Graham once gave his number to a girl. She never called him.

@kellyjackson7889

9 жыл бұрын

Untrue, she just hasn't finished dialing. . ...

@davecrupel2817

9 жыл бұрын

that's awesome xD

@NemosChannel

9 жыл бұрын

Kelly Jackson hahahaha

@davecrupel2817

9 жыл бұрын

33333333333333333333333333333333333333333333333333333333333333333333x3^333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333334

@Jesse-cw5pv

9 жыл бұрын

Ivan & Fritz you wouldn't be able to press that many numbers in a googleplex number of lifetimes even if you could press a googleplex keys every billionth of a second. You wouldnt even get to g1

"somewhere between 13 and graham's number" is one of my favourite phrases now.

@mvmlego1212

8 жыл бұрын

That and the Parker Square.

@HotSauceBear

7 жыл бұрын

"How old are you?" "How many pieces of chicken would you like?" "How many times are you going to use that phrase?" "Somewhere between 13 and Graham's number."

@davecrupel2817

7 жыл бұрын

we've pretty much nailed it, as far as I'm concerned.

@starbeta8603

6 жыл бұрын

All of a sudden, its proved grahams number + 1 can be possible without making that pattern....

@wanderingrandomer

6 жыл бұрын

A card in Cards Against Humanity: Mathematician Edition

B: "What do you want the first digit to be?" R: "Well in binary it's 1!" Clever guy, lol

@vidareggum6118

4 жыл бұрын

Brian Bethea a very nice understatement I think😊

@E1craZ4life

4 жыл бұрын

In base 3, it’s 1 followed by a loooooooooooooooooooong line of zeroes.

@NStripleseven

4 жыл бұрын

Niiiice.

@markiyanhapyak349

3 жыл бұрын

SUPER. UNIMMAGINABLY *SUPER.*

@hexagonist23

3 жыл бұрын

Depends on where you put the MSB

At 3:27 when Graham said "You ain't seen nothing yet.", I knew i was boutta see some THICC numbers.

I think infinity is easier to imagine than this number.

@yahya092

8 жыл бұрын

ILikeWafflz i think thats because infinity is more of a concept instead of a number

@julian7801

8 жыл бұрын

well, you should read about a number called TREE(3). It is so vast that the numbers of arrows needed to reach it is close of TREE(3) itself. This even holds for much smaller number such as Hydra(100), 3&3&3 (Triakulus) and much larger number like BH(100), SCG(13), Loader's number, BB(1000), Xi(10^6) or Rayo(10^100)

@georgeofhamilton

8 жыл бұрын

Fluorosulfuric Acid It cannot be that the number of Knuth's arrows needed to reach TREE(3) is close to TREE(3) itself.

@julian7801

8 жыл бұрын

George Hamilton its exactly what I said :V

@georgeofhamilton

8 жыл бұрын

Fluorosulfuric Acid "[TREE(3)] is so vast that the numbers of arrows needed to reach it is close of TREE(3) itself." Unless you are using a rather arbitrary definition of _close_, your statement is not possible because the function of Knuth's arrows increases numbers by so much.

Graham's wife: "Stop your work and get in the kitchen! I made spaghetti!" Graham: "No! Just ONE MORE ARROW!"

@ILikeWafflz

9 жыл бұрын

StarTrek123456 LOL

@Yumiesthetic

8 жыл бұрын

StarTrek123456 xDD

@kellyjackson7889

8 жыл бұрын

+StarTrek123456 They eat in the kitchen? Where do they cook the food, the bathroom? :D

@slap_my_hand

8 жыл бұрын

Kelly Jackson I have a big table in the kitchen, so i eat there. The only other table i have is in my living room, but i am too lazy to take my food there :D

@cochaviz

8 жыл бұрын

+StarTrek123456 Gawd you made my day xD

This gave me a lot of existential dread

@mackan2277

3 жыл бұрын

I didn't expect my favourite terraria youtuber here :o

@mille7476

3 жыл бұрын

@@mackan2277 I didn't expect my favorite Terraria youtuber or another Swede (tror jag iaf) here

@babyrockproductions7094

3 жыл бұрын

HeIIo

@rioann7167

3 жыл бұрын

E

@ingmarins

2 жыл бұрын

Because this is the top comment, it made me hear music. You know what music😁

You can't even imagine a 4-dimensional world, right. So imagine a world with Graham's number of dimensions

@mfhasler

5 жыл бұрын

well, we do live in a 4-, not 3-dimensional world! We're just not very able to control our movement in the 4th direction and therefore mostly "float" in positive t-direction with more or less uniform speed. (And there are probably 6 - 20 more "hidden" dimensions which are so tighly wrapped up that we'll never notice them...) Yet I agree, that' not much compared to g64.

@Fallkhar

4 жыл бұрын

Well, I'm pretty sure spheres of Graham's Number of dimensions would be pretty inefficient at stacking!

@buzzsawenthusiast1756

4 жыл бұрын

No.

@davecrupel2817

4 жыл бұрын

STOP MAKJING MY HEAD HURT!!

@tzakl5556

4 жыл бұрын

@@mfhasler dimensions in math and not physics are spatial dimensions so time wouldn't count

"You ain't seen nothing yet" True words from a man who has wrapped his head around things that most everyone can't hope to understand

@markiyanhapyak349

5 жыл бұрын

*YES!* 2🙏🏻 ↑(🙏🏻+ 🙏🏻 +🙏🏻 )↑2(🙏🏻 ²🙏🏻³ +10🙏🏻)↑3 🙏🏻

@user-lk1kv6tf2j

4 жыл бұрын

3^^.........^^3

I really liked the part where he said "three"

@JorgetePanete

6 жыл бұрын

Iron Dorito three through the three to the three

@davecrupel2817

6 жыл бұрын

Your comment is 20 likes away from being appropriate (313 likes when i made this comment

@moadot720

6 жыл бұрын

3 replies......................until I came XD

@ozyf

6 жыл бұрын

I would like this comment, but it has 333 likes and I don’t want to ruin it :)

@commoncoolchannel8588

5 жыл бұрын

Don't worry: it has 424 likes. Make that 425 likes.

