Don't miss the extra footage - Tony says it is better than the main video: kzread.info/dash/bejne/e52cxbCaabyngM4.html

@erik-ic3tp

6 жыл бұрын

Do a video about tetration, pentation, hexation etc...!

@erik-ic3tp

6 жыл бұрын

Do a video about extremely big numbers in works of Archimedes!

@Yoyle-gp2xq

6 жыл бұрын

Is this Bigger Tree(3)^Tree(3)

@erik-ic3tp

6 жыл бұрын

Do a video about the number of possible combinations of the Library of Babel!

@erik-ic3tp

6 жыл бұрын

Lex Viduya, Yes, it is. But I mean numbers that are used in a mathematical proof.

The TREE function does have a practical application - the calculation of interest by loan sharks.

@sat2244

3 жыл бұрын

Lol

@krinkovakwarfare

2 жыл бұрын

That’s if they are generous

@IcarusWingsofWax

2 жыл бұрын

And student loans.

@jammehrmann1871

2 жыл бұрын

TREE(3) * TRUE!

@redwolf0331

2 жыл бұрын

So the answer is broken kneecaps?

It's like my little sister counting. "One... three... gazillion billion"

@Eren03eren

4 жыл бұрын

willion

@solicoli

4 жыл бұрын

nillion

@absence9443

4 жыл бұрын

@vakahsj vnabdbn hillion

@absence9443

4 жыл бұрын

@vakahsj vnabdbn oillion

@absence9443

4 жыл бұрын

@vakahsj vnabdbn noillion

Child: I can count to tree. Me: no I don’t think you can.

@no-one-1

2 жыл бұрын

I can count to TREE(3 - 1) + 1.

@SirNobleIZH

2 жыл бұрын

@@no-one-1 you can count to 4

@roblohub2270

Жыл бұрын

lol

@findystonerush9339

Жыл бұрын

@@roblohub2270 League of leagions lets watch!😂😂😂.

@o0hbomb0o

Жыл бұрын

Well, if they are only counting to TREE(1) or TREE(2) it's quite possible for a child.

There's actually an even bigger number known as "tree fiddy" which is named after the ammount of times that damn lockness monster will try and deceive you.

@xanderz101

Жыл бұрын

?

@caineblackknife2443

Жыл бұрын

"Lockness" lol... read a book.

@jedinxf7

Жыл бұрын

there's got to be a morning after

@joshyoung1440

Жыл бұрын

*Loch Ness

@joshyoung1440

Жыл бұрын

@@caineblackknife2443 there's a nicer way to do that.

Continue the logical sequence: 1, 3, ?

@andrewknorpp9415

6 жыл бұрын

Passe-Science really big

@andrewknorpp9415

6 жыл бұрын

Passe-Science or 5

@harry_page

6 жыл бұрын

Could be 9, if it's a geometric sequence

@U014B

6 жыл бұрын

"?" is exactly how big TREE(3) is.

@qutuz9495

6 жыл бұрын

Teachers should have this on exams and everyone fails.

I laughed really hard when he said "We have a lower limit on it. It's bigger than... well it's certainly bigger than three."

@findystonerush9339

Жыл бұрын

What! i didn't laugh! 😐😐😐.

@melon218

Жыл бұрын

@@findystonerush9339 ??

@mdsharfuddinmd5710

Жыл бұрын

Thank you sir

@bitti1975

6 ай бұрын

And everybody knows, anything bigger than 3 is just "big".

@vixguy

6 ай бұрын

Ig it'd be smaller than TREE(4)

_Well that escalated quickly!_

@3vimages471

4 жыл бұрын

A four word sentence and you had to edit it? Interesting.

@redstoneplayz09

3 жыл бұрын

Also that was already commented here a month ago down the comments. I don't even understand it..

@farzanali5910

3 жыл бұрын

Lucien from “The Originals “

@dylanisaac1017

2 жыл бұрын

@@3vimages471 I think it was the italics

Imagine having a small number This post was made by Tree(4) gang

@liongames8776

3 жыл бұрын

Nico Detalo imagine having a smallER number. This post was made by the TREE(5) gang. (There is no TREE(6) hahaha)

@shaansingh6048

3 жыл бұрын

@@liongames8776 why is there no tree(6)

@liongames8776

3 жыл бұрын

Shaan Singh no idea but who knows maybe there is but there is a.... TREE(TREE(3))

@SG2048-meta

3 жыл бұрын

@@liongames8776 no there is a TREE(6) it’s just not shown here

@liongames8776

3 жыл бұрын

@@SG2048-meta there could be a TREE(7), TREE(8), TREE(9), TREE(10), and it could just go on forever

so, TREE(3) came about because someone gave a mathematician a third colouring pencil?

