In classical computing maybe. And with phase space analysis millions or even tens of millions of events can be visualized for emergent attractors that would indicate an underlying pattern.
No. Chaotic systems mean that if you integrate the time horizon out, there'll be a time after which your measurement precision isn't precise enough, and you'll get an unpredictable bifurcation. For a typical you-or-me coin flip, the necessary precision for a hypothetically powerful computer to predict with say 99.99% accuracy is probably well above the quantum-weirdness level of accuracy. And that 99.99% accuracy (or even 90% accuracy) is different from the 50% without the measurement and computer that necessitates a 50% theory or 50% language of coin flipping.
>No. Chaotic systems mean that if you integrate the time horizon out, there'll be a time after which your measurement precision isn't precise enough, and you'll get an unpredictable bifurcation.
how is that substantively different from what i said?
>99.99% accuracy is probably well above the quantum-weirdness level of accuracy.
what is quantum-weirdness scale and what is well above? hbar is 34 zeros out.
You said it's untrue that you can predict a typical coin flip because it's a chaotic system. I laid out the limitations of chaotic systems and argued they don't apply to a typical coin flip. Are you arguing about predicting "essentially perfectly?" I use that to mean predicting with a couple nines of accuracy.
By quantum weirdness scale, I mean that the accuracy (epsilon) of a necessary measurement includes accurate position and momentum measurements. If epsilon is too small, we might not be able to hypothetically measure both to the necessary precision. I'm guessing that the necessary epsilon for essentially perfect prediction is large enough that you can hypothetically measure both to within that precision.
If you like, you can work out the maximum number of degrees of freedom that could theoretically be involved in something you could call a fair coin toss.
Hint: it’s a free body under rotation on a parabolic trajectory. You won’t end up needing Tony Stark hardware for this one.
Bonus factoid before bed: coins flipped by humans empirically have a small (~51%) bias toward heads. Supposedly folks tend to start with heads up more often, and the coin tends to flip over 0 times more often than you’d think, and that adds up to a bias you can measure in an afternoon.
