QI | What is Graham's Number?

[@fatguyonasoapbox1553]

David, saying he doesn't understand the question makes me feel better about myself.

[@ratholin]

Stephen adding in "neither do I" made me feel better.

[@COM70]

Dara O Brían probably did and said nothing!

[@Maerahn]

It was what I said literally a second into Stephen even ASKING the question.

[@sjwimmel]

If you're now curious, the KZbin channel Numberphile has an explanation video of Graham's number, featuring none other than its 'inventor' Ron Graham. I don't think I can put the link in a comment, but it's easy to find.

[@wich1]

kzbin.info/www/bejne/fombk5yeespmpKM

[@ogolthorp]

Day9 has a pretty good explanation of it, too.

[@sjwimmel]

@@wich1 Heh, apparently you can link videos, thanks!

[@harryp7346]

I remember watching this video in the past, as well as a few others on immense numbers. I was amazed at how big big numbers can be! It really did blow my mind, especially that I was probably in my early 30s at the time, and hadn't realised just how enormous big numbers could be.

[@MrAlRats]

@@harryp7346 What do you mean? There is no end to how big a number can be. You can imagine numbers to be as big as you desire.

[@AllenKnutson]

I'm in the throes of a horrible drippy cold and came to this video with a tissue up my nose, so was pleased to see myself in such good company. Also, I knew Ron Graham, but instead of big numbers we mostly talked about juggling. (He was once president of the International Jugglers' Association.)

[@henryginn7490]

My favourite description of the size of grahams number is that if you were to think of the entire thing then your brain would collapse into a black hole because it would break the bekenstein bound of information density

[@rtg_onefourtwoeightfiveseven]

Graham's number is already WAY bigger than the Bekenstein bound. Hell, so is a Googol.

[@nigeldepledge3790]

And yet, by some measures, Graham's Number is trivially tiny.

[@chesh1re_cat]

"Think of a really big number" "Seventeen!"

[@rekagotik2785]

It's possible, it's between 11 and Graham's number so

[@NewMessage]

* insert picture of a man at a table with a sign reading "It ends in a 7. Prove me wrong." here *

[@fluffypink90]

I wish I could return to the innocence of knowing him simply as "a man at a table with a sign"

[@MarkusAldawn]

It's very strange, because for a few years now, I've relied on something like that when asked questions I can't possibly know the answer to. One time someone asked me what I thought the ideal level of immigration was for the UK- putting aside that ideal has many meanings, and that the question is incredibly politically contentious, the idea that I'd have something exciting and new to add kind of confused me, so I just said "I don't know, but it's probably a multiple of seven." Since then, standard procedure for being asked stupid questions has been to say "it's a multiple of seven."

[@fluffypink90]

@Joseph Norm About to curse you with some knowledge, hold on tight. The image that New Message was referencing is an image macro/meme of the scene described. The man in question is American conservative political commentator and LARPer Steven Crowder

[@quarkonium3795]

@@fluffypink90 "Political commentator" with the biggest air-quotes in the world around it

[@fluffypink90]

@@quarkonium3795 Agreed, was seriously considering the quotes, but I thought I'd undermined it enough with the LARPer comment

[@DavidWilson-sm2ym]

Graham's number sounds like something on Hitchhiker's Guide.

[@h.a.p8278]

Saying it’s between 11 and Graham’s number is like someone asking your age and you say somewhere between birth and death.

[@nigeldepledge3790]

Ah, but Graham's Number has been proven to be the upper bound. And there are vastly more numbers larger than Graham's number than there are numbers between 11 and Graham's Number.

[@vercingetorix444]

@@nigeldepledge3790 That is also the case for literally any number larger than 11.

[@nigeldepledge3790]

@@vercingetorix444 - Yes. What of it?

