Saturday, June 25, 2011

How Richard Dawkins might explain a tennis coincidence

[Did this for my Sunday Guardian books column]

“Look into a mirror for a lifetime,” said the poet-filmmaker Jean Cocteau, “and you see Death doing its work.” Having watched nearly half of the eleven-hour match that John Isner and Nicolas Mahut contrived to play at Wimbledon last year, I’d say no mirror is necessary.

If you follow tennis, even casually, you may have heard about the gasps of astonishment at the Wimbledon draw ceremony last week when Isner and Mahut were again drawn to play each other in the first round. This has opened the conspiracy-theory floodgates. Their 2010 match, soul-annihilating though it was, probably got more media coverage and public attention (especially outside sporting circles) than any Slam final. “Arranging” a sequel could be good for ticket sales – so was the draw rigged?

Personally I doubt it: the draw process is a transparent one and the ceremony very public. But the rhetorical question “What are the chances of such a thing happening just randomly?” continues to be asked by tennis fans everywhere – the implication being that this couldn’t have been a coincidence; that organisational (or occult) forces had to be at work.

Actually, the odds aren’t close to astronomical. I won’t bore you with the calculations, but keeping in mind that Isner and Mahut were both among 96 unseeded players, the chance that they would play each other works out to something like 1 in 140, or 0.7 percent. Improbable, yes, but hardly mind-boggling as these things go. Even if you calculate the chance of their meeting in the first round in successive years, you don’t get wildly unlikely numbers. (In fact, the coincidence of the same two players meeting in the 1st round in consecutive Wimbledons has occurred eight times since 1970.)

My favourite writings on the phenomenon of coincidences and how the human mind can get excessively excited about them are in Richard Dawkins’ Unweaving the Rainbow, specifically in the chapters "Hoodwink'd with Faery Fancy" and "Unweaving the Uncanny". Dawkins begins with a simple enough incident: a four-digit personal code number issued to him by his college was exactly the same as the safety code he had just chosen for his bicycle lock. The probability of this happening is 1 in 10,000 – seemingly very large odds – but as he points out, “the number of people in the world is so large compared with 10,000 that somebody, at this very moment, is bound to be experiencing a coincidence at least as startling as mine. It just happens that today was my day to notice such a coincidence.”
Each ordinary day that you or I live through is an unbroken sequence or events, or incidents, any of which is potentially a coincidence. I am now looking at a picture on my wall of a deep-sea fish with a fascinatingly alien face. It is possible that at this very moment, the telephone will ring and the caller will identify himself as a Mr Fish. I'm waiting...

On another occasion his wife bought an antique watch as a gift for her mother, then discovered that the watch had her mother’s initials – “M.A.B.” – engraved on the back. Many people I know, if faced with this situation, would hasten to invoke supernatural causes (presumably because the invisible pink unicorn in the sky has nothing better to do with Her time than spring pleasant little surprises on randomly selected homosapiens), but Dawkins takes out the phone book, checks the frequency of names beginning with M, A and B and then sets about his calculations. It turns out that if each of the 55 million people in Britain bought an engraved watch, we could expect nearly 20,000 of them to experience a coincidence of this magnitude.

Much heft is added to Dawkins' argument by the concept of the PETWHAC (Population of Events That Would Have Appeared Coincidental), a term he coins to show how the pattern-seeking mind can make coincidences appear even more remarkable than they are. (If his wife had discovered the initials of her mother’s maiden name on the watch, or her own initials for that matter, it would have seemed just as impressive – but it would also mean a broadening of the PETWHAC, which would further increase the probability of a coincidence.) Public “mystics” and “psychics” dine out on this sort of gullibility and pattern-seeking all the time.

(More about the PETWHAC here)

Incidentally the title Unweaving the Rainbow comes from John Keats’ observation that science had destroyed the beauty of the rainbow by “explaining” its colours. Dawkins’ response is that the natural world as revealed by scientific understanding can be beautiful and awe-inspiring. “Disarming apparently uncanny coincidences is more interesting than gasping over them,” he says. Whether or not you agree with him, I’d say analysing mathematical probabilities is much more interesting than watching another Isner-Mahut match. Even if you hate maths.

[Here's an old post on Dawkins' Climbing Mount Improbable. And a little more about Unweaving the Rainbow in the postscript of this post.]

Update: Just realised that the Serious Men post I linked to above was written on this day exactly a year ago - now there's another good coincidence for you! (And I swear it wasn't planned.)


  1. What are the chances one shares ones initials(3-character) with a class-mate ? I did.

    What are the chances your vehicle-number, coincides with the birth-date(DDMM format) of a family member ? Mine does

  2. Interesting article. Haven't we all experienced such weird coincidences some or the other time!

    With reference to the last paragraph, might I add something by Richrd Feynman?

