Is the butterfly affect a fantasy or a scientific myth?
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M$2 Answers
The Earth's weather is such a chaotic system. Thus, while it is obviously not the case that each time a butterfly flaps its wings a storm results, it is possible that such a situation *could* occur, if the butterfly flapped its wings at exactly the right time, in exactly the right place, in exactly the right direction, and with exactly the right force.
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M$
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M$
I meant analogy computing verses digital
You must mean analog computing, not analogy. The answer is that since your knowledge of initial conditions is based on measurements, which have limited accuracy, you still cannot calculate an infinitely precise development for a chaotic system.
As for the billiard balls, it's not the friction, which I assumed played no role. It's the initial position, which causes a difference in impact position on the circular wall, which causes a very different rebound angle. That's intended as a simple illustration of a chaotic system. The butterfly, as I mentioned, is a metaphor. There are chaotic systems that have nothing to do with wind, as in the case of my billiard example.
I was explore the boundaries of the butterfly theory rather than analyzing your exact statements.
The buttefly theory was thought to apply to quantum gravity where open strings traveling in another dimension communicated to the surface of branes information. However, I haven't heard whether this theory is widely accepted.
How is the butterfly theory proven? The proves I've seen used digital floating point error to demonstrate deviation. If analogy were used then no error would occur. Does this disprove the butterfly theory?
Not sure what you mean by "analogy" but the Butterfly Effect is not intended to be taken literally. To see a simple example of a chaotic system, look at the trajectory of a billiard ball on a table with no pockets, assuming no friction, and perfectly elastic collisions with any walls, and putting a circular wall in the middle of the table. Take two initial positions, one half-way between the corner of the table and its middle, and the second only 1 mm apart (but not along the same diagonal). Shoot the first ball toward the middle of the table, and it will bounce back and forth along the diagonal. Now hit the second ball along a parallel trajectory. As soon as it hits the circular wall it will have a rebounding trajectory different than the simple reverse of the first ball. In fact, within one or two more bounces, the second ball will be nowhere neat the initial trajectory.
The above is in the physical world, and has nothing to do with information theory, or with analog vs. digital data. The only connection I can think of to digital vs. analog is that digital is in-principal of limited accuracy in general. Thus, for example, a digital representation of 1/3 with say 5 digits would be 0.33333 which is only accurate to ~3 parts in 1,000,000, whereas the analog representation of 1/3 is exact. Thus, in a highly chaotic system, the inaccuracy imposed by using digital numbers means your initial conditions are not known accurately (which in non-ideal systems they never are anyway), so your predictions as to system development will be vastly inaccurate after a "short" time.
I never argued that the universe as a gravitational whole is chaotic. I agree with your statement that a small location change of a small mass in one galaxy is likely to affect things billions of light years away. However, I never stated otherwise.
What was the butterfly effect in the billards example? Are you illustrating how small changes in friction signicantly change the final positions of the balls?