[@vercingetorix444]

@@nigeldepledge3790 Nothing really. What of your comment? They're just facts

[@atrumluminarium]

To be fair, there are WAAY fewer numbers between 11 and GN than there are numbers greater than GN (the latter being an infinite amount of numbers). So no matter how useless of a range it may seem the fact that there is a definite upperbound is actually a big achievement in the grand scheme of things. Also as a bit if context in the field of graph theory/combinatorics, numbers do have the tendency to just blow up in size if you increase a parameter of the subject matter by 1. For instance say we have N people and we want to order them in a queue. The number of ways to order them is given by N! (Pronounced "N factorial"). If we take a sequence of N starting from 0 and progressively incrementing by 1 we get a sequence that looks like this: 1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, ... This means that with 11 people we already have almost 40 million possible ways to order them in a queue

[@UnkleRiceYo]

Out of all the infinite numbers, putting Graham’s number as an upper bound is actually an achievement 😂 it means we know a finite range that the value is in rather than the whole vastness of infinity 😂

[@geddes4253]

So, the good folk of Wikipedia state: "The lower bound of 6 was later improved to 11 by Geoffrey Exoo in 2003, and to 13 by Jerome Barkley in 2008." So... if this episode aired in 2010, why didn't they say the answer is at least 13? I can't believe the elves didn't look it up...

[@skykincaid5644]

Numberphile has a good video on Graham's number.

[@archivist17]

And a lot more informative and enlightening than this. Still, I'm in Rayo's corner for this battle!

[@skykincaid5644]

@@archivist17 Yeah I think Rayo's Number is bigger than Graham's by a pretty wide margin.

[@PhilBoswell]

@@skykincaid5644 you'll like this then: en.wikipedia.org/wiki/Friedman%27s_SSCG_function

[@archivist17]

It was Numberphile which introduced me to Tree (3) as well, which is also mindstretching.

[@lir3379]

THANK YOU! Really. Watched it. Very fun. Totally 'head wrap around-able' (yup, I'm using that as a word).

[@JacksonBockus]

How big is Graham’s number? Oh, vast. To attempt to quantify its bigness would be doing it a disservice.

[@MichaelCoombes776]

The vastly big bigness of the Graham's number.

[@Lord_Skeptic]

You might think googolplex is a big number. That is just peanuts compared to Graham's number.

[@grandmasterj5]

Something's that quite interesting, is that all of QI's video's are half the volume of anything else that I'm subscribed to on KZbin 🤔 Anyone else always having to turn the volume up, only to blow your earholes out on the next thing that you watch? 😁

[@ABirdWithNoName]

They are very inconsistent.

[@grandmasterj5]

@@ABirdWithNoName it consistently quiet for me 😁 Even vids going back years

[@saulknights6635]

The really interesting fact is: Graham's number is so large that, if you memorised it and stored all that data in your brain, your head would turn into a black hole.

[@noatrope]

…I think more accurately your brain would have to already be a black hole to contain that much information, wouldn’t it? You can’t turn something into a black hole just by reorganising its matter/energy, you have to add more?

[@saulknights6635]

@@noatrope I think it's to do with the density of neurological pathways that would be required to store so much data

[@abhir7823]

He should have tried to explain Knuths arrow notation to arrive at Grahams number... to give a vague idea of just how mindbogglingly enormous the number is

[@MisterItchy]

I haven't seen the Sandy laptop outro lately and I must say I approve.

[@fluffypink90]

Shout out to Day[9] for teaching me this and about up-arrow notation

[@JwanCortez]

Wait. Day9? The MTG player? Am I in the wrong channel?

[@cameronphenix2096]

British talk shows have been light-years ahead of American ones for decades. Also check out 8/10 cats does countdown and taskmaster

[@maarten404]

Wow haven't thought about Sean for ages. Funny you bring him up on this channel. Apparently YT isn't that big after all

[@fluffypink90]

@@JwanCortez I think of him as a Starcraft player, but I think we're on the same page :)

[@snickle1980]

@@fluffypink90 I think of him as a award show host who talks to puppets...

[@Hellwyck]

I thought Sean Lock looked rough, it's Dara!

