I am an undergrad at Harvard studying math and theoretical computer science.
I have a blog here: https://gabrieldwu.github.io/
Gabriel Wu
Karma: 95
Low Probability Estimation in Language Models
Theoretical Limitations of Autoregressive Models
Ah yes, I think that’s correct (although I am also not a physicist). A more accurate description would be “In a matter of minutes after the time its gravitational waves reach earth, human events are unfolding in a measurably different fashion than they would have had that electron never existed.”
I agree with everything you’re saying. Probability, in the most common sense of “how confident am I that X will occur,” is a property of the map, not the territory.
The next natural question is “does it even make sense for us to define a notion of ‘probability’ as a property of the territory, independent from anyone’s map?” You could argue no, that’s not what probability means; probability is inherently about maps. But the goal of the post is to offer a way to extend the notion of probability to be a property of the territory instead of the map. I think chaos theory is the most natural way to do this.
Another way to view this (pointed out to me by a friend) is: Butterfly Probability is the probability assigned by a Bayesian God who is omniscient about the current state of the universe up to 10^{-50} precision errors in the positions of atoms.
This is cool, I had never heard of the Ergodic Hierarchy before!
Related to your second point—Alex Cai showed this psychology paper to me. It found that when humans are predicting the behavior of physical systems (e.g. will this stack of blocks fall over?), in their subconscious they are doing exactly this: running the scene in their brain’s internal physics engine with a bunch of initial perturbations/randomness and selecting the majority result. Of course, predicting how a tower of blocks will topple is a lot different from predicting the probability of an event one month into the future.