"ooobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadooba GOODBYE!" Just... WAT?! XD You almost make me want to have kids, Brady.
Fun fact is, that is actually used to make computers slightly better at storing numbers. Computers generally use one of two types of numbers": integers, which is just basic binary, and floating point numbers, which is scientific notation in binary. However, since the coefficient always starts with a one, that first digit is simply omitted, thus freeing that bit to make it a bit (pun intended) more accurate.
Sorry for the late reply, but he wasn't talking to Ron Graham. In order to do that, you need to dial his (Graham's) number and that isn't happening any time soon...
Lol wtf brady. That shit at the end was awesome. Oh and, this extra footage is just what I was looking for. The part where you ask Graham all different questions is what makes it for me. Im sorry to say this, but this is better than the main viddy on numberphile 1. Those that dont subscribe to numberphile 2 are truly missing out.
The "2" channel if really for people like you - who want every last morsel. Others might find their sub box and bit cluttered if they got everything and all the little extras.
Numberphile2 cluttered? lol. If it was at all possible, I'd love you to triple your output. Heck, just put up a never ending live stream! :D Seriously though, you do put out a lot of videos compared to other similar, uh, I can't even say channels, given your structuring - franchises, perhaps? Anyway, but even with all those videos, you don't even come close to seeming like spam. Unhiding videos one by one rather than all at once is a good tactic for that.
+phrasel14 Or just take the upper bound with that number (Graham's number (Graham's number of arrows) Graham's number) of colors and call that upper bound G'1. Then define G'2 as the upper bound with G'1 colors. Then G'3 is the upper bound with G'2 colors. Then repeat the pattern until G'(Graham's number)
The arrows are there just to write the number, you can't arbitrarily add more arrows. Also since the condition of the proof is the same the result will also be the same regardless of how many colors are added.
+Vitorruy1 Looks like you didn't understand the problem. If more colors are added, then the vertices can be colored in many more configurations, making it much easier to avoid one-colored plane configurations. The upper bound to the result would therefore be way bigger than Graham's number.
The New Hampshire-based Chinese professor mentioned here, Dr. Yitang Zhang, that made the proof regarding the twin prime conjecture was my calculus professor at the University of New Hampshire. He was the best math teacher I ever had and was loved by all the students. His humor helped, too. He had a very interesting and long struggle in his career. He published his proof my junior year, and I was very proud of him.
Oddly enough, The end of this video @12:14 is exactly the way I felt after learning the arrow notation & Graham's number. Thanks Brady, for precisely capturing that!
Quite possibly the most appropriate ending for a video about Graham's Number. That's pretty much the way I feel when I try to comprehend its magnitude.
Mathematics is, as it seems, the closest you can get to insanity without being actually insane. However, some mathematicians are pretty close to edge or even drifted beyond it, and my assumption is that the only thing that can keep you off the edge is humour. I must admit, that I haven't found a proof yet, no matter for how many dimensions. At least, Ron Graham seems to be immune. This certainly doesn't apply to Kurt Gödel, whose paranoia eventually caused his death by starvation in 1977. In 1947 he was lucky that his application for the US citizenship wasn't dismissed, when he proved in the hearing that the US constitution is incomplete in the sense that it can't prevent to establishment of a dictatorship by democratic means. It's hilarious in a way, but I'm rather sure that he didn't do so to prove his sense of humour.
I imagine he's such an interesting man to talk to. Brady, you've struck one of life's best gold mines with the videos that you make. I hope to meet you and shake your hand one day.
What did he mean when he said "Numbers get so large, if you double it, it doesn't change." Surely the number does actually change, it's just imperceptible, correct?
Numberphile2 Oh I believe he is... There is even the magic element. Or certainly best math presenter on UA-cam, the main place for video information on the internet, the main information place of the world.
Graham's number is actually quite a small number in the grand scheme of things. There are infinitely many numbers larger than Graham's number, and only a finite number of numbers smaller than Graham's number. That's a ratio of infinity to a finite number. The size of Grahams number is insignificant. It's an excellent bound.
