Coincidence.

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Why Rare Events Happen All the Time

Faye Flam is a Bloomberg View columnist. She was a staff writer for Science magazine and a columnist for the Philadelphia Inquirer, and she is the author of “The Score: How the Quest for Sex Has Shaped the Modern Man.”
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Something weird seems to be happening in the heavens. This week marks a coincidence of the full moon and the summer solstice. Some astronomers are calling this combination of maximum moonlight and the Northern Hemisphere’s longest day a rare event. It comes close on the heels of last month’s rare passage of Mercury in front of the sun, September’s rare pairing of a lunar eclipse with a so-called supermoon, the rare 2014 “tetrad” of lunar eclipses, the rare 2012 transit of Venus, and a plethora of once-in-a-lifetime planetary alignments, one earlier this year, one in 2014 and one in the summer of 2013. Next year there will be a rare total eclipse of the sun.

If these sorts of events are so rare, why do they happen so often?

Ask a statistician. David Hand, a professor at Imperial College London makes sense of world’s abundance of rare events in his 2014 book, “The Improbability Principle: Why Coincidences, Miracles and Rare Events Happen Every Day.”

The funny thing about this week’s coincidence of solar and lunar cycles is that astronomers can’t decide if we should be more surprised that it’s happening or that it hasn’t happened since 1948. Here’s a passage from a press release an astronomy group sent me:

During the broadcast, Slooh host Paul Cox will be joined by Slooh Astronomer Bob Berman to discuss this rare astronomical combination, including why it's been so long since the last one, when such a combination is mathematically predicted to happen every 15 years. Having a full moon land smack on the solstice is a truly rare event," says Berman.

The fact that astronomers could present either the event or its absence as noteworthy makes some sense in light of what Hand calls “the close-enough effect.” This effect comes into play in news stories about people who win the lottery more than once, he said. Often one “win” is really a more commonplace second and third prize. The more you relax the definition of winning, the greater the odds it will happen twice.

The same principle can influence the odds of a full moon solstice. Defining the full moon is like defining the top of a hill. This month’s full moon occured at 7:02 am on Monday in the Eastern U.S. time zone, after which it will get gradually less full. People ultimately decide what counts as a full moon. The summer solstice can also be defined as a point in the earth’s 365.2425-day orbit when the sun reaches its maximum height above the horizon at the North Pole. That happens at 6:34 pm EDT. So these coinciding events are almost 12 hours apart.

According to the astronomers issuing the press release, they are counting the whole day of June 20 as the solstice and also extending the definition of the full moon to encompass several days when the moon looks pretty full. By that definition, a full moon June solstice is expected on average every 30 years. The recent dry spell of nearly 70 years is a little more unusual, but no cause for surprise in a world ruled by the improbability principle.

The cycles of the moon and sun are predictable, but they aren’t in sync so you would expect bunches and gaps.

However, there is still the recent pileup of other rare events to explain – some of them, such as the transit of Venus, much rarer than a solstice full moon. Another facet of the improbability principle can help. It’s called “law of combinations,” which Hand illustrates with a classic puzzle regarding shared birthdays: What are the odds that two people will share a birthday in a group of 23? If you’re in the group, the chance that one of the other 22 people will share your birthday is low, but the odds that any pair will match is better than even.

Likewise, there are many ways that different combinations of the sun, moon and planets can align in some interesting pattern. Planetary alignments are always unique, said astronomer Alan MacRobert, an editor at Sky and Telescope. “Whenever there’s an alignment of planets you’ll read that it has not happened in 20,000 years,” he said. But that’s the case of every night sky. “There are an infinite number of configurations of the solar system and every one is rare,” MacRobert observed. The universe is superabundant with possibilities, and that’s part of what makes astronomy fun.

Next year’s solar eclipse is surprising not because the moon, earth and sun shouldn’t occasionally line up the right way, but because the sun and moon have conspired to be just the right distances and sizes so they appear of identically sized disks in the sky. The odds against this are astronomical, but given the number of other possible such conspiracies, it’s not unexpected.

Down on the ground, the concentration of interacting stuff leads to an even greater apparent frequency of miracles and freak events -– a lottery draw that pulls the same numbers twice in a row, Hand getting two e-mail messages in a row from two different people with the same unusual name, or my being in a restaurant bar talking about a person I’d recently interviewed, only to see the very person walk in the door.

Armed with an understanding of statistics, it takes no magic to explain how the universe could produce an octopus named Paul who would correctly predict the outcome of the 2010 World Cup. That such things should be expected to occur might make the magical look more mundane. But it can also make the mundane seem more magical.

This column does not necessarily reflect the opinion of the editorial board or Bloomberg LP and its owners.

To contact the author of this story:
Faye Flam at fflam1@bloomberg.net

To contact the editor responsible for this story:
Jonathan Landman at jlandman4@bloomberg.net