Keith Lofstrom's Immortality and Overpopulation Rant

Some folks say attempts at immortality are bad because they will lead to catastrophic overpopulation. This is nonsense - what leads to overpopulation is making too many babies, too fast. If a catastrophe is inevitable, immortality might bring it about sooner. On the other hand, if the catastrophe occurs after the decision makers presume they will be dead, they may not bother to fix anything. Immortality will give everyone a motivation to solve the problem.

The first thing to consider is that, for any population with a birth rate above the replacement rate, immortality does NOT change the long term exponential growth rate, it just moves the same exponential curve sooner in time by a few years. That means that you can always achieve more by reducing the reproductive rate and flattening the slope of the curve than by attempting to push the same curve outwards. Alternately put, investing resources in immortality rather than reproduction will reduce the long term population more effectively.

It is important to understand some basic facts about reproductive biology. Human females manufacture eggs while they are still embryos, during their first 5 months of gestation. The egg cell count drops from 4 months before birth to about half the original number at puberty, and decreases exponentially after that. Unless you save the eggs, and manipulate female biology significantly, you will not have women remaining fertile well past 50 or so. "Immortal baby machines" will not happen unless you try hard to make that happen; and what would be the point of that?

So any reasonable population model will assume that the birth rate is some function of the reproductive rate times the population of women between 20 and 40 (approximately). You might be able to extend the upper limit of fertility, but that is an entirely separate issue from extending lifespan.

The ideal expressed by most deathists is "healthy lifespan to biological natural limits", typically claimed to be age 120 or so. While that "ideal" is delusional - natural human death rate is tied to morbidity and highly variable - let's take the deathists at their word. This is their idea of an ideal world - a death rate that steps from zero to infinite at age 120.

Now let's compare that to the ideal expressed by the immortalists - no limits, a death rate of zero forever. Let's assume that the accident and morbidity rates for both populations is negligable, there is just a cutoff for the deathists at age 120. Since people older than 120 are not contributing to the birth rate, the population curves for both "death-world" D and "immortal-world" I are identical for all age-groups and times, up to age 120. They diverge sharply after that.

Let's simplify our model by making it exponential and "steady-state" - the population increases over time, at an exponential but steady rate. The exponential model for the subpopulation of each age group is given by:

P( date, age ) = P0 * exp( (date-age) * rate )

The above equation is the same for all ages between 0 and 120; it drops to 0 in D world and continues to taper off exponentially in I world.

What is rate? We can compute this from the replacement rate. If the replacement rate for is 1.5, that means that the average couple begets three babies over their reproductive years. Lets assume that the worst case, that they have triplets when they are 20 years old (fastest possible reproduction). If they wait to have their three babies, the "rate" decreases. This makes the calculation simple:

P( date, 0 ) = 1.5 * P( date, 20 )

so for this example, rate = ln(1.5)/20 = 0.0203 , about 2 percent a year. In general, rate is given by:

rate = ln( replacement_rate )/( reproduction_age );

Total population on any given date is the integral of this equation over age. For world D, the total population is:

P( date ) = (P0/rate) * exp( date * rate ) * ( 1 - exp( -120*rate ) )

For world I, the total population is:

P( date ) = (P0/rate) * exp( date * rate )

As you can see, the populations differ by a fixed factor ( 1 - exp( -120*rate )). Because this is exponential growth, that can be expressed as a time shift:

time_difference = log( 1 - exp( -120*rate ) ) / rate ;

For our example: replacement age = 20 years, replacement rate = 1.5, the time shift is -4.5 years. Sooner, yes, but not much.

That is, they are the same exponential curve, and they will reach the same crisis, just a bit sooner for the I world, if everything else stays constant.

But things will change ...

Reproductive rates will be different in the I world, however. There is no plausible reason to increase the reproductive rate, and many reasons why it is likely to decrease. Even without societal sanctions and interventions, much more of the economy of I world will be dominated by older people. That will have many effects.

I world adults will be more educated. There will be a higher teacher to available student ratio, and there will be more time to accumulate an education. We will no longer be "disposing" of accumulated education with age and infirmity - it will have to accumulate! How does this affect reproduction rates? For a young person to compete in the marketplace, they will have to spend longer educating themselves; the onset of child bearing will be delayed. Without independent technological innovation, the end of child bearing remains fixed. This will lower both the replacement rate and increase the reproduction age. The exponential flattens - I world will always have a lower population.

In a population of permanently healthy adults, age stratification is likely to be reduced. 200 year olds will have a lot in common with 150 year olds; the "different times" will be a distant memory, buried in a haze of synaptic reconnection. Culture will diverge, but it will not be because of age; 300 year old goths will hang out with 50 year old goths in preference to 300 year old jocks, for example. Affinities will form by predilection. While some personality types might fall into an isolated "young adults making babies" clique, it is far more likely that young people will form more social relationships with older people, and have little incentive to make babies and reduce the time available for other pleasures and affiliations. The effect may be large, or it may be small, but it must be in the direction of reduced child bearing.

Healthy men are attracted to women by the appearance of youth (slim, unwrinkled, healthy) rather than clock time; when clock time is decoupled from appearance, older women become relatively more attractive. With increased experience, an older woman of equal attractiveness is more likely to attract a mate than a younger woman. Again, this will reduce the chances of child bearing.

And yes, there will be societal decisions made to control population growth to a desirable level. Most governments in advanced societies are trying to increase population growth rates, though, so folks that claim this as a population reduction magic bullet are more optimistic than I am. Still, societies usually act more rationally than the politicians that attempt to distort them, so I assume that a combination of economics and social pressure will reduce child-bearing even if politicians and governments act in their usual counter-productive ways.

A market solution?

Being a laissez faire minarchist with occasional fits of pure anarchy, I suggest a market solution to the "overpopulation problem". Everyone is issued a "staying alive" permit. If you don't have one, don't expect protection from the rest of us; you are on your own. Given the small but nonzero number of homicidal psychopaths in the world, your survival chances are reduced without a permit. The permit is virtual, logged in numerous places and numerous ways; it is not something that can be stolen.

You lose your permit involuntarily if you kill somebody who has a permit; then your permit is taken from you and given to the heirs of your victim.

These permits are fungible. You can have more than one, you can buy or sell them. Most importantly, you can bequeath them in your will. This means that there will be a permit for child-rearing by your descendents or others when you die. This makes the abstract "die to make room for others" very real, direct, and measurable.

There should be some mechanism for adding or subtracting permits as the carrying capacity of the Earth increases or decreases. A polluter or land destroyer loses permits (they better have some in reserve!), and an inventor or biome regenerator earns newly created permits. I don't know how to objectively measure that, or set up an incorruptable mechanism to do that, yet.

The purpose of all this is for the deathists to have a real stake in their abstract pronouncements. Make room for the next generation? Sure. At your own expense, not at the expense of the nebulous "we". Most times, people that talk about "we" mean "somebody else" when it comes to costs, and "themselves" when it comes to benefits. The word "we" means "count your silverware".


Folks that are worried about overpopulation should concern themselves with reproductive rate, not longevity. Maintaining a high death rate for old people will not avert an overpopulation catastrophe, but reducing the replacement rate and increasing the age of child bearing will. The most likely way to reduce the population growth rate is to create societies that value maturity more than they value babies. An immortalist society is far more likely than a deathist society to do that.

revision January 19, 2005

last revision July 2, 2009