The Misuse Of Coincidences

Last week I presented some problems that occur when a measurement of a population is assumed to be random in the sense of unbiased sampling. Today we consider a related issue that has likely been the cause of more human misery than any other single thing: coincidences.

How can coincidences be harmful? Coincidences are things that just happen. My dictionary says coincidences are the occurrence of events that happen at the same time by accident, but seem to have some connection. The dangerous part is that word “seem.” One of the powerful mental tools that helped us evolve as far as we have from our primate ancestors is a wonderful ability to extract meaningful patterns from raw data. We do it all the time. We love to do it. Finding patterns is critical to making scientific discoveries. However, in our rush to impose order or patterns on data, we often make mistakes and these mistakes can be long lasting and harmful.

A relatively benign example is construction of constellations. Think of the Big Dipper. There it is in the sky. You would be hard pressed to look at it and not see a pattern. Today we know the stars in the Big Dipper are not closely related to each other. If you stand some light-years away from here, or if you just wait long enough, the Dipper will become something else. But if you did not know about the three-dimensionality of space, you would assume that stars appearing close to each other are related. (The Pleiades are a special case - they are related.) This benign grouping of unrelated stars into constellations has repercussions. Watching the planets move among the stars and looking for other patterns is what burdened humanity with the mixed bag of astrology. I say mixed bag because that false belief did much harm (like getting people burned at the stake) but the rigor needed to make celestial predictions became a facilitating factor for much good.

Coincidences come in many flavors. Sometimes a tree growth or oil spill will resemble the holy symbols of some religious sect and the faithful will flock to see the wonder. Clever hoaxers can take advantage of unplanned coincidences to make people think they have special powers. Uri Geller seems to be particularly good at this according to skeptics.

Generally the false impressions given by coincidences can be overcome by a more rigorous examination of the data. Consider a relatively recent example which I adapted from a new book, “Coincidences, Chaos, and That Math Jazz” by Edward B. Burger and Michael Starbird:

Abraham Lincoln was elected to Congress in 1846.
John F. Kennedy was elected to Congress in 1946.

Abraham Lincoln was elected president in 1860.
John F. Kennedy was elected president in 1960.

Lincoln’s secretary was named Kennedy.
Kennedy’s secretary was named Lincoln.

Andrew Johnson, who succeeded Lincoln, was born in 1808.
Lyndon Johnson, who succeeded Kennedy, was born in 1908.

John Wilkes Booth, who assassinated Lincoln, was born in 1839.
Lee Harvey Oswald, who assassinated Kennedy, was born in 1939.

And so on for many more coincidences. There must be something going on here. How can those two presidents have so many things in common unless there is some mysterious linkage? It probably has to do with pyramids or crystals and certainly demonstrates predestination.

But wait a minute. Before we assign these observations to the realm of the supernatural, let’s ask how many potentials for accidental coincidence were investigated and whether any of the observed coincidences could be related and thus not be independent data. For instance, the fact that both Booth and Oswald were younger than their targets can be due to the fact that younger people tend to me more hot-headed and they can’t be much younger by the condition of the events. Therefore the ages are not random. The time delay between entering Congress and being elected president is not a random number either.

What life events of these two men do not correlate? Consider that they have different birthdays and year of birth. That was not mentioned when the identical (+100) birth years of the vice-presidents were given. They graduated in different years. They married differently. The items where they do not resemble each other outside of events associated with their profession are much more numerous than these few special coincidences, but we tend to fixate of the special coincidences because they are unexpected.

What about the coincidence of a meteor shower when an army is praying for a divine omen? What are the results if the army wins? If it loses?

The most notorious misuse of coincidences occurs when they are looked for and found after the events - such as the comparison of presidents Lincoln and Kennedy. Coincidences can be twisted into explanations innocently or by design. In future articles, we will discuss more how to distinguish between a reasonable relationship and pure coincidence. In the meanwhile, if you have shown that blowing on the dice before throwing them improves your luck, go for it.

If you have interesting examples of the misuse of coincidences, let me know, and I will feature it in a later article.

In response to the interest my original tutorial generated, I have completely rewritten and expanded it. Check out the tutorial availability through Lockergnome. The new version is over 100 pages long with chapters that alternate between discussion of the theoretical aspects and puzzles just for the fun of it. Puzzle lovers will be glad to know that I included an answers section that includes discussions as to why the answer is correct and how it was obtained. Most of the material has appeared in these columns, but some is new. Most of the discussions are expanded compared to what they were in the original column format.

[tags]hoax,decision theory,chaos,astrology,coincidence,omen,portent,simulacrum,kennedy lincoln,oswald booth[/tags]