Graham's number in base Graham's number: 10

@fakefury1198

6 жыл бұрын

I love it. :) Base 11???

@vighnesh153

4 жыл бұрын

It is 1

@Exploshi

4 жыл бұрын

@@fakefury1198 grahams number plus g64^0 or grahams number plus 1

@VivekYadav-ds8oz

4 жыл бұрын

@@vighnesh153 No. x in base x is always 10. 2 in base 2 is 10. 16 in base 16 is 10 (A).

@keonscorner516

4 жыл бұрын

@Graham's Video World What about 10^10bk^(10^bk)?

“You ain’t seen nothing yet” Said after the number is too large to be on the screen or even imagine.

Well, that escalated quickly.

@RollOnToVictory

8 жыл бұрын

Zekzram Reshirom i mean that really got out of hand

@Myrslokstok

9 күн бұрын

Then do that 64 times, even dubble 64 times is huge!

"So, there you go. Graham's number. And if you think you understand it, you probably don't." 😂

@YnseSchaap

7 жыл бұрын

Bit patronizing I thought

@ChristopherKing288

7 жыл бұрын

+Ynse Schaap I think he means no one understands it.

@YnseSchaap

7 жыл бұрын

Christopher King Well Graham obviously does ;-)

@davecrupel2817

7 жыл бұрын

+Ron Volkovinsky mind being precise when quoting the professor, please?

@stevenvanhulle7242

7 жыл бұрын

+Ynse Schaap - I'm pretty sure he doesn't either. Nobody can even conceptualize small numbers like a googol. Write them down, yes. Calculate them, yes. Understand them, no.

3:27 mathematecian goes beast mode

What a legend Ron graham you will be missed

@kevinnguyen552

3 жыл бұрын

He died?

@austinlincoln3414

2 жыл бұрын

Yes I think he did

@jasperthompson9759

2 жыл бұрын

@@kevinnguyen552 yes. Sadly, he passed away on the 6th of July 2020

@deleetiusproductions3497

7 ай бұрын

I didn't even know he died until recently.

"It's a number so big, we had to use Comic Sans." - editor

@suwinkhamchaiwong8382

4 жыл бұрын

Ralph Anthony Espos yes

New use for Graham's number - counting the number of times in his life Graham has said the word 'three'

@aboodyboi

8 жыл бұрын

He talks like a bot tbh

@darkunicorn6669

8 жыл бұрын

+The True Fizz nothing can ever be compared to grahams number realistically that's how phenomenally enormous it is :)))))))

@NKP723

8 жыл бұрын

+The True Fizz 3 to the 3 to the 3...

@davecrupel2817

7 жыл бұрын

cause 3 is a word :|

@NotQuiteFirst

7 жыл бұрын

+Daniel Cannata I said the word "three", which is a word. "3" is a number, but when he speaks it he is saying the _word_.

July 8, 2020, RIP Ron Graham, the big number man...

@TheSmegPod

3 жыл бұрын

Wait what

@jjcika7504

3 жыл бұрын

He died?

Here's the prime factorisation of Graham's Number: 3x3x3x3x3...x3

@AC-fl1le

4 жыл бұрын

But 5 can go into (G64 - 2) because the last digit is 7 and 7 - 2 is 5, so (G64 - 2) isn't prime.

@Xonatron

3 жыл бұрын

Ohhhhh. Nice.

@alihesham8167

2 жыл бұрын

@@AC-fl1le he said G64 not (G64 - 2)

@peterwille8239

2 жыл бұрын

Onyuhhno

@peterwille8239

2 жыл бұрын

Huygcduyhrifdrdfjgfkngkrjjgibghehfrjukrfji(jijmjihdr

whats the leading number? "in binary, its 1" LOLLED

@arielsproul8811

6 жыл бұрын

it has to be lead by a one in binary

@MuddyPuddle

6 жыл бұрын

Ariel Sproul That's the joke

@linh4010

5 жыл бұрын

last digits in base 2 is 1

@maulwurf9414

5 жыл бұрын

Ariel Sproul r/whoosh

Legend has it he's never stopped saying "3 to the 3 to the 3 to the 3 to the 3 to the 3..."

@oz_jones

5 жыл бұрын

Justin Ly i wonder how many lifetimes of our universe it would take if you could say 3 to the 3 every second

@mike-gx1sc

5 жыл бұрын

@@oz_jones a number close to Graham's number

@markiyanhapyak349

5 жыл бұрын

Osmosis Jones: :-| (!!!!!!!!!!). As much as He would live.

@gaurangagarwal3243

4 жыл бұрын

@@oz_jones well I know the no of lifetimes you would take is 3 to the 3 to the 3 to the three to the...

@dozenazer1811

4 жыл бұрын

I want to see 10h version of this

The first time i watched this, a few years ago, i thought there was only 64 arrows. Now understanding it better actually hurts my brain

@knuthalvorsen1196

2 жыл бұрын

Same.

