By Christopher Monckton of Brenchley
Professor Shaun Lovejoy, as he continues the active marketing of his latest paper purporting to prove that “the world desperately needs to drop the skepticism and change course – humanity’s future depends on it”, writes in a hilarious op-ed at livescience.com:
“The majordomo of this deniers’ hub [Watts Up With That] is the notorious Viscount Christopher Monckton of Brenchley, who – within hours [fast on his feet, that Viscount is: strong in him the Force must be] – had declared to the faithful that the paper was no less than a ‘mephitically ectoplasmic emanation from the Forces of Darkness’ and that ‘it is time to be angry at the gruesome failure of peer review’.”
The Professor describes this as “venom”. No, sir, it is eloquence in the service of truth. Perhaps he would prefer a scatological rather than an eschatological metaphor. Happy to oblige. The scientific merit of his paper is aptly described by the third, eighteenth, first, and sixteenth letters of the alphabet, taken sequentially. Or, if he prefers it up him palindromically, the sixteenth, fifteenth, fifteenth, and sixteenth.
Let me put on my major-domo’s tails, white starched wing-collar, maniple, and white gloves, polish up the nearest silver salver, and, Jeeves-like, shimmer in to address some the fashionable pseudo-physics in Professor Lovejoy’s latest Technicolor yawn.
After deploying the hate-screech word “deniers”, he wheels out Svante Arrhenius, who, “toiling for a year, predicted that doubling CO2 levels would increase global temperatures by 5-6 Cº, which turns out to be close to modern estimates”.
The Professor is perhaps unaware (for he does not seem to be aware of all that much in the realm of physics) that Arrhenius is known to have made errors in his line-by-line calculation of the warming effect of CO2 (actually performed at intervals over the long Arctic winter, not over a whole year). He had, for instance, relied on defective lunar spectral data.
Furthermore, Arrhenius – a chemist and not a physicist – had not at that time come across the fundamental equation of radiative transfer, which would greatly have simplified his calculations and made them more accurate.
However, in 1906, in Vol. 1, No. 2 of the Journal of the Royal Nobel Institute, he recanted and divided his earlier climate-sensitivity estimate by three:
“Likewise, I calculate that a halving or doubling of the CO2 concentration would be equivalent to changes of temperature of –1.5 Cº or +1.6 Cº respectively.”
So few of the F. of D. are aware of Arrhenius’ recantation that I am happy to provide a facsimile (Fig. 1) of the quotation from his 1906 paper, published in German (which perhaps explains why the largely English-speaking F. of D. are unaware of it).
Figure 1. Detail in facsimile from Arrhenius, S., 1906, Die vermutliche Ursache der Klimaschwankungen (“The possible cause for climate variability”). Meddelanden från K. Vetenskapsakademiens Nobelinstitut 1: 2, 1ff.
It is also important to note that Arrhenius confined his analysis to radiative transports only. He did not take account of all the numerous non-radiative transports – afternoon convection in the tropics, baroclinic eddies in the extratropics, evaporation everywhere, etc. – that militate homeostatically against any sufficiently small perturbation of the natural climate (such as doubling the tiny concentration of CO2 in the air).
Nor did Arrhenius take account of the biggest unknown in the climate – the behavior of clouds. All other things being equal, returning plant food to the atmosphere from which it came will cause some warming. But we do not know that all other things are equal.
Professor Lovejoy is also incorrect to say that Arrhenius’ original estimate of climate sensitivity was “close to modern estimates”. IPeCaC clings to a sensitivity interval of 1.5-4.5 Cº, entirely below Arrhenius’ original estimate and almost entirely above his revised estimate.
Many “modern estimates” point to a climate sensitivity well below IPeCaC’s interval. We may even see less than 1 Cº of global warming per CO2 doubling (Monckton of Brenchley, 2008, 2010; Douglass & Christy, 2009; Paltridge, 2009; Lindzen and Choi, 2009, 2011; Spencer and Braswell, 2010, 2011; Loehle & Scafetta, 2011, etc.).
Next, the Professor says that in the scientific method “no theory ever can be proven beyond ‘reasonable doubt’”. It would be more correct to say that some hypotheses (though few in physics and very few in climate physics) can be demonstrated definitively.
For instance, it is possible to demonstrate the Theorem of Pythagoras. My own simple proof by inclusion is at Fig. 2.