    Poets said Science takes away from the beauty of stars - mere globs of gas atoms. Nothing is "mere". I too can see the stars on a desert night, and feel them. But do I see less or more? The vastness of the heavens stretches my imagination - stuck on this carousel my little eye can catch one-million-year-old-light. A vast pattern - of which I am a part - perhaps my stuff was belched from some forgotten star, as one is belching there. Or see them with the greater eye of Palomar, rushing all apart from some common starting point when they were perhaps all together. What is the pattern, or the meaning, or the why? It does not do harm to the mystery to know a little about it. Far more marvelous is the truth than any artists of the past imagined! Why do poets of the present not speak of it? What men are poets who can speak of Jupiter if here were like man, but if he is an immense spinning sphere of methane and ammonia, must be silent?

  3. Marvin: that's a nice quote by Feynman. Carl Sagan has often written along the same lines. For instance:

    "In some respects, science has far surpassed religion in delivering awe. How is it that hardly any major religion has looked at science and concluded, 'This is better than we thought! The Universe is much bigger than our prophets said, grander, more subtle, more elegant. God must be even greater than we dreamed'? Instead they say, 'No, no, no! My god is a little god, and I want him to stay that way.' "

  4. Question: What book would you suggest as a starting point for delving into his work? Dawkins, I mean.

  5. Marvin: difficult to answer, but Unweaving the Rainbow might not be a bad start, because it has an episodic structure and can be read as a collection of essays - so you can start by reading the ones that are less technical (like the two chapters I've mentioned here).

    For the books that deal with evolutionary biology in a more consolidated way, I'd probably say The Blind Watchmaker followed by Climbing Mount Improbable - I think these two books are more accessible than The Extended Phenotype (which I still haven't managed to read fully). Then there's the brilliant The Ancestor's Tale, which again doesn't have to be read from beginning to end. Ditto for The Greatest Show on Earth. And The Devil's Chaplain is a nice collection of pieces on various subjects, including his famous skirmishes with Stephen Jay Gould.

  6. Khalil: Of the 45-50 cars that are regularly parked in our colony park, at least three (including mine) have the number 1362.

  7. I see you have refrained from mentioning 'The Selfish Gene' here. Any specific reasons? I haven't read it but it seems to be one of those books that everyone keeps talking about.

  8. Marvin: no specific reason, except that it was just a little too technical for me (again, I haven't managed to read the full book), though of course I appreciate what an important work it is. But his later books about evolutionary biology were probably written with the layman-reader in mind and are more general-interest in that sense.

  9. my dad was allotted a new house just two month prior to my graduation result. my 3 year exam total came out at 1200, which was also my new house number.

  10. Parm: that makes a good case study for the PETWHAC concept. Imagine how much more impressive a coincidence it would have been if your results came out on the same day that you found out your new house number!

  11. @Marvin and @Jabberwock, I had just turned to the comments to add my two bits on Feynman and Carl Sagan.

    At some point, I am a little disappointed with artists who do not realize that two different points of views may provide two different vistas of beauty.

    WRT, Dawkin's works, my personal favourite incidentally is The Selfish Gene, but that is probably because I happened to read the book during a period when I was reading a lot about Game Theory.

    Love The Ancestor's Tale

  12. +1. Also,
    It is far better to grasp the Universe as it really is than to persist in delusion, however satisfying and reassuring. - Carl Sagan


  13. Marvin, awesome quote by Feynman there, thank you.
    By the way , The selfish gene is very important to me for personal reasons - because reading it led me to Buddhism.

  14. : ) The quote is from one of the introductory chapters to 'Feynman's Lectures on Physics'. I would suggest reading the first two chapters even if you are not even remotely attracted to the subject!

    Another quote from the said chapters that is a somewhat lighter take on the debate here:

    A poet once said - The whole universe is in a glass of wine. We will probably never know in what sense he meant that, for poets do not write to be understood. But it is true that if we look at a glass of wine closely enough we see the entire universe. There are the things of physics: the twisting liquid which evaporates depending on the wind and weather, the reflections in the glass, and our imagination adds the atoms. The glass is a distillation of the earth's rocks, and in it's composition we see the secrets of the universe's age, and the evolution of stars. What strange array of chemicals are in the wine? How did they come to be? There are the ferments , the enzymes, the substrates, and the products. There in wine is found the great generalization: all life is fermentation. How vivid is the claret, pressing its existence into the consciousness of the mind that watches it. If our small minds, for come convenience, divide this glass of wine, this universe into parts - physics, biology, geology, astronomy, psychology, and so on - remember that Nature does not know it! So let us put it all back together, not forgetting ultimately what it is for. Let us give us one more final pleasure: drink it and forget it all!

  15. The universe is so full of many small chaotic messes (Earth & humans being one of the cosms), coincidences are bound to happen!

    Btw interesting blog and thoughts...

  16. If you listen to radio, there's a very nice show called Radiolab (part of NPR in the US). They had an episode on stochasticity ("a wonderfully slippery and smarty-pants word for randomness"). Listen to it if you get a chance.


  17. I wouldn't be impressed even if they played another 70-68 final set. I am unimpressed by a lot.

  18. I would like to suggest Robert Wright's 'The Moral Animal' as another seminal work in evolutionary psychology. It is an extension of Dawkin's sociobiology into the field of human psychology.

    Another work very similar to 'Unweaving the rainbow' is Carl Sagan's 'Demon Haunted World'