@rykehuss3435

6 жыл бұрын

No, the TREE sequence arose from graph theory. en.wikipedia.org/wiki/Graph_theory

@richardruiz476

6 жыл бұрын

Rykehuss Annnnd you had to ruin it......

@Yora21

5 жыл бұрын

What about a blue pen?

@koenslotboom1910

5 жыл бұрын

@@Yora21 What have you done

@xueyihon3648

5 жыл бұрын

@@rykehuss3435 r/whoosh

I prefer grahams number. You can understand its growth even as a non mathematician. Tree3 is just... "Yeah, just believe us, it's big"

@WalterKingstone

6 жыл бұрын

That's virtually what Graham's Number is too... "Yeah, it's a bunch of 3s multiplied together..."

@someguydudeGAME

6 жыл бұрын

You can find full explanations, but they are insanely difficult to understand. I can't wrap my head around them.

@DooDooDiaperShitCunt

6 жыл бұрын

Graham's number is an upper bound to a problem whose actual solution may be as small as 13. While Graham's number is impressive in size, it could very well just be a horribly horribly wrong upper bound to a problem. Whereas TREE(3) has a LOWER bound that is known to be far larger than Graham's number. For this reason, TREE(3) is more fascinating to me. Although I respect Graham's number for being the first 'stupidly large' number to be used in a serious mathematical paper.

@cocoyepyep7509

6 жыл бұрын

Retro Game Spacko exactly Agree

@yoshi6236

6 жыл бұрын

Retro Game Spacko lol yeah

The fascinating thing about these numbers to me isn’t that they’re so large, it’s the processes that makes them finite - which is crazy within crazy because it would suggest infinitely itself is easier to understand

What I love about TREE(3) is that unlike other big numbers, they weren't intentionally looking for a huge number. One sprang up out of mathematical inquiry. That makes it more, I guess, legitimate than the likes of Rayo's Number. They had a concept and then out of this curiosity a colossal number emerged.

@thefirstsurvivor

4 ай бұрын

Rayos number is boring

@dxitydevil

3 ай бұрын

Plus its got a funny name, TREE 🔥

“It’s a big number” Me: aight “It puts Graham’s number to shame” Me: ...aight

This just goes to show that even if something feels infinite, you still have to prove it because there's always a chance that it only holds to an unimaginably large number like TREE(3)

@someguydudeGAME

6 жыл бұрын

It also really helps hammer home just how big "infinity" is. When we're constructing these colossal numbers that are nothing compared to infinities.

@LunarDelta

6 жыл бұрын

TBH, I find colossal numbers to be much scarier than infinity. If we say the universe is infinite then there's no need to worry about how big it is, (you might even say it doesn't even have a real size in the normal sense) but if it's TREE(3) light years across that's just nuts.

@anticorncob6

6 жыл бұрын

Lunar Delta If scientists were to discover someday that the universe is infinite, it would make me feel less small and insignificant because literally every finite portion is exactly zero percent the whole universe (there is nothing that isn’t so tiny). But if they discovered that the universe is topologically a 3-sphere and has a volume of 10^130 (or so) m^3 that would make me feel insignificant compared to the large structures.

@__w__o__w__

6 жыл бұрын

Surely just by going off the rules of this tree game you can assume that tree(3) is not infinite. Is some kind of proof required beyond logical reasoning in this case? If you know you know a tree can't contain previous trees then at some point you're going to run out of iterations.

@Frightning

6 жыл бұрын

Tree size isn't a priori bounded, I think the reason why we know that TREE(3) must be finite is because of the graph minor theorem (the whole tree not containing a previous tree thing smacks of the notion of a minor in graph theory, and the graph minor theorem says that every infinite collection of graphs has one that is a minor of some other graph in that collection; there's probably a bit more to the argument because in the TREE game, order matters).

Me, talking to my sibling after borrowing some money: “how much do I owe you?” My sibling: 0:00 - 0:14

@iqbaltrojan

5 жыл бұрын

DAMMMMMMMMMMMMMM

@nnnnick

4 жыл бұрын

THIS IS SO FUNNY

@agniagniagni13

4 жыл бұрын

every time i look at this post i start laughing uncontrollably

@markiyanhapyak349

3 жыл бұрын

😆, 😆, 😜, 😅, 😅!

@elfro1237

3 жыл бұрын

Or 6:49 to 6:55

And I thought planting 20 million trees was a lot, apparently all we need to is to plant 3

More interested in Tree(Fitty).

@cordlefhrichter1520

6 жыл бұрын

LOL

@JohnMichaelson

6 жыл бұрын

Well now I'm startin' to get a little suspicious...

@GruntUltra

6 жыл бұрын

I spit my water out when I read this!