Figure 2. Demonstration of Pythagoras’ Theorem by inclusion. The boundary contains either the square on the hypotenuse (red) and two congruent right triangles or the squares on the other two sides (blue, green) and two more congruent right triangles. Subtract on each view the two right triangles. Then the square on the hypotenuse is equal to the sum of the squares on the other two sides. Q.E.D.
Professor Lovejoy sets out his stall thus:
“Climate skeptics have ruthlessly exploited this alleged weakness, stating that the models are wrong, and that the warming is natural. Fortunately, scientists have a fundamental methodological asymmetry to use against these skeptics: a single decisive experiment effectively can disprove a scientific hypothesis. That’s what I claim to have done. Examining the theory that global warming is only natural, I showed — without any use of GCMs — that the probability that warming is simply a giant natural fluctuation is so small as to be negligible. He compounds this point later by saying “skeptics dismiss the models”.
Well, are the models right? A single experiment demonstrates that, on the central question how much global warming should have occurred since 1990, the modelers’ hypothesis that the trend in global temperature would fall on their predicted interval (the orange region in Fig. 3) has been demonstrated to be false. Skeptics doubt the models not least because the modelers’ confidently-made predictions have been demonstrated, time and again, to be wild exaggerations.
Figure 3. Near-term projections of global warming (IPCC, 1990: orange region), compared with observed outturn taken as the mean of the RSS and UAH monthly global mean surface temperature anomalies, 1990-2014.
Professor Lovejoy says that his “CO2 proxy … predicts with 95 percent certainty that a doubling of CO2 levels in the atmosphere will lead to a warming of 1.9 to 4.2 Cº”. He prays in aid Fig. 4.
Figure 4. “This figure visually shows the strong linear relation between the radiative forcing and the global temperature response since 1880 … showing the 5-year running average of global temperature (red) as a function of the CO2 forcing surrogate from 1880 to 2004. The linearity is impressive; the deviations from linearity are due to natural variability. The slope of the regression line is 2.33±0.22 degrees Celsius per CO2 doubling (it is for the unlagged forcing/response relation).”
I do not pretend to understand this graph. For a start, it seems to show (albeit in exasperatingly non-standard units) that just about half the CO2 forcing since 1750 occurred before 1960, when CO2 concentration last stood at 316 ppmv. However, the official story-line (in standard units) is that the CO2 forcing from 1750 to 1958 was 0.7 W m–2, whereas that from 1958 to 2014 was greater by four-fifths, at 1.2 W m–2. Makes a bit of a mess of the claimed “linearity”, that.
Secondly, the linear trend on the global temperature anomalies since 1880 is 0.87 Cº, (Fig. 5), in response to 1.9 W m–2 of CO2 forcing. A doubling of CO2 concentration would give 3.7 W m–2 of CO2 forcing, according to the current official method.
Therefore, if there were a linear relation between CO2 forcing and temperature change (which there is not), and if all of the warming since 1750 were anthropogenic (which it was not), and if there were no major natural influences on temperature over the period (which there were) the warming in response to a CO2 doubling would be just 1.7 Cº, not the 2.33 Cº suggested in Professor Lovejoy’s caption.
Figure 5. The least-squares linear-regression trend on the mean of the HadCRUT4, GISS, and NCDC monthly mean global surface temperature anomalies from 1880-2014 is 0.87 Cº. The linearity is not particularly remarkable: the correlation coefficient is only 0.69. The oscillations of global temperature following the 60-year period of the Pacific Decadal Oscillation can be clearly seen.
There is demonstrably no linear relationship between the CO2 forcing, which increases monotonically, and global temperature change, which is stochastic. Global temperature change is more closely related to changes in the great ocean oscillations in the short term (Fig. 6), in total sunlight hours at the surface in the medium term (Fig. 7), and in total solar irradiance in the long term (Fig. 8).
Figure 6. The remarkable non-linearity of global temperature change since 1890, showing the two periods of global warming that coincided remarkably with the two positive phases of the naturally-occurring Pacific Decadal Oscillation over the period.
Figure 7. The remarkable non-linearity of global temperature change in the South China Sea, 1880 to 2008, tracking a remarkable non-linearity in the number of sunshine hours in Japan. Not all pyrometer records show this correspondence: but the Japanese record is the longest we have, and one of the most meticulously kept.
