Supporting #TeamTrees on a quest to plant 20 million trees - www.teamtrees.org/ Original brown papers from this video available to support the campaign - bit.ly/brownpapers

@yubullyme2884

4 жыл бұрын

Numberphile you should do tree 20 million

@whatisthis2809

4 жыл бұрын

Tree(20,000,000)

@altfist

4 жыл бұрын

Oh can you do a video on SCG(13)?

@whatisthis2809

4 жыл бұрын

*_ＷＨＹ ＩＳ ＴＨＥＲＥ ＩＮＦＩＮＩＴＥ ＦＩＮＩＴＥ ＮＵＭＢＥＲＳ?!_*

@whatisthis2809

4 жыл бұрын

More googology please :3

"TREE vs Graham's Number" is basically clickbait for mathematicians

@Adraria8

4 жыл бұрын

I mean yeah it’s clickbate but in fairness they weren’t lying

@Danilego

4 жыл бұрын

TREE won by a landslide... A landslide of orders of infinities!

@undercoverdetective463

4 жыл бұрын

no coz if u know this its obvious whats bigger and u gain nothing new from the vid. but people who didnt knew can gain something

@bsinita_wokeone

4 жыл бұрын

I'm not mathematically smart.......but i due enjoy learning about big numbers and I mean BIG numbers like the ones larger than the ones in this video. Like Fish number, etc

@edghe119

4 жыл бұрын

The Gogeta vs Broly of the math world

19:15 - “if omega’s so great, why isn’t there an omega 2, huh?” 19:20 - “oh ok I’ll shut up now”

@sugarfrosted2005

4 жыл бұрын

Incidentally, this doesn't work for uncountable ordinals, like omega_2.

@godoverlordquacken4003

4 жыл бұрын

*Omega timea 2 wants to know your location*

@want-diversecontent3887

4 жыл бұрын

sugarfrosted Yeah, it only works up to ε_0. (ω^ω^ω^ω^...)

@ObjcetSohwRael

3 жыл бұрын

Wut about cantor's ordinal?

@PanduPoluan

18 күн бұрын

Omega acting all gangsta until Epsilon arrives.

A couple years ago, I planted a tree After one year, it was 1m tall After two years, it was 3m tall How tall will it grow in year 3?

@scoutgaming737

2 жыл бұрын

We are gonna die

@petergriffinhentai4724

2 жыл бұрын

Sit on top if you want to evade tax forever

@it_genfailure

2 жыл бұрын

* tree pierces the outer shell of the universe *

@OllyGucci

2 жыл бұрын

@@petergriffinhentai4724 lol

@super-awesome-funplanet3704

2 жыл бұрын

Can you please show me a spread sheet with the heights that the tree has had Not just exactly 1 year after you planted it and exactly 2 years after you planted it but also provide values between 0 years after you planted it and 1 year after you planted it and values between 1 year after you planted it and 2 years after you planted and all the way to now. Ps it should not be too hard to figure out the heights for whole numbers like 0,1,2,3,4... even if some of them you have to use a weird mathematical function to show the answer (Like even weirder than power towers.).

5:16 "You're giving the TREE more juice". This was the funniest, most succinct way to describe the same intuition I had!

@dialecticalmonist3405

2 жыл бұрын

I'm not sure what the term is for "rate expansion". For now "rate expansion" = juice.

@flagmuffin1221

2 жыл бұрын

Juicing the equation

@adarshmohapatra5058

2 жыл бұрын

I thought of it like this. The tree function gives much larger values than the g function. So at the enormous scales that we're talking about, all that matters is what is inside the tree function. So tree(g64) is better than g(tree(64)) because you're giving a bigger number to tree. It doesn't even matter what g is doing at this point.

@bigpopakap

2 жыл бұрын

...in other words, giving the juice to TREE, not g 😉. Give that tree more juice!

@namelastname4077

2 жыл бұрын

some would say he gave it more sauce, not juice

Remember this meme? Marvel: Infinity War is the most ambitious crossover in history. Numberphile: TREE(Graham’s Number).

@MuzikBike

4 жыл бұрын

Nah, let's do TREE(TREE(TREE(...TREE(g64)...))), where TREE is repeated G64 times.

@sinom

4 жыл бұрын

@@MuzikBike why stop there? why not repeat it TREE(G64) times? Or TREE(TREE(G64)) times?

@Theboss24611

4 жыл бұрын

Or just the crossover of Numberphile and Mr Beast.

@simohayha6031

4 жыл бұрын

@@sinom how bout ∞?

@ganaraminukshuk0

4 жыл бұрын

What if we planted TREE(g64) trees?

If each of my brain cells was a brain, lets just call that an omega brain, I still wouldn't understand this.

@BaldAndroid

4 жыл бұрын

This makes my brain feel like it is a brain cell.

@jonadabtheunsightly

4 жыл бұрын

Yeah, but what if each of your brain cells contained as many brains, as your brain has brain cells? No, wait, what if each of your brain cells contained as many brains, as the number of possible permutations on the set of all brain cells in all of the brains in all universes real and imaginary? No, wait, what if all brains were like that, and then what if each of your brain cells could produce that many new brains per nanosecond, for each possible permutation on the set of all of the brain cells in all of those brains?

