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Re: Can anyone here conceieve of an event that MUST be random? [Re: AnonymousRabbit]
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Again, can you please clarify what you mean by self-similarity of particles in brownian motion?


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We are all in the gutter, but some of us are looking at the stars.

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Re: Can anyone here conceieve of an event that MUST be random? [Re: AnonymousRabbit]
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How are the particles in Brownian motion self similar?

What predictions from the 'emerging field of science that uses fractals' are being made that we were previously unable to predict (specifically)?

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Re: Can anyone here conceieve of an event that MUST be random? [Re: AnonymousRabbit]
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You're making too strong an identification between the general definition of a fractal as something possessing a fractal dimension (Hausdorff dimension) in some measure space and the special case of  deterministic fractals, like the Mandelbrot set, a very deterministic AND chaotic algorithm. Brownian motion is understood to be a "fractal" motion because the distance covered by a particle undergoing such motion does not scale as an integer power of the length of the "measuring rod" used to estimate the length of the total trajectory. It doesn't mean that you can predict anything, only that you may know the general trend. You can model statistical moments (averages, variance, kurtosis, etc.) over large ensembles indeed, but nothing about the actual trajectory.

Self-similarity refer to the fact that when you look at the motion on different scale, it looks the same. Provided you're not looking to close to the limiting microscopic and macroscopic scales which are natural cut-off to self-similarity.

Edited by deimya (11/06/08 01:54 PM)

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Re: Can anyone here conceieve of an event that MUST be random? [Re: AnonymousRabbit]
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Yes, most fractals in nature are non-deterministic, like Brownian motion, percolation, lightnings (dielectric breakdown), trees and brocoli. Those beautiful pictures like in your avatar are special cases made by deterministic algorithms. A fractal is in general something possessing a non-integer Hausdorff dimension. Brocolis and the Mandelbrot set both deserve the name of fractal for this reason, although totally different processes lie at the heart of their formation.

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Re: Can anyone here conceieve of an event that MUST be random? [Re: AnonymousRabbit]
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It's still governed by the laws of physics, but any fluctuation at any point is the seed of what's going around. These can be thermal, quantum, pressure or whatever other type of fluctuation you want. Then are these known and unknown laws deterministic ? I think it's a misleading question.

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Re: Can anyone here conceieve of an event that MUST be random? [Re: AnonymousRabbit]
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You can't measure the seed with absolute precision, hence the non-determinism in the whole thing. Actually there is an uncertainty in the state itself, not just imperfect measurement, quantum mechanics and stuff.

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Re: Can anyone here conceieve of an event that MUST be random? [Re: AnonymousRabbit]
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There seem to be a natural intrinsic maximal precision given by the Plank constant, around which causality breaks down and "random" fluctuations take over. It seems you can't do anything about it. Given most laws are non-linear and thus chaotic, these little fluctuations get amplified and after a while your predicting power goes to zero. So no, you can't predict that much in the future and in spatial extension.

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Edited by AnonymousRabbit (05/18/22 11:27 PM)

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Re: Can anyone here conceieve of an event that MUST be random? [Re: AnonymousRabbit]
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But if we were to discover that nothing "causes" these random fluctuations, for causality is an emergent property itself, then your Cartesian idealism would be forever changed wouldn't it ? :wink:

I wish it was as simple as pure causality and determinism, or pure randomness and non-determinism, but something tells me that it's a bit of neither and both, and thus something completely different.

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