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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

#131

Post by spydum »

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......

Obviously I have no evidence, but my suspicions are that its like the pac-man world, it just continuously loops on itself. Its just really big...

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

#132

Post by Retric »

yongjik wrote: post #122
Retric wrote: post #118

Earlier quoted context omitted.

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",…

O, I get it.

There is a basic contradiction in set theory. Called Russell's paradox, there are two ways around it. First is ignoring it, aka everything builds from it's self nothing can become recursive. Or Zer's something or other that basically removed membership and equality and hides in the corner crying.

As such infinity is generally assumed not to exit in R. And causes all this all infinite set's map able to each other are equivalent size crap. It's also why real mathematicians laugh at the set guys.

But, sorry the way R was initially defined it included infinity and you only get to put it into 1 place on your mapping. Or as a math professor said, what angle is the highest number in R mapping to.

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

#133

Post by DonaldFisk »

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.

You can see back as far as the Big Bang, approximately 14 billion years ago, so all matter in the visible Universe is within 14 billion light years of the Earth. However, the space the Universe occupies is only really finite if it's positively curved. If it's flat or negatively curved, the space it occupies is infinite, and if its density is constant, it must contain an infinite amount of matter even though we only see part of it. The Big Bang is a singularity - a point with infinite density. It's hard to get your head around intuitively, but it all makes sense mathematically. (The maths is pretty hard, and rarely covered at undergraduate level.)

The simplest model in rough agreement with observations is called the Einstein-de Sitter Model, and it's flat with a zero cosmological constant. See http://www.britannica.com/science/cosmology-astronomy/Relati...

More general models are covered here: https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtr...

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

#134

Post by deepnet »

tromp wrote: post #129
deepnet wrote: post #126

Earlier quoted context omitted.

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.

In the OP article Norvig suggests 10^172 possible games and games average 200 moves.

Walraet paper has 10^10^103, so 1000 googolplexes - this is very large.

Monte Carlo methods are specifically for guess-timating intractably big searches.

MCTS is close to the human heuristic for evaluating Go positions - counting who currently controls what, multiplied by the strength of each position (in Go 2 'eyes' make a block impervious to harm). Early on this is very subtle to discern - which makes Go a subtle art.

The human heuristic is complex, the MCTS random playout is overly simple but uses gigaflops of random sampling. MCTS was the basis of the best computer (the new innovation is the convnets that prunes the tree before MCTS).

The convnets are trained on a big database of expert games which is why I wonder if the MCTS is the differenting factor & Lee Sedol with an MCTS would beat the Convnet & MCTS.

This is important because: does AlphaGo plan ?

If not, the implication is planning is a poorer heuristic compared with whatever AlphaGo actually does.

The convnet provably doesn't plan, it estimates what a human expert would do and performs tne same whether playing game or just predicting next move from random configurations.

AI research has always held planning in high regard.

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

#135

Post by jakub_h »

Retric wrote: post #115
yongjik wrote: post #103

Earlier quoted context omitted.

1. e + ei is not real. 2. f(x) = x + sqrt(2) if there exists an integer k>=0 such that x - k * sqrt(2) is rational; f(x) = x otherwise. This function maps all real numbers to irrational numbers, 1-to-1.

e is real, e + ei is irrational.

e is irrational, e+ei can't be irrational because it isn't real (all irrationals are reals).

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

#136

Post by iopq »

tromp wrote: post #129
deepnet wrote: post #126

Earlier quoted context omitted.

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.

Actually, MCTS usually doesn't allow eye-filling. That's how it determines a game is over - all of the territory is "eyes". Otherwise, the playout would go on forever, or would stop at an arbitrary stopping point (board width * board length * 3 or something) which is not as accurate.

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

#138

Post by yongjik »

Retric wrote: post #132
yongjik wrote: post #122

Earlier quoted context omitted.

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",…

O, I get it. There is a basic contradiction in set theory. Called Russell's paradox, there are two ways around it. First is ignoring it, aka everything builds from it's self nothing can become recursive. Or Zer's something or other that basically removed membership and equality and hides in the corner crying. As such infinity is generally assumed not to exit in R. And causes all this all infinite set's map able to ea…

Where did you get all this idea? You know enough terms, yet somehow you have an incorrect understanding of pretty much everything.

If you are interested, please read an actual math textbook. (Yes, they can be a giant time sink, but at least you'll learn the correct meanings of sets and functions.)

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

#139

Post by zuminator »

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......

The typical way to picture the universe is like the surface of an expanding balloon, a 2-manifold which happens to be embedded in 3-space. If you picture galaxies as spots on the balloon, there's no "last" galaxy, they're all roughly equidistant from their neighbors. Analogously, our Euclidean universe is thought of (in terms of noncompact spatial dimensions) as an expanding 3-manifold. There's no last galaxy there either. However, if you include time, then at some point in the distant future there will be a last galaxy because old stars will all burn out or be sucked into black holes. And further in the future protons will decay, so there will be no baryonic matter left, plus black holes will eventually evaporate. Much sooner than that though, the continued expansion of spacetime means that galaxies will in time disappear over the expanding cosmological horizon, and future lifeforms will know nothing of the universe outside their own aging galaxies. See: https://en.wikipedia.org/wiki/Future_of_an_expanding_univers...

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

#140

Post by Retric »

pcmonk wrote: post #106
Retric wrote: post #101

Earlier quoted context omitted.

So, you can show the Real numbers between 0 and 1 is larger than the number of Natural numbers. There are an infant number of points between 0 and 1 and an infinite number of points between 0 and 2. The distance between 0 and 2 is larger. The number of points between 0 and 1 is smaller than the number of points on the unit circle AND they are a different class of infinity.

"The distance between 0 and 2 is larger" is a question about the metric of the space, not size of sets. There are the same number of points in both sets, since f(x) = 2x is a bijection between them. Try to make arguments from axioms and definitions rather than asserting things from intuition. Intuition is often a useful tool, but (1) it's not an argument, and (2) it's not very helpful once you step into the infinite…

You say same number, you mean same flavor. Either the 'number' is not in R and thus it's not a number or you end up with a host of contradictions.

But, I have had my fun poking people who don't really get set theory.

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