WINSTON CHURCHILL AND PROBABILITY

None of these calculations have any relation to reality, accord-ing to Formaini. He thinks that events that have never happened before cannot be assigned a probability, and I don't quite know what he means by that. The sun has never risen before at tomorrow's time and date of sunrise. It is true that in "pure" mathematics there are problems with the classical definitions of probability (favorable over possible, or successful over total in a very large number of trials), and I will not go into modern axiomatics which solve them. But "pure" mathematics also provides a proof that by the axioms of algebra 1 is greater than 0. The proof is less than 150 years old; does that mean there could not have been any useful accountants before then?

Is it unreasonable to use demographic statistics to calculate the probabilities of death at a certain age, given that the subject smokes, drinks and is overweight? Winston Churchill's girth was monumental, he was rarely seen without a cigar, and allegedly drank a bottle of whiskey a day, but he lived to age 91; does that mean all risk assessment is subjective nonsense?

Perhaps (one can only guess) Formaini means that deaths have often happened before, but a nuclear accident hasn't. Perplexingly, his description of how such a probability is derived is not that wrong; to use my own words, complex events are a combination of simple events, and if we know the probabilities of the simple events by measurement or derivation, plus the possibilities in which these simple events combine in the complex event, we can calculate the probability of disaster very exactly.

The most common reason why we fail to do so is our imperfect knowledge of how the simple events can combine. The Rasmussen report, for example, which the book uses repeatedly as an ex-ample, grossly overestimated the consequences of a meltdown. It was the absence of radioiodine in predicted quantities at TMI that helped to uncover the reason: it had been unknown, or over-looked, that the dangerous, volatile particles after a meltdown will plate out on the containment building even if it has been breached (at TMI it wasn't). Does that mean Rasmussen's assessment was wrong?

Only to the extent that all ow measurements and predictions are wrong because they must contain an error given by the con-temporary state of knowledge and technology. The Romans thought nothing of giving the time of day with an error of plus-minus half an hour; the National Bureau of Standards cesium clock gives it with an accuracy in the neighborhood of one billionth of one second, and it is still "wrong" because that still leaves an error of many trillionths. Rasmussen found that the probability of a meltdown with 1,000 or more casualties was equal to that of a meteor causing as many. Today we know that the meteor is the more dangerous of the two; but what difference does that make to the risk assessment when you compare it to the risks of coal and the other sources of electricity? In any case, whether the error is small or large, it is given by the state of the art, and is not subjec-tive, as Formaini thinks, but just as objective, if more error-prone, as the NBS time signals.

There are more errors of substance, yet I cannot suppress my irritation at a purely formal matter, the meaning of risk. In proba-bility theory, it means the average penalty, and unlike probability, which is dimensionless, it is measured in dollars, lives or in whatever units penalties are paid and rewards (negative penalties) are received. If the probability of outcomes in a card game are 50% of losing $100,10% of winning $500 dollars and 25% of no loss or gain, then playing this game involves a risk of 0.5 x $100 0.1 x $300 + .25 x 0 = $20 (a fair game has zero risk). Risk assessment uses very advanced mathematical methods, and though it does not have the precision of celestial mechanics, it can, and should, very definitively affect decisions, especially in comparing risks, rather than entering the swamp of "risk-benefit" analysis (how many dol-lars to a human life?).

But in this book, as well as in much newspaper parlance, "risk' has come to mean something akin to "probability of an adverse event" (the half-learned never reveal what their words mean). Of course, a word is merely an identifier of a concept and quite nego-tiable as long as we all use it the same way. Its new use nevertheless raises my hackles thanks to the smooth-tongued politicians who barely know the number of fingers on their right hand, but shoot off their mouths about taking "calculated risks."