Winning the impossible lottery

Photo: Nick See

I wanted to call this post 'The Lottery Paradox', but it turns out that title is already taken by a very similar idea. The version I'm going to discuss is a bit more extreme and has a different focus.

It is inspired by some thoughts I've been having related to the validity of the Anthropic Principle (the subject of my last post), inspired by the comments left by Callum J Hackett on that post.

Suppose the nation of Foobar has a national lottery, but the way it works is that every single day, one of the citizens is chosen at random to win a big prize.

Now suppose that the nation of Foobar has an arbitarily huge number of citizens (say a Googolplex).

I'm going to try to persuade you to believe two completely opposing conclusions about the possibility of believing that you have won this lottery. One of these conclusions is true, and one of them is false. See if you can tell which is which.

A part is more complex than the whole

Here's two apparently unrelated hypotheses for you:

1. The universe contains infinite space and an infinite quantity of stuff.

2. The many worlds interpretation of quantum mechanics is true.

Both of these appear at first glance to be astonishingly wasteful, positing infinities upon infinities of things we can never observe and which can never affect us. As such, they appear to be more complex than ideas which assume that space is finite or that there is only one quantum world.

It would seem that Occam's razor weighs against them.

In this post, I will argue that in fact the reverse is true.