@achtsekundenfurz7876

2 жыл бұрын

And if I'm not mistaken, they still understated the size of even 3↑↑↑3 at 03:07 . 3↑↑↑3 is a power tower of ~7.6 trillion 3's. Well, 3^3^3 (powers are evaluated top to bottom if there are no parentheses) is 3^27, about 7.6 trillion. So, 3 to that power is a bit less than the square root of 10 to that power, which would have 7.6 trillion digits. THAT number has 3.6 trillion digits already, and it's only a power tower of height 4. 3↑↑↑3, power tower of height 3^3^3 is unimaginably huge, and you need another arrow before even starting _Grahamization_ , the process of using G(n) arrows to define G(n+1). 3↑↑↑↑3 is far, _far_ below 3↑↑↑...↑↑↑3 (with 64 arrows), which is in turn tiny compared to the second step, G(2). And THEN, there are another 62 (or 63?) steps to come. BTW, literature about Grraham's number is highly contradictory, often with itself. Some say that 3↑↑↑3 is the starting point G(0), others say it's 3↑↑↑↑3 (with another arrow, like Graham himself did). Then, some treat one of the above as G(0), others as G(1) (and G(0) would be either 3 or 4). Nevertheless, the last number in the sequence is huge beyond comprehension either way.

@Parasmunt

2 жыл бұрын

@@achtsekundenfurz7876 I got that too.7 trillion digits which they have written down for it is nothing compared to a number with trillions of towers of 3. You get to trillions of digits using just maybe 15 towers of 3.

@goatnator1491

Жыл бұрын

@@Parasmunt you get above trillions of digits using just 4 Towers of 3

@TheSpotify95

Жыл бұрын

@@achtsekundenfurz7876 Yeah, when they say about 3↑↑↑3 in the video, what they say is the result is actually just 3↑↑4. 3↑↑4 = 3↑(3↑↑3) = a 3.6 trillion digit number (bigger than Googol). 3↑↑5 = 3↑(3.6 trillion digit number) = bigger than Googolplex. 3↑↑↑3 = 3↑↑(7.6 trillion) which, if each 3 is written as 2cm tall, the tower will stretch to the Sun. And remember that the top 10cm is already bigger than Googolplex. So the result of even 3↑↑↑3 cannot be written down, and remember, 3↑↑↑↑3 has that many iterations in it!

I think its outstanding to have various mathematicians who have decades of experience talk about their work on this channel. Great!

*"In binary it's 1"* Brilliant!

@anonymoususer8036

4 жыл бұрын

Oh i see

@julmusten2488

3 жыл бұрын

Extraordinary.

"Could just be 13, though." >_>

@georgeabreu6392

7 жыл бұрын

Got to love the huge interval between the two.

@davecrupel2817

7 жыл бұрын

huge doesn't even *BEGIN* to cut it. xD

@georgeabreu6392

7 жыл бұрын

Daniel Cannata Indeed.

@steffen5121

6 жыл бұрын

Let's you question the sanity of this guy.

@Mantorok

6 жыл бұрын

How did he calculate that Graham's number is the limit?

This made me have a thought: infinity is exactly that, _infinite._ Graham's number, no matter how abstract it has to be in order to even be measurable, written, or put into language anything can understand, is still finite. Bigger numbers, still finite numbers, are being made all the time. Infinity never ends and goes beyond all of those. Just think of the absurdity of that, though. You can be more precise and make smoother lines with Graham's number (let alone infinity) than you could be making a line with individual strings.

@SadCrabMan23

2 жыл бұрын

Grahams number is closer to 0 than it is to infinity.

@M-F-H

11 ай бұрын

Yep, Grahams number is nearly zero compared to infinity.

@SocksyyAU

9 ай бұрын

@@M-F-H Would it not be practically 0?

My bank account: 3arrow3 My spending: 3arrowarrow3

@bunbunnbunnybun

4 жыл бұрын

I wonder what you bought that cost 3 trillion dollars

@fireinthehole_727

4 жыл бұрын

@@bunbunnbunnybun* > 7.6

@BlokenArrow

4 жыл бұрын

My credit scores 3arrow0

@caringheart34

4 жыл бұрын

@@BlokenArrow Glad you still got 1 dollar in your pockets, eh?

@Slinx92OLD

4 жыл бұрын

You mean 3↑3 and 3↑↑3?

I'm going to have nightmares where I just see seas of 3s and hear 'three to the three to three three three th-..' until i wake up in Graham's dimension.

I used to be a mathematician, then I took some arrows to the knee.

@lumm8063

8 жыл бұрын

lol nice

@leivadaros

8 жыл бұрын

+philphy101 ..... Graham's Number of arrows?

@austindu2592

8 жыл бұрын

+philphy101 an arrow to the three?

@MarcoRoque

8 жыл бұрын

some arrows to the three

@davecrupel2817

7 жыл бұрын

+Marco Roque i was just thinking that 😂

I bet if I jump scared him while he was sleeping he would just wake up saying “3 to the 3 to the 3 to the 3 to the 3” Also my name is graham

game: you take a shot every time Ron says 3

Brb mopping my brain bits off the floor and walls.

@NeedMoreMushrooms

9 жыл бұрын

Need help?

@JohnBrown-vb2cs

5 жыл бұрын

hi thiojoe

@addieperkins2599

5 жыл бұрын

What does brb mean?

@avi8aviate

5 жыл бұрын

Oh, hey there ThioJoe, didn't expect a computer expert to pop up on a math video's comment section.

@avi8aviate

5 жыл бұрын

@@addieperkins2599 Be Right Back.

"Three four-arrows three. That's a big number" - Graham, 2014. Yeah, "quite big".

@WalterKingstone

8 жыл бұрын

+Ricardo Pieper When Ron Graham says it's a big number, you know it's a big number.

@oz_jones

5 жыл бұрын

"For you"

It's amazing that I just saw Ron Graham, a man who met Godfrey Hardy, a man who met Ramanujan.

@otheraccount5252

3 жыл бұрын

Ramanujan number when?

his voice and handwriting are so soothing, i could listen to this guy explain stuff all day.

I was going to tell my girlfriend about my favorite number, Graham's Number, so I asked her what her favorite number was. She said it was two, and when she explained why, I couldn't stop laughing. "I like two because it's one more than one, and it's easy to understand."

