I would really like to take that rubiks cube and ram it down your throat so you would no longer be able to do this kind of extremely annoying rambling.
Graham's number is very small compared to n(4), which itself is very small compared to TREE(3), both of which I believe appeared in a serious mathematical proof. Also, if we look at transfinite numbers, of course they're bigger than any of these or any other finite number.
How would one use numbers of this size in a mathematical scheme? Infinity will always be the largest value of anything, even greater than any unit in the universe if the universe theoretically kept expanding for eternity. But Graham's number is still finite regardless, but it's freakin' unbelievably finite. Infinity is more of a concept than a number, but does this mean that Graham's number is also a concept; but in a different way?
@swygster it was the answer to a problem to a problem of multi-dimensional cubes no one knows the exact amount of digits or what it even begins with, all that is known right now (to my knowledge) is that the number ends in seven
There are 64 G steps in Graham's number. The first step is G1= 3↑↑↑(3↑↑↑3). A googolplexian is less than 3↑↑6, which is a tiny, tiny, minuscule fraction of G1. G2 is 3↑(G1 times)3 and G3 = 3↑(G2 times)3 and so on until G64 is reached. A googolplexian is a truly gigantic number that is FAR FAR beyond our comprehension but size-wise it is an atom compared to the universe next to Graham's number. It is so far beyond a googolplexian it's not even funny.
Even the founder Ronald Graham doesnt know how big it is but he confirms that it is smaller than infinity this GOD, SCIENCE, TIME SPACE what ever you want to call it nfty will Graham's number to shame!!
infinite is larger than Graham's number infinite is a different beast think of Infinite it would take a Graham's number to the power of Graham's number or if you could power towers Graham's number to the known universe cannot come close to inifinite
imagine a computer typing a grahams number amount of numbers a trillionth of a second for a googol number of years.how many numbers will you have at the end?take your anwser and put it to 10 times the power of itself and that is the norris number
@Urbanninja3 Ah, yes, this is because the universe has this weird expansion property, so not only are the furthest parts of the universe moving away at light speed, the space between us and those furthest parts is expanding. Not sure where I got the 156 billion figure from (AndromedasWake maybe) but Wikipedia gives a figure of 93 billion light years on the third paragraph of this page: tinyurl(dot)com(slash)pa68q .
@Mozza314 Ah no worries, Just figured Id help to get your facts in order, Its true the universe does tend to not really make much sense, point being the number of particles in the Universe comes in at around 10^80 which is quite shy of a Googol let alone a Googolplex and Im not really sure what to say about Grahams Number.
@Mozza314 I think the idea is that, the universe is 13.7 billion years old, so it makes sense that it's impossible for anything to have expanded further than 13.7 billion light years from the point of origin, making a circle with a maximum diameter of 27.4 billion light years.
it is correct that the universe expanded faster than the speed of light for some time shortly after the big bang and is therefore larger than (age x speed of light), but the diameter is 78 billion light years (you doubled the number assuming it was the radius while it is already the diamter).
another thing i'd like to point out is that it might be helpful to understand how graham's number is defined (i.e. how the up-arrow-notation works) to get a general idea of its magnitude.
@Ensiferu Yeah I've said a few times that I might make a video on that in the future. I haven't made any videos for ages though. I'll return to it eventually.
@drumstyx6464 no it is impossible to see anything bigger than 13.7 billion light years away, as the universe was created 13.7 billion years ago, the older the universe gets, the more we can see, the universe is expected to be much bigger
@Urbanninja3 According to the most convincing cosmos theory nowadays, the AGE of the universe is 13.7 billion years and the radius of the OBSERVABLE universe is 46.5 billion light years (therefore cross diameter = 93 bly)
@ES350ES350 I hope you realise what that suggests.
The universe is lets say 14 Billion years old. Light from the outmost points would take 14 billion years to reach the center.
If it were 46.5 Billion it would take 46.5 Billion years.
as it stands space is expanding bettween all that. so you can add some extra distance to your calculation. however objects still appear at a range of 14 billion LY.
I was led to believe 42 was the answer to life death the universe & everything - that's gotta be bigger than any start-up like a mere GRAHAM. Ya can't beat a 42.
@anticorncob6 Hmmm, not exactly. The value you would invent would be akin to minus infiinity. While it's not entirely useless to have a number system with infinity/minus infinity, it's not nearly as enlightening as i = sqrt(-1).
HH(n) = H(H(H...(n))) where it's enclosed H(n) times
H_x(n) is x H's enclosed in n. HHH is HH enclosed HH(n) times.
Then I(n) = H_n(n), and II(n) = I(I(...(n))) where the function is enclosed I(n) times, and so on, and so on with J, K, and after Z comes Z2 and Z3. MY number
is Z(Z_1,000,000(1,000,000))_1,000,000(1,000,000)
@anticorncob6 Hehe, sure. If you're interested in how to define very large numbers, consider taking a look here: tinyurl(dot)com(slash)3v69znn . I suspect your number would bow to the superiority of even, say, S(100).
Good video, but hey... I was really distracted because you look like a young and less hairy version of Russell Brand. Next time, wear a funny hat to draw attention away.
So you take the cross product and get G^2 = -(googolplex)(norrisnumber) and if you sove for it, you get norris number is NEGATIVE G^2/googolplex. I know numbers much larger still.
