
On the (Small) Number of Atoms in the Universe - lispython
http://norvig.com/atoms.html
======
boredguy8
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 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/...](http://www.slate.com/articles/technology/technology/2016/03/google_s_alphago_defeated_go_champion_lee_sedol_ken_jennings_explains_what.html)

~~~
sametmax
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.

~~~
harryjo
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.

~~~
tromp
Indeed, enumerating all

208168199381979984699478633344862770286522453884530548425
639456820927419612738015378525648451698519643907259916015
628128546089888314427129715319317557736620397247064840935

positions in Go is impossible.

~~~
dogecoinbase
In your enumeration, what's the board look like at position
348277381979984699478633344862652779770286522453884530548425639456820927419612?

~~~
tromp
I can't say, because I didn't enumerate them. I only counted them. See

[http://tromp.github.io/go/legal.html](http://tromp.github.io/go/legal.html)

for the method used, which is a form of dynamic programming.

~~~
nhaehnle
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 backwards
through the graph, as long as you remember the number of paths ending in every
vertex.

~~~
tromp
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...

------
marai2
Scott 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
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})](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?

~~~
yathern
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.

~~~
d_theorist
Makes sense. Thanks.

------
j1vms
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...](https://capitolhillscience8.wordpress.com/2012/10/03/just-how-small-is-
an-atom-imagine-blueberries-stuffing-inside-the-entire-planet/)]

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)]

~~~
overcast
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.

~~~
evanpw
There's a great Isaac Asimov essay on this topic:
[http://chem.tufts.edu/answersinscience/relativityofwrong.htm](http://chem.tufts.edu/answersinscience/relativityofwrong.htm)

~~~
overcast
Great find, thanks!

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ChicagoBoy11
I'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!

~~~
andy_ppp
[https://www.google.co.uk/search?q=norvig.com&oq=norvig.com&a...](https://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)

There's a few interesting things on there!

------
gyakovlev
And 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
Related 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?

~~~
NegativeK
Knuth'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
I 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)

------
kagia
If 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"?

~~~
yathern
Yes, 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
This numberphile video discusses a similar concept:

The 'Everything' Formula -
[http://youtu.be/_s5RFgd59ao](http://youtu.be/_s5RFgd59ao)

------
barbs
The 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)

------
onion2k
There 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
But electrons interact with each other, don't they? How'd that work?

~~~
yk
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.

~~~
yolesaber
The positrons might be hiding in the protons!

~~~
andrewflnr
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](http://wlsprojects.com/structure-inside-proton.html) . Solves the
matter vs antimatter problem, I guess.

~~~
yolesaber
The explanation I gave was the one used by Wheeler in a famous phone call with
Feynman.

------
jhallenworld
I 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.

~~~
caipre
That is entirely the point of the article.

~~~
cinquemb
It 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.

------
zaro
Reading 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.

------
booleandilemma
[https://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.

------
Nevermark
Assuming 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!)

------
sevenless
I'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".

------
PaulHoule
If 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
It 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
> 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.

------
cynthiapucheanu
The 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?

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satyajeet23
Such a small place, this universe.

Interesting POV.

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PlzSnow
It actually boggles the mind that a 12-pixel image has more combinations than
atoms in the universe (!!!).

~~~
kruczek
Well, 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.

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ObeyTheGuts
but atoms of universe are infinite...guy is so wrong

~~~
gnaritas
You should look up what "observable" universe means.

