31–40 of 171 posts
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
But electrons interact with each other, don't they? How'd that work?
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.
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…
Close?? Wouldn't it still be roughly 10 billion times smaller...?
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…
> the total number of atoms in all those universes combined would be close Close?? Wouldn't it still be roughly 10 billion times smaller...?
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!
Earlier quoted context omitted.
> And would such a theory have any practical use? Yes, sureley. In Computablilty Theory you have the famous Ackermann-function[1]. It is actually an operator-extension, like you just described. It is important, because it grows overexponentially, but is still computable (unlike e.g. the busy-beaver-function). [1]: https://en.wikipedia.org/wiki/Ackermann_function
Given that Graham's Number is an (over-)extension of the Ackermann-function that means that it's still computable, correct? Given the series leading up to Graham's Number, G = g_64 (g_1, g_2, ...), BB(n) will outgrow g_n, right? If so what's the smallest n such that BB(n) > g_n?
[0]: "A Lower Bound on Rado's Sigma Function for Binary Turing Machines" by Milton Green (1964)
[1]: https://en.wikipedia.org/wiki/Busy_beaver#Known_values_for_....
Earlier quoted context omitted.
That 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.
The 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 a…
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…
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.
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.
You don't believe that the product of non-empty sets is non-empty?