Number of the Month

October 2001

Reading between the lines

The BBC’s love affair with junk science seems to be an enduring one. Parenting link to asthma yells the headline. The Trojan number (of children involved in the study) is an unimpressive 150, but the number contracting asthma is given as 28%, which is 42 children. We are further told that those receiving “poor” parenting are more than twice as likely to get asthma (let’s call it twice). We are not, of course, told what proportion of children receive “poor” parenting. Let us be generous and guess at about one quarter. This would all imply that about 17 of the asthmatic children received poor parenting against 21 of the non-asthmatics. The expected number among asthmatics if there were no effect, would be about 10. So the whole claim is based on about seven excess children. Readers of Sorry, wrong number! will note that The Magnificent Seven also turned up in two other fanciful studies. There’s one for the numerologists.

Needless to say that it is all based on anecdotal evidence and value judgments on what used to be called, in pre-PC days, parenthood.

Phony phone physics

The biggest epidemiological study ever is being carried out all over the world, where over half the population in advanced economies are using mobile phones. There has been no outbreak of brain tumours. Yet epidemiologists insist on carrying out piddling little studies in the search for a good scare and their time in the limelight.

It was inevitable that the con-men would climb onto the band-wagon. The BBC again reports that for a mere eighteen pounds a company called Aulterra is offering a sticker that will neutralise radiation from the phones that can damage DNA.

The story really is a collector's item for students of the modern version of snake-oil salesmanship:

Aulterra is an organic compound from a crystalline rock found by Mr Dandurand in 1995.
He found that the substance reacted with the earth's magnetic fields and neutralised radiation from soils.
He told BBC Radio Scotland's Good Morning Scotland programme that the sticker would offer mobile phone users the opportunity of a safeguard if they saw fit.
"The easiest way to describe it is that it neutralises any damaging effect from electro magnetic waves from a cellphone on human DNA," Mr Dandurand said.
"That is what it does. How it works is that it allows the wave to become more coherent or more like a laser beam and less like a flashlight and more of a focus coming from your cellphone.
"Therefore it does not damage the biological system as it goes through it.

 If you are wondering where the number is in all this:

If you put the sticker on the mobile phone then the DNA recovers 100% every time you carry out the experiment.


Trojan Number

Several correspondents have asked for more information on the origin and meaning of the term Trojan Number. The explanation has been moved to the FAQs here.

A voice for science

The great contribution that science has made to human thought is the development of the scientific method. Though this is not easily encapsulated, it revolves mainly around the idea of the critical test. One of the features of life at the turn of the century has been the large scale abandonment of  such ideals and perhaps a prime example is the treatment of  new variant CJD. This has shown the effects of many of the pressures of modern scientific life the scramble for funds, the lust for media coverage and the urge to join a consensus. Your bending author wrote in Sorry, wrong number! about  vCJD :

What also worries me is that I had thought of at least one alternative hypothesis  that was certainly not damaged by this new observation : that the “new” strain of CJD  was always there, but nobody thought of looking for it.

This was in relation to the case of a victim who had been a vegetarian since before the advent of the bovine form of the disease. This would appear to be a major set-back for the orthodoxy, but the "scientists" chose to disregard it. All hail, then, to a new lone voice for science in this affair, one George A Venters . He dares to voice concern that the establishment has been precipitate in plunging into one particular hypothesis that happened to be in tune with politically correct thinking. Without a great deal of confidence Number Watch joins in his plea that there should at  least now be a debate on the matter.

Another load of old bull

Reader Adam Bernard draws attention to another of those tatty stories based on astrology. We are told that 95% of Taureans are likely to indulge in online shopping compared with only 83% of Aquarians. This depends on a  long standing fallacy that arises from the statistics of extremes (for a mathematical explanation see August). We expect, of course, no better from astrologers, whose lucrative business is based on gulling the naive and suggestible, but the frequency with which so-called scientists are climbing onto this particular bandwagon is becoming alarming.  For some further thoughts on such matters see Of birthdays and clusters.

Who lives by the spin shall perish by the spin

The first Number of the Month of this year was 1083, which was the number of so-called spin-doctors employed by the British Government, a wholly new phenomenon in a nation that had traditionally boasted an impartial civil service. This has all come to a bizarre fruition at a time when Tony Blair, the mill master of the modern spinning industry, was in the process of achieving apotheosis as a born again Winston Churchill. Even some of the most cynical of American correspondents to Number Watch had come to the conclusion that he was not such a twit after all, following his unstinting support of Dubya’s just war against terrorism. Nastier old cynics in this author’s village pub opine that the disaster was an ironic godsend to a leader who was heading at high speed for the domestic buffers.

