Wednesday, December 02, 2009

"Possible to live forever"

Iris came to the Institute to have lunch with me. We were sitting and eating the tasty pasta dish she'd made when my friend passed by. He stopped to say hi. Iris picked up on the fact that he was excited about something before I did.

"What's new?" she asked.

"I have discovered that it is possible to live forever," he said, with no hint of irony.

"Oh?," I said, taking another delicious bite of pasta and doing my best to maintain a neutral tone.

He went on to describe how he had noticed that under a set of mathematical assumptions about the pattern of human aging, if one plugs in the right values for various parameters, one can get the result that life expectancy approaches infinity. I'm not going to give away his secrets, or try to explain the bit of calculus he uses, but the whole proof fit on one page including only a handful of equations. There, in black and white was mathematical proof that one could live forever. Well sort of. The math was impeccable, at least I couldn't peck it. The question is how relevant was the mathematical model, and how meaningful were the limits he was taking?

Often when we use mathematical models of the world it is because we think they not only approximate the outcomes of the pattern, but actually describe something about the underlying process. An object fired up into the air will fall to earth in a parabola, a real, honest, no tricks involved parabola. The form arises just from the interplay of momentum and gravity, and the parabola arises, not as a fluke, but under a wide range of gravities and velocities. In other words, we think that sometimes the mathematical ideal is what the world is actually approximating. There is thinking that the mathematical forms my friend employs actually are the underlying form of human aging. They are our best guesses anyway. So maybe, just maybe, exploring the limits of that form tell us something about the limits of possibility when it comes to aging. Unfortunately, relationships that hold under a wide range of velocities often don't hold at the limits. Shoot the object at an improbably high velocity and it will escape Earth's gravity entirely, and likely end up orbiting the Sun, eventually making an ellipse. Shoot the object too slowly and forces such as viscosity, friction and wind become increasingly important, and the object will trace a good approximation of a line-segment to the ground. So while my friend's mathematical discovery is interesting and novel, I remain skeptical that he has found the possibility of immortality. Rather he has shown that if one makes extraordinary and unexpected assumptions, one can arrive at extraordinary and unexpected conclusions. Important, but hardly the key to eternal life.

Sorry to be such a downer.


Fern said...

I left soon after he produced said mathematical proof of eternal life. I will attempt to understand it only if I can live forever!

Dan Levitis said...

Unfortunately, understanding the mathematics is not likely to grant immortality.

GreenEngineer said...

It's very popular these days to hang your hat on a model, while failing to question whether the model is robust, or applicable to the relevant analysis.

Apparently this is a big part of the reason that our financial system imploded. Even those defend the model acknowledge that there was a major failure in its application.

I see exactly the same problem in my work, in the use of building energy models. We are very careful here to ensure that we don't lend the model results more confidence than they deserve, but this level of care is not common to the industry. Of course, this doesn't break the financial system; it just results in buildings that use far more energy than expected (and thus ultimately helps break our energy infrastructure).

One thing that has become clear to me is that people who don't understand these models tend to trust them too much. When you're trying to tell an architect that they've put too much glass in the building (a common refrain for HVAC engineers), it's much more effective to say "the model says so" than to say "my professional intuition and experience says so". Unfortunate, but true.