Figure 8. The remarkable non-linearity of the sunspot record, 1600-2003, from Hathaway et al., (2004). Inset: The remarkable non-linearity of global temperature trend, 1659-2010. The first and most rapid of the three periods (red) of global warming since 1659 (1694-1733) occurred as solar activity began to recover at the end of the Maunder Minimum (1645-1715). The other two periods (1925-1946 and 1977-2000) occurred at the solar Grand Maximum (1925-1995).
Next, Professor Lovejoy makes the startling assertion that the probability that what he calls “rare, extreme fluctuations” in global temperature such as those of the 20th century were natural is 1:1000 to 1:10,ooo.
This is where his omission of any reference to the Central England Temperature Record, or to the Utrecht or Prague temperature records, or to the historical circumstances (the freezing of the Thames, of the Dutch canals, of the Hudson in New York), is so reprehensible.
The rapid warming at the transition from the Maunder Minimum to a more normal climate occurred well before the industrial revolution began. It was not our fault.
Or Professor Lovejoy could have gone back to 1421, at the time when global temperature began to tip downward into the Little Ice Age. An interesting letter in the Vatican archive from the Papal Legate in Greenland to the Secretariat of State reported that the Legate regretted that he could not take up his appointment because “the ice is come in from the north”. Suddenly, ships could not reach Greenland.
By now, anyone who has studied the climate ought to have realized that what Professor Lovejoy calls “rare, extreme fluctuations” are neither rare nor extreme. They are the norm, not the exception.
Moreover, the entire interval of global temperature change since 1750, from the depth of the Maunder minimum to the acme during the Great El Niño of 1988 represents a movement of just 0.9% in absolute mean global surface temperature. By contrast, the change between midday and midnight at one location can be as much as 20% of absolute mean temperature. And the interval between the hottest and coldest places on Earth represents close to half of absolute mean temperature.
Next, the Professor says: “But what about Medieval warming with vineyards in Britain, or the so-called Little Ice Age with skating on the Thames? In the historical past, the temperature has changed considerably. Surely, the industrial-epoch warming is just another large-amplitude natural event?”
He answers his question in the negative, saying large-scale changes can only occur over periods much longer than a century. He would have gotten a nasty surprise if he had been around at the end of the Younger Dryas cooling event 11,400 years ago. At that time, according to the ice cores, the temperature in Antarctica rose by 5 Cº in just three years. As Professor Ian Plimer puts it, “Now, that’s climate change!”
Next, Professor Lovejoy writes: “My result focuses on the probability of centennial-scale temperature changes. It does not exclude large changes, if they occur slowly enough. So if you must, let the peons roast and the Thames freeze solid, the result stands.” No, it doesn’t. Just look at the warming of 1694-1733: 1.7 Cº in just 40 years, a rate equivalent to 4.33 Cº/century.
The Q&A that Professor Lovejoy has issued to prop up his paper says that he regards any change of more than 0.25 Cº over 125 years as exceptional, and likely to occur only 10% of the time. No, it isn’t. As I pointed out in a previous posting, more than a third of all 125-year periods predating the onset of anthropogenic influence on climate in 1950 show warming or cooling of more than 0.25 Cº.
Figure 9. Left: The misleading propaganda claim made by “Skeptical” “Science” that 97% of scientists agree we are the cause of global warming. Right: The true position exposed by Legates et al. (2013): 99.5% of 11,944 climate-science papers did not say we are the cause. They did not even say we are the primary cause.
Next, Professor Lovejoy says IPeCaC has “strengthened its earlier 2007 qualification of ‘likely’ to ‘extremely likely’ that human influence has been the dominant cause of the observed warming since the mid-20th century.” Yes, it has, but it has done so not only on no evidence but in the teeth of the evidence.
As Legates et al. (2013) demonstrated, 99.5% of 11,944 scientific papers on climate published between 1991 and 2011 did not say that most of the global warming since 1950 was caused by us (Figure 9).
Besides, since Professor Lovejoy’s paper plays with statistics a great deal, he should know that no recognizable statistical process performed on any actual dataset (unless science now recognizes a show of hands among scientifically-illiterate, rent-seeking representatives of governments) generated IPeCaC’s “95-99% confidence” value.