@dahemac

4 жыл бұрын

😂

@U014B

4 жыл бұрын

If I had a TREE(g(Γ₀!))-brain for every 1/(TREE(g(Γ₀!))) Planck Volume within the known universe (let's just call that a Ж-brain), and then had Ж Ж-brains for every one of those, I would probably die.

@timothymonk1356

4 жыл бұрын

@@jonadabtheunsightly Even if each of those brains had the combined capacity of the greatest scientists in the history of humanity, you still wouldn't come close to comprehending these numbers

"But I don't need to stop!" He's gone mad with power.

@anhbui-bc4ew

2 жыл бұрын

don;'t

@oz_jones

2 жыл бұрын

*math

@hardnrg8000

2 жыл бұрын

@Nicholas Natale yes.

@finnnaginnn

Жыл бұрын

I've gone madder.

@PC_Simo

7 ай бұрын

Yes. Next, he’ll go mad with tetration. 😅😮😨😱🤯

So sure, Tree(Graham’s Number) is big. But I have just been exploring the harmonic series (1 + 1/2 + 1/3 + 1/4 + 1/5 …). It is divergent. It takes around 10^43 terms just to get it to sum to a hundred, and it gets way way slower after that. So my number (‘Geoff’s Number’ if no one has claimed this before) is: “The number of terms required for the harmonic series to sum to Tree (Graham’s Number)”.

@prod_EYES

Жыл бұрын

Pin this comment

@hybmnzz2658

Жыл бұрын

The amount of terms needed is approximately e^(Tree(Grahamsnumber)-gamma) where gamma is the euler mascheroni constant

@GeoffBeggs

Жыл бұрын

@@hybmnzz2658 I’ll have to take your word on that. Sounds big.

@rafiihsanalfathin9479

11 ай бұрын

@@GeoffBeggswell 1+1/2+1/3+...+1/n approximately ln(n)+euler m constant and the approximation gets better and better the larger the n. Because tree(g(64)) is so massive, e^(tree(g(64)-euler m constant) number of term is super sccurate approximation

@StoicTheGeek

11 ай бұрын

@@GeoffBeggs yes, it is the same size as TREE(Graham’s number). When you are dealing with numbers this big, raising them to a power doesn’t make much difference.

Aleph-null bottles of beer on the wall, aleph-null bottles of beer, take one down, pass it around, aleph-null bottles of beer on the wall.

@ThorHC11

4 жыл бұрын

Best part is that "aleph-null" has the same number of syllables as "ninety-nine." So the rhythm keeps up!

@naresu

4 жыл бұрын

that's a lovely one

@InsertPi

4 жыл бұрын

unfortunately subtraction isn't defined for infinite cardinals

@nate_storm

4 жыл бұрын

Infinity (aleph null) minus one is infinity

@pst9056

4 жыл бұрын

Klein bottles?

Now this video lives up to the name Numberphile.

@MrBlaDiBla68

3 жыл бұрын

Indeed, in math, chess, soccer and boxing, *drive* is important to "win" ;-)

This is absolutely the best explanation I've seen of just how much more massive TREE(3) is than g64.

@AymanTravelTransport

11 ай бұрын

If you look at it through the levels of googology: level 0 is all the single digit and small numbers tending to zero; then level 1 goes from double-digits to a million; then level 2 goes beyond this all the way to a million digits (yes, googol and virtually every number we can practically deal with in our observable universe doesn't even get past level 2); level 3 starts entering the realms of tetration with googolplex and the likes; level 4 goes well beyond googolplexian and so on. You can see how going up just one level in the realms of googology gets to even greater magnitudes much further away than the levels before it. Well, G1 sits around level 6 or 7 and then G64 is much further at level 12, with fw(n) starting here or the level before it (11) let that sink in. So you can see that the difference between 12 levels is the difference between mere counting and shooting past G64 by iterating the number of arrows. Now you run through all the ordinals from omega through epsilon, zeta, eta until you reach the insane gamma-zero; the latter is all the way up to level 100 in the fast-growing hierarchy, meaning that counting to even G(G(...G(64))) [G64 iterations] would be much faster than using the G(n) function (or even f-epsilon0 for that matter) to reach the monsters produced by fgamma-zero(n). However, even then TREE(3) would laugh at this, as it's all the way up in level 120. That's right, an entire 20 levels ahead of fgamma-zero(n), which is insanely further apart than 0-1 and G64 which is merely 12 levels. This means even using fgamma-zero(n) to reach TREE(3) would be much slower (which is still an understatement) than merely counting to G64, even if you were to count in base 1/G64.

It's crazy that such a simple "game" to explain, like TREE(n), which you may easily explain to even a first grader, is so insanely more powerful than even Γ₀, which requires pretty advanced mathematics to even begin conceptualizing. Mathematics is beautiful!

@R3cce

Жыл бұрын

TREE(n) lies between the SVO and LVO in fast growing hierarchy. The SVO is lower bound and LVO the upper bound. It is much closer to the SVO but slightly faster than that

@R3cce

Жыл бұрын

The SVO and LVO is just ridiculous just to let you know. If you want i can link a video to explain these ordinals. Then you will understand why Tony said in the video that anything beyond gamma gets messy😂😂

@bdjfw2681

Жыл бұрын

@@R3cce sound fun , link pls.

