What is Graham's Number? (feat Ron Graham)
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- เผยแพร่เมื่อ 20 ก.ค. 2014
- Ron Graham explains the number which takes his name...
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"Pretty big number...Slightly bigger [than thirteen]"
-Ronald Graham, on Graham's Number
"Bigger than thirteen, smaller than infinity."
Nice pfp
@Username it narrows it down by infinity so that's quite impressive
funsterkeyven but only by a factor of about 2
He might have followed it by "compared to infinity" in his mind.
"But, I'm not afraid. I think I can do it." This person is the honey badger of mathematicians.
HAHAHAHA HAHAHAHA HAHAHAHA ROFL
Lol
false.
RIP Ron Graham. To Graham’s number and beyond!
I would like this comment, but I don't want to change the number of likes from 42 likes! 😊
he died?
@@lukeschroter9389 July 6th 2020
R.I.P Sir
A Graham's Number of prays for you!
Imagine if you lived to Graham’s number years old like what would even happen lol
"You need to THINK; you can't just compute."
--Ron Graham
3:28 Hey, I'm on the video !
LOL
REEEE
LOLOL 😂😂😂😂
REEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Re
Rest In Peace Ron Graham, we'll never forget you.
I know the name is "Graham's Number" and I like the fact that Graham himself calls it that, but part of me wishes he would call it "my number". Just... because...
Red you must be super fun at parties
Well, "Graham's Number" is the name of the number itself. He can't call it "my number" because that's not its name.
It hasn't occurred to any of you his name isn't Graham, it's Ron?
@@cloerenjackson3699 Plz be joking
@@trequor
I'm not joking.
This man is the Bob Ross of mathematicians. The Joy of Numbers on PBS, folks.
Happy little lines.
R.I.P. Ron Graham.
Remember you cannot make mistakes. Just insanely wide margins of error.
does he have instagraham?
Slow clap...
lol xD.
i am actually laughing rofl
raoul herbord
Well done
raoul herbord The Pun!
Ha ha ha ha! XD loool
His voice is so pleasant to listen to. Also, I remember Ron Graham more as the guy who administrated Erdos' life for the better part of a few decades than the guy who came up with that really big number. (For those confused what or who I'm talking about: read The Man Who Loved Only Numbers you're in for a treat)
To me this was more understandable than the other video with two mathematicians taking turns speaking.
yeah that one made no sense
wel thats cause that one tried to picture Grahams number, andthis one explains its purpose
@@pranit8437 agree there
I literally did not understand that video at all, I was so surprised at how simple this video made it
@@_kaleidoyeah that was bad, almost as if they didn’t know what it was about 😂
2:38 And all six leighghemeighhheues are the same color.
Cannot unhear XD
hHhhHhHhhahahahaahhag
XDDD
Oh man xD
XD
4:14 "The answer: no!"
That's sounds amazing!
This man's voice is like a lullaby. It's so soft and soothing, I could fall asleep to it.
+NoriMori He sounds like the old guy from Kings Quest VI. Oh wait, I just realized both of their names are Graham!
+Luke Molwitz Wait… Isn't the protagonist of King's Quest V named Graham? Is it the same character? :O
(I've never actually played any of the King's Quest games; I just watched JonTron's video about King's Quest V.)
Yes. The old guy is just Graham after he grew up. (The same one from all of the King's Quest games.)
+Luke Molwitz Cool!
I recommend LEMMiNO’s voice as well. He’s got an intriguing Swedish accent. Graham’s is very relaxing imo.
R.I.P. Ron Graham (1935-2020)
I love how he doesn't even blink when he says "sometime known as Graham's number" :)
People living in a universe with G(64) dimensions would laugh at us.
I have finally found a understandable explanation about Graham number. When he himself explains it is much easier to understand than any other video or website I have researched. Thanks a lot for it, Numberphile! 👏🏼👏🏼👏🏼👏🏼👏🏼👏🏼
You got to understand the problem to explain it well!
can you do a video about what maths problems the top computers are currently working on?
Justin Giglio Ask Scishow. Also, Here is an answer to your question: Looking for a pattern in Pi.
