Don't you hate when you're trying to prove how big TREE(3) is with finite arithmetic, but then the universe resets itself.

@ruben307

6 жыл бұрын

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

@0menge

6 жыл бұрын

I totally hate it!

@guillaumelagueyte1019

6 жыл бұрын

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

@mrJety89

6 жыл бұрын

That happened to me Tree(3) times already.

@DaniErik

6 жыл бұрын

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

"This IQ test stumps most mathematicians! Finish the sequence 1, 3, ..."

@vampyricon7026

6 жыл бұрын

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

@whatisthis2809

6 жыл бұрын

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

@fossilfighters101

6 жыл бұрын

+

@ghyrt1

6 жыл бұрын

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

@pieffe8

6 жыл бұрын

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

Well now I want to know if TREE(3) is prime

@priyansh1210

4 жыл бұрын

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

@HerrKeuner1948

4 жыл бұрын

@@priyansh1210 That's a dangerous assumption ;)

@nothisispatrick6832

4 жыл бұрын

wonder if its possible to calculate that probability

@number_8903

3 жыл бұрын

First try to prove that tree(3) is odd

@chebichevinovichskic

3 жыл бұрын

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...

If numberphile has Pi as their picture.. Numberphile2 should have Tau as their picture.

@CaseyShontz

5 жыл бұрын

PallyNut you right, you right

@alephnull4044

5 жыл бұрын

Yes!!

@arvasukulkarni3686

5 жыл бұрын

This needs more likes

@leondost3575

4 жыл бұрын

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

@qiki_info

4 жыл бұрын

NumberphileTREE(3) for SERIOUS insiders.

"I've discovered a remarkable proof of Tree(3) theorem but the universe is too small to contain it"

@fossilfighters101

6 жыл бұрын

+

@fibbooo1123

6 жыл бұрын

+

@romajimamulo

6 жыл бұрын

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

@me_too_thanks5062

6 жыл бұрын

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

@ashkara8652

6 жыл бұрын

Only acceptable place to actually use that excuse

In base TREE(3) it is 10.

@zoranhacker

6 жыл бұрын

A odgovor na prvo pitanje?

@subhransu75

6 жыл бұрын

And in binary the first digit is 1.

@vp_arth

6 жыл бұрын

Can you give us their alphabet here?

@joonatanlinkola9059

6 жыл бұрын

What a useful base that is

@DuskKaiser

6 жыл бұрын

Subhransu Mohapatra not necessarily

That TREE(3) will be great for getting LOG(3)s!

@harryw4802

3 жыл бұрын

bruh lol

@harryw4802

3 жыл бұрын

also log(3) ¬ 0.477121

@moodleblitz

3 жыл бұрын

clever

@georgesmyrnis1742

2 ай бұрын

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

@avi8aviate

2 ай бұрын

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

And still, TREE(3) Is closer to 0 than infinity.

@caduaraujo331

4 жыл бұрын

so is every cardinal

@Bogdanko93

4 жыл бұрын

@@SoloLevellor except my ego

@siddhantnagrath8144

4 жыл бұрын

Massimo Del Bianco depends on which infinity

@siddhantnagrath8144

4 жыл бұрын

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

@Shadowwolf-1337

4 жыл бұрын

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

We're gonna need a bigger universe.

@user-ft4pb5vb3e

6 жыл бұрын

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.

@ongbonga9025

6 жыл бұрын

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.

@MikeRosoftJH

5 жыл бұрын

No, you aren't anywhere close.

@CaseyShontz

5 жыл бұрын

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

@justsayapple1381

5 жыл бұрын

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

"The universe will eventually reset itself." "The universe will eventually reset itself."

@myownmeadow1320

4 жыл бұрын

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)

@bigbluetrex__8475

4 жыл бұрын

"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!

@mathmachine4266

4 жыл бұрын

Looks like we had less time than we thought

@HimanXK

4 жыл бұрын

Repetition legitimizes Repetition legitimizes

@uncoolloser6233

3 жыл бұрын

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.

The class: Tree(1) The homework: Tree(2) The exam: Tree(3)

@Aerialyn

3 жыл бұрын

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

@playmaker4700

3 жыл бұрын

TREE(Infinity)

@keafoleafo8368

3 жыл бұрын

@@playmaker4700 Isn't that just infinity anyway?

