Hi, I think I see what you mean. You can certainly say that the flap, as a part of the initial conditions, is part of the causes of the tornado. But this is true in the same sense in which all of the initial conditions are part of the cause of the tornado. The flap caused the tornado together with everything else. All the initial ocean temperatures, the position of the jet streams, the northern annular mode index, everything. If everything is the cause, then “being the cause of the tornado” is a property which carries exactly 0 bits of information, since everything is the cause.
I prefer to think that an event A “caused” another event B if the probability of B, conditioned on A happening, is at least greater than the prior probability of A.
The point is that in this scenario, the tornado does not occur unless the butterfly flaps its wings. That does not apply to “everything”, necessarily, it only applies to other things which must exist for the tornado to occur.
Probability is an abstraction in a deterministic universe (and, as I said above, the butterfly effect doesn’t apply to a nondeterministic universe.) The perfectly accurate deterministic simulator doesn’t use probability, because in a deterministic universe there is only one possible outcome given a set of initial conditions. The simulation is essentially demonstrating “there is a set of initial conditions such that when butterfly flap = 0 there is no Texas tornado, but when butterfly flap = 1 and no other initial conditions are changed, there is a Texas tornado.”
I see, but you are talking about an extremely idiosyncratic measure (only two points) on the space of initial conditions. One could as easily find another couple of initial conditions, in which the wing flip prevents the tornado.
If there were a prediction market on tornadoes, its estimations should not change in neither direction after observing the butterfly.
“there is a set of initial conditions such that when butterfly flap = 0 there is no Texas tornado, but when butterfly flap = 1 and no other initial conditions are changed, there is a Texas tornado.”
Phrased this way it is obviously true.
However, why are you saying that chaos requires determinism? I can think of some Markovian master equations with quite a chaotic behavior.
Hi, I think I see what you mean. You can certainly say that the flap, as a part of the initial conditions, is part of the causes of the tornado. But this is true in the same sense in which all of the initial conditions are part of the cause of the tornado. The flap caused the tornado together with everything else. All the initial ocean temperatures, the position of the jet streams, the northern annular mode index, everything. If everything is the cause, then “being the cause of the tornado” is a property which carries exactly 0 bits of information, since everything is the cause.
I prefer to think that an event A “caused” another event B if the probability of B, conditioned on A happening, is at least greater than the prior probability of A.
The point is that in this scenario, the tornado does not occur unless the butterfly flaps its wings. That does not apply to “everything”, necessarily, it only applies to other things which must exist for the tornado to occur.
Probability is an abstraction in a deterministic universe (and, as I said above, the butterfly effect doesn’t apply to a nondeterministic universe.) The perfectly accurate deterministic simulator doesn’t use probability, because in a deterministic universe there is only one possible outcome given a set of initial conditions. The simulation is essentially demonstrating “there is a set of initial conditions such that when butterfly flap = 0 there is no Texas tornado, but when butterfly flap = 1 and no other initial conditions are changed, there is a Texas tornado.”
I see, but you are talking about an extremely idiosyncratic measure (only two points) on the space of initial conditions. One could as easily find another couple of initial conditions, in which the wing flip prevents the tornado.
If there were a prediction market on tornadoes, its estimations should not change in neither direction after observing the butterfly.
Phrased this way it is obviously true.
However, why are you saying that chaos requires determinism? I can think of some Markovian master equations with quite a chaotic behavior.