Guest opinion: Dr. Tim Ball
In the 1990s a clear divide existed between the east (the Soviet Union and China) who said climate change is cyclical and the west (the US and Europe) who believed it was chaotic. The former argued that all we need to do is determine the major cycles and how they interact to start understanding and to predict. The latter that climate was chaotic as expressed in the Intergovernmental Panel on Climate Change (IPCC) Third Assessment Report and predictions were not possible.
In climate research and modeling, we should recognize that we are dealing with a coupled non-linear chaotic system, and therefore that the long-term prediction of future climate states is not possible.
Chaos theory was the source of the Lorenz based story prevalent at the time that if a butterfly flaps its wings in Japan it arrives as a storm in California many days later.
The media reported the divide as a political difference, a product of the Cold war. In fact, the divide continues with Russia and China consistently offering different views and challenging more extreme claims in the Intergovernmental Panel on Climate Change (IPCC) Reports. Of course, as long as they are listed as “developing nations,” they always vote for a transfer of wealth as set out in the Kyoto Protocol and its replacement, the Green Climate Fund.
My views on the dichotomy began to formulate earlier from empirical evidence. Research and analysis of data quantified from the Hudson’s Bay Company weather diaries and instrumental records detected a very strong 22-year drought cycle in the middle latitude record for York Factory on Hudson Bay. I included the results in my doctoral thesis (1982) against the advice of my supervisor. He did not disagree with my work; he just thought it was too controversial for my committee to accept. I left it in, and it triggered an interesting experience. The chairman of the committee, Professor C. G. Smith[1], who studied historical precipitation records, especially those of the Radcliffe Observatory, did something unusual. After all the committee members asked their questions, he asked them to agree to tell me I had passed so we could then partake in an unfettered discussion about the issue of cycles.
Part of the discussion included the early work on tree rings in North America, particularly the work of A.E. Douglass, founder of the Laboratory of Tree-Ring Research at the University of Arizona in 1937. As that biography notes,
“He discovered a correlation between tree rings and the sunspot cycle.”
His work became the basis of dendrochronology, which triggered work in tree ring sequences as a proxy indicator for a wide range of correlations. Of course, correlation does not mean cause and effect, but it does trigger searches for potential mechanisms.
One graph (Figure 1) illustrates the type of work produced and shows the correlation between the 22-year sunspot cycle and drought periods across the Great Plains as deduced from tree rings.
Figure 1
It is interesting because when I used the graph in presentations to western North American farmers I did not add to it but simply noted that the sequence anticipated a drought in the late 1980s and that is precisely what occurred. Also notice the decline in sunspot numbers associated with the Dalton Minimum from 1790 to 1830. It is tempting to assume the different durations of droughts, one longer from circa 1820 and the other shorter from approximately 1840 was a result of the reduction in sunspot numbers.
Before we organized the conference on the impact of the 1815 volcanic eruption of Tambora, it was assumed the eruption caused the decline in global temperature of the period. While preparing for the conference, it became apparent to myself and fellow organizers, Cynthia Wilson and Richard Harington, that global temperatures were already in decline and a likely explanation was the decline in sunspot numbers. Remember, this was pre-Svensmark’s cosmic theory. Indeed, the idea of even a correlation between sunspots and temperature was just gaining wider legitimacy from the work of John Eddy. As a result, we invited him to be the keynote speaker at the conference. The question that emerged during the conference was how would the impact of Tambora change if global temperatures were rising at the time. The same questions were asked the impact on precipitation patterns, especially droughts. One of my contributions to the symposium was to detail the severe drought in Central Canada from approximately 1816 to 1819. I will return to the significance of these observations later.
Two other experiences reinforced my views on the cyclical versus the chaos controversy. The first occurred when I was invited by the editors to submit a chapter to the book Climate Since A.D. 1500. The editors had each chapter author review another author’s chapter. I worked with Ye. P. Borisenkov, the Soviet historical climatologist, whose chapter “Documentary Evidence from the U.S.S.R” used the Russian Chronicles among other sources. Borisenkov’s work was recognized as a major contribution to the current claims of a cooling over the next few decades by Dr. Abdussamatov.
The second event occurred when I gave a paper at the 1988 Annual Geophysical Society General Assembly in Bologna, Italy that focused on evidence for climate change from historical records. This was among the earliest public presentations of climate research from the vast potential of the Vatican archives. It was also an early public presentation of the remarkable resources from China. In both the Russian and Chinese connections I learned that the leaders, Russian Czars, and Chinese Emperors, kept weather and crop journals for a very practical reason. They needed to prepare for the social unrest that inevitably followed crop failures.

