Today, we learn the story of Graham's Number. My Website: day9.tv/ Me on Twitter: / day9tv Find me on Facebook: / day9tv Fancy Day[9] Swag: day9.tv/store/
Hey Sean, no idea if you'll read this, but on the off chance you do: thank you so, so much for this video. I first saw it when I was in high school, and it inspired me to go on and major in math in college. During undergrad, I really wanted to take graph theory and combinatorics because of how interested you made me in discrete math from this video, and I fell in love with the subjects. In fact, I'm actually doing some research in Ramsey theory right now, which I was introduced to here. I applied for PhD programs over the past couple of months, and I know now for sure that I'm starting my PhD in math this fall, where I want to continue studying combinatorics and graph theory. This video changed my life in an amazing way. Thank you again.
Day[9] either wanted to make a lecture on this number and put the joke in at the end, or he started by brainstorming the most epic "yo mamma" joke possible. I have to believe it was the latter.
+SwenglishGamer He explains it worse and even makes errors. eq. 4x3 is 3x3x3x3. And with grahams number also was he discribed as G0, thats actualy G1. G0 is 4. You Form G1 out of 3 (G0 times up-arrow notation) 3
I watched this video for the first time a couple years ago. Since then I've taken a calculus course, and the E^2X joke is now the funniest thing in the world to me.
derivative of e^x is e^x. Derivative of e^2x is 2e^2x, differentiate again and you get 4e^2x. Basically if you have a function f(x)=e^g(x) its derivative will be e^g(x) * g'(x)
This was one of my favorite videos of all time (both really educational and funny), until the end. Now, it is, without any doubt, the greatest youtube video ever. I'm laughing so hard that I'm crying in the resteraunt where I'm getting lunch, and a family of 4 is staring at me uncomfortably.
Ha, this is great, I took discrete math for CS with professor graham a few years ago, he didn't bring up grahams number until the day before the final and then everyone realized who he was.
There are an infinite number of numbers, so technically speaking most positive numbers - integers to make it easier - are bigger than Graham's number. If you ignore integers, then it's a matter of degrees of infinity and I will leave that to the experts.
Theres no g0 in the definition, the first term is g1=3||||3. Either that, or if you take g0=3||||3, then you should go up to g63, not 64, other wise you end up with a number that unimaginably dwarfes the actual Grahams number.
Henry14arsenal2007 well again, he mentions that in grad school he didnt even look at his grades. Ergo, it's safe to assume based on his claim that he missed that part... Sure g63 must be a massive number, but g64 must be even greater... technically in this vid, Day9 just created a larger number than graham's number. xD
2 year old comment, but apparently g0 is accepted as 4 for some reason. A minor error on Day9's part (or maybe a tremendous error?) but g64 is still a bit large.
Graham's number is one of the most interesting things I've learned about. I've been subscribed to Numberphile since their beginning, fantastic channel.
Calculus was actually my favorite high school class. I love physics so learning about the mathematics that made understanding physics possible was the most interesting thing to me, even more than my physics class. I love the ability you gain to understand physics when you learn about derivatives and integrals, and it's definitely the class I took the most away from so I just love hearing about these things that I'll learn about when I go into higher forms of calculus.
Within the first couple of minutes, you blew my mind. I'd always known that you could color every state in the U.S.A. with four colors, but I'd never known you could do it with any map. I quickly tried to disprove it, and quickly failed. I'm not a math major, but you definitely made me think on a critical level that I haven't experienced in some time. Thanks :)
I started recursively copy and pasting 9^9, which turns into 9^99^99^99^...^99^9 And for some reason, ctrl+v happens faster than holding a key down. I have no idea why.
+Phatnaru0002 This doesn't really make sense. For it to make sense, you'd need to add a number behind the second g. Like g(g(1)). As g1 is already unimaginably big, and you have to do the process where you take the previous g value g1 times, it's more or less too big to even explain. If you then scale it up to g(g(64)), you can't really do much with it, except go "whoa, that's a big number", as it is way to large to imagine. You could do the process infinitely if you want to, always adding a new layer of g's. An example could be g with g64 g64's of arrows.
