The Doomsday Argument Recapitulation And Then New Comments

As this chapter,1 like the others, is intended to be readable in isolation, it starts with a brief recapitulation. The doomsday argument, originated by B.Carter and then published and defended by J.Leslie, with variants by J.R.Gott and H.B.Nielsen, points out that you and I would be fairly unremarkable among human observers if the human race were to end shortly: roughly 10 per cent of all humans born up to today are—because of the recent population explosion—living at this very instant. If, in contrast, the race were going to survive for many more millennia, perhaps colonizing the entire galaxy, then you and I would be very unusually early humans: humans who would eventually turn out to have been extremely near the beginning of time as measured by a Population Clock whose hand had advanced by one step whenever a new human was born. This can strengthen whatever reasons we have for suspecting that the human race will not survive long. People unwilling to accept this point will systematically underestimate the risks humanity runs from environmental destruction, germ warfare and other threats to its prolonged survival.

'Doomsday argument' can be a misleading label since all that is involved is a magnification of risk-estimates. Suppose, for example, that the 'total risk' of Doom Soon—the probability that the human race will, presumably through its dangerous behaviour, become extinct inside some fairly short period—is judged by you to be 10 per cent before you consider the argument. When you do come to consider it, this might lead you to a revised estimate of 80 per cent. But notice that the newly estimated 80 per cent risk of Doom Soon, besides being no excuse for utter despair, would have been arrived at against the background of dangerous ways in which the human race was thought likely to behave. Now what if, of the 10 per cent with which you started, 5 per cent represented the estimated risk connected with environmental destruction? After the 'total risk' had been re-evaluated as 80 per cent, the risk of Doom Soon from Environmental Destruction would have been re-evaluated as 40 per cent, presumably. (40 per cent is one-half of 80 per cent, just as 5 per cent is one-half of 10 per cent. There would seem to be no good reason to change the proportion from one-half into something else.) But whereas it might be impossible to do anything to counter certain other types of risk, for example the risk that some very distant but very violent cosmic phenomenon will suddenly pour its radiation at us, we could be frightened into doing something vigorous to reduce environmental destruction when we looked at that alarming figure of 40 per cent. Now, the Carter-Leslie reasoning is sensitive to new evidence of risk-reduction efforts because, for one thing, such evidence can lead us to revise the view that humans were likely to behave in dangerous ways. Any human who tries to stop environmental destruction is helping to cast doubt on that view.

In generations after successful efforts had been made to clean up the environment, people considering the doomsday argument would very obviously have a right to take account of those efforts. It's silly to think that human efforts could never increase the probability that doom would be long delayed. The doomsday argument says nothing of the sort. It is an argument which could retain some power for as long as the human race continued, but its capacity to frighten would be perpetually changing to take account of new evidence.

The doomsday argument is open to many objections. As the previous chapter made clear, I accept one of them, at any rate. If we live in a radically indeterministic world, there not yet being any usable 'fact of the matter' of how long the human race will last, then the argument may be considerably weakened—the extent of the weakening depending, naturally, on the degree to which humankind's future shares in the indeterminism. But whatever its weaknesses, the argument has a central point which simply cannot be wrong. It does supply grounds for increased reluctance to believe that you and I will turn out to have been very early in time as measured by the above-described Population Clock. In this chapter my main aim will be to support this firm statement with various thought experiments.

How does the current explosion in human numbers form the basis for an interesting doomsday argument? Note, for a start, that the situation today is in many ways radically new. The human race's former ability to survive from century to century may therefore give us little guidance about how much longer it is likely to survive. Carter argues for a shift in estimated probabilities—and even those who have severe doubts about his argument, so that their probability-estimates are hard to alter, may be less resistant to altering them when they are very unsure about them anyway.

A common reason for unwillingness to alter such estimates is this: that the human race is seen as facing, year by year, dangers which remain constant and which have no relation to population size. Supposedly, the situation is as if a Master of the Universe were throwing several dice together in each year, planning to put an end to humankind—perhaps with a gigantic asteroid—when all the dice landed as sixes. Now, if this were an appropriate story to tell oneself and if the dice in the story were radically indeterministic (an important qualification, to be discussed in due course), then the doomsday argument might look very unimpressive. We certainly cannot know that the story is appropriate, however. There are actually quite strong grounds for suspecting the reverse. Today's population explosion, besides being itself a source of new dangers, is the result of technological advances which are dangerous. The doomsday argument could help to convince us of this. In the face of novel and largely unknown risks, why remain confident that numerous humans will live after us?

What if the human race were going to end in the next hour? We should, of course, be very reluctant to believe this. Its initially estimated probability ought to be extremely low. The doomsday argument couldn't make it anything other than extremely low, not even if it led us to re-estimate it as a thousand times greater, because a figure such as 0.0000000000000000000000001 per cent isn't going to yield anything very big even when multiplied by a thousand. What if it were true nevertheless? As noted earlier, it would then be true that something like one in ten humans who had ever been born would be alive when the race ended, so that you and I wouldn't be very surprisingly positioned among all humans ever. But what if humankind instead survived for at least another few centuries? Suppose that population figures stabilized at about ten billion in AD 2050. How many further centuries would pass before it could be said that roughly half the human race had lived at times later than you and me? About two centuries only. If galactic colonization then began, population once again doubling every fifty years as it has in recent times, then by about the year 3000 you and I would have been shown to have lived when at least 99.99 per cent of all humans hadn't yet been born.