Through the work with Borisenkov, I became aware of Nikolai Kondratieff (variously Kondratiev) and his theory of climate and economic cycles. It was this focus on food production, especially subsistence crops like cereal grains, which led to the first practical application of the cyclical approach in Russia. Between 1919 and 1921 Kondratieff plotted the relationship between grain production and drought and produced the K-Cycle. It was a predictive tool based on the idea that all economies and civilizations exist based on their ability to feed themselves. An important idea that led to my dictum that, there are no farms in the cities, but there are no cities without farms. In the west, the most common application of Kondratieff and other climate cycles are in the financial markets. It is summarized in books such as “Climate: The Key to Understanding Business Cycles.” I also learned that other Russian climatologists were doing much better, more open, and innovative work, such as the work on energy balance of Mikhail Budyko.
I later learned more about Chinese climatology when working with Chinese climatologists. The Chinese realized that to improve their economy and achieve greater control required increased food production. They realized, to maintain large work forces in urban areas you required vastly improved food production. I learned very early in studying history that an Agricultural Revolution preceded the Industrial Revolution. The Chinese were already triple–cropping in many parts of southern China but there was vast potential in the north-eastern region. They were charged with working with Canadian climatologists and agronomists to study how and why Canadian farmers were so successful in crop production in cold climates.
Parallel to these different studies and analyses of climate, the philosophical views of the pattern of evolution were changing. In the west the biblical view of Neptunism, the pre-and post-flood worlds was replaced by Uniformitarianism. This was generally adapted and adopted as the notion that change is very gradual over long periods of time. I believe it is a major reason why the unchanging nature of the Sun/Earth relationship remained the view. This persisted, even though Croll and others culminating in the work of Milankovitch, showed it was constantly changing.
The two notions crossed paths in 1960 when MIT meteorologist and computer modeler, Edward Lorenz, introduced the aforementioned butterfly, with its wider application as the Chaos Theory. This view seemed to resurrect and confirm the 19th century claims of Cuvier that changes occurred triggered by extreme events or catastrophes. In the 20th century, Stephen Jay Gould combined the two views with what he called punctuated-equilibrium. This proposed that gradual change was periodically interrupted by catastrophic events. It certainly seems to fit events like the eruption of Tambora, but also applies to events like the asteroid that wiped out the dinosaurs.
These discussions raised important questions about the difference between equilibrium and steady–state. This included the apparent resilience of the atmosphere to catastrophic events and the inevitable role of feedbacks, questions, and challenges still central to climate research and pushed aside by the singular focus of the Intergovernmental Panel on Climate Change (IPCC).
Right now, the easterners, particularly people like Abdussamatov and Usoskin, are making better predictions about the coming cooling trend as they follow the solar cycles than the IPCC, now represented by the IPCC. Of course, there are some of us in the west who believe the Russians are closer to reality. Consider the comments by Joe Bastardi on the trend in this video. But why listen to him? He is one of those deniers. Joe can use my argument that those who call us deniers and are mostly the chaos believers need to be right to explain why their forecasts, both weather, and climate, are so wrong. Is it possible that Joe and all us deniers will become part of the Russian collusion investigation?
[1] Craddock, J. M., and C. G. Smith (1978), An investigation into rainfall recording at Oxford, Meteorol. Mag., 107, 257–271.
Is it possible that Joe and all us deniers will become part of the Russian collusion investigation?
No, probably not. The real issue of collusion in all this is the lack of scepticism from our free press in the west. How many major broadcasters or newspapers produce anything of a sceptical nature on climate change? How many produce what could be considered little more than CAGW propaganda? How many query the delusion that our world and its growing energy needs can be powered by windmills and solar panels?
Climate clearly cyclical. Abdussamatov clearly wrong.
The 1000-year Eddy solar and climatic cycle indicates the present Modern Global Warming should last as a warm period for at least a couple of centuries more.

The climate system is cyclic but non periodic (the length of the cycles changesfrom cycle to cycle, as can be seen from a Power Spectrum analysis of the time series: the Spectrum does not consist of spikes but more or less spreaded peaks). This is the signature of a complex system at the edge of chaos. .There are specific Tools for the non linear analysis of dynamical (chaotic) systems. One of them is the Phase Plan (and it can be linked to time series by using the Takens theorem). Applying this technique to the Vostok data for example, shows clearly the existence of two strange attractors; a tempered one and a colder one ( see: https://www.dropbox.com/s/ouycaeeip4a6aq6/Phase%20plan%20analysis%20of%20Vostok%20data.pptx?dl=0). All the rest are only trajectories around those two attractors. Also, it is useful to hold in mind that a chaotic system is highly unpredictable due to its extreme sensistivity to initial conditions (and thus experimental errors linked to data acquisition) and to the value of the parameters.
