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It's not a solveable problem in general due to some systems having https://en.wikipedia.org/wiki/Chaos_theory#Chaotic_dynamics https://en.wikipedia.org/wiki/Cha
by logicchains 6y ago
It's not a solveable problem in general due to some systems having https://en.wikipedia.org/wiki/Chaos_theory#Chaotic_dynamics https://en.wikipedia.org/wiki/Chaos_theory#Chaotic_dynamics .
"Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general.[6] This can happen even though these systems are deterministic, meaning that their future behavior follows a unique evolution[7] and is fully determined by their initial conditions, with no random elements involved.[8] In other words, the deterministic nature of these systems does not make them predictable."
- dcow 6y agoOne could argue that hidden variables and poor resolution are to blame for chaotic systems.
- HPsquared 6y agoIf you try looking at finer and finer details, you'll quickly run into quantum effects and the uncertainty principle. If even the smallest parts of a system aren't deterministic, how can the outcome be predicted?
- uryga 6y ago> poor resolution afaik the point with chaotic systems is that even if the system is deterministic and your measurement of the initial conditions is near-perfect, your predictions will diverge from the real thing pretty quickly, because any errors get magnified a lot
- devalgo 6y agoJohn Bell would like to have a word with you.
- danwills 6y agoOn top of this some systems are not only sensitive to initial conditions but actually generate randomness (or destroy order, depending how you look at it), such as class-3 cellular automata.