Number of the Month

July 2001


Wild Word Web

From time to time Number Watch receives requests to post reciprocal links with various sites, to which it rarely agrees. These often take the form of anti-anti- sites, taking a view opposing those SIFs who are against such things as tobacco, alcohol, speeding or political incorrectness in general. Unfortunately, such sites are often based on ad hominem attacks or just plain verbal abuse. Most reasonable readers are turned off by a first paragraph in which the opponents are described as crooks, scum etc. This is sometimes a pity, because often buried in there is useful information about the various cabals whose network of intrigue creates the orthodoxy under which we all suffer today.

The web is a wonderful institution, without which reasoned opposition to such palpable myths as anthropogenic global warming would go unheard and they would be propagated without resistance. There is a substantial difference, however, between polemic and invective. There is a heavy price to pay for the freedom of speech that is unique to the web, but it is a price worth paying. Number Watch informs sites to whom it posts a recommending link as a matter of courtesy, but does not expect an automatic reciprocal facility. It is not pro anything per se, other than good science. Equally, it is not anti anything, save bad science. In future, requests for reciprocal links will be ignored. Which will, perhaps, put an end to the sort of abusive correspondence that gave rise to these remarks.

Death-dealing computers

It was only in February that the number of the month ( under the heading mad, mad, mad!) was 15,000, the number of animals that had then been senselessly slaughtered in the response to the foot and mouth outbreak. This number has now risen to an appalling 3.5 million. Now, of course, the recriminations are beginning. The epidemiologists are criticising the government for not slaughtering efficiently enough.

From the Daily Telegraph, July 2nd.

Scientists clash over how to deal with infected animals
By Roger Highfield Science Editor

TWO groups of scientists, epidemiologists and vets, have criticised each other for their handling of the foot and mouth epidemic.
Vets, who questioned whether so many animals had to be killed, suggested vaccination was a better way to control the epidemic and poured scorn on computer models used by the epidemiologists.
"Unproven computer predictions" were driving government policy, according to one letter signed by 40 vets that talked of "a savage attack on what livestock remains".
Among the vets who advised the Government was Dr Paul Kitching, now with the Canadian Food Inspection Agency in Saskatchewan. He likened the computer models to "a bad X-ray where you see breaks and cancers that are not really there".
He said of the Government's scientific advisory group: "There were certainly more modellers than veterinarians. It's a dangerous precedent to take a situation out of the hands of the people whose job it is to control the disease and put it into the hands of people who have got limited experience."
The veterinary community has been accused of being territorial by the science journal Nature. The latest issue says: "Veterinary scientists, both practitioners and researchers, seem resentful of the leading role played by epidemiologists.
"The suspicion is that the complaints are motivated by a desire not to let scientific `outsiders' take credit for delivering generally sound advice."

How typical of the once great Nature to side with junk science and vilify the people who actually know what they are doing! Number Watch says three cheers for the vets.

Déjà vu all over again

One of the annoying things about being in this business is that you write something fairly obvious and months later someone produces the same thing in the form of a big news story. In January (A fishy story) Number Watch, commenting on a particularly silly scare about contaminants in farmed salmon, observed:

Salmon farming is a damned nuisance. Its products are ragged fatty abortions, which contaminate the wild variety with lice, disease and genetic corruption. It is not, however, going to kill anybody. PCBs, dioxins and furans, which are notoriously found in all fish, have probably always been there. They are the natural products of combustion, and nature invented fire long before man.

No less than six months later the Sunday Times (July 8th) comes up with a half page story headed: Fish farms turn salmon into fatty food. To rub salt in the wound the source of the story turns out to be the same nutritionist, one Miriam Jacobs, who produced the original piece of silliness. Furthermore, she uses the opportunity to revisit the whole ridiculous scare, based on almost immeasurably small quantities of contaminant.

What our Miriam has realised is, that to become a successful media don, you have to find a niche and hammer it to hell, so that grateful journalists will turn to you when faced with the terror of a blank page. 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.

The story is also a classical example of the way the media maintain their myths, as used notoriously in the propagation of the global warming scare. You create a headline that looks like something new, then you quickly slip into a repetition of the scare that you have already done, in this case by the third paragraph of about twenty.

