Number of the Month
Thanks you to those who enquired, but your bending author is alive and well and living in Wiltshire. Preparing and delivering a major public lecture took up a great deal of time and, owing to a problem with chronic neck pain, computer time has to be rationed at the moment.
Talking about pains in the neck, thanks also to those Australian readers who felt the need to apologise for the ad hominem attacks emanating from that country. There really is no need – insults from some sources are, in effect, compliments. When people are reduced to name-calling they have already lost the argument.
So much has already happened in the world of silly numbers this month that there is a lot of catching up to do, which is the immediate task.
Readers of the Number Watch Forum will have noted another outbreak of the birth month fallacy, but there was an interesting variation taken up by the media (e.g. The Times of December 13th). This was a rather out of date story about the non-randomness of the British National Lottery. The claim was that ball number 38 had appeared more than it had a statistical right to.
“The chances are under one percent!” cries the statistical expert.
Well, Guv, the fact is that chances under one percent are occurring all the time. They are the ones that get written about. Nobody writes about the other ninety-nine and a bit percent (except for epidemiologists, of course).
Anyway, time has moved on and there are now 870 draws in the statistics and 38 has appeared 137 times. Here are the corresponding distributions for the expected occurrence of the individual balls and the largest value among 49 (as we did for the anorexia study). The probability of the claimed event is now above 2%. Besides which, there are ten different machines and 22 different sets of balls, so what do our academic heroes mean by calling for ball number 38 to be physically examined, and what property of the ball did they think would have a dramatic effect on the probability of it going through the hole?
A flying fish was found in British waters. Interpretation? Evidence for global warming.
Russian Waxwings were seen in Britain. Interpretation? Likelihood of a white Christmas.
That’s the way stuff
Following the discussion of the lottery above, your bending author has been cogitating on the fact that unlikely things are happening all the time, whereas some statistical operators seem to regard a probability of 1% as being virtually impossible. What is the a priori probability of the following happening?
You get out of bed, suffering a bout of insomnia, go to the bookshelf and pick out a long forgotten thriller, some forty years old and yellowing. Before finally succumbing to sleep you are struck by the relevance of a particular passage to the problems of age and decline. Then the very next day you open the sports pages of The Times to find the very same passage quoted (by Simon Barnes on the decline of a once invincible football team, December 17th):
I was reminded of a passage in Midnight Plus One, a very nice thriller by Gavin Lyall, in which the hero, on a high-speed run through France, is “flickering through the night with the precision of a high-powered bullet. It was one of those times when you know exactly, can feel exactly, what the car will do — and the road also. It felt familiar, although it wasn’t. I understood the pattern of it: what it would do next, how tight its bends would be, how steep its slopes.
“It happens. And when it happens, you’re right and you’re safe. But it doesn’t last. And you’re never more wrong, more dangerous, than when it’s stopped lasting and you don’t realise it.”
Well, it happened to your bending author this very day.
The above piece is merely an anecdote about a remarkable coincidence, neither more nor less. For a man to note a paragraph in an obscure book one day and read it in his newspaper the next is an improbable event, startling only to him who has the experience. For a man to be simultaneously in Wiltshire and Wisconsin is an impossible event. For a man to be exactly six feet tall is an event of probability zero.
It is important to distinguish between an impossible event and one of probability zero. Consider something a bit more amenable to measurement, the diameter of ball bearings coming off a production line. Their diameters (x) are distributed with a density, say f(x), and for any small range of diameters dx centred on x the proportion of balls in that range is the product f(x).dx. As dx shrinks to zero, this proportion (or probability) also shrinks to zero. Thus a ball bearing of exactly 1cm in diameter is an event of probability zero, though not an impossible one.
This letter, forwarded to Number Watch seems worth reproducing in full
Dear Hans Labohm,
Thank you for yr article Dec 17 "TCS COP 10 Coverage: Buenos Aires: Kyoto'sWaterloo", online <http://www.techcentralstation.com/121704C.html>
For further use you may notice the following critical and sceptical web pages in EU, too:
Ulrich Berner, Germany: Klimaentwicklung, online <http://www.bgr.de/bt_klima/>
John Brignell, UK: Number Watch, online <http://www.numberwatch.co.uk/number%20watch.htm>
Piers Corbyn, UK: Weather Action, online <http://www.weatheraction.com/>
Hans Erren, the Netherlands: Global warming comments, online <http://hanserren.cwhoutwijk.nl/co2/>
Zbigniew Jaworowski, Poland: online e.g.<http://www.21stcenturysciencetech.com/Articles%202004/Winter2003-4/global_warming.pdf>
Lars Kamél, Sweden, online <http://www.astro.uu.se/~l/>
Martin Keeley, UK: online <http://www.martinkeeley.net/page4.html>
Olavi Kärner, Esthonia: online <http://www.aai.ee/~olavi/>
Marcel Leroux, France: Laboratoire de Climatologie, Risques, Environnement, online <http://www.univ-lyon3.fr/LCRE>
Francis Massen, Luxembourg: Meteorological Station of the Lycée Classique de Diekirch, online <http://meteo.lcd.lu/>
Julian Morris, UK: International Policy Network, online <http://www.policynetwork.net/main/index.php>
Tom V. Segalstad, Norway: online <http://folk.uio.no/tomvs/>
Jim G. Thornton, UK: iGreens Individualist Environmentalists, online <http://www.igreens.org.uk/>
Anton Uriarte, Spain: online <http://homepage.mac.com/uriarte/mayas.html>
Timo Niroma, Finland: online <http://www.kolumbus.fi/tilmari/globwarm.htm>
Klaus Öllerer, Germany: KlimaNotizen, online <http://www.klimanotizen.de/>
Seasons Greetings to you all, dear recipients!