@tinybro5630

3 жыл бұрын

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

@tlep2979

3 жыл бұрын

@@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

Well, at least we know that the entire universe is not just a simulation being run to calculate TREE(3) then.

@tb-cg6vd

4 жыл бұрын

Brilliant. My sense of free will is now secure!

@SledgerFromTDS.

2 жыл бұрын

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

@SledgerFromTDS.

2 жыл бұрын

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

@albert6157

Жыл бұрын

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

@izayus11

Жыл бұрын

Actually , it is. We are just the bootloader.

But is it prime?

@vampyricon7026

6 жыл бұрын

same question

@guillaumelagueyte1019

6 жыл бұрын

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

@connorking984

6 жыл бұрын

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.

@sage5296

6 жыл бұрын

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

@michaeljupille1076

6 жыл бұрын

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

What they teach you in class: Tree(3) What they ask you in the exam: Tree(Tree3)

@SystemOfATool

4 жыл бұрын

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

@sirdonki8085

4 жыл бұрын

😨😨😱😱😭😭😭😭

@MrTheKamir

4 жыл бұрын

My brain just collapsed Tree(3) times

@barsozuguler4744

4 жыл бұрын

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

@pbj4184

3 жыл бұрын

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

"So it's never been done before?" "Whoa-whoa-whoa-whoa there guy. Just hold your horses. The question is CAN it be done?" LOL

1,3, Visible universe collapses into a singularity

"The universe is too small to contain it." I'll use this excuse next time I haven't done a due essay.

Don't you hate it when you're doing proof for your maths homework and the universe just resets itself....

@tangyspy

6 жыл бұрын

+

@FoxyBoxery

6 жыл бұрын

Az A Omg yes

@andrewxc1335

6 жыл бұрын

You said that last recurrence...

@himylongusernameislongbeca7203

5 жыл бұрын

+uvuvwevwevwe onyetenyevwe ugwemubwem ossas MY BRUDA

@CaseyShontz

5 жыл бұрын

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

"Exponentiation on steroids" Best description of Arrow notation I ever heard.

When he wrote Tree (Tree(3)) I got anxious because I thought the universe was going to crash.

It gives me a new appreciation of infinity.

@qiki_info

4 жыл бұрын

But you're still not even close. lol

You know what's even crazier? TREE(3)^0 = 1

@criskity

6 жыл бұрын

And 1/TREE(3) is really small.

@djhokage1

6 жыл бұрын

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

@jackreacher6240

6 жыл бұрын

well ..... -2 is smaller.

@petritdauti6258

6 жыл бұрын

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

@skeletonrowdie1768

5 жыл бұрын

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

I came across TREE (3) yesterday when I was watching an online documentary and it both blew my mind and excited me immensely. I'm not a mathematician, I'm a musician, but this is just so awesome. I love this guy's brains and enthusiasm. Anyway, we were looking for a name for our new band - so calling it TREE (3). I hope no-one else has that name, but I love this so much. Thanks! :)

@masonicmoth

Жыл бұрын

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

@IsaacHarvison-mt5xt

7 ай бұрын

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 😂😂

@bizw

6 ай бұрын

​@@IsaacHarvison-mt5xtwhat

When he started nesting the Tree()’s, my nethers clenched fearing the universe might rend.

Totally dissapointed, this video should’ve been called “(extra foliage)”

@fossilfighters101

6 жыл бұрын

+

@shakesmctremens178

6 жыл бұрын

I knooow!

@Antimimesis

6 жыл бұрын

Emilio Herrera "Lagniappe foliage"

@andrew7taylor

5 жыл бұрын

(extra brown paper)

Is TREE(3) closer to TREE(2) or TREE(4)? Do we know anything about the growth characteristics of the TREE() function?

@vampyricon7026

6 жыл бұрын

+

@HopUpOutDaBed

6 жыл бұрын

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

@norielsylvire4097

6 жыл бұрын

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

@vampyricon7026

6 жыл бұрын

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.

@Nixitur

6 жыл бұрын

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

I love how happy he was at the end describing his joy over this type of math.

