"This IQ test stumps most mathematicians! Finish the sequence 1, 3, ..."
@vampyricon70267 жыл бұрын
I was just thinking about trolling my friends with 1,3...
@whatisthis28097 жыл бұрын
RBuckminsterFuller many answer 5 or 9 or 11 or 18 or 29 or 78 or 722 or even asceding so >3
@fossilfighters1017 жыл бұрын
+
@ghyrt17 жыл бұрын
According to the Online Encyclopedia of Integer Sequences, 4 is an acceptable answer
@pieffe87 жыл бұрын
In the sequence is infinite you can't finish it...
@gdsfish32147 жыл бұрын
Don't you hate when you're trying to prove how big TREE(3) is with finite arithmetic, but then the universe resets itself.
@ruben3077 жыл бұрын
reminds me of Hitchhikers guide to the galaxy. The answer is easy yes it is finite the proof is very long.
@0menge7 жыл бұрын
I totally hate it!
@guillaumelagueyte10197 жыл бұрын
I was so close last time I tried. Oh well, maybe this time I'll have better luck
@mrJety897 жыл бұрын
That happened to me Tree(3) times already.
@DaniErik7 жыл бұрын
"I have discovered a truly marvelous proof of this, which this margin is too narrow to contain."
@heliocentric17567 жыл бұрын
"I've discovered a remarkable proof of Tree(3) theorem but the universe is too small to contain it"
@fossilfighters1017 жыл бұрын
+
@fibbooo11237 жыл бұрын
+
@romajimamulo7 жыл бұрын
fossilfighters101 "also my brain is too small to contain it"
@me_too_thanks50627 жыл бұрын
What a shame we don't live in a quality universe that could fit tree(3)
@ashkara86527 жыл бұрын
Only acceptable place to actually use that excuse
@whyit4874 жыл бұрын
The class: Tree(1) The homework: Tree(2) The exam: Tree(3)
@Aerialyn4 жыл бұрын
The test: tree(3) The finals: tree(tree (3))
@playmaker47004 жыл бұрын
TREE(Infinity)
@keafoleafo83684 жыл бұрын
@@playmaker4700 Isn't that just infinity anyway?
@tinybro56304 жыл бұрын
The Job Interview: Tree(Tree(Tree...(3)))))))))...
@tlep29794 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
@jongalonja92335 жыл бұрын
Well now I want to know if TREE(3) is prime
@priyansh12104 жыл бұрын
You can assume it's prime for now since it doesn't have any known non trivial divisors :P
@HerrKeuner19484 жыл бұрын
@@priyansh1210 That's a dangerous assumption ;)
@nothisispatrick68324 жыл бұрын
wonder if its possible to calculate that probability
@number_89034 жыл бұрын
First try to prove that tree(3) is odd
@chebichevinovichskic4 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...
@kcthewanderer7 жыл бұрын
We're gonna need a bigger universe.
@加州猫主席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.
@ongbonga90256 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.
@MikeRosoftJH6 жыл бұрын
No, you aren't anywhere close.
@CaseyShontz6 жыл бұрын
kcthewanderer I’ll go to Costco and buy one, be back in tree(3) minutes
@justsayapple13816 жыл бұрын
jawad mansoor I’ll have to remember to order one next time the universe resets
@alanturingtesla7 жыл бұрын
In base TREE(3) it is 10.
@zoranhacker7 жыл бұрын
A odgovor na prvo pitanje?
@subhransu757 жыл бұрын
And in binary the first digit is 1.
@vp_arth7 жыл бұрын
Can you give us their alphabet here?
@joonatanlinkola90597 жыл бұрын
What a useful base that is
@DuskKaiser6 жыл бұрын
Subhransu Mohapatra not necessarily
@PallyNut7 жыл бұрын
If numberphile has Pi as their picture.. Numberphile2 should have Tau as their picture.
@CaseyShontz6 жыл бұрын
PallyNut you right, you right
@alephnull40446 жыл бұрын
Yes!!
@arvasukulkarni36865 жыл бұрын
This needs more likes
@leondost35755 жыл бұрын
tau rules, change my mind! also, this needs way more likes :)
@qiki_info5 жыл бұрын
NumberphileTREE(3) for SERIOUS insiders.
@NoriMori19925 жыл бұрын
"The universe will eventually reset itself." "The universe will eventually reset itself."