Brady asks Ron why Graham's number has become kind of a pop culture thing. I feel pretty sure it's because of the fact that it can't be written without very exotic notation, and is in fact technically impossible to write with a notation that already describes numbers that are so big you can't fit all the recursive stacks you need to count it in your head. Because arrow notation is something you can follow, but not finish, and you know that you need incredibly massive numbers just to describe how to make the number you're trying to get to, there's this staggering feeling of what exactly "big" means. Everyone knows that infinity goes on forever, but few actually understand what a big deal going on forever is. They know of numbers they can write on a piece of paper in plain old decimal notation that would take until the end of the universe to count, but how long is that anyway? How could you understand it just from reading a big string of digits? Arrow notation takes numbers that big and uses them as tiny pieces. And then it takes those results and uses them as tiny pieces. And then it does it as many more times as you want. When you try to put G64 in your head, you know what infinity is alot better than if you just thought about a line that never ends, because G64 won't fit there, and it's still LITERALLY NOTHING compared to infinity.
Infinity bottles of beer on the wall! Infinity bottles of beer! You take one down and you pass it around, ... ... ... ... Infinity bottles of beer on the wall!
Here's a conjecture about irrational numbers: Any irrational number with a uniform distribution of numbers in its digits must have any n-digit sequence within the number's first 10^(10^n) digits.
Brady, is there any chance you can get Ron Graham back on Numberphile to explain that ending? I'm not saying you can't explain stuff, but at the end there, it just seemed to turn into gibberish. :)
If tomorrow somebody would be able to give a proof that the real number is 13, what would be the implications? And "how much" do the implications differ if the real number is 13 or, say, 1 million?
If the problem is solved by simple brute force (like just trying every possibility until you have the solution) then I would assume there is no big implication other than the knowledge itself. But imagine someone came up with a general algorithm for this problem. This algorithm has the possibility to be used in other problems as well. It was shown multiple times, that not the solutions of mathematical problems are the "big findings that change the world", but rather the tools and methods used to find said solution.
Emanuel May On a slightly unrelated note "the tools and methods used" being more useful then the solution seems like a similar impact of space exploration.
@@EmanuelMay The thing is, the problem for 13 dimensions is already crazily too big to even start to think about solving it by anything resembling brute force.
Remember that game you played in school where they gave you a short story but didn't give you the names of all of the characters and the objective was for you to figure out who was who through elimination and abstract thinking? I finally understand how that was the best lesson school ever taught me. On a cynical note: This interview is like a toddler asking an adult the same question over and over again xD It's a big number; but, that's not the beauty that the creator of that number finds in it. I'da let the man talk as long as he pleased and just thrown it up on the internet. This is the extras anyways. Good set of videos though. G1/G1
I've got a bigger number than Graham's Number. This was the upper bound for the number of dimensions for a line-coloring problem, involving hypercubes. So how many vertices are there for a hypercube of g(64) dimensions? 2^g(64). I don't need to stop there, though. How many ways can you connect these vertices? Well, thats 2^g(64) choose 2, or (2^g(64)*(2^g(64)-1))/2, which is even bigger. But I can keep going! How many ways can these lines be colored? Well, that's 2^(2^g(64) choose 2), or 2^((2^g(64)*(2^g(64)-1))/2), which is even bigger still! Basically, I can take 2 to the power of that number, then square that, then raise 2 to that. And all of this is part of the problem, which isn't like the g(64)+1 idea most people have!
I like the story of someone explaining how the sun will run out of hydrogen and swell up and fuse helium in about 5 billion years and the guy goes "wait. did you say million or billion?" billion. "oh. thats good" (all relieved, like it matters to him personally)
I laughed so hard XD! I was all concentrated because you brought us amasing content as always and then THAT happened XDDD. Just an advice: can you end all of your videos like that? I mean can you ask all those great mathematicians to do that?? Pleeeeeeeeeease!
The upper bound to the problem Graham talks about has been lowered, in 2019 to be 2^^5138*((2^^5140)^^(2*2^^5137)), which for comparison is much less than the closest tetration of 2^^(2^^5138). Still insanely large!
robofish759 That can't be right. The limit for three colors would have to be higher than the limit for two colors. If you get to the maximum dimension for two colors, you can just start to introduce the third color at that point.
Hi - I watched all your Ron Graham videos. Graham says something like "so called Graham's Number" or "sometimes called Graham's Number" - it kind of implies that Ron Graham himself didn't coin the term. Did he not name the number after himself or someone else did? If he wasn't the one to call it Graham's Number, what did he call it before it was named? Did he have a name for it in his original paper?
