Just to be clear ahead of time, chaos in weather is NOT the same as climate disruption listed below – Anthony
Guest submission by Dr. Andy Edmonds
This is not intended to be a scientific paper, but a discussion of the disruptive light Chaos Theory can cast on climate change, for non-specialist readers. This will have a focus on the critical assumptions that global warming supporters have made that involve chaos, and their shortcomings. While much of the global warming case in temperature records and other areas has been chipped away, they can and do, still point to their computer models as proof of their assertions. This has been hard to fight, as the warmists can choose their own ground, and move it as they see fit. This discussion looks at the constraints on those models, and shows that from first principles in both chaos theory and the theory of modelling they cannot place reliance on these models.
First of all, what is Chaos? I use the term here in its mathematical sense. Just as in recent years Scientists have discovered extra states of matter (not just solid, liquid, gas, but also plasma) so also science has discovered new states that systems can have.
Systems of forces, equations, photons, or financial trading, can exist effectively in two states: one that is amenable to mathematics, where the future states of the systems can be easily predicted, and another where seemingly random behaviour occurs.
This second state is what we will call chaos. It can happen occasionally in many systems.
For instance, if you are unfortunate enough to suffer a heart attack, the normally predictable firing of heart muscles goes into a chaotic state where the muscles fire seemingly randomly, from which only a shock will bring them back. If you’ve ever braked hard on a motorbike on an icy road you may have experienced a “tank slapper” a chaotic motion of the handlebars that almost always results in you falling off. There are circumstances at sea where wave patterns behave chaotically, resulting in unexplained huge waves.
Chaos theory is the study of Chaos, and a variety of analytical methods, measures and insights have been gathered together in the past 30 years.
Generally, chaos is an unusual occurrence, and where engineers have the tools they will attempt to “design it out”, i.e. to make it impossible.
There are, however, systems where chaos is not rare, but is the norm. One of these, you will have guessed, is the weather, but there are others, the financial markets for instance, and surprisingly nature. Investigations of the populations of predators and prey, for instance shows that these often behave chaotically over time. The author has been involved in work that shows that even single cellular organisms can display population chaos at high densities.
So, what does it mean to say that a system can behave seemingly randomly? Surely if a system starts to behave randomly the laws of cause and effect are broken?
A little over a hundred years ago scientists were confident that everything in the world would be amenable to analysis, that everything would be therefore predictable, given the tools and enough time. This cosy certainty was destroyed first by Heisenberg’s uncertainty principle, then by the work of Kurt Gödel, and finally by the work of Edward Lorenz, who first discovered Chaos, in, of course, weather simulations!
Chaotic systems are not entirely unpredictable, as something truly random would be. They exhibit diminishing predictability as they move forward in time, and this diminishment is caused by greater and greater computational requirements to calculate the next set of predictions. Computing requirements to make predictions of chaotic systems grow exponentially, and so in practice, with finite resources, prediction accuracy will drop off rapidly the further you try to predict into the future. Chaos doesn’t murder cause and effect; it just wounds it!
Now would be a good place for an example. Everyone owns a spread sheet program. The following is very easy to try for yourself.
The simplest man-made equation known that produces chaos is called the logistic map.
It’s simplest form is: Xn+1 = 4Xn(1-Xn)
Meaning that the next step of the sequence is equal to 4 times the previous step times 1 – the previous step. If we open a spread sheet we can create two columns of values:
Each column A and B is created by writing =A1*4* (1-A1) into cell A2, and then copying it down for as many cells as you like, the same for B2, writing in =B1*4* (1-B1). A1 and B1 contain the initial conditions. A1 contains just 0.3 and B1 contains a very slightly different number: 0.30000001
The graph to the right shows the two copies of the series. Initially they are perfectly in sync, then they start to divert at around step 22, while by step 28 they are starting to behave entirely differently.
This effect occurs for a wide range of initial conditions. It is fun to get out your spread sheet program and experiment. The bigger the difference between the initial conditions the faster the sequences diverge.
The difference between the initial conditions is minute, but the two series diverge for all that. This illustrates one of the key things about chaos. This is the acute sensitivity to initial conditions.
