More philosophy today! Though this time something a little less out there than the Cryogenic Paradox. I discovered this idea in the intellectual meanderings that have followed my Paradox post. It's one of the marvels of the Internet age that one can find hidden corners of the universe where the most strange and exotic flowers of thought blossom and thrive. Today, however, I wanted to talk about an idea that is deceptively simple. Simple, but with conclusions that are quite profound and, to me at least, somehow spine-chilling, awesome and sad.
First let me ask you the question: how long do you think the human race will last? With nuclear weapons, climate change, environmental degradation and our various other self-made threats, there is reason enough for pessimism. On the other hand, it seems with our resourcefulness that we could survive, if not forever, then millions of years. We might populate the stars and all that. It seems odd that simple probabilistic induction could shed light on what seems a complex matter involving innumerable incalculable factors, but it seems that it can. And the answer is not good. In fact the odds are fifty-fifty that half of all the people who will ever be born (the final sum of the human race) have already been born. It's as likely as not that the human race is already half run. Let me explain why.
Imagine that you are walking in a foreign country where you are completely unfamiliar with the animal life, and out of a bush comes a small furry critter the likes of which you've never seen before. Now you have to guess whether or not the creature you are seeing is a rare or a common sight in this country. Logic dictates that your best guess is that it is a common animal, for the simple reason that common events occur more often than rare ones, by definition. In the same way, in the absence of better information, we should always assume that any given phenomenon we observe is more likely to be unexceptional than exceptional. If, for example, we had no information about where our solar system is in the Milky Way, our best guess would be that it lies in the region where the most stars are. If evidence appeared to suggest that it lay somewhere unusual, like right on the very edge or right in the very centre, that would even be reason for us to doubt that evidence or look for reasons why our position might be other than random - because otherwise our placement would simply be an unbelievable fluke.
This is known as the Principle of Indifference - the selection of phenomena we observe is "indifferent", i.e., random. Now let us consider that the human race almost certainly cannot last forever. In that case there is a certain number of people N that represents the total number of humans who will ever exist. This number N does not have to be determined yet. All we need to assume is that the number one day will be determined. Now let us number each human according to his or her birth position from 1 to N. Let's call this "serial number" s. If we select from that list some random person we can calculate quite simply the odds of this number s being in a certain position, and it obvious enough that the person is equally likely to be in the first half as in the second.
You see where this is going? You are that random person - because your birth order in the human chain follows the Indifference Principle. Therefore it is as likely as not that the human race is already half done! And by the same simple logic, it is 90% likely that we are more than 10% of the way through the total number of humans who will ever be.
One objection that at first glance might appears to contradict the Doomsday Argument is that cavemen could have made the same argument as us today, and of course they would have been completely wrong. Of course it is possible to be wrong, because the argument is probabilistic. But on average, if every person who lives makes the Doomsday Argument based on his or her own birth position, they will tend to be right exactly as often as the argument predicts. By selecting a caveman, we are no longer choosing a random person, and thus violating the Indifference Principle.
Some further, very rough calculations sketch out what this suggests. According to the Population Reference Bureau, the total number of people who have ever lived can be guesstimated at around 106 billion. So (assuming this figure) we can be 90% sure that the number of people remaining to be born is less than around a trillion. The maths does start get to get complicated because of birth rates relative to population size, so I'm going to stick with the simplest, ugliest calculation. If the current worldwide birthrate of 163,000,000 a year remained stable (certainly a false assumption), we could be 90% sure of the human race ending in less than about 6000 years. If we went with the 'best guess' (in which we could admittedly have only a very low level of confidence) and assumed that the human race is half finished already, then that would be cut to about 600 years.
But of course, the population and birth rate will not remain steady. The US census projects world population growing to around nine billion by 2050. Most likely it will continue to grow in this exponential fashion until the earth's capacity constraints cause it to plateau and/or collapse. This large and ever increasing population brings our projected doomsday a lot closer. Even if 90% of humans remain to be born, we can't expect to last anywhere near another 500,000 years - the length of time we could expect if history continued for ten times as long as it has so far. Only if we manage to achieve a far smaller overall population and maintain that level (or if some small tribe of survivors continues after the apocalypse, but fails to repopulate the globe) can we expect a future longer than, say, 100,000 years.
One perhaps startling result is if we look at the other possibility - that we are right at the end of the line. Given the large living population - about 6% of the total of all humans - there would seem to be a roughly 6% chance that doomsday could occur within our lifetimes! However, we should recall that this argument is based on a situation where we lack any better information. Such a catastrophically sudden end seems a lot less likely than 6% (around 1 in 18) given what we see of the world.
Indeed what is hard to see is how our complete extinction comes about. Given our resourcefulness, it would appear likely that we would be able to recover from most catastrophes. A collapse in human population would create the possibility of environmental recovery, which in turn would support the regeneration of the human race. A drastic scenario such as an asteroid collision might explain extinction. However an asteroid collision would be an exceptional event, and our argument is founded on the idea that such exceptions shouldn't be expected.
There is however one scenario that could lead to extinction, and that is climate change. If scientific projections are correct, and any of the worse scenarios eventuate, environmental damage may be so severe that the survival of any stragglers left after the great collapse might be living in an environment so hostile that recovery is impossible. And these effects are projected to occur and worsen over the next several centuries - right in the timeframe that would place me and you at a plausibly 'average' point in the human trajectory.
And people are worrying about their electricity bills going up under a carbon tax!
Whatever occurs, one thing is for sure, and that is that we - not only as individuals but as a race - are mortal. We must pass from this earth, and sooner than we have dreamed. There is something about seeing this inevitability that for me inspires a strange chill - of sadness but of beauty too. I think of our great story as a passing moment, and I think of the silence, the wind, the trees that come after, and I feel a kind of peace.
Perhaps there is a chance for us however. That chance is transformation. Humans may well be halfway to over, but by this same logic animals probably still have a long and rosy future. If we can change, evolve by selection or engineering into some new kind of beast or animal angel, perhaps we can yet find a way to escape the cruel logic of the Doomsday Argument.
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