Yes, that T is finite is an assumption. But this is certainly the case, though perhaps on a very long timescale. Even if the universe continues to expand forever, there cannot be an infinite number of humans as we now understand the term.

]]>*“The most irritatingly overlooked weakness of the doomsday argument is that it has indeed been wrong for most of human history. “*

Not really. In the case of an exponential population increase, it will be wrong for a very long period of *time*, but not for a large fraction of *people*. It is the exponential increase which makes things interesting. If the population is table, then this reduces to Gott’s temporal Copernican principle. In the case of a rising population, the emotional impact is different.

If exponential population increase continues, then colonizing space will hardly make a dent in the problem.

Of course, if the statement is true at 95% confidence, you can always argue that you are among the first 5% of humans. Yes, that caveman would have got it wrong. We expect that a certain fraction will get it wrong. What confuses some people is that this small fraction of people corresponds to most of the time that humans exist.

]]>The problem with the Doomsday argument is that it believes that there’s a Doomsday and from there on everything logically follows. If Doomsday is considered a fact, than yes, probability calculations make sense. But as long as Doomsday is not a certainty (numerically) than giving it a value becomes problematic. Epistemologically speaking, the argument works. Not ontologically though. Or perhaps, then, a different explanation is required. ]]>

For example, consider the fact that we may be a true spacefaring race at some point in the future. Were we to colonize even a tiny fraction of the available worlds in our galaxy — even assuming it took generations to do so — those of us alive in the early 21st century might well represent the first 1% of all the potential humans to come. Assuming such a future, it would be madness to place ourselves in the middle of the human continuum.

Also, for the record, the analogy with the traffic wardens in a Chinese city is a false one. For the wardens number, you are relying on the fact that picking one of the total number of wardens currently in existence gives you some reasonable odds of guessing at the total number. The same logic does not hold for the total number of persons yet to be born. In the Chinese case you are picking one of a currently finite and countable pool. For the doomsday scenario, currently living humans represent a temporal cross-section of a population that stretches in a finite and countable way into the past, but an uncountable way into the future.

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