@myownmeadow13205 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__84754 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!
@mathmachine42664 жыл бұрын
Looks like we had less time than we thought
@AidanXavier14 жыл бұрын
Repetition legitimizes Repetition legitimizes
@uncoolloser62334 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.
@stevekim96625 жыл бұрын
What they teach you in class: Tree(3) What they ask you in the exam: Tree(Tree3)
@SystemOfATool4 жыл бұрын
What they teach you in class: 1 & 3 What they ask you in the exam: Tree3
@sirdonki80854 жыл бұрын
😨😨😱😱😭😭😭😭
@MrTheKamir4 жыл бұрын
My brain just collapsed Tree(3) times
@barsozuguler47444 жыл бұрын
Im scared this like 11!!!!!!!!!!!!!!!!!!
@pbj41844 жыл бұрын
@@SystemOfATool Class: 33 Exam: Tree(3)
@AJ-tr4jx7 жыл бұрын
the universe will eventually reset itself, the universe will eventually reset itself. hah! well played
@BoWeava7 жыл бұрын
A J Lol I scrolled down hoping someone else saw that haha
@carbrickscity7 жыл бұрын
BoWeava They did the same on the poincare recurrence time vid
@livedandletdie7 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.
@BoWeava7 жыл бұрын
CarBricksCity niiice, haven't seen that one
@Bodyknock7 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.
@aza32627 жыл бұрын
Don't you hate it when you're doing proof for your maths homework and the universe just resets itself....
@tangyspy7 жыл бұрын
+
@FoxyBoxery7 жыл бұрын
Az A Omg yes
@andrewxc13357 жыл бұрын
You said that last recurrence...
@himylongusernameislongbeca72036 жыл бұрын
+uvuvwevwevwe onyetenyevwe ugwemubwem ossas MY BRUDA
@CaseyShontz6 жыл бұрын
Az A hold on lemme go buy is a new one at ikea
@felixp5357 жыл бұрын
You know what's even crazier? TREE(3)^0 = 1
@criskity7 жыл бұрын
And 1/TREE(3) is really small.
@djhokage17 жыл бұрын
Yeaaa, the real deal still is Zero, the number which demolishes everything else.
@jackreacher62407 жыл бұрын
well ..... -2 is smaller.
@petritdauti62586 жыл бұрын
Félix Pinchon TREE( TREE(TREE(TREE(3))) )^0=1 too Wtf universe
@skeletonrowdie17686 жыл бұрын
ah so the zeroth root of 1 is TREE(3)! We found the solution boys!
@massimodelbianco4425 жыл бұрын
And still, TREE(3) Is closer to 0 than infinity.
@caduaraujo3315 жыл бұрын
so is every cardinal
@Bogdanko935 жыл бұрын
@@SoloLevellor except my ego
@siddhantnagrath81445 жыл бұрын
Massimo Del Bianco depends on which infinity
@siddhantnagrath81445 жыл бұрын
It’s faster than a function of Epsilon sub script zero
@Shadowwolf-13375 жыл бұрын
Infinity divided by 3 would be closer to zero than infinity. Well, it would also be infinity. Wait, what?!
@L0j1k5 жыл бұрын
"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
@dkranda7 жыл бұрын
But is it prime?
@vampyricon70267 жыл бұрын
same question
@guillaumelagueyte10197 жыл бұрын
Maybe there's a way to prove whether it's odd or even.
@connorking9847 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.
@sage52967 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
@michaeljupille10767 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
@avi8aviate5 жыл бұрын
That TREE(3) will be great for getting LOG(3)s!
@harryw48024 жыл бұрын
bruh lol
@harryw48024 жыл бұрын
also log(3) ¬ 0.477121
@moodleblitz3 жыл бұрын
clever
@georgesmyrnis174210 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.
@avi8aviate10 ай бұрын
@@georgesmyrnis1742 Likely millions of axes, if not even more than that.
@darkshoalproductions5 жыл бұрын
Well, at least we know that the entire universe is not just a simulation being run to calculate TREE(3) then.
@tb-cg6vd4 жыл бұрын
Brilliant. My sense of free will is now secure!
@SledgerFromTDS.3 жыл бұрын
@@tb-cg6vd Brilliant to See your Comment, But there is another Video here
@SledgerFromTDS.3 жыл бұрын
Brome to See your Comment, But there is another Video here
@albert61572 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.