@numberphile

9 жыл бұрын

Taylor Foulkrod love it!!!

@MarkarthCityGuard

8 жыл бұрын

Wowwwww

@MarkarthCityGuard

8 жыл бұрын

Where do you get your paper

@Aqua.man045

8 жыл бұрын

+Taylor Foulkrod Take a drink everytime the word 3 is said. You won't regret it.

@barry6541

8 жыл бұрын

+Aqua Man Until the next morning...

The funny thing about Graham's number is that it's impossible to describe how big it is in simple, understandable terms. For comparison, if you were explaining for example how big the largest prime number found so far is, you can say "it has over 17 million digits", and that gives you a simple picture of how large it is. However, you can't do that with Graham's number. It's so large that no description is sufficient to explain how large it is. You can't say "it has x digits" because x itself is unexplainable in simple terms. You can't say "the number of digits in GN is so large that this number itself has x digits" either because here, too, x is way too large. In fact, the amount of "recursions" you would have to make in this way to make x small enough to be explainable is too large to be explained in simple terms. It quickly becomes so complicated that there just is no way of doing it.

@thechrisgrice

9 жыл бұрын

The way you describe this "inexplainability" is fantastic, by the way.

@frillinho

9 жыл бұрын

Or you can just imagine the size of my.... as a comparison

@punkrockeris666

9 жыл бұрын

That's right. The number of digits in Graham's Number (in any number, by the way) is it's log (rounded downwards) + 1. So even like that you can't imagine how many digits Graham's Number has...

@PeterGeras

9 жыл бұрын

It's interesting because that exact same explanation you used would apply as early as g1 = 3^^^^3.

@PeregrineBF

9 жыл бұрын

Actually, Conway chained arrow notation helps. If you understand how fast arrow chains grow as the terms (and length) increase, you can get an understanding of how much bigger one chain is than another. Eg 3 -> 3 - > 64 -> 2 is less than Grahm's number, but 3 -> 3 -> 65 -> 2 is bigger, and 3 -> 3 -> 3 -> 3 is much, MUCH bigger than Grahm's number.

3:09 makes no sense you said the 3↑↑↑3 has 3.6 trillion digits. the number itself has a tower of 7 625 597 484 987 threes. At the top (level 1): it's 3 level 2: 3^3 = 27 level 3 = 3^27 = 7 625 597 484 987 level 4: 3^ 7 625 597 484 987 (if 3^300 has approx 140 digits, 3^7 trill must have at least thousands) so level 5: 3^(number with thousands of digits) must have millions of digits. And we still have 7 625 597 484 982 threes left in this tower. SO how is the bottom of this tower 3.6 trillion digits long

@ivantchakoff4067

4 жыл бұрын

It's true. The error has the origin in this way of thinking: 3^^^3 = 3^^(3^^3) = 3^^(7.625.597.484.987) = 3 to the power of 7 thrillions. And so, how many digits this operation has? Log 3 * 7.625.597.484.987 = 3.6 thrillions of digits. This is a wrong answer, because the right answer of 3^^(7.625.597.484.987) is 3 to the power of 3 to the power of 3 to the power....and so on 7.6 thrillions of times!!! The real answer to the question "How many digits this operation has?" is "Only the devil, maybe, knows the answer".

@aysilanvilyeia4199

3 жыл бұрын

@@ivantchakoff4067 if you keep multiplying by 3 you will see a pattern. for example if you start at 1 x 3 you get 3, and keep count of how many times you multiply, so that's One, again 3 x 3 = 9 that's Two, and we didn't increase in a digit, of course again will give you 27 and that's Three, so it took three times but actually it's a 1/21 chance this will happen every other time it'll take just Two you will continue until you get an extra digit and the number lies between 1 x 10^n and 1.1111111111111111111..11 x 10^n like 10,460,353,203 (21st multiple of 3) than it's 3 more multiples So 3^7,625,597,484,987 = [1- (1/21)] x 7,625,597,484,987 = 7,262,473,795,218 and / 2 for the difference between 10^n and 3^n to get that extra digit = 3,631,236,897,613 amount of digits.............. 3^3^3^3 or 3^7,625,597,484,987 will have about 3,631,236,897,613 digits.......... The 1/21 is for a little more accuracy, Just know 3^n will have about half as many digits as 10^n.

@kamhargrove8694

3 жыл бұрын

I know right

@bruhmoment8991

11 ай бұрын

yeah the number he showed was 3^3^3^3, not 3^^^3

I never would have thought that trying to understanding the mere number of digits in a number would be such a bamboozle. Terrific video, I enjoyed it very much!

Maybe this is why Valve can't count to 3?

@alimahh1

7 жыл бұрын

I think that Valve ran out of paper.

@Kebabrulle4869

7 жыл бұрын

*Paper change* Now do that 3↑↑3 times.

@Kebabrulle4869

7 жыл бұрын

3↑3 = 3^3 = 27 3↑↑3 = 3↑3↑3 = 3^3^3 = 3^27 = 7'625'597'484'987 3↑↑↑3 = 3↑↑3↑↑3 = 3↑↑(7'625'597'484'987) = ~1.258014298121 * 10 ^ 3'638'334'640'024 3↑↑↑↑3 = 3↑↑↑3↑↑↑3 = 3↑↑↑(~1.258014298121 * 10 ^ 3'638'334'640'024) = *INSANE NUMBER*

@TJ-jv7ke

7 жыл бұрын

After G64 years of development, we cancelled half life 3

@benjaminsambol

7 жыл бұрын

Tristan Jacquel they canceled half life at 3, but apple is still eventually going to make iphone g64? How is that fair?

333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333 This isn't spam, it's a quote from this video.