@Janis_Ukass

6 жыл бұрын

Damn you Loch Ness monster with Tree(Fiddy)

@poiewhfopiewhf

6 жыл бұрын

waddabout tree hunnid this is Sparta!!!

I'm waiting for the follow up "The Enormous Tree(3), but everytime they say tree it gets faster"

@romajimamulo

6 жыл бұрын

Fiyaaah I'll get on that

@annaisabanana6848

6 жыл бұрын

every time they say tree it speeds up by tree(3)%

@romajimamulo

6 жыл бұрын

AnnaIsABanana that's excessive

@benjabean1

6 жыл бұрын

at that rate, the video would just stop by the first time they say "tree"

@artemetra3262

6 жыл бұрын

AnnaIsABanana no, slows down.

I love how "tree" is a mathematical function. :)

@Peter_Schluss-Mit-Lustig

5 жыл бұрын

There are actually around 8 tree related functions two of them even faster than tree

TREE(Graham's number) ?? :D

@theshadowmonster1

4 жыл бұрын

oh no

@lordfeish1927

4 жыл бұрын

aleph null be like hold my beer

@miaomiaochan

4 жыл бұрын

Yet still smaller than infinity.

@franchufranchu119

4 жыл бұрын

TREE(TREE(3))

@persereikanen6518

4 жыл бұрын

TREE(G64)

"No physical process you can use to describe it." That's my favorite way to describe truly large numbers.

Ah, finally a number that can describe the size of my... love for mathematics, gottem

@pomtubes1205

6 жыл бұрын

*GOTTEM*

@SuperCoolMC

6 жыл бұрын

i thought you were gonna say brain and i was thinking "man, this person is full of themselves"

@skystrike3221

6 жыл бұрын

GOTTEM!!!!!!!!!!!!!!!!

@Breeelax

6 жыл бұрын

Gottem did not get the hero it deserved, but the one it needed.

@JorgetePanete

6 жыл бұрын

Iqbal Mala definitely*

Tree(3) is so enourmous since it essentially takes the first tree with 1 seed of Tree(2) which makes you not have any other options that single seed. However, when you still have that seed, it scales up INSANELY

@mdsharfuddinmd5710

Жыл бұрын

Thank you sir

@ThreeTrees475

7 ай бұрын

Huh

TREE(3) is so big it makes short jokes about Graham's Number.

Soooooo.... What about TREE(4)?

@stefan1024

6 жыл бұрын

TREE(4) is actually pretty small, 9 to be exact. Noooooooooo!!! :D

@poseidon4675

6 жыл бұрын

Wait How come that's so small? Surely with four colours you can build the TREE(3) forest without ever using the fourth colour, and then when you've used up all possible trees start using the fourth colour?

@cordlefhrichter1520

6 жыл бұрын

TREE(TREE)

@anticorncob6

6 жыл бұрын

Poseidon He was just joking.

@roderickwhitehead

6 жыл бұрын

Poseidon - What about TREE FIDDY?

I once thought the difference that one arrow notation makes was big But then the difference of tree(2) and tree(3) is just colossal

@lamnguyen-uh4tz

6 жыл бұрын

Meh, I've seen crazier. Also, a nitpick, tree(n)

@lamnguyen-uh4tz

6 жыл бұрын

I'm opening a Discord server dedicated to explaining ordinals and the fast growing hierarchy, which you might be interested in. The end goal will be to reach an understanding of the magnitude of TREE(3) and larger things using only recursion, and lots of it, and you might gain some insight as to how much of a difference one arrow means compared to the difference from TREE(n) to TREE(n+1). discord.gg/5v6ucfN Feel free to join, basic algebra required.

@whatno5090

5 жыл бұрын

nguyen eyyy ninja'd also hi from googology discord

@alonelyphoenix8942

2 жыл бұрын

@@lamnguyen-uh4tz send invite

I think Tree(3) is the most interesting of these giant numbers because this game of trees looks so simple and all it takes is 3 seeds to produce a number that makes Graham's number look like nothing.

@R3cce

Жыл бұрын

Grahams number is effectively zero compared to TREE(3). It is even bigger than GGGG…G64 with G64 iterations of G. In fact the number of times you would need to iterate the G function to beat it is TREE(3) itself, so basically pointless. You can’t even express TREE(3) using chain arrows. That’s just how big it is

@R3cce

Жыл бұрын

Also TREE(n) has a growth rate between the SVO( Small Veblen Ordinal) and LVO( Large Veblen Ordinal) in fast growing hierarchy. For reference the above ordinals is way beyond gamma zero

@xenky2272

6 ай бұрын

@@R3cce " In fact the number of times you would need to iterate the G function to beat it is TREE(3) itself" do you have any reference or explanation to this statement?