I have watched this video every few months now for like three years and it is first now that I can relate to the type o guy who talked about the really curvy lines and enormous polynomials haha
gudpeter100 are you being serious or are you just joking, because I know how to make a black hole, although I don't know how to preform the task of doing so
Kylan Andreychuk If you had an atom for every digit of G stored in memory, and you had all these digits stored in the universe, the density of the universe would pass its Schwartzchild Radius and the universe would collapse in to a black hole.
To express exponential notation. It takes a number like 4x4x4x4x4x4 and comprises it simply into 4^6 which is much easier to display and type into a calculator/computing system. It is used a lot in technical fields that have to understand exponential growth and decay.
Day[9], I watched Numberphile's explanation of Graham's number quite a while before this, but I must say I enjoyed your slides, witticisms, and horrible pun far more.
Hey Day9, just wanna say I've seen Ron Graham actually explain his number and arrow notation; I couldn't understand his own explanation of arrow notation because it was too incoherent. Then I saw you describing it. Thank you for making this. Lol
Day[9] I effing love you man! I'm soo sad I missed the show today I freaking oversleptD: and was planning to sub(Twitch), but by any means I'm soooooooo glad you post these
I really love math! I'm not that good at it but I think it's very beautiful. Two years ago I spend a whole year doing calculus (just lower classes because I never got it) and after really putting effort into it I got straight A's in all my writing and oral exams. I know that compared to the amount of math problems and ways it's not difficult but I never imagined that I would actually appreciate sitting down and differentiate equations before going to class.
I'm a graduated aeronautical engineer (24 years old here) and I have never seen these up arrow notations before. And believe me I was pretty dedicated in college. We don't really need these notations in engineering, since we never really work with numbers or that magnitude. We actually reach for the opposite side of the story, we learn to work with really small numbers due to Finite Elements Methodologies. Each field of science has its own specific beauty about it.
Hey Sean, can I be *that* guy and say ... can we have some more Math videos? your passion and ability to explain really complicated stuff in simple terms is cool :D
THANK YOU DAY 9 I heard of a number so big you cant imagine it and couldnt find it but wanted to tell my friends about it and know it do not only know that it was Grahams Number but i can just show them your video!
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I watch this video every few years and it never fails to destroy me xD
Same lol
same
Now was the yearly watch.
8 years later and I’m still watching these laughing lol. Such a good sense of humour.
Hey Sean, no idea if you'll read this, but on the off chance you do: thank you so, so much for this video. I first saw it when I was in high school, and it inspired me to go on and major in math in college. During undergrad, I really wanted to take graph theory and combinatorics because of how interested you made me in discrete math from this video, and I fell in love with the subjects. In fact, I'm actually doing some research in Ramsey theory right now, which I was introduced to here. I applied for PhD programs over the past couple of months, and I know now for sure that I'm starting my PhD in math this fall, where I want to continue studying combinatorics and graph theory.
This video changed my life in an amazing way. Thank you again.
Did you get your doctorate?
Day[9] either wanted to make a lecture on this number and put the joke in at the end, or he started by brainstorming the most epic "yo mamma" joke possible. I have to believe it was the latter.
Day[9] needs to be on Numberphile
Day 9 needs to own numberphile
+Popo Sandybanks Day 9 is Numberphile.
You do realize they had the man who came up with this number talking about it on Numberphile?
+Miister Cloud Day9 is more entertaining is better
+SwenglishGamer He explains it worse and even makes errors. eq. 4x3 is 3x3x3x3. And with grahams number also was he discribed as G0, thats actualy G1. G0 is 4. You Form G1 out of 3 (G0 times up-arrow notation) 3
Those 17 minutes totally paid off at the end.
5:43 I died at the e^2x joke XD
Rip
did Day9 spend over 17 min educating us just to crack a yo mamma joke? i like to think so and its awesome.
Was that 17minute build up to a "yo mama" joke ? 5/5.
5/7 would watch again
*G* out of *G*
I've literally seen this video at least 10 times and it STILL gets me every time at the end there. Christ, day9
Did Day9 just spend a quarter of an hour teaching us some experimental math, just so he could drop the worlds best yo mamma joke?
Day9 should become a teacher. His students would literally have the best math class in the world.
I watched this video for the first time a couple years ago. Since then I've taken a calculus course, and the E^2X joke is now the funniest thing in the world to me.
Jake Thornton Explain! Explain! Or you will be exterminted!