@TSrock5000

9 жыл бұрын

haha

@davecrupel2817

9 жыл бұрын

that is am impossibly big overstatement.@~@

@lourier3

9 жыл бұрын

Daniel Cannata No it isn't you heard it yourself.

@ContraereaSerba

9 жыл бұрын

696969696969696969696969696969696969 is a better quote

@yangtra2534

6 жыл бұрын

So emotional. So inspiring. Almost cried.

I can't get enough of this "Big Number" stuff on Numberphile.... who knew it could be so intoxicating??? Blows my mind anew everytime I watch it.

What I love about these kinds of numbers is that if you were to physically write the single digits you would need several universes worth of matter just to make the ink.

@alexanderzippel8809

10 ай бұрын

I believe we would run out of Quarks, not Atoms, Quarks, in the entire universe (if it isnt infinite) if we were to assign each quark a digit in Grahams Number

@JohnSmith-nx7zj

9 ай бұрын

@@alexanderzippel8809you’ve not really understood in a conceptual sense how big Graham’s number is if you’re trying to talk about its number of digits. Even 3^^^3 has far too many digits to represent with any physical thing in the universe, be it quarks, atoms or Planck volumes.

"If you think you understand it, you probably don't". this sums up my life

@austinlincoln3414

2 жыл бұрын

And also sums up quantum mechanics lol

"It's your number! What do you want it to - first digit - to be?" "Uh... Well, in binary, it's one!" Cracks me up.

And in video about tree(3) they say "Graham number is effectively zero compared to tree(3)".

@r.a.6459

2 жыл бұрын

Given that Graham's number is g(64).. The size of TREE(3) is probably bigger than g^(g^(g^(g^(.... )(64))(64))(64))(64) with g(64) storey power tower high

@vincentvandergoes444

2 жыл бұрын

@@r.a.6459It's worse than that.. the G function just doesn't grow fast enough to be relevant to TREE(3). Writing universes full of stacked G functions still doesn't get anywhere close. You need pretty advanced mathematics to even describe how fast the TREE function grows.

@r.a.6459

2 жыл бұрын

@@vincentvandergoes444 you know functions can go beyond exponentiation (i.e. repeated iteration). Functions can be _tetrated onto itself_ right, not just integers. Like (g↑↑g)(n). It works the same way as the up arrow notations. Now imagine (g↑↑↑↑g)(63) which is: (g↑↑↑g↑↑↑g...g↑↑↑g)(63) with g(63) 'g's. ...but comparing (g↑↑↑↑g)(63) to TREE(3) is like comparing the size of 11D Universe to 3D planck volume!! Now, how big is TREE(4) is, compared to TREE(3)??? It's beyond human logic, it involves dimensions alien to us.

@user-rs5ps1rz5c

3 ай бұрын

​@@r.a.6459≈3{{3}}g64

Ron was the coolest prof I TAed for when I was in Uni. A legend.

"You ain't seen nothing yet." - Ron Graham

I was following along with all of this just fine! But then, I took an insane triple arrow to the three.

@jasataja

9 жыл бұрын

How does this comment not have more likes

@Pizkol

9 жыл бұрын

The best adaptation of a meme I've ever seen.

@undead890

9 жыл бұрын

I actually fell out of my chair I was laughing so hard at this. Well done sir, well done.

@jacksainthill8974

9 жыл бұрын

Very well, since nobody else will do it, I volunteer to be the one who admits that I to not get this joke.

@undead890

9 жыл бұрын

Jack Sainthill Look up Arrow to the Knee meme

I’ve seen this video at least 5x..it’s still mind blowing each time I see it

2:04 "...3 or 3 to the 3 this is 3 3 to the 3..."

I lost him at "3".

@j-r-m7775

3 жыл бұрын

Nice. Had to smile at that comment.

@pleasuretokill

2 жыл бұрын

After that is another 3, I believe.

@austinlincoln3414

2 жыл бұрын

Lol

Hey look, the average global word usage list has updated, and three has risen >90%

R.I.P. Ron Graham 🙏🏻

RIP Ron Graham You will be forever missed.

@spiderjump

3 жыл бұрын

Covid 19 got him?

@hungryfareasternslav1823

3 жыл бұрын

@@spiderjump IDK but probably not

You can always use the back of the paper...saves you money and trees.

@numberphile

9 жыл бұрын

The marker usually shows through.... Also, the papers are sometimes sold to raise money for various reasons (extra production costs, charity, etc) so they do not go to waste.

@davidg1396

8 жыл бұрын

+MegaHayzer When you deplete the tree farm, what do they do? They plant more, but if they need bigger production, they have to increase the area, which is very bad for the environment because it's not at all like a forest, it's like agricultural ground, which is really really detrimental. You're deluded if you think it's 100% solved...

@ChristopherKing288

7 жыл бұрын

+Numberphile if you guys wrote down Graham's number, how many sheets of paper could you give away?

@user-zz2uc2dm2k

7 жыл бұрын

+Christopher King It's actually literally impossible to write down Graham's number. There are 10^82 atoms in the (observable) universe, which is just a laughable fraction of the number of digits in the number ^^

@ChristopherKing288

7 жыл бұрын

박수연 I think you mean in the *observable* universe.

Now factorialize it...

@gredangeo

8 жыл бұрын

+Pixelater4 I'm pretty sure that number wouldn't even be close to g65. 27 Factorial is nowhere near the 7.6 Trillion monstrosity.

@NoobLord98

8 жыл бұрын

+gredangeo He means factorialise Grahams number, not 27.

@WalterKingstone

8 жыл бұрын

+gredangeo Actually, 27! has 29 digits, far bigger than 7.6 trillion which has 13 digits.

