Graham's Number - Numberphile

A number so epic it will collapse your brain into a black hole! Yet Tony Padilla and Matt Parker take the risk of discussing its magnitude. Watch with caution.
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Videos by Brady Haran

[NoriMori]

I love Wikipedia's description of how big Graham's number is: "It is so large that the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies one Planck volume … But even the number of digits in this digital representation of Graham's number would itself be a number so large that its digital representation cannot be represented in the observable universe. Nor even can the number of digits of that number—and so forth, for a number of times far exceeding the total number of Planck volumes in the observable universe."

[petertimowreef]

Mathemathicians are so funny.
"Imagine a number that's unimaginably high. And then the answer is between that number, and 11. Childsplay really, let's go to the pub."

[ve]

"Can you give me a ballpark"
"It's between 11 and Graham's number"
"That's

[leisulin]

But even as they almost literally said: Graham's number is unimaginably large, but it's still closer to zero than it is to infinity! Which boggles the mind even more.

[nthgth]

"There's still an infinite number of numbers that're bigger than Graham's number, right?  So frankly, we pretty much nailed it as far as I'm concerned."  Lmao

[MordredMS]

I actually came up with an even bigger number.
Graham's Number+1.
I call it "Mr. Whiskers".

[theviniso]

g64/g64=1. That's the only operation that I can do involving this number.

[The_Story_Of_Us]

What makes Graham’s Number so great is that despite its (literally) unfathomable size, we can using less than a page’s worth of word’s describe how to get there. We can describe what 3↑3 means, we can describe what 3↑↑3 means, what 3↑↑↑3 means and what 3↑↑↑↑3 means, then we can describe what G1 is, all the way up to G64, all of it a process of iteration. And using just the power of these symbols and descriptive iteration, we can arrive at a number with 100% precision that arithmetic literally can’t even come close to describing. So when we say that we can’t picture Graham’s Number, I think that’s doing our brains a disservice.

[games]

Graham's number is so insanely large that the number representing the number of digits in Graham's number would have an incomprehensible number of digits itself!

[X-K]

So basically, this number happened because someone gave a Mathematician a coloring book.

[ottoweininger]

The bit where he said we've narrowed it in from between 6 and Graham's Number, to between 11 and Graham's Number made me laugh.

[onebigadvocado]

"There's a very easy analogy"

(Promptly fails the analogy)

[squirrelknight]

"Frankly, we pretty much nailed it!"
Lol that cracked me up

[megatrix]

now... Gn↑↑↑↑↑...↑↑↑↑↑Gn.
|---Gn times---|

Let the universe collapse.

[livinlicious]

The first digit of Grahams Number is 1. (in Binary)

[sproins]

Other mathematicians explaining big numbers: You'd run out of space to write down all the digits.
Matt Parker: You'd run out of pens in the universe.

[doemaeries]

In the next math test I just write 6<x<Graham's Number when it asks me for x

[ckmishn]

According to the holographic principle the most data (bits) that can be stored in a volume is equal to the area of a bounding sphere in Planck lengths squared divided by 4. The visible universe is about 10^26 meters in length and Planck length is ~10^-35, so very roughly the visible universe can contain something like 10^122 bits of data before being "full" and collapsing into a black hole.

Writing out, or otherwise listing the full expansion of a number without resorting to exponents, arrow-notation, recursion or other methods of compression requires a number of bits equal to the log of the number.

Saying that your brain would collapse into a black hole if you had all the digits of Graham's Number in your head is one of the all-time biggest understatements. The entire visible Universe actually can't even contain the expansion of 3(three arrow)3. In fact even if you use exponents but just insist on printing out the exponents you still can't print out the expansion of 3(four arrow)3. Even resorting to arrow notation I think it's impossible to print out the expansion for the number of arrows any more than three levels lower.

[grantmayberry]

8:30 "We pretty much nailed it as far as I'm concerned." Never mind the fact that that number is longer than the observable universe.

[girormk]

i will give the man who tells me the entire graham's number a nobel peace prize for stopping the chaos going inside my head right now