So you don't understand what "Greeem's #"" means...
THANKS 4 NOT (yes,yes, mate)... actually NOT explaining how it works... and being ****ing annoying at the same time. Thanks, mate..... hope you get stung by a Jack Jumper!... meant to say "jack jumpa'" you kiwi twit! :)
How about this: Graham's number followed by one of Conway's horizontal arrows (that is, as used in Conway's Chained Arrow Notation), followed by Graham's number again, then by another horizontal arrow and Graham's Number again, and so forth, until you have a row of Graham's numbers repeated Graham's number of times, all separated by Conway's horizontal arrows. Now THAT'S a big number!
you people are trying to hard to compute this in laymans terms.......maybe trying to elaborste too much...i can state this number in a simple form that a 10 year old would understand quite easily....when dealing with this kind of magnitude grains of sand and atoms are a fruitless comparable, most people are lost instantly...
@ItsSamTheMainMan Sure, it's possible that there are unknown particles on small enough scales that outnumber Graham's Number. That's pretty meaningless though; you could say that about any number.
@ItsSamTheMainMan I don't think you grasp just how detached from reality Graham's Number is. You can talk about the number of digits in Graham's Number, and the number of digits in that number, and in that number, and so on and so on and we can talk about the digits in the number of digits in the number of digits in the number all day and you would still have a number which is unimaginably massive by comparison to any quantities you have alluded to.
I just wander if the number of mere "layers" in the tower that is g1 step 3^^^^3 is more than the number the author described when he said "a googolplex layers high tower of googolplexes".
Because according to wikipedia I only guess 3^^^3 is smth like googolplex in the power of itself. And 3^^^^3 contains 3^^^3 towers (not layers).
And this means you count the first tower, then the number you get is the number of layers in the next "tower". And ditto this operation 3^^^3 times. Oh man.
So if it's larger than all the permutations of all particles, positions etc. , that means that Graham's number probably contains in itself the sequences of all digital strings of information - videos, music, books and games. Graham's number has somewhere in itself the sequence of digits that your video has, so Graham can sue you for copyright infringement ... !
your sent to hell until you write out (accurately) the entirety of grahams number on paper, and when you get to the end, if you have any mistakes, you have to start alllllllll over until you get it right. you must finish this before you can enter heaven.
any idea as to how many earth years this endeaver might take?
@wilft1 Ha! I think your brain would turn to mush long before you made any significant progress. Perhaps part of the punishment would be that your brain didn't stop functioning. The time it would take would be something like k*log(G) where k is some 'reasonable' number (something you could imagine fairly easily, I'm just not bothering to calculate it). But k*log(G) would still be unreasonably large to imagine (G = Graham's Number).
remember i said that you'd be in hell when you did it, so time there would be meaningless, not to mention that you'd have already left your body behind, so, it might take halfway to forever to get it done, but in the afterlife timescale, you could do it.
it would just really suck balls to have to take on a calculation of that magnitude, in this life, or the next
heck, it probably makes god's brain hurt trying to figure the number.
Great that you show this approach to Big numbers doesn't work. Very funny!
The Buddhists of the 2nd century used a similar type of visualisation - cascades of buddha worlds in atoms of buddha worlds. They came further than you, but still didn't make it halfway to Graham's number ;-)
Is there a negative Graham's number? ( -graham's number) Since nobody knows what this number of Graham's is, it doesn't really exist as a measure of a positive amount. Is it imaginary? Seems irrational, as it has no use whatsoever. Graham really should have got out more, or had a wider field of interests. I DONT GET THE POINT! IT SEEMS PLAUSIBLY CLEVER. In reality, it's pretty dumb I reckon.
The Last 481 digits are 26026771622672160419810652263169355188780 38814483140652526168785095552646051071172000997092 91249544378887496062882911725063001303622934916080 25459461494578871427832350829242102091825896753560 43086993801689249889268099510169055919951195027887 17830837018340236474548882222161573228010132974509 27344594504343300901096928025352751833289884461508 94042482650181938515625357963996189939679054966380 03222348723967018485186439059104575627262464195387
Chuck Norris can count from 1 to Graham's number and back in just 3 and a half minutes. And he does that while karate-chops Mr. T in the head with 1 hand and types the entire encyclopedia with the other.
@saradawn6 That's VASTLY understating it, to say the least. The number of atoms in the universe is far closer to the number 1 than it is to Graham's number. A Googol, which is roughly a trillion times the number of atoms in the universe, is itself an atom compared to the universe when set next to Graham's number. It is impossible to state the real size of Graham's number in terms that any human could possibly comprehend.
@saradawn6 It's at LEAST that. The upper estimate for the number of atoms in the observable universe is given roughly as 10^87 and as low as 10^78. A Googol is10^100. A trillion in the short scale is written as 10^12 and we can see then that 10^100 is at least a trillion times bigger than 10^87. In fact 10 trillion times bigger so I was wrong by a magnitude of 10. ;) If the estimate of 10^78 is correct then a Googol is much, much bigger again.
Ok we know Graham's number is 64 layers starting at 4 arrows. Now, to imagine TREE(3) consider one layer with 187196 arrows. Even though that isn't jack compared to Graham's number, its only the number of LAYERS. So compare Graham's 64 layers with TREE(3)'s whatever number you get from 3 (187196 arrows) 3 layers.