@AymanTravelTransport

11 ай бұрын

@@R3cce If you look at it through the levels of googology: level 0 is all the single digit and small numbers tending to zero; then level 1 goes from double-digits to a million; then level 2 goes beyond this all the way to a million digits (yes, googol and virtually every number we can practically deal with in our observable universe doesn't even get past level 2); level 3 starts entering the realms of tetration with googolplex and the likes; level 4 goes well beyond googolplexian and so on. You can see how going up just one level in the realms of googology gets to even greater magnitudes much further away than the levels before it. Well, G1 sits around level 6 or 7 and then G64 is much further at level 12, with fw(n) starting here or the level before it (11) let that sink in. So you can see that the difference between 12 levels is the difference between mere counting and shooting past G64 by iterating the number of arrows. Now you run through all the ordinals from omega through epsilon, zeta, eta until you reach the insane gamma-zero; the latter is all the way up to level 100 in the fast-growing hierarchy, meaning that counting to even G(G(...G(64))) [G64 iterations] would be much faster than using the G(n) function (or even f-epsilon0 for that matter) to reach the monsters produced by fgamma-zero(n). However, even then TREE(3) would laugh at this, as it's all the way up in level 120. That's right, an entire 20 levels ahead of fgamma-zero(n), which is insanely further apart than 0-1 and G64 which is merely 12 levels. This means even using fgamma-zero(n) to reach TREE(3) would be much slower (which is still an understatement) than merely counting to G64, even if you were to count in base 1/G64.

@R3cce

11 ай бұрын

@@AymanTravelTransport According to Googology, the TREE sequence has the ordinal of (SVO times Omega) in the fast growing hierarchy

Every other KZreadr: "let's plant 20,000,000 trees!" Numberphile: “let's plant TREE(Graham’s Number)!”

@AlabasterJazz

4 жыл бұрын

Not enough matter in the conceivable universe to plant that many trees

@ABaumstumpf

4 жыл бұрын

i would highly advise against turning the entire observable universe into to strange matter with more than tree(3) trees in every possible location..... Also it would cost a lot of money.

@Ken-no5ip

4 жыл бұрын

BACHOMP There probably isnt enough quarks to reach that number

@ABaumstumpf

4 жыл бұрын

@@Ken-no5ip in the entire observable universe, filled to the limits of the pauli exclusion principle, would not be nearly large enough. Those numbers are just too insanely large.

@theheckl

4 жыл бұрын

that factorial at the end

Last time on Number Ball Z! Graham’s Number: “It’s no use, he’s too strong!” TREE (3) : “We have one option. We have to combine!”

@nowonmetube

4 жыл бұрын

@Nix Growham

@omri9325

4 жыл бұрын

It's not even his final form!!

@omri9325

4 жыл бұрын

It's over 9,000!

@Redhotsmasher

4 жыл бұрын

@@omri9325 WHAT 9000?!

@imveryangryitsnotbutter

4 жыл бұрын

@@omri9325 I mean, you are technically correct.

I love that he sounds like a mad scientist while talking about the function growth. Mathematicians working with these impossibly large numbers definitely feels like the mathematical equivalent of reading from the Necronomicon or discovering the sunken city of Ry'leh. Finding something that was not meant to be found

@joeblog2672

7 ай бұрын

Ah but then man would never have learned how to fly, rocketed to the moon and back or explored the ocean's deepest expanses (in a safe submersible!). All of these were said to be impossible throughout history. As a species gifted with reason (though not always accepted) we must stride boldly towards new humility for humility is always the beginning of knowledge! That said, these math guys are just plain out of their gourds here!

@thebaconguy1661

6 ай бұрын

@@joeblog2672safe submersible..

Man I love this guy's charisma, he's so genuine.

@notmarr2000

Жыл бұрын

His book is amazing as well: "Fantastic numbers and where to find them."

@fernandourquiza4593

Жыл бұрын

@@notmarr2000 can you like this comment just to remember myself to buy it?

@notmarr2000

Жыл бұрын

@@fernandourquiza4593 the book is utterly mind blowing. I am half through (last chapter "Graham's Number, current chapter TREE (3)). The book is more than about math - he gets into a lot of physics, the concept of how big would the universe have to be before you would find an exact double of yourself, is the universe that big? Ect.

@SyenPie

8 ай бұрын

@@fernandourquiza4593 4th like after 8 months just checking in if you bought it 😄

I remember, on the schoolyard, when the biggest number was “a BAZILLION”🤯

@boudicawasnotreallyallthat1020

4 жыл бұрын

Bazillion + 1.

@xexpo

4 жыл бұрын

@@boudicawasnotreallyallthat1020 I don't mean to obliterate you.. but I raise you 2 bazillion.

@teriww

4 жыл бұрын

....2 bazillion plus infinity🙀🙀🙀🙀

@user-fk6cb9en8v

4 жыл бұрын

@@xexpo 2 bazillion-fantastillion

@wallonice

4 жыл бұрын

I remember it being "uncountable"

_looking at all the youtubers making tree videos_ "Oh yeah. It's all coming together."

@jinjunliu2401

4 жыл бұрын

although some trees were probably harmed due to the amount of brown paper used here

@Snort70

4 жыл бұрын

Hey it’s me you stole my comment cool idc

@Snort70

4 жыл бұрын

Germaphobe I don’t care tho

@carbrickscity

4 жыл бұрын

Nothing beats this one since pretty sure none of the others could come up with something like TREE(3)

It's amazing that even without the ordinal Mathematics, we can still tell that TREE function grows (way) more quickly than Graham's function. TREE(n) literally goes from 1 to 3 to something that is way way way way way bigger than Graham's number, while G(n) needs 64 layers to go from 3^^^^3 to Graham's number. It's absolutely safe to say that at least the numbers G(1) to G(64) are all within the gap between 3 and TREE(3). The jumping between G(n) is essentially stationary compared to that between TREE(n).