Thanks for that personal history lesson, Dr. Ball. Very interesting.
“Is Climate Chaotic or Cyclical?”
It’s both.
“Of course, correlation does not mean cause and effect”
Especially when there is no correlation, like in this case.
Niles Eldridge and Steven Jay Gould’s model of punctuated equilibrium does not describe alternations between uniformitarianism and catastrophism, which are models of geological evolution. Punctuated equilibrium is an evolutionary biology model proposing that speciation tends to follow long periods of evolutionary stasis interrupted by sudden rapid sequences of speciation in response of a number of environmental, biological, dispersal, climatological, and/or geological events. Punctuated equilibrium was contrasted with Darwin’s notion of phyletic gradualism, in which species evolve very slowly over long periods of geological time. It grew out of Ernst Mayr’s ideas of allopatric (major dispersal events) and peripatric speciation occurring in isolated peripheral populations associated with genetic drift. Otherwise a very interesting and enlightening article. Thanks, Dr. Ball.
Climate is cyclic and chaotic, like a tire on your car. Depending how the motion is graphed, and the placement of the base point, it is cyclic or it appears linear and chaotic.
Climate is daily, yearly, monthly sun spotly and other cyclical. Plotted over time you also get the chaotic bumps in the road.
Whether climate is chaotic or cyclical is theoretically easy to prove. If cyclical, a perfect global temperature data-set over a time period long enough to include the lowest frequency signal could be described by a Fourier series of infinite length in time, the null hypothesis. If the temperature data-set includes chaotic signals,existing GCMs cannot predict future global temperatures, and the trillions of dollars allocated for climate research should be redirected to research with a positive cost-benefit.
Is this a Sunday morning epiphany or a delusion.
Whether climate is chaotic or cyclical is theoretically easy to prove. If cyclical, a perfect global temperature data-set over a time period long enough to include the lowest frequency signal could be described by a Fourier series of infinite length in time, the null hypothesis. If the temperature data-set includes chaotic signals,existing GCMs cannot predict global temperatures, and the trillions of dollars allocated for climate research should be redirected to research with a positive cost-benefit.
Is this a Sunday morning epiphany or a delusion.
Essentially alarmists are claiming that climate is neither cyclic or chaotic. Regardless of what they say, boiled down to the basics, they are claiming that climate is more or less stable-at least until man messes up the “delicate balances.” Absurd of course.
KT66 wrote: they are claiming that climate is more or less stable-at least until man messes up the “delicate balances.”
_Exactly, they are, ironically, climate change deniers, who say that climate does not change unless man changes it, and therefore all climate change is evidence that human activities are changing the climate._
I noted that many years ago on one of Willis’ articles dealing with volcanoes. The same is so with Krakatoa. The temperature data sets (which of course are not reliable) were showing temperatures falling prior to that eruption. Would they have continued to fall, who knows. Was the drop in temperature trend greater and ran for a longer period because of Krakatoa, again, who knows.
I suspect that we do not fully understand the impact of volcanoes. Another natural phenomenon on which we have yet to get on top of because we do not study natural cause and natural variation no doubt because of the funding going toward looking at manmade climate change.
On many occasions I stated that the tectonics is a neglected factor. For few years before eruptions of many of the islands’ volcanic eruptions happen the nearby sea floor tectonic vibrations may have critical effect in disrupting stratified layers of the ocean currents, taking huge amounts of cold waters to the surface, reducing evaporation followed by fall in the water vapour’s gh effect, hence an ‘a priori’ volcanic cooling.
Richard V wrote:
“I suspect that we do not fully understand the impact of volcanoes.”
https://wattsupwiththat.com/2017/09/20/from-the-the-stupid-it-burns-department-science-denial-not-limited-to-political-right/comment-page-1/#comment-2616345
NOT A WHOLE LOTTA GLOBAL WARMING GOIN’ ON!
Unlike the deeply flawed computer climate models cited by the IPCC, Bill Illis has created a temperature model that actually works in the short-term (multi-decades). It shows global temperatures correlate primarily with NIno3.4 area temperatures – an area of the Pacific Ocean that is about 1% of global surface area. There are only four input parameters, with Nino3.4 being the most influential. CO2 has almost no influence. So what drives the Nino3.4 temperatures? Short term, the ENSO. Longer term, probably the integral of solar activity – see Dan Pangburn’s work.
