monkey's uncle

To Serve Man

January 2nd, 2009 · 5 Comments

So there I was. 23 hundred hours, New Year’s Eve 2008 at my in-laws’ in Corvallis, Oregon. Kids asleep in the other room. Spouse headed in the same direction. Insomniac from lack of activity and feelings of general physical displacement. Not much prospect for a party or other New Year’s antics. Sounds like the perfect set-up for a Twilight Zone marathon, no? I think that I managed to make it through about 8 episodes in the wee hours of the first day of 2009. I wonder what that augers for the new year?

One of the episodes I managed to watch was “To Serve Man” (viewable freely in its entirety here). It’s your standard aliens land, aliens altruistically transfer advanced technology, aliens solve all of humanity’s problems, aliens turn out to have ulterior motives, aliens plan to eat all of humanity kind of plots. You see, the Kanamits have come to Earth to bring humanity back to their home world to eat them. The book that the Kanamits spokesman leaves in the United Nations (the big tease…) turns out to be a cookbook, a fact that the crack cryptographic team headed by protagonist Michael Chambers discovers too late. Chambers is already boarding the ship bound for his vacation getaway to the Kanamits’ home world when the real brains of his outfit, the beautiful Pat, comes running to inform him (and, maddeningly for humanity, only him) of the horrible news. He’s shipping off to get eaten. Get it? “Serve” as in provide assistance vs. “serve” as in provide a meal?

Toward the end of the episode, Michael Chambers, says in soliloquy that the recollections he has just shared represent the life cycle of Man “from dust to dessert.” He comments that every person will ultimately share his fate (i.e., being served): “Sooner or later, we’ll all of us be on the menu.” This is what got me. Surely not. This doesn’t seem like very good natural resource management on the part of the Kanamits.

The classical theory of natural resource management suggests that there should be a maximally sustainable yield for farmed humans. We will assume that human population growth can be written in terms of its current size and some function of size $\dot{N}= N f(N)$, where $\dot{N}$ indicates the derivative of population size with respect to time $t$. For simplicity’s sake, let’s assume that the effect of density on the human growth rate is linear such that $f(N) = r(1  N/K)$, where $r$ is the intrinsic rate of natural increase $K$ is the carrying capacity (i.e., the maximum number of people the Earth could potentially support).

Now, I should note that this is a purely hypothetical exercise meant simply to illustrate basic concepts. In any real Soylent Green like future where we are faced with fattening Peter to save Paul, we would need a much more sophisticated population model. Among other things, the idea of a carrying capacity for humanity is a maddeningly elusive one. The eminent demographer Joel Cohen has written a whole book on the matter and comes up with no particularly satisfying answer to the seemingly basic question of How Many People Can The Earth Support?

For argument’s sake, let’s just say that the maximum intrinsic rate of increase is $r=0.04$ (4% annual growth, which is high, but remember, humanity has just received this remarkable technology transfer) and the carrying capacity is $K=10^{10}$ (i.e., 10 billion). Population growth changes with population size. We can plot the incremental increase (recruitment) as a function of population size. The maximum point of this so-called recruitment curve, where $d\dot{N}/dN=0$ is the MSY.

For the simple linear model of density-dependence (i.e., the logistic growth equation) and with no time preferences on the part of the Kanamits, the maximum sustainable yield (MSY) occurs at $MSY=K/2$ or 5 billion souls. So, you can now understand my dismay at 0200 (or whatever it was) on the first day of 2009. Why would everyone necessarily meet the fate of Michael Chambers? Under optimal harvest management, only half should be harvested. I can think of at least three explanations for this conundrum:

1. Michael Chambers is either misinformed (he was a cryptographer, after all, and not a wildlife manager) or was exaggerating for dramatic effect.
2. The Kanamits, while advanced in the physical sciences, had not developed an adequate theory of natural resource management or population dynamics more generally. Perhaps this is why they needed to come all the way to Earth to acquire their dessert?
3. Perhaps the Kanamits actually had a very sophisticated understanding of population biology and realized that the human intrinsic rate of increase was less than the prevailing discount rate. Under these conditions, the optimal resource-management strategy is liquidation of the stock.

I’m leaning toward explanation #3. That was an awful long way to come, after all.

Sobering thoughts with which to commence the new year.

5 comments on “To Serve Man”

1. jhj1 on said:

I suppose I should add that $K/2$ is only the optimal harvest when there is no time preference. More generally, the optimal harvest rate is where the $ddot{N}/dN=delta$, where $delta$ is the discount rate.

2. Sadie on said:

Is there some allee effect that comes in when people despair of escaping the aliens and entirely stop trying to have children? Allieeen effect?

3. daedalus2u on said:

I would like to point out that it is virtually impossible that humans would be edible food to aliens that evolved in a completely different biome.

In eukaryotes the terminal digestion of food occurs in the lysosome. All eukaryotes have lysosomes which they use to recycle and degrade cellular contents when those cellular contents become degraded, for example mitochondria. Eukaryote proteins are digestible because the lytic enzymes that are ported into those lysosomes are related and are capable of degrading the structural and other components of other eukaryotes. Some of those components are not fully degraded but are utilized as larger components (i.e. as peptides not as amino acids).

One of the reasons human flesh is so digestible (for humans) is because the lytic enzymes used in autophagy have co-evolved with the structural proteins that humans require to be degraded.

It is quite unlikely that a completely alien metabolism would be compatible with using a random eukaryote as food. I think there might be particular difficulties dealing with heme, iron, copper and other Fenton active metals as proteins containing them are degraded.

If the Kanamits are not using humans as food, perhaps they are using them as drugs. It is not unreasonable that some human constituents would mimic Kanamit signaling compounds and so cause drug-like effects. This would require much smaller quantities and the indigestibility might not be an issue. There was another movie about this called “liquid sky”. That might explain the non-sustainable harvest (before the alien DEA acts to eradicate the drug source).

4. jhj1 on said:

Though I deal in theory much of the time, at heart, I am an empiricist. The Kanamits had a cook book for humans, which presumably means they had multiple ways of preparing us. It seems that the facts of the case tell us that the Kanamits ate humans. It is then up to our science to explain how they were able to do so when it seems that they shouldn\'t be able to.

5. daedalus2u on said:

Humans consume multiple types of leaves by a variety of processes, tobacco and coca are smoked, tea and coca are extracted in hot water and drunk, coca is processed with alkali and chewed, tobacco is processed with sweetners and chewed. A variety of leaves are used as flavoring agents and provide little or no nutritive value.

I didn\'t see the film, so can\'t really comment on the fidelity of the data and whether it could be used to distinguish between a \"cook book\" and a \"preparation book\" (which to me seems a subtle difference).