If we look at this the other way round, suppose that you only had the series, and let’s assume to make it easy, that you know the form of the equation but not the initial conditions. If you try to make predictions from your model, any minute inaccuracies in your guess of the initial conditions will result in your prediction and the result diverging dramatically. This divergence grows exponentially, and one way of measuring this is called the Lyapunov exponent. This measures in bits per time step how rapidly these values diverge, averaged over a large set of samples. A positive Lyapunov exponent is considered to be proof of chaos. It also gives us a bound on the quality of predictions we can get if we try to model a chaotic system.
These basic characteristics apply to all chaotic systems.
Here’s something else to stimulate thought. The values of our simple chaos generator in the spread sheet vary between 0 and 1. If we subtract 0.5 from each, so we have positive and negative going values, and accumulate them we get this graph, stretched now to a thousand points.
If, ignoring the scale, I told you this was the share price last year for some FTSE or NASDAQ stock, or yearly sea temperature you’d probably believe me. The point I’m trying to make is that chaos is entirely capable of driving a system itself and creating behaviour that looks like it’s driven by some external force. When a system drifts as in this example, it might be because of an external force, or just because of chaos.
So, how about the weather?
Edward Lorenz, (1917, 2008) was the father of the study of Chaos, and also a weather researcher. He created an early weather simulation using three coupled equations and was amazed to find that as he progressed the simulation in time the values in the simulation behaved unpredictably.
He then looked for evidence that real world weather behaved in this same unpredictable fashion, and found it, before working on discovering more about the nature of Chaos.
No climate researchers dispute his analysis that the weather is chaotic.
Edward Lorenz estimated that the global weather exhibited a Lyapunov exponent equivalent to one bit of information every 4 days. This is an average over time and the world’s surface. There are times and places where weather is much more chaotic, as anyone who lives in England can testify. What this means though, is that if you can predict tomorrows weather with an accuracy of 1 degree C, then your best prediction of the weather on average 5 days hence will be +/- 2 degrees, 9 days hence +/-4 degrees and 13 days hence +/- 8 degrees, so to all intents and purposes after 9-10 days your predictions will be useless. Of course, if you can predict tomorrow’s weather to +/- 0.1 degree, then the growth in errors is slowed, but since they grow exponentially, it won’t be many days till they become useless again.
Interestingly the performance of weather predictions made by organisations like the UK Met office drop off in exactly this fashion. This is proof of a positive Lyapunov exponent, and thus of the existence of chaos in weather, if any were still needed.
So that’s weather prediction, how about long term modelling?
Let’s look first at the scientific method. The principle ideas are that science develops by someone forming an hypothesis, testing this hypothesis by constructing an experiment, and modifying the hypothesis, proving or disproving it, by examining the results of the experiment.
A model, whether an equation or a computer model, is just a big hypothesis. Where you can’t modify the thing you are hypothesising over with an experiment, then you have to make predictions using your model and wait for the system to confirm or deny them.
A classic example is the development of our knowledge of the solar system. The first models had us at the centre, then the sun at the centre, then the discovery of elliptical orbits, and then enough observations to work out the exact nature of these orbits. Obviously, we could never hope to affect the movement of the planets, so experiments weren’t possible, but if our models were right, key things would happen at key times: eclipses, the transit of Venus, etc. Once models were sophisticated enough, errors between the model and reality could be used to predict new features. This is how the outer planets, Neptune and Pluto were discovered. If you want to know where the planets will be in ten years’ time to the second, there is software available online that will tell you exactly.
Climate scientists would love to be able to follow this way of working. The one problem is that, because the weather is chaotic, there is never any hope that they can match up their models and the real world.
They can never match up the model to shorter term events, like say six months away, because as we’ve seen, the weather six months away is completely and utterly unpredictable, except in very general terms.
This has terrible implications for their ability to model.
I want to throw another concept into this mix, drawn from my other speciality, the world of computer modelling through self-learning systems.
This is the field of artificial intelligence, where scientists attempt to create mostly computer programs that behave intelligently and are capable of learning. Like any area of study, this tends to throw up bits of general theory and one of these is to do with the nature of incremental learning.
Incremental learning is where a learning process tries to model something by starting out simple and adding complexity, testing the quality of the model as it goes.
Examples of this are neural networks, where the strength of connections between simulated brain cells are adapted as learning goes on or genetic programming, where bits of computer programs are modified and elaborated to improve the fit of the model.
From my example above of theories of the solar system, you can see that the scientific method itself is a form of incremental learning.