Next, the Professor asserts that “skeptics … insist that warming results from natural variability”. No, we don’t. We assert that in the present state of knowledge it is impossible adequately to distinguish between natural variability and anthropogenic influence.
The Professor digs his hole ever deeper: “The new GCM-free approach rejects natural variability, leaving the last vestige of skepticism in tatters.” Here is an honest version of that sentence: “I reject natural variability aprioristically, so I bished and bashed the numbers till they fitted my preconception, leaving the last vestige of my scientific credibility in tatters.”
Yet he rants blithely on to the effect that the Canadian government has “axed climate research” (hurrah!); that it gave him no funding for his research (so he got more than he deserved); that it has “shamelessly promoted the dirtiest fuels” (but CO2 is not dirty, it is the stuff of life); that it has “reneged on its international climate obligations” (no, it took lawful and timeous advantage of the opt-out clause in the Kyoto Protocol and, therefore, has no “international climate obligations”); that “two decades of international discussion have failed to prevent emissions from growing” (along with crop yields and net primary productivity of trees and plants, thanks to CO2 fertilization); and, finally, that “the world needs to drop the skepticism and change course – humanity’s future depends on it” (but, as T.H. Huxley said, to the scientist “skepticism is the highest of duties, blind faith the one unpardonable sin”, and whenever someone says humanity’s future depends on something he means his income depends on it).
ferdberple says:
April 24, 2014 at 5:50 pm
Nope. Your assertion is obvious nonsense.
The glacial cycles are largely under Milankovitch cycle control. That means that cycles of 21,000, 26,000, 41,000 & ~100,000 years, plus insolation, will align in similar configurations only on longer time scales. The more recent past will thus be less likely to resemble progression of each factor into the future. Guaranteed. I would have thought that this was obvious. If you imagine otherwise, please explain why.
Bear in mind that professional students of Milankovitch cycles have found that MIS 11 more closely resembles the Holocene than the do the previous three interglacials. But if proximity in time counts, then the Eemian should rule, & it lasted 5000 years longer than has the Holocene to date.
Besides which is the issue that other proxies besides ice core data are available which confirm the length of the most apropos prior interglacial, the Hoxnian.
Chris apparently thinks that paleoclimatology isn’t important, for some reason, but IMO showing the natural variability of climate is key to gutting CACA.
I look forward to your explanation as to why the three most recent interglacials count but MIS 11 doesn’t.
All Chris had to do was make a similar statement instead of calling me a troll because I happened to know more about the topic than he does. Were he really interested in science, the exchange would have gone like this: I say, “The end of the Holocene is not overdue. Look at the Eemian”. Then, instead of calling me names & a troll, he would have asked, “My arithmetic based on this paper says it is. Granted the Eemian lasted longer, but look at the previous two interglacials”. Then I would have replied, “The most relevant interglacial is MIS 11, which most closely reproduces the orbital mechanics of the Holocene, plus there are other proxies besides ice cores, etc.” See how much more educational for all that would have been than making up cutesy names for me & calling me & anyone else who dares to challenge Discount Monkeytown (see how easy it is?) a “troll”?
Milodonharlani,
If this was your original argument:
Lord Monckton has refuted this claim. Perhaps he’s wrong, but not laughably so. For him to be laughably wrong he’d have to have been left without a plausible argument. He has made plausible argument, here, and here.
Your continued pursuit of your quest to beat Lord Monckton down into an apology and admission of error is starting to border on the manic and abusive. Obviously he may be wrong, but his statement wasn’t the laughable absurdity you tried to demonstrate it was. Give. It. up.
Mark Bofill says:
April 24, 2014 at 6:16 pm
He has no plausible argument because including just one more interglacial, the one that happens to be the most relevant, blows his average totally out of the water. Instead of overdue by 4000 to 5500 years, the average becomes something like 15,000 years more to go, just by adding one more interglacial, the most relevant one. But the average is meaningless, because what most matters is the orbital mechanics, not a grade school level arithmetic mean, ie average.
As an MA from Cambridge in History & Philosophy of Maths ought to know.
It’s laughable because so totally wrong-headed, & yet so easily checked. The most rudimentary Internet search would have showed Chris that MIS 11 is the most relevant previous interglacial.
milodonharlani says:
April 24, 2014 at 6:05 pm
re dberple says:
April 24, 2014 at 5:50 pm
======================
Nope. Your assertion is obvious nonsense.