From what I understand, this is kind of a thing that happens in academia whenever something important happens. The author doesn't generally name it, because they aren't thinking of it as something that needs a name; it's just part of their paper. Then everyone reads the paper and it has a number so buttblowingly huge that you can't fit the process of writing it down into your head, and all the other researchers talking about the paper refer to "that crazy wackjob's giant number," but that's not very polite, so they start calling it "Graham's number."
so the n-dimensional k-colouring problem would have n stacks of something like Grahams number (but for k colours)? Or would it be n instead of the 3? Either way, the complexity class of that problem is several orders beyond EXPSPACE. That's unfortunate with respect to scope pinning (for example registry assignment) in quantum computers, where the compiler conceivably would have to try.
That ending though ....
"ooobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadoobadooba GOODBYE!"
Just... WAT?! XD
You almost make me want to have kids, Brady.
Math... not even once.
Austin Locke So much agar...
Austin Locke Does this smell like chloroform to you?
I was kind of scared by the ending.
12:14 that's what so many 3's and Arrows does to you
best comment 2016 hahahahahaha
Walter Kingstone
Hahahahahhahaha this comment is golden
hahaha, best comment ever
LOL
Most random ending ever
shut up
it was fabulous
ultradude 54 :P
lol
i love how he said he has no idea of the first digit, except that in binary it's 1
That number is so big, it starts with 2 in binary.
It’s also 1 in ternary.
@@void9720 That's pretty bold statement
Fun fact is, that is actually used to make computers slightly better at storing numbers. Computers generally use one of two types of numbers": integers, which is just basic binary, and floating point numbers, which is scientific notation in binary. However, since the coefficient always starts with a one, that first digit is simply omitted, thus freeing that bit to make it a bit (pun intended) more accurate.
@Henrix98 I think Void meant balanced ternary (w/ digits for -1, 0, +1; no 2). You're right concerning the vanilla ternary system (0, 1, 2).
We're you talking to Ron Graham on the phone at the end?....
I always knew maths was an alien language....
Mahrai Ziller this is the greatest comment I’ve ever read in my life
Congrats 😂
when i'd do that in school, they would usually make me leave the class.
i was suspecting that i was onto something.
Sorry for the late reply, but he wasn't talking to Ron Graham. In order to do that, you need to dial his (Graham's) number and that isn't happening any time soon...
This is like having an interview with Socrates or Aristotle. We're incredibly lucky. Thanks Brady.
...and in the end of the video, Brady shows you his foolproof technique for handling telemarketers. Enjoy!
I think you'll just end up making their day, so they may just call you every time they're in need of a laugh.
After intense thinking I get "guba guba" at the end. Priceless.
the ending is a proof of how insanely big it is :D
12:14 the actual proof of this number
12:23 an addendum to the proof
Lol wtf brady. That shit at the end was awesome. Oh and, this extra footage is just what I was looking for. The part where you ask Graham all different questions is what makes it for me. Im sorry to say this, but this is better than the main viddy on numberphile 1. Those that dont subscribe to numberphile 2 are truly missing out.
The "2" channel if really for people like you - who want every last morsel.
Others might find their sub box and bit cluttered if they got everything and all the little extras.
Numberphile2 Make this channel's profile pic of Tau, because your first channel pic is Pi, and 2 x Pi = Tau, because Numberphile2.
Is there a channel of just that stuff at the end, now that I understand.
Numberphile2 cluttered? lol. If it was at all possible, I'd love you to triple your output. Heck, just put up a never ending live stream! :D
Seriously though, you do put out a lot of videos compared to other similar, uh, I can't even say channels, given your structuring - franchises, perhaps?
Anyway, but even with all those videos, you don't even come close to seeming like spam. Unhiding videos one by one rather than all at once is a good tactic for that.
Uranium Willy It sounded like gibberish to me. Gobbledygook.
"It's big. Yeah."
-R. Graham
My favorite Numberphile quote ever.
Who wants to find upper bound when you use Graham's number of colors?
+phrasel14 Or just take the upper bound with that number (Graham's number (Graham's number of arrows) Graham's number) of colors and call that upper bound G'1. Then define G'2 as the upper bound with G'1 colors. Then G'3 is the upper bound with G'2 colors. Then repeat the pattern until G'(Graham's number)
The arrows are there just to write the number, you can't arbitrarily add more arrows.