A rather large cat was let out of the bag by one Jo Moore, known in the trade as Spinning Jenny, whose e-mail to colleagues was inadvertently leaked to the press. On the day of the New York atrocity it advised that this would be a good time to “bury” stories that were embarrassing to the Government. The depth of hypocrisy at the heart of British Government, of which this incident is so symptomatic, is revealed in startling relief by reformed super-spinner Charlie Whelan in the Sunday Telegraph. His article merits preservation as a historic document. It tells everything you need to know about New Labour.

As it happens, Jo had at the time a rather embarrassing body to bury. This was the cunning plan to nationalise Railtrack without compensation to its shareholders, many of whom were its employees. Born out of a singularly incompetent privatisation by the Thatcherites, Railtrack had through its short history reeled from crisis to crisis, exacerbated by the hostile attitude of the new Government. Jo managed to offend the Sunday Times by telling one of its reporters that he would look like a “fucking idiot “ if he published a story that her boss, one Stephen Byers, was planning to kill off Railtrack and make off with the assets, which he did the very next day.

Byers stood by his special adviser (paid £51,000 a year by the taxpayer). Commendable loyalty you might say, except that he had only just sacked a civil servant in the Department of Transport who had refused to spin against Bob Kiley, the London Transport Commissioner. It was Byers who gave rise to this author's rant last year in paranoid corner. His career has been marked by similar distinction ever since he gave up his former career in education, a history that led to a snobbish but delightfully apposite opinion in the Saturday Telegraph:

City Comment is scornful, saying that this week Railtrack shareholders discovered what it must be like to live in a Banana Republic where a jumped up polytechnic lecturer can steal your property. They have learned a brutal lesson about Cool Britannia and more importantly when Tony Blair returns from saving the world and sees Stephen Byers' handiwork, he may learn one too.

What has this all to do with Number Watch? If you look at the opening page its mission is to nail lies. We expect politicians to lie, but the British Government is unique in basing its whole philosophy on prevarication and mendacity. Like the long-lived Government of Margaret Thatcher it is sustained not by its own worth, but by the complete absence of a credible alternative.

Beware the Jabberwock

Cross your bridges when you meet them.
Calmly heed each warning drum.
The troubles that seem hardest

are the ones that never come.

Your bending author went for his annual flu jab this month – a sensible precaution (in one humble opinion) against a major known and avoidable risk. In this modern world, however, it is becoming more and more difficult for the ordinary punter to distinguish between the sensible and the insensate.

The Boston Globe reports, in a remarkably perceptive article by Patricia Wen,

The United States is in the midst of the biggest bioterrorist attack in its history. One man is dead and at least a dozen others have been exposed to anthrax, causing a rush across the country for the one approved treatment of the rare disease. 

Yet, even as Americans clean out drug store supplies of the anthrax-killing antibiotic, Cipro, public health officials know there is something even more important that they won't get - flu shots. 

Plain old influenza and pneumonia kill 67,000 Americans each year, yet millions of people who are most vulnerable to the diseases don't get the vaccine that could protect them. With so much focus on anthrax and other exotic diseases this year, federal health officials fear immunization rates may be lower than usual……...

Do read the rest of this article. It is a tonic.


The greatest ally that international terrorists have is the western media. They can be relied upon to magnify any minor and cowardly coup into a devastating threat to life as we know it. Let’s face it, there’s nothing like a dose of hysteria to sell newspapers and television advertising. Commenting on the aftermath of September 11th, Number Watch expressed the pious hope that people would turn from imaginary dangers to real ones. Some hope!

The epidemiologists continue to pour out their tacky junk science. Their branch of science has become so degenerate that they are now unlikely to do anything else, but it is the endless appetite of the media for scares that encourages them. Typical was a story from the US published in The Times: Cancer risk for women on night shifts. It exhibits all the usual clichés – Trojan numbers from data dredges, silly risk ratios (as low as 1.08) ad hoc theories and of course the mincing language:

  several studies had indicated that night shift work could be linked to breast cancer

A number of studies have now hinted that night shift work could affect breast cancer risk

There is clearly a need for more research to clarify this effect

night shifts may also increase the risk of some types of male cancer, such as prostate cancer

The whole thing is a farrago of unmitigated rubbish. Why do readers of a once great newspaper have to put up with it? But there it is, alongside real and terrible events, dulling the senses and repetitively crying wolf, until ordinary folk are unable to differentiate between real matters of concern and empty scares.

