Number of the Month

August  2005

A bit of a breakthrough

“Here’s another fine mess you’ve gotten us into.”
The immortal Ollie

Admittedly its is only the Daily Telegraph, which, though normally adhering to the party line on so-called environmental matters, has recently developed a disturbing tendency to go all scientific; and it is only the House of Lords, which, despite the Great Leader’s efforts to pack it with robotic cronies, still takes an independent and disinterested view of science; but could it represent the first green shoots of revival after a long winter of discountenance for real science?

It is an opinion article by Neil Collins, the man who spilled the beans about the Royal Society plot to suppress scientific debate about the theology of the flagellant priests of Kyoto. Throw in the equivocal response of G8 at Gleneagles plus the emergence of the Asian-Pacific Partnership on Clean Development and Climate and you have a nice little stew for the European Oligarchs to try to escape from.

Collins is an unusual columnist, in that he not only notices what is going on, but he also remembers it. He is aware of the German Kyoto Hoax, for example, and the farce over the European stability pact, which exposed rule zero of the EU. Successful organisms learn from experience, but the leaders of the EU do not come into this category. The Russian Government is also heading for interesting times, having chosen to ignore its own scientists and attend instead to the bribes from the EU. Virtually none of them is going to reach the target, but will they pay the fines? It is all very well to argue that black is white (or, more aptly, red is green) in the debating chamber, and to convince yourselves that it is true, but when you choose to back your hunches with an economy-crushing system of fines you are likely to come up against that brick wall known as reality, the result being a bloody nose.

The leaders of the old EU have lectured the world from their high podium and, intoxicated with the exuberance of their own high blown rhetoric, ignored the fact that the time comes when you have to deliver. They have wrecked their own economies with well-meaning environmental and social legislation and are genuinely surprised that others seem unwilling to follow them. With any luck they will soon be gone. Unfortunately for civilisation there is no such practical test for international organisations such as the UN IPCC and WHO. They can continue to peddle their snake oil, indulge in outrageous fraud and misdirection, safe in the knowledge that they will not be put to the test and that the taxpayer dollars will continue to roll in unimpeded.

Nevertheless, it might be a small thing, but we have had a breakthrough. Perhaps our man in Puerto Rico was not entirely wrong in his outbreak of unseemly optimism last month.

Footnote: an interesting link from Aaron Oakley, of fond blogospheric memory.


Strange company

Thanks to correspondents for drawing attention to two recent links.

Nigel (usual soubriquet omitted in the circumstances) Hawkes gave Number Watch and The epidemiologists a mention in his review in The Times holiday book columns.

There was a more surprising mention in Real Climate. It was all rather friendly until a later intervention from one Steve Latham, who has read some of Number Watch, but perhaps somehow managed to miss all the mentions of record cold weather, particularly during Europe’s record hot year of 2003, to say nothing of five years worth of sifting the evidence. The invitation to join in statistical testing games, particularly with computer predictions, is respectfully declined, especially as these tend to accord with our definition of climate change.  He finishes with rather a neat example of the non sequitur. There might be record levels of krypton, for example,  in the atmosphere, but it would be no occasion for loss of sleep.

Incidentally, there is no clash between the two analyses of extreme events. They are related by the fact that the logarithmic function is the integral of the rectangular hyperbola (1/x). By only dealing with the one dimension of time, however, a misleading impression is created. The world is a big place and the extreme value fallacy conducted over such a large area gives players of the game of ratchet phenology a big playing field. As our previously quoted retired meteorologist said “a month without a record would be a record.”


Inside story

The EU appears frequently in these pages as one of the world’s premiere sources of nonsensical numbers. Only last month, we featured the problem of traditional garden chemicals being replaced by more expensive alternatives from monopoly suppliers. A Google on one insecticide showed that its appearance was as a result of direct contact between the manufacturer (Bayer) and EU officialdom. Smaller businesses are denied such facilities. The EU, not for the first time, also gave us the number of the month.

Regular correspondent Grant Perk draws attention to a valuable account by independent MEP Ashley Mote. It confirms all our worst fears and deductions about how the EU actually works. Pass it on.


