The Measure Problem and the Youngness Paradox

[Salamon]

I have read Max Tegmark's book "The Mathematical Universe" and he describes this thing called The Measure Problem as the biggest problems in physics. I am having difficulty understanding the problem so I will try to sum up my understanding of what he said.

As a result of inflation, the volume of space doubles every 10^-38 seconds.
So there should be 2¹⁰³⁸ more big bangs occurring each second than in the previous second. Therefore, it is 2¹⁰³⁸ more times likely that we would find ourselves in a universe that is one second younger than the current universe we live in.

So in essence, is the measure problem that we never should have existed to begin with because it is always infinitely more probable that we would originate in a universe in the future?

Can't you just get around this problem by applying the anthropic principle and saying that if our universe was different than it is then we wouldn't be here?

I just don't see how this is a physics problem.

 

[Chalnoth]

The measure problem is a different issue. It's a problem of counting probabilities with infinities. For example, if you have eternal inflation, that universe is infinite in extent into the future. This presents a problem with regard to computing probabilities because there is no unique way to assign probabilities. You simply cannot count up the relative number of outcomes X compared to outcomes Y, because both X and Y are infinite and their ratio depends upon how you do the counting.

The youngness paradox occurs because of one particular way of adding up those infinities. But it's very easy to take a different definition that doesn't have that problem.

Perhaps the best way to avoid this problem is to consider a model of the universe that is explicitly finite, and recently a few theorists have done precisely that. For example:
http://worldsciencefestival.com/videos/multiverse_switching_to_the_finite