@PC_Simo

Жыл бұрын

Exactly 👌🏻.

@caringheart34

Жыл бұрын

G(0) is also 4 so basically the entire graham sequence

@PC_Simo

Жыл бұрын

@@caringheart34 I thought the same thing 🎯.

@R3cce

Жыл бұрын

@@PC_SimoTREE(n) grows at a rate between the SVO and LVO in fast growing hierarchy. These ordinals are beyond gamma. I can link a video to explain these ordinals if you want. You will then understand why Tony said in this video that anything beyond gamma gets messy😂

@Empiro3

10 ай бұрын

Things can start slowly then get really big later though. Tree is still a computable function. The Busy Beaver function has pretty reasonable values for small values, but it grows much faster than any computable function.

I love how mathematicians get to a point where they're so smart they start making up numbers a 5 year old would spout off and then act profoundly amazed by a finite number within infinity.

@homer4340

6 ай бұрын

Mathematicians after creating the number galleohalivitoxipityisnlotopiscisis22: 😮

"Anything beyond gamma zero gets really messy." Yes, all was beautifully in order before then ;)

@TheAlps36

3 жыл бұрын

Ironic that they're called "ordinals"

@chaohongyang

2 жыл бұрын

I can confirm this, many post gamma zero notations are off the scale complex for new people to understand

@The360MlgNoscoper

2 жыл бұрын

Gamma gamma zero (;

@j.hawkins8779

2 жыл бұрын

@@chaohongyang actually, its ridiculously easy to go past it.

@scathiebaby

2 жыл бұрын

@@j.hawkins8779 Add 1

Is it me, or does 20 million suddenly sound like a pathetically small number

@sadhlife

4 жыл бұрын

time to plant TREE(3) trees

@anixias

4 жыл бұрын

Time to plant TREE(TREE(TREE(....tree(64) times...))) trees

@yvesnyfelerph.d.8297

4 жыл бұрын

120million digits sounds like nothing at all, given what they are looking at

@DirtyRobot

4 жыл бұрын

That's basically a day's worth of disposable chopsticks in China. Thanks internet, Now Chinese can enjoy eating for an extra day.

@schenkov

4 жыл бұрын

Actually first thing I thought when I heard about that project was:"20 million threes are not so much at all"

21:17 you can’t fool me, you’re just drawing squiggles now

This is the most intense AND my favorite part of this whole channel.

"This is starting to terrify me now." "But I don't need to stop!"

@jolez_4869

4 жыл бұрын

ITS TIME TO STOP

@ValexNihilist

3 жыл бұрын

@@jolez_4869 laughed too hard at that

@renanmaas3502

3 жыл бұрын

That guy: Reaches an Unthinkably fast growing function that starts to bend the fabric of space-time. Also That guy: i CaN CArRy oN...

@TheAlps36

3 жыл бұрын

Please...please stop. In the name of sanity please stop

@Parasmunt

Жыл бұрын

Don't go into the TREES stop stop.

Brady's "more juice power" proof. I like it.

@DFPercush

4 жыл бұрын

Graham-ade, it's got what TREE craves!

@bigpopakap

4 жыл бұрын

it's rigorous enough for me!

@PC_Simo

7 ай бұрын

So do I 🧃. P.S. You’re welcome for your 512th like. 👍🏻

@PC_Simo

7 ай бұрын

@@DFPercush Exactly 👌🏻🎯😅.

@PC_Simo

7 ай бұрын

@@bigpopakap Same here 😌.

"512, quite big number" 7:10

@LeBronJames-sj7ds

3 жыл бұрын

LOLOLO

@dylanmcadam8509

3 жыл бұрын

Compared to the number in this video there is like no difference between 512 and -googleplex

I'm at just over 14 minutes and am going to have to rest my mind and finish this tomorrow. Have just watched the 2 videos on tree(3) beforehand. This feels like staring into the abyss and it's rather terrifying, and as well, my mind feels like it's melting down from struggling to comprehend such enormity. Who knew that maths could get kind of terrifying?!

They pulled out ordinal collapsing functions on us. They really brought the big guns for this fundraiser.

@AndrewBlechinger

4 жыл бұрын

And yet they didn't get to Aleph-one

@DarkestValar

4 жыл бұрын

A Large countable ordinal, but not quite an ordinal collapsing function.

@imperialguardsman135

4 жыл бұрын

Ordinal what?

@Peter_Schluss-Mit-Lustig

4 жыл бұрын

Well they didn't even talk about fundamental sequences

@ig2d

4 жыл бұрын

It's all about the juice

“Well, the problem is that you’re just dealing with finites.” This problem is indeed found in so many situations.

@etfo714

4 жыл бұрын

Newton/Leibniz be like this when inventing calculus.

