I like how Ken Jennings dealt with the 'Go complexity' analogy:<p>"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 <i>understates</i> the computational problem. There are about 10^170 board positions in Go, and <i>only</i> 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 <i>total</i> number of atoms in <i>all</i> those universes combined would be close to the possibilities on a single Go board."<p><a href="http://www.slate.com/articles/technology/technology/2016/03/google_s_alphago_defeated_go_champion_lee_sedol_ken_jennings_explains_what.html" rel="nofollow">http://www.slate.com/articles/technology/technology/2016/03/...</a>
Scott Aaronson's blog post on large numbers is also a very interesting read:<p><a href="http://www.scottaaronson.com/writings/bignumbers.html" rel="nofollow">http://www.scottaaronson.com/writings/bignumbers.html</a>
Here's another great one - and ballpark calculations point to it being likely true:<p>"..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." [<a href="https://capitolhillscience8.wordpress.com/2012/10/03/just-how-small-is-an-atom-imagine-blueberries-stuffing-inside-the-entire-planet/" rel="nofollow">https://capitolhillscience8.wordpress.com/2012/10/03/just-ho...</a>]<p>Edit: well, except that the Earth is shaped more like an oblate spheroid [<a href="https://en.wikipedia.org/wiki/Figure_of_the_Earth" rel="nofollow">https://en.wikipedia.org/wiki/Figure_of_the_Earth</a>]
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!
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"?
The unintuitiveness of how many combinations you can get from such a small amount of items is why the birthday "paradox" is so interesting.<p><a href="https://en.wikipedia.org/wiki/Birthday_problem" rel="nofollow">https://en.wikipedia.org/wiki/Birthday_problem</a>
There is a theory that states the number of atoms (well, electrons) in the universe is exactly 1.<p><a href="https://en.wikipedia.org/wiki/One-electron_universe" rel="nofollow">https://en.wikipedia.org/wiki/One-electron_universe</a>
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.<p>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 :)<p>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.
<a href="https://en.m.wikipedia.org/wiki/The_Library_of_Babel" rel="nofollow">https://en.m.wikipedia.org/wiki/The_Library_of_Babel</a><p>This is a fun, thought-provoking story about a large combination of things.
Assuming space is quantized at the Planck scale, the numbers of atoms in the universe is tiny compared to the number of space points.<p>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!)
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.<p>From this point of view this article is inappropriately comparing two scales. It's nothing more than saying "e^x >> x for big x".