
Post by acidohm on Sept 28, 2019 22:55:01 GMT
I apologise in advance, this thread is technically 'offtopic' yet can't be at the same time. Likelihood is if noone else posts here it'll be very self indulgent. Despite this, id like to post, initially, excerpts for the good book that is Chaos: Making a new science, by James Gleick The purpose is to expand the idea that everything we discuss here is a product of Chaos, structured by it, functions by it, in fact everything natural and by extension us, is formed by it. These facts are, i think, entirely missed by those who understand our world is going to end because of you know what. These, as im sure to most/all of you, are not new concepts to me, however i am finding the way these concepts are put a across in this book rejuvenate/expand/concentrate these ideas and become far more relevant to the 'now" So, by all means ignore all of the following, if noone comments/likes ill feel no slight......but shall post more anyway!
So, in no particular order...first excerpt:
In the age of computer simulation, when flows in everything from jet turbines to heart valves are modeled on supercomputers, it is hard to remember how easily nature can confound an experimenter. In fact, no computer today can completely simulate even so simple a system as Libchaber’s liquid helium cell. Whenever a good physicist examines a simulation, he must wonder what bit of reality was left out, what potential surprise was sidestepped. Libchaber liked to say that he would not want to fly in a simulated airplane—he would wonder what had been missed. Furthermore, he would say that computer simulations help to build intuition or to refine calculations, but they do not give birth to genuine discovery.



Chaos
Sept 28, 2019 22:59:04 GMT
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Post by acidohm on Sept 28, 2019 22:59:04 GMT
He spent several nights in that basement, watching the green dot of the oscilloscope flying around the screen, tracing over and over the characteristic owl’s mask of the Lorenz attractor. The flow of the shape stayed on the retina, a flickering, fluttering thing, unlike any object Shaw’s research had shown him. It seemed to have a life of its own. It held the mind just as a flame does, by running in patterns that never repeat. The imprecision and notquite–repeatability of the analog computer worked to Shaw’s advantage. He quickly saw the sensitive dependence on initial conditions that persuaded Edward Lorenz of the futility of longterm weather forecasting. He would set the initial conditions, push the go button, and off the attractor would go. Then he would set the same initial conditions again—as close as physically possible—and the orbit would sail merrily away from its previous course, yet end up on the same attractor.



Chaos
Sept 29, 2019 0:14:07 GMT
Post by Ratty on Sept 29, 2019 0:14:07 GMT
The IPCC used to understand the principle of chaos:
IPCC 2001: "The climate system is a coupled nonlinear chaotic system, and therefore the longterm prediction of exact future climate states is not possible."



Chaos
Sept 29, 2019 7:28:09 GMT
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Post by acidohm on Sept 29, 2019 7:28:09 GMT
Shaw brought some assumptions of classical mechanics out of the shadows. Energy in natural systems exists on two levels: the macroscales, where everyday objects can be counted and measured, and the microscales, where countless atoms swim in random motion, unmeasurable except as an average entity, temperature. As Shaw noted, the total energy living in the microscales could outweigh the energy of the macroscales, but in classical systems this thermal motion was irrelevant—isolated and unusable. The scales do not communicate with one another. “One does not have to know the temperature to do a classical mechanics problem,” he said. It was Shaw’s view, however, that chaotic and nearchaotic systems bridged the gap



Post by nautonnier on Sept 29, 2019 12:00:24 GMT
"Convection also can occur on smaller scales  in cups of hot coffee, in pans of warming water or in rectangular metal boxes heated from below. Lorenz imagined this latter smallscale example of rolling convection and set about deriving the simplest equations possible to describe the phenomenon. He came up with a set of three nonlinear equations:
dx/dt = σ(yx) dy/dt = ρx  y  xz dz/dt = xy  βz
where σ (sigma) represents the ratio of fluid viscosity to thermal conductivity, ρ (rho) represents the difference in temperature between the top and bottom of the system and β (beta) is the ratio of box width to box height. In addition, there are three timeevolving variables: x, which equals the convective flow; y, which equals the horizontal temperature distribution; and z, which equals the vertical temperature distribution.
The equations, with only three variables, looked simple to solve. Lorenz chose starting values  σ = 10, ρ = 28 and β = 8/3  and fed them to his computer, which proceeded to calculate how the variables would change over time. To visualize the data, he used each threenumber output as coordinates in threedimensional space. What the computer drew was a wondrous curve with two overlapping spirals resembling butterfly wings or an owl's mask. The line making up the curve never intersected itself and never retraced its own path. Instead, it looped around forever and ever, sometimes spending time on one wing before switching to the other side. It was a picture of chaos, and while it showed randomness and unpredictability, it also showed a strange kind of order.
Scientists now refer to the mysterious picture as the Lorenz attractor."More at science.howstuffworks.com/mathconcepts/chaostheory4.htmWhat is not said here is that Lorenz came to this chaotic modeling by accident. Trying to save and rerun meteorological models in fixed point precision rather than floating point, he found that minor changes in the precision of the initial parameters of iterative processes lead to extremely divergent outputs. I have two books behind me now  "Chaos  The Amazing Science of the Unpredictable" by James Gleick, and the more evocatively titled based on an Einstein quote: "Does God Play Dice" by Ian Stewart. Both as much worth a read. The motion of the Sun around the galaxy, the planets around the Sun, the fluid flows of atmosphere, oceans and even the continents on this rotating planet in orbit around the Sun are all chaotic and all influence what we experience as the weather and climate. The problem that we have is that we have only seen a few orbits around one strange attractor and we don't really know if those will repeat nor do we really know how many other attractors (states) there are or how close we are to flipping to the orbit around one of the other attractors nor do we know what parameter would cause that change of attractor. They are not all simple butterfly shapes....