@gilbertoortega32745 жыл бұрын
When he wrote Tree (Tree(3)) I got anxious because I thought the universe was going to crash.
@RobertSzasz5 жыл бұрын
1,3, Visible universe collapses into a singularity
@glendrake92687 жыл бұрын
It gives me a new appreciation of infinity.
@qiki_info5 жыл бұрын
But you're still not even close. lol
@Yebjic7 жыл бұрын
Well, TREE(3) is clearly smaller than the sum of all natural numbers, therefore, an the upper bound of TREE(3) is -1/12
@migfrarummet19077 жыл бұрын
bivtyfrcygvubugwerdcfuvgibjhvibobhjhb! I can't take this!
@petritdauti62586 жыл бұрын
Yebjic Yeah thats something i dont get about infinity too
@jannegrey6 жыл бұрын
Only in Riemann Zeta function. Watch Mathologer video for full explanation. The one done in response to Numberphile video on -1/12.
@maxhaibara88286 жыл бұрын
We do have the upper bound for TREE(3) It is clearly less than TREE(3)+1
@whatno50906 жыл бұрын
@@vishalarya93 yes, welcome to the joke
@zemc776 жыл бұрын
"Exponentiation on steroids" Best description of Arrow notation I ever heard.
@astroash11 ай бұрын
It is a tradition for me to come back to Graham's number and TREE(3) every once couple of years.
@huwman2 жыл бұрын
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 Жыл 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 Жыл бұрын
@@IsaacHarvison-mt5xtwhat
@claudiuacsinte47577 жыл бұрын
"Exponantiation on steroids"
@Anaklusmos427 жыл бұрын
scalpian your thing, to the power of TREE(TREE(TREE(3)))
@andymcl927 жыл бұрын
ExponenTREEation!
@y__h7 жыл бұрын
Symbol juggling on meths.
@JorgetePanete6 жыл бұрын
Claudio Acsinte Exponentiation*
@phampton67817 жыл бұрын
"The universe is too small to contain it." I'll use this excuse next time I haven't done a due essay.
@noir-jaune6957Ай бұрын
Update?
@Skippy3rd7 жыл бұрын
Is TREE(3) closer to TREE(2) or TREE(4)? Do we know anything about the growth characteristics of the TREE() function?
@vampyricon70267 жыл бұрын
+
@HopUpOutDaBed7 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
@norielsylvire40977 жыл бұрын
Scot Brown TREE (3) is way closer to -TREE (3) than to TREE (4)
@vampyricon70267 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.
@Nixitur7 жыл бұрын
+HopUpOutDaBed - I like the way you think, that's a very elegant proof!
@ineedtoeatcake5 жыл бұрын
I love how happy he was at the end describing his joy over this type of math.
@swagswag62865 жыл бұрын
Thanks to this channel I have fallen in love with math and I am really considering studying maths!
@walexander8378 Жыл бұрын
Did you study maths
@emilioherrera63457 жыл бұрын
Totally dissapointed, this video should’ve been called “(extra foliage)”
@fossilfighters1017 жыл бұрын
+
@shakesmctremens1787 жыл бұрын
I knooow!
@Antimimesis7 жыл бұрын
Emilio Herrera "Lagniappe foliage"
@andrew7taylor6 жыл бұрын
(extra brown paper)
@VigoHornblower7 жыл бұрын
What if you filled the universe with mathematicians the size of a plank length and then they split up the work?
@mattsmith4576 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.
@jaysephisdeadpool88135 жыл бұрын
yeah they not gonna get nowhere
@axelpeneau22885 жыл бұрын
Won't work either
@altrag5 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.
@rodwayworkor92025 жыл бұрын
Where would they add the symbol?
@balazslovenberg7 жыл бұрын
Surely TREE(n) grows faster than LOG(n)
@romajimamulo7 жыл бұрын
Balazs Lovenberg it sure does
@ImMataza7 жыл бұрын
Man that's an amazing comment , I wish I thought of it :)
@chimkelvin57056 жыл бұрын
You should also consider ROOT(n), because it grows slower than TREE(n) too.
@GlobalWarmingSkeptic6 жыл бұрын
Hard to tell but yes I think if we examine the growth the TREE function just edges it out.
@suyashshandilya98916 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...…...
@jimgeary5 жыл бұрын
When he started nesting the Tree()’s, my nethers clenched fearing the universe might rend.
