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From: bill.sloman on 4 Dec 2008 10:28 On 4 dec, 03:22, Bill Ward <bw...(a)REMOVETHISix.netcom.com> wrote: > On Wed, 03 Dec 2008 16:14:08 -0800, bill.sloman wrote: > > On 3 dec, 19:12, Bill Ward <bw...(a)REMOVETHISix.netcom.com> wrote: > >> On Wed, 03 Dec 2008 03:08:12 -0800, bill.sloman wrote: > >> > On 1 dec, 10:55, Bill Ward <bw...(a)REMOVETHISix.netcom.com> wrote: > >> >> On Mon, 01 Dec 2008 07:43:58 +0000, Don Klipstein wrote: > >> >> > In article <492FF152.3ED3E...(a)hotmail.com>, Eeyore wrote: > > >> >> >>z wrote: > > >> >> >>> bill.slo...(a)ieee.org wrote: > > >> >> >>> > > > > Besides, models only model LINEAR systems ! > > >> >> >>> > > > Oh really? Then the Spice models of transistors (which > >> >> >>> > > > exhibit an expotential - not linear - relationship between > >> >> >>> > > > base voltage and collector current) don't exist. > > >> >> >>> > > That IS a linear system as we describe them now. > > >> >> >>> > This is a minority opinion. Any student sharing it with their > >> >> >>> > examiner would fail that aspect of their exam, but since you > >> >> >>> > clearly exercise your mind by believing six impossible things > >> >> >>> > before breakfast I suppose we can write this off as part of the > >> >> >>> > price you pay to maintain your genius-level IQ. > > >> >> >>> well to be fair, he only said "linear"; could be he didn't mean > >> >> >>> the usual sense of "straight line" > > >> >> >>Quite so. A LINEAR equation can contain power, log, exp terms > >> >> >>etc. > > >> >> >>But it CANNOT model CHAOS. And that's what weather and climate are. > > >> >> > Chaos is in weather, not in climate. > > >> >> Climate is low-passed (averaged) weather. Filters cannot remove > >> >> chaos. Therefore climate is chaotic. Chaos is unpredictable. > > >> >> > And I would call El Ninos, La Ninas, oceanic Rossby waves and the > >> >> > surges and ebbs of the North Atlantic and Arctic "oscillations" to > >> >> > be weather phenomena, even though the longer term ones are oceanic > >> >> > in origin - chaotic deviations from the much nicer longer term > >> >> > trends that are climate. > > >> >> They are still chaotic, no matter how low the filter corner frequency > >> >> is. > > >> > The planetary orbits in the solar system are chaotic, but they look > >> > pretty regular over periods of a few million years, and low-pass > >> > filtering works fine there. The human heart rate is also chaotic, but > >> > - with a healthy heart - it looks pretty regular (at least until you > >> > get into the fine detail and find out that stroboscopic imaging of the > >> > heart doesn't work too well) and low pass fitlering works fine. > > >> > Waving your magic wand and cyring "chaotic"doesn't actually invalidate > >> > modern climatology - though it does tend to invalide any claim you > >> > might kmake to know something about it. > > >> So math is a magic wand to you. I think I see your problem. > > > I've certainly found it useful, not least in catching out frauds like you. > > >> If you really believe what you say, you should make a fortune in the > >> chaotic stock market. Let us know how that goes. > > > Bad call. The stock market isn't chaotic. Too many impulsive speculators > > inject an irreproducible element of genuine randomness. Your magic wand > > has failed you yet again. > > http://www.maths.uq.edu.au/~infinity/Infinity9/lorenz.html > > <begin excerpt> > > Lorenz's discovery shocked the scientific world. Chaotic systems soon > began to be recognised in all branches of science. As mathematicians > started to unravel its mysteries, science reeled before the implications > of an uncertain world intricately bound up with chance. The human > heartbeat is chaotic, the stock market, the solar system and of course the > weather. In fact the more we learn about chaos the more closely it seems > to be bound up with nature. Fractal structures seem to be everywhere we > look: in ferns, cauliflowers, the coral reef, kidneys Rather than turn > its back on chaos, nature appears to use it and science is beginning to do > the same. I think you will find that the stock market isn't chaotic in the narrow mathematical sense. Public relations puffs aren't all that reliable on this kind of point. -- Bill Sloman, Nijmegen
