----- Original Message -----
From: "Doug Henwood" <dhenwood at panix.com>
> Globe and Mail (Toronto) - May 4, 2002
>
>
> Scientists' deaths are under the microscope
> By ALANNA MITCHELL, SIMON COOPER AND CAROLYN ABRAHAM
> COMPILED BY ALANNA MITCHELL
>
> It's a tale only the best conspiracy theorist could dream up.
=======================
Comment Elsewhere
Name your Poisson
David McKie Guardian
Thursday March 14, 2002
Twin 70-year-old brothers were killed yesterday by lorries within hours of each other while riding bicycles on the same stretch of road. Police said the first accident occurred at 9.29am on an icy road, 370 miles north of Helsinki. Two hours later the other twin, unaware of his brother's fate, was hit and killed a mile away by another lorry. - Associated Press report in the Guardian.
Years ago I read a short story, I think by Irwin Shaw though it sounds rather more like Ray Bradbury, about a restaurant in California where one night no one turns up. Unable to understand what is happening, the proprietor goes on to the street where he sees further disquieting signs that something odd is afoot. Eventually he comes to a bridge where the traffic is pouring into town just as it always does - but no one is driving out of it. It is then that the awful truth dawns on him. The law of probability, which rules so much of our lives, has collapsed.
We spend a lot of our time, far more than we usually recognise, calculating probabilities. The train to Victoria is due out of the station seven minutes from now: will we make it, or ought we to wait for the next one? What time will it reach the terminus? (South London commuters on the basis of recent experience now habitually add 10 minutes to the advertised time of arrival.) Yet few of us understand even the simplest ground rules.
Toss a coin and it comes down heads. Try again, and it's heads again. Trying to be judicious, we now call tails, for surely the balance of probabilities is due to give tails a turn. Not so, say statisticians: for any toss of a coin, the chances are 50-50. People playing the national lottery, noting a run of success for, say, 37, will decide to avoid it this week. Yet the chance of it coming up in any draw will always be exactly the same.
Last week a man in a restaurant disputed some statement I made on the grounds that it didn't fit with Poisson's distribution. When I said I had never heard of Poisson, let alone of his distribution, he gave me a look of disbelief blended with pity. Poisson - as he explained, though I've mugged up more of him since - was a French mathematician, born 1781, died 1840, whose insights unlocked essential truths about mechanics and physics. He propounded a law about elasticity, and published a seminal treatise on the movements of the moon. For the purposes of our conversation, however, the relevant text is his Recherches sur la probabilité des jugements, published in 1837. This developed a technique for estimating the likely occurrence of the kind of events that could happen at any time, but in fact do so rarely - more frequent occurrences having already been dealt with by theories of binomial distribution.
I have gathered from various textbooks examples of what you can do using Poisson's formula. The most famous deals with the likelihood of a cavalryman being kicked to death by a horse - more of a worry in those days, perhaps, than now. Others cited include the rate at which one might expect postilions to be struck by lightning; the number of major earthquakes to be recorded in any one year; and even the number of copies of the Independent which a newsagent ought to order (though surely this newspaper's sales can't be as rare as all that?).
A website conducted by Chuck Anesi (Anesi at anesi.com) contains a kind of do- it-yourself device for applying the Poisson distribution. Assume, he says, that on average, each square mile of the earth's surface is struck by one meteor of a certain size every year. How many square miles will not be hit by a meteor, and how many by more than five? The answer, he says, is that 73,575,888 square miles will escape, while 731,969 will be hit five or more times. This is just the point my friend in the restaurant was trying to make. We ought to expect such outcomes to be clustered rather than distributed with the kind of impeccable equity that Guardian readers might hope for.
So where does that leave the unfortunate twins struck down on the road 370 miles north of Helsinki? I must say I found the story astonishing, as no doubt did whoever put it into the Guardian, a paper which rarely bothers itself with road deaths in Finland. Yet the eyebrows of statisticians may have been raised by a margin significantly less than that of the average eyebrow among the rest of the readership. "If two events are independent," one source rules austerely, "the occurrence of one does not affect the probability of the other event taking place." But I don't suppose that teaching would have reached the ears of the cycling twins of Helsinki. And now they will never know.