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Chaos Researchers Can Now Predict Perilous Points of No Return

09/15/2022 9:29 PM

Systems with non-linear feedback typically behave chaotically, the typical example being the weather. If a parameter changes, these systems can reach a tipping point and change their behavior. Interestingly, according to this article, a neural network can watch and learn from a chaotic system, even with a tipping point, and predict its future response.

"Predicting complex systems like the weather is famously difficult. But at least the weather’s governing equations don’t change from one day to the next. In contrast, certain complex systems can undergo “tipping point” transitions, suddenly changing their behavior dramatically and perhaps irreversibly, with little warning and potentially catastrophic consequences."

"In a series of recent papers, researchers have shown that machine learning algorithms can predict tipping-point transitions in archetypal examples of such “nonstationary” systems, as well as features of their behavior after they’ve tipped. The surprisingly powerful new techniques could one day find applications in climate science, ecology, epidemiology and many other fields."

https://www.quantamagazine.org/ai-algorithm-foresees-chaotic-tipping-points-20220915/

https://www.quantamagazine.org/machine-learnings-amazing-ability-to-predict-chaos-20180418/

A chaotic system that changes its behavior.

https://www.crystalinks.com/chaos.html

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#1

Re: Chaos Researchers Can Now Predict Perilous Points of No Return

09/15/2022 10:42 PM

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#5
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Re: Chaos Researchers Can Now Predict Perilous Points of No Return

09/17/2022 8:21 PM

There is a difference between Random and Chaotic. If a signal is random, there is no way that a series of samples can predict the next sample, i.e. it is indeterministic. You can, however, gather statistical data. For example, the histogram of the distribution might produce a Bell curve (gaussian).

Chaotic systems are deterministic but act randomly in that, two very close values will evolve differently. A tiny bit of "noise" will be amplified over time. This was discovered by Edward Lorenz, who in 1961 was running weather models on a simple computer.

"In 1961, Lorenz was using a simple digital computer, a Royal McBee LGP-30, to simulate weather patterns by modeling 12 variables, representing things like temperature and wind speed. He wanted to see a sequence of data again, and to save time he started the simulation in the middle of its course. He did this by entering a printout of the data that corresponded to conditions in the middle of the original simulation. To his surprise, the weather that the machine began to predict was completely different from the previous calculation. The culprit: a rounded decimal number on the computer printout. The computer worked with 6-digit precision, but the printout rounded variables off to a 3-digit number, so a value like 0.506127 printed as 0.506. This difference is tiny, and the consensus at the time would have been that it should have no practical effect. However, Lorenz discovered that small changes in initial conditions produced large changes in long-term outcome.[15]

Lorenz's discovery, which gave its name to Lorenz attractors, showed that even detailed atmospheric modelling cannot, in general, make precise long-term weather predictions. His work on the topic, assisted by Ellen Fetter, culminated in the publication of his 1963 paper "Deterministic Nonperiodic Flow" in Journal of the Atmospheric Sciences, and with it, the foundation of chaos theory.[2][14] He states in that paper:

"Two states differing by imperceptible amounts may eventually evolve into two considerably different states ... If, then, there is any error whatever in observing the present state—and in any real system such errors seem inevitable—an acceptable prediction of an instantaneous state in the distant future may well be impossible....In view of the inevitable inaccuracy and incompleteness of weather observations, precise very-long-range forecasting would seem to be nonexistent."

His description of the butterfly effect, the idea that small changes can have large consequences, followed in 1969."

https://en.wikipedia.org/wiki/Edward_Norton_Lorenz

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#7
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Re: Chaos Researchers Can Now Predict Perilous Points of No Return

09/18/2022 9:16 AM

A good, visualizable example of chaos is turbulent fluid flow. Two nearby parcels of liquid at one point in the flow are far apart a short time later and were far apart a short time before. The fluid can change from turbulent to laminar flow and back again, all the time deterministically following the equations of Navier-Stokes.

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#2

Re: Chaos Researchers Can Now Predict Perilous Points of No Return

09/16/2022 5:25 AM

I seem to remember from my pre-digital education that analogue "computer" models were able to predict when systems would become unstable (tipping point) and even model that through the failure process that was eventually observed.