Chaos
Sept 29, 2019 19:06:01 GMT
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Post by acidohm on Sept 29, 2019 19:06:01 GMT
Know a fellow who was looking into the human heart beat, his PHd in physics and MD degree were the tools he used to attempt to create a working model to predict heart attacks. Last I heard the team had no luck, the heart beat was too random, too much chaos. Just a quick grab from the previously mentioned publication, however there is a few pages on the subject... EVEN DAVID RUELLE HAD STRAYED from formalism to speculate about chaos in the heart—“a dynamical system of vital interest to every one of us,” he wrote. “The normal cardiac regime is periodic, but there are many nonperiodic pathologies (like ventricular fibrillation) which lead to the steady state of death. It seems that great medical benefit might be derived from computer studies of a realistic mathematical model which would reproduce the various cardiac dynamical regimes.” I'd suggest there is actually nothing random in chaos, id have to copy/paste the entire book to highlight this statement, however, order and randomness are interlinked in stunning ways.....



Chaos
Sept 29, 2019 19:30:08 GMT
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Post by acidohm on Sept 29, 2019 19:30:08 GMT
Know a fellow who was looking into the human heart beat, his PHd in physics and MD degree were the tools he used to attempt to create a working model to predict heart attacks. Last I heard the team had no luck, the heart beat was too random, too much chaos. Feigenbaum knew what he had, because geometric convergence meant that something in this equation was scaling, and he knew that scaling was important. All of renormalization theory depended on it. In an apparently unruly system, scaling meant that some quality was being preserved while everything else changed. Some regularity lay beneath the turbulent surface of the equation. But where? It was hard to see what to do next. Summer turns rapidly to autumn in the rarefied Los Alamos air, and October had nearly ended when Feigenbaum was struck by an oddthought. He knew that Metropolis, Stein, and Stein had looked at other equations as well and had found that certain patterns carried over from one sort of function to another. The same combinations of R’s and L’s appeared, and they appeared in the same order. One function had involved the sine of a number, a twist that made Feigenbaum’s carefully workedout approach to the parabola equation irrelevant. He would have to start over. So he took his HP–65 again and began to compute the perioddoublings for xt+1 = r sin π xt. Calculating a trigonometric function made the process that much slower, and Feigenbaum wondered whether, as with the simpler version of the equation, he would be able to use a shortcut. Sure enough, scanning the numbers, he realized that they were again converging geometrically. It was simply a matter of calculating the convergence rate for this new equation. Again, his precision was limited, but he got a result to same three decimal places: 4.669. What the above shows, and I'm using the quotes a bit ham fisted, is different systems when analysed chaotically, conform to the same result. There is a universality. I think the issue your friend came up against is a difficulty in predicting recognisable patterns prior to fibrillation. Tho as i type the above, noise is something that would prevent identifying the signal as required. Many physicists have gone to incredible lengths to isolate their experiments from noise to isolate the signal.



Chaos
Sept 29, 2019 20:17:57 GMT
Post by nautonnier on Sept 29, 2019 20:17:57 GMT
Reminds me of The Golden Mean"The Golden Mean (or Golden Section), represented by the Greek letter phi, is one of those mysterious natural numbers, like e or pi, that seem to arise out of the basic structure of our cosmos. Unlike those abstract numbers, however, phi appears clearly and regularly in the realm of things that grow and unfold in steps, and that includes living things. The decimal representation of phi is 1.6180339887499... . "goldenmean.vashti.net/



Chaos
Sept 29, 2019 20:25:15 GMT
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Post by acidohm on Sept 29, 2019 20:25:15 GMT
Reminds me of The Golden Mean"The Golden Mean (or Golden Section), represented by the Greek letter phi, is one of those mysterious natural numbers, like e or pi, that seem to arise out of the basic structure of our cosmos. Unlike those abstract numbers, however, phi appears clearly and regularly in the realm of things that grow and unfold in steps, and that includes living things. The decimal representation of phi is 1.6180339887499... . "goldenmean.vashti.net/[brĺ] Not far off actually....i had the same thought when i saw the diagram.