Pff and now it's been two years since I took calculus and I don't remember shit from it :P
haha
derivative of e^x is e^x. Derivative of e^2x is 2e^2x, differentiate again and you get 4e^2x. Basically if you have a function f(x)=e^g(x) its derivative will be e^g(x) * g'(x)
Now that is the best "yo momma" joke ever
17 minute buildup to a mom joke. Has to be in the top 5 mom jokes of all time
I come back every six months or so to relive one of the sickest burns I've ever witnessed.
Wow! Coming back and seeing this at the end of the decade, 2019. Amazing how much Sean has changed, and is yet very much the same.
This number doesn't even come close to the debt I owe after college.
Literally the greatest thing I've seen in possibly my whole life.
This was one of my favorite videos of all time (both really educational and funny), until the end. Now, it is, without any doubt, the greatest youtube video ever. I'm laughing so hard that I'm crying in the resteraunt where I'm getting lunch, and a family of 4 is staring at me uncomfortably.
Ronald Graham of Graham's number just died this week and made me remember this old day[9] video. Thanks for spreading your enthusiasm for math!
I just watched a 17 minute set up to a your mama joke. I'm not sure how i feel about this.
+Matthew Szubelak i wish i could have seen the chat for this
You ruined the fun....
I physically applauded.
Not like "i'm clapping for real right now"
I actually clapped for real, just now.
Ha, this is great, I took discrete math for CS with professor graham a few years ago, he didn't bring up grahams number until the day before the final and then everyone realized who he was.
i watch this every couple of years, still great
Also, the format of how the up arrow affects the thins after it makes my brain very happy.
"I want you to think of the biggest number you can think of"
The Busy Beaver function with Graham's number as its argument.
WHERE IS YOUR GOD NOW
Boo-yah! And thanks for sending down a multi-hour rabbit hole learning about Turing machines!
Ackerman(TREE(G64),TREE(G64))
Large Number Garden Number: pathetic
day9...i wish you were my math teacher in high school
This is by far the best video on the entire internet. And it will be on top, even if there's graham's number of videos out there
Best setup for a "yo mamma" joke ever. But, seriously, this is just as informative and even more entertaining as the videos by Numberphile
But almost every number is bigger than Graham's Number!!!
Though that's technically true, you can also argue that any number is tiny.
There are an infinite number of numbers, so technically speaking most positive numbers - integers to make it easier - are bigger than Graham's number. If you ignore integers, then it's a matter of degrees of infinity and I will leave that to the experts.
Theres no g0 in the definition, the first term is g1=3||||3. Either that, or if you take g0=3||||3, then you should go up to g63, not 64, other wise you end up with a number that unimaginably dwarfes the actual Grahams number.
Henry14arsenal2007 well again, he mentions that in grad school he didnt even look at his grades. Ergo, it's safe to assume based on his claim that he missed that part... Sure g63 must be a massive number, but g64 must be even greater... technically in this vid, Day9 just created a larger number than graham's number. xD
+Henry14arsenal2007 you can make a arrow lol ↑
2 year old comment, but apparently g0 is accepted as 4 for some reason. A minor error on Day9's part (or maybe a tremendous error?) but g64 is still a bit large.
I think he may have said that because he does programming and indexes should start at 0.
@@uknownada My initial thought was that g0 should be 4, because if g1 = 3||||3 and g2 = 3(|*g1)3, then it follows that g1 = 3(|*g0)3 therefore g0 = 4
Graham's number is one of the most interesting things I've learned about. I've been subscribed to Numberphile since their beginning, fantastic channel.
I saw this video when it was first published and 9yrs later the yo mamma still gets me everytime
My brain hurts so good
I think I saw the Numberphile vid on this and I think you explained it quite well. - Nicely done :)
I saw a different vid on Grahams number, I think it was Numberphile but can't remember
I love you, and I love day[9] story time. I'm watching this over and over again. More math and more stories!
I have been waiting for story time all week!
I would love to listen to this guy talking about math in a podcast!
when h said yo mama i fucking died.
That comment just made my life complete. I can now die happy. Thank you, sir, here is your nobel prize.
The numberphile video about Graham's number was good. But this... you have taken it to the next level.
