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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

#61

Post by harryjo »

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 don't think anyone believes that Go is somehow more complex than the universe it is a subset of. The point is that enumerating all cases of Go is impossible and always will be, so more sophisticated analysis is required.

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

#62

Post by evanpw »

overcast wrote: post #10
j1vms wrote: post #5

Here's another great one - and ballpark calculations point to it being likely true: "..the number of atoms in a grapefruit is about equal to the number of blueberries you would need to fill up the entire sphere of planet Earth." [ https://capitolhillscience8.wordpress.com/2012/10/03/just-ho... ] Edit: well, except that the Earth is shaped more like an oblate spheroid [ https://en.wikipedia.org/wiki/Figure_of_the_Eart…

Actually the Earth is nearly perfect, far more perfect than most any sphere with interact with in day to day life. The equatorial bulge is 20 miles or so, which is approximately .33% Technically an oblate spheroid, but barely.

There's a great Isaac Asimov essay on this topic: http://chem.tufts.edu/answersinscience/relativityofwrong.htm

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

#63

Post by pron »

jobigoud wrote: post #58
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

I think that the context matters. While his actual statement is now false, he was really talking about a "solution" to Go, i.e. an algorithm that can compete with any opponent (and back then, Go programs couldn't "even" beat humans). Google's algorithm is (probably) nowhere near a "solution" to Go, but an algorithm that can beat currently-living human opponents. I.e. it is quite likely that a rather simple algorithm would still beat Google's program, only that people's minds don't (or can't) employ that algorithm when they play.

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

#64

Post by tromp »

harryjo wrote: post #61
sametmax wrote: post #39

Earlier quoted context omitted.

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 don't think anyone believes that Go is somehow more complex than the universe it is a subset of. The point is that enumerating all cases of Go is impossible and always will be, so more sophisticated analysis is required.

Indeed, enumerating all

208168199381979984699478633344862770286522453884530548425 639456820927419612738015378525648451698519643907259916015 628128546089888314427129715319317557736620397247064840935

positions in Go is impossible.

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

#67

Post by levemi »

dsfuoi wrote: post #45
Retric wrote: post #43

Earlier quoted context omitted.

Don't conflate the "Observable Universe" with the actual Universe. We flat out don't know how big the actual Universe is. So, it could be 10^80, 10^800, or even A(10, 80)* Atoms. * https://en.wikipedia.org/wiki/Ackermann_function

It could be infinite.

If that is the case was the universe once finite and then went infinite during the early (big bang) expansion? I don't understand how something could have expanded if it was always infinite in size. I'm not even sure the concept of expansion even makes sense. What is infinite + 1? It's just infinite. It seems more like the expansion is a distribution of internal things.

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

#68

Post by d_theorist »

yathern wrote: post #60
d_theorist wrote: post #47

Earlier quoted context omitted.

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.

Makes sense. Thanks.

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

#69

Post by DougWebb »

levemi wrote: post #67
dsfuoi wrote: post #45

Earlier quoted context omitted.

It could be infinite.

If that is the case was the universe once finite and then went infinite during the early (big bang) expansion? I don't understand how something could have expanded if it was always infinite in size. I'm not even sure the concept of expansion even makes sense. What is infinite + 1? It's just infinite. It seems more like the expansion is a distribution of internal things.

Off the cuff thought: the overall universe is infinite and not expanding, and it's only the visible universe that's expanding into that infinite space.

Now try to wrap your mind around this: someone that's one light year to the left is going to see a slightly different visible universe, also expanding, into the same infinite space. But if we look in their direction, we see the edge of our visible universe expanding into the void, but from their point of view looking in the same direction our edge is one light year short of their edge. So what's our edge expanding into?

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

#70

Post by Retric »

levemi wrote: post #67
dsfuoi wrote: post #45

Earlier quoted context omitted.

It could be infinite.

If that is the case was the universe once finite and then went infinite during the early (big bang) expansion? I don't understand how something could have expanded if it was always infinite in size. I'm not even sure the concept of expansion even makes sense. What is infinite + 1? It's just infinite. It seems more like the expansion is a distribution of internal things.

Math includes the idea of orders of infinity. There are infinite prime numbers, there are more positive integers, even more integers (positive and negative), even more rational numbers (A/B), and even more numbers (rational + irrational {e, Pi} etc)...
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