Chaos umpire sits,
And by decision more embroils the fray
By which he reigns: next him high arbiter
Chance governs all.
Milton – Paradise lost
When a huge natural catastrophe occurs there are two aspects that shock, the awesome power and the terrible randomness. It brings home the pathetic hubris of mankind in claiming to have mastered nature. It also brings into perspective the triviality of the manufactured scares that dominate our media and hence our lives. To see and hear of familiar and much loved places reduced to instant chaos, their populations killed, injured or rendered homeless, is to be brought face to face with the stark realities of the world and the insignificance of man. A minor tectonic shift, the transition from one point of equilibrium to another, is nothing on a world scale; yet it is total disaster to the minuscule beings affected. They are as helpless as the occupants of the ants’ nest under the gardener’s spade.
Equally, humankind is rendered powerless by the sheer unpredictability of such occurrences. Even in well-controlled laboratory experiments on the failure of materials, reliable predictors of the occurrence of the crucial tipping point prove totally elusive. We can apply statistics after the events, using the theory of extremes, calculate return periods and distributions of intensity, but we can say nothing about when it is going to happen. Much scope here for charlatans looking for a niche, just as there is for the scaremongers who seek to exploit our natural and justified fear of terrible individual life events, such as cancer.
The chance of catastrophe is part of the human condition. We are obliged as members of the human race to help the survivors and the bereaved, try to mitigate the horror, but, apart from installing such alarm systems as might be feasible, dwelling on what random events might happen in future serves no purpose.
Happy the man, and happy he
He who can call today his own:
He, who secure within can say,
Tomorrow do thy worst, for I have lived today.
Horace (trans. Dryden)
The fourth annual Numby Awards
Once a year and once again the Balls Pond Road rouses itself from its customary slumbering dignity. The excited crowds began to gather early round the entrance to the assembly rooms above the Takeaway Kebab. The venue was even more glamorous this year, thanks to the efforts of the Balls Pond Boys Brigade and the bulk purchase of paint from Morry’s emporium opposite. Most of the cracks in the plaster have now been filled and the décor is a uniform shade of puce with trimmings in battleship grey.
The awards committee has been afforced with new members in order to reflect the changing world. One was Roger Doffen, author of the forthcoming best-seller Man of Destiny: the Michael Meacher story. Another was the up and coming starlet Constance Exeter, who was short listed for the part of the receptionist in the forthcoming Hollywood super-hero block-buster Earwigman meets Volewoman. A third newcomer was Tracey Hirst, the well known artist, whose construction Slug in a beer bottle was shockingly overlooked by the Turner Prize panel.
As last year, the master of ceremonies was Old Ned, who really looked the part in his white and gold Elvis suit. The trophies were presented by a lady New Labour MP, one of “Blair’s Babes” (unfortunately, when your reporter come to check his notes with others present, no one could quite remember her name). She showed great poise, even when her foot accidentally went through a patch of dry rot on the dais. She was clearly moved by the occasion, as tears glistened in her eyes. After the ceremony she departed with great dignity, even though she was wearing only one high-heeled shoe, and she parted with a merry quip, calling out “You will be hearing from my lawyers.”
As is traditional, tribute was paid to former Numby laureates who had continued in the work that had brought them recognition. Throughout the year Professor David King has maintained the momentum that brought him the award for chutzpah (see January and July). Gordon (Means Test) Brown demonstrated in his Autumn Statement that he was in a league of his own when it comes to numerical prestidigitation. A particular coup was the announcement of a new science initiative during the very week that the University of Exeter was obliged to close its Chemistry Department through under-funding. He also nominated Newcastle as one of his science towns, when it has just closed its Physics Department, one of over a hundred science departments that have closed under the present government. Foreigners might wonder why a finance minister is announcing science and industry policy, but with the Prime Minister busy changing the world from his sofa and the Cabinet having all but disappeared, such things have to be delegated. Margot Wallström (the spell checker suggested Maelstrom) has been moved sideways at the EU Commission; not, as malicious critics have suggested, to limit the damage she can do, but because her skills are needed to make us all love the EU.
The theme of this year’s awards was Creativity and Imagination, which was celebrated in a banner that stretched across the famous thoroughfare, until the unfortunate incident with the double-decker bus.