Funny to think he actually talked to Brit about this when they started dating xD
6:10 Jokes on him because I was thinking of TREE(3)
Calculus was actually my favorite high school class. I love physics so learning about the mathematics that made understanding physics possible was the most interesting thing to me, even more than my physics class. I love the ability you gain to understand physics when you learn about derivatives and integrals, and it's definitely the class I took the most away from so I just love hearing about these things that I'll learn about when I go into higher forms of calculus.
Within the first couple of minutes, you blew my mind. I'd always known that you could color every state in the U.S.A. with four colors, but I'd never known you could do it with any map. I quickly tried to disprove it, and quickly failed. I'm not a math major, but you definitely made me think on a critical level that I haven't experienced in some time. Thanks :)
yo day 9 , when you were a math major how many times did you get asked if you were going to teach?
I'm at 23.
Well I am only 15 years old and asked at least 50 times. I win.
you are a math major at 15?
StarCraft related question; if G64 is Graham's number, what's GG?
It's when you keep going with g65, g66, g67... all the way till gg0
gg is basically infinity then^^
or divinity?
Apparently it's extremely hard to comprehend considering nobody in Bronze League ever mentions it
I saw that mama joke coming from a mile away...very nice, my hat off to you!
I'm so happy to see these in my inbox :D
He's the best storyteller EVER!!!
Thanks for 5:45 mate. I jokingly used it as a pickup line on a girl who's crazy about math. Shit worked surprisingly well. We're currently dating.
Did it work so well that you are still together?
You should teach Math. I would fly 3↑↑↑↑3 miles to sign up for your class.
Idk why more people haven’t seen this. It’s such a great video for learning obscure math facts
6 years later this is still my favorite joke on UA-cam.
Fucking see?! This is why Sean doesn't get supply blocked.
The numbers of times you have to date girls for find your future wife is between: 1 and Grahams Number. So dont be sad. It will happen^^
that makes me feel better Kappa
hahaha! nice one
I've never understood Graham's number before. This was fantastic. You're a wonderful teacher. I have to send this video to all my math friends!
Graph theory, number theory, counting, and geometry are the best parts of math in my opinion. So much fun.
I thought i was being smart by imagining 600 googolplex, but... holy shit.
I started recursively copy and pasting 9^9, which turns into 9^99^99^99^...^99^9
And for some reason, ctrl+v happens faster than holding a key down. I have no idea why.
Ferrohazard And then you pressed "=". R.I.P. computer you were a good friend.
Oh, no, I put it in notepad. Then I just looked at it. It was kinda like Hitler from Inglorious Basterds. "NEIN NEIN NEIN NEIN NEIN!"
Ferrohazard
LOL
So how big is Gg?
+Phatnaru0002 This doesn't really make sense. For it to make sense, you'd need to add a number behind the second g. Like g(g(1)). As g1 is already unimaginably big, and you have to do the process where you take the previous g value g1 times, it's more or less too big to even explain. If you then scale it up to g(g(64)), you can't really do much with it, except go "whoa, that's a big number", as it is way to large to imagine. You could do the process infinitely if you want to, always adding a new layer of g's. An example could be g with g64 g64's of arrows.
It was a joke... ya know "GG!"
this is the best video, im so glad you posted it
Makes a long, amazing explanation of an incredibly complex mathematics idea, ends it with a "yo mama" joke.
I love Day9.
That some sort of mathturbation.
Isn't 3||||3 supposed to be g1, not g0? That makes a pretty big difference. (How big? Bigger than yo mamma...)
This is true, but in both cases, g64 is retardedly big
I have watched this video every few months now for like three years and it is first now that I can relate to the type o guy who talked about the really curvy lines and enormous polynomials haha
ty day9, just made my day so much better
pretty sure that 3||4 already has more digits than particles in our universe
Number of particles in the universe: 2^80, so you are correct
How could we have possibly measured the particles in out universe, when the light from most of the universe hasn't even reached us yet?
*****
It is of course an estimate of the particles in the observable universe and the estimates varies.
Ok, so, only the observable universe, meaning that we could very well have more particles than that.
