is Graham's Number a galactic number?
Galactic Algorithm
11–20 of 74 posts
Re: Galactic Algorithm
#12> 1729 Why is this hyperlinked? I was hoping the link would help explain why 1729 and not some other number, but it’s just trivia... > One immediate practical effect would be to earn the discoverer a million dollar prize from the Clay Mathematics Institute. I mean, I can’t argue with the practicality of that.
I'd argue that it shouldn't be linked, because it's being used in the wrong context. It would be like linking an music album titled "Outer space" to the Wikipedia article on outer space.
Re: Galactic Algorithm
#13is Graham's Number a galactic number? https://en.m.wikipedia.org/wiki/Graham's_number
You could say so:
> As with these, 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, possibly the smallest measurable space. 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.
Re: Galactic Algorithm
#14> 1729 Why is this hyperlinked? I was hoping the link would help explain why 1729 and not some other number, but it’s just trivia... > One immediate practical effect would be to earn the discoverer a million dollar prize from the Clay Mathematics Institute. I mean, I can’t argue with the practicality of that.
I can't explain it, but it's the algorithm discussed here, if you want to read up on it: https://news.ycombinator.com/item?id=19474280
Re: Galactic Algorithm
#15is Graham's Number a galactic number? https://en.m.wikipedia.org/wiki/Graham's_number
But have you heard of Rayo's number?
Re: Galactic Algorithm
#16> 1729 Why is this hyperlinked? I was hoping the link would help explain why 1729 and not some other number, but it’s just trivia... > One immediate practical effect would be to earn the discoverer a million dollar prize from the Clay Mathematics Institute. I mean, I can’t argue with the practicality of that.
I also wonder why that number. But as others said, it's a pretty famous number all by itself so it makes sense for there to be some notice paid to that- if there were no hyperlink I would've thought it's weird and maybe someone made a mistake.
1729 has no special meaning for the multiplication algorithm. In the paper Harvey writes:
> In Section 5 we establish (1.3) with the explicit constant K= 1728, and in Section 5.4 we list some optimisations that improve it to K= 8.
> In Section 5, we will simply take d:= 1729 (any constant larger than K would do)
Re: Galactic Algorithm
#17Ah. I still remember my computational geometry professor telling us about an algorithm to do triangulation (composing a polygon into triangles) in linear time: "It's very complex. I don't think anyone has actually implemented it". It shocked me at the time that there were algorithms like this. https://en.wikipedia.org/wiki/Polygon_triangulation#Computat...
What was shocking about this? Seems like something you could always solve by hand, even if you couldn't quite enumerate the steps you need to take to do it. I guess that's sort of my baseline for whether I expect an algorithm to exist.
Re: Galactic Algorithm
#18is Graham's Number a galactic number? https://en.m.wikipedia.org/wiki/Graham's_number
You could say so: > As with these, 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, possibly the smallest measurable space. 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 represent…
> for a number of times far exceeding the total number of Planck volumes in the observable universe.
Just so I'm clear. They're saying that not only can I not fit Graham's Number in all the Planck volumes of the universe; and I can't even count the digits of GN and write that in the Planck volume of the universe (and so on), but the number of "indirections" is itself so large as to not fit in the universe?
Like:
1. GN (can't fit).
2. Number of digits in GN (can't fit).
3. Number of digits in #2 (can't fit).
4. Number of digits in #3 (can't fit).
...
N. Re: Galactic Algorithm
#19Ah. I still remember my computational geometry professor telling us about an algorithm to do triangulation (composing a polygon into triangles) in linear time: "It's very complex. I don't think anyone has actually implemented it". It shocked me at the time that there were algorithms like this. https://en.wikipedia.org/wiki/Polygon_triangulation#Computat...
What was shocking about this? Seems like something you could always solve by hand, even if you couldn't quite enumerate the steps you need to take to do it. I guess that's sort of my baseline for whether I expect an algorithm to exist.
The shocking thing was that it is a known algorithm but (presumably) nobody ever implemented it.
Re: Galactic Algorithm
#20Earlier quoted context omitted.
Yeah not sure why it's hyperlinked, it's a rather dull number.
“But it’s not dull at all,” Ramanujan replies, “it’s actually the first number that can be written as the sum of two cubes, two different ways!”
But imagine he had said, "it's the number of dimensions your Fourier transform needs for the fastest way to multiply two numbers" :)
BTW who things the other person was really just baiting Ramanujan to say something like this?