No, they aren't looking for patterns in Pi. I don't know why they would continue to calculate digits of pi, it is conjectured to be normal (and most mathematicians believe this, no proof yet, however) and would be pretty wasteful to do.
Most supercomputers currently work on quantum mechanics, climate research, chemical research, nuclear simulations, and cryptanalysis.
Christopher Bell *conjectured*
Lot of simulations. Climate, fluid patterns, astronomy. Probably a few crunching prime numbers.
5:41 "It's uncheckable. You can't check that. It's impossible. You need to _think._ You can't just compute."
4:31 "Pretty big number". Understatement of the year.
Use of the word understatement here is a understatement.
Comic sans... didn't expect to see you here.
Test
One of the few cases where it isn't totally out-of-place, tbh.
"In defense of comic sans" is actually a video.
@@nowonmetube *_Vsauceeee_*
I find it interesting that Ron Graham explains it so well here, in the context of what the number was actually for, yet in the other Numberphile video on the number, which used a different analogy to make things 'simpler', is even more confusing!
Ikr, sometimes explaining thing in abstract form (cubes and connecting verticies) is much easier than taking it to the real world! (connecting.... people at a table?)
True, the committee thing was completely baffling
Please do a video explaining TREE 3
And loader's number.
And rayo's number.
And BIG FOOT.
Ok, i'll stop here.
Rarity Sparkle I want Rayo's number
twiggie is at it again
Numberphile already did a video on TREE(3).
It's more fair to say they *just* did a video on TREE(3).... he posted this comment a year ago.
This series really is the best on youtube, closely followed by periodic videos. Thanks for all the hard work!
"2^120, already beyond what computers can do"
*prints calculation on screen*
That wasn't the calculation that was just the number itself.
+purekeynoob How can you write a number without calculating it...
Chris Bandy
That wasn't the proposed calculation he was referring to that can't be calculated, it is just the number of calculations that a computer is unable to perform.
+purekeynoob Ohh, I see what you mean, thanks. A computer can calculate 2^120 but it can't test 2^120 ways.
Even then I thought it was funny that Graham said "nobody can do 2^120" and then it pops up right below.
I'm honestly not sure if this show has a dry sense of humor or if they did it unintentionally, but every episode seems to have something like this.
"I'm not afraid" What a hero! This guy's a legend.
What I _really_ want to know, is how Dr. Graham even proved that this number is the upper bound for unavoidability.
Does anyone remember that Simpson's Treehouse of Terrors episode where Homer hides behind a bookcase and gets zapped into the 3D world?
And Dr. Frink is trying to explain to everyone what's happened, and he sketches a cube on a chalkboard... and everybody gasps in horror?
That's the feeling at 3:25
Mr. Graham, thanks for your contribution to mathematics.
In fact this is the best part about mathematics. It's just mind blowing that such an insanely large number can ever be a part of mathematics.
RIP Ron Graham
In other words... the amount of money the next iPhone will cost.
No. *SIMPLY NEVER.*
Theres only one number bigger than Grahams Number - Jobs Number.
You are one of the most popular educational channels on TH-cam, featuring a VERY famous mathematician. This is 2014, many years after the release of the original font and with thousands of free alternatives available.
So why.
THE FUCK.
*ARE YOU USING COMIC SANS.*
But good video! :D
+TristanBomb It's just a font. Hardly warrants an F-bomb.
Timo Komulainen Yes, it does! Fonts are important business, man!
It's the message they're trying to send, IT'S UNAVOIDABLE!
+TristanBomb It's not Comic Sans, it's Courier New in bold.
+TristanBomb I like Comic Sans.
Day[9] talks about Graham's Number, and how an entirely new type of notation needed to be developed in order to describe it.
July 8, 2020, RIP Ron Graham, the big number man...
So Graham's Number > 12
You need to think, you can't just compute!
what a piece of wisdom!
1:05 He sounds like Bob Ross.
Heavyboxes DIY Master That's why I enjoy listening to him so much...
