But I really dislike a lazy and innumerate argument commonly used to "prove" the non-existence of God, which can be summarized in the following false dichotomy:
Either there is no God and the universe just 'poofed' into existence, or there's an infinite number of Gods, because the plane of existence for each God has to be created by a higher-level God.This is a false dichotomy: it could well be that our universe was created by a powerful being from a higher-order universe, but that universe poofed into existence without a creator. Or maybe it did have a creator, whose universe poofed into existence; or that third universe may have had a creator...
Hey, this looks like dynamic programming. I know dynamic programming.
Let's say that universes are recursively nested until one of them just poofs into existence. Of course we can't see outside our universe, but we can build simple models.
So, our universe either poofed into existence (say with probability $p$) or it was created by some higher being (with probability $1-p$). Now we iterate the process: 'level 2' universe either poofed into existence (with some probability $q$) or was created by a 'level 3' universe being (with probability $1-q$); and so on.
Time for a simplifying assumption, or as non-mathematicians call it, making things up. Let's assume that all these universes share the poofed/created probabilities, so that for any 'level $k$' universe, it poofed into existence with probability $p$ and was created by a being from a 'level $k+1$' universe with probability $1-p$.
Note that it's still possible to have an infinite number of universes, but with this formulation, the probability of a 'level $k$' universe (with us being 'level 1') being the last level is
$p (1-p)^{k-1}$.
This probability gets small pretty quickly, which suggests the 'infinite regress of universes' argument gets thin very fast.
Now we can compute the expected number of universes as a function of $p$:
$\mathbb{E}(n) = p + 2(1-p)p + 3 (1-p)^2 p + \ldots N (1-p)^{N-1} p + \ldots$
or
$\mathbb{E}(n) = p/(1-p) \times ( \text{ sum of series } N (1-p)^N )$
The sum of series $N (1-p)^N$ is $(1-p)/p^2$, so
$E(n) = 1/p$
Therefore, if we believe that the probability of a universe poofing into existence is 0.1, there are an expected ten universes; for 0.2, five universes; for 0.5, two universes.
Very far from 'turtles all the way down.'
Of course, these calculations were unnecessary, because as we know from the revelations of the prophet Terry Pratchett, it's four elephants on the back of the Great A'Tuin swimming in the Sea of Stars.