@antonhelsgaun

3 жыл бұрын

A problem when looking at my account balance

@dAvrilthebear

2 жыл бұрын

I encounter this problrem when paying for my gaughter's tutors)

@douche8980

2 жыл бұрын

Sounds like a racist statement :(

@miaomiaochan

Жыл бұрын

The only finite thing that's a problem is the finite nature of human intelligence.

the thing I dislike about numberphile is that they never explain how people figured out anything and so you're just left feeling as though you didn't really learn anything but instead just heard of something

@smallkloon

Жыл бұрын

I agree, but I understand why they don't.

@douche8980

Жыл бұрын

Its pretty easy for folk like me with an IQ of 80 so these folks with IQ nearly fifty percent higher can understand these numbers and the growth rate by which numbers are made. That is true but the FGH they mention in this video is like addition compared to the highest ordinal they mentioned ok said video. This process goes on for infinity. So absolutely infinity can't exist since there is more than an infinite amount of such.

It was quite intuitively obvious to me that Tree(n) was way bigger than g(n), the best way I can describe is that 3 is the first number in the Tree sequence to unlock it's full power, as you always have a first sacrificial colour, so you're kinda playing the game with n-1 colours. 0 colours for n=1 obviously stops, 1 colour for n=2 also has to fundamentally stop really quickly, but for n=3 you finally have 2 colours to play with. If 2 colours already gives the illusion that Tree(3) might be infinite at first glance, and remember this is the first "real" amount of colours to unlock the Tree game, then it only follows that this graph is exploding quicker with any more colours to play with from that point than anything you can make with normal iterations of mathematical functions, no matter how awesome a way you have to write them to become really big.

@PC_Simo

Жыл бұрын

Also, you only have to climb up to the 3rd branch of the TREE-function to already be off-the-scale massively higher, than g(64), which is the 64th rung on Graham’s ladder.

@AymanTravelTransport

11 ай бұрын

@@PC_Simo If you look at it through the levels of googology: level 0 is all the single digit and small numbers tending to zero; then level 1 goes from double-digits to a million; then level 2 goes beyond this all the way to a million digits (yes, googol and virtually every number we can practically deal with in our observable universe doesn't even get past level 2); level 3 starts entering the realms of tetration with googolplex and the likes; level 4 goes well beyond googolplexian and so on. You can see how going up just one level in the realms of googology gets to even greater magnitudes much further away than the levels before it. Well, G1 sits around level 6 or 7 and then G64 is much further at level 12, with fw(n) starting here or the level before it (11) let that sink in. So you can see that the difference between 12 levels is the difference between mere counting and shooting past G64 by iterating the number of arrows. Now you run through all the ordinals from omega through epsilon, zeta, eta until you reach the insane gamma-zero; the latter is all the way up to level 100 in the fast-growing hierarchy, meaning that counting to even G(G(...G(64))) [G64 iterations] would be much faster than using the G(n) function (or even f-epsilon0 for that matter) to reach the monsters produced by fgamma-zero(n). However, even then TREE(3) would laugh at this, as it's all the way up in level 120. That's right, an entire 20 levels ahead of fgamma-zero(n), which is insanely further apart than 0-1 and G64 which is merely 12 levels. This means even using fgamma-zero(n) to reach TREE(3) would be much slower (which is still an understatement) than merely counting to G64, even if you were to count in base 1/G64.

The paper change is the real reason we watch this channel.

@BobStein

4 жыл бұрын

Yep. That joke's got layers, man.

@AndrewTyberg

4 жыл бұрын

Ummm... Not true....

@pleasuretokill

3 жыл бұрын

It's the one thing here I can comprehend

@Ishub

2 жыл бұрын

@@pleasuretokill same

@waldothewalrus294

6 ай бұрын

The jingle on it keeps me living

12:28 My brain just collapsed into a black hole. Edit: Now after seeing the whole video, my brain collapsed into so many black holes that the number of black holes itself collapsed into a black hole and then another black hole and this happened so many times that the number describing it also collapsed into a black hole.

@goutamboppana961

2 жыл бұрын

and so onnnn

@adwitraj4923

2 жыл бұрын

P O T A T O

I love hoe much passion he has for numbers!!

"This next guy, I'm not going to write it out, because it has 121 million digits." This has to be in the top ten Numberphile videos of all time. Maybe top three even?

@nocktv6559

Ай бұрын

Top TREE

Recommended reading for the course - Vsauce's How to count past infinity.

@NoriMori1992

4 жыл бұрын

Dyani K. Seriously. That video's the only reason I had the slightest understanding of the omega stuff.

@zmaj12321

4 жыл бұрын

If I haven't already seen that video I would have no clue what I was watching.

@gdash6925

4 жыл бұрын

Yea that inspired me to watch this numberphile video.

@billvolk4236

3 жыл бұрын

Vsauce, where we give disingenuous answers to clickbaity loaded questions without ever explaining what's fundamentally wrong with them.

@dvkprod

3 жыл бұрын

@@billvolk4236 dude, what is your problem

The mathematicians went out of control, somebody please stop them

@geekjokes8458

4 жыл бұрын

NEVER

@EpicMathTime

4 жыл бұрын

no

@FrankHarwald

4 жыл бұрын

Not their fault - one of them SUPER busy beavers outta control!...

@otakuxgirl6

3 жыл бұрын

No

Vsauce: What's the biggest number you can think of? Me a googol Numberphile: Tree(g(64))

@Eric4372

4 жыл бұрын

A googolplex factorial to the power of a googolplex squared, times Graham’s number!

