Guest Post by Willis Eschenbach
Stuck in the Nadi Airport in Fiji for the day, waiting for my flight to Brisbane. So … I read. I found a most clearly written and fascinating article in Quanta Magazine entitled “‘Next-Level’ Chaos Traces the True Limit of Predictability“.
Basically, it seems to be Godel’s Theorem meet the Turing Halting problem.
And it seems to me that their conclusions mean that future climate states are indeed fundamentally unpredictable, but NOT for the reason usually posited, that we cannot specify the starting conditions. It’s been referred to as the “butterfly problem”, that in a chaotic system a tiny change in starting conditions can lead to huge changes in outcomes.
That issue you can kinda get around by doing a bunch of runs with different starting conditions, and by using an ensemble of a whole bunch of models … although, of course, you have no way of knowing if the starting conditions or the ensemble members have fully explored the parameter space.
But this kind of unpredictability is a brand new one. They’ve shown that even if we knew the position and motion of all the molecules in the ocean, the future state of ocean currents still isn’t predictable.
Me, I’m curious about other folks’ take on what this finding means to climate science.
Best to all from F1J1,
w.
… reminds me of an old joke. Werner Heisenberg is speeding in his car when he’s pulled over by a policeman, who asks him “Do you know how fast you were going?”
“No,” said Werner, “but I know where I was!”
PS—I’m at my mate’s house in Oz, and it’s my first time going online with SpaceX Starlink. Here’s the Ookla Speedtest results … not exactly blazing fast, but it works very well.
The mathematical model could have the same initial conditions but the way it is coded in computer models could result to variation after the first iteration it is as if the initial conditions are not equal and after several iterations, the variations in results could be as high as 200 percent. I think Kip has a good explanation to an article posted a long time back where T raised to the fourth power is coded as TxTxTxT in one computer model, and T^2xT^2 in another, and TxT^3 in another. As the number of computer bits increases, it take longer for the difference to be detectable. That was a computer model of a fixed plate and a fixed source of energy in a vacuum– or the most simple of climate change model unlike the earth which tilts, moves around the sun in elliptical orbit, has variations in surface reflection and absorption of the solar energy, variations in tilt, distance from the sun, and the sun having its own dynamic behavior.
Reading suggestion: Against The Gods, the remarkable story of risk. By Peter Bernstein.
An enjoyable tale of how statistics and the measurement of risk came about.
https://fivebooks.com/book/against-gods-by-peter-l-bernstein/
………..
Meanwhile in poor Britain we continue our self impoverishment through net Zero resulting from bad science and risk assessment.
Willis,
you say that
“But this kind of unpredictability is a brand new one. They’ve shown that even if we knew the position and motion of all the molecules in the ocean, the future state of ocean currents still isn’t predictable.
Me, I’m curious about other folks’ take on what this finding means to climate science.”
But as far as I can tell your statement is incorrect. What they have shown is that
there is a “speed limit” to our ability to predict the future of certain systems. Nobody is saying that we cannot predict with absolute certainty the state in 100 years or 1000 years but only that it is impossible to predict in a finite amount of time the state at
infinity. After all that is what the halting problem is about — can you write a program that will say in a finite number of steps whether or not a second program will run to infinity. That is impossible but it is clearly always possible to predict the output of an
arbitrary program after a finite number of steps (which is what a universal Turing machine does).
And since in climate science people are not worried about the future state of the climate over such long time frames nothing in this work has anything to do with climate models.
“Nobody is saying that we cannot predict with absolute certainty the state in 100 years or 1000 years but only that it is impossible to predict in a finite amount of time the state at
infinity.”
I’m saying that. Quantum mechanics is statistical. That means you might know the most probable result but sometimes the least probable outcome actually happens. Where you will wind up in the future is actually unknowable (other than the heat death of the universe).
You wrote –
“Nobody is saying that we cannot predict with absolute certainty the state in 100 years or 1000 years . . .”
I am. Why do you think I am wrong?
You are a computer jockey! A computer spits out a definite answer every time doesn’t it? That means you can always get a definite prediction if only you had enough computer power to compress the time it takes to compute an answer.
You have obviously never dealt with building something only to find out that every time you run a experiment to test it you obtain different results. You can run computer generated tests to get a million runs, and guess what you get? A probability distribution. What does a probability distribution tell you? Does the mean always occur? Nope. That’s why you have a distribution. Any point on that distribution can occur and you’ll never know which one is next.
Everything is chaotic but still predictable. We predict seasons, weather, eclipses etc etc.
How is it possible?
Because the chaos doesn’t mean everything goes. For one thing, the chaotic systems typically have attractors –strange or otherwise. Having an attractor means that the dynamics is limited to a small part of the possible phase space.
Also, when the chaoticians refer to unpredictability, they mean position and velocity of all N particles that comprise the system. But we are not interested in this–we want to know large-scale quantities such as pressure or temperature at a particular location at a particular time. Such large-scale quantity may be predictable even if the system in its 6N variables is not. The gases obey gas laws while the microscopic level is unpredictable, after all.
“We predict seasons, weather, eclipses etc etc.”
Not at all – at least not better than a smart 12 year old. That’s nothing to write home about,
is it?
You also wrote “Also, when the chaoticians refer to unpredictability, they mean position and velocity of all N particles that comprise the system.” I don’t know where you got that from, and I expect you made it up. Chaoticians study chaos.
