## Blowing out candles with your very last breath

by

Today is the birthday of Henry White, a mathematician who had tremendous influence on the development of the US mathematical community at the turn of the 20th Century; most notably, he was involved in the leadership of the American Mathematical Society, played a role in the creation of the AMS Colloquium Series, and served as editor of Annals of Mathematics as well as the Transactions of the AMS.

Today is also the anniversary of Henry White’s death.

The MacTutor History of Mathematics website notes that he is the only person in their database whose birth and death dates coincide. As they have thousands of biographies on their site, most of which apply to deceased individuals, and a significant number of which should have reliable birth and death dates, this dearth of birthday-death is a tad surprising.

How likely is one to die on one’s birthday?

Some assumptions:

• We’ll limit ourselves to individuals who reach “maturity”; one expects childhood illnesses and other factors cause the very young to have a radically different distribution of death dates measured relative to birth dates mod 365 than one would find in the adult population.
• We’ll ignore those who are born or who die on a Leap Day.

As a working hypothesis, we’ll assume that one is as likely to die on one’s birthday as on any other day of the year. Under that hypothesis, the probability that one would die on one’s birthday is 1/365.

At this point I would love to be able to go into the details of a hypothesis test, using the data from the MacTutor site as a sample. [It isn't a random sample, but one might posit the assumption that the bias of choosing famous mathematicians from history will have no impact on the birthday-deathday relationship.] Their data, though, isn’t so easy to compile into a spreadsheet, and I have a class to teach in a few hours….

I did, however, find a different data set on the web: the site Who’s Alive and Who’s Dead posts lists of (mostly 20th C) celebrities (actors, musicians, politicians, and the like) who satisfy the criteria for inclusion that the site uses (essentially: someone has to be famous, and potentially the subject of a “Is so-and-so still living? I haven’t seen them in anything lately.”).  Again, not a representative sample of the public at large, but a sample whose biases [hypothetically] would have no impact on the likelihood of dying on one’s birthday. And most importantly, I was able to capture the data into Excel and hack on it.

The Who’s Alive and Who’s Dead data list birth and death dates for 953 individuals; of those, 4 of them died on their birthday: actors John Banner, Ingrid Bergman, and Mike Douglas, and social activist Betty Friedan. The sample size is still a bit small to apply an hypothesis test, but certainly 4 out of 953 is consistent with the claim that the theoretical probability is 1/365.

Several studies have attempted to show a connection between one’s birth and death dates, for a variety of populations. One published study went so far as to claim that celebrities manage to postpone their deaths until after their birthdays — that celebrities are less likely to die in the month prior to their birthday, and more likely to die in the month afterwards. Certainly one can craft plausible scenarios to explain such a pattern, but doubts have been raised as to whether such a pattern exists at all. (Heather Royer and Gary Smith take on the myth of a “death dip” in an article in Social Biology.)

The data on celebrities from Who’s Alive and Who’s Dead show that 82 of the 953 died in the 30 days prior to their birthday; 84 died within 30 days after their birthday. (One would expect on average 78 or so.) This data is consistent with Royer and Smith’s claim that no such death dip occurs.

Gary Smith’s website includes other articles of interest, including work debunking the notion that Americans of Chinese and Japanese ancestry are more likely to die on the 4th day of a month (putatively because of fears generated by cultural perceptions of 4 as an unlucky number), and a study refuting the claim that people with unpopular names have shorter life expectancies.  Highly recommended reading for the statistically inclined.