Also since the condition of the proof is the same the result will also be the same regardless of how many colors are added.
+Vitorruy1 Looks like you didn't understand the problem. If more colors are added, then the vertices can be colored in many more configurations, making it much easier to avoid one-colored plane configurations. The upper bound to the result would therefore be way bigger than Graham's number.
JJJMMM1 hum.
+JJJMMM1 Then probably there wouldn't even be a bound at all.
The last part made me laugh so hard.
Thanks for brightening my day :)
The New Hampshire-based Chinese professor mentioned here, Dr. Yitang Zhang, that made the proof regarding the twin prime conjecture was my calculus professor at the University of New Hampshire. He was the best math teacher I ever had and was loved by all the students. His humor helped, too. He had a very interesting and long struggle in his career. He published his proof my junior year, and I was very proud of him.
That ending is about how I feel about mind-boggling math like this!
I've got Graham's Number of bottles of beer on the wall, Graham's number of bottles of beer. Take one down, pass it around...
12:00 omg that was so funny and random.
cool. thanks for the extra footage. Also. cool that you got Graham himself to explain it :D
The lat 5 seconds of the video is a pretty accurate representation of how I reacted trying to understand Graham's number :P
The explanation for Graham's Number at the end of this video (12:14) is actually the best!
Truly a Tower of Power!
I'd give this video 64 arrows up if I could.
How long was your reddit marathon?
I hope that ending gets talked about on HI
Oooh I bet it will!
Oddly enough, The end of this video @12:14 is exactly the way I felt after learning the arrow notation & Graham's number. Thanks Brady, for precisely capturing that!
Quite possibly the most appropriate ending for a video about Graham's Number. That's pretty much the way I feel when I try to comprehend its magnitude.
This guy had a great voice. R.I.P.
Were you talking to Ron Graham at the end?
I think he was talking to CGPgrey. That'll be part of the next podcast for sure.
At the end of your video is that how you speak to Ron Graham when you think the cameras are off?
lol
OMG Brady, that ending put a huge smile on my face :)
At the end of the video we get to see what happens when CGP Grey finally answers the phone.
After thinking about Graham's number for any extended period of time, baby talk can be extremely liberating. As demonstrated. :D
Mathematics is, as it seems, the closest you can get to insanity without being actually insane. However, some mathematicians are pretty close to edge or even drifted beyond it, and my assumption is that the only thing that can keep you off the edge is humour. I must admit, that I haven't found a proof yet, no matter for how many dimensions.
At least, Ron Graham seems to be immune.
This certainly doesn't apply to Kurt Gödel, whose paranoia eventually caused his death by starvation in 1977. In 1947 he was lucky that his application for the US citizenship wasn't dismissed, when he proved in the hearing that the US constitution is incomplete in the sense that it can't prevent to establishment of a dictatorship by democratic means. It's hilarious in a way, but I'm rather sure that he didn't do so to prove his sense of humour.
I love the end reward for watching all of the fascinating footage about Graham's Number! Thanks, Brady!
I imagine he's such an interesting man to talk to. Brady, you've struck one of life's best gold mines with the videos that you make. I hope to meet you and shake your hand one day.
Clearly a brilliant individual. Rest in peace
Which professor was that on the phone?
This is fantastic. Thank you Brady!
So glad I stayed for the ending. :-D
best numbephile so far
Tohle poslední video tak nějak dodalo smysl všem předcházejícím. Skutečně fascinující.
Thanks, Brady, for tacking on that end piece that shows what happens if you try to comprehend the size of Graham's number. ;)
The end of this video is amazing! Made my day :D
Rest in peace my mathematics Grandpa
The phrase "another step up the mountain" must have been music to Bradys ears. Hard as nails, that guy.
What did he mean when he said "Numbers get so large, if you double it, it doesn't change." Surely the number does actually change, it's just imperceptible, correct?
Is Brady Haran the Martin Gardner of our generation?
I'm pretty sure that I am not! :)
But thank you...
Numberphile2 Oh I believe he is... There is even the magic element.
Or certainly best math presenter on UA-cam, the main place for video information on the internet, the main information place of the world.
Graham's number is actually quite a small number in the grand scheme of things. There are infinitely many numbers larger than Graham's number, and only a finite number of numbers smaller than Graham's number. That's a ratio of infinity to a finite number. The size of Grahams number is insignificant. It's an excellent bound.