@scarletevans44749 ай бұрын
Djinn : "what do you wish for?" Alladin : "using finite arithmetic prove that TREE(3) is finite." ...and this is how Djinns got extinct!
@batbawls7 жыл бұрын
This should've been included in the original video!
@numberphile27 жыл бұрын
I know a true believer like you would watch, but if you post a 19-minute video to KZbin 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?
@N0Xa880iUL7 жыл бұрын
Numberphile2 why not a 3rd? Or maybe 4th! I surely won't mind :)
@franklinruan38077 жыл бұрын
Numberphile tree (3)
@vampyricon70267 жыл бұрын
You could have at least posted the pre-emptive TREE(TREE(3))
@Tahgtahv7 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?
@somethingsinlife56007 жыл бұрын
And This is why mathematicians have more fun :) They're just not bounded by the physical reality :)
@Life_42 Жыл бұрын
I agree :)
@Splandrocity Жыл бұрын
Love the excitement of Tony while educating here, these massive numbers are just jaw-dropping from the explanation alone.
@TIO540S15 жыл бұрын
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_Friend2 жыл бұрын
In fact proportionally, EVERY number is bigger
@TIO540S12 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.
@vepiru5734 Жыл бұрын
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.
@tangyspy7 жыл бұрын
Have been waiting for this number since over a year
@frizider27 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-sv8mv7 жыл бұрын
hey ash
@amiss88287 жыл бұрын
could you say you've been waiting for this number since over T(3) years?
@Sakkura17 жыл бұрын
@frizider2 look up SSCG(3), or even worse SCG(3).
@carbrickscity7 жыл бұрын
SCG(13)
@zaephou28437 жыл бұрын
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.
@kannarzoltan70067 жыл бұрын
Big FOOT
@zaephou28437 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.
@sage52967 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
@snajper91113 жыл бұрын
Absolutely love this topic. I’ve watch this episode about x20 times over the last year and I smile every time. Great work guys
@tyleralmquist76065 жыл бұрын
Spongebob: you know what’s -bigger- than tree(3)? Patrick: what? Spongebob: Tree(4)
@thunderstrom8783 жыл бұрын
And you know what function is faster and larger than TREE ? Subcubic Graph and Busy Beaver 😂
@oliverbrankodignum28176 жыл бұрын
His neck tendon pops out while he talks. These guys are so beautifully passionate.
@drjuju33317 жыл бұрын
I love how excited these guys get about this stuff!! Very interesting
@fireeye13867 жыл бұрын
I have discovered a truly remarkable proof that tree(3) is finite, which this universe is too small to contain...
@Craccpot7 жыл бұрын
fire eye exact words from Fermat if he is still alive today
@theviniso7 жыл бұрын
lol
@NoobOfLore6 жыл бұрын
You have a weird concept of "discovering" something that categorically cannot be contained by your brain.
@simoncarlile51907 жыл бұрын
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).
@geelzwarteaardbij4 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!
@efulmer86754 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...
@antonhengst86673 жыл бұрын
Sounds like you're asking if TREE is monotonic
@Anklejbiter5 жыл бұрын
Oh, the universe reset itself again. Man, I hate it when that happens.
@aasyjepale52105 жыл бұрын
no need to repeat, we can see itno need to repeat, we can see it
@Anklejbiter5 жыл бұрын
@@aasyjepale5210 haha, haha.
@evesolis61335 жыл бұрын
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
@MrGrumbleguts5 жыл бұрын
"The universe resets itself - This is a disaster." Literally that is what disaster means, the disappearance of stars.
@MitruMesre3 жыл бұрын
"dis" in disaster refers to unluckiness, not disappearance.
@nutmegninja234 жыл бұрын
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.
@TheSmegPod2 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
@joanalbertmirallespascual36066 жыл бұрын
2:31 "you might remember what this arrow notation is... exponentiation on steroids" lol
@JB-gi5ph2 жыл бұрын
I love the quick reset of "The universe resets itself." Well played!
@strangequark4202 жыл бұрын
This is one of the few KZbin videos that I watch over and over again. I'm iterated.
