Living forever is surprisingly difficult · 8:06pm Apr 14th, 2014
I am uncertain how many of you read Saturday Morning Breakfast Cereal, but today's comic brought up an important point that many folks don't really think about as far as immortality goes; that is to say, even if you eliminate aging and senescence as a cause of death, people still die, of accidents, of disease, and of random other things.
How many people?
Well, in the US, which is a fairly well-off country, 25-34 year olds in 2007 died at a rate of 104.9 per 100,000 in the United States - or at a rate of very slightly more than .1% per year.
This may seem like a very slow rate of death, but as it turns out, this would significantly cull the population of immortals over time; at even this very low death rate, you have a 50% chance of dying within 634 years, and on average, will live only 914 years - only about a third of the population (36.8%) make it so long. Indeed, only a third of the population will survive to their thousandth birthday.
Thus, even among immortals, Celestia, at an age north of a thousand years, would actually be above-average in her age.
And this is assuming modern United States death rates for this age cohort; in years past, death rates due to accident, violence, and disease were higher than they are today, which might mean that, historically, immortals would have lived less long, which might well mean that Celestia has actually gotten quite lucky.
This also means that it is entirely possible that there were other immortal beings in the intervening years, other alicorns even, and that all of them died of violence, disease, accidents, suicide, or "hey bro, hold my cup while I do this".
However, merely because Celestia has made it so long doesn't mean she doesn't have much time left to live; because of the nature of unchanging death statistics, at any given point in her life, assuming she has the same life expectancy, she has the exact same odds of making it that much longer.
But out of the present population of four immortal alicorns (assuming Twilight, Cadance, and Luna are all immortal), odds are in another 1,266 years, there will be only one of them left (and indeed, odds are that it would happen sooner than that). There's still a good 1 in 16 chance that Luna and Celestia will both still be drawing breath at that point, though, though more depressingly, nearly a 1 in 3 (31%) chance that none of them would make it to that point.
Immortals may live for a long time, but even those who never die of age don't necessarily live forever.
You assume here that in terms of injury or illness they're exactly as able to be killed as a mortal in the prime of life. While in some settings this could be the case, in most settings with immortal beings there are a number of factors at work that don't come into play when dealing with even young mortals..
We've seen that Celestia can be overpowered, and Cadance can be weakened, but we have no way to gauge the force of power required to do that. There's no indication of what kind of trauma it would require for an alicorn to be killed. One could assume, for example, that Luna's stay on the moon indicates that alicorns don't really need to breath. In that case, trauma to the lungs wouldn't kill them, just act as an inconvenience provided they could avoid massive blood loss. And, without the need for oxygen to be distributed to their bodies, I'm not even sure how much blood loss it might take to kill them. (Or one can assume the moon of Equestria has an atmosphere. This uncertainty is kind of my point here.)
We also don't know if that level of magical power makes them more resistant to disease, or even if they could be killed by disease-- many brands of immortals like Tolkien elves or vampires are immune to mortal diseases, drastically reducing their risk of being infected by something that affects them if they're a small or isolated population.
It's interesting to consider, but without knowing more of the rules of a particular fantasy setting you can't really use the statistics of a mortal population to compare to something like that. Even assuming they can be killed somehow, there are a lot of things that could be in play making it much less likely to happen than it would in a mortal population.
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And even after you've adjusted for that, you're still assuming that death rates in Equestria are dictated by biology and physics, instead of Narrativium. In the latter case, Celestia and Luna can live as long as they need to.
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I did actually think about this, but it requires a lot more assumptions.
If they are indeed immune to disease, that would decrease their odds of dying, though not by a whole lot - 25-34 year olds seldom die of infectious disease, though it does happen. On the other hand, they are most decidedly not typical ponies; they're the leaders of their country, and they may be powerful warriors, but they also have to take risks (such as fighting Queen Chrysalis and King Sombra) which might not be expected of the general population. The odds of being assassinated are higher for leaders; for instance, the US has had four presidents assassinated in only 225 years, meaning that their odds of being assassinated in any given year are 1.8% - vastly higher than the odds of a random member of the population being murdered - and there have been unsuccessful assassination attempts, most notably that of Ronald Reagan - my mother's first question, when she heard about it, was the extremely sensitive "Did they get him?" Andrew Jackson also survived an assassination attempt (both of his assassin's guns misfired, at which point Andrew Jackson's aids had to prevent the angry president from beating the hapless man to death - the powder may have been wet, but Cracked suggests that the true reason that he survived was that the bullets, like everyone else, were just scared of him), and there have been numerous other attempts which have been headed off.