@bestofanimaniacs Nope. There are 64 steps to reach Graham's number. Just the first step has 3^3^7.5 trillion towers in it. I've no idea what 3^3^7.5 trillion is but it's WAY WAY bigger than a Googolplex. And that's just the first step! There's another 63 steps with each step being unimaginably bigger than the previous one. Graham's number is far beyond our comprehension.
One way to think of how big it is might be to consider a Googolplex, when written as an exponent (power tower) is 10^10^100. That number written out in decimal (1,000,000 etc) would take a trillion times more space than the known universe provides. Now just the power tower of Graham's number (3^n...n) is so vast that there's not enough space in the universe to even write that out. Just the exponent of Graham's number is bigger than a Googolplex!
best way to understand graham's number, visulaize every atom in the universe as a jar of ink. now vizualze a never ending sheet of paper. If you were to write out graham's number, you would run out of ink b4 u got 2 the decimal point.
about that whole "googolplex to a googolplex, googolplex times" thing. how does number theory even begin to make comparisons with numbers so incalculable?
the final digit to graham's number is 7 and you would need to times all particles in the known universe by a googleplex to the power of a googleplex to get any where near grahams number
I understate a lot of stuff, usually when I'm working, which is probably the worst time to do so.
And it's amazing, because Graham's number is such a large number... but it still doesn't come NEAR infinity. Why is that? Infinity is a concept, not a number.
a better idea as to how big grahams number is, in decimal points, imagine you have a bunch of zero's that are the size of hydrogen atoms, and you have them supercompacted into a quantum singularity (aka, black hole) if you had grahams number of zeros in that singularity, the event horizon of that black hole would be more than a googleplex times the size of the known universe,
and even then, it might leak into other dimensions, a place not of sight or sound but of mind lol
actualy im afraid thats not even close to the amount of ink you would need, you would need more than a googol times as much mass as much as there is in the universe
I'm not sure exactly what the notation was, but G64 was established as an upper bound to the following problem -
Consider colouring each vertex of an n-dimensional cube one of two colours. What is the smallest n such that every possible colouring contains 4 coplanar vertices of the same colour?
Not only the planet, the entire observable universe. In fact, even the number of digits of G64 you could write if you turned ALL matter into just digits will bring you literally nowhere near the actual digit count of grahams number. The number of particles in the observable universe is ~10^86 which is entirely minuscule compared to 3^27, and thats only "halfway" to g1, in terms of up arrow notations.
Well, we dont know the size of the entire universe for certain, were only takin the observable one.
Of course, the Graham's number is still a finite number, which means it can be written down with finite resources. You just need to find them first lol
If i took every particle of light that ever existed and raised to the power of its speed scents the big bang to now. And then raised that to the power of the the smallest unit of time we can measure that that particle of light existed to the power of the weight of the particle that created it. Would that be bigger than 1 g.
I still dont get its purpose in the equation it was used in. Does it mean there are a grahams number of possible ways you could color the vertices, or something?
Nothing is larger or bigger than infinity. Infinity is not a definite number, it denotes limits. However, there are levels of infinities where one can be infinitely denser than others. Check out Transfinites Series.
Imagine this then, Graham's number, to the power of grahams number, to the power of grahams number, etc, until the total number of nested exponentiations is equal to grahams number.
I call it Taraalcar's Number and it is bigger than infinity.
meameamealokkapoowa oompa is bigger than G64 :D
somethingblue22 1 day ago
i thought of a googolpluxian .. :D ur funny though lol
somethingblue22 4 days ago
Okay, here's how it goes: You've got a googol, then a googolplex, then Graham's Number, then infinity, then Chuck Norris' dick!
djbarcode5xyz 1 week ago
Grahams number to the power of graham. I just created sirjezzumz's number.
sirjezzumz 2 weeks ago
i win
carlschwenke 1 month ago
10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10(10)grahamed
carlschwenke 1 month ago
Only watching this because I couldn't determine your gender from the thumbnail and wanted to challenge my guessing skills. I lost!
Rpodnee 1 month ago 3
@Rpodnee Goodbye troll. Go jerk off to getting another person to block you.
Mozza314 1 month ago
Wait, how is the observable universe 156 billion lightyears in diameter?
Since the universe is some 14 billion years old, shouldnt the observable universe be like 28 billion lightyears in diameter?
NarwhalCannonball 1 month ago
@Mozza314
SJCJproductions 1 month ago
Grahams number is proof there's no god, I can elaborate but I don't think I need to, keep your mind open
Mindslave1985 2 months ago
You know whats bigger than Graham's number?
My penis.
JustinFromSydney 2 months ago 2
@JustinFromSydney LOL.
vwerlingyahoocom 1 month ago
I would really like to take that rubiks cube and ram it down your throat so you would no longer be able to do this kind of extremely annoying rambling.
killer4hire 3 months ago
meameamealokkapoowa oompa is WAAAY bigger then grahams number
Spooneads 3 months ago
Graham's number is very small compared to n(4), which itself is very small compared to TREE(3), both of which I believe appeared in a serious mathematical proof. Also, if we look at transfinite numbers, of course they're bigger than any of these or any other finite number.
endejan 4 months ago
How would one use numbers of this size in a mathematical scheme? Infinity will always be the largest value of anything, even greater than any unit in the universe if the universe theoretically kept expanding for eternity. But Graham's number is still finite regardless, but it's freakin' unbelievably finite. Infinity is more of a concept than a number, but does this mean that Graham's number is also a concept; but in a different way?
swygster 4 months ago
@swygster Graham's number is as much a number as 1, 2, or 3. Graham's number was proven to be an upper bound to a problem.
