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gwern comments on Open thread, February 15-28, 2013 - Less Wrong Discussion
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If false, this could be easily falsifiable with a single counterexample, since if true, no coin tosser, human or robotic, should be able to do significantly better than chance if the toss is reasonably high.
EDIT: according to this
the premise has already been falsified.
The link discusses normal human flips as being quantum-influenced by cell-level events; a mechanical flipper doesn't seem relevant.
Even humans can flip a coin in such a way that the same side comes up in all branches of the wave function, as described by E.T. Jaynes, but IIRC he himself refers to that as "cheating".
I'm not sure that's what they mean either. I take them as saying 'humans can flip in a quantum-influenced way', not as 'all coin flips are quantum random' (as shminux assumed, hence the coin-flipping machine would be a disproof) or 'all human coin flips are quantum random' (as you assume, in which case magicians' control of coin flips would be a disproof).
I'd guess something along the line of typical human coin flips being quantum-influenced.
If their model makes no falsifiable predictions, it's not an interesting one.
I'm honestly not sure. I find myself confused. According to the article, they say:
But what would that look like exactly? Naively, it seems like the robot that flips the coin heads every time satisfies this (classical probability: ~1). Or maybe it uses a pseudo-random number generator to determine what's going to come up next and flips the coin that particular way and then we bet on the next flip (constituting "a use of classical probabilities that is clearly isolated from the physical, quantum world"). But presumably that's not what they mean. What counterexample would they want, then?
The authors claim that all uncertainty is quantum. A machine that flips heads 100% of the time doesn't falsify their claim (no uncertainty), and neither does a machine that flips heads 99% of the time (they'd claim it's quantum uncertainty). As for a machine that follows a pseudorandom bit sequence, I believe they would argue that a quantum process (like human thought) produced the seed. Indeed, they argue that our uncertainty about the n-th digit of pi is quantum uncertainty because if you want to bet on the n-th digit of pi, you have to randomly choose n somehow.
If they're saying all sources of entropy are physical, that seems obvious. If they're saying that all uncertainty is quantum, they must not know that chaotic classical simulations exist? Or are they not allowing simulations made by humans o.O
They're saying all uncertainty is quantum. If you run a computer program whose outputs is very sensitive to its inputs, they'd probably say that the inputs are influenced by quantum phenomena outside the computer. Don't ask me to defend the idea, I think it's incorrect :)
Chaotic classical simulations? Could you elaborate?
Well, you can run things like physics engines on a computer, and their output is not quantum in any meaningful way (following deterministic rules fairly reliably). It's not very hard to simulate systems where a small uncertainty in initial conditions is magnified very quickly, and this increase in randomness can't really be attributed to quantum effects but can be described very well by probability. This seems to contradict their thesis that all use of probability to describe randomness is justified only by quantum mechanics.
I think there seems to be a mismatch of terms involved. Ontological probability, or propensity, and epistemological probability, or uncertainty, are being confused. Reading over this discussion, I have seen claims that something called "chaotic randomness" is at work, where uncertainty results from chaotic systems because the results are so sensitive to initial conditions, but that's not ontological probability at all.
The claim of the paper is that all actual randomness, and thus ontological probability, is a result of quantum decoherence and recoherence in both chaotic and simple systems. Uncertainty is uninvolved, though uncertainty in chaotic systems appears to be random.
That said, I believe the hypothesis is correct simply because it is the simplest explanation for randomness I've seen.