The first trophy, for the most promising newcomer, went to Professor Graham MacGregor, head of cardiovascular medicine of St George's Hospital Medical School, for his very own virtual body count. The creation of this figure of 5,800 corpses from a scattering of a few points obtained from minuscule studies brilliantly illustrates the theme. Like many successful laureates he is notable for his dedication to his cause and remaining undeflected by other irrelevant statistics, such as the similar number of real corpses being created by the spread of MRSA in our filthy national hospitals. There is also his ability to ignore well-established principles such as homeostasis, as noted by James Le Fanu in October. In January he and his fellow enthusiasts will be making the annual presentations to ministers and MPs at Westminster, who will no doubt continue to harangue the population on the grounds of this evidence.
The award for sheer persistence goes to Paul Simons, who is author of the daily Weather Eye column in The Times. At Numeric Towers the office staff run a sweepstake on which day of the week he will get in a mention of global warming. While he has a little trouble with the elementary theory of planetary motion, as we saw in February, he is a master of the uses logic to make his case, including selectivity of evidence, non-sequiturs and bold statements. He can call on more proxies than a New Labour election official operating the postal vote. In Christmas week, his plug occurred on December 23rd. Noting that there have been only four white Christmases in the UK since 1900, he stated baldly that global warming will make them even rarer in future. Here are a couple of quotations from February alone
After the bitterly cold winter of last year, this recent freeze may be giving Americans the illusion that global warming is not worth worrying about.
More importantly, daylight is now increasing rapidly. Because the Earth’s orbit around the Sun is oval-shaped, the hours of daylight change very slowly near the winter solstice. But now we are gaining almost three minutes’ extra daylight each day until the spring equinox — and that means more solar heating and the first signs of spring.
A related award is the one for sheer consistency, which goes to Professor John Collinge. As we noted last month, he can be counted on to make at least one attempt per annum to keep the CJD scare in the air. As the projected numbers of corpses dwindle from millions to thousands to hundreds to dozens, more and more ingenious experiments, mainly on mice, are summoned up to shore up employment in this particular area of science.
There was obviously something special going on when the early crowds outside the assembly rooms began to chant to the tune of Guantanamera:
There’s only one Ol’
There’s only one Ol’ Thousan’s
One Ol’ Thousan’s
There’s only one Ol’ Thousan’s
Yes, it was the Nigel (thousands to die) Hawkes Fan Club. Only last month Number Watch was asking where is our Nige? He gave his answer this month with a double whammy on the two front pages of The Times (see above), but the clincher was when he followed up the very next day with a front page banner Household chemicals in direct link to asthma rise. Three major scares in two days is remarkable going for any operator. You can predict the moans from the carping critics (correlation is not causation, central heating, fitted carpets etc, etc) but you cannot take away the achievement from such mastery of a genre. He has achieved at least a couple of dozen mentions in Number Watch alone. Thus there was only one possible destination for the special award for lifetime achievement.
To mark the uniqueness of the occasion, for the first time ever, the quotation engraved about the base of the trophy was from the recipient himself (April 2003), which makes you wonder what might have been:
Far too many scares are whipped up by journalists and those who feed them information. Several years ago, after reading some American research about the effect of such stories on readers, I resolved to write fewer of them.
This year, the ceremony was televised as promised, but many missed it, as it was on a digital channel in between a programme about a revolutionary exercise machine and one in which young ladies sitting in underclothes invite gentlemen to telephone them on a premium rate line.
So another great occasion came to an end. For hours afterwards hoarsened voices singing to the tune of Guantanamera could be heard fading away into the hidden recesses of the darkling historic boroughs of North London – Islington, Highbury, Hackney, Hoxton, Haggerston, Shoreditch and Clerkenwell – names with a magic of their own. The last stragglers, kebabs in hand, faded into the side streets and the Balls Pond Road returned to its customary silent majesty.
Even the most evil and horrific circumstance delivers advantages. The tsunami and its consequences have almost driven false scares and junk science out of the media. Apparently, even in those circles there is a sense of proportion and conscience. The solitary notable silly number penetrating the BBC is a Trojan Number, but it is only 100. This is the number of people (including the control group) in a study of exercise in the elderly. It is a remarkable piece of experimental design. The fifty in the “control group” were given a book to encourage them to take exercise, while the other fifty were put on a variable regime of exercise. So where did the headline Exercise 'cuts older heart risks' come from? The “scientists” did not actually measure heart disease, but something called metabolic syndrome, a vaguely defined set of symptoms that include “high levels of unhealthy cholesterol in the blood.” Some authoritative sources (but not establishment ones) question whether this is a significant factor.
The numbers are absurdly small, the differentiation between the groups is vague and the objectives are ill-defined, so, as a former academic colleague, Hugh Glaser, would say, stubbing his forefinger on a beer mat, “What is the bloody point?”
Of course, the real number of the year is large and unknown, but to dwell on the death toll in the aftermath of the tsunami would be to risk trivialising it, so, playing for safety, this is a number that is trivial, stupid and meaningless. It is, of course, the theoretical number of corpses produced in the UK by excess salt intake. There are a several quite extraordinary aspects of this number.
It’s a funny old world.