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Am I Going To Die This Year? A Mathematical Puzzle

Wednesday, January 08, 2014 - 08:27 AM

A few years ago, physicist Brian Skinner asked himself: What are the odds I will die in the next year? He was 25. What got him wondering about this, I have no idea, but, hey, it's something everybody asks. When I can't wedge my dental floss between my two front teeth, I ask it, too. So Brian looked up the answer — there are tables for this kind of thing — and what he discovered is interesting. Very interesting. Even mysterious.

Obviously, when you're young (and past the extra-risky years of early childhood), the chances of dying in the coming year are minuscule — roughly 1 in 3,000 for 25-year-olds. (This is a group average, of course.)

Robert Krulwich/NPR

But eight years later, the tables said, the odds will roughly double. As Brian writes in his blog post, "When I'm 33 [the chances of my dying that year] will be about 1 in 1,500."

Robert Kruwwich/NPR

And eight years after that, he says, the odds double again: "It will be about 1 in 750."

Robert Krulwich/NPR

And eight years later, there's another doubling. Looking down the chart, you'll see that keeps happening and happening and happening. "Your probability of dying during a given year," Brian writes, "doubles every eight years." Hmmm. When I looked at the latest tables (Brian's came from 2005), he's more or less right. Which got me wondering ...

Robert Krulwich/NPR

Why eight? Why the doubles?

This wasn't Brian's discovery. A British actuary, Benjamin Gompertz, noticed this pattern back in 1825, and ever since it's been called the Gompertz law of human mortality — yes, death creeps closer, but it creeps closer in orderly steps (for humans about every eight years).

Robert Krulwich/NPR

Doubling of this sort, when plotted on a chart, looks scary in the later years, but every interval early in the curve is also a doubling. So the same thing keeps happening, only the effects become more pronounced. Anyone reaching the age of 100 seems to have a 1 in 2 chance of getting to 101.

Looking at his pattern, Brian writes, "I can say with 99.999999 percent certainty that no human will ever live to the age of 130." (That's assuming, which one shouldn't, that we have no new, heroic medical advances.)

OK, so this happens. The pattern, says Brian, "holds across a large number of countries, time periods and even different species. While actual average lifespan changes quite a bit from country to country and from animal to animal, the same general rule that 'your probability of dying doubles every X years' holds true."

But here's the dangling question: Why the regular interval? Why eight years for humans?

Robert Krulwich /NPR

Brian's answer: "It's an amazing fact, and no one understands why it's true."

Really? Shouldn't there be some obvious explanation?

It's pretty obvious that when surveying a large population, death is not really a random, sudden bolt of lightning out of the blue. If it were, as Brian points out, the bolt would hit randomly, and in any collection of people ...

Robert Krulwich/NPR

... the babies would be as likely to die as the oldsters, youngsters, middle-agers. But that's not how it works. Older people die more frequently than younger people (in peacetime, anyway).

So — random, death isn't.

Couldn't the latest biological explanations for aging explain an eight-year doubling pattern? Brian considers this question in his essay. He calls it the "cops and criminals theory." (It's based on a short paper by Boris Shklovskii.) As Brian describes it:

Imagine that within your body is an ongoing battle between cops and criminals. And, in general, the cops are winning. They patrol randomly through your body, and when they happen to come across a criminal, he is promptly removed. The cops can always defeat a criminal they come across, unless the criminal has been allowed to sit in the same spot for a long time. A criminal that remains in one place for long enough (say, one day) can build a 'fortress' which is too strong to be assailed by the police. If this happens, you die.



Robert Krulwich/NPR

Lucky for you, the cops are plentiful, and on average they pass by every spot 14 times a day. ... But what happens if your internal police force starts to dwindle? Suppose that as you age the police force suffers a slight reduction, so that they can only cover every spot 12 times a day? ... The difference between 14 and 12 doesn't seem like a big deal, but the result was that your chance of dying during a given day jumped by more than seven times. And if the strength of your police force drops linearly in time, your mortality rate will rise exponentially.

