think about.

And almost every positive integer is bigger than tree(3)

Woah yeah ... wow

a stupidly mindblowingly correct statement

Darn you for exploding my head

Shouldn't that be a computerphile video. n-state turing machines.

It's already on the Computerphile, and prof. Brailsford videos are one of the best ones there.

I'd love to see a proof that TREE(n) is a computable function. I'm not sure about that and I haven't seen a proof - although I've seen it being mentioned that it is computable several times.

@@isuller A function is computable if there is an algorithm that can (given enough time) compute it. The simplest proof that the Tree-function is computable would be an implementation of that algorithm - it doesn't even need to be very efficient. We can even do it a normal programming language. The naive algorithm that requires the least imagination would be to do an exhaustive search of all possible forests for the given n and return the number of trees in the largest legal forest. The trickiest part would probably be to do the test for inf-embedding - but still conceptually doable. Feel free to reply if there are any questions! :)

Just a note but this actually happened and he spoke about them in the video regarding Rayo's Number.

John Thimakis It happens when they change something.....

That was the universe resetting itself

Wait a glitch in the matrix? glitch in the matrix?

Was it the same gesture or different gesture?

If the universe did reset itself, how would we know?

...TREE(TREE(TREE(Grahams number)))... Until TREE(Grahams number) amount of TREE functions put into ...TREE(TREE(TREE(Grahams number)))... amount of TREE functions ...TREE(TREE(TREE(Grahams number)))... times

In fact proportionally, EVERY number is bigger

@@Amethyst_Friend Yes. If you select a random positive finite integer (yes, the concept of a "random integer" is problematic, but you know what I mean!), the probability of that integer being smaller than any defined integer (Rayo's number, whatever) is 0.

Steve's Mathy Stuff well, it is not necessarily green, it could be black, or red, or maybe blue, or even purple

I think we can just get away with assuming, without loss of generality, that it is green.