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William Grimes reviews a book outside his field

Probability is a tricky topic, as Monte Hall showed

We believe we have found a prime example of the sad incompetence of the typical arts graduate when faced with mathematics or science, and the inappropriateness of assigning one to review a book on a mathematical topic, in today’s (Jan 20 Fri) NY Times book review, The Quirky Moments When Lightning Does Strike Twice by William Grimes.

The book is full of coincidences, and Grimes quotes some of them, including one which is a classic.

On the other hand, it is deeply satisfying to know that a Canadian farmer named McDonald has the postal code EIEIO,


The New York Times

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January 20, 2006

Books of The Times | ‘Beyond Coincidence’

The Quirky Moments When Lightning Does Strike Twice


A woman in Alabama decided to visit her sister. Her sister, unbeknownst to her, decided the same. They hit each other head-on on a rural highway. Both died. And both drove Jeeps. That counts as a rare coincidence, although not as rare, perhaps, as the case of Roy Cleveland Sullivan, a Virginia forest ranger who was struck by lightning seven times, or the existence of an ice dealer named I. C. Shivers.

The laws of chance operate strangely. This is the main point in Martin Plimmer and Brian King’s “Beyond Coincidence,” a collection of stranger-than-fiction anecdotes wrapped loosely in colorful intellectual tissue paper. It is a superior example of the genre known as a toilet read, with a few halfhearted excursions into the psychology and mathematics behind the uncanny coincidences that the writer Arthur Koestler called “puns of destiny.”

Just as nature abhors a vacuum, human beings resist the idea that events occur in random fashion. They are highly receptive to divine messages that suggest otherwise, as in the strange tale of Mrs. Willard Lowell of Berkeley, Calif., who discovered that she had locked herself out of her house when the postman arrived with a letter. In the letter was her spare front-door key, returned by her brother, who had taken it home with him by mistake after a recent visit.

Events like this send a shiver down the spine, but the math behind strange coincidences shows that most people simply have a poor grasp of statistics. The odds against meeting someone else at a party with your birthday are not 365 to 1. In a room with just 23 people, the chances that two of them will share the same birthday are better than even.

A world without a constant barrage of bizarre coincidences would be much more remarkable than the reverse. It is not all that unusual to have a dream that accurately predicts a future event, or for two golfers to achieve a hole in one on the same hole. On average, everyone should have a prophetic dream once every 19 years, and the odds of a double hole-in-one, although apparently staggering at 1.85 billion to 1, ensure that this occurs about once a year.

It is a very safe bet that more such coincidences are on the way, as the world becomes more populated, and the volume of information grows. As the authors put it, “The statistician’s law of large numbers states that if the sample is very large, even extremely unlikely things become likely.” That includes the perfect hand dealt out to the four members of a British whist club in 1998, who each received 13 cards of a single suit.

Something deep in the mind resists the explanations of the statisticians, however. Evolution may be to blame. “We have been so successful as a species precisely because we are good at making connections between events and spotting patterns and regularities in nature,” explains Christopher French, a psychologist. “The price we have paid is a tendency to sometimes detect connections and patterns that are not really there.”

That tendency would account for the discovery that playing the Pink Floyd album “Dark Side of the Moon” while watching “The Wizard of Oz” generates almost as many startling coincidences as the correspondences detailed in “The Bible Code,” a numerological analysis of the Bible that uncovered, among many other things, a prediction of Yitzhak Rabin’s assassination.

Mr. Plimmer and Mr. King, who first explored this territory in a series of shows for BBC Radio 4, scramble to fill their allotted pages. They spend far too much time with Richard Wiseman, author of “The Luck Factor,” and his training programs designed to turn miserable, unlucky skeptics into lucky winners.

They stuff the book with several anecdotes that sound too good to be true, and even more that are too true to be good. George Frideric Handel and Jimi Hendrix lived at adjacent addresses in London. Nine women at a British supermarket, all working at the same cash register, became pregnant in a 10-month period. A man trying to console his next-door neighbor after a painful breakup put the former couple’s favorite record on the turntable. Ooooh.

On the other hand, it is deeply satisfying to know that a Canadian farmer named McDonald has the postal code EIEIO, and there is at least half a screenplay in the tale of a bank robber who, hitting the same bank and the same teller a second time, escaped because the bank guard and the managers were in a back office reviewing videotapes of the first robbery.

The award for the most painful coincidence in recorded history must go to the poet Simon Armitage, who chanced upon a used copy of a book of his poems in a trash bin outside a thrift store. On the title page was the following inscription, in his own handwriting: “To Mum and Dad.”

* Copyright 2006The New York Times Company

But is William Grimes the right man for this book? He is an English graduate who became a food critic. He was the restaurant critic for the Times from 1999 until recently.

