12 ms·
On the (Small) Number of Atoms in the Universe
- barbs 10y agoThe unintuitiveness of how many combinations you can get from such a small amount of items is why the birthday "paradox" is so interesting. https://en.wikipedia.org/wiki/Birthday_problem https://en.wikipedia.org/wiki/Birthday_problem
- sevenless 10y agoI'd argue the natural scale for thinking about the number of combinations is the log scale - in other words, the entropy. Entropy, like the number of atoms, is an additive property of a system. From this point of view this article is inappropriately comparing two scales. It's nothing more than saying "e^x >> x for big x".
- zaro 10y agoReading this made me think how can you know the number of atoms in the universe (observable, smellable, touchable, whatever ). So I go and check on Wikipedia and of course its just a guesstimation based on assumptions and hypothesuses. This again reminds me how science today is no different than religion. Of course there is nothing wrong with having the number based on assumptions , but take it out of the field of study and suddenly it is a fact :) Like in this article and the discussion in HN where its just the number and its name, and the fact that this him be is just somebody's wild guess is totally ignored. Same with Jesus , he exists and he loves you and the fact that it was just somebody's idea is totally left out.
- jhallenworld 10y agoI think he's comparing apples with oranges: maybe 10^80 is not so big, but the number of configurations of the 10^80 atoms is huge.
- jameshart 10y agoI think that was his point.
- caipre 10y agoThat is entirely the point of the article.
- deleted 10y ago[deleted]
- cinquemb 10y agoIt would be cool if there were more talk about properties we have observed of these configurations/which are more probable at any given instance, and efficient ways of computing such.
- j1vms 10y agoHere'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-how-small-is-an-atom-imagine-blueberries-stuffing-inside-the-entire-planet/ 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_Earth https://en.wikipedia.org/wiki/Figure_of_the_Earth]
- nsxwolf 10y agoThat actually makes the Earth seem small to me. I wouldn't have blinked if someone had told me the blueberries would fill up a sphere the size of the Solar System. Just shows how hard it is to visualize these numbers.
- lisper 10y agoThe 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 away. And not only do you live on a poppy seed, you live on a very thin layer on the surface of this poppy seed. Blow the poppy seed up to the size of a basketball and the habitable layer is about the thickness of a sheet of paper.
- jeff_tyrrill 10y ago> Alpha Centauri is about four miles away. Actually, around 500 miles. Distance to Alpha Centauri: 4.37 light years = 276,364 astronomical units. In your diagram, the Earth is 10 feet from the Sun. Multiply by 276,364 to get 2,763,640 feet, or 523 miles. The scale jump from distances around the Solar System to the next closest star is mind boggling.
- ObeyTheGuts 10y agobut atoms of universe are infinite...guy is so wrong
- gnaritas 10y agoYou should look up what "observable" universe means.
- cynthiapucheanu 10y agoThe parallel you drew between such a day to day object and such an important matter is interesting. Do you know of another comparison like this?
- gyakovlev 10y agoAnd it's even smaller if compared to Graham's number. Every time I try to imagine that one it feels like I'm going to mental asylum.
- amelius 10y agoRelated only to large numbers, but is there some theory about generalizing and extending our usual mathematical operators +, ×, and ^ (power)? + applied N times becomes ×N × applied N times becomes ^N ^ applied N times becomes ...? etcetera And would such a theory have any practical use?
- abengoam 10y agohttps://en.wikipedia.org/wiki/Hyperoperation https://en.wikipedia.org/wiki/Hyperoperation
- NegativeK 10y agoKnuth's up-arrow notation is one of a few ways to address the addition->multiplication->exponentiation->tetration->... extensions: https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation As for practicalities, the mathematician in me will let the scientists deal with that.
- dack 10y agoI like the description of graham's number (by graham) using the up-arrow notation https://youtu.be/GuigptwlVHo?t=31 https://youtu.be/GuigptwlVHo?t=31
- drjesusphd 10y agoGraham's number comes from such an extension, and is about 64 such operations deeper. It's useful in the sense that it provides an upper bound for some proof that hasn't yet been proven for ALL numbers. http://waitbutwhy.com/2014/11/1000000-grahams-number.html http://waitbutwhy.com/2014/11/1000000-grahams-number.html
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- PaulHoule 10y agoIf you believe in the axiom of choice (I don't) then you can imagine a process which has more degrees of freedom in in than anything at all.
- krastanov 10y agoIt is an axiom, it is not something that you believe in. You assume it and you prove stuff with it. You do not and you prove stuff without it. If you are really good, you show what theorems require it. You can believe or not in some physical reality to math (I happen to), and then the axioms do become somewhat more than just logic statements, but that is different.
- umanwizard 10y ago> You can believe or not in some physical reality to math (I happen to) I'm not so sure. Is there any evidence that the value of any physical quantity is an irrational number? Math was originally inspired by physical reality, but I'm not sure it's so closely related that the concept of the Axiom of Choice being "true" even means anything.
- dogecoinbase 10y agoYou don't believe that the product of non-empty sets is non-empty?
- GregBuchholz 10y agoYou could always be a intuitionist/constructivist, and enjoy "choice" as a theorem. It seems completely reasonable to give up uncountable infinities. http://arxiv.org/abs/math/0404335 http://arxiv.org/abs/math/0404335
- marai2 10y agoScott Aaronson's blog post on large numbers is also a very interesting read: http://www.scottaaronson.com/writings/bignumbers.html http://www.scottaaronson.com/writings/bignumbers.html
- d_theorist 10y agoVery 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}) 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?