Many years ago, your bending author once took part in one of the EU’s expert committees. It was all very pleasant – luxury hotel, fine food etc. and a complete waste of time and money – but the invitation was never repeated. Was it something I said?

Footnote (Prof David Barron)

I had a similar experience. But in my case it was something I said: I told them that the whole exercise was a pointless boondoggle.

The fallacy of the incomplete balance sheet

Balance sheets are the very stuff of life to the denizens of the financial world. They are also meat and drink to various fraudsters and a trap for fools. Science is not immune from the dangers. Your bending author first became aware of this over thirty years ago when challenged on using a formula which was at variance with one found in a number of textbooks (see technical footnote below). Politicians in particular are adept at presenting balance sheets with what are known in the trade as black holes. Britain’s Chancer of the Exchequer is a past master at it, using devices such as the Private Finance Initiative to hide huge debts that will be millstones round the necks of his successors, as will public sector pension liabilities.

Anyway, what prompted this line of thought was a correspondent pointing out that a piece of global warming propaganda, besides offering some extremely dubious numbers,  had grossly misrepresented what Number Watch had to say about the Greenhouse Effect. In contrast it approvingly quoted a piece entitled Bad Greenhouse, which readers familiar with our links will know that Number Watch claims is wrong.

Oddly enough, the two articles quoted actually contradict each other. Here are two quotations:

  1. Because the atmosphere is such a good absorber of longwave infrared, it effectively forms a one-way blanket over the earth's surface.
  2. Bad Meteorology:
    The greenhouse effect is caused when
     gases in the atmosphere behave as a blanket
     and trap radiation which is then reradiated to the Earth.

The second one goes on to explain the “real” Greenhouse Effect:

The surface of the Earth is warmer than it would be in the absence of an atmosphere because it receives energy from two sources: the Sun and the atmosphere.

This is a fine example of the fallacy, because it leaves out of the balance sheet the energy that the atmosphere receives from the surface of the earth. This must be exactly equal to the energy flowing the other way, as the two components are in thermal equilibrium. If they were not, one would heat up until they were, a requirement of the second law of thermodynamics.

It is entirely unreasonable to treat the dirt, the wet and the air as separate bodies. They are in intimate contact and (on average) in thermal equilibrium. The only way to understand the Greenhouse Effect is to treat them as one body, the Earth. Very roughly speaking, the water in the thin skin that we call the atmosphere paints the Earth blue so that, not being a black body, it has to raise its temperature to be in equilibrium with the sun and outer space.

The most glaring and common example of the incomplete balance sheet, however, occurs in the calculated costs to the health service of various target substances and modes of behaviour. Premature death, even if it is a real effect, costs the health service less, not more, since the deceased no longer require hip replacements, maintenance in dementia and other expensive forms of geriatric medicine. 

Technical footnote:

An equation widely used in electronics gives the current due to a charge moving between two electrodes. The derivation gives the correct answer until you introduce a stationary charge. Then, contrary to the principle of superposition, the derivation predicts a modified current. The reason is that it leaves out of the energy balance the change in energy of the induced bound charge on the electrodes.

Ref: Brignell and Evison, Current due to a probe charge moving through a static space charge, J.Phys. D: Appl. Phys., Vol 6, 1973, pp L55 - 57

Afterthoughts: As a matter of clarification, the above simplification refers to the colour of water and not to Rayleigh scattering.

It is interesting to note that many global warming sites refer to the comparative temperatures of Venus and Mars without mentioning the inverse square law.


Correspondence received

You should be informed that your explanation of the greenhouse effect 
on your page is fundamentally flawed. To wit, the assertion that 
greenhouses operate on the principal of selective re-radiation is 
fallacy. Greenhouses operate by preventing convective cooling, IR 
light having little to nothing to do with it. This can be seen 
empirically from the fact that greenhouses have been constructed out 
of materials such as rock salt, which is transparent to IR, and they 
operate equivalently to ones made of glass.

