Uh, probability is in the map. Uncertainty is in the map. Bayesianism and Frequentism are not at odds. The prior is invisibly the fraction of possible past worlds one can imagine. The probability of an election outcome is the fraction of possible future worlds one can imagine that can emerge from the possible past worlds one had imagined. All that’s needed is fine-graining and counting. There is no need for nonlinearity and chaos.
This also resolves the so called logical uncertainty: the probability of the n-th digit of pi being 0 depends on the agent doing the estimate. Some agents have more detailed and accurate maps than others, and their probabilities may converge with each other, such as that 3^^^^3 digit of pi is 0 with probability 1⁄10, even though it will likely never be calculated by anyone. My personal probability that the 20th digit of pi is 0 with probability 1⁄10, up until I look it up and then it snaps to either 0 or 1, or more like 10^(-5) away from those, since my senses and google can lie to me.
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.
Well, I guess you can say that, due to chaos, even the best map requires probabilities, which, in a way, makes it a feature of the territory, because it is common to all maps.
Probability is only in the map of it isn’t in the territory as well. The theory that it is in the territory as well is not known to be tue, but is scientifically respectable. As Gabriel writes:
One response is to reject determinism. Maybe in Newton’s day we believed the universe was deterministic, but now we know about wave functions and Heisenberg uncertainty and all of that stuff. If we accept that there is true randomness occurring on the quantum level, then the outcome of the next election isn’t predetermined — it will depend on all of the quantum interactions that occur between now and 2024. With this view, it makes complete sense to assign fractional probabilities.
Uh, probability is in the map. Uncertainty is in the map. Bayesianism and Frequentism are not at odds. The prior is invisibly the fraction of possible past worlds one can imagine. The probability of an election outcome is the fraction of possible future worlds one can imagine that can emerge from the possible past worlds one had imagined. All that’s needed is fine-graining and counting. There is no need for nonlinearity and chaos.
This also resolves the so called logical uncertainty: the probability of the n-th digit of pi being 0 depends on the agent doing the estimate. Some agents have more detailed and accurate maps than others, and their probabilities may converge with each other, such as that 3^^^^3 digit of pi is 0 with probability 1⁄10, even though it will likely never be calculated by anyone. My personal probability that the 20th digit of pi is 0 with probability 1⁄10, up until I look it up and then it snaps to either 0 or 1, or more like 10^(-5) away from those, since my senses and google can lie to me.
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.
Well, I guess you can say that, due to chaos, even the best map requires probabilities, which, in a way, makes it a feature of the territory, because it is common to all maps.
Probability is only in the map of it isn’t in the territory as well. The theory that it is in the territory as well is not known to be tue, but is scientifically respectable. As Gabriel writes: