From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Fri Sep 19 1997 - 16:49:36 MDT
Mikael Johansson wrote:
>
> I've had a discussion with my maths-teacher about a gravityproblem in
> association with the n-body-problem, and my question is this:
>
> The n-body-problem is unsolvable due to the gigantic computing powers it
> would take just for three interacting bodys, right?
Not at all. Any computer can easily simulate N gravitationally interacting
bodies using N^2 cycles. My computer could easily handle a thousand-body problem.
The n-body-problem is "unsolvable" because the only way to get an answer is
through an actual simulation. With other problems, you can plug time 't' into
some equation and calculate the result directly.
In other words, a solution to the n-body-problem would require a position
function of 't' that gave an answer in constant time for any 't', rather than
linear time (what it takes to run a simulation).
> When we now, as the Bovine has shown, can use an almost infinite amount
> of computer power, with a distributed computing system, over the
> internet; wouldn't then that be a solution to the n-body-problem?
> Wouldn't this system be enough to run a simulation of the solar system?
> If not now, wouldn't it in a few years?
My ancient Mac Plus could run a simulation of the solar system and do it in
its sleep - although not with General Relativity.
--
sentience@pobox.com Eliezer S. Yudkowsky
http://tezcat.com/~eliezer/singularity.html
http://tezcat.com/~eliezer/algernon.html
Disclaimer: Unless otherwise specified, I'm not telling you
everything I think I know.
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