Anthropic Bias Observation Selection Effects in Science and Philosophy Nick Bostrom
The incorrectness of Gott’s argument
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The incorrectness of Gott’s argumentA crucial flaw in Gott’s argument is that it fails to take into account our empirical prior probability of the hypotheses under consideration. Even granting that SSA is applicable to all the situations and in the manner that Gott suggests (and we shall argue in a later chapter that that is not generally the case, because the “no-outsider requirement” is not satisfied), the conclusion would not necessarily be the one intended by Gott once this omission is rectified. And it is quite clear, once we focus our attention on it, that our prior probabilities must be considered. It would be foolish when estimating the future duration of Stonehenge or the Berlin wall not to take into account any other information you might have. Say you are part of a terrorist organization that is planning to destroy Stonehenge. Everything has been carefully plotted: the explosives are in the truck, the detonators are in your suitcase; tonight at 11 p.m. your confederates will to pick you up from King’s Cross St. Pancras… Knowing this, surely the odds of Stonehenge lasting another year are different from and much lower than what a straightforward application of the delta t argument would suggest. In order to save the delta t argument, Gott would have to restrict its applicability to situations where we in fact lack other relevant information. But then the argument cannot be used to estimate the future longevity of the human species, for we certainly have plenty of extraneous information that is relevant to that. So Gott’s version of DA fails. That leaves open the question whether the delta t argument might not perhaps provide interesting guidance in some other estimation problems. Suppose we are trying to guess the future duration of some phenomenon and that we have a “prior” probability distribution (after taking into account all other empirical information available) that is uniform for total duration T in the interval  , and is zero for T > Tmax:
Suppose you make an observation at a time t0 and find that the phenomenon at that time has lasted for (t0 - 0) (and is still going on). Let us assume further, that there is nothing “special” about the time you choose to make the observation. That is, we assume that the case is not like using the delta t argument to forecast the prospects of a friend’s marriage at his wedding. We have made quite a few assumptions here, but if the argument could be shown to work under these conditions it might still find considerable practical use. Some real-world cases at least approximate this ideal setting. Even under these conditions, however, the argument is inconclusive because it neglects an important observation selection effect. The probability that your observation should occur at a time when the phenomenon is still ongoing is greater the longer the phenomenon lasts. Imagine that your observation occurs in two steps. First, you discover that the phenomenon is still in progress. Second, you discover that it has lasted for (t0 - 0). After the first step, you may conclude that the phenomenon probably lasts longer than your prior probability led you to expect; for it is more likely that you should observe it still in progress if it covers a greater time interval. This is true if we assume that your observation was made at a random point in a time interval that is longer than the expected duration of the phenomenon. The longer the time interval from which the observation point is sampled compared to the prior expected duration of the phenomenon, the stronger the influence that this observation selection effect will have on the posterior probability. In particular, it will tend to compensate for the “Doomsday-effect” – the tendency which finding that the phenomenon has lasted only a short time when you make the observation has to make you think that the duration of the phenomenon is relatively short. We will show this in more mathematical detail when we study the no-outsider requirement in the next chapter. For now, it suffices to note that if your observation is sampled from a time interval that is longer than the minimum guaranteed duration of the phenomenon – so that you could have made your observation before the phenomenon started or after it had ended – then finding that the phenomenon is still in progress when you make your observation gives you some reason to think that the phenomenon probably lasts for a relatively long time. The delta t argument fails to take account of this effect. The argument is hence flawed, unless we make the additional assumption (not made by Gott) that your observation point is sampled from a time interval that does not exceed the duration of the phenomenon. And this entails that in order to apply Gott’s method, you must be convinced that your observation point’s sampling interval co-varies with durations of the phenomenon. That is to say, you must be convinced that given the phenomenon lasts from ta to tb, then your observation point is sampled from the interval [ta, tb]; and that given that the phenomenon lasts from ta’ to tb’, then your observation point is sampled from the interval [ta’, tb’]; and similarly for any other start- and end-points that you assign a non-zero prior probability. This imposes a strong additional constraint on situations where the delta t argument is applicable.45 The failure of Gott’s approach to take into account the empirical prior probabilities and to respect the no-outsider requirement constitute the more serious difficulties with the “Copernican Anthropic Principle” alluded to in chapter 3 and are part of the reason why we replaced that principle with SSA. Directory: preprints preprints -> Digitally-assisted discovery and proof preprints -> Reorienting the Logic of Abduction preprints -> Supplementary Material Table 1 Download 9.31 Mb. Share with your friends:
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