Are you worried we don't have enough? :p
My goal in life is to calculate this monster using a computer
Kylan Andreychuk The consequences of doing so, if it ever would be possible, which it won't, would turn your computer into a black hole.
gudpeter100 are you being serious or are you just joking, because I know how to make a black hole, although I don't know how to preform the task of doing so
Mustache
Kylan Andreychuk Too much information in a confined space would inevitably form a black hole. Nothing more, nothing less
Kylan Andreychuk If you had an atom for every digit of G stored in memory, and you had all these digits stored in the universe, the density of the universe would pass its Schwartzchild Radius and the universe would collapse in to a black hole.
To express exponential notation. It takes a number like 4x4x4x4x4x4 and comprises it simply into 4^6 which is much easier to display and type into a calculator/computing system. It is used a lot in technical fields that have to understand exponential growth and decay.
I love math too! I'm a math major as well. This video really hits home with me. I love it. :)
What if we did graham's number.... to the power graham's number...
That number is dwarfed by simply going to G65.
julian villaruz but i counter with my G66!
Chris Werth I beat all of you with G(G)
LOL the GG has spoken! O.O
You would get a meaningless number.
Math S.
Is a contraction of the word MathematicS
Math is what a catholic with a lisp attends on Sundays.....
Its MATHS ...MATHS.... MATHS....
Podcast for story time. This needs to happen!
"But math isn't just used for the torture of small children"
Haha, laughed my coffee right outta my nose
Day[9], I watched Numberphile's explanation of Graham's number quite a while before this, but I must say I enjoyed your slides, witticisms, and horrible pun far more.
The 1st 8 seconds of Numberphile's video on Graham's Number is hilariously good at giving an idea of it.
Never thought I'd find a youtuber that I could relate to so well.
The pixeled Triforce shirt is amazing.
This was the greatest video I've ever seen. The perfect ending.
thank you for not doing the typical youtube choppy video editing. wish you had talked about the motivation for coming up with Graham's number though.
Wow! You're math folk. Pleasant surprise of the day.
Honestly Day[9] is the best storyteller ever
Hey Day9, just wanna say I've seen Ron Graham actually explain his number and arrow notation; I couldn't understand his own explanation of arrow notation because it was too incoherent. Then I saw you describing it. Thank you for making this. Lol
The end of this was amazing!
Professor Graham is also an awesome teacher :D learned so much from him. He also does magic tricks and juggles in class XD
I'm so happy I watched this until the end lol, that made it all worth it
you understood what Day[9] said perfectly, well done.
Day[9] I effing love you man! I'm soo sad I missed the show today I freaking oversleptD: and was planning to sub(Twitch), but by any means I'm soooooooo glad you post these
only day9 could make a 17 minute and 44 second long yo mama joke. well done.
I really love math! I'm not that good at it but I think it's very beautiful. Two years ago I spend a whole year doing calculus (just lower classes because I never got it) and after really putting effort into it I got straight A's in all my writing and oral exams. I know that compared to the amount of math problems and ways it's not difficult but I never imagined that I would actually appreciate sitting down and differentiate equations before going to class.
I'm a graduated aeronautical engineer (24 years old here) and I have never seen these up arrow notations before. And believe me I was pretty dedicated in college.
We don't really need these notations in engineering, since we never really work with numbers or that magnitude.
We actually reach for the opposite side of the story, we learn to work with really small numbers due to Finite Elements Methodologies.
Each field of science has its own specific beauty about it.
What day9 talks about is exactly what I do in computer science. Math is awesome, if taught correctly!
this is like the best tedx talk
17 minutes to bring it to a yo’ mama joke! Not to mention a math joke that ‘I just keep getting bigger’ earlier. I love this man.
I just lol'd myself into a facepalm at the end there. Damnit, that was brilliant..
Hey Sean, can I be *that* guy and say ... can we have some more Math videos? your passion and ability to explain really complicated stuff in simple terms is cool :D
your stories are legen.....DARY!
Ok, as a math guy myself, that e^2x joke is one of the funniest jokes I’ve ever heard
What? This is why am is beautiful! It's so fun to imagine things that can barely be imagined.
day[9] is my hero
So I think it math teacher when I was in collage was fan of yours because he told this same joke, the same way you did. Hahaha great math lesson.
THANK YOU DAY 9 I heard of a number so big you cant imagine it and couldnt find it but wanted to tell my friends about it and know it do not only know that it was Grahams Number but i can just show them your video!