[@_rlb]

Stephen: Graham's number is really big TREE(3): *Nope, it's practically zero*

[@eggled1566]

Not only is TREE(3) the superior ridiculously large number just by virtue of being ridiculously larger, it's also much easier to explain. Most people's eyes just glaze over once you mention n-dimensional hypercubes.

[@MichaelCoombes776]

AFAIK Graham's number is (was? Things might've changed) the largest number to be used in a mathematical proof, whereas TREE (3) is just a big number for the sake of being big. Might be wrong though.

[@jonaderjona5805]

I tend to talk about deranged stuff like Graham's number a lot when I get drunk. One time a friend asked me how big that number actually was and I answered, in a slightly euphoric yet sacral tone: "God".

[@alimanski7941]

No math problem needs to have an excuse to be worked on, but this kind of problem usually involves creating new types of proofs and new mathematical tools - if anyone wonders why mathematicians work on this kind of thing, you might at least be satisfied that the solution is not an isolate, but it very well connects with many other fields of maths.

[@ratholin]

this sort of crazy shit is often used in microcircuit design where red is positive and black is negative or red is capicitive and black is resistive. But it's still enough to give you a headache and make you want to go back to paper and ink.

[@donaldasayers]

Grahams number was an upper bound on the answer.

[@finlaylavery8408]

Look Around You told us that the largest possible number was 45,000,000,000. But some scientists and mathematicians think that there maybe even more numbers! 45,000,000,001?

[@zalibecquerel3463]

Ah yes, cDonald's theorem.

[@strivingformindfulness2356]

Yes, this takes me back to second grade, when our teacher, Mrs. Morrow, told us 7-year olds that there can never be a largest number ever, because we can always add 1 to it, or add 50 to it, or add 96744 to it, or add.... We 7-year-olds were 🤯🤯🤯.

[@zalibecquerel3463]

@@strivingformindfulness2356 You need to be careful doing that sort of thing. If you pick a number too high, it can cause Helvetica.

[@rsrt6910]

Pish posh, Chuck Norris uses Graham's Number as his PIN for the ATM.

[@MySerpentine]

He must have a Hell of a lot of time on his hands, the universe won't last that many attoseconds.

[@glenjones6980]

I have only just mastered the inner workings of the flux capacitor and now this!

[@98.11Deet]

Tree(3) would like a word. Though as much as I know that "g" is dwarfed by a few other extreme numbers, it's always the o.g. big number to me.

[@georgetyler816]

This clip is so old that Dara has hair

[@paulwallis7586]

I looked up the basics, and figured out that there must be a better way to describe the basics.

[@williamfothergill6212]

You have to respect the person who edits this

[@decodolly1535]

Between eleven and a number so large all the matter in the universe couldn't produce enough ink to write it out. I agree with Graham Norton - that's not really an answer.

[@hjt091]

It's all a matter of perspective. Numbers go on for ever, so having any kind of limits, even ones as vague as that, are (literally) infinitely more accurate than 'basically anything'.

[@ianwhite4821]

It’s based on a series of base 3 numbers. Hence you can easily work out the last digit

[@EnteiFire4]

It's basically a huge tower of powers of 3, so something like 3^3^3^3^3^3^3^3^3^... (composing from right to left). The great thing is that powers of numbers follow a pattern when you look at the last digit. For 3, that pattern is 1 (3^0 = 1, 3^4 = 81, 3^8 = 6561), 3 (3^1 = 3, 3^5 = 243, 3^9 = 19683), 9 (3^2 = 9, 3^6 = 729, 3^10 = 59049) and 7 (3^3 = 27, 3^7 = 2187, 3^11 = 177147). We know that the number is 3^3^3^3^3^3^3^3^3^3^..., so now we can just look at the exponent of the first 3, which is 3^3^3^3^3^3^3^3^3^... (basically the same thing, but with one less 3). Now, you can look at the exponent and ask yourself: if I divide it by 4, what is the remainder? - If it's 0, then the last digit is a 1 - If it's 1, then the last digit is a 3 - If it's 2, then the last digit is a 9 - If it's 3, then the last digit is a 7 Turns out, you can do the same trick again with the remainders of 4 with the powers of 3, and you only get two possibilities: The remainder is 1 if the power is even, and 3 if the power is odd. Because the exponent of 3 is obviously odd (3 multiplied by itself any number of times is always odd), we know that the remainder by 4 is 3. Since the remainder of the exponent (with 4) is 3, that means that the last digit is a 7. Technically, with similar maths, you could find out what are the last 100 digits for example.