They never give up

Two stories juxtaposed on the BBC morning television news, 19th October. The first was about the struggle for rural pubs to survive and the dire effects on villages when they close, while the second was a call for a Los Angeles style smoking ban in all bars. In these columns and the associated book, frequent mention has been made of the EPA study into passive smoking. This needs no apology, as that study is the pinnacle of fraudulent science. It actually demonstrates that passive smoking is harmless, but the figures were crudely manipulated to suggest otherwise. The British equivalent of the EPA is the CIEH, and their annual conference received the results of new “research” by one Maurice Mulcahy, an environmental health officer from Ireland, who states that the average barman smokes the equivalent of half a cigarette every day. Do they not realise that we have been hearing and dealing with this sort of estimate for years, or do they believe, like the average newspaper editor, that most punters have a memory no longer than a few days? Incidentally, the BBC slipped in the big lie that 300 of the British die of passive smoking every year – no evidence, just the bald lie. Like the EPA’s 3,000 Americans they are an outrageous fabrication.

For those who do not accept these truths we offer our Ten Commandments as a way to conduct their lives.


For those who were affronted by the numerological nonsense spewed out by Uri Geller and the like, following the terrorist attacks (see September), here is a riposte from one David Pawson, which arrived indirectly from e-mail. 

Oh my God! How worried should I be? There are 11 letters in the name "David  Pawson!" I'm going into hiding NOW. See you in a few weeks.
Wait a sec ... just realized "YOU CAN'T HIDE" also has 11 letters! What am I gonna do? Help me!!! The terrorists are after me! ME! I can't believe it!
Oh crap, there must be someplace on the planet Earth I could hide! But no  ..."PLANET EARTH" has 11 letters, too!
Maybe Nostradamus can help me. But dare I trust him? There are 11 letters in "NOSTRADAMUS."
I know, the Red Cross can help. No they can't... 11 letters in "THE RED CROSS," can't trust them.
I would rely on self defense, but "SELF DEFENSE" has 11 letters in it, too! Can someone help?
Anyone? If so, send me email. No, don't... "SEND ME EMAIL"has 11 letters....
Will this never end? I'm going insane! "GOING INSANE???" Eleven letters!!
Nooooooooooo!!!!!! I guess I'll die alone, even though "I'LL DIE ALONE" has 11 letters.....
Oh my God, I just realized that America is doomed! Our Independence Day is July 4th ... 7/4 ... 7+4=11!
~ Dave
PS. "IT'S BULLSHIT" has 11 letters also.

 Letters from America

Our regular correspondent from Puerto Rico, Jaime Arbona, has been taking a break from numerology by finding anagrams for Number Watch. They appeal to your bending author, who is a lifelong setter and solver of crosswords. Here is a selection of the best:


And last, but not least:


They never give up (2)

Should anyone doubt the claim in Another load of old bull (above) about the frequency with which so-called scientists jump on the bandwagon that is the birth month fallacy, within a week of the posting of the paragraph a fine example of the genre turned up. The article is entitled Does month of birth affect risk of Crohn's disease in childhood and adolescence? Published by the BMJ (naturally) and publicised by the BBC (who else?) it purports to show that there is a relationship between the month of birth and the occurrence of the disease. Here is the graph upon which it is based.


The Trojan number is 627 cases considered, but just to add a bit of obscurity the graph is plotted as cases per 10,000 births. This has the effect of an arbitrary multiplier of 0.49 before plotting. Let us take the numbers from the graph (rounded to the nearest integer) and see what they tell us.

First, let’s get rid of the chartmanship by restoring the zero and removing the fitted curves.

You might well think that the evidence for periodicity is now somewhat less than convincing, but just how significant is this variation?

The numbers add up to 307, the largest is 30 and the smallest is 19, while the average is 25.6 and the scatter (standard deviation as a fraction of the mean) is about 12%.

What would we expect to get if we put 627 objects into 12 boxes at random? Well, considering each month individually, it is a simple binomial distribution with n=627 and p=1/12. Including the arbitrary multiplier, the expected average is then np, which is 25.6. The theoretical scatter is about 19% of the mean. The expected (characteristic) largest value is 30 and the expected smallest value 21.