12:23 is what happens if you try to store Graham's number in your head.
Man, that last bit was so good.
Brady asks Ron why Graham's number has become kind of a pop culture thing. I feel pretty sure it's because of the fact that it can't be written without very exotic notation, and is in fact technically impossible to write with a notation that already describes numbers that are so big you can't fit all the recursive stacks you need to count it in your head. Because arrow notation is something you can follow, but not finish, and you know that you need incredibly massive numbers just to describe how to make the number you're trying to get to, there's this staggering feeling of what exactly "big" means. Everyone knows that infinity goes on forever, but few actually understand what a big deal going on forever is. They know of numbers they can write on a piece of paper in plain old decimal notation that would take until the end of the universe to count, but how long is that anyway? How could you understand it just from reading a big string of digits? Arrow notation takes numbers that big and uses them as tiny pieces. And then it takes those results and uses them as tiny pieces. And then it does it as many more times as you want. When you try to put G64 in your head, you know what infinity is alot better than if you just thought about a line that never ends, because G64 won't fit there, and it's still LITERALLY NOTHING compared to infinity.
Infinity bottles of beer on the wall!
Infinity bottles of beer!
You take one down and you pass it around,
...
...
...
...
Infinity bottles of beer on the wall!
Crazy thought - somewhere out there is a gap between two prime numbers that is bigger than Graham's Number.
It's probably true! And it's probably not even hard to prove!
It's so big you apparently just don't care anymore... Thanks for including that last bit!
Here's a conjecture about irrational numbers:
Any irrational number with a uniform distribution of numbers in its digits must have any n-digit sequence within the number's first 10^(10^n) digits.
We all can agree that the best part of this is the ending.
Also the “hello” at 12:12 i don’t know how to describe it.
The end really helps to explain Graham's Number.
i dont know why i watch your video's im not a scintist and they make my head hurt but i just cant stop watching
Brady, is there any chance you can get Ron Graham back on Numberphile to explain that ending?
I'm not saying you can't explain stuff, but at the end there, it just seemed to turn into gibberish. :)
If tomorrow somebody would be able to give a proof that the real number is 13, what would be the implications? And "how much" do the implications differ if the real number is 13 or, say, 1 million?
If the problem is solved by simple brute force (like just trying every possibility until you have the solution) then I would assume there is no big implication other than the knowledge itself. But imagine someone came up with a general algorithm for this problem. This algorithm has the possibility to be used in other problems as well. It was shown multiple times, that not the solutions of mathematical problems are the "big findings that change the world", but rather the tools and methods used to find said solution.
Emanuel May On a slightly unrelated note "the tools and methods used" being more useful then the solution seems like a similar impact of space exploration.
@@ormod11 Yeah
@@EmanuelMay The thing is, the problem for 13 dimensions is already crazily too big to even start to think about solving it by anything resembling brute force.
Remember that game you played in school where they gave you a short story but didn't give you the names of all of the characters and the objective was for you to figure out who was who through elimination and abstract thinking? I finally understand how that was the best lesson school ever taught me.
On a cynical note: This interview is like a toddler asking an adult the same question over and over again xD It's a big number; but, that's not the beauty that the creator of that number finds in it. I'da let the man talk as long as he pleased and just thrown it up on the internet. This is the extras anyways. Good set of videos though. G1/G1
I've got a bigger number than Graham's Number.
This was the upper bound for the number of dimensions for a line-coloring problem, involving hypercubes. So how many vertices are there for a hypercube of g(64) dimensions? 2^g(64).
I don't need to stop there, though. How many ways can you connect these vertices? Well, thats 2^g(64) choose 2, or (2^g(64)*(2^g(64)-1))/2, which is even bigger.
But I can keep going! How many ways can these lines be colored? Well, that's 2^(2^g(64) choose 2), or 2^((2^g(64)*(2^g(64)-1))/2), which is even bigger still!
Basically, I can take 2 to the power of that number, then square that, then raise 2 to that. And all of this is part of the problem, which isn't like the g(64)+1 idea most people have!
I like the story of someone explaining how the sun will run out of hydrogen and swell up and fuse helium in about 5 billion years and the guy goes "wait. did you say million or billion?" billion. "oh. thats good" (all relieved, like it matters to him personally)
That bit at the end is what happened when he finally grasped how big G64 is
best ending I have ever seen,
I laughed so hard XD! I was all concentrated because you brought us amasing content as always and then THAT happened XDDD.
