3 ms·
What would make you think that? Deterministic doesn't imply predictable, reducible, or low complexity. Even a purely deterministic simple system can be capabl
by otakucode 10y ago
What would make you think that? Deterministic doesn't imply predictable, reducible, or low complexity. Even a purely deterministic simple system can be capable of (and most are) chaotic behavior whose information content would grow faster than any system smaller than itself could predict. In other words, the only way to "simulate" the system would be to completely reproduce every bit of it, and let it evolve in realtime. And practically speaking, we can't even approach that.
- jayajay 10y agoFor example, the double pendulum: https://en.wikipedia.org/wiki/Double_pendulum https://en.wikipedia.org/wiki/Double_pendulum. That said, the phase space of a double pendulum is bounded.
- duckingtest 10y agoIt's really funny that something as simple is impossible to predict over longer times, because you would need perfect information. Yet climate science is 'settled'.
- jayajay 10y agoTake an undamped double pendulum and divide the space up into 2 sections. Suppose you can only check which section the pendulum is every N seconds. Every time you check, you record the value, and over time you build up a sequence of K numbers: 1,0,1,0,0,1,1,1,1,0,0,1,0,... Suppose you know the exact initial state (dx/dt, x) of the pendulum. What bounds on K and T are required such that the sequence of numbers is asymptotically indistinguishable from a purely random sequence? So, because of a silly thought experiment, one might think there is very simple order to the apparent randomness. But, as Pauli would say, "it's not even wrong"...