@arthurgrandao5 жыл бұрын
I love how excited he is! You can see he just loves math
@wyboo2019 Жыл бұрын
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
@64lundyco5 жыл бұрын
Love the universe resetting itself editing joke
@ObsessiveClarity3 жыл бұрын
Stumbling across these numberphile videos in 9th grade, I for once was curious about something related to math. "Related to math." I didn't realize at the time that this *is* math, and this is largely how math feels to mathematicians. Exploratory, creative, boundless, surreal, and objective??? All at once? Wow. Fast forward a few years, and I'm just obsessed with math. I'm a math major. Thanks for the awesome videos!
@merek69864 жыл бұрын
Im facinated by the concept of " this number is so big that i cannot describe it but i know is finite and can be proved"
@FreeAsInFreeBeer7 жыл бұрын
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!
@livedandletdie7 жыл бұрын
Shouldn't that be a computerphile video. n-state turing machines.
@synchronos17 жыл бұрын
It's already on the Computerphile, and prof. Brailsford videos are one of the best ones there.
@isuller6 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.
@FreeAsInFreeBeer6 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! :)
@iainh2 жыл бұрын
Just a note but this actually happened and he spoke about them in the video regarding Rayo's Number.
@axelitoxer7 жыл бұрын
4:22 "the universe will eventually reset itself" "reset itself"
@JorgetePanete7 жыл бұрын
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_J6 жыл бұрын
😂😂
@ilikeunderratedgachatubers71946 жыл бұрын
The universe must of reset 3 times before you thought of that
@CaseyShontz6 жыл бұрын
Jorge C. M. I prepared to be mind blown... But I wasn’t... Because I have no idea what that means.
@Dexuz6 жыл бұрын
Omg I love math jokes.
@maxonmendel57576 жыл бұрын
What's sigma? I understand it means "a portion of" but what's the textbook word for that function?
@loweshaw5 жыл бұрын
Bravo on the cliffhanger from the first video to the second
@canatronYT7 жыл бұрын
They used the same editing joke about the poincare repeat conjecture twice! They used the same editing joke about the poincare repeat conjecture twice!
@gaspytheghost Жыл бұрын
I just wanted to find out how big TREE(3) is, not have an actual existential crisis about the universe resetting itself.
@bsuperbrain5 жыл бұрын
When he says the universe resets itself, the running frame in the video resets itself. Funny trick! :D
@s.bucher14074 жыл бұрын
And still there are more numbers between 1 and 2 than all the numbers of this video multiplied with each other. I feel like my brain should ache now. But it doesn't , and now I feel stupid. What a rollercoaster of emotions I just went through.
@douggale5962 Жыл бұрын
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.
@Fiddlesticks865 жыл бұрын
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 😂😂
@Froggeh927 жыл бұрын
Shouldve gotten Prof Moriarty to do it so he can say "Tree Tree" over and over again.
@Lauraphoid7 жыл бұрын
I had the same thought! That would be quite enjoyable
@vampyricon70267 жыл бұрын
+
@lovrebabajko7 жыл бұрын
+
@Froggeh927 жыл бұрын
Lauraphoid hah would be pretty cute
@Markovisch7 жыл бұрын
Matt Parker should estimate TREE(3)
@kannarzoltan70067 жыл бұрын
Markovisch He could, but he doesn't bother doing it.
@vampyricon70267 жыл бұрын
At least he tried XD
@skepticmoderate57907 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."
@TheGeneralThings7 жыл бұрын
His answer would be a Parker Tree.
@vampyricon70267 жыл бұрын
PARKER(3)=10
@iluxa-40006 жыл бұрын
Why am watching these? After every video I want to watch about something else, like Graham's number, or reset of the universe. And it is neverending loop
@arturslunga34153 жыл бұрын
This guy's enthusiasm is contagious!
@pcajanandanjali6 жыл бұрын
"Universe resets before you can complete the proof" Awww....There goes my plans for the weekend..
@pixlark42877 жыл бұрын
FYI: It's spelled KRUSKAL'S if you're interested in looking into it.
@MagnusSkiptonLLC7 жыл бұрын
I know that the first digit of Tree(3) is 1 in binary
@coolguy49897 жыл бұрын
Skippy the Magnificent and in base TREE(3) the first digit is also a 1
@eliorahg5 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-me7hx8zf9y5 жыл бұрын
@@coolguy4989 underrated comment
@lunox84175 жыл бұрын
@@eliorahg explain 2
@PattyManatty5 жыл бұрын
@@lunox8417 2 is "10" in binary.