@srizic1136

4 жыл бұрын

@@Eric4372 To the tree(g(64))th tetration

@zzasdfwas

4 жыл бұрын

But you can always define something bigger by iteration. Tree(tree(g(64))). Or tree(tree(...n times) (g(64))). And then you can iterate that.

@haeilsey

3 жыл бұрын

zzasdfwas and then you develop notation to recursively iterate the iteration, like idk Conway chain arrows on steroids in hyperspace as the gods

@FlowiYT

3 жыл бұрын

Me: TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(TREE(g64)))))))))))

Fascinating that g and TREE are so fast growing that you need transfinite ordinals to put them in a hierarchy. This is probably the best way to convey their power.

The TREE function impresses me everytime. It's so simple yet it blows everything away.

@knightoflambda

4 жыл бұрын

Just wait, one day they'll finally explain the Busy Beaver function BB(n), which grows so fast there literally cannot exist a function that can compute any of its digits. It's insane just how fast it grows. I heard that even getting a lower bound on BB(20000) is impossible in ZFC. Of course, BB(n) is tiny compared to its relativized cousins. And we aren't even out of the lower attic yet. In the middle and upper attic, there are numbers so large that you need to add extra axioms to ZFC in order for them to exist.

@yogaardianto2269

4 жыл бұрын

@@knightoflambda what is the most faster growing fiction in googology?

@pierrecurie

3 жыл бұрын

@@knightoflambda I think they already did an episode on BB. Scott Aaronson proved that computing BB(~8000) requires proving the (in)consistency of ZFC (basically brute forces some statement that is true IFF ZFC is consistent).

@purpleapple4052

3 жыл бұрын

@@knightoflambda they mentioned and explained some Busy Beaver stuff in the video about Rayo's number

@isuller

3 жыл бұрын

@@knightoflambda actually it is true that BB(n)>TREE(n) for n>k for some k value. But my guess is that "k" is huge itself - I mean it may be bigger than Graham's number. So while it is true that BB is a faster growing function than TREE it doesn't mean that in the region of "normal" numbers BB(n) is bigger than TREE(n) :-)

David Metzler has an excellent 40 part series on the fast growing hierarchy, ordinals and much much further.

@michellejirak9945

3 жыл бұрын

I thought this was a joke until I looked it up. Well, now I know what I'll be doing for the next month.

@OrbitalNebula

3 жыл бұрын

There's also Giroux Studios

@chaohongyang

3 жыл бұрын

@@OrbitalNebula And you, btw you need to make more FGH vids, they are so damn gud

@OrbitalNebula

3 жыл бұрын

Oh yeah. I'm now actually on the progress of making the next big numbers vid. It's just taking me quite long to make.

@chaohongyang

3 жыл бұрын

@@OrbitalNebula i fully support you, do whatever you want at your own pace homie :)

one thing that i find interesting is that tree(65) is already way bigger than g(tree(64))

These big number videos make me unimaginably excited...

Never thought transfinite ordinals could be useful with something finite like sequences of integers. Amazing video!

@martinshoosterman

4 жыл бұрын

Oh man. You should look up the proof of Goodsteins theorem, using trans finite ordinals. Its a statement about sequences of numbers which is proven using ordinals.

@watcher8582

4 жыл бұрын

All the ordinals that were mentioned in this video were still countable, i.e. they can be viewed as representing a (non-standard) ordering of the natural numbers. That is to say, the transfinite ordinals play the role of intrudcing jumps (in this case the jump is taking the diagonal in the constuction of f's). As such, the cardinalities of any of those ordinals is N, and thus all still smaller than that of the reals R.

@Lexivor

4 жыл бұрын

@@martinshoosterman Goodstein's theorm is fun. The function that calculates the length of Goodstein sequences has an ordinal of epsilon_0, much bigger than Graham's, but nothing compared to TREE.

This is literally the biggest collaboration in KZread history. And it's for the best possible cause. I'm genuinely proud of this community.

@erik-ic3tp

4 жыл бұрын

Me too. This's a 10 out of 10 for Humanity today.

@googleuser7771

4 жыл бұрын

@@erik-ic3tp is 20 million trees a lot of trees?

@erik-ic3tp

4 жыл бұрын

Google User, Yes.🙂

"You're giving the tree less juice there but more juice here" The cameraman really gets the limitations of my brain power 😂

When I was in engineering classes, I would have LOVED to have him as my teacher.

Even when ignoring the awesome fundraiser, I think this is the coolest video you guys have ever made. Talking about stupidly giant numbers with no physical significance just because it’s fun. I love it, congratulations.

The amount of times I just yelled "No way!" alone in my room is only slightly embarrassing.

@austinlincoln3414

2 жыл бұрын

lol

This is one of the most mind blowing mathematical things I have ever seen. This is completely outrageous!

I’m kinda scared when a toddler says “I can count two trees!”

@xerosfs

2 жыл бұрын

_”I can count three trees!”_

@xerosfs

2 жыл бұрын

@Lakshya Gadhwal lol

TREE(g64): exists g(TREE64): Finally, a worthy opponent. Our battle will be legendary

@jolez_4869

4 жыл бұрын

TREE(TREE(3)) joins the game

@AndrewTyberg

4 жыл бұрын

But the second number is basically 0 compared to the first number.

