Probability Paradoxes of Existence

You had zero probability of existing; yet people very like you are certain to exist somewhere and somewhen

Photo by Drew Beamer on Unsplash

I studied measure theory, the foundation of probability theory, years ago under the great mathematician Paul Halmos. One of the paradoxical results, as I recall it, was that there are infinite subsets of measure zero among the Real numbers. For example, the set of all rational numbers (ratios of two integers) has measure zero, which means that if you were to choose a Real number at random, your probability of that being a rational number would be 0. The chance of it being an irrational number, like the square root of 2, or even a transcendental number, like Pi or e, would be 100 percent. Yet there would be rational numbers both greater than and less than that number, as close in value to it as you like.

So it seems with our individual lives, and with planets like ours. Each of us people or planets had 0 probability of existing exactly as we do. Yet in our universe there are, were, or will be individual people or planets extremely similar to us — so much so that it would be nearly impossible to tell them apart from us.

Even on this finite planet, among all the people living or who have lived or will live, there are people who, like identical twins, are…