Thus the monthly variations in the study are actually slightly less than we would be entitled to expect at random.

Readers who have Mathcad® can easily simulate this process with 0.49.rbinom(12,627,1/12). Here is one such simulation


You might be surprised just how often you can see an apparent periodic pattern in there. The authors note that a similar study in Britain revealed a peak in the first half of the year. They also note that their peak/trough ratio of 1.58 is larger than the British 1.14 (95% confidence interval 1.01 to 1.30). As we can see from the above, the theoretical expected value of the largest/smallest value is 1.42. These authors use a test called chi-square to demonstrate the significance of their results. This is a very friendly form of test, since the pattern they think they see is built into it.

One could start curve fitting to the random data, but it all gets a bit boring. However you look at this statistical molehill it refuses to turn into a mountain.

So what is the end result of all this? Five authors have another paper to their names and CVs (but note the question mark in the title). The BBC has generated yet another non-news story (but note the weasel word may). The faltering reputation of the BMJ and its referees is even further diminished. Apart from a few eccentrics, such as the author of Number Watch and its regular readers, nobody cares and nothing will be done about it.

And from the Ministry of Truth

One of the notable areas for fraudulent numbers is in policy on speed control on the roads (see for example The big lie yet again in December, Double double toil and trouble in April or Target practice in June). The latest toy for ministers and bureaucrats is the speed camera. Reader Alwyn Davies provides a startling example of statistical chicanery from figures of road fatalities issued by the bureaucrats to justify a massive investment in these devices, following a trial introduction in 2000:
























































Thames Valley


















South Wales









They claim a “huge” reduction of 49 fatalities between 1999 and 2000 when the cameras were introduced. We are not supposed to notice that there was an almost equally huge increase of 44 fatalities between 1998 and 1999, for no apparent reason at all. Thus the change over two years was less than 1%, monumentally insignificant.

Excess speed has been shown frequently to be a minor cause of accidents. The fact is that Big Brother wants to expand his watching of you and, if it requires a big lie to justify it, that is what you get.

Return of the Finger Prince

It really beggars belief, but the Sunday Telegraph devoted a whole broadsheet page to a story carrying the headline Is your son at risk of heart disease? Look at his hands. It actually took two people to write the story, though why is difficult to understand, as the next day the Daily Mail carried exactly the same story obviously from the same press release. Junk science is always, of course, published by press release before scientific journals. Regular readers of will remember Liverpool University’s Dr John Manning as the great expert on manual ejaculation matters. For it was he who in 1998 established that men with asymmetrical hands produced fewer sperm, and he did it all with a sample of only 60 men.

Now he is getting really ambitious and his Trojan number has risen to 151, which is the number of heart disease victims he subjected to digital monitoring. Complete with diagrams, the article demonstrates that one’s cardiac health depends on the ratio of the length of the index finger to the ring finger. At a ratio of 0.9 you are unlikely to have a heart attack before your mid seventies. At 0.97 you are unlikely to have a heart attack before the mid fifties, but at 1.00 you may be at risk from the mid-forties. There are, of course, no numbers given that would enable the claims of statistical validity to be examined, so we must look forward to the heralded publication in the British Journal of Cardiology, but it does illustrate our injunction on the way to become a successful media don (see Déjà vu all over again): whether it is pylons, mobile phones, red meat or the humble salmon, the rule is to establish your gimmick then plug it for all you are worth. Dr Manning’s gimmick is to put two fingers up to science.

In the piece Letters from America above, one of the anagrams of Number Watch was censored on the grounds of taste, but as a tribute to Dr Manning’s contribution to the advancement of science we re-introduce it:

The stupid audacity!

From the Daily Telegraph;

Morris attacks class divide at university
By John Clare, Education Editor
(Filed: 23/10/2001)

IT was indefensible that pupils from middle-class backgrounds were five times more likely to go to university than those from working-class homes, Estelle Morris, the Education Secretary, told vice-chancellors yesterday.

She said: "Universities are not a birthright for the middle classes. Richer kids are not brighter than poorer children." However, she acknowledged that middle-class children were four times more likely to pass three A-levels than those from lower socio-economic backgrounds………….