- aardvark179 10y agoNope, see the description of titration on on wikipedia.
- yathern 10y agoNot 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.
- d_theorist 10y agoMakes sense. Thanks.
- jobigoud 10y agoHa, trip down memory lane: > And in Go even an amateur human can still rout the world’s top-ranked computer programs
- pron 10y agoI 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.
- onion2k 10y agoThere is a theory that states the number of atoms (well, electrons) in the universe is exactly 1. https://en.wikipedia.org/wiki/One-electron_universe https://en.wikipedia.org/wiki/One-electron_universe
- creshal 10y agoBut electrons interact with each other, don't they? How'd that work?
- yolesaber 10y agoIt's the same electron interacting with itself at different times is what I think Wheeler would argue Disclaimer: I am not a physicist, but I love this theory
- richmarr 10y agoThe rules probably aren't the same as they are in Back to the Future.
- yk 10y agoThe 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.
- txdv 10y agoFeynman 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.
- yolesaber 10y ago
- boredguy8 10y agoI 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 atoms in the universe. That means that if there were as many parallel universes as there are atoms in our universe (!), then the total number of atoms in all those universes combined would be close to the possibilities on a single Go board." http://www.slate.com/articles/technology/technology/2016/03/google_s_alphago_defeated_go_champion_lee_sedol_ken_jennings_explains_what.html http://www.slate.com/articles/technology/technology/2016/03/...
- IsaacL 10y agoGo 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).
- Retric 10y agoDon'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 https://en.wikipedia.org/wiki/Ackermann_function
- ChicagoBoy11 10y agoI'm curious how the author found the link to this - I looked at Norvig's home page but could not find it, which made me wonder how many more goodies he's got up there that we don't know about!
- RobertDeNiro 10y agoIt's in the RSS feed.
- nitrogen 10y agoSome search engines have a "link:" modifier that you might already be aware of. That can help you find paths leading to a particular page.
- andy_ppp 10y agohttps://www.google.co.uk/search?q=norvig.com&oq=norvig.com&aqs=chrome..69i64j0l5.12302j0j1&sourceid=chrome&es_sm=119&ie=UTF-8#q=site:norvig.com https://www.google.co.uk/search?q=norvig.com&oq=norvig.com&a... There's a few interesting things on there!
- booleandilemma 10y agohttps://en.m.wikipedia.org/wiki/The_Library_of_Babel https://en.m.wikipedia.org/wiki/The_Library_of_Babel This is a fun, thought-provoking story about a large combination of things.
- PlzSnow 10y agoIt actually boggles the mind that a 12-pixel image has more combinations than atoms in the universe (!!!).
- SapphireSun 10y agoAs a rule of thumb, it looks like 59! is about the number of atoms in the universe. 59! =~ 1.38 × 10^80
- kruczek 10y agoWell, I think the example with 12-pixel image is a bit misleading, because the picture focuses reader's attention on those 12 pixels, while skipping over the fact that each pixel can have ~17 million colors. More appropriate representation would be a cuboid made of 3x4x24 blocks.
- deleted 10y ago[deleted]
- satyajeet23 10y agoSuch a small place, this universe. Interesting POV.
- kagia 10y agoIf 12megapixels can produce 10 to the power 86696638 images, and we came up with a way of enumerating those images, could we then build a function that given anyone of those images return the index of that image within reasonable time with current hardware. ie. "you have just taken 3999999987493th image"?
- chrismbarr 10y agoA friend of mine made a tool that did exactly this, but with Haikus instead. He had a dictionary of syllables, and then just iterated through the syllables (following the rules of a haiku). You can type in a haiku and find its index, or just iterate through the indices to see the (mostly nonsense) generated haikus.
- tfgg 10y agoIt's the number represented by that file's full binary value (all the bytes concatenated together).
- yathern 10y agoYes, but it wouldn't save any space. As a thought experiment, think of it this way: How would we enumerate all these several gazillion image possibilities? Well. Let's say number one is all black. Every pixels and every channel is all zero in its value. And let's say the last image to be enumerated is all white. 255 for each pixel and each channel. Every conceivable image is created in between these two ends. For example, image two is all black, but the last pixel has a value of 1 instead of 0 for its value channel. Image 1840274917 has pixel 27581 slightly reddish. Hey, wait a minute, you've just created an image format for describing the data within the image! The only space you're saving is that (given this format) you save space on darker images, because they're likely lower in the sequence. But that's only because this specification demands that each image be the same exact size and can make assumptions based on that. A lossless format like PNG would be able to perform much better over a wider range of images. (Eg all white will be huge in our system, but cheap in PNG)
- rrauenza 10y agoThis numberphile video discusses a similar concept: The 'Everything' Formula - http://youtu.be/_s5RFgd59ao http://youtu.be/_s5RFgd59ao
- Nevermark 10y agoAssuming space is quantized at the Planck scale, the numbers of atoms in the universe is tiny compared to the number of space points. Assuming the many worlds interpretation of quantum physics is true, then the number of atoms includes all combinations of locations, momentum, etc., and the real number of atoms is vastly vastly greater than combinations of just about anything else you might imagine. (Except for combinations of configurations of quantized spacial points!)