Mozza314 4 months ago
@swygster it was the answer to a problem to a problem of multi-dimensional cubes no one knows the exact amount of digits or what it even begins with, all that is known right now (to my knowledge) is that the number ends in seven
Bennet8212 4 months ago
There are 64 G steps in Graham's number. The first step is G1= 3↑↑↑(3↑↑↑3). A googolplexian is less than 3↑↑6, which is a tiny, tiny, minuscule fraction of G1. G2 is 3↑(G1 times)3 and G3 = 3↑(G2 times)3 and so on until G64 is reached. A googolplexian is a truly gigantic number that is FAR FAR beyond our comprehension but size-wise it is an atom compared to the universe next to Graham's number. It is so far beyond a googolplexian it's not even funny.
BruceyBoy 4 months ago
1:00 there are 1929770126028800 combinations on a rubiks cube.
Spooneads 4 months ago
"Suppose you say 'Graham's number +1' ...Well then you would be an annoying motherfucker!" BAHAHA XD
Seriously though...this video didn't explain the "power tower" notation, so it was practically useless, but it was funny as hell anyway. XD
MrKasey361 4 months ago
@MrKasey361 Yeah well, that was the intention :-P.
Mozza314 4 months ago
So how much is grahams number is it 10 to the power of googolplexian?
BuRaK0210 5 months ago
@BuRaK0210 Nah, the solution to 10^x = Graham's Number is unthinkably large even by comparison with a googleplex.
Mozza314 4 months ago
Even the founder Ronald Graham doesnt know how big it is but he confirms that it is smaller than infinity this GOD, SCIENCE, TIME SPACE what ever you want to call it nfty will Graham's number to shame!!
theonlywaytofun 5 months ago
infinite is larger than Graham's number infinite is a different beast think of Infinite it would take a Graham's number to the power of Graham's number or if you could power towers Graham's number to the known universe cannot come close to inifinite
theonlywaytofun 5 months ago
how many digits are in grams number. does it have a googleplex of digests.
Berserk100 5 months ago
@Berserk100
Think of an infinity of numbers. There we are starting to get close to Graham's number.
OriginalMindTrick 5 months ago
I wonder if God has created a Graham's number of universe or is the number of universe in God's creation...dare I say...infinite??????
19792403 6 months ago
graham's number is 13 letters long.
infinity is 8 letters long.
It's bigger than INFINITY!
Gmaster350 6 months ago
@Gmaster350 LOL!
bogidon 4 months ago
imagine a computer typing a grahams number amount of numbers a trillionth of a second for a googol number of years.how many numbers will you have at the end?take your anwser and put it to 10 times the power of itself and that is the norris number
LordShadowHack 6 months ago
Known universe has a radius of about 13.7 Billion light years, so end to end your looking closer to 27.4 Billion Light years. just pointing it out.
Urbanninja3 6 months ago
@Urbanninja3 Could you give me a timestamp where I contradict your point? Makes it easier for me to check.
Mozza314 6 months ago
@Mozza314 1:24 You say "Its a big sphere which is 156billion light years from one side to the other."
Urbanninja3 6 months ago
@Urbanninja3 Ah, yes, this is because the universe has this weird expansion property, so not only are the furthest parts of the universe moving away at light speed, the space between us and those furthest parts is expanding. Not sure where I got the 156 billion figure from (AndromedasWake maybe) but Wikipedia gives a figure of 93 billion light years on the third paragraph of this page: tinyurl(dot)com(slash)pa68q .
Mozza314 6 months ago
@Mozza314 Ah no worries, Just figured Id help to get your facts in order, Its true the universe does tend to not really make much sense, point being the number of particles in the Universe comes in at around 10^80 which is quite shy of a Googol let alone a Googolplex and Im not really sure what to say about Grahams Number.
Urbanninja3 6 months ago
@Mozza314 As big as Grahams number is I would just lke to point out that Aleph Null is very much bigger, but it is something of a cheat.
Urbanninja3 6 months ago
@Mozza314 I think the idea is that, the universe is 13.7 billion years old, so it makes sense that it's impossible for anything to have expanded further than 13.7 billion light years from the point of origin, making a circle with a maximum diameter of 27.4 billion light years.
drumstyx6464 5 months ago
@drumstyx6464 Yeah I understand the reasoning, the point is it doesn't take into account the space expansion thing.
Mozza314 5 months ago
@Mozza314
it is correct that the universe expanded faster than the speed of light for some time shortly after the big bang and is therefore larger than (age x speed of light), but the diameter is 78 billion light years (you doubled the number assuming it was the radius while it is already the diamter).
another thing i'd like to point out is that it might be helpful to understand how graham's number is defined (i.e. how the up-arrow-notation works) to get a general idea of its magnitude.