There is a graph that is universal in incremental learning. It shows the performance of an incremental learning algorithm, it doesn’t matter which, on two sets of data.
The idea is that these two sets of data must be drawn from the same source, but they are split randomly into two, the training set, used to train the model, and a test set used to test it every now and then. Usually the training set is bigger than the test set, but if there is plenty of data this doesn’t matter either. So as learning progresses the learning system uses the training data to modify itself, but not the test data, which is used to test the system, but is immediately forgotten by it.
As can be seen, the performance on the training set gets better and better as more complexity is added to the model, but the performance of the test set gets better, and then starts to get worse!
Just to make this clear, the test set is the only thing that matters. If we are to use the model to make predictions we are going to present new data to it, just like our test set data. The performance on the training set is irrelevant.
This is an example of a principle that has been talked about since William of Ockham first wrote “Entia non sunt multiplicanda praeter necessitatem “, known as Ockham’s razor and translatable as “entities should not be multiplied without necessity”, entities being in his case embellishments to a theory. The corollary of this is that the simplest theory that fits the facts is most likely to be correct.
There are proofs for the generality of this idea from Bayesian Statistics and Information Theory.
So, this means that our intrepid weather modellers are in trouble from both ends: if their theories are insufficiently complex to explain the weather their model will be worthless, if too complex then they will also be worthless. Who’d be a weather modeller?
Given that they can’t calibrate their models to the real world, how do weather modellers develop and evaluate their models?
As you would expect, weather models behave chaotically too. They exhibit the same sensitivity to initial conditions. The solution chosen for evaluation (developed by Lorenz) is to run thousands of examples each with slightly different initial conditions. These sets are called ensembles.
Each example explores a possible path for the weather, and by collecting the set, they generate a distribution of possible outcomes. For weather predictions they give you the biggest peak as their prediction. Interestingly, with this kind of model evaluation there is likely to be more than one answer, i.e. more than one peak, but they choose never to tell us the other possibilities. In statistics this methodology is called the Monte Carlo method.
For climate change they modify the model so as to simulate more CO2, more solar radiation or some other parameter of interest and then run another ensemble. Once again the results will be a series of distributions over time, not a single value, though the information that the modellers give us seems to leave out alternate solutions in favour of the peak value.
Models are generated by observing the earth, modelling land masses and air currents, tree cover, ice cover and so on. It’s a great intellectual achievement, but it’s still full of assumptions. As you’d expect the modellers are always looking to refine the model and add new pet features. In practice there is only one real model, as any changes in one are rapidly incorporated into the others.
The key areas of debate are the interactions of one feature with another. For instance the hypothesis that increased CO2 will result in run-away temperature rises is based on the idea that the melting of the permafrost in Siberia due to increased temperatures will release more CO2 and thus positive feedback will bake us all. Permafrost may well melt, or not, but the rate of melting and the CO2 released are not hard scientific facts but estimates. There are thousands of similar “best guesses’’ in the models.
As we’ve seen from looking at incremental learning systems too much complexity is as fatal as too little. No one has any idea where the current models lie on the graph above, because they can’t directly test the models.
However, dwarfing all this arguing about parameters is the fact that weather is chaotic.
We know of course that chaos is not the whole story. It’s warmer on average away from the equatorial regions during the summer than the winter. Monsoons and freezing of ice occur regularly every year, and so it’s tempting to see chaos as a bit like noise in other systems.
The argument used by climate change believers runs that we can treat chaos like noise, so chaos can be “averaged out”.
To digress a little, this idea of averaging out of errors/noise has a long history. If we take the example of measuring the height of Mount Everest before the days of GPS and Radar satellites, the method to calculate height was to start at Sea level with a theodolite and take measurements of local landmarks using their distance and their angle above the horizon to estimate their height. Then to move on to those sites and do the same thing with other landmarks, moving slowly inland. By the time surveyors got to the foothills of the Himalayas they were relying on many thousand previous measurements, all with measurement error included. In the event the surveyor’s estimate of the height of Everest was only a few hundred feet out!
This is because all those measurement errors tended to average out. If, however there had been a systemic error, like the theodolites all measuring 5 degrees up, then the errors would have been enormous. The key thing is that the errors were unrelated to the thing being measured.
There are lots of other examples of this in Electronics, Radio Astronomy and other fields.