Rip Ron, even 4 years after his death his words strike fear in the eyes of most college studends
I love his optimism when tackling what seems to be a difficult problem, that is what got me through math (i never studied or kept up in math)
RIP Ron, thanks for the number
wow, didn't expect Graham to explain it himself :D
And since thinking about his number alone is rather difficult, imagining a cube with that dimension is, well, a mess, I guess.
Watching this late but what an honor! RIP Graham, you have given the world a real beauty
Thank you Brady so much for making this video! It was Grahams number that first made me a numberphile and your original Grahams Number vid that got me into your channels.
I didn't expect to ever be HUMBLED by a number. I was wrong.
A great video (two videos, to be precise), thanks Brady! I really liked that you included some segments of you speaking to the camera, it helped me understand what was going on and it also made the video flow nicely.
Awesome, I finally understand the problem! Because the problem is often described in a single sentence, it's been kinda baffling until now.
Rest in peace professor.
Yea, live in a world with Graham’s number dimensions/directions.
This number has been my favourite number since your first video explaining it. Thanks for the video tutorial on how it was used! And featuring Graham himself! Wow
Look up Ridiculously Huge Numbers on youtube. You'll come up with a series of videos by David Metzler. They go WAAY past Graham's number.
Yes, but graham's number is the biggest number ever used in a proof. Certainly you can add 1 to his number and get a bigger number, but thatwouldn't have been used for anything useful
dragoncrystal24 Yeah, but they do a lot more than add one. Seriously, they get to numbers bigger compared to Graham's number than Graham's number is to 1. And also it's just fun to make huge numbers, they don't need to have a use, at least in my opinion. And who knows? There may be a use for numbers bigger than Graham's number one day. And I think that Graham's number may not be the biggest number used in a proof anymore. I'm not sure though.
I know they do more than add one. That was just me making a point that anyone can make a number larger than graham's number (though maybe not as skillfully or stylishly as experts).
To each their own, though
@@THENEWS01010101 I think there's not really a winner here, since there's no such a thing as "the largest number". But what I like about Graham's number in particular is the way to construct it. It's a bonus too since Graham's number _actually_ have uses.
And yes, you can *always* make a number bigger than the current largest known number (Like, I define my number as a number that is a googol times bigger than the current largest number), but whatever the chance that it has uses? That's what make Graham's Number special.
This further solidifies Graham's Number as my favorite number. Amazing mathematician AND has a great sense of humor (4:31). Watching it a second time, I can't help but feel he is (jokingly) make a nod at himself in case people didn't know that he was the one who created Graham's Number. I could be wrong.
Second favorite mathematician? Conway.
THIS VIDEO IS MY TOP 5 ALL TIME FAVORITE TH-cam VIDEOS SINCE I FOUND TH-cam IN 2006!
I love his voice and want more videos narrated by Ron Graham.
what if you used 3 colours on your lines?
and what if you used Graham's number colours on your lines?
Brain detonates
What if you used Graham's number of dimentions?
Now that's just implementing the TREE function on Graham's Number lol-
RIP legend 🙏😭😭 :( :(
R.I.P. Ron Graham 🙏🏻
I got Graham's Number tattooed on my ankle today. Original instead of an infinity tattoo 😂😂
Brady! Please make your next video about Rayo's number, Loader's Number, or TREE(3)!!! They're even bigger than Graham's number, with Rayo's # being the largest!
They should definitely cover TREE(3) here on numberphile and Loader's number on computerphile.
I feel like Rayo's number might be beyond the scope of most of the viewers here. I mean, if you look at how many people on the earlier Graham's number video confused G for something vastly smaller (and its size was even explained in the video) then I don't see much hope for a lot of people having any chance in comprehending its size. At least not without a video on the fast growing hierarchy first.
Peter Geras I really curious about tree(3), what is this mysterious thing is?
MaxRideWizardLord Well I don't want to spoil the surprise in case Numberphile makes a video about it!
Peter Geras are they going to make video about it?? Hey man, were you the guy who help me understand what graham number is awhile ago??
MaxRideWizardLord I'm not sure, but many of us are hoping so.
Possibly! I've helped many people understand it so I could have forgotten your name.