Ensiferu 5 months ago
@Ensiferu Yeah I've said a few times that I might make a video on that in the future. I haven't made any videos for ages though. I'll return to it eventually.
Mozza314 4 months ago
@drumstyx6464 no it is impossible to see anything bigger than 13.7 billion light years away, as the universe was created 13.7 billion years ago, the older the universe gets, the more we can see, the universe is expected to be much bigger
Bennet8212 4 months ago
@Urbanninja3 Actually it`s about ~93billion light years due to the acceleration
TAz69x 6 months ago
@Urbanninja3 According to the most convincing cosmos theory nowadays, the AGE of the universe is 13.7 billion years and the radius of the OBSERVABLE universe is 46.5 billion light years (therefore cross diameter = 93 bly)
ES350ES350 5 months ago
@ES350ES350 I hope you realise what that suggests.
The universe is lets say 14 Billion years old. Light from the outmost points would take 14 billion years to reach the center.
If it were 46.5 Billion it would take 46.5 Billion years.
as it stands space is expanding bettween all that. so you can add some extra distance to your calculation. however objects still appear at a range of 14 billion LY.
Also to put Grahams number into context.
AlephNull
Urbanninja3 5 months ago
Graham's^Graham's^Graham's...and so on for Graham's number times. LOL
aserath01 6 months ago
graham's number^graham's number
problem?
LuceoLeo 6 months ago
@LuceoLeo Using Graham's number itself is cheating, hence my comment about Graham's number + 1.
Mozza314 6 months ago
2^(G(G-1)/2)
is bigger. :) And I've even used it in a proof! TAKE THAT!!!
anticorncob6 6 months ago
Why do I want to punch you in the face so badly?
drmoroe30 7 months ago
did you pick the stickers off the rubix cube
mizzou4life1993 7 months ago
@mizzou4life1993 Nope, I can solve the rubik's cube in about 40 seconds.
Mozza314 7 months ago
@Mozza314 thats tight
mizzou4life1993 6 months ago
I was led to believe 42 was the answer to life death the universe & everything - that's gotta be bigger than any start-up like a mere GRAHAM. Ya can't beat a 42.
camelfoot64 7 months ago
I <3 3.15.
Nekrostyles 7 months ago
The amount of inches of Chuck Norris' penis comes close to exceeding Graham's number. But not quite.
wingsofliberty437 7 months ago
10^x = 0
There is no solution for x, even in the complex number system. Is it legal to invent such a value for x, in the same way we did for x^2 = -1?
anticorncob6 7 months ago
@anticorncob6 Hmmm, not exactly. The value you would invent would be akin to minus infiinity. While it's not entirely useless to have a number system with infinity/minus infinity, it's not nearly as enlightening as i = sqrt(-1).
Mozza314 7 months ago
Graham's number is nothing compared to TREE(3) though
Hendurik 7 months ago
H(n) = n^^^^....n
HH(n) = H(H(H...(n))) where it's enclosed H(n) times
H_x(n) is x H's enclosed in n. HHH is HH enclosed HH(n) times.
Then I(n) = H_n(n), and II(n) = I(I(...(n))) where the function is enclosed I(n) times, and so on, and so on with J, K, and after Z comes Z2 and Z3. MY number
is Z(Z_1,000,000(1,000,000))_1,000,000(1,000,000)
MY NUMBER IS BIGGER ADMIT IT
anticorncob6 7 months ago
@anticorncob6 Hehe, sure. If you're interested in how to define very large numbers, consider taking a look here: tinyurl(dot)com(slash)3v69znn . I suspect your number would bow to the superiority of even, say, S(100).
Mozza314 7 months ago
@Mozza314 Well at least my number is COMPUTABLE. And I forgot when I wrote H(n) I meant there are n arrows.
Now take Aleph_(my number). It's bigger then INFINITY!
anticorncob6 7 months ago
@anticorncob6 Well it's precisely the computability of your number that's likely to make it much smaller :-P.
Mozza314 7 months ago
@Mozza314 (And strictly speaking, the function S is incomputable, individual values or finite sequences of values are computable (I think).)
Mozza314 7 months ago
imagine graham's number factorial
mgcgyugitradeco 8 months ago
Good video, but hey... I was really distracted because you look like a young and less hairy version of Russell Brand. Next time, wear a funny hat to draw attention away.
wazzel2u 9 months ago
@wazzel2u lol
Mozza314 9 months ago
1:59-2:12 like justin beibers penis lol
LordShadowHack 9 months ago
Grahams number is to the norris number like
a negative googolplex is to a positive grahams number.
LordShadowHack 9 months ago
@LordShadowHack So you're saying...
G/(norris number) = (-googolplex)/G
So you take the cross product and get G^2 = -(googolplex)(norrisnumber) and if you sove for it, you get norris number is NEGATIVE G^2/googolplex. I know numbers much larger still.
anticorncob6 8 months ago
So you don't understand what "Greeem's #"" means...
THANKS 4 NOT (yes,yes, mate)... actually NOT explaining how it works... and being ****ing annoying at the same time. Thanks, mate..... hope you get stung by a Jack Jumper!... meant to say "jack jumpa'" you kiwi twit! :)
DRAKULU 9 months ago
The Norris number is bugger
LordShadowHack 9 months ago
Comment removed
anticorncob6 9 months ago
WTF? That's creepy. How'd you know my name? The first thing that came to mind was to stick Graham's number in the args of the ackermann function.
