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# The mysterious case of Mme. Calment

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Here’s a statistical series, laying out various points along the 100 longest known durations of a particular event, of which there are billions of known examples.  The series begins with the 100th longest known case:

100th:  114 years 93 days

90th: 114 years 125 days

80th: 114 years 182 days

70th: 114 years 208 days

60th: 114 years 246 days

50th: 114 years 290 days

40th: 115 years 19 days

30th: 115 years  158 days

20th: 115 years 319 days

10th: 116 years 347 days

9th: 117 years 27 days

8th: 117 years 81 days

7th: 117 years 137 days

6th: 117 years  181 days

5th: 117 years 230 days

4th 117 years 117 248 days

3rd: 117 years 260 days

Based on this series, what would you expect the second-longest and the longest known durations of the event to be?

These are the maximum verified — or as we’ll see “verified” — life spans achieved by human beings, at least since it began to be possible to measure this with some loosely acceptable level of scientific accuracy about 70 years ago or so (consistent public health records didn’t exist anywhere before the middle of the 19th century, so maximum life spans prior to the middle of the 20th century are largely conjectural).

Some notes:

(1) There are about 80 known cases of someone reaching the age of 114, and then dying before reaching the age of 115.

(2) There are 24 cases of someone reaching the age of 115, then dying before reaching the age of 116.

(3) There are ten cases of someone reaching the age of 116, then dying before reaching the age of 117.

(4) There are seven cases, supposedly, of somebody reaching the age of 117, then dying before reaching the age of 118.  I say “supposedly” because five minutes of googling reveals that at least one of these seven cases — that of Lucy Hannah — may well involve attributing a much greater age to Hannah than she actually reached. (Indeed, as we shall see, her case may be far from unique in this regard).

Given the mortality rates observed between ages 114 and 117 in the series above, it would be somewhat surprising if anybody had actually reached the age of 118. Thus it’s very surprising to learn that #2 on the list, an American woman named Sarah Knauss, lived to be 119 years and 97 days.  That seems like an extreme statistical outlier, and it makes me wonder if Knauss’s age at death was recorded correctly (I know nothing about how her age was verified).

But the facts regarding the #1 person on the list — a French woman named Jeanne Calment who was definitely born in February of 1875, and was determined to have died in August of 1997 by what was supposedly all sorts of unimpeachable documentary evidence, after reaching the astounding age of 122 years, 164 days — are more than surprising.

I’m no statistician, but that age seems almost like a statistical impossibility, given known mortality rates among the very oldest human populations.  Consider that the age gap between Calment and Knauss is equal to that between Knauss and the 18th oldest known person — and again, note that Knauss’s lifespan is already a massive statistical outlier.  More striking yet is the fact that the gap between Calment and the third-oldest known person (Nabi Tajima, a Japanese woman who died last year) is nearly five years, meaning that many hundreds of people have come closer to achieving Tajima’s life span than Tajima came to reaching Calment’s purported age.

That seems . . . unlikely.

A Russian mathematician named Nikolay Zak has just looked into the matter, and concluded that, despite the purportedly overwhelming evidence that made it certain beyond a reasonable doubt that Calment reached such a remarkable age, it’s actually quite likely, per his argument, that Jeanne Calment died in the 1930s, and the woman who for more than 20 years researchers all around the world considered to be the oldest person whose age had been “conclusively” documented was actually her daughter, Yvonne.

It’s a fascinating piece of detective work, and, while far from definitive in regard to the specific question of Calment’s age and identity, it raises all sorts of broader questions about the production of knowledge in both science and history.

I do find some of Zak’s arguments to be pretty weak: for example, a random sample of more than 200 people were shown a photo of Calment taken on her 117th birthday, and asked to estimate her age, and the average age estimated was 95, which would have been Yvonne’s age exactly. This seems dubious, methodologically speaking. For example, the oldest person I’ve ever spent time with had reached the age of 96 the last time I saw her, so that’s my baseline for what an extremely old person looks like. I imagine most people have the same problem I do in this regard, which is that I have no idea what a person who is significantly older than that is “supposed” to look like.

But several of his other arguments seem much more compelling, although I would want to know a lot more than I know (which is nothing) about French inheritance law in the 1930s before drawing any strong conclusions.

Anyway, it’s a fascinating case, and I suggest reading Zak’s paper in full if you’re at all intrigued either by the specific issue, or the more general methodological and statistical questions it raises.

. . . Andrew Gelman has some thoughts.  He points out that the clustering at 117 is probably just random, and that if you assume a constant annual mortality rate of around 50% after age 110 (there is a good deal of evidence suggesting this is the case, although of course the data on annual death risk become extremely sparse after 114-115) one person reaching the age of 122 out of a total pool of around 100 114-year-olds isn’t extremely improbable, although it’s still pretty unlikely.  His main point though is that from a Bayesian perspective all claims of people reaching 116+ should be treated with appropriate skepticism, given how extremely unlikely this is from an ex ante perspective for any individual (And in fact several such claims have been debunked, even among people whose ages had been supposedly verified by good documentation).