Busy doing nothing

Zero is this month’s change in the high central bank interest rates in Euroland and the UK, in sharp contrast to the Fed, which seems to be able to keep some sort of hold on reality. Not particularly surprising as the leaders of those august institutions (Wim Duisenberg and Steady Eddie George) are notorious serial deflators, and were appointed as such. Number Watch has largely refrained from commenting on economic matters, since this is a calling that is grossly over-populated, but we appear to be in the process of entering interesting numerical times. The numbers now seem to be completely out of kilter, particularly the indices of consumer confidence and the state of industry. Politicians and journalists have been startlingly complacent over the past two years, but the signs are that even they are beginning to notice.

In Sorry, wrong number! your bending author wrote a piece on the recession that never was. Written long before the dotcom collapse, it referred to a recession in manufacturing industry that was completely ignored by politicians and the media, and went on:

As the recession developed, so the foreign investors in the UK withdrew their favours. One by one they closed down or postponed factory developments: Seimens, Fujitsu, Philips and many others retracted into their home bases. Nevertheless the stock market carried on booming, the 1999 budget was built on optimistic assumptions about economic growth. The stock market rose from one record level to the next week after week. The internet stock bubble was a particularly dominant feature. The official line was that there was no recession and there was not going to be one. Indeed, in macro-economic terms there was no recession. Manufacturing industry might be closing down, throwing people onto the streets, but the service industries were booming, the City was awash with money, fuelling an explosion of share prices that belied the actual value of the companies involved. The same thing was happening in the USA.

Of course, not only had manufacturing gone into recession, it has never come out of it. The effect of it was largely hidden behind the froth of the Internet boom, but it has in fact continued to deepen, recently at an accelerating rate. The above piece continued:

In the face of all this, the complacency shown in the West beggars belief. As late as September 1998, when I sat down to edit this section, Wim Duisenberg, the President of the European Central Bank, declared that Europe would remain “an oasis of peace”. The Bank of England ‘s Monetary Policy Committee declined to reduce interest rates, which were at a destructive 5% above inflation and business failures were rising. Manufacturing, which after two decades of neglect had been reduced to a mere 20% of GDP, but still represented 60% of exports, was entering a downward spiral, with exports at a 15 year low.

The headline in the Sunday Times (July 8th) tells us Brown warns of further world trade slow down. Ministers are of course completely different people before and after an election, but the switch from unjustified euphoria to realistic gloom is unusually dramatic. The Sunday Times goes on:

"There are risks in the world economy at the moment," Brown said yesterday in a BBC interview. "The downturn in the world economy has not reached its bottom. It is in many ways far more severe than we expected a few months ago because it has spread from America, in particular to Germany and, of course, we have no growth at all in Japan."

Who is this “we”? Include me out.

There will be many interesting numbers to watch out for over the summer – world unemployment, the US external debt, the British balance of trade (the present numbers for which would have caused panic only a few years ago) etc. The personal debt situation will also be interesting. Between all the TV adverts from compensation lawyers are those from credit pushers that are deliberately targeted at the credit-unworthy and from debt restructuring companies; targeted at the thousands who are already in a mess. Also of interest will be the performance of the vaunted service sector, particularly for nasty old cynics who doubted that a nation could survive economically by taking in each other’s washing.

Or will the US Cavalry, under General Alan Greenspan, come riding over the hill and save the day at the last moment?

Accidental circumstances

The tragic death of a little girl, who drowned in a lake while on a school holiday in France, has set the Precautionary Principle Pushers on the march, giving them a golden opportunity to elaborate the cocoons that surround our children and diminishing their lives. Before they start handing out the blame, the interfering bureaucrats, who have tied the education system up in knots, might ask themselves why so few of the youngsters are now taught to swim. Presumably the theory is that, once they are completely housebound, there will be no need for them to have skills that will help them save their own lives.

Here is a number for the PPPs to think about. According to the Royal Society for Prevention of Accidents, in 1999 5,945 accidents were caused by trousers. What do they propose to do about that?