2:31 "you might remember what this arrow notation is... exponentiation on steroids" lol

Surely TREE(n) grows faster than LOG(n)

@romajimamulo

6 жыл бұрын

Balazs Lovenberg it sure does

@ImMataza

6 жыл бұрын

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

@chimkelvin5705

6 жыл бұрын

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

@GlobalWarmingSkeptic

6 жыл бұрын

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

@suyashshandilya9891

5 жыл бұрын

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

the universe will eventually reset itself, the universe will eventually reset itself. hah! well played

@BoWeava

6 жыл бұрын

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

@carbrickscity

6 жыл бұрын

BoWeava They did the same on the poincare recurrence time vid

@livedandletdie

6 жыл бұрын

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.

@BoWeava

6 жыл бұрын

CarBricksCity niiice, haven't seen that one

@Bodyknock

6 жыл бұрын

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.

Thanks to this channel I have fallen in love with math and I am really considering studying maths!

@walexander8378

6 ай бұрын

Did you study maths

Oh, the universe reset itself again. Man, I hate it when that happens.

@aasyjepale5210

4 жыл бұрын

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

@Anklejbiter

4 жыл бұрын

@@aasyjepale5210 haha, haha.

"Exponantiation on steroids"

@Anaklusmos42

6 жыл бұрын

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

@andymcl92

6 жыл бұрын

ExponenTREEation!

@y__h

6 жыл бұрын

Symbol juggling on meths.

@JorgetePanete

6 жыл бұрын

Claudio Acsinte Exponentiation*

This should've been included in the original video!

@numberphile2

6 жыл бұрын

I know a true believer like you would watch, but if you post a 19-minute video to KZread 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?

@N0Xa880iUL

6 жыл бұрын

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

@franklinruan3807

6 жыл бұрын

Numberphile tree (3)

@vampyricon7026

6 жыл бұрын

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

@Tahgtahv

6 жыл бұрын

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?

And 2yrs later, TREE(Graham's number) has been discussed That escalated quickly

@redvine1105

4 жыл бұрын

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

@abombata

4 жыл бұрын

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

@isaacwebb7918

4 жыл бұрын

@@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) And TREE(TREE(TREE(TREE(TREE(TREE(...TREE(3))))))) still doesn't match SSCG(3), even if you nest it TREE(3) layers deep.

They used the same editing joke about the poincare repeat conjecture twice! They used the same editing joke about the poincare repeat conjecture twice!

Well, TREE(3) is clearly smaller than the sum of all natural numbers, therefore, an the upper bound of TREE(3) is -1/12

@migfrarummet1907

6 жыл бұрын

bivtyfrcygvubugwerdcfuvgibjhvibobhjhb! I can't take this!

@petritdauti6258

6 жыл бұрын

Yebjic Yeah thats something i dont get about infinity too

@jannegrey593

5 жыл бұрын

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

@maxhaibara8828

5 жыл бұрын

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

@whatno5090

5 жыл бұрын

@@vishalarya93 yes, welcome to the joke

What if you filled the universe with mathematicians the size of a plank length and then they split up the work?

@mattsmith457

6 жыл бұрын

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.

@jaysephisdeadpool8813

5 жыл бұрын

yeah they not gonna get nowhere

@axelpeneau2288

4 жыл бұрын

Won't work either

@altrag

4 жыл бұрын

@@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.

@rodwayworkor9202

4 жыл бұрын

Where would they add the symbol?

Love the universe resetting itself editing joke

Spongebob: you know what’s -bigger- than tree(3)? Patrick: what? Spongebob: Tree(4)

@thunderstrom878

2 жыл бұрын

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

And This is why mathematicians have more fun :) They're just not bounded by the physical reality :)

@Life_42

Жыл бұрын

I agree :)

10:30 There's one contender to the TREE function that can absolutely batter it - SCG (Simple Subcubic Graphs). The problem is that I can't even begin to understand how and why that number is so big, so I guess my video request would be one on SCG.

@kannarzoltan7006

6 жыл бұрын

Big FOOT

@zaephou2843

6 жыл бұрын

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.

@sage5296

6 жыл бұрын

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

Love the excitement of Tony while educating here, these massive numbers are just jaw-dropping from the explanation alone.

How about TREE(TREE(3))? EDIT: damit, already done in video

Matt Parker should estimate TREE(3)

@kannarzoltan7006

6 жыл бұрын

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

@vampyricon7026

6 жыл бұрын

At least he tried XD

@skepticmoderate5790

6 жыл бұрын

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

@TheGeneralThings

6 жыл бұрын

His answer would be a Parker Tree.

