Reading the first post of the sequence (Probabilities are not the right concept) is recommended but not required for understanding this post.^[1]

Infinite ethics

Once you start looking at infinities, all ethical systems get confusing.

Intuitively, it's good to plant an apple tree. But if the universe already has infinitely many apple trees, why bother? Infinity plus one is still infinity. And there are the classic paradoxes: an infinite grid of houses, each with three happy people and one unhappy person, seems better than the reverse. But you can rearrange people between the two configurations, since both the happy and unhappy populations are infinite. Does this mean you can make the world better just by shuffling people around?

These questions matter because our universe is quite likely infinite in one way or another. The world very well might be spatially infinite. The many-worlds interpretation of quantum mechanics is pretty popular, and some versions of it imply infinite worlds, though boundaries are not well-defined. And I have a fondness for the Tegmark-IV multiverse theory where every computable mathematical structure exists in a real sense.

And even if you only give 1% credence to the universe being infinite in some way, naive expected value calculation would still imply that this small chance of infinity overwhelms everything else.

A classic answer to the problem of infinite worlds is that you need a measure. You don’t want to just say that bringing an umbrella helps you in infinitely many quantum branches and hurts you in infinitely many branches, so it’s all equal. You shouldn’t have infinite value in both directions; positive and negative must integrate to something finite. Whatever multiverse you believe in, you should define some measure over points in it, and these measures must add up or integrate to .

Even if you don’t believe in any type of multiverse, I think a very similar logic applies, since the space of hypotheses is infinite.

Even if you believe there is just one real world, you still need to decide if you want to bring an umbrella with you or not. Bringing an umbrella helps you under some hypotheses, and hurts you under some others. There are infinitely many hypotheses (it’s not going to rain because a hippo is going to slurp up all the water! no, a giraffe!), so you can’t just count them, you need to put weights on the diffe...

Probabilities and Infinities

Probabilities and Infinities