Read on

Your bending author grew up half a century ago in one of the poorest parts of Tottenham in North London. He went to one of the finest schools in the world, which was subsequently gratuitously destroyed by a Labour Government in an unprecedented act of vandalism (not to say economic incompetence) all in the name of social engineering. He went to university, at no cost to his family, to take bachelor’s and doctor’s degrees, and spent a life time in higher education teaching young engineers, many from similar backgrounds to his own, to contribute to society.

The present Labour Government have eliminated university grants and instituted loans and fees that would have terrified any working class family in former times. They have deliberately and cold bloodedly savaged academic standards, so that anyone who is prepared to pay can get into almost any university, whether they are capable of benefiting (and contributing) or not, to take courses that are often worthless by any traditional measure.

It is difficult to put into temperate words one’s reaction to the arrogant, insensitive, patronising, self-justifying  pap from this appalling person. We are now going to have a “fundamental review” and by now everyone knows what that means. It is characteristic of Labour governments that, when they are up against it, they try to start a class war in education as a diversion.

O tempora, O mores!

Law of the bungle 

Oh, my prophetic soul!

 When the September offering opened with a rant entitled This is the dawning of the age of incompetence, it could not be foreseen that subsequent events would validate the claim quite so thoroughly, but they certainly did. There could be no clearer illustration than The case of the wrong brains. Unbelievably, long term research into the possibility of BSE entering the sheep stock turned into a fiasco when it was discovered that the scientists had been looking at cattle brains by mistake. The whole thing was made worse by the subsequent attempts by politicians and bureaucrats to spin their way out of trouble. To make it even worse, plans had been formulated to cull all 40 million sheep if the result was positive. This would have made the holocaust of four million animals destroyed so far look like a vicarage tea party. The murderous tendencies of the politicians and bureaucrats, egged on by the epidemiologists and their computers, have transcended all bounds of human reason.

Why should this all happen now? One reason is:

The purge of the scholars

Your bending author is one of the many in the British professoriate who have elected to take early retirement, rather than stay on and witness the willful debauching of everything they have devoted their lives to. The ones leaving are nearly all traditional scholars, while their replacements are the new “stars”. For academics are now judged solely by how much money they bring in. It is the ultimate triumph of Thatcherism. As in much of the rest of society, the emphasis is on immediate gratification. All those adjectives that used to accompany the word scholarship, such as meticulous and painstaking, have been dismissed into the oblivion of redundant archaisms. We are continually being caught out by major crises because the wealth of specialists, who spend their lives beavering away at some obscure branch of science, are no longer there. BSE, vCJD, anthrax are all examples of events that have taken the world by surprise. The setting up of instant laboratories is a long way from being a substitute for having in place facilities and knowledge that have built up over generations. Gaffs that were once considered unforgivable are now dismissed as peccadilloes only to be expected. 

The money saved by offloading all those old scholarly fossils is now steered into instant institutes, designed to gratify the predilections of the bureaucrats who hold the purse strings.

A classical example of all this is the Climate Research Unit at the University of East Anglia. There are people high in the British civil service whose first allegiance is to Greenery. As a result tens of millions of pounds have been diverted from real research into manufacturing evidence for global warming. That indefatigable Lone Ranger,  John Daly , has nailed what he kindly calls the lack of quality control at CRU. Again the whole effect was exacerbated by the attempts to spin out of a corner. It is no accident, but the same phenomenon that produced the case of the wrong brains. The thrust is for instant fame. It is immediacy that matters, headlines and the esteem of the paymasters, while the careful and respectable obscurity of a life of real science is no longer regarded as a desirable proposition. Mislabelling samples and mishandling data were the capital crimes of real science. They might be just forgivable in a lone researcher, but in publicly funded bodies with huge complements of staff they are not.

Incidentally, there is an interesting theory for the causes of exaggerated claims of global warming here, but let us not allow reason to get in the way of a good story:

 Suppressio veri suggestio falsi

Philip Stott draws attention to a remarkable supplement to The Observer (28th October), which is part of the softening up process for the next round of climate change talks. He suggests that we respond. Here is this author's effort.


I have just read your supplement on Climate Change. This is a unique document. In the whole tawdry history of junk science there had never been such a collection of one-sided, mendacious, selective and tendentious propaganda. The most offensive lie is that "Almost all scientists are now agreed that human induced climate change is under way".

John Brignell

The are many quotations to savour in the Observer travesty. My favourite is "The IPCC is quite honest about this."


Number of the month

In honour of all the sheep whose lives were only saved by the discovery of an unforgivable blunder, the number of the month is 40 million.