@vampyricon7026

6 жыл бұрын

PARKER(3)=10

I have discovered a truly remarkable proof that tree(3) is finite, which this universe is too small to contain...

@Craccpot

6 жыл бұрын

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

@theviniso

6 жыл бұрын

lol

@NoobOfLore

5 жыл бұрын

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

I watched both these videos, but I'm still curious HOW they know it's such a huge number.

@SomeGuy-ty7kr

2 жыл бұрын

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

"The universe resets itself - This is a disaster." Literally that is what disaster means, the disappearance of stars.

@MitruMesre

3 жыл бұрын

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

Have been waiting for this number since over a year

@frizider2

6 жыл бұрын

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)

@ABc-sv8mv

6 жыл бұрын

hey ash

@amiss8828

6 жыл бұрын

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

@Sakkura1

6 жыл бұрын

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

@carbrickscity

6 жыл бұрын

SCG(13)

I'm curious if the size of Tree(n) increases with any kind of regularity as n gets larger. Like if you had an ungodly Cartesian graph where x = n and y = Tree(n), would there be some sort of recognizable pattern in, say, the first 100 y-values? Or does something crazy happen like Tree(57) isn't as large as it "should" be based on all the previous Trees? I really want to know more about the growth of the Tree function. I don't really know how much progress has been made (or can be made) in analyzing it this way. After all, Tree(3) doesn't have an upper bound (aside from definitely being finite).

@geelzwarteaardbij

3 жыл бұрын

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!

@efulmer8675

3 жыл бұрын

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...

@antonhengst8667

2 жыл бұрын

Sounds like you're asking if TREE is monotonic

I wasn’t paying too much attention bc this was background noise to me kinda, but if TREE(3) is 2^^1000, the last digit is a 6. Assuming I’m doing this correctly, 2^^1000 = 4*2^^999 = 16*2^^998, etc. since 16 ends in a “6”, and any number ending with a “6” squared results in a number ending in a ”6”, BOOM! You have one of the digits you need. Progress has been made.

@TheSmegPod

2 жыл бұрын

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

Absolutely love this topic. I’ve watch this episode about x20 times over the last year and I smile every time. Great work guys

I expected you to use FOREST(n,m) instead of TREEm(n)!

@norielsylvire4097

6 жыл бұрын

Zejgar is that a factorial?

@felipe970421

6 жыл бұрын

Might as well be, the cheeky fucker.

@mellowfellow6816

6 жыл бұрын

Can't see one for the other though

@judychurley6623

6 жыл бұрын

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

I know that the first digit of Tree(3) is 1 in binary

@coolguy4989

6 жыл бұрын

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

@eliorahg

4 жыл бұрын

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.

@user-me7hx8zf9y

4 жыл бұрын

@@coolguy4989 underrated comment

@lunox8417

4 жыл бұрын

@@eliorahg explain 2

@PattyManatty

4 жыл бұрын

@@lunox8417 2 is "10" in binary.

You touched on the thing that fascinates me the most. Staying strictly with finite numbers, it's still the case that, no matter how you define a large number - TREE, iterated TREE, busy beaver, whatever, almost every number is larger than the number you've defined. Thinking of that fills me with wonder.

@Amethyst_Friend

2 жыл бұрын

In fact proportionally, EVERY number is bigger

@TIO540S1

2 жыл бұрын

@@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.

7:40 I'm surprised the paper didn't implode into a black hole destroying the entire universe from what you just wrote on it 😂😂

Shouldve gotten Prof Moriarty to do it so he can say "Tree Tree" over and over again.

@Lauraphoid

6 жыл бұрын

I had the same thought! That would be quite enjoyable

@vampyricon7026

6 жыл бұрын

+

@lovrebabajko

6 жыл бұрын

+

@Froggeh92

6 жыл бұрын

Lauraphoid hah would be pretty cute

FYI: It's spelled KRUSKAL'S if you're interested in looking into it.

The universe reset itself: an overflow error probably occured.

I got a bit lost after "tree"

4:23 There was a glitch in the matrix.

@davecrupel2817

6 жыл бұрын

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

@namewarvergeben

6 жыл бұрын

That was the universe resetting itself

@sage5296

6 жыл бұрын

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

@gorillaau

6 жыл бұрын

Was it the same gesture or different gesture?

