The following is from a self-published book, Essays From Another Paradigm.  At the time I wrote it I was unaware that others were also "discovering" this idea.  Everyone at my cafeteria table laughed at the idea, and I unfortunately didn't pursue it.  Now I know that it is receiving serious attention (see the link below) by others less swayed by naysayers.
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A NEW ESTIMATE FOR THE END OF HUMANITY

1990.06.10

Intuition is probably worthless when it comes to matters outside the common experience of our ancestors.  Only if an issue has an abundance of metaphorical counterparts will our intuition serve us.  Consequently, I have tried a totally new approach to the problem of estimating the time of Humanity's demise.

It's based on a thought experiment.  First, consider that Humanity does have an end.  This may sound like a big assumption, for it assumes that we will not adopt space travel to establish populations around other stars.  For the moment, assume that the colonization of other stars does not occur, that the entirety of Humanity's future resides within our solar system.  It is estimated that our sun will explode as a nova in approximately 5 to 10 billion years, and this event will evaporate the earth and the other 8 planets.

With this assumption it is inescapable that there will be a finite number of humans born during the entirety of time.  Let this number be Ntot.  Imagine creating a tiny capsule for each person and placing information about them in the capsule.  One piece of information is the birth sequence number, going from 1 (the first person arbitrarily identified as existing) to Ntot.  All the capsules are then put in a large bowl, and the capsules are mixed.  One of them is drawn at random.

Now, what information might this capsule contain?

Before answering this, let's consider a simpler thought experiment.  Suppose two people engage in a game called "How long is the sequence?"  One person selects (at random) a sequence length, such as 100, then randomly selects a number from the population of numbers in that sequence, and announces the random number to the other player.  How well can the second player guess the length of the sequence?  The best strategy is to simply double the number provided, and offer that as the best estimate of the sequence length.  This strategy gives acceptable answers 50% of the time, if acceptable is defined as anything between 50% and 150% of the correct answer.  (I just "shelled out" of this word processor, and wrote a program to test this trivial concept, and produced an "acceptable" answer 4 out of 10 times).

Now let's try to apply this strategy to the question of Humanity's demise.  I will argue that you, dear reader, are a random member of the total set of Humans!  This is a crucial step in the derivation, so let's consider it some more.

Einstein developed ways of thinking about time that, ironically, demolished its common meaning.  He suggested that it be viewed as a 4th dimension.  To simplify what he's asking us to consider, imagine collapsing one of the 3 dimensions of ordinary 3-D space, producing a 2-D stage upon which all things happen.  Now allow the 3rd dimension to be time.  A point in this universe refers to one specific physical location and one specific time.  Volumes in this imaginary 3-D universe refer to all happenings within a specified physical space that occur between two temporal boundaries.

After thinking with such an altered viewpoint on reality it becomes easier to apply spatial concepts to the temporal domain.  For example, if we're dropping marbles on a checkerboard we know how to think about probability distributions of where the marbles fall.  Likewise, if we go into a "set" of all people who have ever lived (in the past), and draw one out at random, we know how to address this problem.  We treat it the same way we treat spatial problems; in this case we could consider a ladder and think in terms of landing on a rung at random.

It is alleged that Einstein thought about a person's existence in just such abstract terms.  The future that was to unfold was, for him, just as real as the past which has already occurred.  The existence of one is no less real than the existence of the other.  It is a short conceptual step to attach the "set" of all humans not yet born to the "set" of all humans already born, and thereby create one "super set" of all humans who ever have, and ever will, exist.

This is what I ask you to do:  imagine this "super set" of all humans, stretched out along a sequence that goes from 1 to Ntot.  Try to accept the idea that you are not special - any more than now is special in relation to all time.  You are not at the forefront of anything, since all future humans exist just as much as you and your contemporaries, or those who have lived and died before you.  All humans are equal members of this "super set" called Humanity.  Try to absorb the meaning of the randomness of your location in the sequence.

Now, let's ask how we might estimate Ntot, the size of the super set "Humanity."  The suggestion, as you have already guessed, is to calculate how many humans have already lived, then double that number.

How many humans have already lived?  I've used a population history to calculate that at this time 36 billion people have lived since 50,000 BC.  Doubling 36 billion yields 72 billion.  Recalling our previous argument, there is a 50% chance that our estimate is between 75% and 150% of the correct value.  If the correct value is C, then 72 billion is between 0.75*C and 1.5*C.  In mathematical notation, 0.75*C < 72 billion < 1.5*C.  Solving for C, we find that the size of the super set Humanity is between 48 and 108 billion.

What does this mean in terms of dates?  We can use population projections, and integrate forward until the total number (from the beginning) enters the region 48 to 108 billion.  I have done this, and the dates are 2040 to 2100.

Thus, we calculate that the end of Humanity will occur sometime between the years 2040 and 2100!  Or that there's a 50% probability of this.  The most likely date, corresponding to the time when the integrated human population reaches 72 billion, is the year 2075.  That is just 85 years from now!

 THE END

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I now believe the calculations presented above are inacurrate, according to a more thorough analysis.  See "A NEW TIMESCALE FOR PLACING HUMAN EVENTS, DERIVATION OF PER CAPITA RATE OF INNOVATION, AND A SPECULATION ON THE TIMING OF THE DEMISE OF HUMANITY" (a 1993 re-analysis).  Also, see The Anthropic Principle, an external web site that contains several other related links.

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This site opened:  March 16, 2000.  Last Update: March 16, 2000