Post by acidohm on Sept 30, 2019 7:03:32 GMT
A PHYSICIST HAD GOOD REASON to dislike a model that found so little clarity in nature. Using the nonlinear equations of fluid motion, the world’s fastest supercomputers were incapable of accurately tracking a turbulent flow of even a cubic centimeter for more than a few seconds. The blame for this was certainly nature’s more than Landau’s, but even so the Landau picture went against the grain. Absent any knowledge, a physicist might be permitted to suspect that some principle was evading discovery. The great quantum theorist Richard P. Feynman expressed this feeling. “It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?”



Post by acidohm on Sept 30, 2019 7:30:57 GMT
Yorke understood. “The first message is that there is disorder. Physicists and mathematicians want to discover regularities. People say, what use is disorder. But people have to know about disorder if they are going to deal with it. The auto mechanic who doesn’t know about sludge in valves is not a good mechanic.” Scientists and nonscientists alike, Yorke believed, can easily mislead themselves about complexity if they are not properly attuned to it. Why do investors insist on the existence of cycles in gold and silver prices? Because periodicity is the most complicated orderly behavior they can imagine. When they see a complicated pattern of prices, they look for some periodicity wrapped in a little random noise. And scientific experimenters, in physics or chemistry or biology, are no different. “In the past, people have seen chaotic behavior in innumerable circumstances,” Yorke said. “They’re running a physical experiment, and the experiment behaves in an erratic manner. They try to fix it or they give up. They explain the erratic behavior by saying there’s noise, or just that the experiment is bad.”



Post by acidohm on Sept 30, 2019 7:38:19 GMT
But unlike most physicists, Marcus eventually learned Lorenz’s lesson, that a deterministic system can produce much more than just periodic behavior. He knew to look for wild disorder, and he knew that islands of structure could appear within the disorder. So he brought to the problem of the Great Red Spot an understanding that a complex system can give rise to turbulence and coherence at the same time. He could work within an emerging discipline that was creating its own tradition of using the computer as an experimental tool. And he was willing to think of himself as a new kind of scientist: not primarily an astronomer, not a fluid dynamicist, not an applied mathematician, but a specialist in chaos.



Post by missouriboy on Sept 30, 2019 8:27:20 GMT
Seems we are seeing other specialists in chaos more frequently of late.



Chaos
Sept 30, 2019 8:35:32 GMT
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Post by acidohm on Sept 30, 2019 8:35:32 GMT
Every scientist who turned to chaos early had a story to tell of discouragement or open hostility. Graduate students were warned that their careers could be jeopardized if they wrote theses in an untested discipline, in which their advisors had no expertise. A particle physicist, hearing about this new mathematics, might begin playing with it on his own, thinking it was a beautiful thing, both beautiful and hard—but would feel that he could never tell his colleagues about it. Older professors felt they were suffering a kind of midlife crisis, gambling on a line of research that many colleagues were likely to misunderstand or resent. But they also felt an intellectual excitement that comes with the truly new. Even outsiders felt it, those who were attuned to it. To Freeman Dyson at the Institute for Advanced Study, the news of chaos came “like an electric shock” in the 1970s. Others felt that for the first time in their professional lives they were witnessing a true paradigm shift, a transformation in a way of thinking.



Chaos
Sept 30, 2019 8:41:05 GMT
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Post by acidohm on Sept 30, 2019 8:41:05 GMT
Nonlinearity means that the act of playing the game has a way of changing the rules. You cannot assign a constant importance to friction, because its importance depends on speed. Speed, in turn, depends on friction. That twisted changeability makes nonlinearity hard to calculate, but it also creates rich kinds of behavior that never occur in linear systems. In fluid dynamics, everything boils down to one canonical equation, the NavierStokes equation. It is a miracle of brevity, relating a fluid’s velocity, pressure, density, and viscosity, but it happens to be nonlinear. So the nature of those relationships often becomes impossible to pin down. Analyzing the behavior of a nonlinear equation like the NavierStokes equation is like walking through a maze whose walls rearrange themselves with each step you take. As Von Neumann himself put it: “The character of the equation…changes simultaneously in all relevant respects: Both order and degree change. Hence, bad mathematical difficulties must be expected.” The world would be a different place—and science would not need chaos—if only the NavierStokes equation did not contain the demon of nonlinearity.