[@angrytedtalks]

@@EnteiFire4 Quite obvious really. **Removes 3 boxes of kleenex from left nostril**

[@EnteiFire4]

@@angrytedtalks What kind of simpleton couldn't comprehend this triviality? ;) It's not super fancy math all things considered, but it's not the type of math that people will stumble upon unless they have some interest in math. I'm sure you could learn it if you really wanted to.

[@angrytedtalks]

@@EnteiFire4 How rude. Do you think the panelists are stupid or ignorant? I can assure you they are not and neither am I.

[@MyName-sx3mr]

@@angrytedtalks I do believe the initial part of the comment was made in jest, good sir. This, I believe is made further clear by the fact he claims it is knowledge reserved only for those who take an interest, which these panelists likely have not, though I do not presume to know.

[@DK_Son]

2:10 Classic "that's what she said"

[@-Gorbi-]

David Mitchell put the tissue up his nose and didn’t sound any different

[@angrytedtalks]

So, between "some" and "a great many". And I did that without any tissues. But my name isn't Graham...

[@bsjeffrey]

the answer is 42

[@Protector0ne]

but what is the question

[@tessesmom]

😁I see what you did there lol

[@-Gorbi-]

I miss steven

[@AdamBechtol]

Ah, it's things like this that sometime make us suspect high-level mathematics is all some ploy- A sort of Emperors New Clothes, where a small cabal of geniuses stay employed offering uncheckable answers to imaginary problems. 😋

[@Jonksy]

The problem with maths is usually you can find an answer that you reckon is correct, and it probably is, but you would need several genius mathematicians spending several years to write out a proof

[@Lightning_Lance]

"...where a small cabal of geniuses stay employed offering uncheckable answers to imaginary problems." That's exactly what it is. Except the answers are checkable in theory, but you may need a supercomputer to check them for you. Anyway, the problems seem useless but every once in a while something important comes along that we need an answer to, and it turns out to be the same problem that was already solved some other way when you boil it down to its essentials. And then all of a sudden something silly becomes invaluable.

[@dannis8552]

Theoretical physics for example?

[@impossiblemission4ce]

"imaginary problems" Was this a complex numbers pun?

[@the-chillian]

They only wish it were so. It has been the embarrassment and disappointment of those mathematicians devoted to the idea of their subject as a purely Platonic field, where pure thought uncovers truths applicable only in some abstruse, transcendent world of ideas, that nearly every mathematics they have devised turned out to have a practical application. It can take awhile, but the concrete sciences always seem to find a use for it.

[@swingardium706]

Why was the outro slowed down a tiny bit?

[@daniel.sandberg.5298]

An n-dimensional hypercube and connect each of the vertices to contain the complete graph 2 to the power of inverts

[@nurmeran]

can i request for english subtitles as i am slow learner in english

[@miracinonyx265]

Yes, this one had some parts that were particularly difficult to make out, didn’t it (and I’m a native English speaker, moderately hearing impaired).

