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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

#121

Post by tromp »

deepnet wrote: post #105
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.

Compared with a googol our Universe has negligible atoms , 10^100 - 10^80 = ~10^100 Compared with a googolplex (10^(10^100)) the entire Evrettian metaverse is negligible as (10^(10^100) - 10^80^2 * (average quarks in atom) * leptons(10^200) * dark multiplier(10^2) = ~1 googolplex Has anyone ever used a googolplex for anything ? [For ~ read approximately]

Matthieu Walraet "used" a googolplex as a lower bound on the number of possible Go games, in http://matthieuw.github.io/go-games-number/GoGamesNumber.pdf

Does that count:-?

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

#122

Post by yongjik »

Retric wrote: post #118
pcmonk wrote: post #116

Earlier quoted context omitted.

I believe you mean "complex". You can form a bijection between the reals and the complex numbers by interleaving the digits, as any Google search can tell you.

For every point on your mapimg I define two points X + 1 and x + 1i. You can assign infinity to one of them but not both.

I'm afraid you have some basic confusion with mathematical concepts, including "mapping", "irrational", "complex", and "infinity".

So, after you define x+1 and x+i, now what? Also please bear in mind that "infinity" is neither real nor complex: if you have a well-defined mapping into complex numbers, then by definition, it never maps to infinity.

(Yes, there are some "functions" like y = 1/x that "maps to infinity", but it's simply mathematicians being lazy and abusing notations because everybody around them understands what's going on.)

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

#123

Post by stouset »

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.

Take the set of positive integers (0, 1, 2…). Double them, so you have (0, 2, 4…). You had an infinite list of numbers, all "compact" (no room for more positive integers inbetween them), and with a simple mathematical transform, you've given yourself space for a second equally-sized infinity of integers to fit neatly inside of them.

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

#124

Post by stouset »

Retric wrote: post #93
pcmonk wrote: post #86

Earlier quoted context omitted.

Where in math is the subset partial ordering used to describe one set as larger than another? Diagonalization isn't showing that a number in set A isn't in set B - that's obviously true for reals and integers, but it's also true for rationals and integers. It's showing that there does not exist a mapping from B to A where there's an element in B for each element in A. We're obviously not using the same definition of…

Cardinality is the number of elements in a set. If every element in set A is in set B, and there are elements in set A left over it's larger because that's what larger means. {A,B} There are countable and uncountable infinite set's. All countable set's have a bijection with N. However, there are more than two sizes of infinite sets. Real numbers < Imaginary numbers.

The cardinality of the set of prime numbers and of rationals are both aleph-null[1]. Same with the list of all integers, the list of all positive integers, and the list of all even integers. They all have the same cardinality, and that cardinality is aleph-null.

But please, continue to argue with mathematical definitions that have been established for over a century.

[1]: https://en.wikipedia.org/wiki/Aleph_number#Aleph-naught

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

#125

Post by lern_too_spel »

deepnet wrote: post #105
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.

Compared with a googol our Universe has negligible atoms , 10^100 - 10^80 = ~10^100 Compared with a googolplex (10^(10^100)) the entire Evrettian metaverse is negligible as (10^(10^100) - 10^80^2 * (average quarks in atom) * leptons(10^200) * dark multiplier(10^2) = ~1 googolplex Has anyone ever used a googolplex for anything ? [For ~ read approximately]

Graham's number - one googolplex raised to the googolplexed power =~ Graham's number, which has been used in a proof. There have been larger numbers used in proofs but none yet as famous as Graham's number, about which Martin Gardner wrote a popular mathematics article. http://iteror.org/big/Source/Graham-Gardner/GrahamsNumber.ht...

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

#126

Post by deepnet »

tromp wrote: post #121
deepnet wrote: post #105

Earlier quoted context omitted.

Compared with a googol our Universe has negligible atoms , 10^100 - 10^80 = ~10^100 Compared with a googolplex (10^(10^100)) the entire Evrettian metaverse is negligible as (10^(10^100) - 10^80^2 * (average quarks in atom) * leptons(10^200) * dark multiplier(10^2) = ~1 googolplex Has anyone ever used a googolplex for anything ? [For ~ read approximately]

Matthieu Walraet "used" a googolplex as a lower bound on the number of possible Go games, in http://matthieuw.github.io/go-games-number/GoGamesNumber.pdf Does that count:-?

That is a staggering amount of possible Go games, no wonder tree search failed to improve without the Convnet pruning.

Makes me wonder if Deepmind could learn Go without first learning from the big dataset of expert games to train the convnet to prune the tree.

Which implies that Deepmind couldn't learn to play Go without first being taught by us (the expert games).

So AlphaGo learnt Go from us. It took a human brain to crack the problem of Go and the AI learned from our solutions it did not discover them itself - still a very great breakthrough.

Would Lee Sedol have won if he could use MCTS to assist his evaluation ?

( Arguably the MCTS is a non-AI component of deepmind & does not learn ).

MCTS = Monte Carlo Tree Search, where repeated random playouts evaluate moves by randomly sampling the tree of following (googolplex) possible moves.

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

#127

Post by Razengan »

Razengan wrote: post #109
DougWebb wrote: post #69

Earlier quoted context omitted.

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 i…

I've always wondered; is there a "last" galaxy in any direction, such that for an observer in that galaxy, no further light or radiation can be detected from that direction? (outside that galaxy) That, must be a terrifying place to live in......

Too late to edit, but I must add that I'm not necessarily asking if there's an "edge" of the Universe.

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

#128

Post by Razengan »

hellameta wrote: post #120
Razengan wrote: post #109

Earlier quoted context omitted.

I've always wondered; is there a "last" galaxy in any direction, such that for an observer in that galaxy, no further light or radiation can be detected from that direction? (outside that galaxy) That, must be a terrifying place to live in......

I don't see how our situation is any less terrifying haha

It's certainly less terrifying than having to look at an infinite abyss.

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

#129

Post by tromp »

deepnet wrote: post #126
tromp wrote: post #121

Earlier quoted context omitted.

Matthieu Walraet "used" a googolplex as a lower bound on the number of possible Go games, in http://matthieuw.github.io/go-games-number/GoGamesNumber.pdf Does that count:-?

That is a staggering amount of possible Go games, no wonder tree search failed to improve without the Convnet pruning. Makes me wonder if Deepmind could learn Go without first learning from the big dataset of expert games to train the convnet to prune the tree. Which implies that Deepmind couldn't learn to play Go without first being taught by us (the expert games). So AlphaGo learnt Go from us. It took a human brain…

The tree searched by MCTS is WAY smaller than a googolplex, since it excludes the eye-filling moves that allow games to go on past 400 or so moves.

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

#130

Post by hasenj »

Razengan wrote: post #109
DougWebb wrote: post #69

Earlier quoted context omitted.

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 i…

I've always wondered; is there a "last" galaxy in any direction, such that for an observer in that galaxy, no further light or radiation can be detected from that direction? (outside that galaxy) That, must be a terrifying place to live in......

I think they would have to be at the edge of their galaxy for this effect to take place ..
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