@mapari00

4 жыл бұрын

This could be perfectly fine in the context of the quote, as tai lung thought he would defeat the dragon warrior, but in fact got stomped as if he was nothing. Later in the fight: “The Wu Shi finger hold?!?!?! Shi Fu didn’t teach you that!!!!!!!” “Nah, I figured it out. Scadoosh!!”

@isaacwebb7918

4 жыл бұрын

@@jolez_4869 Even TREE(TREE(3)) won't match SSCG(3). SSCG is for 'simple sub-cubic graph,' and it works similarly to the tree problem and resulting function, except there are fewer rules for simple sub-cubic graphs, making more graphs possible, and therefore (much, much, much...) longer sequences. SSCG(n) forms a similar sequence to TREE(n) (in that it describes maximum lengths of non-repeating sequences for a given number of tags, and in starting small and exploding by n=3), but outpaces it easily -- SSCG(3) is greater than TREE(TREE(TREE(TREE(TREE(...TREE(3)))))) -- if you nested that TREE(3) layers deep. TM,DR (Too math, didn't read) -- there's always a bigger function.

@jolez_4869

4 жыл бұрын

@@isaacwebb7918 Wow damn. Thats interesting!

You can go beyond gamma zero. f gamma zero: "This isn't even my final form!!!"

@martinshoosterman

4 жыл бұрын

Yeah. As far as I know you can go as far as f ω₁ ie, you can have f of anything smaller than ω₁ but you cannot define f for ω₁

@donandremikhaelibarra6421

Жыл бұрын

@@martinshoosterman yes but you surely can’t have an f of an inaccessible cardinal right?

@martinshoosterman

Жыл бұрын

@@donandremikhaelibarra6421 you can't even do f(omega_1) much less an inaccessible cardinal.

@donandremikhaelibarra6421

Жыл бұрын

@@martinshoosterman is the inaccessible cardinal bigger than an infinite amount of alephs nested together?

18:50 "this terrifies me... but I don't need to stop!" A true classic

I read a cool description of Graham's number somewhere, in terms of trying to picture it in universal physical terms. If my memory serves me, it went like this: It said that even the integer describing the number of digits in Grahams number could not be represented if you made every particle in the universe a digit, and the same would be true for the number of digits in THAT number, and even if you went down that "number-of-digits-in-the-previous number" scale, with each level down being represented by a single particle in the universe, you still would not able able to fit it into the known universe. I wish I could find that again.

@r.a.6459

Жыл бұрын

In fact, g(1) itself, defined as 3↑↑↑↑3, is bigger than googolplexplex...plexplex (with googolplex 'plex'es)

@vokuheila

7 ай бұрын

In fact, the number of digits in Graham's number is approximately Graham's number...

@hurricane3518

Ай бұрын

its on wikipedia

20:40 funny how its called epsilon 0 cause usually epsilon is used for small numbers

@B0b0K1w1

3 жыл бұрын

MILDLY INTERESTING

@pandabearguy1

2 жыл бұрын

Thats \varepsilon

Numberphile: Donate for Trees! Also Numberphile: USES TREMENDUS AMOUNT OF PAPER

@franzlyonheart4362

3 жыл бұрын

Entirely logical. They need many MANY moar trees for all their paper. So they ask people to fund more trees. Makes eminent sense to me!

These videos are so amusing to watch, even for a nerdy med student❤

in the first 3 hours they are past 1 Million, hope this keeps afloat for a while

@erik-ic3tp

4 жыл бұрын

It's mind-blowing what crowdfunding could do if done right.

@Veptis

4 жыл бұрын

@@erik-ic3tp it's a giant collaboration, so that is unprecedented.

@pluto8404

4 жыл бұрын

@@Veptis "collobaration" you mean the 1% sit back and take all the credit while their followers donate all the money.

@Veptis

4 жыл бұрын

@@pluto8404 no, if it weren't for those people to initiate it and produce unified content on the topic. such an effort wouldn't be possible uncoordinated.

@pluto8404

4 жыл бұрын

@@Veptis I suppose we do need a large unification to combat all the carbon their Manson's and sports cars put out.

KZread: Let's all talk about trees. Numberphile: Challenge accepted

Half this video is just Tony trying to find words to express the magnitude of these sizes, and we love it

This channel is 100x more interesting than any math class I have ever had

This was geniunely one of my favorite videos ever to have been uploaded to this channel.

Best Numberphile video in a while, but NOT for the faint of heart.

I looked up how to express TREE(3) in terms of Gx. Here is the lower bound: G3[187196]3 (compared to G3(64)3). No wonder the growth is so astounding with TREE(x).

@Dexuz

2 жыл бұрын

That doesn't seem right at all, you can't express the value of TREE(3) in a function that grows infinitely slower than the TREE(3) function, just as you can't express the value of Graham's Number in any F(finite ordinal).

@R3cce

Жыл бұрын

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

@xyz.ijk.

7 ай бұрын

​​@Dexuz I agree, but I'm reporting what I looked up, I wouldn't dare claim to have calculated such a thing!

@thefirstsurvivor

2 ай бұрын

theres no proof it's between those@@R3cce

Super fun ride here. Thanks. Had previously caught Vsauce's Supertasks video (as well as NP Graham/Tree videos). That helped my orientation as the ride got wild. Fascinating stuff.

I'm no mathematician, but thanks to your past videos I laughed out loud when I saw what this one was about, knowing we were in for another round of "STUPID big"!

