Mathematics

The laws of freak chance

Do luck and coincidence truly exist,or can everything be explained scientifically by the laws of probability? Meeting a lost friend on a train could be just a case of mathematics,not fate.

When Sue Hamilton was working alone in her office in July 1992 when the fax machine broke down. Unable to fix it, she decided to call her colleague Jason Pegler, who had set off home a little earlier. Finding his home number pinned up on a notice board, she called him and began to explain the problem. But Jason quickly stopped her: "I'm not at home", he explained. "I just happened to be walking past this phone box when it rang, and I answered it!" .
The number Sue found on the notice board was not Jason's home number at all. It was his employee number - which was the same as the number of the phone box he was walking past when she called. It was a bizarre coincidence, one of those that fascinate and perplex us. From a chance meeting with a long lost friend to weird parallels between world events, coincidences hint at "spooky" laws in our universe.
Last year an amazing set of coincidences put Paula Dixon in the headlines - and saved her life. On a flight from Hong Kong to London, she began to feel ill. A call went out to any doctors on board the plane, and two - Professor Angus Wallace and Dr Tom Wong - duly emerged.

Did chance save this woman's life...
...with these bizarre bits and pieces?

Paula Dixon needed life-saving surgery on a long -haul flight to London.There were two doctors on board,both trauma experts - one even had the right text book on him
Paula had a potentially fatal collapsed lung.The doctors punctured her chest with a hangar sterilised in brandy,and put a tube in to drain air via suction into a water bottle

The presence of two doctors was not so surprising. But Paula had a "potentially fatal collapsed lung-and Professor Wallace was not only an expert in aecident surgery, but had just finished a course dealing with precisely this type of crisis. DrWong turned out to have with him the one textbook needed to help them carry out the surgery. They saved Paula's life - and won world-wide acclaim.
But scientists claim coincidences are simply the result of remembering a few "amazing" concluences of events, but forgetting all the times when nothing amazing happens A classic example is the "small world" effect, where two strangers at a party discover they have a friend in common. People at parties tend to be from the same social class, level of education, income bracket and the same area. So the likelihood of meeting someone with whom you share a trait is higher than it might seem.
Sociologists have found that individuals typically have around 150 people whom they regard as "close". Therefore each of us typically has an entourage of around 23,000 "friends of a friend". Say we have about five acquaintances for each close friend, the number swells to 600,000.

Fancy seeing you here
The chances of meeting someone on a train with whom you share an acquaintance are therefore surprisigly high: for the UK population, it's around 1 in 100. If you also include socio-ecomomic factors that boost the numbers of people from particular backgrounds travelling by train to particular destinations, the chances rise even higher.
Take another "coincidence": discovering you share the same birth- day as someone. How big a gathering of people do you think you'd need to get odds better than 50:50 that at least two shared your birthday?As there are 365 possible birthdays you might guess the answer to be about half of 365-about 180 people. In fact, you need just 23.
This is because you're not asking for a match between a specific birthday - say ,April 12. All you want is a match between any two birthdays and any two people.This reduces the numbers of people needed to produce the "coincidence". To find at least two people born on April 12, you'd need over 250 people to give odds better than 50:50.
The less specific you are about what you want, the more likely coincidences become. If you stand by phone-boxes waiting for a re-run of Jason Pegler's experience, you're in for a long wait. But if you only want someone somewhere in the UK to have something similar happen to them as they pass a phone-box, the chances increase dramatically.
There is another effect at work behind some coincidences. They often seem surprising because we mix up two different probabillties: one - the chances of something interesting happening,and,two-the chances of something interesting happening after it has been given many opportunities to occur.

Luck or just mathematics?

  • 1 in 36 - chance of throwing a double six 1 in 2-chance of a double 6 in 36 throws
  • 1 in 100 - chance of meeting someone you know on a train
  • 23,000 - that's the number of people you probably know

For example, the chances of getting a winning "double six" in a single throw of two dice is 1 in 36. But the probability of getting at least one from 25 attempts is 50:50.The more you try, the better your chances - but it's easy to forget the number of "tries" involved in real-life coinciences. How many millions of people walk past phone boxes each day, but never find a friend on the other end of the line if it happens to ring? Psychologists' research shows that people judge the chance of coincidences using simple - and apparently very sensible - rules. Roughly speaking, if one coincidence is twice as "outlandish" as another, people regard it as twice as unlikely. But probability theory shows that the likelihood of coincidences varies in a more complex, non-linear way "It's not surprising we're poor at assessing coincidences", says psychologist Dr Susan Blackmore. "We acquire skills by constant practice, but we don't go around all day deliberately seeking out coincidences. If we did, we'd soon realise that we live in a sea of them and would be far less surprised when they popped up." Although scientists regard every day coincidences with contempt, they treat them seriously when they occur in science.