In addition, your assertion that humans are assembled in utero from 
DNA by a process that recreates evolutionary steps, the old ontogeny 
recapitulates phylogeny idea, also known as the "biogenetic law", 
first laid out by Enrst Heckel in the 1800s, is utter nonsense. It 
has been known for over 100 years, pretty much since its inception, 
that it was false. see also
In particular, your assertion regarding information dynamics and 
storage vis-á-vis DNA is completely wrong. Nor does it even address 
your fundamental point, that it disproves the viability of 
intelligence in nano-scale self replicating machines. You write:

 >The strand of DNA contains a program to control a development 
process in the egg or womb that rehearses the whole evolutionary 

Aside from the fact that this, again, is not true, it is also 
irrelevant to your argument, since you do not propose a reason why 
machines can not follow a similar path. If DNA is sufficient to 
encode the manufacturing sequence for a person, no matter what route, 
it is of an appropriate size to do the same for an immensely less 
complicated nanomachine. Simply stating that you know of no means to 
o so does not make it impossible, This is a basic logical fallacy.

 >If the human brain had to contain the information to build a human 
it would be the size of a planet. (obtuse self-referencing positive 
feedback references omitted)

First, the human brain does not have to contain the information to 
build a human (although it does.) Do you suggest that mothers are 
consciously (or even unconsciously) manufacturing fetuses in utero? 
Thus this argument is specious at best. Second, you have a site 
dedicated to number accuracy, yet feel perfectly free to pull figures 
out of thin air or manufacture them out or whole cloth. Where, pray 
tell, is your source or justification for the estimate of human brain 
size (that of a planet) needed to recreate a human? Obviously an 
upper limit of the size of the object needed to encode a human is not 
a planet, or a human itself, or even a human brain, but simply the 
single egg cell formed upon fertilization. A more accurate estimate 
is that of the chromatin itself.

 >However, he did in fact  concede that human flight might one day be 
possible, but only by the discovery of some completely new material 
or force of nature, which  is just what happened. The Wright Brothers 
employed principles of Aerodynamics and Fluid Mechanics that were 
completely unknown to Physics at the time and which they did not 

You are entirely incorrect. All the physical principals involved in 
flight were available to Kelvin, and others. It is simple newtonian 
mechanics. And spare me the drivel about Bernoulli's Principal, as it 
has NOTHING whatsoever to do with flight. (see Coanda effect and 
Newton's 2nd Law for correct explanation.)

Your site is replete with other logical errors, scientific 
inaccuracies, and outright fabrications, but time is, unfortunately, 
not an infinite commodity.

Mark Choi


Matters arising

Thanks to those who wrote in about the above critique. They and it prompted a few thoughts in your bending author, viz:

Some laws of publication

If you publish a piece there will always be people who do not read beyond the first paragraph, yet are prepared to criticize it on that basis.

The most vehement criticism will be about something you did not say.

If you quote a character in the humorous literature (such as Marvin, the paranoid android) without spelling it out, there will always be some plonker somewhere in the world who will take it literally.

The rule is – if still in doubt, always finish up with a sequence of abusive generalizations, pleading lack of time to go into the evidence.

Furthermore, while it is usually a mistake to respond to such attacks, it is irresistible to observe that:

The Coanda effect, though a red herring, was discovered more than two decades after the deaths of Lord Kelvin and Simon Newcomb.

The disparate topics of greenhouses and aerofoil sections illustrate the fact that some people cannot cope with the concept of two mechanisms operating simultaneously. Oversimplified explanations of lift are both wrong (and both, to some extent, right). Although the Navier-Stokes equations had been known for nearly a century when Orville Wright took off, they had proved impossible to solve analytically and it was only the coming of the computer that enabled lift and drag to be calculated accurately. Lord Kelvin had been a student of Stokes, but this did not give him access to the solution of the equations.

It is odd that people have such a propensity to resuscitate the naïve disputes of a previous generation. It so happens that thirty five years ago your bending author was working briefly at the University of  Grenoble on the topic of electrohydrodynamic instability, involving the augmented Navier-Stokes equations, which makes it difficult to preserve one’s customary equanimity in the face of such gratuitous hectoring at such an uninformed level.

What the quoted reference actually says about  Haeckel’s Hypothesis is that it “ has been discredited in its absolute form, although recognised as being partly accurate.”

Anyway, how did Bernoulli’s head teacher come into it?