Bill’s post is here.
https://wattsupwiththat.com/2016/09/23/lewandowsky-and-cook-deniers-cannot-provide-a-coherent-alternate-worldview/comment-page-1/#comment-2306066
Bill’s equation is:
Tropics Troposphere Temp = 0.288 * Nino 3.4 Index (of 3 months previous) + 0.499 * AMO Index + -3.22 * Aerosol Optical Depth volcano Index + 0.07 Constant + 0.4395*Ln(CO2) – 2.59 CO2 constant
Bill’s graph is here – since 1958, not a whole lotta global warming goin’ on!
My simpler equation using only the Nino3.4 Index Anomaly is:
UAHLTcalc Global (Anom. in degC, ~four months later) = 0.20*Nino3.4IndexAnom + 0.15
Data: Nino3.4IndexAnom is at: http://www.cpc.ncep.noaa.gov/data/indices/sstoi.indices
It shows that much or all of the apparent warming since ~1982 is a natural recovery from the cooling impact of two major volcanoes – El Chichon and Pinatubo.
Here is the plot of my equation:
https://www.facebook.com/photo.php?fbid=1106756229401938&set=a.1012901982120697.1073741826.100002027142240&type=3&theater
I added the Sato Global Mean Optical Depth Index (h/t Bill Illis) to compensate for the cooling impact of major volcanoes, so the equation changes to:
UAHLTcalc Global (Anom. in degC) = 0.20*Nino3.4IndexAnom (four months earlier) + 0.15 – 8*SatoGlobalMeanOpticalDepthIndex
The “Sato Index” is factored by about -8 and here is the result – the Orange calculated global temperature line follows the Red actual UAH global LT temperature line reasonably well, with one brief deviation at the time of the Pinatubo eruption.
Here is the plot of my new equation, with the “Sato” index:
https://www.facebook.com/photo.php?fbid=1443923555685202&set=a.1012901982120697.1073741826.100002027142240&type=3&theater
I agree with Bill’s conclusion that
THE IMPACT OF INCREASING ATMOSPHERIC CO2 ON GLOBAL TEMPERATURE IS SO CLOSE TO ZERO AS TO BE MATERIALLY INSIGNIFICANT.
Regards, Allan
https://wattsupwiththat.com/2017/10/04/cooler-global-temperatures-ahead-indications-are-that-la-nina-is-returning/comment-page-1/#comment-2627440
[excerpt]
Tropical Pacific Ocean temperature (e.g. Nino3.4 area) increases tropical humidity and temperature ~3 months later, and global humidity and temperature ~4 months later.
Not all that complicated, is it, for a “non-linear, chaotic, blah blah blah” climate system?
https://www.facebook.com/photo.php?fbid=1443923555685202&set=a.1012901982120697.1073741826.100002027142240&type=3&theater
References – Allan MacRae and Bill Illis:
https://wattsupwiththat.com/2017/09/15/report-ocean-cycles-not-humans-may-be-behind-most-observed-climate-change/comment-page-1/#comment-2613373
https://wattsupwiththat.com/2017/09/20/from-the-the-stupid-it-burns-department-science-denial-not-limited-to-political-right/comment-page-1/#comment-2616345
We know to a reasonable degree of confidence what drives global temperature and it is almost entirely natural and has an INSIGNIFICANT causative relationship from increasing atm. CO2:
– in sub-decadal to decadal time frames, the primary driver of global temperature is Pacific Ocean natural cycles, moderated by occasional cooling from major (century-scale) volcanoes;
– in multi-decadal to multi-century time frames, the primary cause is solar activity;
– in the very long term, the primary cause is planetary cycles.
Dr. Tim Ball says:
“Research and analysis of data quantified from the Hudson’s Bay Company weather diaries and instrumental records detected a very strong 22-year drought cycle in the middle latitude record for York Factory on Hudson Bay.”
Three or four years ago I looked into the changes in the magnetic field of NE Canada, since until 1995 the area in the vicinity of the Hudson Bay had strongest geomagnetic field in the N. Hemisphere, until it was overtaken by the central Siberia.
The area is also subject to the large postglacial uplift; it is assumed that about 30% of the longer term changes in the magnetic field is due to the variability in the uplift, while on the decadal scale that may be more than 30%.
