# [Cosmology Talks] New Probability Axioms Could Fix Cosmology's Multiverse (Partially) - Sylvia Wenmackers

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# 18

Sylvia is a philosopher of science. Her focus is probability and she has worked on a few theories that aim to extend and modify the standard axioms of probability in order to tackle paradoxes related to infinite spaces. In particular there is a paradox of the "infinite fair lottery" where within standard probability it seems impossible to write down a "fair" probability function on the integers. If you give the integers any non-zero probability, the total probability of all integers is unbounded, so the function is not normalisable. If you give the integers zero probability, the total probability of all integers is also zero. No other option seems viable for a fair distribution.

This paradox arises in a number of places within cosmology, especially in the context of eternal inflation and a possible multiverse of big bangs bubbling off. If every bubble is to be treated fairly, and there will ultimately be an unbounded number of them, how do we assign probability?

The proposed solutions involve hyper-real numbers, such as infinitesimals and infinities with different relative sizes, (reflecting how quickly things converge or diverge respectively).

The multiverse has other problems, and other areas of cosmology where this issue arises also have their own problems (e.g. the initial conditions of inflation); however this could very well be part of the way towards fixing the cosmological multiverse.

By the way, Shaun is beloved in the local EA community, and Sylvia's work has been cited around these parts more than once in discussions surrounding UDT.

Multiverse measure assignment is interesting, along with the anthropic binding problem, it's a necessary part of getting an indexical prior. While anthropic measure gives you comparisons between observers within universes, multiverse/time cosmological measure gives you a comparison between the universes.

# 18

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Thanks for posting Mako. I even mention Effective Altruism/Longtermism at one point in the video!

and Silvia's work

Typo: it's Sylvia.