Just an advice: can you end all of your videos like that? I mean can you ask all those great mathematicians to do that?? Pleeeeeeeeeease!
Physicists: fAcToRiALs aRe BiG
Ron Graham: Hold my beer
Funniest thing I've seen in a long while.
I can imagine Brady ending his interview with Graham the same way.
Holy crap!
.. There's two of these channels?
Graham's number just blew Brady's mind at 12:13
I had a nightmare about Graham's number the other night. I blame your video, Brady (the non-extra footage video)
:)
12:14 this is what happens to people who try to imagine Graham's number
Graham's office is the best. It looks like it took an entire forest to make. Reminds me of my Grandpa's.
@12:24 Dat akward moment when your mom barges in thinking you are learning Math and hears this...
I liked Mr. Graham's commentary and the out takes. Sadly I can only provide a single up-vote, so you and Mr. Graham will have to share it.
I love this guy.
That was Brady's boss on the phone then?
That ending is what happens when you try imagining that number ^^
The upper bound to the problem Graham talks about has been lowered, in 2019 to be 2^^5138*((2^^5140)^^(2*2^^5137)), which for comparison is much less than the closest tetration of 2^^(2^^5138). Still insanely large!
Ubabubabuba indeed Mr Haran ...
Proof that Brady is a normal (crazy?) person at the end! Had me laughing, so maybe we're both crazy (normal?).
Poor Brady lost it at the end (damn you, Graham's number!)...will pray for you, Brady
Liked the video solely for that ending.
Gardner called himself not a mathematician, but how much mathematics do you need to know before you are one? He certainly knew more than me.
Dude what's the piece of music written about Graham's number called? I have to hear it! 😃
Graham's Number has driven Brady mad
I want to know how Graham would know G64 is the stopping point if it's a number so large you can't even imagine what it is.
After end credits: "well, I guess it's enough internet for today"
thank you for this video and all the great work you do!
The last part of the video was a new mathematical breakthrough.
Hahaha... Brady, you are the best... I woldn´t have the guts to use that noises on a video...
Best Ending. Eva. I love unlisted videos.
So what's the limit for three colors? Is there a number of colors for which the pattern is always avoidable, no matter how high the dimension?
+PhilBagels its in another video i think he said its about the 12th or 13th dimension that it stops working
robofish759 That can't be right. The limit for three colors would have to be higher than the limit for two colors. If you get to the maximum dimension for two colors, you can just start to introduce the third color at that point.
it was the limit for 2 dunno about 3
+PhilBagels What's the limit for a graham's number of colors?
+Nick Manning Some number bigger than 12 I imagine.
Maybe put the last half minute or so on Numberphile3 :-D
Hi - I watched all your Ron Graham videos. Graham says something like "so called Graham's Number" or "sometimes called Graham's Number" - it kind of implies that Ron Graham himself didn't coin the term. Did he not name the number after himself or someone else did? If he wasn't the one to call it Graham's Number, what did he call it before it was named? Did he have a name for it in his original paper?
From what I understand, this is kind of a thing that happens in academia whenever something important happens. The author doesn't generally name it, because they aren't thinking of it as something that needs a name; it's just part of their paper. Then everyone reads the paper and it has a number so buttblowingly huge that you can't fit the process of writing it down into your head, and all the other researchers talking about the paper refer to "that crazy wackjob's giant number," but that's not very polite, so they start calling it "Graham's number."
12:14
Poor man. You can tell that he tried to understand the Graham's number
.. to the 3 to the 3 to the 3 to the 3 to the 3 to the 3 to the 3 to the 3 to the 3 to the 3 to the 3 to the 3 to the 3 to the 3 to the 3 to the...
12:14 and 12:23 are the consequences of trying to picturize Graham's number
Every video should use this outro "oobaoobaoobaoobaooba goodbye!"
so the n-dimensional k-colouring problem would have n stacks of something like Grahams number (but for k colours)? Or would it be n instead of the 3? Either way, the complexity class of that problem is several orders beyond EXPSPACE. That's unfortunate with respect to scope pinning (for example registry assignment) in quantum computers, where the compiler conceivably would have to try.