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One again you descend to childish insults.
LM has satisfied me to the logic of his comments. I do not have to agree 100%, but he is consistently logical.
David A says:
April 24, 2014 at 6:56 pm
Ferd calling a comment nonsense, without any supporting verbiage whatsoever, is not childish, but a reply with cogent & factual reasoning is?
Interesting.
BTW, MIS 19 might be an even better model (dare I use that term?) for the Holocene than MIS 11, but the point is, it takes hundreds of thousands of years for rough realignment to occur (the moon yet again to be in climatic if icy Aquarius, as it were).
http://meetingorganizer.copernicus.org/3ICESM/3ICESM-11.pdf
milodonharlani,
I went to your wikipedia links, and I do not agree that Lord Monckton was either incorrect or “laughably” incorrect. I did find this: In contrast to most other interglacials of the late Quaternary, MIS 11 cannot be straightforwardly explained and modelled solely within the context of Milankovitch forcing mechanisms. According to various studies, the MIS 11 interglacial period was longer than the other interglacial stages. The sustained interglacial warmth may have lasted as long as it did, because orbital eccentricity was low and the amplitude of the precessional cycle diminished, resulting in several fewer cold substages during this period and perhaps also induced abrupt climate change at MIS 12–11 transition, the most intense of the past 500 kyrs. It is notable that MIS 11 developed just after one of the most “heavy” Pleistocene δ18
O glacials (MIS 12). According to some authors, MIS 12 is likely to represent a “minimum” within the 400-kyr cyclicity (which is apparently “stretched” into ca. 500-kyr cycles in the Pleistocene), same as the MIS 24/MIS 22 complex (ca. 900 ka; Wang et al., 2004). In support of this inference is the observation that these dramatic glacial intervals are coincident with periods of major climate reorganisation, namely the “Mid-Brunhes Event” (Jansen et al., 1986) and the “Mid-Pleistocene Revolution” (Berger & Jansen, 1994), respectively. In view of its pattern of astronomically-driven insolation, MIS 11 may be the best analogue for the near future insolation situation. A 2-D Northern Hemisphere climate model used to simulate climate evolution over MIS 11, MIS 5 and into the future implied that the climatic features and length of MIS 11 may be comparable to the present-future interglacial in the absence of anthropogenic forcing. This consideration has led some authors to the conclusion that actual interglacial period (begun 10 kyr) would have continued for approximately 20–25 kyrs even in the absence of anthropogenic forcing.
It looks like your case is full of holes, and Lord Monckton’s choice of the three most recent interglacials was justifiable.
you wrote this: The glacial cycles are largely under Milankovitch cycle control. That means that cycles of 21,000, 26,000, 41,000 & ~100,000 years, plus insolation, will align in similar configurations only on longer time scales. The more recent past will thus be less likely to resemble progression of each factor into the future. Guaranteed. I would have thought that this was obvious. If you imagine otherwise, please explain why.
Why was it obvious, when you have not even bothered to link to the supporting evidence? Do you have a criterion for “largely” under Milankovitch cycle control? “The more recent past will thus be less likely … ” does not actually follow; would you care to put in the missing details, with links to the literature?
PS: I’m happy you’re satisfied, but arithmetical operations on an inappropriate set is not science. Just so you know.
Matthew R Marler says:
April 24, 2014 at 7:01 pm
Your understanding appears full of holes. Nothing that you quote in any way vitiates the fact that MIS 11 (& 19) are analogs of the Holocene, while the Eemian, MIS 7 & 9 aren’t. If you can’t grasp that, then I can’t help you.
Chris probably gets it, though. Even if Ferd doesn’t. Still waiting to hear back from him.
Lovejoy’s 2.33 C per CO2 doubling is just wishful thinking. Look at Figure 4. The y-axis is temperature change. It is independent of the x-axis. We can put any variable in the x-axis. Example, let’s put duck population in the x-axis. If duck population is increasing over time, we can find the regression line and the slope is defined as A increase in temperature per B increase in duck population (dy/dx). Then we can blame ducks are responsible for global warming.