This is the Gompertz law, in cartoon form: Your body is deteriorating over time at a particular rate. When its 'internal policemen' are good enough to patrol every spot that might contain a criminal 14 times a day, then you have the body of a 25-year-old, and a 0.03 percent chance of dying this year. But by the time your police force can only patrol every spot seven times per day, you have the body of a 95-year-old with only a 2 in 3 chance of making it through the year.

This sounds right, that our immune system deteriorates at a steady pace, leaving us with fewer and fewer cops to remove the troublemakers in our bodies. As a metaphor, it works. But, says Brian, "unfortunately, the full complexity of human biology does not lend itself readily to cartoons about cops and criminals." There is no biological finding that explains the eight-year pattern we find in the mortality tables. The idea is nice. But the math? It has no obvious logic, no explanation — not yet. We know death is approaching, but why does it like the number eight?


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Comments [6]

Nate from X324-Y4

The funny thing is 8 is my favorite number...creepy.

Apr. 25 2016 10:21 AM
Charles Wells from Houston, TX

Two things make this really cool. One, it shows you that if you're curious and like to play with data, you could possibly stumble into seeing a pattern that no one ever realized was there before.

The second thing is their cops and criminals analogy. Even though it's a little cartoonish, once you get a good analogy, it can lead you to even more insights.

Anyway, you can now play with data in ways that no one could before. There was a site called "blogpulse" that if you entered search terms, would graph the frequency of those terms (as used in blogs) by date. So you could make up your own experiments. I wonder how "important" Christmas is compared to Thanksgiving in people's minds. I wonder about when in the spring mosquitoes start to emerge. I wonder which subject students hate the most (and if proximity to finals makes a difference.) Although blogpulse is gone, google has some tools like its ngram graphs.

There is so much to learn about our world, and so many new ways to learn it!

Apr. 22 2016 10:40 PM
Ernie from Mars

The doubling at a constant interval is interesting, but there should be more focus on the fact that they're just milestones on a trendline with a constant rate of change.

Apr. 18 2016 02:48 AM
Hi mom from Atlanta, GA

Honestly it doesn't seem that strange. The graph clearly shows an exponential trend (specifically f(x) ~= 2^x), the doubling every 8 years just happens to describe where the trend falls. That's why it makes sense that other cultures may have a doubling every 6 years, etc. as described in your article- the number 8 is a red herring, it seems to me.

Apr. 18 2016 02:43 AM
FMisch from Oklahoma

I think there must be some connection to the Golden Ratio/Fibonnaci sequence in which there are many patterns noticed in nature that follow the Ratio. Perhaps elucidating a relationship between mortality rates and the Ration might further answer why they exist in their observed forms. I have seen the Ratio described it is such as a natural consequence of the growth of any living thing. But that still begs the question why growth follows the ratio.

Apr. 02 2016 02:08 PM
marley engvall from florence, massachusetts

This is why it makes sense for me to conduct my 9/11 hunger strike this year, not next year, not eight years from now. I am presently in no great danger of dying, so if you, Robert Krulwich, allow me to die in September, because you are too weak and money-driven to speak honestly, and to stand on the side of the human race, your complicity in the crime of 9/11 will be complete. You cannot hide from this judgment.

The idea that the death of Jesus could somehow absolve believers of their sin, is the greatest psyop over perpetrated on the human race. Our sins belong to nobody but ourselves.

I am prepared to die for your sins -- and believe me, these are your sins, just as they are mine, taxpayer.

Lest this statement be construed as my painting myself messiah or christ, let me assure you, my death will not absolve anyone of their sins, especially not myself. Not only would my dying compound your sin of silence, in the face of great evil, it would constitute a new and grievous crime for each of you to add to your list of transgressions, leaving a six-year-old boy without his father, two loving parents without their only son.

Is it self-censorship that makes every mainstream voice a cowardly, dishonest sack of shit, or is there some covert martial law that prohibits you from speaking truthfully on air?

I have always wondered if you were hinting at this in your piece, 60 Words.

Whatever the case, your silence is complicity in the crime of 9/11. May history revile the lot of you.

Apr. 01 2016 11:07 PM

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