@johannvonbabylon7 жыл бұрын
I've always been a philosophy/sociology/history/psychology kind of guy and never really enjoyed math, but stuff like this really makes me appreciate math because it even strains philosophy...
@bengsynthmusic4 жыл бұрын
The greatest device man can invent is not the time machine, but rather a calculator that can display TREE(3) as soon as the = button is pressed.
@michadreksler24014 жыл бұрын
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. 😊
@willk71845 жыл бұрын
I watched both these videos, but I'm still curious HOW they know it's such a huge number.
@SomeGuy-ty7kr3 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
@wan-hewtran10467 жыл бұрын
What's the most number of nodes in any tree in TREE(3)?
@connorrcompton7 жыл бұрын
Sarthak Bansal TREE(3) means three types of nodes. Not nodes in general.
@adamweishaupt37337 жыл бұрын
Sarthak no it's 3 colors of nodes, the nth tree can have n nodes, but they can only contain 3 colors.
@OctagonalSquare7 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.
@livedandletdie7 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)
@limbridk7 жыл бұрын
That is the last tree Octagonalsquare, not the largest tree.
@Catman_3212 жыл бұрын
The best part of these videos is that every time he tries to describe is is making an incredible understatement Even what I just said was an understatement
@ayushkumarjha99212 жыл бұрын
Still remember the time when I first learn about a number called Trillion and that blown my mind and here are we now.
@johnny_eth5 жыл бұрын
New excuse for not sound homework: "there's not enough entropy in the universe to contain my homework"
@spudhead1694 жыл бұрын
I find it fascinating that mathematicians can play around with numbers for which there's not enough space in the universe to fully represent. It's nuts.
@Supware5 жыл бұрын
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..?
@nigeldepledge37905 жыл бұрын
Tree(3) blew my mind. To even contemplate the enormous potential of Tree(Tree(3)), never mind the multiplicative recursion, just makes parts of my brain run away and hide, gibbering, in a corner. H. P. Lovecraft has nothing on these truly gargantuan numbers.
@laz0014 жыл бұрын
Dude, thank you for making maths fun to listen to!
@blackkittyfreak7 жыл бұрын
When he started trying to top TREE(3), I almost had a panic attack.
@arnbrandy5 жыл бұрын
-So, if we write the symbols of this proof in a series of videos, KZbin wouldn't even be able to show it in our channel? -Yes! -I see. And so they created Numberphile2.
@AzazeoAinamart7 жыл бұрын
I literally hear GNASHING OF BOLTS HOLDING EDGES OF THE UNIVERSE when he started making TREE of TREEs
@cabbageboi63652 жыл бұрын
I love how the extra footage is longer than the original video
@DjVortex-w4 жыл бұрын
Even with Graham's Number I like this approach at conceptualizing how big it is: Even if you wrote a digit of Graham's number on each particle that exists in the universe, there would not be enough particles. How many digits is that? To write _that_ number there wouldn't be enough particles in the universe. And how many digits does _that_ digit have? Again, there wouldn't be enough particles in the universe to write it down. How many iterations of this "how many digits does the previous quantity have?" would you need to go through before you get a number that could be written in our universe? The amount of iterations itself (of doing the above needed for the number to become small enough) is too big to be written into the particles of the universe.
@jamirimaj68804 жыл бұрын
Fun fact: By definition, even if you can write those absurd tree symbols as small as an atom and fill the universe, you would still need LOTS OF SPACE to write Rayo's number.
@加州猫主席6 жыл бұрын
4:39 I just got the image of some guy writing on a piece of parchment scrolling by incredibly fast, and then everything on the parchment disappears and the guy is like, "It reset again???"
@OxidoPEZON7 жыл бұрын
I love this guy, please make an interview about his life interests... PLEASE XD
@craftyraf7 жыл бұрын
Subscribe to the Numberphile channel and you'll know...
@OxidoPEZON7 жыл бұрын
Raf M. I am, and know tidbits from him, but I don't know... Where does he get all this interesting topics if he works on physics. How does he know so much math, or is it not much, just what is asked for theoretical physics?
@calamorta7 жыл бұрын
Isn't he a Liverpool fan?
@donjorgenson99067 жыл бұрын
Man, I love this guy! Big up Tony!
@Unidentifying3 жыл бұрын
somehow these huuuuge numbers are tickling my curiosity so much
@tomschang22257 жыл бұрын
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 Жыл 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 Жыл 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.