"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.

Parameterization of the Damned

I have had a headache for the last two days trying to figure out a theoretical problem related to my work. My best attempt to explain the problem, and the closest to a solution I have thus come up with, can be found in the email below, written to one of my research assistants. This is the kind of symbolic thinking that makes my forehead tie itself in a knot. Tell me if what I wrote means anything to you, 'cause it doesn't say a whole lot to me.


Hey Nik-

I have another favor to ask. I've been wracking my brains trying to figure out a problem, that we have no null hypothesis for what G should be. I try to explain the problem and what I'd like to do about it below.

Post-Reproductive Lifespan as measured by G cannot be negative, in that an individual cannot invest in reproduction after her death. G cannot even meaningfully be zero unless every individual dies at age M, the age at which fertility drops of to 5% of its former maximum. If even one individual in the study population lives past age M, G is non-zero. This has left me struggling to figure out what a meaningful null hypothesis for G could be. The answer seems to be that there isn't one. G is a parameter designed for a quantitative, rather than qualitative distinction. Human G is very different from G of non-human primates, but it isn't meaningful to ask if G of non-human primates is different than zero, because we know without knowing anything about the populations that it will be.

The relevant question is: is senescence in fertility offset in age/time from actuarial senescence? If M, is the parameter we use to demarcate the end of fertility, we can use the exactly analogous measure, Z, to demark the end of meaningful survivorship. Z is defined as the last age for which p(x)≥0.05*max(p(x)). ( By the way, in case we don't have p(x) in the data you have, p(x)=1-q(x))
So then the question becomes, how much different is M from Z? Z-M is the post reproductive period, and (Z-M)/(Z-B) is the portion of the adult lifespan that is post reproductive. If we define S=(Z-M)/(Z-B), then S gives us a decent measure of how much reproductive senescence is offset from actuarial senescence. And one that I can at least imagine being zero, in that the rates of survival and fertility can drop simultaneously, even if each individual reproduces only before she dies.

Would you be so kind as to have Access calculate Z and S for the populations we have in the database, and then send me a spreadsheet with B, Z, S and M for each population? I'd like to get a sense of how these variables behave.

Thanks,
Dan

Population Doubling

As I am preparing for my talk, I am doing some intense demographic analysis of my rotifer data set. One interesting factoid I have calculated is that the population doubling time, assuming I could keep an infinite number of rotifers and didn't have to get rid of any, is 28 hours.

A related calculation: If I started with one newly hatched rotifer and let the population grow (with my average age-specific reproductive rates and death rates), after one month I would have 159 million rotifers.

The average volume of a rotifer is about .001 cubic millimeters. A million of them pressed together makes one milliliter. A billion makes a liter. 10^27 would be a cubic kilometer. Earth's oceans have a total volume of 1.347*10^9 cu km, meaning I would need 1.347*10^36 rotifers to fill them completely with no space between rotifers. At the demographic rates they maintain in my lab, assuming I didn't cull any, this would take 138 days.

I only have time, container space and staff to keep track of 450 rotifers at a time, so I end up culling a significant portion of my population every day.

Depth vs. Depth

One of the questions on the exam I am grading asks the students to pick a physical characteristic of ocean water (pressure, density etc.) and draw a plot of that against depth into the ocean, to show how the measurement changes with depth.

One of the students decided to draw a graph of how depth changes with depth. This would technically be a good answer, except that when she plotted depth against depth she got a parabolic curve.