For sure one of the best videos on my favorite channel. Such elegant insanity. Love it!

"The Feferman-Schütte ordinal Γ0 is the largest thing you can create using these kind of recursion methods" Me: Γ0 + 1

@laxxius

4 жыл бұрын

As far as I know you're allowed to do that.

@harryw4802

3 жыл бұрын

that's not recursion methods.

Understanding the math sequence is beyond me. But watching Tony get excited about math is so entertaining.

People: there's no way Numberphile can join the #teamtrees thing Numberphile: hold my beer

@masterimbecile

4 жыл бұрын

Hold my Klein bottle.

@yuvalne

4 жыл бұрын

@@masterimbecile darn it should have seen that joke

@TheScarrMann

4 жыл бұрын

With the amount of paper used in these videos I'd be shocked if they didn't

@triqky9301

4 жыл бұрын

Well he did use paper...

@trevorx7872

4 жыл бұрын

Hold my juice

You have combined my two favorite numberphile videos! Thank you!

These have to be the most interesting math videos I've come across. Always enjoy the pit stop to one of your videos

The fact that he describes these gargantuan functions as "this guy" and "that guy" is a nice touch

Making all these videos Brady practically became a mathematician.

Ah the iconic “Paper Change” music returns

wow today at work i ask me that question what sequence is bigger (actually) and now i find a video where u explain it perfectly!! ty so much

This is a tremendous video, thank you Brady and Ron! With TREE and G and Busy Beaver numbers, I've always wondered how to categorically compare their growth. BTW, you should totally do a video on the Busy Beaver number sequence!

Just got flashbacks to the vsause vid about ordinal numbers

@SpektralJo

4 жыл бұрын

But his video was about cradinals

@twigwick

4 жыл бұрын

same lol

@naresu

4 жыл бұрын

Was reminded about aleph

I remember the VSauce video on Ordinal Numbers and Infinities; I was prepared for this one. Still amazing that TREE grows even faster than that!

This should be a thing done every year!

This should probably be added to the “big numbers” playlist

One of the best videos of Numberphile!

So nice to see so many channels contribute to #TeamTrees

Just the fact that no finite f(n) hierarchy could describe the growth rate of Graham's number, let alone TREE(n), blows mind mind. Truly shows how unimaginably large those numbers are.

Im terrible at math but I'm facinated at how incomprehensible these numbers are and how i still feel that somehow i could fathom it knowing i never will.

This really exceeds my ability to comprehend.

@DFPercush

4 жыл бұрын

Don't worry, it exceeds the physical universe's ability to comprehend too.

Finally, a worthy opponent! Our battle will be legendary!

These videos are fascinating.

LOVED this video.

Loved this video. The like button wasn’t enough for me. I’ve always used to do this sick thing of imagining very very big numbers, steps and distances since I was 5-6 y/o and it got to a point that I had to stop doing that. This video made me feel a part of my life which I’ve never been able or tried to share with someone else. I reply “speed” when I’m asked about my favorite thing in the world, and they think I just like to drive fast. In fact, I mean exponential growth of exponential growth of .... .

@geekjokes8458

4 жыл бұрын

I understand that feeling very well... im not sure about it being my favourite, but i do get excitedly anxious, it kinda hurts, about this sort of big...ness It's so unthinkably big, profoundly and absolutely indescribable... art, it seems, like the cosmic horror style of storytelling, is the only thing that can "properly" assign some meaning to this feeling, maybe precisely because it forgoes logic. Art, and mathematics.

@erik-ic3tp

4 жыл бұрын

iUFOm, Same for me too.😊

@NoriMori1992

4 жыл бұрын

That's beautiful.

@NoriMori1992

4 жыл бұрын

Have you ever watched the Vsauce video "How To Count Past Infinity"?

@erik-ic3tp

4 жыл бұрын

NoriMori, I’ve watched it yes.🙂

Oh, I’ve missed the “Brown Paper Chronicles”. Thank you for this 😚

I'd love to see more explanation videos on these higher level infinities. Also, despite being messy, I'm so curious about what stuff comes after Gamma Zero (or f(gamma zero)! I come back to this video a lot. how big numbers can get is so interesting to me.

@R3cce

10 ай бұрын

The Small Veblen Ordinal (SVO) is the next ordinal after Gamma zero. After the SVO comes the Large Veblen Ordinal (LVO)

I've been watching David Metzler's videos and these Numberphile videos (multiple times!) and this is the first time I've understood how diagonalisation works to produce omega. Supercool!

I love the hint of fear that trickles through his enthusiasm when discussing the functions over Gamma-Naught: "We must tread lightly here, lest we disturb the Old Ones who dwell in these regions..."

This reminds of dreams I have when I have a fever... A tiny point would suddenly explode to gargantuan size, then compound upon its own size, until it filled my mind. Or marbles would arrange themselves into huge sparse, patterns while multiplying all the time....

@Crazylom

4 жыл бұрын

Newer thought there would be something so out of world and so "same" at the...same...time.

@drumroll7073

3 жыл бұрын

U are not alone. Also this dream has a very bad taste. i hate this dream for no reason...

@jpdemer5

3 жыл бұрын

That's why I stopped doing drugs.

It's been nice knowing you guys. My head is going to explode now.

15:19 "that escalated quickly" best use of that idiom ever.