The math of eternal life

In The Infinite Book, mathematician and cosmologist John Barrow writes about the many ways in which humans approach the idea of forever.

Using a play by Karel Čapek about a women named Elina Makropulos, who chooses, then after 342 years, renounces, immortality, and another novel by Arthur C. Clarke, Barrow raises an interesting problem and then follows with a surprising insight.

The question is this: wouldn't an infinite life exhaust friends, experiences and knowledge? Wouldn't it ultimately be boring? Barrow:

[Philosopher] Bernard William's mediation on the case of Elina Makropulos convinces him that death is a bad thing, because it closes of possibilities that would otherwise be open to us. None the less, immortality should not be preferred to mortality - at least if we retain or present human nature - because mortality imbues life with its most important goals. Thus, although at any moment there is good reason to try to live longer, there is no reason to continue living forever. This dichotomy is similar to some of the features of infinite series that we have encountered in previous chapters. We have seen that it is possible for the sum of an infinite number of terms to have a property that is not shared by any member of the series. Williams's dichotomy is not dissimilar in its jump to a negative conclusion, despite all that has gone before.

I like here how Barrow uses a mathematical example (in the supplied italics) to illustrate that a future, even one the runs infinitely long need not be the same. Its sum - its meaning if you will - need not be predictable.

Having set the table, here's how he applies that unpredictability:

All these evaluations of the pros and cons of living forever that we find in the works of philosophy are similar in one interesting respect. There is never a mention of anyone but oneself.... Elina Makropulos didn't look to future of helping other people.

By this I think he means that in any eternal future, shared meaning can result in infinite possibilities. Predictable?



Wikipedia: set theory