Chaos Researchers Can Now Predict Perilous Points of No Return

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

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.

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.

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?

$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.

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