The Doomsday Argument

The Doomsday Argument was posited by the astrophysicist, Brandon Carter, fifteen years ago. The argument includes two competing hypothesis:

(1) an urn contains 10 balls, and

(ii) an urn contains 1,000,000 balls.

The balls are numbered sequentially 1,2,3,…,etc. One flips a coin to determine from which urn a ball shall be removed. Remember, looking at an urn, one does not know if it contains 10, or 1,000,00 numbered balls.

Ball #7 is drawn from the urn. Chances are quite good (99.999%) that the urn from which the ball was taken now has 9 balls.

Now, instead of balls and urns, consider the following two hypothesis:

(i) the number of humans having ever lived will reach 10 exp 11 (doom soon), and

(ii) the number of humans having ever lived will reach 10 exp 14 (doom later).

Applying the same logic, it has been argued, leads one to the conclusion of doom soon. Those of you interested in a reference, please see Investigations into the Doomsday Argument, by Dr. Nick Bostrom.

Regarding the balls in the urns, there is a certainty that one urn holds 10 balls, while the other urn houses 1,000,000 balls. In the second set of hypotheses, one finds that the number of humans having ever lived will reach 10 exp 11, or the number of humans having ever lived will reach 10 exp 14. While the balls in the two urns are mutually exclusive, the humans in the two hypothesis are NOTmutually exclusive. In fact, such an invariant distinction is completely lacking!

By positiing that the ‘number of humans having ever lived will reach 10 exp 11, one is notstating that the number of humans having ever lived will not continue on to 10 exp 14. As such, if we were to number each of the humans as was done with the balls, the first 10 exp 11 would be sequentially numbered and the REMAINING 10 exp 14 - 10 exp 11 would be numbered beginning at 10 exp 11 +1. Because the content of the first hypothesis is a necessary, but not a sufficient condition for the truth of the second hypothesis, the cardinality must reflect such a dependence.

In essence, one must accept and integrate such indeterminancy into one’s mathematical representions of such situations.

(c) 2005 Kenneth L. Stein Distribution is authorized only if the author attribution is included and only for display in electronic format. For print rights, contact the author at kstein@plexav.com.