You can understand climate modellers would hope for the same to be true of chaos. In fact, they claim this is true. Note however that the errors with the theodolites were nothing to do with the actual height of Everest, as noise in radio telescope amplifiers has nothing to do with the signals from distant stars. Chaos, however, is implicit in weather, so there is no reason why it should average out. It’s not part of the measurement; it’s part of the system being measured.
So can chaos be averaged out? If it can, then we would expect long term measurements of weather to exhibit no chaos. When a team of Italian researchers asked to use my Chaos analysis software last year to look at a time series of 500 years of averaged South Italian winter temperatures, the opportunity arose to test this. The picture below is this time series displayed in my Chaos Analysis program, ChaosKit.
The result? Buckets of chaos. The Lyapunov exponent was measured at 2.28 bits per year.
To put that in English, the predictability of the temperature quarters every year further ahead you try to predict, or the other way round, the errors more than quadruple.
What does this mean? Chaos doesn’t average out. Weather is still chaotic at this scale over hundreds of years.
If we were, as climate modellers try to do, to run a moving average over the data, to hide the inconvenient spikes, we might find a slight bump to the right, as well as many bumps to the left. Would we be justified in saying that this bump to the right was proof of global warming? Absolutely not: It would be impossible to say if the bump was the result of chaos, and the drifts we’ve see it can create or some fundamental change, like increasing CO2.
So, to summarize, climate researchers have constructed models based on their understanding of the climate, current theories and a series of assumptions. They cannot test their models over the short term, as they acknowledge, because of the chaotic nature of the weather.
They hoped, though, to be able to calibrate, confirm or fix up their models by looking at very long term data, but we now know that’s chaotic too. They don’t, and cannot know, whether their models are too simple, too complex, or just right, because even if they were perfect, if weather is chaotic at this scale, they cannot hope to match up their models to the real world, the slightest errors in initial conditions would create entirely different outcomes.
All they can honestly say is this: “we’ve created models that we’ve done our best to match up to the real world, but we cannot prove to be correct. We appreciate that small errors in our models would create dramatically different predictions, and we cannot say if we have errors or not. In our models the relationships that we have publicized seem to hold.”
It is my view that governmental policymakers should not act on the basis of these models. The likelihood seems to be that they have as much similarity to the real world as The Sims, or Half-life.
On a final note, there is another school of weather prediction that holds that long term weather is largely determined by variations in solar output. Nothing here either confirms or denies that hypothesis, as long term sunspot records have shown that solar activity is chaotic too.
Andy Edmonds
Short Bio
Dr Andrew Edmonds is an author of computer software and an academic. He designed various early artificial intelligence computer software packages and was arguably the author of the first commercial data mining system. He has been the CEO of an American public company and involved in several successful start-up businesses. His PhD thesis was concerned with time series prediction of chaotic series, and resulted in his product ChaosKit, the only standalone commercial product for analysing chaos in time series. He has published papers on Neural Networks, genetic programming of fuzzy logic systems, AI for financial trading, and contributed to papers in Biotech, Marketing and Climate.
Short summary: AA discussion of the disruptive light Chaos Theory can cast on climate change, for non-specialist readers. This will have a focus on the critical assumptions that global warming supporters have made that involve chaos, and their shortcomings. While much of the global warming case in temperature records and other areas has been chipped away, they can and do, still point to their computer models as proof of their assertions. This has been hard to fight, as the warmists can choose their own ground, and move it as they see fit. This discussion looks at the constraints on those models, and shows that from first principles in both chaos theory and the theory of modelling they cannot place reliance on these models.
On his Website: http://scientio.blogspot.com/2011/06/chaos-theoretic-argument-that.html
Discover more from Watts Up With That?
Subscribe to get the latest posts sent to your email.
Contrary to what the author wrote it remains a tenet of physics that any system is predictable given enough information about it both forward or backward in time. In point of fact there is no such thing as “time”. Time itself is an illusion created by the law of entropy. Chaos is an illusion created by lack of information. “Quantum uncertainty” is a misleading term. It does not render the universe non-deterministic. Quantum uncertainty is the inability to simultaneously measure two or more properties such as position and velocity. As a measurement of position gets more and more precise simultaneous measurement of velocity gets less and less precise. Thus if we have obtain complete information about the position of a particle we cannot obtain complete information about its velocity. This is an observational constraint not a constraint of nature. The quantum wave formula is unitary and time reversible.