Footnote (added by Adrian Gaylard)

So aerodynamic lift is entirely inviscid then?  This is a manifestation of a wrong-headed analysis that was touted around the UK above five years ago by an oddly misinformed US physicist and a junior aerodynamics professor, who a colleague of mine forced to recant during an e-mail exchange!
 The explanation (the Newtonian bit of it anyway) is not a bad approximation for lift from a stalled aerofoil, but that's not really much use.
 I think one of the reasons that this analysis got so much coverage (including an article in the Telegraph) is that the "standard" explanation given to so many students is wrong (air has further to travel over the top of a wing, so has to move at higher velocity thus reducing the pressure).   Therefore people were seduced into thinking that as the advocates of a purely "Newtonian" explanation were able to demonstrate this then their alternative must somehow be correct.
Two of my colleagues and I had a (somewhat abbreviated) letter published in the Telegraph when it picked up on the issue.  The guilty parties (as far as promulgating this overly simplistic notion of aerodynamic lift is concerned) are Anderson and Eberhardt (  Unfortunately, there now seem to be more than a few converts.
 It baffles me that people get hung up on the downwash as an explanation of lift, as this is clearly an effect of the pressure distribution over the body which is fundamental to the process.

Any further comments via the Forum, please.


Move over Quasimodo

In the USA the game ain’t over ‘til the fat lady sings. In the UK the silly season hasn’t got going until the heir to the throne has appeared on the front page of The Times. He has a whole host of pseudo-scientific theories in his armoury, such as organic gardening and grey goo, but this time he is back to alternative therapies. One of his favourites is homeopathy. In the whole tawdry history of nonsense-based scams was there ever one to match selling gullible punters pure water? It beats snake oil by a mile. They put some substance into water then repeatedly dilute it until there is none left, claiming that the water “remembers” it. The structure of liquids was fairly well known when your bending author was obliged to research it nearly half a century ago. There has been considerable improvement in knowledge of water since. Water molecules, being highly polar, tend to align themselves and form crystallites. These however, are buffeted about by thermal energy and they are extremely short lived (picoseconds) unless the temperature is reduced to zero Celsius. There is no mechanism in such a scenario for water to remember anything. There is nothing to debate about it – the whole thing is an unmitigated scam based on total nonsense.

The Prince’s latest stunt is to appoint an economist (yes, believe it or not an economist) to report on “savings” to be made by providing alternative therapies on the NHS. How appropriate that it should be in the month when we discussed the fallacy of the incomplete balance sheet!

Just how you make savings by selling the punters and the taxpayers something that cannot possibly work is one of those mysteries only revealed to the likes of economists. Ordinary placebos would be considerably cheaper.

Quasimodo was elected Prince of Fools. There is now a more qualified candidate. Britain has been long blest with a gracious and wise sovereign with great benefits, not least being protection from having a politician as head of state (President Blair does not bear thinking about). The Murdoch press, with its republican agenda, is only too pleased to give every possible airing to the effusions of  the noble ninny. So we say, once more with feeling, “God save the Queen!”

Meanwhile, the silly season has been gathering its usual momentum.......


Vioxx populi

Several correspondents and members of our forum have been rightly incensed at the latest coup by American scumbag lawyers in obtaining hundreds of millions of dollars from the manufacturers of the arthritis drug Vioxx (Rofecoxib). The biggest losers will be those deprived of pain relief by the withdrawal of a drug on spurious statistical grounds.

Data, like vegetables, do not improve in quality by being overcooked. That was the thought prompted by wading through the report of the FDA Advisory Committee on Vioxx (rofecoxib). It is hard going, turgid and turbid, with a mass of  jargon, many irrelevant observational studies.

Two points would appear to be glaring. First, the difference in mortality between the placebo and rofecoxib groups is precisely zero. Second, what the study actually shows is not that rofecoxib increases the rate of incidences but that giving a placebo decreases it!


The rate of incidents with the drug stays constant at about 1% per eight months, while the rate with the placebo appears to tail off to zero after a couple of years. Does this not mean that the correct ruling would not be to withdraw the drug but rather to supply the whole population with placebos? Just look at the size of the gap between the error bars, and that is for the undemanding confidence interval of 95%!

