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On the (Small) Number of Atoms in the Universe

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Re: On the (Small) Number of Atoms in the Universe

#51

Post by tomrod »

sametmax wrote: post #39
boredguy8 wrote: post #29

I like how Ken Jennings dealt with the 'Go complexity' analogy: "Go is famously a more complex game than chess, with its larger board, longer games, and many more pieces. Google’s DeepMind artificial intelligence team likes to say that there are more possible Go boards than atoms in the known universe, but that vastly understates the computational problem. There are about 10^170 board positions in Go, and only 10^80…

Comparing combinations with numbers of items is unfair. In Go, the number of items is the number of pieces, and it's very small. In the universe, the number of combinations of positions of all the atoms is, well, wonderful.

I _love_ the way you stated this. Thank you!

Re: On the (Small) Number of Atoms in the Universe

#53

Post by randommodnar »

boredguy8 wrote: post #29

I like how Ken Jennings dealt with the 'Go complexity' analogy: "Go is famously a more complex game than chess, with its larger board, longer games, and many more pieces. Google’s DeepMind artificial intelligence team likes to say that there are more possible Go boards than atoms in the known universe, but that vastly understates the computational problem. There are about 10^170 board positions in Go, and only 10^80…

While this comparison highlights that yes, there are very many possible Go games, it's really apples to oranges.

The real comparison would be the number of pieces on a Go board (19x19 = 361) compared to the number of atoms in the universe. And then to compare the number of possible board positions in Go, with the number of possible atom positions in the universe, and in this case I think the universe wins.....

Re: On the (Small) Number of Atoms in the Universe

#55

Post by lisper »

nitrogen wrote: post #38
lisper wrote: post #11

Earlier quoted context omitted.

The earth is small. If you build a scale model of the solar system the size of a football field, with the sun and one end and Neptune at the other (Pluto has been laid off as a planet) then the sun will be about the size of a ping pong ball and the earth will be the size of a poppy seed (and it will be about ten feet from the sun). Jupiter is about the size of a pea at this scale. Alpha Centauri is about four miles a…

Planets seem like a really big waste of mass in that sense. Computational dust in a cloud around a sun would be a more efficient allocation.

That really depends on your quality metric. If you care about computational speed (because there's only a finite amount of time before the heat death of the universe) then the speed of light starts to be a limiting factor, and concentrating all the computation in a small space makes sense.

Re: On the (Small) Number of Atoms in the Universe

#56

Post by snowwrestler »

nitrogen wrote: post #38
lisper wrote: post #11

Earlier quoted context omitted.

The earth is small. If you build a scale model of the solar system the size of a football field, with the sun and one end and Neptune at the other (Pluto has been laid off as a planet) then the sun will be about the size of a ping pong ball and the earth will be the size of a poppy seed (and it will be about ten feet from the sun). Jupiter is about the size of a pea at this scale. Alpha Centauri is about four miles a…

Planets seem like a really big waste of mass in that sense. Computational dust in a cloud around a sun would be a more efficient allocation.

"The Integral Trees" by Larry Niven is a novel in which people live in a free-floating cloud of atmospheric gas that is gravitationally stable in a multi-star system. They live on enormous trees with canopies on each end, which are blown in opposite directions by the winds (so they look like the integral sign).

Re: On the (Small) Number of Atoms in the Universe

#57

Post by robotresearcher »

nitrogen wrote: post #38
lisper wrote: post #11

Earlier quoted context omitted.

The earth is small. If you build a scale model of the solar system the size of a football field, with the sun and one end and Neptune at the other (Pluto has been laid off as a planet) then the sun will be about the size of a ping pong ball and the earth will be the size of a poppy seed (and it will be about ten feet from the sun). Jupiter is about the size of a pea at this scale. Alpha Centauri is about four miles a…

Planets seem like a really big waste of mass in that sense. Computational dust in a cloud around a sun would be a more efficient allocation.

But pretty great in surface area. Success is all about the metric you choose.

Re: On the (Small) Number of Atoms in the Universe

#58

Post by jobigoud »

marai2 wrote: post #22

Scott Aaronson's blog post on large numbers is also a very interesting read: http://www.scottaaronson.com/writings/bignumbers.html

Ha, trip down memory lane:

> And in Go even an amateur human can still rout the world’s top-ranked computer programs

Re: On the (Small) Number of Atoms in the Universe

#59

Post by dack »

randommodnar wrote: post #53
boredguy8 wrote: post #29

I like how Ken Jennings dealt with the 'Go complexity' analogy: "Go is famously a more complex game than chess, with its larger board, longer games, and many more pieces. Google’s DeepMind artificial intelligence team likes to say that there are more possible Go boards than atoms in the known universe, but that vastly understates the computational problem. There are about 10^170 board positions in Go, and only 10^80…

While this comparison highlights that yes, there are very many possible Go games, it's really apples to oranges. The real comparison would be the number of pieces on a Go board (19x19 = 361) compared to the number of atoms in the universe. And then to compare the number of possible board positions in Go, with the number of possible atom positions in the universe, and in this case I think the universe wins.....

especially considering all go boards exist _within_ the universe!

Re: On the (Small) Number of Atoms in the Universe

#60

Post by yathern »

d_theorist wrote: post #47
marai2 wrote: post #22

Scott Aaronson's blog post on large numbers is also a very interesting read: http://www.scottaaronson.com/writings/bignumbers.html

Very enjoyable. However, I think I found a mistake: "For example, ‘5 tetrated to the 3’ means 5 raised to its own power 3 times, or 5^5^5" (I am paraphrasing slightly here because the essay uses an image to show 5^5^5 in normal notation ( http://www.scottaaronson.com/cgi-bin/mimetex.cgi?5^{5^5}) ) However, shouldn't this be 5^5^5^5, if we're raising 5 to its own power three times?

Not quite - think of it this way:

5 x 3 = 5 + 5 + 5

5 ^ 3 = 5 x 5 x 5

5 t 3 = 5 ^ 5 ^ 5

Where t is tetration. Each one counts 3 fives.

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