This common misconception that the universe is chaotic by nature (non-deterministic) is well described in a letter from an MIT/Harvard physicist to a science writer at the New York Times who made the same mistaken assumptions as the author of this WUWT article.
http://bemasc.net/wordpress/2008/07/17/decoherence-theory/
“And if you want solid evidence of the benefits of increased CO2, just ask.”
For most of the history of the earth, including most of the past 100 million years, CO2 levels were higher than at present and the oceans were more acidic, and life did very well.
If you accept that CO2 drives temperature, that means the the low levels of CO2 in the past few million years are a contributing factor to the ice ages we have experienced, which are not in general beneficial to life.
Thus, if you believe CO2 drivers temperature, this leads to the conclusion that increasing CO2 makes the next ice age less likely. It also is mo0re natural, as it returns the earth to a state more similar in which life evolved, The low levels of CO2 over the past few million years being unlike most of the past history of the earth, it represents an unnatural state and thus a stress to life rather than a help.
The caustic nature of the present oceans can be traced to the low levels of CO2 over the past few million years, which is also a threat to life as caustic environments dissolve living material. A return to higher CO2 levels and more neutral oceans would therefore likely assist life, because for most of the past 100 million years the oceans have been more acidic than they are now and life has evolved to take advantage of those conditions.
The ice ages were beneficial to polar bears and penguins, but that is not a good reason to keep CO2 levels low enough to bring on the next ice age. Most life forms are not cold weather adapted. Human’s did comparatively better during the ice ages because we domesticated fire, which gave us a survival advantage. If we ban fossil fuels this advantage may not be there for the next ice age.
Dave Springer says:
June 13, 2011 at 11:27 am
“Contrary to what the author wrote it remains a tenet of physics that any system is predictable given enough information about it both forward or backward in time.”
Enough information = the complete state of the system at one moment in time.
“Chaos is an illusion created by lack of information. “Quantum uncertainty” is a misleading term. It does not render the universe non-deterministic. Quantum uncertainty is the inability to simultaneously measure two or more properties such as position and velocity.”
In other words, you will not get enough information to predict the development of the system – Heisenberg’s uncertainty relationship prevents it.
But besides that, even if you could get the information you couldn’t run the model. See Wolfram’s principle of computational irreducibility – how would you emulate a physical system? You’d need a larger system to run the emulation on; you can’t take shortcuts due to the chaotic (not, i didn’t say nondeterministic) nature of the system. The emulating system must be bigger than the original system because it runs a program on a kind of universal computer; so to emulate the Earth you’d need a computer bigger than the Earth.
Dave, Chaos is not an illusion but a classifier. It classifies a system as having a deterministic but chaotic behaviour.
This article actually contains thoughts, clearly formulated and explained.
What a miracle.
“We know of course that chaos is not the whole story. It’s warmer on average away from the equatorial regions during the summer than the winter. Monsoons and freezing of ice occur regularly every year, and so it’s tempting to see chaos as a bit like noise in other systems.
The argument used by climate change believers runs that we can treat chaos like noise, so chaos can be “averaged out”.”
In a binary chaotic system one can easily, especially during summer vacation, trig the system with a beer, or a six pack or two, and super easy just remove one bit from the equation, thusly leaving only 50%, or one bit if you really must know, that ends up being the complete, and very only, answer.
Thusly, summer, autumn, winter, and spring, hurricane season, indian summer, autumn rains, and a 20 foot snow pack at midsummer, is the noise. It just tend to happen, pretty much always, every year, pretty much around the same time each year, what with us, on puny planet earth, being on an ever merry go round around old “silent” Sol.
The irony, of course, is that you’re a right any how, the hippies thinks they can average it out anyway.
KR: “Any two models that retrodict the same past are identical regardless of their internal construction”
Rubbish!
So with the volcano erupting spewing S02 into the stratosphere we should believe thusly:
1. If there is a drop in temperature that is within “normal variations” for the past millions of years, then the drop
is “explained” by “natural variation”. There is no need to look at the volcano as the source of the cooling. After all the cooling, if it occurs, will be within the range of “natural variability”. Nothing here to see, the earth cools all the time.
2. If a model successfully predicts this cooling, there is also no point to that. Chaos rules and that means we can say nothing about the trajectory that external forcings have on the system. Heck, even if the sun were to double its output we cannot predict that it will get warmer, because well, Chaos rules.