“Before that, he wrote on food and drink for the newspaper’s dining section, and for many years covered the arts for the Times. He earned a degree in English from Indiana University and a doctorate in comparative literature from the University of Chicago. He is the author of the books Straight Up or on the Rocks: The Story of the American Cocktail and My Fine Feathered Friend, the tale of a mysterious chicken that came to roost in his backyard.”

We are quoting from the site of the New York Public Library, which ran an interview with Grimes in 2002.

The interview includes the following exchange:

How did you start writing about food?

I was working at Esquire and I was drafted into doing a cocktail column. That got me into writing about food history. When I came to the Times, I did a fair amount of writing for the Travel section and the Living section on food-related subjects. The biggest leap came when the Times redesigned the dining section in 1997 and the editor asked me to come over from the Culture section and be the food writer. Instead of writing about food in a scattershot way, I was doing it full time. Then when Ruth Reichl quit the critic’s post to become editor of Gourmet I was asked to be the critic, which became official on April 1, 1999.

It’s all been very haphazard. Your own enthusiasm catches up with you from behind. You were doing it but didn’t realize you were doing it. By sheer accident things fell together in a particular way.”

This is the traditional way in which assignments have reached members of the daily press, where beats can change rapdily and bear no relation to one’s expertise.

So it is not unusual that a food critic is the man that the Times editors assigned to read and review “Beyond Coincidence: Amazing Stories of Coincidence and the Mystery and Mathematics Behind Them” by Martin Plimmer and Brian King (Thomas Dunne Books/St Martins Press).

The general idea is that a book written for the general interest reader can be properly reviewed by one of the non-experts that they are designed for.

Now we don’t know much statistics ourselves, but enough to ask, is this policy wise in the case of statistics? It seems likely that Mr Grimes will probably not appreciate every nuance of this kind of book. It is easy to make a mistake in this field if you are not familiar with it, as countless incorrectly done AIDS studies testify.

Take this paragraph, for instance from the review, which seems plainly wrong:

Events like this send a shiver down the spine, but the math behind strange coincidences shows that most people simply have a poor grasp of statistics. The odds against meeting someone else at a party with your birthday are not 365 to 1. In a room with just 23 people, the chances that two of them will share the same birthday are better than even.

Surely the odds of you meeting someone else with the same birthday at a party of 23 people are 23/365? Of course, the chances of any person present making a match are much higher, as stated. But the chance that it will be you is still pretty low. It is correct as stated, but does seem to imply that he is confused.

It seems that Mr Grimes himself has a poor grasp of statistics. Still, one can never be sure – unless one has training in the field, which is our point.

We are certainly not going to make anything of it. The last time we made something out of a mathematical puzzle, we nearly made fools of ourselves by writing a letter to the Times accusing it of being wrong when it was quite right.

The Monte Hall game show puzzle

The story concerned Monte Hall, the host of a show (Let’s Make A Deal) on TV who presented a contestant with the final choice of three doors. Behind two of the doors was a worthless object like a toy duck and behind the third door was a $1 million prize. The contestant was offered the choice of A, B or C, and chose A.

The host then opened one of the two other doors – say B – to show it had been hiding a duck. He then offered the contestant the choice of the two remaining doors, A or C.

The question posed in the puzzle was this: should the contestant switch doors, from his original door A to the new choice of C? Would he increase his chances of winning by doing so?

The answer, of course, is that he should, since obviously he increases his chances of winning. This is the anwer the Times gave, saying that the most intelligent woman in the world had written so in her column on puzzles.

Needless to say, like many others we immediately drafted a letter to the Times pointing out that this was wrong. Obviously, we wrote, it would make no difference at all whether he stuck to door A or moved to door C. Anyone could see that. The chances were one in three he was right the first time, and choosing C instead would also be a one in three chance of winning.

Luckily we checked with a professional mathematician before sending the letter, and were set straight before risking public ignominy.

On the original show, Monte Hall did not allow switching of doors for that reason. The chances of winning go up from 1 in 3 to 2 in 3, according to the Wikipedia.

We would have guessed they went up to 1 in 2 from 1 in 3, but that is probably exactly why we should never argue about probability. Not without carefully examining the analysis, that is.

One analysis of the Monty Hall problem is at Wikipedia.

The key to the problem is simple enough, though at first it seems counter intuitive. The choice of a door by the host is constrained – he has to choose one with a duck, and not the one you have already chosen. His choice, therefore, reveals information, and makes the choice of the door C rather than door A one which is more informed.

Perhaps the simplest way to look at it is that one’s initial choice could be either a duck, the other duck or the prize. If you choose either duck, switching will win. If you choose the $1 million prize, switching will lose.

So switching stands to win two out of three times.

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