Any variable that increases over time will do. We can put obesity, cancer incidence, etc., etc. and blame fat people for global warming. This is the folly of using correlation without common sense. Physics support only 1.1 C per CO2 doubling without feedbacks. Greater or less than that is correlation and conjecture.
===================================================================
I”ll count that as a quote worth remembering.
milodonharlani, the quote that I provided from your wikipedia link contains: MIS 11 may be the best analogue for the near future insolation situation.
upon “may be” hangs your assertion that Lord Monckton was “laughably” wrong; but everything that you provided all together only shows that he “may be” wrong, not that he is wrong.
If you can’t grasp that, then I can’t help you.
Of course I understand that. But it isn’t necessarily true on evidence that you have linked to. What we have in conclusion is “may be”.
Matthew R Marler says:
April 24, 2014 at 7:22 pm
Another reply lost in the aether.
It may reappear later, so will summarize.
Thanks for connecting a point to your prior cutting & pasting.
The “may be” refers not to MIS 11 v. subsequent interglacials, which definitely are not good analogues for the Holocene. However MIS 19 might be even better.
milodonharlani says:
April 24, 2014 at 7:30 pm
PS: Note 380,000 years required to get all the Milankovitch parameters very approximately back into similar positions, a period not surprising, except perhaps for its shortness.
MIS 11 was at 374 to 424 kya, while MIS 19 at 755 to 788 kya.
http://www.nature.com/ngeo/journal/v5/n2/fig_tab/ngeo1358_F4.html
“””””…..John Whitman says:
April 24, 2014 at 4:07 pm
Mathematics is applied reasoning about something that is physical.
The physical things it reasons about are: ‘quantities of things’; their ‘measurement validation process’; and ‘relations between quantities of things’.
Mathematics is systematically applied and integrated into a body of knowledge.
Therefore mathematics is a physical science. And it is as much of a physical science as is physics and is just as physical as any physics proposition……”””””
That is a little hard to swallow, given that nothing; not a single thing in any branch of mathematics, actually exists anywhere in the physical universe.
We have no points, no lines, no circles, no spheres, no anything, because we invented these concepts to manipulate our models, which tend to behave exactly like the mathematics says.
Now the real physical universe never behaves exactly like our models, and for some fundamental reasons, besides ignorance; Heisenberg for example.
The area where “proof” is lacking, is in the construction of our physical models, so that they behave (according to the correctly applied mathematics) just as our measured observations say the real universe seems to be behaving.
The mathematical tools, ensure that our physical models WILL do exactly what they are supposed to do.
That is different from saying they WILL emulate reality, as observed, and measured.
And M of B has mentioned, mathematics also stimulates our creative minds.
The starting point for this line of discussion was that his lordship cited the Pythagorean theorem as a counter-example to Professor Lovejoy’s claim about no scientific theory being proved beyond reasonable doubt.
My objection (and apparently that of Messrs Mosher and Lee) is that Professor Lovejoy was talking about empirical science whereas the Pythagorean theorem is not an example of empirical science. I still maintain that this was a slip on his lordship’s part.
(In passing, his lordship might have taken the discussion in a different direction. Lovejoy used the phrase “proved beyond reasonable doubt”. This is legal terminology. It has no place in logic or mathematics. We do not prove a mathematical theorem beyond reasonable doubt. We either prove it or we don’t. Reasonable doubt just don’t enter into it. Proof beyond reasonable doubt in a court of law is much less demanding than mathematical proof or corroboration, not proof!, in physics. If we had to validated the theory that A murdered B with the same rigor as a mathematical theorem or the second law of thermodynamics, we would almost never get a conviction. If we apply “reasonable doubt” to science, we’re using a legal metaphor, and some people might reasonably claim, within this slippery metaphor, that some scientific theories have been proved beyond reasonable doubt. At least, I wouldn’t have bothered to say anything to contradict that, though like Mr Lee, I would be dubious about it.)
Whereas there are proofs of mathematical theorems, there can never be any proof of a law of physics. There are different ways of bringing out this difference, but I still like Leibniz’s. A mathematical theorem is true in all possible worlds whereas a physical law true in our world might be false in a different possible world. God could have made a world with a different law of gravity but he could not have made a world in which there is a highest prime.
No law in empirical science is ever proved, though sometimes a purported law can be disproved. One of the problems with the currently dominant group in climate science is that they will not specify any observation that could refute their theory, and in this way they tend to drift into unfalsifiability, unchecked by observational testing, thus leaving science behind.
