I have studied physics.


Now we must distinguish. If you speak of a situation in terms of pure classical physics you are right. Take the Sinai-billard, for instance, http://www.mathematik.com/Sinai/index.html
If you would only know all the forces acting on the billard ball and the initial condition, you could (unfortunately only theoretically, because even the least rounding errors will make you fail) calculate and predict the behaviour in future. The result is a behaviour which manifests itself to be extremely sensitive to even the most subtle changes. But, you are right, if you would only know all the details, you could predict the behaviour in future. In the weather example, yes the flap of butterfly could eventually change the weather from calmness to tornado and yes you could predict it, if you would only know the butterfly and its far-reaching activity. Yes, everything is deterministic, no space for randomness. The weather activity seems to occur randomly, but it's entirely deterministic, we are only not capable to get a true set of data of the intial condition and all the factors contributing.

So far, we could, at least theoretically, build a Laplace Daemon, if we could only get a proper set of data of some initial condition and if we would only know all the forces' laws and conservation laws, etc.

But, dear Joseph, what I'm talking about is an additional factor, which additionally influences the behaviour of this billard ball. Now we include the quantum mechanics. The uncertainty principle states, that you cannot absolutely exactly define the initial condition, because the uncertainty relation, for instance dx x dp >~ h, is valid.
In the above we could assume, that when exactly knowing the location of ball and its momentum (means the speed and direction of movement) at a certain moment and when exactly knowing all the acting forces, that we can exactly calculate the location of ball at a later date. Of course, there's no room for any randomness, the situation is entirely deterministic, or we can say that there's a causality, or we can say that the ball moved from A to B is a direct consequence.
But if we take the uncertainty principle seriously, then making dx ~ 0 would cause a huge rise of dp. The consequence is, that we can neither define a point A nor B, more, because of that we even cannot speak of a movement along a path. Then, we can no longer conclude from the statement "ball being at point A" will cause "ball being at point B at a later date". The strong causality is no longer valid, randomness, in a qunatum mechanical sense enters our system.

The interesting question is now: Will we notice the uncertainty principle in our world, means in macroscopic dimensions?
The answer is yes, we will! There's a nice thesis from the physicist Roman Sexl, who calculated this billard ball experiment I reported about earlier. He could demonstrate, that when hitting the first billard ball in a row of seven additional billard balls, the uncertainty principle makes that it's not predictable whether the seventh billard ball will hit the eighth. (In the original post I stated from memory, that it's the fifth ball, but consulting my "archive" told me, that it's the seventh.)

The uncertainty principle makes, that the Laplace Daemon cannot be built and that the behaviour of a physical system cannot be predicted in total detail. So, even when making the grid of weather model finer and when making the super computer more powerful, there's a natural limit of precision introduced by the uncertainty principle.
The interesting point is now, that if even the most subtle changes can have a deep influence in chaotic systems, then even the very subtle quantum mechanical "noise" can finally result in relevant changes.



YES, SIR, CAPTAIN, SIR! :)


That's a question of defintion. I have learned something different.

Kai