Hi Francis,
right on, that's exactly what I was pointing at. I come from biology and there, you have a lot of potentially chaotic processes - think logistic equation. Now, usually these processes are discrete. Negative feedback then creates a nonlinear dynamic that leads to either stable states, oscillation , period doubling and chaos. Usually those processes are againmodeled with discrete steps, so you get a return map etc. And specifically, as you say, as random as they look and as much as they pass all tests for autocorrelation etc, they are ultimately very deterministic. What surprised me about this electronics experiment, is that here you have a purely analog circuit that behaves like a typical discrete deterministic chaos - with the additional stunner, that you can actually synchronize a similar, but necessarily slightly different physical analog circuit to it. I mean, what happened to sensitivity to initial conditions ;-)
So the whole thing opens up a huge area of research - anything from noise reduction , signal detection etc - IF you can come up with a "general" method opf synchronizing.
The other article (ID scan) is interesting inasmuch as it shows a simple and generalized applicatiuon of randomness that is not random. But in a way this can still be explained by some classic features such as autocorrelation. If it was truly maximum AIC how can you correlate two samples? those 2 samples come from some other spot of the same material... they must again have a nontrivial nonrandom feature in their makeup - a pattern, really. Hmm, food for thought. I read about the AIC problem in Kauffman, but I wasn't aware of Chaikin btw.
What strikes me in the electronics experiment is that the source of the likely somehow deterministic chaotic signal (i.e. pseudorandom) is analog. This is the only thing btw that interests me in the audio feedback discussion: I have a hunch that deep down in analog circuits you can find an irreducible "discreteness" in time - a step by step process. That's why I am somehow interested by the idea of "delay". That's also why I find the usual ensuing explanation by classic, linear modeling so unimaginative. Otherwise the question of feedback or not would be just a quastion of boring technical optimization. But there is something deeper here. There is an ocean of truly interesting stuff to be had that goes beyond the textbook approximations.
BTW Wolfram is interesting (as is Mandelbrot) but I'm more intrigued by such processes which operate in the quasi chaotic realm, yet show predictable ordered outcomes...
right on, that's exactly what I was pointing at. I come from biology and there, you have a lot of potentially chaotic processes - think logistic equation. Now, usually these processes are discrete. Negative feedback then creates a nonlinear dynamic that leads to either stable states, oscillation , period doubling and chaos. Usually those processes are againmodeled with discrete steps, so you get a return map etc. And specifically, as you say, as random as they look and as much as they pass all tests for autocorrelation etc, they are ultimately very deterministic. What surprised me about this electronics experiment, is that here you have a purely analog circuit that behaves like a typical discrete deterministic chaos - with the additional stunner, that you can actually synchronize a similar, but necessarily slightly different physical analog circuit to it. I mean, what happened to sensitivity to initial conditions ;-)
So the whole thing opens up a huge area of research - anything from noise reduction , signal detection etc - IF you can come up with a "general" method opf synchronizing.
The other article (ID scan) is interesting inasmuch as it shows a simple and generalized applicatiuon of randomness that is not random. But in a way this can still be explained by some classic features such as autocorrelation. If it was truly maximum AIC how can you correlate two samples? those 2 samples come from some other spot of the same material... they must again have a nontrivial nonrandom feature in their makeup - a pattern, really. Hmm, food for thought. I read about the AIC problem in Kauffman, but I wasn't aware of Chaikin btw.
What strikes me in the electronics experiment is that the source of the likely somehow deterministic chaotic signal (i.e. pseudorandom) is analog. This is the only thing btw that interests me in the audio feedback discussion: I have a hunch that deep down in analog circuits you can find an irreducible "discreteness" in time - a step by step process. That's why I am somehow interested by the idea of "delay". That's also why I find the usual ensuing explanation by classic, linear modeling so unimaginative. Otherwise the question of feedback or not would be just a quastion of boring technical optimization. But there is something deeper here. There is an ocean of truly interesting stuff to be had that goes beyond the textbook approximations.
BTW Wolfram is interesting (as is Mandelbrot) but I'm more intrigued by such processes which operate in the quasi chaotic realm, yet show predictable ordered outcomes...
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