@bobibest89

4 ай бұрын

​@@R3cce It would be fun If someone does a video vizualization Tree(3)'s size. Similar to the videos that visualize the size of the Universe compared to a Plank length.

@shiinondogewalker2809

3 ай бұрын

@@xenky2272 he isn't exactly correct. for example if you iterate G function TREE(3) - 1 times you certainly get a larger number than TREE(3). he's right in the sense that you will be hard pressed to put a number using any meaningful algebra or combination of G functions to reach TREE(3). For example a number such as G(G(G(G(G(G(G(G(G(G(G(...(G64)...))))))))) where you have applied the G function G(64) number of times, is still nothing compared to TREE(3)

I still prefer Graham's Number because you can see the process by which you get there and (to a very limited extent) wrap your head around how absurdly large the number is. TREE(3) is, well, just a really big number. Yes, it's countless magnitudes _larger_ than Graham's Number, but as I like to say, "It's not the size of the pen that matters, but the poetry you write with it." I'm still interested in TREE(3) enough to learn more about out it, and find out why it behaves the way it does, but it still doesn't have that daunting, step-by-step escalation that Graham's Number does.

@findystonerush9339

Жыл бұрын

So why don't you like G64!

@AbsoluteZero-zg9gj

Жыл бұрын

TREE3 we only know that it's way bigger than Graham Number. We don't know actually how big is it

@shanggosteen9804

11 ай бұрын

Rayo(10¹⁰⁰) is probably my favourite big number. It's easy to visualize, and it's reasonable. There are many ways to interpret it. Tree(3) is just like, a number. There's not really another way to visualize it other than it's original meaning, which is kind of boring

@richardterroni9433

9 ай бұрын

​@@AbsoluteZero-zg9gjWe sort of do, we know that it's smaller than other massive numbers

@alansmithee419

6 ай бұрын

@@AbsoluteZero-zg9gj There are specific known lower and upper bounds for TREE(3), though the upper bound is less well-researched. The fact that it's bigger than Graham's number is not remotely "all we know." If you want to know more there is a lot of learning to do to get there, but these number can be parsed more thoroughly than you're aware. Indeed there are estimations comparing the entire TREE(n) function's growth rate as compared to the functions in the Fast Growing Hierarchy (which if you like Graham's number, and don't know about already, I highly suggest looking into).

And still, almost all natural numbers are bigger than that.

@spinn4ntier487

6 жыл бұрын

Infinite natural numbers are larger than that

@bengtbengt3850

6 жыл бұрын

This is great

@piguy3144

6 жыл бұрын

Precisely 100% of natural numbers are bigger than that

@maxnullifidian

5 жыл бұрын

Yeah, piguy314, and they all contain the digit 3...

@ukdavepianoman

5 жыл бұрын

Almost all natural numbers are bigger than any natural number anyone cares to name.

But how do you even calculate this? Graham's number could be "grown" via arrow notation, but what about this?

@someguydudeGAME

6 жыл бұрын

I've seen attempts to actually show how to "explain" it, but that requires a ton of really weird formulation on how all of the stuff Tony is talking about looks on paper. It can be done, but it's insanely technical.

@jacks.4390

6 жыл бұрын

So Graham's number is G64 iirc. Which G would TREE(3) be? Also, is it known which is the first busy beaver number greater than TREE(3) (or at least greater than the lowerd bound)?

@dawson6294

6 жыл бұрын

You couldn't express it using the "G" system used for Graham's Number, it's just too big.

@jacks.4390

6 жыл бұрын

It's even bigger than G(G(G(....(G(64))...))) for a reasonable number of iterations?

@dawson6294

6 жыл бұрын

Yes. There is no way to describe how big this number is in layman's terms the way you can explain Graham's number, it requires more advanced mathematical concepts to explain.

I love rewatching this video

Love both this and the extra footage video! I cannot explain the joy watching these big number videos brings me; I completely empathise with Tony's excitement 😄

stopped doing my maths to watch maths

@MrSkinnyWhale

6 жыл бұрын

Maths can really sneak up on you. You think you're ok doing it once, you start with 2+2, maybe someone teaches you some things about real and complex numbers in a dark alley. Next thing you know you're hooked on TREE(3).

@hans1059

6 жыл бұрын

It's truly horrible... I've recently seen a documentation about an addict, he already started doing it in elementary school.

@whatisthis2809

5 жыл бұрын

Math*

@BluJellu

5 жыл бұрын

Connor K a

@CharlesPanigeo

5 жыл бұрын

Same. I got distracted from my abstract algebra homework to watch a video on graph theory lol. I can't wait to take my graph theory course next semester

My question is, do we have any way of knowing or determining the first n steps of the optimal sequence of trees for TREE(3)?