Seems like digital modelling is getting to where we were back in the late '70's.

Bounded/unbounded input/output systems used initially to train in motor generator systems, but then eventually for everything from river flow systems (flood modelling) and such. Usually combinations of hardwaired RLC components. Steady state outcome (if it happened) observable within seconds, but constructing models took weeks/months and they were only suited to the item being modelled.

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#3

Re: Chaos Researchers Can Now Predict Perilous Points of No Return

09/16/2022 8:18 AM

IMHO: There is no such thing as random or chaos.There are simply events for which we cannot presently determine the present or future state of.

Applying Newton's law,"Every action results in an equal and opposite reaction".

Therefor, IMHO,the big bang started everything,and the near infinite number of dominoes began to fall,branching,and dividing many times.Any action is preceded by a previous action,but if there are too many actions involved,we cannot analyze them,therefor we call them Random.

Some "random" actions are being analyzed and predicted and as our knowledge increases, we will nibble around the edges of Random and digest all that we can,but the Random cookie is very large,and we will never consume it all.

Radioactive decay was once considered random,but it has been discovered that sunspot activity affects the decay,even before the flare reaches Earth.

https://kottke.org/10/08/sun-may-affect-radioactive-decay-rates

What other unknown forces may affect the "randomness"of the universe?

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#4

Re: Chaos Researchers Can Now Predict Perilous Points of No Return

09/17/2022 11:11 AM

$1 says this will be the basis of the next algoreithm duct taped on future gen climate "models". Just $1? Hey, I figured no sane chap of you would risk more $. (LOL) S.M.

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#6
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Re: Chaos Researchers Can Now Predict Perilous Points of No Return

09/18/2022 12:42 AM

You are right of course after all the climate scientists, ran dumb, oh sorry random predictions for the glowing balls warming still abound.

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#8

Re: Chaos Researchers Can Now Predict Perilous Points of No Return

09/18/2022 2:16 PM

Two reminders. Numbers themselves are related. When you use numbers......you establish a mathematical relationship automatically. So, all that is described by numbers is related by the language of numbers. A unified relationship comes from using numbers. This simple obvious fact.....has turned into a physical cosmic dogma for many. It's idolized.

And, with all measurements, the/a reaction is included in the result. The result is not pure. The reaction is included with the stimuli. When we measure light interacting with matter, the result includes the reaction of the matter from the light stimuli.........giving us a "wave function".

These two facts gives us mathematical randomness, probability, chaos OR resonance, and order......depending on what set of numbers are used. All these mathematical states can be found in any system. Especially a system of flux. A fluid is a flux too.

Math is one of our most valuable tools, but it can be a snake.

It has led us to believe that light is a continuous wave, instead of a discreet intermittent strobe. Light is only 1/2 of what we think it is. It is not continuous stream, it blinks. A flux of blinks measures to be continuous.....like current. Current is a flux of intermittence and can contain multiple waveforms, randomness, chaos, noise......all at the same time because of it.

A radio station is a single blinker. Your transmitting antenna is a quick blinker, not a speaker......it squeaks, does not hum........and I believe I can show you how to blink/squeak it.....one blink/squeak at a time. And measure one way light. The duty cycle of that blink, will reveal the emitter velocity and the detector velocity. A valuable tool that is not used.

Not to mention the disprovement of spacetime and the constant velocity of light, and that time and length are absolute.

If there are environmental tipping points, they should be easy to spot. What "dead" areas we do see, don't last long. It's not the environment that controls the diversity and density of life..........it's the predators. Innate fear is the motivator for the organization of life. Eating and mating are not the goal......NOT being eaten is the goal. This can be seen with insects and mammal populations and diets. And it probably affects plant life too. Probably bacteria and virus too.

Life is more than we can comprehend. It remains a mystery. Just like matter and physicality remain a mystery.

What true knowledge do we really have?

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#9
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Re: Chaos Researchers Can Now Predict Perilous Points of No Return

09/18/2022 7:38 PM

There you've hatched a conundrum, mans' struggle to define the unknown in terms that are universal....this has led to this effort to use precise language to explain an ever changing reality fueled by ever expanding knowledge...so it's all mostly guess work...

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