RIP Ron Graham, he died on the 6th of July 2020
how
@@lukeschroter9389 he died because of a lung desease called “bronchiestasis”
RIP Ron Graham :(
I just love his voice.
Wow, you got Mr. Graham to explain his own number :D That's awesome, thanks ^.^
R. i. p
Rest in Peace great man
Rest In Peace!
2:06 I love the fact "AVOID SOMETHING" is in comic sans.
2:38-2:39 Ron has a short stroke...
Hahahahaha
One of my favorite videos.
His explanation was amazing and very clear
Rest in Peace, the professor that guide my interest into googology.
so much beautiful comic sans. there is a dimension in which you cannot avoid comic sans in your cosmological model. so far it looks like a lower bound of 4, but maybe it is unavoidable in higher states if it was a theoretical random model universe where the planck length is the minimum distance allowed for a differing level of entropy in comparative areas.
how many dimensions would it take with this random model universe of practically any size to never be able to avoid comic sans?
seriously go out an waste your time on this. go go go!
Here I comment that your comment is the best comment.
Thanks Brady. Been waiting for this for a while and it's great. Love it.
R.I.P. Ronald Graham
Just found out that he died in July. RIP
So... If I understand correctly, Graham's number was the first discovered upper bound to the question of how many dimensions it takes for you to be unable to paint the edges of a hypercube without getting a 2D face of the same color.
So what about the same question posed with painting an entire 3D cube of the same color? Is it always possible to avoid it, or is there another upper bound?
If there is an upper bound, is there a point where you *can* avoid it? So is there a number of dimensions for the same-color structure for which there is no upper bound?
yeah, i wanna see the meta answers of these questions. i wish i could do this, but i dont know math that well myself.
Coming back after 7 years
RIP Graham
Thanks for putting this vid together! It made my day!
First John Conway, then Ron Graham? why is 2020 snatching up mathematicians? RIP
"And then there's the other slightly bigger number. I can try to write it."
Wow. Or more accurately, wau.
Great upload. Thank you both.
The way he challenged the idea of the premise is tbh more impressive than the size of the number. At least, in the perspective of someone who's learned about a lot of very big numbers.
Wow! How did you get Graham to be in your video?
Graham's number best number in the world !
no
Look up the Ridiculously Huge Number videos. They go way past Graham's number.
This is awesome, thank you for this video.
finally! I understand the purpose of Grahams number. thanks!
Have to say it...
Comic Sans.
Whats the fastest way to make the biggest number?
I liked Ron Graham's explanation a lot better than the thing about committees from the other video. Like I still don't really get what you were trying to say with that but I can understand lines and colors. Really cool that you had Graham explaining his own number, as far as journalism goes you can't get a more primary source than that.
Thanks so much for being such a good pal of Paul Erdös.
*Where's the SALT ?*
It's 2 am and im learning of impossibly big verticis and numbers...wtf is wrong with me?
WELCOME to the INTERNET
I was just listening to this and just for a second I was expecting him to add a pretty little tree in there. Lol maybe a tree 3.
Rest in peace :(
there was a guy who commented somewhere saying, what is the use of doing all this and here's an answer for that...
you wanna know when do we ever use such things, don't you? I'll tell you. The Graham's number is a proof that our Universe is not singular in existence. Because if our Universe was Graham's number meters large in size, it would mean the value of dark energy calculated by scientists would be literally 0 because the energy would have to be spread evenly across the stretches of the entire universe. however, it is not, infact even if the Universe was GooglePlex meters in size, the same thing would be observed, the value of dark energy is the order of 0.000000000000000000000000000000000000000000000000000001 which with the unusual value and the fact that beyond 13 billion light years , we don't see many Galaxies means its highly improbable that we'll find repetitions, There are 10^10^70 ways of arranging all the atoms within 1 m cubed of spacial volume. if the Universe was Graham's number meters large, it means beyond a certain distance we should be able to see the same structures again, in other words be able to find a doppleganger of yourself or myself or of some structure in the Universe such as some planet or Galaxy. Since the number of Galaxies keeps decreasing as we go towards 14 billion light years and the rate of the acceleration of all Galaxies away from each other keeps increasing under the presence of an external force, the Universe is most likely a Multiverse with other Universes gravity or field acting upon ours. In that case , the value of Dark energy for our Universe is justified since it is just one of the possible values that may exist amongst all other Universes in the Multiverse. Next time you ask a question, think about the other areas where people actually work such concepts :) and Have a nice day :)
Thoughtful and knowledge person.