@gpt-jcommentbot4759

11 ай бұрын

For the first step at least, yes.

"What is it useful for? What does any of this got to do with anything that's important?" End cut with no answer

"To explain what TREE(3) comes from, well it comes from a game of trees." Well, great, thanks professor.

FOREST(3) = TREE(TREE(...TREE(3))...)

@DeltaWither

5 жыл бұрын

Not too much bigger than TREE(3)

@Peter_Schluss-Mit-Lustig

5 жыл бұрын

SSCG(3) is still way bigger (not even talking about SCG(3) or SCG(13).)

@Peter_Schluss-Mit-Lustig

5 жыл бұрын

@@metachirality and the Uncomputable functions

@Dexuz

5 жыл бұрын

@@DeltaWither WAAAAAY bigger than TREE(3) But also smaller than an infinite number of naturals.

@DeltaWither

5 жыл бұрын

@@Dexuz it's not way bigger than TREE(3) if you compare them using the fast growing hierarchy. The difference between TREE and FOREST is literally just adding 1 to a pretty large infinity

YES! Finally! I waited for a TREE(3) Numberphile episode for ages!

@RizzerixLP

5 жыл бұрын

and next Loader's Number :D

The definition of "that escalated quickly"

I can actually imagine Tree (3) being mind-bogglingly huge. Because the third and fourth tree that you draw in Tree (3) game only cancels out a fraction of possibility for the fifth tree that you draw. And this fraction gets smaller with each tree in a logarithmic fraction. As the trees become more complex it becomes easier not to have that same arrangement in the next tree. So already without even being told that tree 3 is very huge, I can somehow imagine it being bigger than a trillion if that makes sense.

@ferociousfeind8538

2 жыл бұрын

Ah ah, TREE(3) dwarfs all numbers in common use. "Bigger than a trillion" is an understatement. TREE(3) is so huge that mathematicians in the comments are having trouble explaining it to laypeople. If you were to take the number of atoms in the universe (a big number) and produce a billion-core, terraherz-speed supercomputer for each atom, computers so strong that they can effectively execute any arbitrary exponentiation a billion times every nanosecond, and set them all to work exponentiating 2 and passing their results to the next computer... (in short, if you imagine anything from real life, distorted within reasonable bounds...) they would reach the result of TREE(3) eventually given a stupidly large amount of time, but ONLY because TREE(3) technically isn't infinite. If you imagine that scenario, and then put a time limit on it, any time limit you want, and ask "can they reach or exceed the result of TREE(3)?" The answer would be a resounding "nope!" Crazy big number...

@SaladDongs

2 жыл бұрын

@@ferociousfeind8538 That's a fine explanation but can I ask, what does "reasonable bounds" mean? I mean I know kind of what it means, but how do you define what is reasonable? I've seen it a lot in these comments.

@ferociousfeind8538

2 жыл бұрын

@@SaladDongs as in, as long as your answer isn't "I want to use TREE(3) computers to do it!" The answer will be "it will take an inconceivably long time to calculate the size of TREE(3)

@djdjbeje

Жыл бұрын

of course it is bigger than a trillion dummy

@TheSpotify95

Жыл бұрын

Tree(3) isn't just bigger than a trillion, it's bigger than Graham's Number!

"Grahams nunber is effectively zero compared to tree 3" very funny way to start a vid

@tim40gabby25

2 жыл бұрын

'Effectively' zero should mean 'not zero' - or the 'effectively' is redundant?. or is one allowed different sorts of zeroes? Struggling with this one :)

@zenthichutt7071

2 жыл бұрын

@@tim40gabby25 "effectively zero" refers to the fact that grahams number is so unbelievably small compared to TREE(3) that it might as well be the same as 0 for all intents and purposes when you're on the scale of TREE(3)

@tim40gabby25

2 жыл бұрын

@@zenthichutt7071 understood, thanks :)

Finally easy video about TREE(3)!!!! Thank you!

@poseidon4675

6 жыл бұрын

MajkG MajkG unexpected factorial

@majkgmajkg2613

6 жыл бұрын

You're right. I shouldn't mix my excitement with mathematic. :D

@SpektralJo

6 жыл бұрын

MajkG MajkG TREE(3)!!!! is a large number indeed

@quantumbanana

6 жыл бұрын

TREE(3) and TREE(3)!!!! are essentially indistinguishable, so they are effectively the same size.

@zionj104

6 жыл бұрын

same dude same

Looking at these numbers makes you realize how scary eternity is, for example, when we talk about being immortal, literally immortal, no matter what happens you can't die, you could live Graham's number in years, TREE (3) in years, and still wouldn't have lived even a fraction of your entire life, not even close, you will live literally FOREVER, eternity is scary.