Notice that the Carter-Leslie reasoning could be understood as strengthening either of two competing hypotheses in this area: the first, that the human race will end shortly, and the second, that galactic colonization would never be feasible, no matter how long the race lasted. (In fact, it could strengthen the two hypotheses simultaneously. Although they compete, their plausibilities could both be raised. Compare how Bob's absence from his usual desk can support both 'Bob has been promoted as he demanded' and 'Bob has carried out his threat to leave the firm.')

The human mind is ill suited to handling probabilities. On a throw of two fair dice together, Leibniz considered two sixes exactly as probable as a six and a five. An even worse error was made by d'Alembert, for whom the results to be expected from tossing the same coin three times differed from those of tossing three coins at once. And while Carter's doomsday argument certainly faces some interesting objections, it also meets with many others which are really very weak but which are stated with tremendous confidence by intelligent people. This one, for instance: that the argument fails at once since 'as everybody knows' nothing probabilistic can be concluded from a single case, and your own observed position in human population history is indeed a single case, while it would be a mere joke to try to widen your evidential base by asking your contemporaries what their positions were. In answering such an objection, a thought experiment can be useful. Imagine two urns each containing just one ball marked with your name. In the first urn there are a thousand balls altogether, bearing different names; in the second, only ten. Unsure that the left-hand urn contains the thousand, but thinking this 75 per cent probable, you draw a ball at random from it. Your name is on the ball. Of the perhaps ten and perhaps a thousand names in the urn, yours has been the very earliest to be drawn. Shouldn't this reduce your confidence that there are still another 999 names waiting to be drawn? It certainly should. A straightforward calculation suggests that you should shift to thinking it roughly 97 per cent probable that there are only nine names remaining. Now, while so simple a thought experiment cannot establish the doomsday argument's correctness, one point seems clear. You mustn't protest that because the experiment involves drawing just a single name, and because 'as everybody knows' probabilities cannot be determined from single cases, it follows that the early drawing of your name could show nothing whatever.

Disregard all the books which thunder that no probability should ever be derived from a single test. Those books are in error. Imagine two urns. One contains a million black balls and one white; the other, a million white balls and one black. Not having a clue as to which urn is which, you pick one of them with the help of a tossed coin. You draw a ball, and it is white. What are the odds that it came from the urn containing the million white balls? Answer: a million to one in favour. To arrive at this answer, simply consider the million and one equally probable ways in which a white ball could have been drawn. A million of them involve draws from the urn with the million white. Only one involves a draw from the other.

Odds of a million to one in favour of some hypothesis are rather good odds. There is no magical unreliability attaching to results just because they are results of single trials. Consider the hypothesis that a coin is double-headed, arrived at when seventeen tosses yield seventeen heads. The odds against this occurring with a fair coin are much less impressive than a million to one. (Repeating the urn experiment several times, in each case choosing the same urn after replacing the drawn ball and shaking vigorously, can in some sense 'greatly improve' the reliability of the judgement that the urn contains the million white. But this only means that after, say, three successive whites have been drawn, the odds favouring this judgement are increased to a million million million to one. In another sense, those odds are no great improvement: the first odds were already overwhelmingly good.)

Thought experiments can often be replaced by actual experiments. Suppose you meet a sceptic who persists in thinking that 'because, of course, you cannot establish probabilities by single trials' a single draw of a white ball couldn't in the least strengthen the theory that the urn was the one with the million white. (I have met two such sceptics, a philosopher and a physicist. They had no doubts about their rightness.) Filling urns with hundreds of thousands of balls may be overly time-consuming, yet you can readily set up an experiment with two urns each containing twenty balls: nineteen black and one white in the first case, nineteen white and one black in the second. Invite the sceptic to choose an urn and to draw just one ball from it. In advance of the choosing and the drawing, he or she must please make an even bet, a dollar against your dollar, that the remaining balls in the urn will be black if the drawn ball is white, and vice versa. You will almost certainly win the bet. Repeat again and again with different urns and different balls, and expect to win almost always.

In what follows, though, we shall be making thought experiments which could only with immense difficulty be replaced by actual experiments. What's more, there will actually be a case where it would seem right for you to bet in a way which would cause most people in your circumstances to lose their money.

Before beginning the thought experiments we need to consider one last point. When wondering what degrees of probability we ought to attach ('subjectively'?) to various untidy real-life matters, we often rightly ask what the probabilities would ('objectively'?) be of getting various outcomes in tidy trials involving dice, coins, or balls pulled from urns. If past experience gives you equal reasons for thinking that Jones will and will not be in town tomorrow, and if the same applies to Smith and to Brown, and if past experience also indicates that the movements of all three are uncorrelated, then what should be your estimate of the probability that Jones, Smith and Brown will all be in town? It is as if 'Jones' were scratched on one face of a first coin, 'Smith' on one face of a second, 'Brown' on one face of a third, the issue being how likely you'd be to see all three names after tossing the coins. Saying this isn't 'confusing subjective and objective probabilities'. It is just using common sense.

The distinction between 'subjective' and 'objective' can be hard to draw, anyhow, because (a) there are often strong excuses for declaring that probabilities are simply 'subjective' expressions of ignorance, while on the other hand (b) it can be considered 'objective' that all persons having such and such evidence ought to view various matters as probable to exactly such and such degrees. Even when a series of events is ultimately deterministic, so that what we call its uncertainties are really only blindnesses in ourselves, we can succeed in modelling it with coins and dice— which should cause no surprise, surely, when nobody really knows whether the behaviour of coins and dice is ultimately indeterministic, a matter of probabilities 'out there in the world', 'objective in the fullest sense'.

Now for the experiments. Since they will be thought experiments only, let us say that the experimenter is always God or else the Devil. All the people involved are created specially for experimental purposes.

Continue reading here: The Small Room And The Large

Was this article helpful?

0 0