From: bill.sloman on 4 Dec 2008 10:38 On 4 dec, 04:04, Bill Ward <bw...(a)REMOVETHISix.netcom.com> wrote: > On Wed, 03 Dec 2008 16:28:46 -0800, bill.sloman wrote: > > On 3 dec, 21:14, Bill Ward <bw...(a)REMOVETHISix.netcom.com> wrote: > >> On Wed, 03 Dec 2008 11:01:02 -0800, bill.sloman wrote: > >> > On 3 dec, 19:22, Bill Ward <bw...(a)REMOVETHISix.netcom.com> wrote: > >> >> On Wed, 03 Dec 2008 03:25:06 -0800,bill.slomanwrote: > >> >> > On 2 dec, 02:54, Bill Ward <bw...(a)REMOVETHISix.netcom.com> wrote: > >> >> >> On Mon, 01 Dec 2008 17:40:46 -0500, Whata Fool wrote: > >> >> >> > Bill Ward <bw...(a)REMOVETHISix.netcom.com> wrote: > > >> >> >> >>On Mon, 01 Dec 2008 06:31:17 -0500, Whata Fool wrote: > >> >> >> >>> The bottom line is that _IF_ N2 and O2 can't cool > >> >> >> >>> without GreenHouse Gases, then the atmosphere would be warmer > >> >> >> >>> than now, meaning the present GreenHouse Gas theory is faulty, > >> >> >> >>> as the basis was a comparison of Earth and moon temperatures.. > > >> >> >> >>> So when will somebody start thinking, rethink the > >> >> >> >>> basics, and concede that GreenHouse Gases cool the atmosphere? > > >> >> >> >>I think they do, but in the process, they keep the surface from > >> >> >> >>cooling as fast as it would otherwise. > > >> >> >> > Does GISS use surface temperatures for anything? > > >> >> >> > The temperature of the air is the big factor, think of > >> >> >> > your windshield on a summer night and a winter night with the > >> >> >> > same humidity. > > >> >> >> > And it is the N2 and O2 that hold most of the thermal > >> >> >> > energy. > > >> >> >> > While radiation is clearly the mechanism for cooling the > >> >> >> > Earth, the amount of sideways radiation warming/cooling of the > >> >> >> > atmosphere has not been shown to be as active as the vertical > >> >> >> > radiation claimed. > > >> >> >> > With all the resources available, there just hasn't been > >> >> >> > the documentation of things like horizontal radiation. > > >> >> >> > The amount of effort in computer models and averaging > >> >> >> > numbers is lopsided compared to the testing of assumptions. > > >> >> >> That's for sure! > > >> >> >> They went for the details before they really understand the > >> >> >> basics. > > >> >> > This from someone who thinks that a chaotic system always generates > >> >> > 1/ f noise in any frequency band, ignoring the obvious fact that > >> >> > the solar system is chaotic, which doesn't prevent the sun from > >> >> > coming up at a predictable time every day. > > >> >> And obviously Sloman has no idea what a corner frequency is. > > >> >> Maybe this will help: > > >> >>http://en.wikipedia.org/wiki/Cut-off_frequency > > >> > Since it doesn't mention 1/f noise, it represents just one more case > >> > of Bill Ward trying to look clever by citing stuff he doesn't > >> > understand. > > >> The 1/f was yours. I don't remember mentioning it, but it is a good > >> example of the limitations involved in trying to filter noise out of > >> signals: > > >>http://en.wikipedia.org/wiki/Pink_noise > > >> "Interestingly, there is no known lower bound to pink noise in > >> electronics. Measurements made down to 10-6 Hz (taking several weeks) > >> have not shown a ceasing of pink-noise behaviour.[citation needed] > >> Therefore one could state that in electronics, noise can be pink down to > >> 1 = 1/T where T is the time the device is switched on." > > >> In physics, it goes back to the big bang. > > >> And of course, it doesn't change the fact you can't filter out chaos. > >> Try reading the filter link for content, or look deeper into chaos > >> theory. It's quite interesting. > > > Sure it's interesting. It's also totally irrelevant to climate modelling > > over the period in which we (and the IPCC) are interested. > > Chaos theory is relevant in that it proves mathematically that you can't > predict climate with any model, no matter how much history you have. The > prediction will soon rapidly diverge from the signal. > > > You can't see 1/f noise when it is swamped by good old white noise, > > right down to the 1/f noise corner frequency. In the solar system > > everything looks like clockwork for the first few tens of millions of > > years. > > You still can't seem to keep your stories straight. Above you > complained I was "ignoring the obvious fact that the solar system is > chaotic", now you seem to be denying it. It is, has always been, and > always will be, chaotic. So is weather and climate. The time scales are > different, which you don't seem to understand. What you don't seem to understand that is that identifying a system as chaotic doesn't of itself prove that it is unpredictable and not susceptible to computer modelling. The solar system is a particularly obvious counter-example, and the climate - despite your fautous claims - is another. > > The climate records over the last million years also look pretty regular > > - Milankovich cycles don't look like a drunkards walk or 1/f noise - and > > your invocation of chaos still looks exactly like a loser retreating in > > a cloud of obfustication. > > The Milankovich cycles are part of the solar system, chaotic on very > long time scales. Weather is chaotic, with a much shorter time scale. > The M cycles modulate the weather, and the result can be lowpassed down to > "climate" to ignore the short time fluctuations, but it's still chaotic > and can't be predicted. This may be true over a sufficiently long time scale, but is utterly false for the time periods we happen to be interested in, as you should have the wit to realise. > Trends mean nothing in chaotic systems. All you can know is that the > signal will change slope, not when or how much. The solar system is chaotic, so we don't know where all the planets are going to be for the next few million years? Do try and engage your brain before you start typing. -- Bill Sloman, Nijmegen
From: Bill Ward on 4 Dec 2008 12:21 On Thu, 04 Dec 2008 07:28:38 -0800, bill.sloman wrote: > On 4 dec, 03:22, Bill Ward <bw...(a)REMOVETHISix.netcom.com> wrote: >> On Wed, 03 Dec 2008 16:14:08 -0800, bill.sloman wrote: >> > On 3 dec, 19:12, Bill Ward <bw...(a)REMOVETHISix.netcom.com> wrote: >> >> On Wed, 03 Dec 2008 03:08:12 -0800, bill.sloman wrote: >> >> > On 1 dec, 10:55, Bill Ward <bw...(a)REMOVETHISix.netcom.com> wrote: >> >> >> On Mon, 01 Dec 2008 07:43:58 +0000, Don Klipstein wrote: >> >> >> > In article <492FF152.3ED3E...(a)hotmail.com>, Eeyore wrote: >> >> >> >> >>z wrote: >> >> >> >> >>> bill.slo...(a)ieee.org wrote: >> >> >> >> >>> > > > > Besides, models only model LINEAR systems ! >> >> >> >> >>> > > > Oh really? Then the Spice models of transistors (which >> >> >> >>> > > > exhibit an expotential - not linear - relationship >> >> >> >>> > > > between base voltage and collector current) don't exist. >> >> >> >> >>> > > That IS a linear system as we describe them now. >> >> >> >> >>> > This is a minority opinion. Any student sharing it with >> >> >> >>> > their examiner would fail that aspect of their exam, but >> >> >> >>> > since you clearly exercise your mind by believing six >> >> >> >>> > impossible things before breakfast I suppose we can write >> >> >> >>> > this off as part of the price you pay to maintain your >> >> >> >>> > genius-level IQ. >> >> >> >> >>> well to be fair, he only said "linear"; could be he didn't >> >> >> >>> mean the usual sense of "straight line" >> >> >> >> >>Quite so. A LINEAR equation can contain power, log, exp terms >> >> >> >>etc. >> >> >> >> >>But it CANNOT model CHAOS. And that's what weather and climate >> >> >> >>are. >> >> >> >> > Chaos is in weather, not in climate. >> >> >> >> Climate is low-passed (averaged) weather. Filters cannot remove >> >> >> chaos. Therefore climate is chaotic. Chaos is unpredictable. >> >> >> >> > And I would call El Ninos, La Ninas, oceanic Rossby waves and >> >> >> > the surges and ebbs of the North Atlantic and Arctic >> >> >> > "oscillations" to be weather phenomena, even though the longer >> >> >> > term ones are oceanic in origin - chaotic deviations from the >> >> >> > much nicer longer term trends that are climate. >> >> >> >> They are still chaotic, no matter how low the filter corner >> >> >> frequency is. >> >> >> > The planetary orbits in the solar system are chaotic, but they look >> >> > pretty regular over periods of a few million years, and low-pass >> >> > filtering works fine there. The human heart rate is also chaotic, >> >> > but - with a healthy heart - it looks pretty regular (at least >> >> > until you get into the fine detail and find out that stroboscopic >> >> > imaging of the