Spectral composition of the NE Canada’s postglacial uplift variability as implied by the changes in its magnetic field is shown here
http://www.vukcevic.talktalk.net/NECIUS.gif
Not only there is a clear presence of the 22 year solar magnetic cycle component but also well known and widely accepted 60+ years global temperature’s component.
Question is how the solar magnetic cycles could affect the postglacial uplift.
Indirectly: solar cycles ‘have been linked’ to the Arctic polar vortex circulation, which in turn causes changes in the meridional excursions of the polar jet stream and the wider atmospheric circulation that is cause of the 22 periodical disturbances in the earth’s rate of rotation and consequently the 22 years judders in the PG uplift followed by changes in the magnetic field of the area.
http://www.vukcevic.talktalk.net/LODvsHALE.gif
Therefore, clearly Dr. Bell was correct in his claim.
I guess bau is the go then.
As I said in the Abstract above 11/25/7:28 pm
“Earth’s climate is the result of resonances and beats between various quasi-cyclic processes of varying wavelengths. It is not possible to forecast the future unless we have a good understanding of where the earth is in time in relation to the current phases of those different interacting natural quasi periodicities. Evidence is presented specifying the timing and amplitude of the natural 60+/- year and, more importantly, 1,000 year periodicities (observed emergent behaviors) that are so obvious in the temperature record. Data related to the solar climate driver is discussed and the solar cycle 22 low in the neutron count (high solar activity) in 1991 is identified as a solar activity millennial peak and correlated with the millennial peak -inversion point – in the UAH6 temperature trend in about 2003.”
Circulation Models (GCMs) attempt to describe the climate dynamics using sets of differential equations. This modelling approach is of no value for predicting future temperature with any calculable certainty because of the difficulty of sampling or specifying the initial conditions of a sufficiently fine grained spatio-temporal grid of a large number of variables with sufficient precision. In addition, Essex 2013 (1) proved that models with the number of variables in the GCMs are simply incomputable. This does not mean that the data or climate is chaotic – just that it cant be computed from the bottom up.
No cycle ever repeats exactly in timing or amplitude- eg the effect of the 60 year cycle on temperatures (the emergent property) will differ depending its phase relative to the millennial cycle .It will also change because of its relationship to other quasi-cyclic decadal and centennial periodicities in the data . It is very obvious by simple inspection of Figs 2,3,4,7,8 10, and 12 that, at this time, most of the temperature variability can be captured and the future projected with useful probability of success by convolving the millennial and 60 year cycles.
See https://climatesense-norpag.blogspot.com/2017/02/the-coming-cooling-usefully-accurate_17.html
No useful forecast can be made if the early 21st century peak and inflection point in the temperature data is ignored.
Dr Norman Page
“that are so obvious in the temperature record”
You keep using these words, but that is simply not a statement of fact but an opinion. In my opinion you are incorrect, i.e. there ‘may’ be something there but it is a long, long way from being “obvious” – as in: clear, self-evident, or apparent.
Tony. Take the time to read Section 2 of the paper. What specific Figs ,Data or text do you disagree with. It all seems fairly obvious to me.
http://climatesense-norpag.blogspot.com.au/2017/02/the-coming-cooling-usefully-accurate_17.html
Evidence is presented specifying the timing and amplitude of the natural 60+/- year and, more importantly, 1,000 year periodicities (observed emergent behaviors) that are so obvious in the temperature record.
Fig. 2 Greenland Ice core derived temperatures and CO2 from Humlum 2016 (8)
The millennial cycle peaks are obvious at about 10,000, 9,000, 8,000, 7,000, 2,000, and 1,000 years before now as seen in Fig. 2 (8) and at about 990 AD in Fig. 3 (9).
Calling it obvious is a value judement and in my opinion is incorrect. Yes, you can see a few spikes and yes some of them are sort of spaced at 1000 year increments, but eyeballing it I would say that could just as easily be random fluctuations.
Look you may be right in your conjecture. But calling it “obvious” is a gross overstatement.
Btw Norman.
For a laugh, go back up to your post at: Dr Norman Page November 25, 2017 at 7:28 pm.
My response to your contribution was:
“that are so obvious in the temperature record”
You are placing quite a bit of weight on this single piece of evidence.
That seems rather tame to me but just have a little browse through the rubbish that erupts. Smh.
OT…but Mt Agung erupted had a strong eruption today. All flights in the area have been canceled due to the height of the eruption. …https://www.youtube.com/watch?v=Kds2IamqvoM
Could this lead us into a noticeable cooling trend for the next several years?