[@asheep7797]

Ok, here you go: Stephen Fry: Yeah, because it seems that the quickest way to improve your verbal reasoning is to shove a tissue up your left nostril, so let's see how well these tissues will work. Consider, right, an n-dimensional hypercube, and connect each pair of vertices to obtain a complete graph of 2 to the power n vertices- ??? (Graham Norton?): Each of them? Stephen Fry: Yup. Then color each of the edges of this graph using only the colors red and black. What, that's my question, what is the smallest number (the smallest value of n) for which every possible such coloring must necessarily contain a single colored complete subgraph of 4 vertices which lie in a plane? Graham Norton: Six! Stephen Fry: That is exactly what people used to think! (Laughter) Stephen Fry: That's amazing! How!? Dara Ó Briain: Further! Further-" Stephen Fry: That's absolutely extroadinary! Dara Ó Briain: Further up there, further! Yeah (there we go?)! Stephen Fry: Yeah, until 2003, most graph theorists thought the correct answer was probably 6. Graham Norton: I can only apologize! Stephen Fry: But... Dara Ó Briain: Get out of here with your old graph theory... (?) David Mitchell: It's so difficult, is it, when you've got a busy showbiz lifestyle like yours to keep up with the graph theory! 8 or 9 hours a day you've evoted to it now! Stephen Fry: Well, by the way, I've got Graham's number. So you got Graham's number? Alan Davies: No, I've not got that sort of relationship. Stephen Fry: You've not got that sort of relationship! Stephen Fry: There is such a thing, which is relevant to this; it's Graham's number, but it's bigger than 6. ???: 'Course it is! Stephen Fry: It is so- It's really big! Try and think of a really really big number! Alan Davies: 17 Stephen Fry: It's- You know what, it's even bigger than that! This number, alright, now get a hold of this, this number is so big that all of the material in the universe, right, couldn't make enough ink to write it out! It's called Graham's number, named after a fellow called Ronald Graham, and weirdly enough, Scientists know it ends in a 7. Graham Norton: Well if it ends in a 7, could you just turn it into an 8, then it's a bigger number! Stephen Fry: I didn't say it was the biggest number ever, it's just- Graham's number (which is huge), you could have another Graham's number; you could have Norton's number- Graham Norton: Yeah, Graham Norton, and I'll make it an 8 at the end! Stephen Fry: Well, if you can remove your tissues now. David Mitchell: I think I'll miss it now... Stephen Fry: Oh, would you? Graham Norton: I'm worried about what might come out when I pull it. Stephen Fry: The fact is this problem; its a graph problem it seems, to imagine a cube with lots of different dimensions, where each corner of the shape is connected with red or black lines to every other, what is the fewest number of dimensions that you must end up that at least one single colored square with the same colored diagonals? Until 2003, they thought it was 6, now it's been shown it must be at least 11, and the answer may now well be 12, but its somewhere between 11 and Graham's number. That enormous number. Which is (???) for error! Graham Norton: Yeah, it's not really an answer, is it? Stephen Fry: Greatest mathematical minds in the world just don't know what the answer is. It seems- David Mitchell: I don't understand the question. Stephen Fry: Neither do I. Neither do I. Dara Ó Briain: (???) I'm really hoping nobody checks. Stephen Fry: What they do know is, it ends in a 7.

[@fintanbeirne7261]

I like that Stephen, Graham and Dara have formed a gay to Irish spectrum

[@flyiasf5668]

well that means it for sure isnt infinite, which is quite a game changer

[@henryginn7490]

That's the thing about bounds in maths, the size of the bound really isn't that important, it's just that it exists. Another famous example would be "are there infinitely many prime numbers with a gap of 2 between them", and there wasn't any known way to get control on the size of the gaps. Someone proved that there were infinitely many primes that had gaps smaller than about 77 million or something and many papers quickly followed with better bounds (when the original author made the bound they didn't try to make it tight so there was opportunity to find a tighter bound at several points)

[@andrewgraham7659]

There's not enough ink in the entire universe to write the number out - but it definitfely ends in a 7 - so there might end in a 17? No Sandi I was commenting when you started talking so I won't be making a selection from the clips you suggested.

[@bubbaguy4411]

CLEARLY...the answer is 42

[@aviinthepast]

wrong, it is now 11. not 6.

[@devilsadvocate1597]

I'm just happy that a Graham Norton's number is bigger than a Googolplex! Now which celeb is gonna shame the density of a blackhole?