heart doesn't work too well) and low pass fitlering >> >> > works fine. >> >> >> > Waving your magic wand and cyring "chaotic"doesn't actually >> >> > invalidate modern climatology - though it does tend to invalide any >> >> > claim you might kmake to know something about it. >> >> >> So math is a magic wand to you. I think I see your problem. >> >> > I've certainly found it useful, not least in catching out frauds like >> > you. >> >> >> If you really believe what you say, you should make a fortune in the >> >> chaotic stock market. Let us know how that goes. >> >> > Bad call. The stock market isn't chaotic. Too many impulsive >> > speculators inject an irreproducible element of genuine randomness. >> > Your magic wand has failed you yet again. >> >> http://www.maths.uq.edu.au/~infinity/Infinity9/lorenz.html >> >> <begin excerpt> >> >> Lorenz's discovery shocked the scientific world. Chaotic systems soon >> began to be recognised in all branches of science. As mathematicians >> started to unravel its mysteries, science reeled before the implications >> of an uncertain world intricately bound up with chance. The human >> heartbeat is chaotic, the stock market, the solar system and of course >> the weather. In fact the more we learn about chaos the more closely it >> seems to be bound up with nature. Fractal structures seem to be >> everywhere we look: in ferns, cauliflowers, the coral reef, kidneys… >> Rather than turn its back on chaos, nature appears to use it and science >> is beginning to do the same. > > I think you will find that the stock market isn't chaotic in the narrow > mathematical sense. Can you post a link that shows why you think that? > Public relations puffs aren't all that reliable on > this kind of point. So show a more authoritative one. You can start here: http://en.wikipedia.org/wiki/Chaos_theory <begin excerpt> An early pioneer of the theory was Edward Lorenz whose interest in chaos came about accidentally through his work on weather prediction in 1961.[14] Lorenz was using a simple digital computer, a Royal McBee LGP-30, to run his weather simulation. He wanted to see a sequence of data again and to save time he started the simulation in the middle of its course. He was able to do this by entering a printout of the data corresponding to conditions in the middle of his simulation which he had calculated last time. To his surprise the weather that the machine began to predict was completely different from the weather calculated before. Lorenz tracked this down to 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 was printed as 0.506. This difference is tiny and the consensus at the time would have been that it should have had practically no effect. However Lorenz had discovered that small changes in initial conditions produced large changes in the long-term outcome.[15] Lorenz's discovery, which gave its name to Lorenz attractors, proved that meteorology could not reasonably predict weather beyond a weekly period (at most). The year before, Benoît Mandelbrot found recurring patterns at every scale in data on cotton prices. [...] Mandelbrot described both the "Noah effect" (in which sudden discontinuous changes can occur, e.g., in a stock's prices after bad news, thus challenging normal distribution theory in statistics, aka Bell Curve) and the "Joseph effect" (in which persistence of a value can occur for a while, yet suddenly change afterwards). <end excerpt> There are many more references showing markets are chaotic in nature. Have fun.
From: Bill Ward on 4 Dec 2008 12:40 On Thu, 04 Dec 2008 07:38:38 -0800, bill.sloman wrote: > On 4 dec, 04:04, Bill Ward <bw...(a)REMOVETHISix.netcom.com> wrote: >> On Wed, 03 Dec 2008 16:28:46 -0800, bill.sloman wrote: >> > On 3 dec, 21:14, Bill Ward <bw...(a)REMOVETHISix.netcom.com> wrote: >> >> On Wed, 03 Dec 2008 11:01:02 -0800, bill.sloman wrote: >> >> > On 3 dec, 19:22, Bill Ward <bw...(a)REMOVETHISix.netcom.com> wrote: >> >> >> On Wed, 03 Dec 2008 03:25:06 -0800,bill.slomanwrote: >> >> >> > On 2 dec, 02:54, Bill Ward <bw...(a)REMOVETHISix.netcom.com> >> >> >> > wrote: >> >> >> >> On Mon, 01 Dec 2008 17:40:46 -0500, Whata Fool wrote: >> >> >> >> > Bill Ward <bw...