@asperRader

8 жыл бұрын

+Pixelater4 here's a large number g128!^(g128!^(g128!^...(g128!)))) the tower is g64! layers -i think thats what the amount of powers is called, im no expert at maths- high, and the trend continues

@rainverrev2307

8 жыл бұрын

Now take the square root of it!

seeing as 3^^3 is 3^(3^(3) ), does that mean 2^^2 equals 2^2? if it's number of exponents on the tower than it doesn't matter how many arrows there are, using 2s always results in 4.

@Xnoob545

5 ай бұрын

Yes, you are correct. For example 2^^^^^^2 = 2^^^^^2 = 2^^^^2 = 2^^^2 = 2^^2 = 2^2 = 2*2 = 2+2 = 4 (The pattern even continues to the lower operations before the arrows)

@Bartek72491

2 ай бұрын

2↑^∞ 2= ∞ or 4

What are the practical applications of such a number?

@tusharmaharana3373

2 жыл бұрын

None

I prefer to explain the size of Graham's number in terms of scientific notation. We all know scientific notation, right? Something like 4*10^15. It's used to write big numbers, and it's helpful because it tells us how many digits are in the number in the exponent. In that example, it's 16 digits, which is 15+1. Now, lets start looking at just the exponent when we start putting arrows between 3's. (Also, because there's no easy arrow character, I'm going to use ! for an arrow) 3!3 is 27, which is 2.7*10^1. So 2 digits. 3!!3 is about 7.63*10^13. So 14 digits. 3!!!3 is about 1.26*10^3638334640024. That's a big enough number that I would tell you how many digits are in the number of digits in the original number. (13) This number is so big, that even if you had a typical 1 TB hard drive, you could not store this number in regular form. You would need 37 TB of storage (which of course, does exist, but it's not for mass-consumer use). Now, just look at how insanely fast the digits are piling up when you add just one arrow. For 3!!!!3, I'd probably need to tell you how many digits are in the number of digits of the number of digits of the original number. No computer anywhere could store this number. Even if you built a universe-computer in which every subatomic particle in the observable universe was its own bit, you would not be able to store this number. Such a computer could easily store every program, every song, every game, every youtube video, every file of every type, millions upon millions of times over, but would still not be able to comprehend the true form of 3!!!!3. And 3!!!!3 is only g1. g2 is 3(insert g1 arrows)3. g3 is 3(insert g2 arrows)3. Continue this pattern to g64. That's Graham's number. Long story short? Nothing in the universe can comprehend the true form of even g1. And g1 may as well be infinitely smaller than g64. On a side note, Graham said that it's unlikely that anyone will know the leading digits of g64. That's true, because it's impossible. Knowing the leading digit implies you know all the digits, and as I just demonstrated, that is impossible.

@GMann43

9 жыл бұрын

3!!!3 is a lot bigger than the value you gave; it's already far too big to represent with scientific notation or anything remotely like it. How did you arrive at that value?

@Manabender

9 жыл бұрын

GMann43 I pulled it from the video, at 3:13. It could be wrong, I dunno. EDIT: It's correct. I used logarithmic logic to determine so. Since 3!!!3 is 3!!(about 7 trillion), and 3!!(that number) is 3 times 3 times 3 times 3...repeated that number of times, I reasoned the the exponent of the 10^n part would increase by log(3) (base 10) for each multiplication by 3. In other words, the exponent would be equal to that number times log(3). I chucked that into Wolfram Alpha and indeed got the same number.

@GMann43

9 жыл бұрын

Manabender Nope - the problem that is that 3!!(7 trillion) isn't 3x3x3x3..... It's actually 3^3^3^3..... (exponents, not multipliers.) I just noticed that in the description of the video, they acknowledge the error. Just to give you an idea, 3^3^3^3 is already bigger than the number that you and the video gave. And that stack is only four-high; 3!!!3 is a stack 7 trillion-high.

@Manabender

9 жыл бұрын

***** I was referring to its natural, unabbreviated form. Of course you can store it in that form. I'd wager that, given your icon however, you already knew that...

@ILikeWafflz

9 жыл бұрын

Manabender For future usage, you can press shift + 6 for ^ for arrow notation.

Let's make a new number, but instead of repeating that 64 times, we repeat Graham's Number times.

@kaskade333

8 жыл бұрын

+David Andrei Norgren the mind blowing thing is, no matter what you do with it or how many times you multiply exponentially by graham;s number or anything, it would still be infinitely smaller than infinity

@RonWolfHowl

8 жыл бұрын

Let’s actually make a number where you repeat that process Graham’s number of times.

@SarimFaruque

7 жыл бұрын

hoi te doi

@lincolnpepper816

6 жыл бұрын

grahamplex

@MrPruske

6 жыл бұрын

Stuff by David why? What does it solve/help/prove/convey?

Grate vid, thank you to Ron Graham what a legend!

Rip the legend ❤️❤️

Three.

@davecrupel2817

6 жыл бұрын

MrTristan [TREE]3 sit down, son.

@sicklymoonlight

6 жыл бұрын

Daniel Cannata Loader's Number: Shut up, TREE(3).

@JohnDoeRando

5 жыл бұрын

FOUR!!!!!

@jazzybank

5 жыл бұрын

SSGC(3)

@user-gd2bj3dp1l

4 жыл бұрын

3^^3^^3^^3^^3^^^^^^^^

Not that it matters much to the size of Graham's Number, but there is a mistake in the video :-) You wrote that 3↑↑↑3 is 1.25*10^3638334640024, but that number is actually "only" 3^(3^27) or 3^3^3^3. The actual 3↑↑↑3 is a tower of 3's 7625597484987 high (3^27), as was also written in the video and that is MUCH MUCH bigger than 1.25*10^3638334640024 which is only the 4 first 3's.

R.I.P Ron Graham 🙏

Well at least they're getting closer, in the other video they talked about from 2012, they said the answer was somewhere between 11 and grahams number. So in 2 years they narrowed it down from between 11 and g64 to 13 and g64. Keep it up, you'll get there eventually!

