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> 0 probability means that even infinitely many pieces of evidence will not change your assessment Well no, this isn’t really what probability 0 means. An even

> 0 probability means that even infinitely many pieces of evidence will not change your assessment Well no, this isn’t really what probability 0 means. An event is not impossible if it has a probability of 0. More importantly probability informs you about how many times you should expect an event to occur, not what to do with this information if the event does or does not arise. In the Bayesian view, your probability measures how confident you are about an event occuring. In the frequentist view it measures the expected number of times an event will occur in n trials. But neither of these really mean you’d be impossible to convince :) Probabilities 0 and 1 are legitimate, and correspond to the statements “almost never” and “almost surely” in mathematics [1]. A good theoretical example of probability 0 is picking any given real number x out of an interval a < x < b. The probability of choosing x is 0 but it’s not impossible. A “real world” analogue of this would be flipping a coin infinitely many times and never getting heads. That is not impossible, but it has probability 0. I wouldn’t personally use probability 0 for cryogenics either, but if someone insisted on it the way to interpret that would be to say, “Out of uncountably many trials, a successful resurrection occurs only countably many times.” _____________________ 1. https://en.wikipedia.org/wiki/Almost_surely https://en.wikipedia.org/wiki/Almost_surely

FeepingCreature 8y ago
I think there's a legitimate question as to whether every real number is actually physically real. [1] It seems credible that our universe can only actually present us with a finite number of possible sensory experiences, in which case an event with probability 0 actually couldn't ever happen. That said, even if the universe can present you with an infinity of observations you can certainly only consider a finite number of classes of them, leading to the same outcome. [1] https://arxiv.org/abs/math/0411418 https://arxiv.org/abs/math/0411418
- throwawaymath 8y ago
  Yep, this is why I wouldn't personally use 0 probability to describe anything in the real world. It technically works, it's just the realm of pure measure theory rather than anything applicable to finitely many trials.
taejo 8y ago
> I wouldn’t personally use probability 0 for cryogenics either, but if someone insisted on it the way to interpret that would be to say, “Out of uncountably many trials, a successful resurrection occurs only countably many times.” It'd be a weird universe in which uncountably many cryogenics trials occurred, but I concede that the concept of almost-certainty would be relevant in that universe. On the other hand, seeing even trillions of occurrences (each with probability 0) I would still be forced to conclude that it was more likely that something with non-zero probability occurred, e.g.: I'm in a simulation, I'm going mad, I've been hallucinating for the last million years (I'm assuming here that one can only see a million cryogenic revivals a year), etc.
red75prime 8y ago
It doesn't matter. Bayes' rule will not allow to update prior probability of 0. Zero times anything is zero or undefined.
taejo 8y ago
> More importantly probability informs you about how many times you should expect an event to occur, not what to do with this information if the event does or does not arise. Bayesian probability absolutely tells you what to do when evidence of an event arises: Bayes' theorem precisely tells you how to update your certainty when evidence arises (and "seeing" an event is only fairly strong but not certain evidence of its occurrence).

FeepingCreature 8y ago

I think there's a legitimate question as to whether every real number is actually physically real. [1] It seems credible that our universe can only actually present us with a finite number of possible sensory experiences, in which case an event with probability 0 actually couldn't ever happen. That said, even if the universe can present you with an infinity of observations you can certainly only consider a finite number of classes of them, leading to the same outcome. [1] https://arxiv.org/abs/math/0411418 https://arxiv.org/abs/math/0411418

throwawaymath 8y ago
Yep, this is why I wouldn't personally use 0 probability to describe anything in the real world. It technically works, it's just the realm of pure measure theory rather than anything applicable to finitely many trials.

taejo 8y ago

> I wouldn’t personally use probability 0 for cryogenics either, but if someone insisted on it the way to interpret that would be to say, “Out of uncountably many trials, a successful resurrection occurs only countably many times.” It'd be a weird universe in which uncountably many cryogenics trials occurred, but I concede that the concept of almost-certainty would be relevant in that universe. On the other hand, seeing even trillions of occurrences (each with probability 0) I would still be forced to conclude that it was more likely that something with non-zero probability occurred, e.g.: I'm in a simulation, I'm going mad, I've been hallucinating for the last million years (I'm assuming here that one can only see a million cryogenic revivals a year), etc.

red75prime 8y ago

It doesn't matter. Bayes' rule will not allow to update prior probability of 0. Zero times anything is zero or undefined.

taejo 8y ago

> More importantly probability informs you about how many times you should expect an event to occur, not what to do with this information if the event does or does not arise. Bayesian probability absolutely tells you what to do when evidence of an event arises: Bayes' theorem precisely tells you how to update your certainty when evidence arises (and "seeing" an event is only fairly strong but not certain evidence of its occurrence).