Looking at the sample trees for TREE(3), the fact that the function suddenly explodes after n=2 is maybe a little more intuitive than it first appears. Whatever colour you choose for the first tree cannot be used again in the sequence ever, so if you only have one or two to choose from to begin with, you're going to run out of options rapidly. But for n>2, you essentially have a "freebie" disposable seed for the first tree, and then all bets are off after that.

We've all been waiting for this since the Graham's number videos

How big are the roots of these trees, and how much wood could a woodchuck chuck from them?

@michaeltomecsek10

6 жыл бұрын

John Michaelson probably allot

@AJJJJJJJJJJJJ

5 жыл бұрын

ohhh as in plant roots hahahah nice joke

@Dexuz

5 жыл бұрын

@asd Spoiler, TREE(3)th root of 1 is small.

@nilesspindrift1934

4 жыл бұрын

@@Dexuz TREE(3)th root of 1 is 1

@Dexuz

4 жыл бұрын

@@nilesspindrift1934 Honestly, I don't even know why I said root, I should have said 1 divided by TREE(3)

Tony Padilla is on fire here.

This video is one of my favorites over the years...

I think Ackermann numbers (and Ackermann functions) would make for a really great topic on Numberphile, mainly for people who like stupidly big numbers- like me!

@SpektralJo

6 жыл бұрын

Hi Ho Wolverhampton how stupidly big should the numbers get?

@Abdega

6 жыл бұрын

I think the Ackermann functions were talked a little bit about in Computerphile It would be nice to see another look at them in Numberphile

@natemoorman4562

6 жыл бұрын

Seconded!

@abcdefzhij

6 жыл бұрын

Look up Googology wiki, it's a great resource for this stuff. You can look up the Ackermann function there as well. BTW, don't get too excited, Ackermann function isn't nearly as powerful as TREE() and you're never going to define a number as large as TREE(3) just using the Ackermann function; You CAN easily pass Graham's number with it, though.

@timecomfort8556

5 жыл бұрын

Like them? I love them .

this timing is amazing, i spent two hours yesterday reading technical explanations of TREE(3) and here it is in a nice, more approachable form. cheers

Mathematicians have what is considered an "extremely weak lower bound" for TREE(3). That number is greater than GG1, but less than GG2. In other words, it is greater than G of G1, but less than G of G2.

@DavenH

4 ай бұрын

I've got an even weaker lower bound of 1

what a smart trick playing with 3 seeds is to use the 1st type of seed only to start the game and never use it again after that. so, basically, the game goes on only with 2 types of seed, giving us more of a tree(2) than (3), and it still heads somewhere to the infinity... now imagine what crazy horror starts when we ACTUALLY have 3 different types playing the Tree(4)

So excited! I've been waiting for this video ever since tree(3) was alluded to in the original Graham's number video.

I like how he already sounds tired of its bigness as he goes to draw the very first tree of it at 6:15

The size of a tree(3) number of Planck volumes is unimaginably larger than if the entire observable universe were Graham's number times wider

OMG I've been waiting years for you to cover this! Thank you!

This must explain why I sometimes call 3 tree. One, two, tree, four...

@CaseyShontz

5 жыл бұрын

Double Dare Fan are you Irish by any chance

@gpt-jcommentbot4759

3 жыл бұрын

TREE(TREE) Aha!

@AHTOH2010

3 жыл бұрын

tree it's 3 (три) in russian, lol

@liongames8776

3 жыл бұрын

stop looking at my profile pic TREE(TREE(TREE))

@kp2k

3 жыл бұрын

its one, two, TREE(3), four

"I can't express how really big it is. It's off the scale big" That's what he said.

You were being awfully cheeky there lol. Your explanation of TREE(2) and then the graphic of TREE(3) showing a node with 5 coming off THEN 4 coming off THEN 3 three coming off as a way of getting around the common ancestry. I saw that, thought about it for a second, then my head almost exploded. That is crazy!

I love how exciting you guys can make numbers and math. I love learning, in general, and you guys make it so easy and fun

I am confused by the Knuth triple down arrow notation in the description?

@JohnMichaelson

6 жыл бұрын

I think it means "this way lies madness" as a warning not to try comprehending it.

I still love that you can try picturing the numbers on a visual plane. still so impossible like grahams number. awesome!

Tree(3) is my favorite of all these giant numbers. It a proof of an old Chinese idiom: 1 generates 2; 2 generates 3; and 3 generates everything!

And now. Number 3. The Larch.

@asagoldsmith3328

6 жыл бұрын

The... Larch.

@gustavkrogsbygaard3254

6 жыл бұрын

Very nice

@EnoVarma

6 жыл бұрын

Beautiful.