[@major7thsmcgee973]

It's essentially 3 to the power of holyfucktillion

[@SilentGamesBread]

Hello 👋

[@DonkeyYote]

Graham's number is not the largest number. It's the SMALLEST number that we are sure is an answer to the problem.

[@chrislawley6801]

What is is infinity minus 1 ?

[@mrfocigaz4942]

It is is still infinity.

[@Earthandbeyond905]

Greatest mathematical minds don't know what the answer is.. And here I am not being able to understand the question *Legend* status achieved

[@esdisaysaloha]

Coincidentally, the first anniversary of Ron Graham's death is Tuesday next week.

[@FreakyLeek]

Well please come on... what was the question again?

[@MrDJAK777]

Reupload?

[@ritchiebesas631]

"im worried about what might come out when i pull it" 💩

[@ReegusReever]

Fuck; OG Sandy is back in the outro to set about us all

[@TheGamblermusic]

and now look for the number "Tree(3)"

[@THEchiQ]

Maths is so whimsical and silly.

[@ellelka]

Took me a lot of replays to figure out he said "noted it ended in a 7" 😅

[@miniepicness]

"scientists know that it ends in a 7" right?

[@SaintPhoenixx]

That suit makes it look like Stephen's head had been shrunk so they could get it all on camera.

[@bravelyHomoSapien]

In other words…they couldn’t figure it out and gave up

[@djinnkinn]

is it just me or did they change the key of the music at the end?

[@MichaelCoombes776]

They did (well, they slowed the end-clip down). Sandi's voice is lower as a result.

[@geitekop507]

Yeah, they have done that to some videos! However, I've noticed the pitch changes mostly when the outro is Sandi speaking on a laptop, and someone closes it.

[@afiqghfr]

are the QI hosts really smart or just reading the script/cue card?

[@tessc-b1886]

He's reading off a script

[@trevisonclark7135]

Why does Dara look like Mr Rumbold

[@bradameerbeg2154]

Bigger than 17! You must be mad!

[@puirYorick]

Seventeenth and proud of it.

[@timparenti]

Wow, seventeen. That's a big number! ;)

[@lir3379]

@@timparenti ya' saw what you did there. Big sigh - I miss being around quick witted people.

[@TallSilentGuy]

Nought. The clue is in his name.

[@Protector0ne]

You think his name is Graham Noughton??

[@noatrope]

Nought by Noughtwest

[@randomcreek]

you could think his name is Grapham Norton

[@JoeBleasdaleReal]

*Tiss you*

[@andrewjameshenderson1389]

I understood nothing.

[@torfrida6663]

This is just a transparent excuse for dodging doing the chores. Doesn't fool me!

[@SwordQuake2]

Such a condescending and ridiculing video. If you don't understand something just shut up and don't downplay it.

[@Fiyaaaahh]

Connecting each pair of vertices results in a graph of n*(n-1)/2 vertices, not 2^n. The elves didn't do their homework on this one.

[@JacksonBockus]

Nope, an n-dimensional hypercube, as described by the question, contains 2^n vertices. A complete graph with n vertices contains n*(n-1)/2 EDGES, which may be what you were thinking of.

[@Fiyaaaahh]

@@JacksonBockus ah yes, I mixed up what n stood for. I'm so used to it being vertices, but in this cases it was dimensions.

[@NibberKSmooth]

Maths is utter ball ox

[@noatrope]

No, physics is the field where you assume a spherical cow

[@noatrope]

But with maths, if you separate it into the right pieces it can be rearranged to make two utter ball oxen of the same size :D

[@noatrope]

(I had two jokes and I couldn’t pick which one to make)

[@tashn3911]

Second

[@cyrusrendil1109]

Not really.

[@esquilax5563]

Grahamth

[@klaxoncow]

@@esquilax5563 Grahamth... but with an 8 at the end.

[@peterlustig329]

Young Graham Norton looks like Alan from 2 and a half men

[@siomhaithwarren739]

The answer is 42

[@murraycarew]

It could well be!