Ormaaj 9 months ago
@Ormaaj LOL
Mozza314 9 months ago
graham's number plus one's last digit is 8...I am not kidding.
PoliMeim 9 months ago
How about this: Graham's number followed by one of Conway's horizontal arrows (that is, as used in Conway's Chained Arrow Notation), followed by Graham's number again, then by another horizontal arrow and Graham's Number again, and so forth, until you have a row of Graham's numbers repeated Graham's number of times, all separated by Conway's horizontal arrows. Now THAT'S a big number!
italorican 10 months ago
thats what she said...... grahms is bigger ( my name is grahm)
MrTripleAvideos 10 months ago
It ain't bigger than my ego :O.
Ripley747 11 months ago
you people are trying to hard to compute this in laymans terms.......maybe trying to elaborste too much...i can state this number in a simple form that a 10 year old would understand quite easily....when dealing with this kind of magnitude grains of sand and atoms are a fruitless comparable, most people are lost instantly...
boomboxbadboy1 11 months ago
@ItsSamTheMainMan Well, not according to quantum mechanics, same goes for sizes of particles. Try googling "planck length" or "planck time".
Mozza314 11 months ago
@ItsSamTheMainMan Sure, it's possible that there are unknown particles on small enough scales that outnumber Graham's Number. That's pretty meaningless though; you could say that about any number.
Mozza314 11 months ago
@ItsSamTheMainMan I don't think you grasp just how detached from reality Graham's Number is. You can talk about the number of digits in Graham's Number, and the number of digits in that number, and in that number, and so on and so on and we can talk about the digits in the number of digits in the number of digits in the number all day and you would still have a number which is unimaginably massive by comparison to any quantities you have alluded to.
Mozza314 11 months ago
@ItsSamTheMainMan You would need a much bigger strip of paper to write Graham's Number down.
Mozza314 11 months ago
@ItsSamTheMainMan What do you mean? The number of atoms in a googolplex of universes? If so, Graham's number is way bigger.
Mozza314 11 months ago
You can look up Kruskal's Tree Theorem on wikipedia to learn about TREE functions.
steverichichi 1 year ago
TREE(3) is bigger than Graham's number. Just saying.
steverichichi 1 year ago
@steverichichi What's this "TREE" function? It's hard to look that up, you know, "tree" being such an everyday word.
Mozza314 1 year ago
And this number was actually used in a mathematical proof
david52875 1 year ago
whats graham's number divided by 0???
david52875 1 year ago
I just wander if the number of mere "layers" in the tower that is g1 step 3^^^^3 is more than the number the author described when he said "a googolplex layers high tower of googolplexes".
Because according to wikipedia I only guess 3^^^3 is smth like googolplex in the power of itself. And 3^^^^3 contains 3^^^3 towers (not layers).
And this means you count the first tower, then the number you get is the number of layers in the next "tower". And ditto this operation 3^^^3 times. Oh man.
oddictive 1 year ago
i said to my self gram's number times 10 LOL
bluewisdomtriforce 1 year ago
What I learned from this video:
Graham's # > 5
Mattprole 1 year ago
how about INFINITY!!! ha
W0lfster 1 year ago
googolplexian!
pgy002 1 year ago
So if it's larger than all the permutations of all particles, positions etc. , that means that Graham's number probably contains in itself the sequences of all digital strings of information - videos, music, books and games. Graham's number has somewhere in itself the sequence of digits that your video has, so Graham can sue you for copyright infringement ... !
djbanizza 1 year ago
graham's number + 0.000000000000000000000000000000000000000000000000000000000000000000000000001 ;)
TheScars75 1 year ago
how's this for Hell,
your sent to hell until you write out (accurately) the entirety of grahams number on paper, and when you get to the end, if you have any mistakes, you have to start alllllllll over until you get it right. you must finish this before you can enter heaven.
any idea as to how many earth years this endeaver might take?
wilft1 1 year ago
@wilft1 Ha! I think your brain would turn to mush long before you made any significant progress. Perhaps part of the punishment would be that your brain didn't stop functioning. The time it would take would be something like k*log(G) where k is some 'reasonable' number (something you could imagine fairly easily, I'm just not bothering to calculate it). But k*log(G) would still be unreasonably large to imagine (G = Graham's Number).
Mozza314 1 year ago
@Mozza314
remember i said that you'd be in hell when you did it, so time there would be meaningless, not to mention that you'd have already left your body behind, so, it might take halfway to forever to get it done, but in the afterlife timescale, you could do it.
it would just really suck balls to have to take on a calculation of that magnitude, in this life, or the next
heck, it probably makes god's brain hurt trying to figure the number.
MANDPMOMMY 1 year ago
@Mozza314
i accidentally made the response on my wifes account, so that last comment from mandpmommy was me.
wilft1 1 year ago
Great that you show this approach to Big numbers doesn't work. Very funny!