@jacobr7729

5 жыл бұрын

And now...... THe LArcH

What always fascinates me about large numbers is that they can have very different properties from small ones. Many of the properties of numbers we think about are found in small examples: we have small primes, small perfect numbers, etc. But there are (presumably) types of numbers where there aren’t any small examples, and which potentially exhibit behaviours very unlike any we are used to thinking about. This is kind of incredible thing: usually we conceptualizer large numbers as being like small ones, just bigger, but there may be ones that are very different.

You have a secret: Tree 1 You tell another person: Tree 2 You tell a second person: Tree 3

Friend: What's your favorite number? Me: Oh it's just Tree, nothing much.

Other interesting questions I have: Is TREE(n) bounded? Is TREE(n)/TREE(n-1) bounded? Or even structured in any way?

@coyraig8332

4 жыл бұрын

TREE(n)/TREE(n-1) can't have n

@magicmulder

2 жыл бұрын

1. You mean if there is a constant C so that TREE(n) 2. Neither. Because of its growth hierarchy, this goes off to infinity too (even though every TREE(n) is finite).

@R3cce

Жыл бұрын

@@magicmulder2 TREE(n) is bounded between the SVO and LVO in fast growing hierarchy

Parker could've gotten TREE(2) up to 10. He would have used 4 colors though.

@walterrobinson9796

5 жыл бұрын

Ah yes, a Parker Tree

@martintuma9974

5 жыл бұрын

@@walterrobinson9796 :-)

@randomdude9135

4 жыл бұрын

But if you use 4 colours then you're technically calculating TREE(4)

@randomdude9135

4 жыл бұрын

@PiggyKillerQ Explain the joke then

@randomdude9135

4 жыл бұрын

@PiggyKillerQ Oh, thanks 😂👍

Him: Tree(3) is so big! U can't imagine anything bigger! Me: Ok, so what about Tree(3)+1 ?

@lucasxue2031

3 жыл бұрын

PhantomGaming Tree(tree(tree ........ (tree 3)) Tree 3 times

@fakenightbot1880

3 жыл бұрын

TREE(3) is {3, 6, 3 [1 [2 \ 3 ¬ 1, 2] 2] 2}

@sarotarnin9923

3 жыл бұрын

I'm about to cry, I can't find a simple explanation for notations stronger than than Ackermann one

Even Tree(Graham's Number) is closer to 0 than it is to infinity. Goes to show how big infinity really is. 😂

@R3cce

3 ай бұрын

Infinity is not a number. It is a concept of something that has no end

@Youaveragecountryhumansfan

3 ай бұрын

@@R3cceTHANK YOU!

But what if we play that game with Grahams cubes? With 1 color the upper bound is 1. With 2 colkrs it is already g(12) (mich smaller than G(64) but still huge). And with 3 colors?

3:30 when scientists discover humans originated in Ethiopia

This weirdly mirrors chemistry with simple carbon compounds [ Carbon, hydrogen and oxygen ]

@somethingismissing1482

3 жыл бұрын

When you look at the trees you notice they are actually only using two colors, because they need to use one in the first step and then can never use that again. And the second one where they use one color two times is another huge reduction of possibilities...chemistry (I dont know much about molecules) I think actually likes to reuse earlier structures?

Tree(1): I'm weak... Tree(2): I'm just 2 more than the weak one... Tree(3): Graham's number? Oh, You mean my younger brother?

@Rorschach003

3 жыл бұрын

Graham's Number? You mean that ant in my yard?

@fly6538

3 жыл бұрын

Graham's number? Do you mean that tiny cell in my body?

@SG2048-meta

3 жыл бұрын

Tree(7): Graham’s number? oh you mean that atom through the microscope?

Graham's Number is alot easier to understand than TREE(3) but TREE(3) is much cooler because it is WAY WAY WAY WAY bigger than Graham's Number and Graham's Number is already unimaginably huge!

Which is bigger? G(TREE(3)) or TREE(Graham’s Number)?

@lamnguyen-uh4tz

6 жыл бұрын

TREE(Graham’s Number) >> TREE(4) >> G(TREE(3))

@ethanhuyck4704

5 жыл бұрын

well, the tree function does grow faster than grahams number does with increasing iterations.

@mauricioubillusmarchena6660

5 жыл бұрын

G(TREE(3) is much much much much smaller than TREE(Graham's Number)

@keerthivasan5650

4 жыл бұрын

Congrats! You've got a video!

@ValexNihilist

3 жыл бұрын

They made a video answering it!

Excellent video and concept.

Still remember the time when I first learn about a number called Trillion and that blown my mind and here are we now with Graham's number, TREE(3)...etc

I relatively recently discovered this channel. It has a great spirit!. TREE(3)... Thank you!

