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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

#151

Post by jbclements »

Retric wrote: post #119
pherq wrote: post #102

Earlier quoted context omitted.

Assuming you consider the dimensions/axes/whatever of the 2d space to be indexed by reals (which is conventional), then yes one can construct a bijection: - normalise x and y coordinates in the shape into the interval (0, 1) - interleave the bits of the normalised x and y coordinates This gives a single real value in the interval (0, 1), which exists and is unique for every point in the space (so it is an injection),…

You used a countable infinity to tile an uncountable one. The set of 0 to 1 line segments being a countable infinity. 0 to 1 maps 1, 1 to 2 maps to 2 ect.

I believe you misread the text you're replying to. The bijection is between the points in the 2d space and the points in the line segment. Both of these are uncountably infinite.

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

#152

Post by andrewflnr »

yolesaber wrote: post #73
yk wrote: post #41

Earlier quoted context omitted.

The electron goes forward and backward in time and interacts with itself. (In quantum field theory you can replace a positron with an electron going backwards in time). Regrettably the theory does not work, since it would predict the same number of electrons and positrons in the universe.

The positrons might be hiding in the protons!

Physics is sufficiently weird that I can't tell if this is just spitballing or an actual theory I haven't heard of before.

Edit: holy crap, these people think nucleons are made of muons that are made of electrons and positrons: http://wlsprojects.com/structure-inside-proton.html . Solves the matter vs antimatter problem, I guess.

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

#153

Post by tromp »

nhaehnle wrote: post #146
tromp wrote: post #112

Earlier quoted context omitted.

I can't say, because I didn't enumerate them. I only counted them. See http://tromp.github.io/go/legal.html for the method used, which is a form of dynamic programming.

Though if it is dynamic programming, then it should be possible for you to answer dogecoinbase's question using not much more computational power than you used to count them in the first place, right? If you think of dynamic programming as counting the number of paths in a directed graph (in this case, from skimming the paper, the nodes correspond to border states), then given a path number, you can trace the path ba…

Yes, you could if you preserved all intermediate counts. But the graph I used has 362 layers each of which can have up to 363 billion nodes, so I had to recycle the space used for the counts (4TB per layer). Also, I didn't even compute with full counts. I reconstructed them using the Chinese Remaineder theorem from 9 separate modular counts. So, yes it's possible, but highly impractical...

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

#154

Post by txdv »

yk wrote: post #41
creshal wrote: post #26

Earlier quoted context omitted.

But electrons interact with each other, don't they? How'd that work?

The electron goes forward and backward in time and interacts with itself. (In quantum field theory you can replace a positron with an electron going backwards in time). Regrettably the theory does not work, since it would predict the same number of electrons and positrons in the universe.

Feynman later proposed this interpretation of the positron as an electron moving backward in time in his 1949 paper "The Theory of Positrons".[2] Yoichiro Nambu later applied it to all production and annihilation of particle-antiparticle pairs, stating that "the eventual creation and annihilation of pairs that may occur now and then is no creation or annihilation, but only a change of direction of moving particles, from past to future, or from future to past."[3]

This sounds like SciFi material.

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

#155

Post by dsfuoi »

DonaldFisk wrote: post #133
levemi wrote: post #67

Earlier quoted context omitted.

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 s…

Radius of the visible universe is actually 45.7 billion ly.

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

#156

Post by [deleted] »

gnaritas wrote: post #18
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…

The earth is more round than a pool ball; it'd be a perfect sphere to any human eye at virtually any scale. The bulge is too small to notice.

[deleted]

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

#157

Post by skissane »

lern_too_spel wrote: post #125
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]

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...

Rayo's number is so big it is almost impossible to convey how big it is. It is certainly much much much bigger than Graham's number. (Unlike Graham's number, it appears not to serve any useful purpose beyond winning "who can name the biggest number?" games.)

https://en.wikipedia.org/wiki/Rayo%27s_number

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

#158

Post by drKarl »

zuminator wrote: post #139
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......

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 e…

I wonder if there would be a Restaurant at the End of the Universe

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

#159

Post by IsaacL »

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…

Go is very complex, and the fact that DeepMind could tackle this complexity is a huge technical achievement. No minimax-based AI could have tackled such a large state space.

However, other problems have even larger state spaces. Imagine writing an AI which read project Euler problem descriptions (in English) and output working code (in some given programming language). Keep outputs limited to 100-line scripts, max 80 characters per line.

There's roughly 100 usable characters in ASCII, so the possible space of 100-line programs is roughly:

(10^2)^(80 * 100) = 10^16000.

You could simplify this by having the AI work with predefined tokens rather than individual characters, but it's still a vast amount of combinations. Then consider 1000-line or 10000-line programs, and you see how high a mountain AI still has to climb. Humans are able to "compress" this state space via conceptual reasoning, which is much more complex than the "pattern recognition" many deep learning researchers are chasing.

(See "Introduction to Objectivist Epistemology" for more on how humans think in concepts - I'm planning to write more at some point on how this book shows where the practical limits of AI lie).

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

#160

Post by Razengan »

zuminator wrote: post #139
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......

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 e…

> If you picture galaxies as spots on the balloon, there's no "last" galaxy

What about looking "up" and "down?" i.e. into the inside of balloon or away from its surface?

I have a hard time wrapping my head around the balloon surface analogy, because galaxies seem to be in all directions of each other..

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