The Buddhists of the 2nd century used a similar type of visualisation - cascades of buddha worlds in atoms of buddha worlds. They came further than you, but still didn't make it halfway to Graham's number ;-)
novaloka.nl/bigCourtesy/Avatamsaka/chapter30.html
exwaan 1 year ago
As I recall, Graham's number was one possible solution to a particular question. The other possible answer was six.
chrisofnottingham 1 year ago
so that means graham's number times your penis size is about 50,000. that's my estimate.
quidnick 1 year ago
douglas??
hulanahula 1 year ago
Is there a negative Graham's number? ( -graham's number) Since nobody knows what this number of Graham's is, it doesn't really exist as a measure of a positive amount. Is it imaginary? Seems irrational, as it has no use whatsoever. Graham really should have got out more, or had a wider field of interests. I DONT GET THE POINT! IT SEEMS PLAUSIBLY CLEVER. In reality, it's pretty dumb I reckon.
hulanahula 1 year ago
The Last 481 digits are 26026771622672160419810652263169355188780 38814483140652526168785095552646051071172000997092 91249544378887496062882911725063001303622934916080 25459461494578871427832350829242102091825896753560 43086993801689249889268099510169055919951195027887 17830837018340236474548882222161573228010132974509 27344594504343300901096928025352751833289884461508 94042482650181938515625357963996189939679054966380 03222348723967018485186439059104575627262464195387
Primus2X 1 year ago
@Primus2X PROVE IT!
hulanahula 1 year ago
but graham's number is no way near infinity
Supermegamachinedog 1 year ago
You have thoroughly broken my brain. Thanks a lot.
andros1984 1 year ago
This has been flagged as spam show
Chuck Norris can count from 1 to Graham's number and back in just 3 and a half minutes. And he does that while karate-chops Mr. T in the head with 1 hand and types the entire encyclopedia with the other.
ES350ES350 1 year ago
Grahams numbers bigger than the amount of atoms in the known universe.
Simple. Cut to the point.
saradawn6 1 year ago
@saradawn6 That's VASTLY understating it, to say the least. The number of atoms in the universe is far closer to the number 1 than it is to Graham's number. A Googol, which is roughly a trillion times the number of atoms in the universe, is itself an atom compared to the universe when set next to Graham's number. It is impossible to state the real size of Graham's number in terms that any human could possibly comprehend.
BruceyBoy 1 year ago
@BruceyBoy
A 100 Zeros is not a trillion times bigger than the amount of atoms.
saradawn6 1 year ago
@saradawn6 It's at LEAST that. The upper estimate for the number of atoms in the observable universe is given roughly as 10^87 and as low as 10^78. A Googol is10^100. A trillion in the short scale is written as 10^12 and we can see then that 10^100 is at least a trillion times bigger than 10^87. In fact 10 trillion times bigger so I was wrong by a magnitude of 10. ;) If the estimate of 10^78 is correct then a Googol is much, much bigger again.
BruceyBoy 1 year ago
I use grahams number to determine the number of times I've been to ur moms house
XGllClLUTClHll 1 year ago
Super graham's number
like graham's number but you replace every 3 with G(G(G.......G(g4))) <-a Google iterations og G(x)
apvansel 1 year ago
useful for what? what was graham's number useful for?
mana2432 1 year ago
Ok we know Graham's number is 64 layers starting at 4 arrows. Now, to imagine TREE(3) consider one layer with 187196 arrows. Even though that isn't jack compared to Graham's number, its only the number of LAYERS. So compare Graham's 64 layers with TREE(3)'s whatever number you get from 3 (187196 arrows) 3 layers.
xA13dx 1 year ago
Is...
a googleplex^^^^^^^^...^^(a googleplex arrows)googleplex comparable to Graham's number?
bestofanimaniacs 1 year ago
@bestofanimaniacs Nope. There are 64 steps to reach Graham's number. Just the first step has 3^3^7.5 trillion towers in it. I've no idea what 3^3^7.5 trillion is but it's WAY WAY bigger than a Googolplex. And that's just the first step! There's another 63 steps with each step being unimaginably bigger than the previous one. Graham's number is far beyond our comprehension.
BruceyBoy 1 year ago
@bestofanimaniacs NO, not even close!
pifibbi 1 year ago
I found a Graham's dollar bill. Awesome!
TAz69x 1 year ago 15
@TAz69x So can I get a 1% tip for enlightening you to its meaning?
Mozza314 1 year ago
@Mozza314 I'll be generous, 10%
TAz69x 1 year ago
@TAz69x Hoorah!
Mozza314 1 year ago
@TAz69x
Maybe if we're lucky Zimbabwe will have one before the heat death of the universe.
Dealjobber 1 year ago
@TAz69x you could buy EVERYTHING with it. but no one would take your money cause theres nothing left to use ur money for
vodizzzle 6 months ago
One way to think of how big it is might be to consider a Googolplex, when written as an exponent (power tower) is 10^10^100. That number written out in decimal (1,000,000 etc) would take a trillion times more space than the known universe provides. Now just the power tower of Graham's number (3^n...n) is so vast that there's not enough space in the universe to even write that out. Just the exponent of Graham's number is bigger than a Googolplex!
BruceyBoy 1 year ago
best way to understand graham's number, visulaize every atom in the universe as a jar of ink. now vizualze a never ending sheet of paper. If you were to write out graham's number, you would run out of ink b4 u got 2 the decimal point.
coffee4everyoneMD 1 year ago
about that whole "googolplex to a googolplex, googolplex times" thing. how does number theory even begin to make comparisons with numbers so incalculable?
also: TREE(3) >> G(64), or so they tell me.