@numberphile

4 жыл бұрын

Thanks

6:48 Very gladdening to hear a mathematician describe a number's bigness as "really really really really really really really really ...... "

How to keep a toddler occupied: explain this game and give him 3 coloured crayons.

*Spends 6 minutes playing a math game* “So yeah, this number tree3 is so big”

I do not know the last digit of TREE(3), the first digit of TREE(3), or how many digits are in TREE(3). But I do know that 2 * arctan(TREE(3)) = 3.141592653589793 rounded to 15 decimal places.

6:36 Could somebody explain why the 4th one isn't contained within the 6th? Both have 3 blacks and a red as a chain.

I'm still confused by one thing: For the examples used in TREE(3), they show trees that go from 7 nodes down to 4 nodes to avoid common ancestors. However, unless orientation matters, there's a three node section you can rotate 90 degrees & it matches the first 3 node tree in the graphic. So is it more proper to say the tree just shouldn't have a common ancestor or contain the tree immediately previous to it?

Fun fact: In aviation, standard radio phraseology is to pronounce the number three as “tree.”

Hello, Hi - would you please make an episode on SCG (13)? Thanks in advance

I know tree(3) is already so ridicolously huge that cannot be processed but I wonder... do we have an idea on "how quickly this function grows"? I mean, what is the growth rate from tree(3) to tree(4)? Is the difference somehow proportional to the distance we have from tree(2) to tree(3)? Is it growing much faster? Does someone has an idea and does this really matters since tree(3) is already out of every scale?

@R3cce

3 ай бұрын

TREE(4) is even bigger than putting TREE(3) in the repeated G sequence namely GGG…..G(TREE(3)) with TREE(3) number of G’s This shows how insane the function grows! 🤯

@R3cce

3 ай бұрын

in the fast growing hierarchy it is between the SVO and LVO ordinals

6:20 He starts drawing and knows, he will sit there myraids and myraids of millenia. How many brown sheets will he need?

Great video, I nearly understood what you're talking about.

The explanation seemed great. But I still didn't understand shit.

@Isacc142

6 жыл бұрын

Thomas Cheng Just watch it twice. At first I didn't understand it either, however it's not that difficult to grasp.

@poiewhfopiewhf

6 жыл бұрын

No this guy is very subpar at explaining things, so convoluted especially with increasing number of seeds and increasing number of colors and how he talks about the forest dying and even the contained example I got the first go round but wasn't done so nicely. I don't doubt he's a great mathematician but teaching is a seperate skill and requires more focus and putting yourself in other peoples brains so to speak. however I was happy to read other dudes comment. watching it a second time and getting it more

@poiewhfopiewhf

6 жыл бұрын

+poiewhfopiewhf also how he keeps calling it a game, and never explained how the escalation in amount of seeds per tree is the maximum amount. extremely careless and confusing

@tedlemoine5587

6 жыл бұрын

He sort of assumes you know colors are seeds & that common ancestors means colors. The part he doesnt explain well is the middle can be different as long as the outer points contain the same colors n the same spots.

@flamingpaper7751

6 жыл бұрын

Thomas Cheng It's an extremely compacted topic. They hardly touched on ir

TREE(TREE(3))

@Nylspider

4 жыл бұрын

Boi

I like to think of regression as "the line thru the swarm", no matter the dimension. Clustering and classifications seems like two of the same kind, like grouping, involving defining and then applying. Both being a question of group fit. Anyway, the method presented is provingly the way to go. Nice graphics too!

I feel like if I played that tree game with 3 seeds, I would get stuck very quickly and surmize that Tree(3) is like 50 or so lol

@R3cce

3 ай бұрын

yeah, you could end the game early if you want to but the longest game you could play is this TREE(3) which is unimaginably big

I know this might be crazy but do you know that 2 and 5 are the 1st and 3rd primes? When you divide by them, it's guaranteed to terminate. Maybe the TREE(3)-ith prime is somewhat divisible by a lot of numbers... Now I don't mind if this is irrational but it's me!

@Tulanir1

Жыл бұрын

The TREE(3)th prime is by definition not divisible by any number except itself and 1. It's a prime number.

imagine the number "TREE(3)" representing the number of nodes allowed. So, TREE(TREE[3])

@ValexNihilist

3 жыл бұрын

You need to stop.

@aronclaro2133

3 жыл бұрын

What have you done

@MrWillsonx

3 жыл бұрын

this Nummer would be SO big we couldnt even *Imagine* it i think

@mariafe7050

3 жыл бұрын

TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))

@xenotronia6681

2 жыл бұрын

@@MrWillsonx we can't imagine this one either

TREE(3) is the number of years I will have to wait before seeing my favorite rugby team become world champions. Friendships from France

I just wish that people who study these mesmerizing stuff of maths, have an amazing life :)