Nuances of language

The softening up process before a new round of Kyoto talks is under way. Even the Royal Society has contributed a new bit of environmental junk. How are the mighty fallen! The Times contributes a lengthy Kyoto special, but somewhat uniquely actually gives voice to the opposition. As we have often observed in these columns, the impact of numbers is often conditioned by the verbiage that surrounds them. Here is how The Times introduces the doubters (my emphasis):

Not everyone believes the world is slowly baking its way to catastrophe. A considerable band of hardened sceptics either dispute the evidence for global warming, or say that even if it is happening, there is no proof that human beings have perpetrated it. If our contribution to climate is indeed negligible, the Kyoto protocol will stand as one of the most monumental wastes of money in human history.

That one little adjective colours all that follows. Whatever the force of their arguments, with this one word, the opponents are cast as flinty, adamant Scrooges who are unlikely to change their views in the face of reason. At least the likes of Fred Singer and Phillip Stott are allowed a small quote each. Hardened? You are unlikely to meet a jollier couple of fellows.

Number Watch will refrain from repeating the arguments. Trying to explain that two plus two does not equal five, over and over and over again, is not the most stimulating of occupations.

 World domination

Friday the thirteenth and the first anniversary of the launch of Number Watch. It also happens to be the birthday of the author, though fortunately neither suffers from paraskevidekatriaphobia. Six months previously, the end of term report noted the rather surprising total of over 3,000 hits per month that had been achieved. That report, while celebrating the worldwide nature of the interest shown in what Number Watch had to say, also mourned the fact that it seemed to be a prophet without honour in its own country. Our annual report shows that this local uninterest persists, though the number of hits per month has almost doubled. Using the statistical methods established by modern epidemiology, we can therefore proudly claim that by the end of the decade everybody in the world will be reading Number Watch.

A Collector's item

While on the subject of epidemiology, when you are in the business of monitoring and commenting on the outer reaches of statistical nonsense, it is easy to become blasé about it all. Every now and then, however, there comes along an example of the insouciance of  that branch of non-science that simply takes your breath away. One such from Canada (spotted, of course, by provides an abstract that deserves full reproduction:

 Epidemiology and Cancer Prevention

Lifetime residential and workplace exposure to environmental tobacco smoke and lung cancer in never-smoking women, Canada 1994-97

Kenneth C. Johnson, Jinfu Hu, Yang Mao, The Canadian Cancer Registries Epidemiology Research Group

Surveillance and Risk Assessment Division, Centre for Chronic Disease Prevention and Control, Health Canada, Ottawa, Ontario, Canada

Although the risk of lung cancer among never-smokers living with a spouse who smokes has been extensively studied, the impact of lifetime residential and workplace environmental tobacco smoke has received less attention. As part of a large population-based case-control study of lung cancer, we collected lifetime residential and occupational passive smoking information from 71 women with lung cancer and 761 healthy control subjects, all of whom reported being lifetime nonsmokers. The adjusted odds ratio (OR) for lung cancer associated with residential passive exposure only was 1.21 (95% confidence interval [CI] 0.5-2.8). Although more years of and more intense residential passive smoke exposure tended to be associated with higher risk estimates, no clear dose-response relationship was evident. The OR for women with passive exposure as a child and as an adult was 1.63 (95% CI 0.8-3.5) and for those only exposed as an adult 1.20 (95%CI 0.5-3.0). Exposure to environmental tobacco smoke only in the workplace was associated with an adjusted OR of 1.27 (95% CI 0.4-4.0). Risks associated with increasing occupational exposure year tertiles were 1.24, 1.71 and 1.71. Total smoker-years of residential and occupational exposure combined resulted in a statistically significant trend (linear test for trend p = 0.05) with ORs for tertiles of exposure of 0.83, 1.54 and 1.82. Our results are consistent with the literature suggesting that long-term, regular exposure to either residential or occupational environmental tobacco smoke is associated with increased lung cancer risk in never-smoking women. © 2001 Wiley-Liss, Inc.

 As one would expect, the results of this study are statistically insignificant on a grand scale (if you will forgive the oxymoron), but the beauty of this specimen is in the detail. Not only do the authors quote a risk ratio that is considerably less than the barely acceptable value of 2, they also quote a ninety five percent confidence interval. They are actually telling us that they can state, with 95% confidence, that exposure to tobacco smoke actually halves the risk of lung cancer. The wide interval derives, of course, from the derisory size of their sample, 71. Regular number watchers will also note the dependence on anecdotal evidence and the lovely "significant" linear test for trend from such a sample size. Laugh you may, but this stuff will all go into the accumulated evidence on the evils of passive smoking.

