Causality and the Doomsday Argument--论文代写范文精选

关于世界末日的观点,一个人必须考虑的情况是有多少人会出生。假设我们分配每一个人类个体独特的诞生。到当代人类出生可能在600亿左右(到目前为止,有史以来大约600亿人类)。构建世界末日的论点,我们假设一个有限数量的人类,否则人类将继续殖民星系和数千年灭绝之后。

Abstract 
Using the Autodialer thought experiment, we show that the Self-Sampling Assumption (SSA) is too general, and propose a revision to the assumption that limits its applicability to causally-independent observers. Under the revised assumption, the Doomsday Argument fails, and the paradoxes associated with the standard SSA are dispelled. We also consider the effects of the revised sampling assumption on tests of cosmological theories. There we find that, while we must restrict our attention to universes containing at least one observer, the total number of observers predicted in each universe is irrelevant to the confirmation of a theory. The Doomsday Argument (Bostrom 1997, 2002; Leslie 1989, 1996) concludes that the prior probability we assign to the short-term extinction of humanity is greatly magnified by our observation that we exist at the present time in human history. Before we discuss the Doomsday Argument itself, it is instructive to examine one of the thought experiments that is held up as its analogue. The following experiment, Cubicles, is a minor variation of the original Incubator described by Bostrom (2002).

To get to the Doomsday Argument, one must argue that the Cubicles scenario is analogous to the question of how many humans will ever be born. Suppose we assign every human individual a unique birth rank. Adam and Eve would be numbered one and two, respectively, and contemporary humans would have birth ranks in the 60 billion range (to date, about 60 billion humans have ever lived). To construct the Doomsday Argument, we suppose that a finite number of humans will ever live, and theorize that humanity will either go extinct sometime in the next century (Doom Soon), or else humans will go on to colonize the galaxy and go extinct after thousands of years (Doom Late). 

Let's say that Doom Soon is the equivalent of the last human to be born having a birth rank of 100 billion, and that Doom Late equates to the last birth having rank of 100 trillion. Suppose that our birth ranks are analogous to the cubicle numbers in the Cubicles experiment. The Doomsday Argument is the corresponding claim that we should consider our own observation of our birth rank (about 60 billion) as being a single, random sample of all possible observations of one's birth rank. If the claim is true, then, as in the Cubicles experiment, Bayes' theorem tells us that the prior probability of Doom Soon is greatly amplified. Unless we had prior reason to believe that Doom Late was a thousand times more improbable than Doom Soon, we should now expect Doom Soon to be more likely.

Likewise, the probability of dialing booth #2 after having previously dialed booth #1 is also unity. Indeed, we don't learn anything about the coin toss until we make the eleventh phone call, despite the fact that we are only calling populated booths. From a probability theoretical point of view, the Sequential Autodialer fails to gain information from the first 10 samples because it is not randomly sampling from the population probability distributions of the two theories. Only the Intelligent Autodialer is sensitive to the occupancy of all of the phone booths, so it is the only variant that can be used to learn something about the coin flip without sampling booths 11 to 100. 

This particular autodialer plays the role of the existence of the observer in the Cubicles experiment. Just as the Intelligent Autodialer cannot dial an empty phone booth, so the cubicle occupant cannot find herself in booth #5 and also find that booth #5 is empty. We can see that the scenario depicted in the Doomsday Argument is homologous to the Sequential Autodialer, not the Intelligent Autodialer. We cannot know our own birth rank before all of those humans before us have sampled their own birth ranks in sequential order. Even if we initially have no idea of our own birth rank, our rank can only be measured (or provided to us) by having counted-off birth rank observations from the first human. Unlike the numbers painted on the outside of the cubicles, our birth rank observations are causally connected with those of all previous observers. By analogy, we see that the Doomsday Argument fails for the reason cited by Sowers: its sampling is not random. The posterior probability of Doom Soon is exactly equal to the prior probability of Doom Soon.

Multiple Occupancy 
The aforementioned thought experiments can teach us even more when we start adding multiple occupants to our cubicles and phone booths. We can ask what would happen to the Intelligent Autodialer experiment if we placed 10 occupants in each of the first 10 phone booths, no matter what the result of the coin flip. During the first phone call, we might speak to any number of occupants of booth #5, and each of them will reply that they are in booth #5. The probability calculations remain unchanged despite the fact that we have varied the total number of observers predicted by each theory. The analogous change to the cubicles experiment would be to place two occupants in each of the first 10 cubicles regardless of the coin toss. 

As long as we have a mechanism to ensure that, before the cubicle number is revealed, the occupants cannot tell how many people share their cubicle, the prior probabilities remain the same. Let's say that the occupants are blindfolded until it comes time to reveal their cubicle number. Again, this modification does not alter the probability calculation. In contrast to this simple result, a literal reading of the SSA would have us change our posterior probability assessment based on the number of blindfolded occupants who share our cubicle. So it seems that the original SSA is inconsistent with the results we would expect in the case of multiple occupancy.

Due to this normalization, we should prefer theories that favor q0 over theories that, say, maximize the total number of observers over all q with p(L|q) > 0. For example, suppose p(q|B) is nonzero for all inhabitable universes whereas p(q|A) is nonzero only for q0. In that case, the observational data confirms theory A, not theory B, even though the total number of observers in B will be larger. This result is in contrast with what we would expect under the standard SSA. The SSA weights the prior probabilities by p(L|q) so that theories which favor highly populated universes are preferred over theories that favor universes physically like our own. Is the assumption of equation (5) a valid one? It is claimed here that this assumption is always valid. It is difficult to see how two scientific theories could predict different values for p(L|q). Surely, q would parameterize any possible physical or historical factors that would impact the evolution of life. If we discovered some new kind of physical phenomena that influenced the likelihood of life evolving, we would have to either explain it as a function of our existing parameters or invent a new physical constant. For example, if we determined that the universe was subject to some previously unknown cosmological contraction that limited the amount of time that life had to evolve, we would most certainly parameterize the effect. The observation that we exist is not causally-independent of the observation of the physical parameters of our universe. Thus, if we accept the CISSA, our posterior probabilities do not depend on the number of intelligent observers in each universe. 

Conclusion 
We derive a a new Causally-Independent Self-Sampling Assumption (CISSA) by restricting the SSA to groups of observers who can make random, causally-independent observations. The CISSA is consistent with physics, and ensures that we don't double-count observers. Under the CISSA, the Doomsday Argument fails, and the paradoxes associated with the standard SSA are dispelled. Consequently, it is shown that the posterior probabilities we compute for cosmological models are independent of the number of observers in each universe. However, we must be sure to correctly normalize our prior probability distributions over all universes which have at least one observer.

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