@legendgames128

2 жыл бұрын

Now it's 13 and 2^^^16

Could Graham just say: "my number"?

@BenTheSkipper

5 жыл бұрын

😂he's sooo humble

@TimThomason

4 жыл бұрын

"The so-called 'Graham's number.'" - Ron Graham

@KalOrtPor

4 жыл бұрын

He probably calls it "so-called" because this was the publicized much bigger version, the actual number he used in the proof had G1 equal to 2↑↑↑↑↑↑↑↑↑↑↑↑3 and he defined the number at G7.

@sebastianjost

4 жыл бұрын

It's not really his number. It's named after him. That's the name of the number. He doesn't own the number.

@a.u.positronh3665

3 жыл бұрын

@@KalOrtPor Isnt it 2↑↑↑↑6?

Nice video Brady! You should ask Ron if he will be disappointed if the answer ends up simply being 13! (Also, ask if him Graham's number +2 is prime!)

RIP to a legend.

Rest in peace Ron Graham😔

Graham's numbers last 500 digit's frequency: 0 - 56 2 - 56 9 - 56 5 - 55 6 - 54 1 - 49 3 - 47 4 - 46 6 - 46 7 - 35

@autodidactusplaysjrpgs7614

8 жыл бұрын

No eights? :_:

@strengthman600

8 жыл бұрын

How do you know this?

@Vitorruy1

8 жыл бұрын

Sammy I got the last numbers from wikipedia and feed them into a character frequency program.

@skyler114

8 жыл бұрын

+Autodidactus Communitati Thats an interesting observation.

@skyler114

8 жыл бұрын

+Autodidactus Communitati actually look at that chart he just accidentally listed 6 and 8 as 6

You are really doing an awesome job here! I thought that the usual explenations were very interesting and enlighting, but getting a problem explained by the person who actually solved it first takes it to a whole new level. I'm looking forward to more greate videos! Thank you Brandy for doing what you're doing!

Watching this video makes me happy if I'm feeling down.

The upper bound to the problem has since been lowered significantly, in 2019 it was established to be 2^^5138*((2^^5140)^^(2*2^^5137)), which for comparison is much less than the closest tetration of 2^^(2^^5138)

"In binary is one", "it's called a small gap in our knoledge". Love Graham! :D

Here's a new number: G64↑↑↑↑G64 = A1 A1↑↑↑↑(A1 times)A1 = A2 A2↑↑↑↑(A2 times)A2 = A3 ... A64↑↑↑↑(A64 times)A64 = B1 repeat until Z64.

@davecrupel2817

9 жыл бұрын

No. Just no.

@themanwiththepan

9 жыл бұрын

Yeah okay

@Sgt.Hartman

9 жыл бұрын

themanwiththepan or TREE(4) that would kick any of the "i cam eup with a big number" comments.

@MaxRideWizardLord

9 жыл бұрын

theoretical physicist What about TREE(G)?? or TREE(TREE(3)) ?? or TREE(Fish number 7). And yet, I still don't know how actually TREE(3) does actually work...

@Sgt.Hartman

9 жыл бұрын

MaxRideWizardLord yeah neither do i... would be cool so see (and hopefully understand the mathematics of it.

I don't stand anything but the paper and his voice are satisfaying

3:01: Someone make a remix out of this.

@Bartek72491

2 ай бұрын

Hi @SuperWindows78

So if I understood that correctly: Graham's Number is the number of dimensions after which every dimensions HAS to have that configuration at least once in it?

i begun feeling sick at 5:45 ... i'll talk to my cat about it and see his opinion

@axa122

5 жыл бұрын

here I am imagining you talking to your cat and the cat replying to you his honest opinions regarding on that topic which seemingly somehow makes sense to you and agreed while nodding.

@rajeshwarsharma1716

5 жыл бұрын

This is the greatest comment ever. I will lol 3 to triple arrow 3.

@ferrariscuderia4290

4 жыл бұрын

Schrodinger's cat?

@haylanmarks7965

4 жыл бұрын

"Hey Bastet come to see that sht"

Math teacher: do you understand Me: uhh yeah... My brain: wtf

I'd really like to know, why his proof works for G64 but not for G63. Wouldn't that make a nice video??

@bobbob3630

6 жыл бұрын

Yeah I can't seem to find how this was actually used in a proof, I don't understand how a number bigger than we can understand was used to prove anything :(

@shaikhmullah-ud-din1964

6 жыл бұрын

or G69

@WarDaft

6 жыл бұрын

Actually, Graham's original proof was for a "much" smaller number, though still huge. However, the pop math author writing about it (Martin Gardiner) found this version to be easier to explain. The current upper bound is 2↑↑2↑↑2↑↑9, where even 2↑↑9 is equal to 2^2^2^2^2^65536. There's already no point in talking about how many digits this number has - your next reduction is to ~ 2^2^2^2^2.0035e19,728. 5 layers up is a number with almost 20,000 digits. Next reduction is to ~ 2^2^2^Xe(6.0312e19,727) - there's no point in figuring out what that X is though, as multiplying Xe(6.0312e19,727) by 10 gives you Xe(1+6.0312e19,727). But we would have to add 1e19,723 inside the parenthesis to even get to Xe(6.0313e19,727), so we can just discard the 1+. So at this point we can just flip over all the instances of 2^ into 1e, and get 1e(1e(1e(1e(6.0312e19,727)))). The 1s genuinely don't matter anymore. It doesn't matter how many we add either, from 2^^5 onward, you just tack on one more "1e(" at the beginning. Try to picture the jump from the number X to some number with X digits as you basic operation - then 2^^n means making that jump n-5 times starting with 6.0312e19,727. [Note that Numberphile actually got this wrong - 3^^(3^^3) is not a seven trillion digit number, its a number where you make the jump from X to a number with X digits seven trillion times. Seven trillion cases of "1e(" to write the number down with nested scientific notation.] 2↑↑2↑↑9 then is a number with 2↑↑9 cases of "1e(" in it. You no longer care even whats at the top of the tower, because the exact height of the tower has five *layers* of "put what digit you want here, it doesn't matter" to describe it. 2↑↑2↑↑2↑↑9 then has so many cases of "1e(" that we don't even care precisely how many cases of "1e(" it takes to describe how many there are. Silly big, yet not even the tip of the iceberg for large numbers. That analogy falls short though. Every analogy other than "literally nothing by comparison" sells the difference short, and even that is both just barely appropriate and at the same time too extreme to be factually accurate. Think about that - to try to communicate the scale of these numbers in succinct English, YOU HAVE TO LIE.