Kruskal's tree theorem
ATL45 1 year ago
Grahams number in the Ackerman function,
lol
n7275 2 years ago
17.692 × 10−105 m³
n7275 2 years ago
it use to hold the record! What holds it now!?
narpokxd 2 years ago
"maybe you would say grahams number plus 1, then you would be an annoying motherfucker!" LMAO
RSKullcrusha 2 years ago 14
...and yet it's no nearer to infinity than the number 1
Vasyukov 2 years ago
the final digit to graham's number is 7 and you would need to times all particles in the known universe by a googleplex to the power of a googleplex to get any where near grahams number
shaggy592 2 years ago
@shaggy592 Its far bigger than that.
neil9327 2 years ago
That still isnt anywhere near grahams number... no closer to it than 1.
lukeeeh92 2 years ago
Can we just agree that you'd need a shitload of computer memory to hold Graham's Number?
Scorp316 2 years ago
Well, that's still a massive understatement, but I guess so.
Mozza314 2 years ago
I understate a lot of stuff, usually when I'm working, which is probably the worst time to do so.
And it's amazing, because Graham's number is such a large number... but it still doesn't come NEAR infinity. Why is that? Infinity is a concept, not a number.
Scorp316 2 years ago
heh true but grahams number is no closer to infinity than the number one
FuckNewbs 1 year ago
U would need 1 Graham byte of memory xD
shikakahh 1 year ago
@Scorp316
a better idea as to how big grahams number is, in decimal points, imagine you have a bunch of zero's that are the size of hydrogen atoms, and you have them supercompacted into a quantum singularity (aka, black hole) if you had grahams number of zeros in that singularity, the event horizon of that black hole would be more than a googleplex times the size of the known universe,
and even then, it might leak into other dimensions, a place not of sight or sound but of mind lol
wilft1 1 year ago
you are very annoying
rossatron777 2 years ago
if you want to wricht down the number you need 10milion times all of the atoms in the world and than turn everything in inkt
rubikfan1 2 years ago
or 1 computer with alot of memory
afatchild 2 years ago
im afraid even a computer a trillion times the universe coudnt have the memory needed
JimothyJimson 2 years ago
actualy im afraid thats not even close to the amount of ink you would need, you would need more than a googol times as much mass as much as there is in the universe
JimothyJimson 2 years ago
there is a number bigger than graham's number. It is Graham's number plus one.
toweronepower 2 years ago
so the last digit is 8
afatchild 2 years ago
does anyone know where I can find this number written out? Or can the internet not handle showing it?
luno44 2 years ago
No, it can't be written out.
Mozza314 2 years ago
what's the part at the end when you say it appeared in a serious mathematical proof? Did it appear as "G64"?
luno44 2 years ago
I'm not sure exactly what the notation was, but G64 was established as an upper bound to the following problem -
Consider colouring each vertex of an n-dimensional cube one of two colours. What is the smallest n such that every possible colouring contains 4 coplanar vertices of the same colour?
Mozza314 2 years ago
i'm having a hard time picturing this. do you have a vid on it?
luno44 2 years ago
I heard on 'QI' That if all the matter in the entire planet was made into ink, there would not be enough ink to write this number down.
toweronepower 2 years ago
@toweronepower
Not only the planet, the entire observable universe. In fact, even the number of digits of G64 you could write if you turned ALL matter into just digits will bring you literally nowhere near the actual digit count of grahams number. The number of particles in the observable universe is ~10^86 which is entirely minuscule compared to 3^27, and thats only "halfway" to g1, in terms of up arrow notations.
Henry14arsenal2007 2 years ago
So this is sort of a philosophical question also is it not? Can we really say that this number exists if we cannot observe it?
toweronepower 2 years ago
Well, we dont know the size of the entire universe for certain, were only takin the observable one.
Of course, the Graham's number is still a finite number, which means it can be written down with finite resources. You just need to find them first lol
Henry14arsenal2007 2 years ago
Aleph one is a transfinite number that is bigger than all finite numbers but is not yet infinity thanks to cardinality
UgotJoshD 2 years ago
If i took every particle of light that ever existed and raised to the power of its speed scents the big bang to now. And then raised that to the power of the the smallest unit of time we can measure that that particle of light existed to the power of the weight of the particle that created it. Would that be bigger than 1 g.
IMakeOrWatchVideos 2 years ago
Your description is kind of sloppy, but it definitely sounds far inferior to 1 g by any reasonable interpretation.
Mozza314 2 years ago
I agree. Im not good writer. But still my god that 1g is big.
IMakeOrWatchVideos 2 years ago
I still dont get its purpose in the equation it was used in. Does it mean there are a grahams number of possible ways you could color the vertices, or something?
Taraalcar 2 years ago
Nothing is larger or bigger than infinity. Infinity is not a definite number, it denotes limits. However, there are levels of infinities where one can be infinitely denser than others. Check out Transfinites Series.
vdtmh 2 years ago
Of course.
Mozza314 2 years ago
Imagine this then, Graham's number, to the power of grahams number, to the power of grahams number, etc, until the total number of nested exponentiations is equal to grahams number.
I call it Taraalcar's Number and it is bigger than infinity.
Taraalcar 2 years ago