The Calculus Diaries - Jennifer Ouellette [78]
The Gompertz mortality curve is another sigmoid function, wherein growth is slowest at the beginning and end of a given time period, much like epidemiological models; in fact, Gompertz based his model on the demographic model of Malthus. The slope of the tangent line at any given point (age) along that curve gives us the rate of actuarial aging in the form of a derivative. To get the probability of living to a certain age, all we have to do is integrate the mortality rate over time. The result is that sigmoid curve: the “Gompertz function.”
That’s right: The body has a built-in expiration date. For example, a twenty-seven-year-old American has a 1 in 3,000 probability of dying during the next year, but by the time the person is 35 that probability has increased to 1 in 1,500; by age 43, it has narrowed to about 1 in 750, and so on, so that, if one reaches 100, there is only a 50 percent chance one will live to see 101. The probability that you will die during any given year doubles every eight years. It still holds true today, despite all the advances in nutrition, medicine, and quality of life, and it holds across countries, centuries, even across species, once the different rates of aging are factored into the equation. Scientists don’t understand why this should be true, but it is—for the most part. There are certain age-independent factors at work as well, but in a low-mortality country, like Japan or the United States, this component is usually negligible. Gompertz himself died at the ripe old age of 86. He was working on a paper for publication in the journal of the newly formed London Mathematical Society when he suffered a paralytic seizure.
Working out and eating right to ensure better health is a noble endeavor, but sooner or later the Gompertz law of mortality kicks in. We’re all going to die one day. So it is quality of life that counts, and our overall degree of happiness; being healthy increases our quality of life. Perhaps that is the real benefit of the Green Microgym concept: It might not save the planet, one workout session at a time, but it saves the gym a bit of cash and makes people feel good about their efforts, in addition to keeping them fit. “There’s a certain satisfaction when you work out and feel like you’ve actually accomplished something, instead of just spinning your wheels,” Taggett has said.
Just in case good vibes aren’t enough, Boesel offers gym members special bonus points: For every hour of electricity a member produces, she or he will earn coupon points redeemable at local businesses. Most important, as I found during my own brief session on Boesel’s retrofitted machine, the Green Microgym raises awareness of just how much energy we consume without thinking—and what it costs to generate that energy in the first place.
8
The Catenary Tales
As hangs the flexible chain, so but inverted stands the rigid arch.
—ROBERT HOOKE
It is a bitterly cold February afternoon in St. Louis, the kind of day that finds most people opting to curl up by a roaring fire with a good book and a nice cup of tea. But I am only in town for a few short days while attending a conference and thus join a handful of other hardy souls visiting the famed Gateway Arch. It is a landmark structure that opened in October 1965 to commemorate Thomas Jefferson’s Louisiana Purchase and now dominates the St. Louis skyline. Five of us cram into the little egg-shaped tram and ride to the peak of the arch, where we can gaze out over the frozen expanse of this Gateway to the West, named in honor of the early pioneers who migrated west through St. Louis on the first leg of the Oregon Trail.
The spectacular view is marred somewhat