People tend assume that in a fully deterministic system, where the present determines the future, the approximate future can be determined from the approximate future. Not true – in a chaotic system there is no minimum change to the present which may result in completely unpredictable outcomes.
If you don’t like chaos or chaoticians, the uncertainty principle of quantum physics leads to precisely the same conclusion.
Averages, numerical prediction, pretty computer graphics won’t help. Sorry about that. You might be confusing prediction with assumption – the sun will rise tomorrow, for example.
“ pressure or temperature”
Temperature alone is not a predictor of climate. Pressure alone is not a predictor of climate. Even together they don’t predict climate, other factors apply. And climate models don’t predict pressure.
“Such large-scale quantity may be predictable“
The operative word here is “may”. Glaciation is a large-scale quantity. Can the climate models predict when the next ice age will begin?
The reason these things can be predicted is because they are autocorrelated. Tomorrows temperature will be close to todays. Summer comes after spring, always.
Defining global temperatures as an average of all temperatures on earth doesn’t allow for predicting the different combinations that can occur at any given place. Do I know where any given atom may be? Yes. Do I know where the electrons in that atom are. No. Does an EM field affect their location? You bet. Does that complicate the prediction of where electrons are at any point in time? Certainly.
To make accurate predictions you must be able to localize what occurs. Otherwise, one must admit that a global average doesn’t tell anyone what to expect. Climate science’s predilection. with a global average just doesn’t allow that.
I’m curious about other folks’ take on what this finding means to climate science.
Whatever the daily findings it always means we’re doomed-
Global sea level rose faster than expected last year alarming scientists
The whole universe is chaos.
Entropy is in the driver’s seat.
“It’s been referred to as the “butterfly problem”, that in a chaotic system a tiny change in starting conditions can lead to huge changes in outcomes.”
My PhD was on this subject, except Lorenz hadn’t written his paper terming it ‘chaos’ at that time. We used to call it non-linear dynamics. In the system I studied it was possible to predict the result of a small change in a variable, as to whether it would result in a stable result, an unstable result or an oscillation. Not all such systems are the same of course. The system I studied involved combustion reactions, the heat release was nonlinear and the cooling was linear, the steady state solution was the result of the intersection of the two, under some conditions it was possible for the cooling to be tangential to the heating in that case a slight increase in temperature led to a rapid jump in temperature (an explosion).
In my understanding, it’s not a simple as “the “butterfly problem”, that in a chaotic system a tiny change in starting conditions can lead to huge changes in outcomes. That issue you can kinda get around by doing a bunch of runs with different starting conditions, and by using an ensemble of a whole bunch of models”.
Model ensembles do not and cannot overcome the basic Initial Conditions problem. Using more and more models, using more and more sets of initial conditions, only multiplies the Initial Conditions Problem. One can use a single model, using infinitely different initial conditions, to produce an infinite series of possible futures over an infinite number of time steps. This does absolutely nothing to inform us of the condition to expect on the 19th of June 2089.
The Initial Conditions Problem means that prediction of exact future states of chaotic systems is impossible.
Real World Physical Systems — meaning systems that actually exist — all come with differing physical boundaries of what is possible. For the current Earth, it is not possible to have a tropical North Pole and a ice-bound equator simultaneously. It is not possible for the ocean to approach or exceed 100 degrees C. These are boundaries imposed by the laws of physics. (I am not a physicist, so I might be little off in my examples – please supply your own.)
The undecidability being discussed in the the Quanta article is quite different.
Climate science already uses modified short-form, linearized physics formulas in its models, meaning that they are wrong from the start. add in the Initial Conditions Problem and all bets are losers.
An excellent comment.
Too many mathematicians have never dealt with physical systems in a hands on manner. I am reminded of those kids in college who could deal with the math of resistors, capacitors, and inductors like geniuses. Give them a parts bin and soldering iron and they were in a survivors role in the middle of a jungle with no guidance.
Too many folks here and in climate science are mathematicians that expect a definitive answer to be derived from what is a probability distribution. The countless measurement uncertainty discussions here amply demonstrate that. The answer is always the more measurements you make, the better and more accurately you know the correct answer, that is., the mean of the probability distribution. It is a blind spot generated from years of schooling where the teacher expects a definitive answer to a question.
They don’t seem to be able to ever recognize that 68% of the possible occurrences lie within one standard deviation, ~95% within 2 standard deviations, etc. Which occurrence in the distribution will occur next can never be predicted with certainty because they are random events. Any value inside the variance can occur at any instant in time and it can’t be predicted with any certainty. Both the highest and lowest values in the range of data will occur and you simply can’t know when.
StarLink … still can’t out perform a station wagon full of backup tapes, but much better throughput than carrier pigeons chirping through copper wires, and even works out on the Seward Peninsula.
Isn’t it a bit like trying to predict the next giant wave – relative or absolute?
Apparently Newton knew that the orbits of the planets became unpredictable after long times. The reason is the effects of unknown small perturbations.
The same problem accrues to water molecules in the ocean. Thermal motions are random. Even knowing initial molecular positions perfectly, there is no way to predict positions after long times.
Richard Feynman made almost exactly the same statement quite some time ago, to illustrate how classical physics is no more determinate than quantum physics. His point was that even in classical physics there is no such thing as a perfect measurement; the effects of measure error simply propagate through the particle system with time, as an emergent phenomenon.