Sinister bowel movement

Your bending author thought he was suffering from delusions brought about by reading too much epidemiology when he saw a story about the relationship between disease and left-handedness, but it had disappeared from the BBC text service when he went back to check the details. Anyway, a correspondent from the UK reported the same problem, which made us both feel a bit better. Does this mean that even the BBC is capable of embarrassment?

Well the story eventually turned up again from Reuters (via, of course). It turned out to be from a data dredge conducted at University College Hospital Medical School and, indeed, claims that left-handers are twice as likely to get inflammatory bowel disease as the rest of us.

The Trojan number (of people in the study) is 17,000, but according to the rate of incidence of the disease stated only about 50 of these would have had the bowel problem. Since only about 11% of people are left-handed, the expected number at random would be about five, so with a claimed risk ratio of two, the total recorded must be about ten.

 We can illustrate the probability of such an observation happening by accident with a plot of the Poisson distribution for an expected value of five:

As we can see, ten would be an unusual observation, but not all that unusual (about a 1% chance of occurrence) particularly in a data-dredge, where you might be looking at hundreds of combinations of factors and diseases.

A few readers have asked for an explanation of risk ratio and Trojan number. This is an excellent illustration of both and a confirmation that you can get a silly answer even at a risk ratio of two.

One man’s fishy is another man’s Poisson

As we have often observed on these pages, the world of numbers is full of little ironies. Just when the University of Oxford came under blistering attack from the retiring president of Harvard, Neil Rudenstine, for its slide into under-funded mediocrity, it launched its own little essay into junk science that would even make the junk world champions blush. The champions are, of course, the Harvard School of Public Health, whose catalogue of fatuous scares and breakthroughs usually leaves the competition standing.

Dr. Michael F. G. Murphy and his “team” have come with an observation of such mind-blowing banality and inconsequence that it merits some sort of award. The headline from Reuters proclaims Childhood cancer less common in twins, but the details of the story are well worth a browse by any aficionado of scientific garbage. The claim of a 20% shortfall of cancer in twins is based on their observation that their sample only produced fifteen cases, when in comparison with the general population they expected nineteen. To judge the significance of this we have to turn to our old friend Poisson. The Poisson distribution for an expected value of nineteen is as follows:

Clearly, the observation of fifteen cases is just about as unsurprising as you can get. In fact the probability of getting fifteen or less is about 21%. Even the EPA itself has never operated on a significance level greater than 10%, and that only once in its notorious passive smoking fraud. The search for possible explanations of the “mystery” in the press story is really quite quaint when you observe that the phenomenon is no more mysterious than some men being under five foot nine in height.


A reader has asked why we apply Poisson’s distribution in this type of case. It is named after the great French mathematician Simeon Poisson (1781-1840) and is one of the most beautiful pieces of statistical mathematics, because of its simplicity. It applies only in the case of relatively rare events, but in such cases, unlike with the binomial or normal distributions, you only need to insert one parameter into the formula to be able to obtain the probability that any given number of instances will occur. It was applied famously and successfully to the number of cavalryman killed by horse-kicks in one year. The parameter to be inserted is the average or expected number of occurrences. In this case and the one above, the event is sufficiently rare for Poisson to be expected to apply accurately. We know the probability of cancer occurring in the general population of children of the same age, so multiplying this probability by the number of twins we get the published expected number of nineteen. Inserting the parameter nineteen into the Poisson formula then gives us the probability of any particular number of instances occurring.


Regulars at Number Watch will readily accept that Californians will believe almost anything, but the number that astonishes is the price the inhabitants of the Dark State of Insanity are prepared to pay for hogwash. A survey of the hoary old chimera of electro-magnetic fields cost them a cool $7 million. Please read it; it is nothing less than a masterpiece. It has the whole Californian dream – expensive litigation, “trained” epidemiologists, empty scares galore and much, much more. Among the informatic delights of this report you will find such gems as:

It is "more than 50 percent possible" the scientists reported, that EMFs at home or at work could cause a "very small increased lifetime risk of childhood leukemia, adult brain cancer, and amyotrophic lateral sclerosis known as ALS or Lou Gehrig's Disease."