Me: My PIN is the last four digits of Graham's Number lololol get rekt *Watches rest of the video* Me:

@ivantchakoff4067

4 жыл бұрын

So, your pin number is 5387? All the pirates in the web are very thank you, they will try to hack all your bank's accounts now.

@gunay1321

3 жыл бұрын

@@ivantchakoff4067 😱😱😱😱😱😱😱😱😰😰😱😰😱😱😱😱😱😱😱😱😱😰😰😰😰😰😰😰 OMG SO SCARY😱😱😱😱😱😱😱😱😱😱😱😱

@jessieyao8177

3 жыл бұрын

04575627262464195387

@ionisator1

3 жыл бұрын

@@ivantchakoff4067 it can't end on a 7

@ivantchakoff4067

3 жыл бұрын

@@ionisator1 Watch all the vídeo. And You Will see.

He has such a relaxing voice

3:06 Wrong. 3^3^3^3 contains 3.6 trillion digits. Not 3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3.... with over 7 trillion 3's. I assume they made the mistake of evaluating the power tower from the bottom up, which is incorrect, exponentiation is right-associative.

@findystonerush9339

9 ай бұрын

THEY DID UNDERESTIMATE THE ->s

Hi Brady - thank you for making this video, it was fascinating to hear Graham explain the number named after him....

I love that paper change transition! XD

@twotwoisfive

9 жыл бұрын

Hahahaha best ever!

There is an error at 3:51. 3(3arrows)3 is not a 'trillion digit number' a trillion digit number is just the top 5 3s of the trillion high tower which is 3 (3arrows)3. This number is fascinating the way it grows like a Fractal, imagine yourself on a power tower of 3s and then each branch grows outwards into a size of the trunk and then these spout branches and each of those branches grows out to the size of the trunk and the rate at which this happens then also accellerates to an insane degree with each step and there are so many steps. It's like they sat down and thought about a mathemathical formula that would cause a number to grow the fastest.

@IsaacHarvison-mt5xt

8 ай бұрын

Only thing that can solve graham number is quantum computer to figure the first numbers 😂😂

@Parasmunt

8 ай бұрын

@@IsaacHarvison-mt5xt Won't make a difference i suspect. The number is too big.

@Parasmunt

8 ай бұрын

@@IsaacHarvison-mt5xt This number is well beyond quantum computing too.

rest in peace graham, we will miss you.

Did you know? If you were to take every atom in the known universe, and expand them to all be the size of the universe, then turn them all into solid lead, the weight of all that lead in pounds would still be less than Graham's number! In fact, the only thing that weighs MORE than Graham's Number of pounds... is your mother!

@llllllllllllllllllllllllIIIIl1

8 жыл бұрын

To be fair, osmium is denser than lead.

@RichartI

8 жыл бұрын

+Xhinope I, too, watch day9

@jakethornton7

8 жыл бұрын

+Xhinope Lol thanks dayj

@FrancisHatesStairs

8 жыл бұрын

+Xhinope The number you came up with I am fairly certain isn't even 3(3 arrows)3

@monkeydog8681

8 жыл бұрын

+Xhinope Correction.. The observable universe. The universe could be infinite.

So to summarise .... Pretty big

I always thought there must be something to represent repeated exponents, like how exponents are repeated multiplication, and how multiplication is repeated addition, and now I finally know how to write it.

RIP graham 😭🙏 :( :(

So Mr. Graham thinks that this number is so mind-bogglingly massive that we might never know what the first digit is...except that in binary, the first digit is 1. Which raises the even more mind-boggling concept of writing this massive number in binary. I think I need Graham's Number of Aspirin tablets to make my brain stop crying.

@legendgames128

2 жыл бұрын

Well in tenary, it's 1 followed by a lot of 0s.

@R3cce

Жыл бұрын

It ends in a 7

"you ain't seen nothing yet." you Just put 3^27 trillionth power, what next?!

"Now that's a big number." You don't say....

„Mr. Graham - what is your last wish?“ - „Just write my number on my tombstone“

Actually I think there's a mistake at 3:08 : they say that 3↑↑↑3 is a number that contains 3.6 trillion digits. I think it actually contains way, way more than that. 3↑↑↑3 is a tower of 3's 7.6 trillion levels high. Now if we look at the top this tower and work our way down : 3 = 3 3^3 = 27 3^3^3 = 7,625,597,484,987 3^3^3^3 = a 3.6 trillion-digit number, already bigger than a googol (10^100) 3^3^3^3^3 = a number with a 3.6 trillion-digit exponent, bigger than a googolplex (10^googol) and so on. So far we've gone down 5 levels. The tower goes down 7.6 trillion levels. So I think this number is going to be impossible to comprehend, and contain a insane number of digits, way more than 3.6 trillion. Correct me if you think I'm wrong !

@pingouin7

8 жыл бұрын

Oops, didn't see the little box there. Looks like he corrected himself already. Well anyway, it gave me an excuse to say things.