@RolandHutchinson

5 жыл бұрын

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

4:22 "the universe will eventually reset itself" "reset itself"

If you take tree(3) and substract 10% of it, and add all the numbers together, and then add all the numbers together, and so on as long as it will be just one number I bet this number is 9. 😊

"Universe resets before you can complete the proof" Awww....There goes my plans for the weekend..

When he started trying to top TREE(3), I almost had a panic attack.

Dr Tony Padilla, I would love if you talked about busy beavers! I mean, Tree(3) is big alright, but it's still a computable function. Big fan of your videos, really love your enthusiasm!

@livedandletdie

6 жыл бұрын

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

@synchronos1

6 жыл бұрын

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

@isuller

5 жыл бұрын

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.

@FreeAsInFreeBeer

5 жыл бұрын

@@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! :)

@iainh

Жыл бұрын

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

Mathematics really feel like magic. By playing a simple game on a piece of paper, you can actually write a concept that is bigger than existence itself. This is mindblowingly elegant.

I love how the extra footage is longer than the original video

I literally hear GNASHING OF BOLTS HOLDING EDGES OF THE UNIVERSE when he started making TREE of TREEs

I love how excited these guys get about this stuff!! Very interesting

These numbers just embarrass the size of space-time.

Sometimes I get the unexplainable nervousness when they write down things like TREE(TREE(3)) as if the universe is gonna explode simply by some sentient being conceiving those numbers.

"...how quasi is your ordering?" .."It's well quasi mate"

What's the most number of nodes in any tree in TREE(3)?

@connorrcompton

6 жыл бұрын

Sarthak Bansal TREE(3) means three types of nodes. Not nodes in general.

@adamweishaupt3733

6 жыл бұрын

Sarthak no it's 3 colors of nodes, the nth tree can have n nodes, but they can only contain 3 colors.

@OctagonalSquare

6 жыл бұрын

It would be 1. As with TREE(1) and TREE(2) you only use one of the single seed options until the very end. Once you have no options that don't include a previous tree, then you use your single seed options. If you use them at any point before the last two, then they will appear in other trees immediately, thereby ending the game prematurely.

@livedandletdie

6 жыл бұрын

Octagonalsquare that was not the question though, his question was as followed. What is the global maximum f(x) on the curve that is the curve of nodes pertaining to each iteration of x in the well defined function TREE(n) when n does equal 3. Now as far as I'm concerned the upper bound to that question is TREE(3)^(1/3)

@limbridk

6 жыл бұрын

That is the last tree Octagonalsquare, not the largest tree.

I love how excited he is! You can see he just loves math

TREE(Graham's number) did I break the internet?

@ses694

4 жыл бұрын

...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

And yet it's true to say, almost every integer contains tree(3)

@AndrewHSW

6 жыл бұрын

tdurran That's something to think about.

@oz_jones

6 жыл бұрын

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

@sage5296

6 жыл бұрын

Woah yeah ... wow

@AnCoSt1

5 жыл бұрын

a stupidly mindblowingly correct statement

@austinbryan6759

4 жыл бұрын

Darn you for exploding my head

My mind is not abstract enough for this. I kind of get it when he explains it but I’m like “but how do they *know*?

I just wanted to find out how big TREE(3) is, not have an actual existential crisis about the universe resetting itself.

It is a tradition for me to come back to Graham's number and TREE(3) every once couple of years.

What if you could prove tree(3) was prime...

@DiamondSane

6 жыл бұрын

Call them when you have supersublinear algorithm.

@ydg7670

5 жыл бұрын

2^(13*TREE(3))-1=Big number, could be a prime. Maybe not.

@Double-Negative

4 жыл бұрын

@@ydg7670 100% not. There's a proof it's not.

I'm going to say it... be prepared... because: We gave birth to the tree function, we chopped it down to the log function, and it was so naturally done (ln) that 'i' celebrated it with ∑ π.

@Philip_J

5 жыл бұрын

😂😂

@ilikeunderratedgachatubers7194

5 жыл бұрын

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

@CaseyShontz

5 жыл бұрын

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

@Dexuz

5 жыл бұрын

Omg I love math jokes.