Technical footnote: your bending author has spent many hours covering sheets of paper with equations in order to try to understand these plots. It would seem to be perfectly reasonable for the shape to be an exponential, rising to saturation. What is not reasonable is that the time constant should be only of the order of a year. It is therefore the placebo plot that is anomalous. The fact is that the estimator used to overcome the problem of censoring of the data produces increasing uncertainty, as can be seen from the length of the error bars. If there is any demand, a more detailed analysis could be added.

Incidentally, this is a nice example of the use of the Trojan Number. At the start of the study there were over 2,000 in each group, but at the point for which significance is claimed this was reduced by attrition to about 400.


The inconsequences of statistical fallacy

This letter in The Sunday Times says it all:

BRIAN DEER’S article Vioxx death toll may hit 2,000 in UK (News, last week) revealed that Merck had evidence from clinical trials as early as 2000 that Vioxx could damage patients’ hearts but ignored this human data in favour of studies in monkeys, mice and rats which suggested that Vioxx protects the heart. 

Estimates are 150,000 deaths and more than 400,000 non- fatal events (mainly heart attacks and strokes) worldwide. Dr David Graham, associate director of safety at America’s Food and Drug Administration freely admits “there’s blood on the FDA’s hands as well”. 

Companies and governments are taking unacceptable risks with the public’s health by relying on animal tests instead of sophisticated new techniques such as microdosing and tests involving human DNA chips and human tissues. Human-based tests could have prevented the Vioxx tragedy. 

Patient safety organisation Europeans for Medical Progress is calling, via “early day motion 92”, for an independent scientific evaluation of the use of animals in drug safety testing. In light of Vioxx, this is the only responsible course of action. 

Tony Benn
London W11 

Footnote: Tony Benn (aka Lord Stansgate or Anthony Wedgewood Benn) was a long serving left wing Labour MP. As a minister he presided over the Wedgestock era of industrial reorganisation when, in an unholy alliance with Arnold Weinstock, he instigated the destruction of large swathes of British industry, which included the elimination of many important industrial research laboratories, a feat only exceeded later by the monetarist period of the Thatcher Government. As can be seen above, he was never one to miss a passing bandwagon, or fail to offer a nice derangement of non sequiturs.


Number of the month – $253 million

The best actors in the world, either for tragedy, comedy, history, pastoral, pastoral-comical, historical-pastoral, tragical-historical, tragical-comical-historical-pastoral, scene individable, or poem unlimited.

Tony Benn in his Euphuistic diatribe describes it as a tragedy. Farce might be a better description. Consider the following:

The Texas Jury decided upon these damages against the manufacturers of Vioxx, which were based on evidence from the FDA report. Even if that report were correct, the chances of the death being caused by the drug are less than evens.

In the report the FDA noted twice that the “result” was caused not by a change in the plot of the drug takers but by “a relative flattening of the placebo curve after eighteen months, compared with the previous eighteen months.”

Did they not think it odd that patients, recruited at a variety of ages, should all become immune to a range of diseases (from a swollen toe to a fatal heart attack or stroke) within 30 months of starting a course of placebos?

Here is a plot of the numbers at risk as the study progresses. The “result” was largely controlled by the final numbers.

The expected error increases as the number left in the study declines. If they had continued the study they would have run out of patients.

A relative risk of 1.96 is not accepted as significant in real science. Exceptions can be made with double blind studies that produce highly significant results. A CI range of 1.20 to 3.19 is hardly indicative of a highly significant result, especially at the traditional but dubious level of 95%. The question of confounding factors still remains. Patients relieved of arthritic pain, for example,  can have a major change of lifestyle (this is a personal testimony).

As the report says, we all love a David beats Goliath story, but the losers in this case are those deprived of an effective pain relieving drug.

The research reported by the FDA had cardio-vascular disease as a by-product of some other study. Multi-disease studies are at risk of falling into a common fallacy related to the concept of the weakest link, both in regard to the data dredge effect and the premature termination of studies.

How could anyone possibly overlook the glaring fact that there was no difference in mortality between the two groups?

01/09/05 (publication delayed owing to a power cut in an electrical storm).


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