(a)REMOVETHISix.netcom.com> wrote: >> >> >> >> >> >>On Mon, 01 Dec 2008 06:31:17 -0500, Whata Fool wrote: >> >> >> >> >>> The bottom line is that _IF_ N2 and O2 can't >> >> >> >> >>> cool without GreenHouse Gases, then the atmosphere would be >> >> >> >> >>> warmer than now, meaning the present GreenHouse Gas theory >> >> >> >> >>> is faulty, as the basis was a comparison of Earth and moon >> >> >> >> >>> temperatures. >> >> >> >> >> >>> So when will somebody start thinking, rethink >> >> >> >> >>> the basics, and concede that GreenHouse Gases cool the >> >> >> >> >>> atmosphere? >> >> >> >> >> >>I think they do, but in the process, they keep the surface >> >> >> >> >>from cooling as fast as it would otherwise. >> >> >> >> >> > Does GISS use surface temperatures for anything? >> >> >> >> >> > The temperature of the air is the big factor, >> >> >> >> > think of your windshield on a summer night and a winter night >> >> >> >> > with the same humidity. >> >> >> >> >> > And it is the N2 and O2 that hold most of the >> >> >> >> > thermal energy. >> >> >> >> >> > While radiation is clearly the mechanism for >> >> >> >> > cooling the Earth, the amount of sideways radiation >> >> >> >> > warming/cooling of the atmosphere has not been shown to be as >> >> >> >> > active as the vertical radiation claimed. >> >> >> >> >> > With all the resources available, there just >> >> >> >> > hasn't been the documentation of things like horizontal >> >> >> >> > radiation. >> >> >> >> >> > The amount of effort in computer models and >> >> >> >> > averaging numbers is lopsided compared to the testing of >> >> >> >> > assumptions. >> >> >> >> >> That's for sure! >> >> >> >> >> They went for the details before they really understand the >> >> >> >> basics. >> >> >> >> > This from someone who thinks that a chaotic system always >> >> >> > generates 1/ f noise in any frequency band, ignoring the obvious >> >> >> > fact that the solar system is chaotic, which doesn't prevent the >> >> >> > sun from coming up at a predictable time every day. >> >> >> >> And obviously Sloman has no idea what a corner frequency is. >> >> >> >> Maybe this will help: >> >> >> >>http://en.wikipedia.org/wiki/Cut-off_frequency >> >> >> > Since it doesn't mention 1/f noise, it represents just one more >> >> > case of Bill Ward trying to look clever by citing stuff he doesn't >> >> > understand. >> >> >> The 1/f was yours. I don't remember mentioning it, but it is a good >> >> example of the limitations involved in trying to filter noise out of >> >> signals: >> >> >>http://en.wikipedia.org/wiki/Pink_noise >> >> >> "Interestingly, there is no known lower bound to pink noise in >> >> electronics. Measurements made down to 10-6 Hz (taking several weeks) >> >> have not shown a ceasing of pink-noise behaviour.[citation needed] >> >> Therefore one could state that in electronics, noise can be pink down >> >> to ƒ1 = 1/T where T is the time the device is switched on." >> >> >> In physics, it goes back to the big bang. >> >> >> And of course, it doesn't change the fact you can't filter out chaos. >> >> Try reading the filter link for content, or look deeper into chaos >> >> theory. It's quite interesting. >> >> > Sure it's interesting. It's also totally irrelevant to climate >> > modelling over the period in which we (and the IPCC) are interested. >> >> Chaos theory is relevant in that it proves mathematically that you can't >> predict climate with any model, no matter how much history you have. >> The prediction will soon rapidly diverge from the signal. >> >> > You can't see 1/f noise when it is swamped by good old white noise, >> > right down to the 1/f noise corner frequency. In the solar system >> > everything looks like clockwork for the first few tens of millions of >> > years. >> >> You still can't seem to keep your stories straight. Above you >> complained I was "ignoring the obvious fact that the solar system is >> chaotic", now you seem to be denying it. It is, has always been, and >> always will be, chaotic. So is weather and climate. The time scales >> are different, which you don't seem to understand. > > What you don't seem to understand that is that identifying a system as > chaotic doesn't of itself prove that it is unpredictable and not > susceptible to computer modelling. Actually, it does. It just depends on the time scale. Weather is short (hrs), climate is long (decades), the solar system really long (Gyr). > > The