People hate your tone. I believe that is the reason why no one respond or like this post.
Yumei Jin not really :D if they did i wont have 31000 subs :P
I think that the Universe is so large (there are over a septillion number of stars in our known Universe and most of them probably have a number of planets associated with them), that somewhere in the Universe there is an exact copy of me, you, and everyone else.
rlt152 The claim that there exists an exact copy of every person can easily be disproved. An exact copy of me, for example, would involve an exact copy of MY consciousness. However, I know for a fact that I do not exist anywhere else, for the rather obvious reason that I am only conscious of this existence here on planet earth. If this other 'me' has some other consciousness, then that person is no longer 'me', but someone else. If so, that would rule out a natural or materialistic basis to consciousness, since a materialistic view of the cause of consciousness must entail that a particular consciousness (a particular "ME-awareness") arises when there is a specific configuration of DNA. And if we can show that consciousness does not have a purely material basis, then all the naturalistic arguments in support of parallel universes - or parallel lives within this universe - collapse.
It's hard to say, some people even say that the actual universe (vs the observable universe) is infinitely big in that case there must exist an exact copy of you (see the video on googolplex's)
this seems to be the only video i have watched today with absolutely no audio and i double checked with another video it is not on my PC end
There is a small number of people whose computers seem incompatible with whatever process I am doing to produce my videos and I cannot figure it out - I have asked tech people at TH-cam... What is your set-up and how are you watching?
It is driving me nuts!!!!
I'm running Windows Vista SP2 i've watched other videos of yours before with no issue this seems to be the first one i have had issues with.
Richard Fox if anyone with any technical skill sees this exchange and has any ideas what am doing wrong just by looking at the files or something (and without asking me for a detailed explanation of my process) I will be much indebted!
Numberphile I'm only getting audio on my center channel of my 5.1 audio system. I think you are either encoding the audio as mono or possibly as 6 channel. try stereo instead.
***** okay, I am encoding the Graham's Number extras video (coming soon to Numberphile2) in a different way... Can you let me know if it works differently when it is done... I will re-post the link here for you.
This explanation was clearer than the analogy presented in the other video
Well it is the man who made it explaining
Awesome video! Graham's number is one of my favorite numbers.
googolplex: hahaha! Beat that!
grahams number: hold my beer
I REALLY have a mental issue to imagine a 4 dimension cube. Seriously, I just can't imagine it. I think it's only mathematically possible to have such thing, because my brain does not accept. Maybe Hawkin's brain does.
Now try a Graham's Number dimensional cube.
There is something I don't really get. I don't think it's possible to actually draw a 4d cube, Let me make you an example. If I consider time as a 4th dimension, then it's possible to draw 2 planes, not perpendicular, which don't cross each other. You just draw one when the time is, for example at t0 and another one when the time is t1. It's an easy way to understand how dimentions work, because we see it every day. We can't place 2 objects in the same 3d location, but we can place 2 objects in the same 3d location if we have a 4th dimension. But i really can't see how we can visualize an object occupying a 4d location. What you see in some videos on TH-cam, in which they show what they call a hypercube, is nothing but the "shadow" that the hypercube would cast on a 3d world. But still, I don't fully understand that. Sorry if I made some english mistake, but I'm Italian.
Sinth Teck it isn't possible to drar a three-dimensional figure either thus it's on a two-dimensional surface
Claes Henriksson Indeed I never said it's possible. Even in that case you would draw the shadow that the surface would cast on the paper.
Its really impossible; to do it, you have to be able to envision another axis, that is perpendicular to X, Y, & Z.
Its not something our 3D minds can really envision.
"You need to think, you can't just compute"
Ron Graham 2014
I'm totally lost but still fascinated.