Mathematics |
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Do luck and coincidence truly exist,or can everything be explained scientifically buy 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? |
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| 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.
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Luck or just mathematics?
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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.
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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
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| Richard Nixon (right) idolised Thomas Jefferson(below),
drafterof the American Declaration of Independence, and some people claim
there are bizarre links between the two. |
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| 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). |
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| 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. |
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| 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:
Further reading
Well did you ever? |
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Jul96 p26