Other oddities abound as well - Celestia can teleport, but she seems to choose to take conventional transportation at many times, and we don't really know the death rate for either of those; both could potentially increase her death rate relative to the general populace, as she likely travels more than the population at large does. If she is tougher than average, though, that may mean that ordinary transportation accidents are very unlikely to kill her - though it may not as well, it depends on how it works.
I think it is difficult to draw any conclusions about the physiology of alicorns; when Luna was sent to the moon, it appears that she was in some sort of magical stasis INSIDE the Moon, with her face showing up on the surface, rather than being forced to live there outside for a thousand years.
One other somewhat amusing note - given the general risk of "big bad guys" relative to general background mortality rates, sending out heroic mortals to deal with big bad guys has two major advantages. One major advantage is stability - even if some of the mortal heroes die, the government is not affected (or not affected as much) as if one of the immortal alicorn leaders went out and fought the big bad and died. Indeed, from the point of view of value, this is wise - a 25 year old hero is not going to live more than 75 more years or so, and really is probably only going to make it 50-60, while an immortal alicorn can survive indefinitely. Thus, from the point of view of years of life, risking on the order of 12 mortals is equivalent to risking one alicorn, and possibly more than that.
Another factor is that, if becoming an immortal alicorn is something which is mostly achieved by heroes, then sending out heroes in this fashion is likely to increase the population of immortal alicorns.
So indeed, in their society sending poor Twilight off to beat down King Sombra may make perfect sense.
Setting aside the debate about the death rates for archmages (because the most important point is that the is a death rate[1]) then the issue becomes "What is the replacement rate for alicorns to maintain a stable population of four?"
If I'm understanding the math right, a new alicorn appears, on average, about once every 914 years. If they're appearing more often than that then the population is actually growing.
[1] assuming they're immortal in the Tolkienian sense, and not in the Hellenic sense.
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The problem with birth rate = death rate is that while it works well for a large population, it is exactly that - a statistical average. It has very strange effects when you take into account a population where the death rate does not increase over time for any given individual, because you end up with much less predictable end of life, and it doesn't help that, in the case of alicorns, they are created at random, not born. This causes a lot of weird effects.
Now, the average alicorn may last 914 years, but that's the AVERAGE age. However, there is no maximum age - if you had a mere 1000 immortals, you would still have 3-4 of them left at this kind of death rate after 5000 years. But the problem is that these 3-4 still have the exact same future life expectancy after 5000 years - in other words, they'd be indistinguishable from and identical to the rest of the population.
With 4 alicorns, the odds of an alicorn dying in any given year are extremely low. But the odds of every one of those 4 alicorns being dead in 914 years is actually relatively high - any individual one of those four alicorns only has a 36.8% chance of surviving 914 years. About 1.8% of the time, you would have 0 alicorns at that point. You would have 1 alicorn left 12.6% of the time; you'd have 2 left 32.4% of the time; you'd have 3 left 37.2% of the time, and you'd still have all 4 left 15.9% of the time. Thus you can see you could easily end up with extremely large variations in the actual population size, even though you are adding alicorns at the same rate at which you are removing them. Moreover, this leads to additional weirdness because the "old" alicorns are no more likely to perish than the "new" ones - meaning that if you have all four left, you now have a "stable" population of five alicorns, whereas if you had none left at all, now you've got one.
When you think about this in the long term, you realize that the number of alicorns which die per year is a function of how many alicorns are alive in any given year, while the generation of new alicorns is not. The result of this is that any non-zero population is more likely to get smaller than it is to get larger, over time, so your long-term stable population of immortals is actually 0 - you'd expect to spend a pretty significant fraction of the time without any alicorns, and the likeliest number other than 0 is 1, with 2, 3, 4, ect. growing increasingly unlikely.
This is something of a variation on the gambler's ruin - basically, in the long run, your population will actually decrease to 0 from any larger number, and indeed, it only takes a few thousand years to hit 0 from 4 immortals most of the time; note that, rarely, you will generate a fairly large number of immortals at a time (I've gotten all the way up to 6 from 0), you won't really get huge populations of them, and the long term trend is for them to drop to 0. In fact, it is common for multi thousand year stretches to have zero immortals in them.
And yes, I wrote an immortal population simulator for this in C# for shits and giggles to confirm my thought process.
If you wanted to have a stable population of alicorns, you would have to set the birth rate equal to the odds of any one alicorn in a population of X alicorns dying in a given year. If you set annual birth rate = annual death rate of ONE alicorn, you will be more likely than not to end up with 0-1 alicorns.