Mt. Agung is not yet a big eruption – as reported here 27 Nov.
http://www.bbc.com/news/av/world-asia-42133563/mt-agung-is-large-bali-volcano-eruption-inevitable
The 1963–64 eruption of Mt. Agung was VEI5.
The 1982 eruption of El Chichon was VEI5.
The 1991 eruption of Mt Pinatubo was VEI6, roughly an order of magnitude higher.
I suggest that the eruptions of both El Chichon and Pinatubo had significant temporary global cooling effects – I have less data for Agung 1963, but it is probable that some global cooling was also caused then.
I think that cooling is what lies ahead regardless of a volcanic eruption. I also have noted that large eruptions may be more likely to occur during strong solar cooling periods, which is what I see as the most probable scenario for the next 15+ years. A large eruption would then enhance and deepen the cyclical cooing trend.
I agree goldminor
I wrote in 2002 in a newspaper article that natural global cooling would commence by 2020-2030.
I am now leaning towards circa 2020 or even earlier.
Last paragraph, rephrase:”than the IPCC, now represented by the IPCC”.
I’m glad to hear talk about how climate models all have a sensitive dependence on initial conditions – possibly even chaotic, with fractal attractors – making accurate predictions impossible. I did my masters thesis in computer science in ’92 on a simple question related to chaos and computing. My background reading from that time – e.g. Lorenz, Mandelbrot, Poincare, Feigenbaum – was fun and enriching though I never applied it to my subsequent career in software. I think it was because of that background I always thought it folly to expect long-term predictions coming out of climate models to have any accuracy. Enjoyed the article – thanks.
Instead of chaotic, or cyclical, how about periodic?
An irregular, unpredictable, alternating mild warming periods and mild cooling periods
that don’t matter (harmless) unless you are a hysterical leftist,
between huge glaciations that do matter
(harmful, unless you can ice skate)
I forgot to mention the huge glaciations might be cyclical,
rather than periodic.
The smart money is on “all of the above”.
Only those with only a casual, sophomoric view of Chaos object to its application to climate studies. The earth climate system is composed of two interacting dynamically chaotic (remember, this word “chaotic” is used in the special sense of Chaos Theory) physical systems — the Atmosphere and the Oceans — and these two systems are linked and both act as cause and effect on the other.
Chaotic systems have many characteristics that aren’t normally thought of when the word chaotic is applied — among these are 1) a stubborn stability, 2) cyclical repeating patterns and 3) inescapable patterns called “attractors”, which themselves often appear cyclical.
The bottom line is: We simply don’t have enough data to to arrive at a deep understanding of the climate system.
Re Kip Hansen, 11/28/17 @ur momisugly 3:50 pm:
Stove called the founder of the Post Modern Science, the species of science practiced almost exclusively and exhaustively in academia, the man, generally regarded as one of the 20th century’s greatest philosophers of science (Wikipedia>Karl Popper), irrational. That’s Karl [I am not a scientist] Popper, the butterfly who created another kind of chaos in academia, who described his model of science with these words:
I have no intention of defining the term ‘observable’ or ‘observable event’, though I am quite ready to elucidate it by means of either psychologistic or mechanistic examples. I think that it should be introduced as an undefined term which becomes sufficiently precise in use: as a primitive concept whose use the epistemologist has to learn, much as he has to learn the use of the term ‘symbol’, or as the physicist has to learn the use of the term ‘mass-point’. Popper LogSciDisc (1934/1959) p. 85.
Stove missed that simple admission to rely on undefined terms, that confession to be irrational, a confession applicable to any dialog in any field. Wolfram MathWorld says, It turns out that even textbooks devoted to chaos do not really define the term. That’s academic (Post Modern) science – that’s Popper – that’s irrational.
Kip Hansen puts a new twist on irrationality. He claims the observation that the definition of chaos doesn’t fit the Real World is sophomoric, adding a totally vague reference to some special use of the term. Of course, anyone is free to define chaos any way he wishes, but define it he must, one way or another, for the purposes of science. An unsupported claim of existence is not science, much less honest. Since Lorenz first defined the term for technical use (cited above), it has applied only to equations with initial conditions, or, equivalently, to systems controlled by such equations. These have the name dynamical systems. References available.
No equations of any type exist in the natural world. All equations are manmade. Man’s equations do not control the natural world. The Real World is neither chaotic nor linear nor nonlinear nor in equilibrium.
These observations are supported by Wolfram MathWorld, Wikipedia, Stanford Encyclopedia of Philosophy, and surely more.