If I suggested that the Pythagorean theorem applies only in Euclid, that was careless on my part. What I meant was that there are non-Euclidean geometries in which it does not apply.
The fact that mathematics was treated as an art in ancient (medieval?) universities does not cast doubt on my assertion that mathematics is not an empirical science.
Of course, Popper did not make the mistake of supposing that mathematics is an empirical science! (“Wissenschaft” normally has a broader connotation than “science” and is often used to include mathematics, so a German speaker would be likely to add the qualifier “empirical” where an English speaker would omit it, because the most common understanding of “science” in English is indeed confined to the empirical sciences and excludes mathematics.)
His lordship says that it is possible to refute a mathematical conjecture “empirically with a single counter-example”. It is indeed possible to refute a mathematical conjecture by a counter-example, but not an empirical counter-example. Here we must consider what mathematics is “about”. One may use an abacus in performing calculations, but the calculations are not “about” beads on a wire; they are about numbers, which are not empirically observable objects. When we say that 5 + 7 = 12, we are not talking about anything observable by the senses, with or without the aid of special instruments. Similarly a computer may be programmed to observe some graphics, but (if the computer is doing math rather than doing empirical science) the graphics are merely proxies for the mathematical entities.
People’s motivations are immaterial; what matters is the quality of the arguments. Furthermore, people’s motivations are often very uncertain, so we may mistakenly attribute evil motives to someone who just doesn’t see the world the way we do.
“””””…..Mike McMillan says:
April 24, 2014 at 3:10 am
george e. smith says: April 23, 2014 at 4:06 pm
… Is not the restriction of Pythagoras even more than you cited. It only applies to two dimensional Euclidean space. Has no rational meaning in three dimensional Euclidean space.
Pythagoras’ theorem applies to three-dimensional Euclidean space. The distance between any two corners of a box is the square root of the sum of the x, y, and z squares……”””””
Well it looks like I went to a sub standard high school.
We learned that “tri” meant three, as in sides or angles, and in this case both.
But I never knew that a “box” was also a “triangle” and had a “hypotenuse”. Seems like a box has far more than three of everything.
But I’m able to achieve the result you cite in two sequential applications of Pythagoras’ theorem to two different PLANE “triangles”.
And it would seem trivial to expand the scope of your definitions of the specifics; “tri”, “hypotenuse”, “right angle” to include boxes and corner cubes in any number of dimensions.
Can you also extend the mathematical discipline called “Projective Geometry” to three or more dimensions ?? Does the Line at Infinity, become a Plane at Infinity, or how does that work ??
And what about the two Circular Points at Infinity, that all circles pass through; does that morph into three or some other number of “Spherical Points at Infinity” ??
My head, can’t even comprehend that. Can one prove the existence of any more points, than seven, in three dimensional projective geometry, because that is the provable maximum number of points in plane projective geometry ??
I’d have to research M of B’s Hyperbolic Geometry to figure out how Pythagoras works there. I can’t swear, that I’m familiar with Hyperbolic Geometry, although I’m quite familiar with the conic sections, and general three dimensional second order figures. I even use them frequently in the design of non-imaging optical systems.
Philip Lee says:
April 24, 2014 at 5:50 pm
The only difference between pure and applied mathematics is the source of the problem attacked.
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not so. the difference is in the techniques and the relative importance of time.
pure mathematics seeks to provide an exact solution, and may wait infinite time to achieve this.
applied mathematics seeks to provide a “good enough” solution in the time available.
So for example, applied mathematics will “guess” the answer and iterate to reduce the error. Once the error is small enough, applied mathematics is satisfied.
Pure mathematics on the other hand will seek to describe the iterative process at the limits, where you iterate to infinity and the error is zero. The result will be an equation or process that provides the exact answer, without requiring infinite time.
milodonharlani says:
April 24, 2014 at 6:05 pm
The glacial cycles are largely under Milankovitch cycle control.
==================
You are falsely stating your belief as a fact. The correct statement is:
The glacial cycles are believed by some to be largely under Milankovitch cycle control.