It is more than 50 percent possible that EMFs at home or at work could cause a five to 10 percent added risk of miscarriage.

Would anyone care to try to translate this last one into English and mathematics (without resorting to bivariate distributions)?

 There is more

"It is 10-50 percent possible that residential or occupational EMFs could be responsible for a small increased lifetime risk of male breast cancer, childhood brain cancer, suicide, Alzheimer's disease, or sudden cardiac death."

"It is very unlikely - two to 10 percent possible - but not impossible, that residential or occupational EMFs could be responsible for even a small fraction of birth defects, low birth weight, neonatal deaths, or cancer generally."

And the crowning glory

There is a chance that EMFs have no effect at all.

It's lucky that those nice environmentalists have managed to engineer all those power cuts. Think of all those lives that might be 50% possibly saved when Californians sit in the dark, cooking over candles, free from all those nasty fields.

The biter bit

Another nice little irony from a data dredge carried out in Wagga Wagga (a name that brings a smile to the faces of oldies in Britain, where it was made famous by a popular Australian comedian, Bill Kerr). Polyunsaturates double the risk of asthma in young children. A product of the great cholesterol scam, polyunsaturates have spawned a huge industry selling products with silly names (like I can’t believe it’s not butter) to the chattering classes. The Trojan number is a little disappointing, almost 1,000 parents having completed the questionnaire, but according to The Times (July 19th) polyunsaturates account for about seventeen percent of the cases studied. Since we are told that one in five suffered from asthma we may deduce that fewer than 34 children actually fitted the bill.

Although the study is nonsense on a statistical basis, it is interesting to conjecture on possible confounding factors. The chattering classes are more likely to seal their children up in sterile cocoons and feed them all the dietary nostrums that their gurus specify. Is it any wonder that their immune systems fail to develop properly?

Which all leads us to an unusually encouraging thought for the month, adapted from the Gospel according to St Matthew:

All they that take the junk shall perish with the junk

Power mad

O wad some pow’r the giftie gie us
To see oursels as others see us!

OK, so you don’t expect everybody to be able to distinguish between a quantity and its rate, but when reporters write about technical subjects, we are entitled to expect them to do a little homework.

On Yahoo news, July 19th we read:

Calif. Selling Off Surplus Power

By KAREN GAUDETTE, Associated Press Writer

SAN FRANCISCO (AP) - Unseasonably cool weather has turned the California power crisis on its head, with recent energy shortages giving way to a glut that's prompted the state to sell excess power at a loss.

In some cases, traders say, energy bought at an average of $138 per megawatt is being sold for as little as $1 per megawatt.

You do not sell power, you sell energy. Power is measured in watts and energy is measured in watt-hours (each of which is 3,600 joules in SI units). Selling power is like claiming your travelling expenses in miles per hour.

In the immortal words of Ollie, the citizens of the dark state of insanity are entitled to say to their rulers “Here’s another fine mess you’ve gotten us into”. The fundamental reason, however, is not that they are buying energy cheap and selling it dear, which they are. It is that they have not made provision for short-term peaks and troughs by providing power sources that can be switched on to the network at short notice. These in general will be nasty hydrocarbon burning plants and not eco-friendly, bird-slicing windmills, or even nuclear installations, so they are not welcome in California. Now that global warming has failed to deliver the scorching summer so confidently predicted, the air conditioners have mostly remained switched off. The energy that California thought it would need is surplus. It cannot just be stored and saved for another day, it has to be sold or wasted.

And the cup is awarded to -

 The Number Watch cup for the first major story of the silly season has to go to Professor Deborah Withington of Leeds University. Furthermore we add the blue riband for re-inventing the wheel. Believe it or not, she has rediscovered white noise (Sunday Telegraph, July 22nd). Not only that, her “new sound” is being taken up by companies all over the world. Big names include Tesco, BOC, Volvo and Yamaguchi.

White noise has been used as a signal source by electronic engineers since the foundation of their subject. The reason is that it is uncorrelated (its autocorrelation is a delta function) which makes it ideal for applications as system identification and location. Engineers tend to prefer pseudorandom noise for statistical reasons. Your bending author has been writing papers and books about the topic for over forty years, in addition to providing consultancy to companies involved in such areas as sonar location. In fact, he was so obsessed with it at one time, his research students called the pseudorandom binary sequence "the Brignell signal". This author's surround sound system has provision for a white noise test signal to be cycled round the five speakers, because of the well known ease of locating such a sound source.