In regards to cost/benefit balances for increased CO2, I’ll point you at http://www.skepticalscience.com/global-warming-positives-negatives-intermediate.htm
This is a summary of some of the benefits (yes, there are some) and the costs (and yes, there are costs too) of CO2 driven climate change, with references to 60+ papers (pictures, charts, data, analysis, sorry, I don’t think there are any cartoons) on the issues. More than I care to type into a blog posting – go read the references.
In regards to the specifics of plant growth and CO2 – we can expect limited increases in productivity of some plants (considerable differences between C3 and C4 cycle plants, mind you), although most of the increase in plant mass will be in the woody/non-food portions of the plants. Plant ranges will change considerably – the California Central Valley is expected to lose ~50% productivity over the next century, and that currently provides 8% of US food production. Pests will also change ranges with temperature.
Total change in plant productivity is expected to be only a slight increase.
This was an excellent post, but I think you might have missed the bigger differences between the nature of chaos in the weather and in the climate. Two very different things that display deterministic chaos in two very different ways and different scales of time and space. This statement you made gets to the point:
“Climate scientists would love to be able to follow this way of working. The one problem is that, because the weather is chaotic, there is never any hope that they can match up their models and the real world.”
Climate scientists (versus meteorologlists) are not particularily concerned with the chaotic nature of weather, so that kind of chaos is not a problem for them. Climate scientists are concerned with long-term forcings that can tip the climate one way or another into a different regime. To see the difference between the chaos of weather and the chaos of climate it’s best to use a simple analogy of the sandpile as way of illustration that many can readily understand.
Sandpiles are often used for illustrating a chaotic system, and are in fact studied directly for what they can teach us about the nature of deterministic chaos. See for example: http://pre.aps.org/abstract/PRE/v52/i6/pR5749_1
http://www.jmu.edu/geology/ComplexEvolutionarySystems/SOC.htm
So when it comes to weather and climate, we could the sandpile analogy to say that the general state of the sandpile could be likened to the climate, and the general state of any indivdual grain in that pile could be likened to a specific weather event or forcing within that overall climate sandpile. Thus as the sandpile changes over time, by the adding of grains of sand for example, the nature of weather patterns within that sandpile change over time. Milankovitch forcings (the primary natural driver of long term climate changes) could be likened to adding grains of sand to the climate sandpile, very slowly, one at time. At some critical point, not random at all, but completely determined by frictional forces working between the grains of sand and gravity, the addition of just one grain of sand causes a collapse of the sandpile until it reaches a new point of equalibrium. This is exactly what happens with Milankovtichs cycles. It is the slow change in solar insolation on the planet, one year at a time that eventually reaches some critical point that there a collapse of the climate sandpile and a new glacial period begins or ends.
We know that there are points of criticality in the climate. All things being equal (i.e. the composition of the atmosphere, the strength of solar radition, etc.) we can be pretty confident that we know what the climate of the earth will generally be at a given point in the Milankovitch cycles. And so, though it may be remarkable it is true that it may be harder to predict the weather two weeks from now than it is to predict the earth’s climate 25,000 years from now based on Milankovtich forcings. What we currently don’t know as well as we know Milankovtich cycles is the sensitivity of the climate to other “grains of sand” that may play a role in climate such as variations if cosmic rays or the addition of small quantities of GH gases each year to the atmosphere.
One mistake that seems almost universal in this forum is that we talk about climate and weather as if they have some inherent meaning that we all understand. I don’t think so. We should focus on some reasonably well-known natural phenomenon, such as La Nina, and create a description of it which embodies descriptions of the several natural regularities that make it up. Each description of a natural regularity is one or more physical hypotheses. These natural regularities are predictable. They are also the physical reality that makes up La Nina. Once the system or regularities is well understood then La Nina will be well understood. Then we can decide whether to call it weather or climate, but I think that question will have become irrelevant.
Here’s some more good reading on quantum determinism. It was a scholarly war between arguably the two greatest living theoretical physicists: Leonard Susskind and Stephen Hawking.
http://en.wikipedia.org/wiki/Susskind-Hawking_battle
In a nutshell Hawing argued that information could be destroyed, or at least permanently removed from the observable universe, when it fell through the event horizon of a black hole. This situation violates quantum determinism and Susskind objected saying that outcome violates a most deeply held tenet of physics – determinism.
http://en.wikipedia.org/wiki/Susskind-Hawking_battle
It took Susskind 28 years to prove it to Hawking who famously conceded to their bet and Hawking paid off giving Susskind an encyclopedia of Baseball. I followed the debate on and off all those years.