Milankovitch doesn’t explain the 100k year problem, the LIA, the Medieval Optimum, the Roman Optimum, the Minoan Optimum, the Holocene Optimum, etc. etc. http://en.wikipedia.org/wiki/100,000-year_problem
And most of all, if Milankovitch does explain these, then why does it not explain the Modern Optimum?
milodonharlani says:
April 24, 2014 at 7:51 pm
PS: Note 380,000 years required to get all the Milankovitch parameters very approximately back into similar positions
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There may well be a Milankovitch 400k year super cycle, super-imposed on the 100k year cycle. However the odds of “all things being equal” are much less in comparison to more recent events. thus one should not conclude that our records from 400k years ago are more reliable indicator of the future than our records from 100k years ago.
ferdberple says:
April 24, 2014 at 9:46 pm
Milankovitch cycles demonstrably control the ~100,000 year glacial cycles, & the interglacials within them, which are what is at issue. Fluctuations within interglacials are not the issue, as I would have thought was obvious. Your raising the Holocene Optimum & subsequent variations within the current interglacial is a nonsense, since I didn’t suggest that orbital mechanics control those fluctuations. No one knows what does, which uncertainty lies at the heart of the weakness of CACA.
On the scale of tens to hundreds of thousands of years, Milankovitch cycles rule. It’s not just that some people think they do, but that they have been convincingly demonstrated to do so.
Why is such a simple distinction so hard for you to understand? Please quit spouting nonsense. Thanks.
ferdberple says:
April 24, 2014 at 9:54 pm
The 400,000 year “supercycle” isn’t imposed upon the orbital mechanical cycles. It is composed of them, superimposed upon each other. Why is this hard to understand?
Can you now grasp why the more recent interglacials are not relevant to Holocene duration but certain of the older ones are? I would have thought it intuitively obvious.
ferdberple says:
April 24, 2014 at 9:30 pm
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That is IMV precisely true. One apple plus one apple is precisely two apples. However, all apples have different weights, moisture content, sugar content, colors pigments, molecules, atoms etc. (How precise do you want or need to be.) Math is a tool to “measure”; and a hemi demi semi, can be virtually infinite.
And
– – – – – – – – – –
Christopher Monckton,
Please note my reference to Platonic imagery and abstract knowledge in the comment of mine to which you refered.
As Plato’s dual reality metaphysics is not correct (there is no separate ideal/abstract reality that exists outside of this physical reality) then the representation of the science of mathematics as a ideal or abstract science is a problematic metaphysical (and epistemological) concept.
Therefore, there is the physical science of mathematics as I described in my comment (John Whitman on April 24, 2014 at 4:07 pm) that covers all of reality.
Note: In that respect a very similar dual reality error applies to Kant’s dual reality metaphysics (and therefore his dual reality epistemology). Kant is essentially Neo-Platonism in that respect.
John
Mr Steele does not understand the meaning of the word “empirical”. It means “by trial”. It comes from the Greek word “empeirein”, to try. Any process by which a counter-example to a conjecture in mathematics is sought by testing various possibilities is, whether he likes it or not, an empirical process. He also appears to consider that every demonstration in mathematics is definitive: but, though some are, some are not. It remains the case that it is possible in physics, as in mathematics, to demonstrate a hypothesis “beyond reasonable doubt”, and Dr Lovejoy was incorrect in his attempt to justify his own approach by suggesting otherwise.
Mr Lee continues to conduct himself mendaciously, which is unwise. Having been caught out a couple of times misrepresenting points upthread when he had lost the argument, he now again misrepresents what I had said earlier by describing my assertion that it is possible to demonstrate matters in physics beyond reasonable doubt as “new”. Read the head posting.
Mr Lee says Popper would not agree with me on that point. However, he did so. The end and object of the scientific method is to approach the truth as closely as possible. There comes a point, as the scientific method continues to operate, where some hypotheses has survived long enough to be regarded as having been demonstrated beyond reasonable doubt. Mr Lee, whose knowledge of distinctions between terms is poor, may not perhaps have appreciated the distinction between definitive proof, which is very rare in physics, and proof beyond reasonable doubt, which is not so rare.
Mr Lee says I stated that applied mathematics is a science. I do not recall having said that, though I do recall that in the ancient universities mathematics is considered an art. He goes on to say “the only difference between pure and applied mathematics is the source of the problem attacked”. Nonsense: pure and applied mathematics each have several unique methods, though some methods are in common.