Professor Withington adds:
“I believe it’s not only a world-beating British invention, but it is going to save thousands of lives every year.”

Number Watch withdraws and stands back in awe.

Blind faith

In the kingdom of the blind, the one eyed man is king.

So, nearly 180 nations have come to an agreement to recognise the global warming myth. It is tempting to comment that this is bizarre and unique in human history. But men have not only always clung on to their myths; they have tortured, burned and killed to enforce them on others. What is more, the more implausible the myth the more firmly it is adhered to, and there are few myths less plausible than man-made global warming.

George W in his isolation might wish to consider an allegory in the form of an H G Wells short story called The country of the blind.

The protagonist stumbles upon a virtually inaccessible valley in which the entire population is eyeless. He immediately thinks that with the advantage of sight he will become the de facto ruler of these people. They, however, become increasingly concerned about his bizarre behaviour and his claims to have perceptions beyond the norm. He is taken into custody and physicians decree that his madness is caused by two lumps of jelly in his face that appear to be connected to his brain. The only cure is to remove them surgically.

The most extraordinary thing is that the world should opt for such a pointless act of economic self-destruction when it is already standing on the edge of an economic precipice, and has been for the five years since the Hashimoto government in Japan launched its enormous and futile tax hike. It seems that only a few individuals, such as Alan Greenspan, actually know what is going on in the world, though there are at last signs that the complacency in Europe is beginning to get a bit shaky.

 Déjà vu all over again, again

Sometimes it is actually gratifying when someone repeats what you have been saying for years. Here is a quotation from David Smith’s piece “Going down together” in the Sunday Times, July 22nd:

Stephen Roach, Morgan Stanley's chief economist in New York, declared last week that the world economy was officially in recession, with growth having slumped to half its long-term rate.

"The global recession of 2001 is very much a by-product of the previous downturn of 1998," he said. "Indeed, I would argue that the two downturns should be viewed more as a continuum of one long and drawn-out global business cycle - one that could go down in history as the world's first recession of this modern era of globalisation.

Markets and their journalistic acolytes are so imbued with short term thinking that they find it difficult to conceive of any phenomenon lasting more than a few months. How was it that the recession begun by the Japanese tax-hikes five years ago seemed to turn into an economic boom against all the odds? It was all, of course, illusory, being based on the communications bubble. There were many factors involved: the mores of the venture capital industry, the naiveté of investors, particularly in America, the reluctance of governments to face up to reality, particularly with elections looming, the willingness of individuals and nations to take on debt and, above all, corporate behaviour. Which brings us to the number of the month.

Number of the month

The number of the month is 30,000,000,000

The reasoning is explained in this e-mail from Professor David Barron:

A candidate that comes to mind is 30 billion pounds sterling.
This is

a) the size of the cash mountain that Arnold Weinstock accumulated for GEC

b) the size of the deficit that his successors have accumulated
(after re-naming the company Marconi and spending all the cash they inherited) in an effort to become a world leader in telecoms.

c) the size of the deficit that BT accumulated in an effort to
become a world leader in telecoms.

d) (after rounding) the market value of BT at the time that its debt hit 30bn.

The phrase 'the curse of telecoms' comes to mind.



 P.S Imagination boggles that Marconi should ditch all the defence work they inherited from GEC. All those cost-plus nice little earner contracts ...  Whom the Gods wish to destroy etc.

It's a mad world. I think I shall be glad to be out of it when my time comes.

Yes, the reason that the recession was hidden from view is that corporations like Marconi and BT in the UK, and many similar in the rest of the world, went on a buying spree. In particular, they all joined in the hysteria that accompanied the auctioning of third generation mobile licences. Markets rose out of the sheer euphoria created by the acquisition mania that valued companies way above their real values.

Among those who will be caught out is the British Chancer of the Exchequer , Gordon Brown, he who was going to get rid of “boom and bust” with his prudence that switched to a spending spree as the election approached.

By the way, none of this is hindsight. It is all in Sorry, wrong number!