Coincidence or conspiracy?

Consider these well known historical connections:

TITANIC:  In 1898, a British author wrote a story about a luxury liner, 800ft long, which was travelling at full speed when it hit an iceberg in the North Atlantic, and sank with the loss of 2500 people. The loss of life was so great because the ship didn’t carry enough lifeboats. Its name – The Titan!

D-DAY:    In May 1944 a schoolteacher, Leonard Dawe, who composed the daily crossword for a London newspaper, included over a couple of weeks words which were not only the names of two of the D-Day (June 1944) landing beaches, Utah and Omaha, but several of the key code-words – Overlord, Mulberry and Neptune. No-one outside General Eisenhower’s staff was supposed to know these words, so Dawe was arrested as a spy only to be released shortly after when it became clear that the words were randomly chosen.

LINCOLN and KENNEDY:    Both presidents Lincoln and Kennedy were elected 100 years apart (1860 and 1960)  and both were assassinated. They were both succeeded by Southerners named Johnson, who were themselves born 100 years apart. Both assassins were killed before being tried, and were born … 100 years apart! Lincoln was shot in a theatre, his assassin cornered in a warehouse: Kennedy was shot from a warehouse, and his assassin caught in a theatre. Lincoln was shot in Ford’s Theatre, Kennedy was shot in a Ford Lincoln. Both presidents had bodyguards named William.

In two of these cases, we are in fact looking at remarkable coincidences (can you guess which?) – whatever conspiracy theorists may say, or whether it is true that all of human history is simply an experiment by extra-terrestrial scientists. It is pretty well impossible to compute mathematically the odds of such coincidences occurring, but the point really is this. Given the billions of human interactions that are occurring every day, it would be remarkable if there weren’t a number of such coincidences – perhaps for every coincidence which occurs, there are 10 billion which don’t. (It is likely that Dawe heard these words from the boys in his school who used to visit the local American base, and where security was a bit lax).

Of course, in much more controlled situations, the probability of events which look like extraordinary coincidences can be calculated. For example, it can be shown that if you have 23 people in a room, there is more than a half chance that two of them share a birthday. Intuitively (try asking people), you might expect to have 180 people before you get to somewhere near a half chance. Another example: try dealing out two packs of standard playing cards, side by side, one card at a time. What is the probability that, before you get to the end, you will simultaneously turn up exactly the same card. Believe it or not, it’s around two thirds! In other words, such an event should happen two times every three deals. Try it and see.