solar system is a particularly obvious counter-example, and the > climate - despite your fautous claims - is another. > >> > The climate records over the last million years also look pretty >> > regular - Milankovich cycles don't look like a drunkards walk or 1/f >> > noise - and your invocation of chaos still looks exactly like a loser >> > retreating in a cloud of obfustication. >> >> The Milankovich cycles are part of the solar system, chaotic on very >> long time scales. Weather is chaotic, with a much shorter time scale. >> The M cycles modulate the weather, and the result can be lowpassed down >> to "climate" to ignore the short time fluctuations, but it's still >> chaotic and can't be predicted. > > This may be true over a sufficiently long time scale, but is utterly > false for the time periods we happen to be interested in, as you should > have the wit to realise. Weather (climate) was one of the first examples of chaos studied. See Lorenz. >> Trends mean nothing in chaotic systems. All you can know is that the >> signal will change slope, not when or how much. > > The solar system is chaotic, so we don't know where all the planets are > going to be for the next few million years? No, not exactly. The prediction error accumulates. More dramatically so for asteroids and comets, but for planets also. It's the differing time scale that's apparently throwing you off. Chaos is chaos regardless of time scale. > Do try and engage your brain before you start typing. Read some chaos theory.
From: Bill Ward on 4 Dec 2008 13:10
On Thu, 04 Dec 2008 00:51:37 -0800, Martin Brown wrote: > On Dec 4, 3:04 am, Bill Ward <bw...(a)REMOVETHISix.netcom.com> wrote: >> On Wed, 03 Dec 2008 16:28:46 -0800, bill.sloman wrote: > >> > Sure it's interesting. It's also totally irrelevant to climate >> > modelling over the period in which we (and the IPCC) are interested. >> >> Chaos theory is relevant in that it proves mathematically that you can't >> predict climate with any model, no matter how much history you have. >> The prediction will soon rapidly diverge from the signal. > > That isn't what chaos theory says at all. The heart beat and solar system > planetary orbits are both formally chaotic systems but they are also quasi > periodic with a very high degree of long term reproducibility. You are > deliberately confusing "random" with chaotic. > > Typical chaotic systems for modest amounts of non-linear feedback tend to > gryrate around a limit cycle centred on one or more stable attractors with > some kind of roughly periodic behaviour but never returning to exactly the > same state. They only become random and in effect totally unpredictable > for the more extreme cases. Weather is hard to predict but long term > climate can smooth this out well enough to extract any systematic trends. Nope. Read the wiki below. Attractors may be limited to specific regions in phase space, but that doesn't make them predictable. Look closer at the dimensions of phase space. >> > right down to the 1/f noise corner frequency. In the solar system >> > everything looks like clockwork for the first few tens of millions of >> > years. >> >> You still can't seem to keep your stories straight. Above you >> complained I was "ignoring the obvious fact that the solar system is >> chaotic", now you seem to be denying it. It is, has always been, and >> always will be, chaotic. So is weather and climate. The time scales >> are different, which you don't seem to understand. > > Although the solar system is chaotic (and no formal proof of stability is > known - although Ovendens conjecture of minimum interaction is widely > believed to be true and relevant) that does not preclude it having > properties that can be accurately determined and simulated for millions of > years past and future (especially when the integrations are tied in to > known total solar eclipses recorded in the historical record). VSOP87 is > still widely used for predicting planetary positions for epochs +/- 4000 > from present with a high degree of accuracy. > > http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1988A%26A...202..309B&data_type=PDF_HIGH&type=PRINTER&filetype=.pdf > > >> > The climate records over the last million years also look pretty >> > regular - Milankovich cycles don't look like a drunkards walk