@maxonmendel5757

5 жыл бұрын

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

His neck tendon pops out while he talks. These guys are so beautifully passionate.

This guy's enthusiasm is contagious!

i think the awesome part of Tree(3) and some other large numbers is that they were not discovered with the intention of finding a large number. im not a part of it but in the Googology fandom there's all these efforts to create simple mathematical situations that give large numbers, but i just like to imagine that, when studying these trees, someone just accidentally stumbled upon Tree(3). its not even close to being as large as Tree(3) but the Monster Group is one of these; a fundamental building block of groups with just completely unexpected size and connection to modular forms

New excuse for not sound homework: "there's not enough entropy in the universe to contain my homework"

Man, I love this guy! Big up Tony!

This is one of the few KZread videos that I watch over and over again. I'm iterated.

When he says the universe resets itself, the running frame in the video resets itself. Funny trick! :D

I like the enthusiasm, but I feel like I'm missing a bit more depth on the explanations. Just saying "it's really, really, really big" does not really explain how can you know that. For instance, I believe you when you say that TREE(3) > 2 ↑↑1000, because I don't think you are making this up. But how do I, the viewer, can understand the methods used to prove such claims? Maybe with some insights on these kind of questions we can share more of the amazement that this quantities brought to you...

@matthiasp3225

6 жыл бұрын

It's the poof that TREE(3) is finite using only finite arithmetic, that needs at least 2 ↑↑1000 symbols. I suppose if there is a way to explain why to a non mathematician it would need as much genius and effort as coming up with the more abstract and technical explanation that you can find online, but yes they could try it! It's the same with Grahams Number, Numberphile didn't accomplish to tell why it is an upper bound for the respective problem.

@eyvindjr

6 жыл бұрын

I tried, there is a lengthy video series on youtube about E, diagonalisation and fast-growing-functions, how it dwarfs Graham's numger, ending up in explaining Tree(3), but I was not even close to being able to finish it. It is very heavy and advanced stuff!

@abcdefzhij

6 жыл бұрын

He wasn't saying that TREE(3) is greater than 2^^ 1000, lol. He was saying something much more profound that went over your head about the size of TREE(3).

@mrnarason

5 жыл бұрын

xnick go read up some graph theory then

@mattdombrowski8435

5 жыл бұрын

All of these papers that they use are publicly available (to varying degrees of paywall, however). You can satisfy your curiosity with those, although understanding them be difficult

Tree (tree (3)) makes my heart heavy

Bravo on the cliffhanger from the first video to the second

I think it's beautiful that such ridiculous ideas come out of graph theory, given its simple axioms. I feel like I should get this experience from every field of math at some point..?

What about REDWOOD(TREE(3))?

@sage5296

6 жыл бұрын

BLUEWOOD(TREE(3))

Djinn : "what do you wish for?" Alladin : "using finite arithmetic prove that TREE(3) is finite." ...and this is how Djinns got extinct!

Elementary School math class teachers be like: "Solve Tree(3). And show your work."

I think another really cool sequence that seems to be ridiculous is: 1, infinity, 5, 6, 3, 3, 3, 3, ... I really wonder how quickly Tony and the others of Numberphile would figure out what it represents (I only know because we talked about these numbers in some class).

@DavenH

5 ай бұрын

# of Platonic solids (regular polyhedra) in n-space. For your curiosity it took a couple of minutes testing obvious things, then noticed the 5 -> 6 -> 3 which is an unnatural-looking inflection and I recalled that this sequence peaks at 6 in 4D.

@DavenH

5 ай бұрын

Although you can readily get a sequence that looks weird like that: round((3*x - 1)/(x - 1) + 3^(x-2)/((x-2)^3)!), for whole number x, => [1, infinity, 5, 6, 3, 3, 3...]. There are probably simpler generating functions but I'm lazy.

Just mesmerizing to know that a game involving 3 seeds can exhaust the universe. All that happens during the day, how small you feel you are in the city, how magnificent or insignificant you find yourself, how much crazy thoughts you run through every second, how the existence of all creations of human non human, are not even holding a candle to a small game whose rule can be explained in 3 minutes

I love the quick reset of "The universe resets itself." Well played!

Yes, this is how I explain that some things truly are impossible: when there isn't enough energy in the observable universe to do the thing, even if you used it all, with no losses, and did it as perfectly as it could be.