My emphasis:
Information appears to follow one of the basic laws of physics most of us will recoginize:
Conservation of Energy – energy may not be created nor destroyed, it can only change form.
This implies determinism and determinism implies that chaos is no more than an illusion created by insufficient information.
Thus chaotic weather and climate are manifestations of human ignorance rather than a consequence of the laws of nature.
“This common misconception that the universe is chaotic by nature”
The three body problem shows that the universe is chaotic at a fundamental level. A deterministic universe implies that the universe is finite. That at some level of scale we will find the end of the inverse. This would then allow us to predict everything. An infinite universe implies that there is no level of scale that is sufficient to make the universe deterministic. Like a fractal, no matter how big or how small our ruler, the universe extends further, leading to a fundamentally chaotic nature.
Smokey,
So, I followed yout first link, to a photo of trees growing better under increased levels of CO2. I then googled “more co2 is good”, the 4th result was to to this page:
http://mind.ofdan.ca/?p=2374
It’s contains a youtube video, which goes into some detail about why increased CO2 is not necessarily better for plants, and also describes some harm being done, and expected to be done, in the near future as a result of increased CO2. Please, watch the whole thing. (BTW, I don’t know anything about “Dan”, but the video is by “Peter Sinclair”, whom I suspect you may have heard of.
Conclusive? No, of course not. But it as least as good as your photo. Better, because he cites evidence and doesn’t just appeal to a superficial reaction to a single photograph of a tree grown in unrealistic conditions.
Really, if a grade schooler supported an essay with evidence like your photo, what sort of marks do you think they would get? I suppose it would depend on whether their teacher was a “skeptic”.
How about somoeone else addresses one of Smokey’s other pieces of “QED” evidence?
Reposted from another discussion on this topic
The difference between a chaotic initial value system (weather) and a boundary limited system (climate) is the difference between trajectory details and trajectory averages.
Weather is highly susceptible to initial conditions, and predicting weather and it’s details (rain or not, where will the pressure systems go?) requires detailed information and a lot of computing power to predict even a few days out. This is a very hard problem, as even a small error or approximation of initial conditions will inevitably cause the prediction to deviate from reality a few days out.
Climate, however, is a boundary condition system. We don’t know what days in March 2012 it will rain, but we can predict even this far out what the average temperature is likely to be with high certainty. When a particular bit of weather departs from the averages, it will (statistically) return to the average, and spend some time on the other side as well.
So why is climate a boundary limited system? It depends on total energies. If energy leaving the climate exceeds energy coming in, we’ll get colder, and less heat will leave – back to the average as determined by the insolation and thermal radiation. If we have a hot season, the climate will radiate above the average, and we’ll cool down. The weather will vary around those averages in a difficult to predict way, but it will vary around the averages determined by energy conservation! And those averages are what climate predictions are about.
Boundary conditions drive any deviations back to the averages for that system. So while we cannot state whether it will be sunny on your birthday – we can still note that winters will be colder than summers, and that reducing the amount of energy leaving the climate at any temperature (with GHG’s) will make the average temperatures higher.
Sorry, left out the link to the related discussion on weather, climate, and chaos
http://www.skepticalscience.com/chaos-theory-global-warming-can-climate-be-predicted-intermediate.htm
Chaotic does not imply uncontrollable.
As an example consider the neutron flux at the core of a nuclear reactor. Fission is occurring randomly throughout the core. We cannot say with certainty how many neutrons will be emitted from each fissioning atom, but we can say, on average 2.5 neutrons will emit due to fission. We can now control the flux by adjusting neutron leakage and absorption around a flux setpoint. We can also control the flux shape via neutron suppression in some areas while unsuppressing it in another area (flux tilting). So in this specific case, we can model chaotic and complex systems. GK
so in practice, with finite resources, prediction accuracy will drop off rapidly the further you try to predict into the future
Isn’t this equally true of a false model? How then could one ever prove a given chaotic model fits reality?