Day to day flukes do not impress scientists, but coincidences in nature can be vital

Apparent coinciences in nature have often led to major scientific breakthroughs.
When the chemical elements are arranged according to their atomic weight, for instance, they seem to fall into groups with similar properties. Coincidence? The Russian chemist Dmitri Mendeleev didn't think so - and in 1871 published his Periodic Table, now found on the walls of countless laboratories. It emerged that the "coincidence" was the result of a deep principle controlling the behaviour of electrons in atoms.
The famous discovery of the double helix of DNA also benefited from a coincidence. In the early 19505, an Austrian biochemist noted that the amounts of key chemicals in DNA - codenamed A,T, G and C - seemed to follow a rule. If the amounts of A and T were combined, they always equalled the levels of G and C. Cambridge scientists Crick and Watson thought this was a clue, and used it to find the structure of DNA.This "coincidence"won them a Nobel Prize and launched the whole field of modern genetics.
Cosmologists have based entire theories on "coincidences". The most enigmatic, the Large Number Coincidence, was first pointed out in the 1930s by the British Nobel prize-winner, Paul Dirac. Take the age of the universe, and divide it by the amount of time needed for a ray of light to cross a sub-atomic particle. The result is a colossal 10 to the power 38. Now, take the strength of the electromagnetic force inside the hydrogen atom, and divide it by the strength of gravity inside the atom. The result is 40 to the power 38.
So what links gravity, sub-atomic particles and the age of the universe? Some think the connection is just a coincidence, others that it hints at an undiscovered link between the sub atomic world and the entire cosmos. This is the real fascination of coincidences. Usually they're just flukes thrown up at random. Yet some times they really are significant. Spotting the difference is tricky-but it can win you a Nobel Prize.

The "spooky" Titanic coincidence- explained
In 1898, a book was published in America called The Wreck of the Titan. Its author Morgan Robertson told the story of The Titan, a huge, 46,000-ton liner, deemed unsinkable by its builders. On its maiden voyage from England to New York in April, it struck an iceberg in the North Atlantic and sank. With too few lifeboats many passengers drowned.
Fourteen years later, in the early hours of April 15,1912, the "unsinkable" 45,000 ton Titanic hit an iceberg on its maiden voyage from England to New York and sank. Half the passengers were drowned - there were too few lifeboats. An in a final spooky twist, the Titanic said to have sunk with a copy of The Wreck of the Titan in its library.
Uncanny? Perhaps - until you start to look at the parallels more closely. Firstly,if you're going to write an exciting book about an ocean liner, it's unlikely to focus on the 56th trip of the world's 223rd largest ship. It's more likely to feature the maiden voyage of the biggest liner ever.
The size of the ship effects the choice of name - the SS Midget doesn't really work. So, look up synonyms for "huge" and you'll find "gigantic","colossal" and ..."titanic". The real surprise is that the author of The Wreck of the Titan didn't get the name exactly right.
What's the most dramatic thing that can happen to a ship? Sinking, of course. And what could sink such a huge liner ? Icebergs are the obvious choice: long before The Wreck of the Titan, icebergs in the Atlantic were a notorious hazard. They sank the SS Pacific in 1856, and Cunard's Persia hit an iceberg on its maiden voyage in the same year. And how about adding a bit of drama by having too few lifeboats to go round?
"Spooky" parallels between The Wreck of the Titan and the Titanic highlight a key to understanding coincidences: many of the parallels - such as the similar huge size and : names of the ships - are related to each other. Probability theory shows that this makes them far more likely to appear together than if they were totally unconnected.

When coincidences set the bells ringing
Among the most controversial explanation for coincidences is the : "morphic resonance" theory, first put forward in 1981 by former : Cambridge University research fellow, Dr Rupert Sheldrake. He claims that all living creatures are bound together by a "morphic field" which allows them to share and benefit from the experiences of others.
It may sound like a lot of New Age mumbo-jumbo, but Sheldrake claims there is evidence that people throughout the world find it easier : to do a thing once one group some- where has mastered it.
Such a coincidence took place last : year in the arcane world of bell-ringing. For 250 years, people had wondered whether a certain bell-ringing pattem - called "common bob Stedman triples"-could be rung. On 22 January 1995 a team at St John's Church, London, finally succeeded. Within days it emerged that two other groups, both working independently, had also solved the centuries-old mystery. A mere coincidence? Dr Sheldrake,at least,thinks there's more to it than that.
Robert Matthews

All the presidents' coincidences

Can you always find a link between any two people? And are US presidents really flukey?

Richard Nixon (right) idolised Thomas Jefferson(below), drafterof the American Declaration of Independence, and some people claim there are bizarre links between the two.
Both presidents were suceeded by southerners with the first name James. (James Carter and James Madison). Also both had vice- residents who became embroiled in scandal (Spiro Agnew, for tax evasion and Aaron Burr for killing a rival in a duel).
Many coincidences are said to surround John F Kennedy (right), linking him with Abraham Uncoln, Jesus and even the obscure President Oregon of Mexico, shot in 1928.
Expert extras
Robert Matthews, a visiting research fellow at Aston University, has studied the impact of probability theory on everyday life. His research has been published in the following academic journals:
  • The Law of Credulity, Robert Matthews - Mathematical Gazette vol 77, 1993
  • Why are Coincidences so Surprising?, Susan Blackmore and Robert Matthews Perceptual Motor Skills, vol 80

Further reading

  • Serendipity - Accidental Discoveries in Science, Royston Roberts (Wiley, 1989)
  • Bizarre Beliefs, Simon Hoggart and Mike Hutchinson (Richard Cohen Books, 1995)
  • A New Science of Life, Rupert Sheldrake (Anthony Blond Books, 1985)

Well did you ever?
Write to Focus with your bizarre coincidences. We'll publish the freakiest flukes in a future issue.


Concerning Richard Parker - in the film LIFE OF PI the tiger was called 'Richard Parker' - the story is related by actor Irrfan Khan,who also appeared in Amazing Spiderman - Peter Parker's father in the film is called Richard.

Steven Hawking died on Pi day and Einstein's birthday.


Unbelievable Coincidences

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Jul96 p26