or 1/f >> > noise - and your invocation of chaos still looks exactly like a loser >> > retreating in a cloud of obfustication. >> >> The Milankovich cycles are part of the solar system, chaotic on very >> long time scales. Weather is chaotic, with a much shorter time scale. >> The M cycles modulate the weather, and the result can be lowpassed down >> to "climate" to ignore the short time fluctuations, but it's still >> chaotic and can't be predicted. > > Chaotic does not mean that it cannot be predicted. You are confusing > random with chaotic. I am inclined to believe that this is deliberate > misdirection on your part. Nope. Chaotic means prediction errors accumulate exponentially. Try this: <http://en.wikipedia.org/wiki/Chaos_theory> <begin excerpt> Distinguishing random from chaotic data It can be difficult to tell from data whether a physical or other observed process is random or chaotic, because in practice no time series consists of pure 'signal.' There will always be some form of corrupting noise, even if it is present as round-off or truncation error. Thus any real time series, even if mostly deterministic, will contain some randomness.[31] All methods for distinguishing deterministic and stochastic processes rely on the fact that a deterministic system always evolves in the same way from a given starting point.[32][31] Thus, given a time series to test for determinism, one can: 1. pick a test state; 2. search the time series for a similar or 'nearby' state; and 3. compare their respective time evolutions. 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.[33] Essentially all measures of determinism taken from time series rely upon finding the closest states to a given 'test' state (i.e., correlation dimension, Lyapunov exponents, etc.). To define the state of a system one typically relies on phase space embedding methods.[34] Typically one chooses an embedding dimension, and investigates the propagation of the error between two nearby states. If the error looks random, one increases the dimension. If you can increase the dimension to obtain a deterministic looking error, then you are done. Though it may sound simple it is not really. One complication is that as the dimension increases the search for a nearby state requires a lot more computation time and a lot of data (the amount of data required increases exponentially with embedding dimension) to find a suitably close candidate. If the embedding dimension (number of measures per state) is chosen too small (less than the 'true' value) deterministic data can appear to be random but in theory there is no problem choosing the dimension too large – the method will work. When a non-linear deterministic system is attended by external fluctuations, its trajectories present serious and permanent distortions. Furthermore, the noise is amplified due to the inherent non-linearity and reveals totally new dynamical properties. Statistical tests attempting to separate noise from the deterministic skeleton or inversely isolate the deterministic part risk failure. Things become worse when the deterministic component is a non-linear feedback system. [35] In presence of interactions between nonlinear deterministic components and noise the resulting nonlinear series can display dynamics that traditional tests for nonlinearity are sometimes not able to capture.[36] <end excerpt> Now consider the fact Lorenz discovered chaos as he was trying to predict weather, and explain why you think I am confusing random and chaotic behavior in weather. Maybe looking up the "butterfly effect" would help. >> Trends mean nothing in chaotic systems. All you can know is that the >> signal will change slope, not when or how much. > > Chaotic systems can also be quasi periodic. The really nasty problem > with a chaotic system is that you can have *very* unpleasant surprises > when you slightly change the driving parameters so that the old dominant > attractor is outflanked by a new one. In the case of the Earths climate > this could result in a very rapid shift to a new metastable state quite > different to the weather patterns we see at present. Always has, always will. That's the nature of chaos. Remember, the "system boundary" may be the Milky Way. I suggest you at least read the wiki on chaos before you say much more. |