Good article, but you should correct some misinformation… Chaos is much older than Lorenz… Bernoulli found it in his work… http://sgtnd.narod.ru/science/hyper/SAW/eng/saw.htm
And… Chaos is currently the topic of research for new areas of communication systems…
Lastly… Chaos is deterministic. Given a particular identical set of initial conditions, the same result will occur. However, if you don’t know the entire set of initial conditions, a chaotic system remains non predicative — not non-deterministic…
BTW there’s a new book coming out on chaotic communication system design…
Synchronization Techniques for Chaotic Communication Systems
ISBN: 3642218482
Sorry for the formatting, I’m very tired today…
A 1960s geography text is a pretty good predictor of today’s climate, and probably won’t be that far off in the year 2100 barring a climate tipping point being reached such as a plunge to a new ice age. That said, climate is a nonlinear dynamic system, but the models don’t even meet basic requirements for linear systems. They have documented errors larger than the phenomenon of interest, namely an energy imbalance of under 1 W/m^2. Beyond that, even when combined into ensembles they have documented correlated biases on the same scale as the change in CO2 forcing. In linear systems the correlated biases would not cancel out like it is hoped that uncorrelated errors would. In a nonlinear system, such cancellation would be a surprising and unlikely coincidence.
Theo Goodwin says:
June 13, 2011 at 11:56 am
One mistake that seems almost universal in this forum is that we talk about climate and weather as if they have some inherent meaning that we all understand. I don’t think so. We should focus on some reasonably well-known natural phenomenon, such as La Nina, and create a description of it which embodies descriptions of the several natural regularities that make it up. Each description of a natural regularity is one or more physical hypotheses. These natural regularities are predictable. They are also the physical reality that makes up La Nina. Once the system or regularities is well understood then La Nina will be well understood. Then we can decide whether to call it weather or climate, but I think that question will have become irrelevant.
We’re taking another look from a few new angles on El Nino at the moment. SOme insightful comment is coming forward. http://tallbloke.wordpress.com/2011/06/12/the-timing-of-el-nino-in-relation-to-the-solar-cycle/
I appreciate this post on chaos theory, and believe there are chaotic elements to the climate system. However, there is a constant danger that it get’s used as a lazy way out of working out what the relationships are, and how they work.
Dave Springer says:
June 13, 2011 at 12:06 pm
“This implies determinism and determinism implies that chaos is no more than an illusion created by insufficient information.
Thus chaotic weather and climate are manifestations of human ignorance rather than a consequence of the laws of nature.”
There are many deterministic yet chaotic systems, like coupled penduluums. Determinism and chaos are no opposites, just like “alkoholic” and “cold” are no opposites.
The unique quality of a chaotic system is that you can determine its future state only by completely simulating it through every timestep without taking any shortcut (which in practice gets impractical very fast). You cannot approximate the future state via a shortcut – you can be arbitrarily wide off the mark when it’s a chaotic system.
Chaos is not an illusion but a property of certain dynamic systems. Whether such a system is deterministic is a different matter. (Indeterminism usually makes it even harder to predict, but indeterminism and a chaotic nature are not the same thing)
Shouldn’t some proof of this be required first…………..
“Our assessment affirms the conclusion that late 20th century warmth is unprecedented at hemispheric and, likely, global”
I mean, that is an assumption and everything after it is an assumption…………….
“There are many deterministic yet chaotic systems”
Good observation. From wikipedia:
Define the error as the difference between the time evolution of the ‘test’ state and the time evolution of the nearby state. A deterministic system will have an error that either remains small (stable, regular solution) or increases exponentially with time (chaos). A stochastic system will have a randomly distributed error.[63]
http://en.wikipedia.org/wiki/Chaos_theory
So, even is climate is completely deterministic, if it is chaotic then the size of the error between the real climate and and anything less than a “perfect” model grows exponentially with time. For all intents and purposes impossible, very quickly the prediction of a climate model will be overwhelmed by the size of the error bars. We predict the temperature will increase over 100 years by 3 C, plus or minus 300 C.
The argument that you can average chaos and arrive a non-chaotic solution implies that if you average exponential error growth over time, it will no longer be exponential. This is not true. The average of an exponential still gives an exponential. Thus it seems unlikely that climate is not chaotic.
Oh my gosh!!!!! Your post was nothing short of eye candy!!!! My brain cells have been delectably fed a gourmet meal.