|
|
|
|
|
|
by analog31
2798 days ago
|
|
|
In my view, dealing with genuinely random phenomena is rare. More common is that our knowledge is limited. I have my own "take" on math. Of course we enjoy math as an end unto itself. But when we use it for practical purposes, we choose math tools that we expect to work for the problems that we're trying to solve. In the case of probability and statistics, those tools are useful for situations where we know something about a set, but not everything. There are other situations where we use calculus, algebra, and so forth. Incomplete knowledge corresponds to a lot of problems and situations in our world, and so prob & stats are useful for modeling those situations. But it doesn't require the world to be fundamentally probabilistic. |
|
|
Quantum mechanics is the best thing we have to an exactly correct physical theory, and it is tied completely up with probability. So probability in the form of "genuinely random" is very fundamental.
As you go up from that level, our knowledge is limited at every turn, so it's hard to separate the one from the other ("genuinely random" vs. limited knowledge).
For example, you may have a large-scale physical system governed by differential equations, but the boundary conditions are not exactly known or knowable, or the governing equations are not closed (i.e., they depend on other things outside the system).