3 ms·

> The probability of an event depends on your knowledge. This is a false statement and hints at the dissonance in the argument made for hard determinism.

ves 10y ago
How is this statement false at all? Conditioning on sigma-algebras, which are the objects at the base of probability theory and which further function as a reasonable model of "knowledge," is at the heart of how we understand probability today. The experimenter and the subject mentioned by the GP both hold different information and we can model that by constructing different sigma-algebras for each, F_e and F_s respectively. It's not at all absurd to think that P(E | F_e) != P(E | F_s) where E is the event in question. This idea holds in general, as you might imagine. I won't address your latter point but the former is definitely not true.
- kordless 10y ago
  I believe that, under certain circumstances, the probability of something occurring can be well known to one aggregate and completely different or unknown to the other. To illustrate this, that little island in the South Pacific that has no outside contact is still likely to experience rising ocean levels due to global warming based on current calculated probabilities. Just because they don't know the chances doesn't mean the external chances aren't still valid based on current knowledge somewhat within their scope of perception (i.e. they live on the planet but choose not to know the knowledge about the levels rising). There likely exist other probability based variables we cannot see because of our own dissonance on matters under scrutiny. An opposition to global warming which got funding cut on a program which was starting to be able to refine the probabilities a bit further would result in us "knowing" the probabilities were wrong but not "knowing" what they actually were because we didn't do the work to figure them out. My whole point is that "probabilities" can be internally or externally represented and that stating the probability of an "event" occurring depends on "your" knowledge about that event is inaccurate at best.
justinpombrio 10y ago
I'm not saying what you think I'm saying. I'm not saying that if we had full knowledge, then the future would be deterministic (on the contrary, I agree that this is false). However, we almost never have full knowledge, and how much knowledge we have and what that knowledge is determines the probability of something. For example, what's the probability that a RNG produces 38434 as its next u32 output? Usually, it's 1/(2^32). However, if I just wrote a program to reverse engineer your computer's RNG as part of an attack, that program knows exactly what the next output will be, and to it, the probability is either 0 or 1. Or take another example. You're teaching a probability class, and I'm a student who has just taken your test. What's the chance that I fail? To you, who doesn't know much about me, the probability is 5%, since only 5% of your students fail the first test. But I know that I didn't study, and peg it at 50%. So again, the probability of an event depends on your knowledge.
- YeGoblynQueenne 10y ago
  But your knowledge of stochastic events depends on the number of observations of the outcomes of those events. If you know only how well you do in probability tests, you can peg your chances to pass at 50%, but that doesn't tell you anything about the chances of the rest of the class. I think you're arguing that you're just another observer, however you're not. You're the event and you have some sort of expectation about your outcomes. The observer here is the tutor, who has seen enough of you and others like you to have some more or less justifiable state of belief about the outcomes of the class. Are you needlessly complicating what amounts to a very simple and reasonable point? You can't know what you don't know until you've seen enough of it to know it. This goes for both deterministic and probabilistic knowledge. If you observe all possible outcomes of an event, you can deterministically predict its outcomes. If you observe sufficiently many outcomes of a stochastic event, you can probabilistically predict its outcomes. If you don't observe enough outcomes - and an infinite event will never give you enough outcomes - then you're stuck with inaccurate predictions for ever.
  - justinpombrio 10y ago
    > You're the event and you have some sort of expectation about your outcomes. The event is the test grade. I am not a test grade, I am a person. If it's problematic that I'm taking the test, how about I tell my friend that I didn't study, and my friend give a 50% probability that I fail? > you can peg your chances to pass at 50%, but that doesn't tell you anything about the chances of the rest of the class. I wasn't talking about the rest of the class, I was talking about the probability that the professor would give me of failing the test. Is your probability theory so weak that it refuses to make a prediction for that? What are we supposed to use instead, our gut feelings? > If you observe all possible outcomes of an event, you can deterministically predict its outcomes. If you observe sufficiently many outcomes of a stochastic event, you can probabilistically predict its outcomes. The laws of probability apply just as well to deterministic and stochastic events. There is no useful distinction between a deterministic event of which we have partial knowledge (enough to assign a good "probability" to each outcome), and stochastic events of which we have full knowledge. As an example, take a board game that uses dice. How does the gameplay change if we replace the dice with a seeded RNG picking numbers from 1-6? Moreover, think of your favorite (classical) stochastic process. What if it's secretly deterministic, but only you know enough information -- an impractically large amount of information? What changes?
pasquinelli 10y ago
i think the point is that probability is, in essence, a human assessment, and so depends on the knowledge of the assessor.
Nomentatus 10y ago
It's an accurate statement: in fact, as your knowledge increases, the odds of a given event may fluctuate back and forth! Consider a card placed face down in front of you, randomly selected from a deck. Now you're allowed to turn over cards one at a time from the rest of the deck, and asked what the probability is that the face-down card is the ace of spades after every reveal. If the selected card isn't the ace of spades, the chances that it might be increase with every new reveal - until suddenly they become zero, when the ace of spades is revealed.

ves 10y ago

How is this statement false at all? Conditioning on sigma-algebras, which are the objects at the base of probability theory and which further function as a reasonable model of "knowledge," is at the heart of how we understand probability today. The experimenter and the subject mentioned by the GP both hold different information and we can model that by constructing different sigma-algebras for each, F_e and F_s respectively. It's not at all absurd to think that P(E | F_e) != P(E | F_s) where E is the event in question. This idea holds in general, as you might imagine. I won't address your latter point but the former is definitely not true.

kordless 10y ago
I believe that, under certain circumstances, the probability of something occurring can be well known to one aggregate and completely different or unknown to the other. To illustrate this, that little island in the South Pacific that has no outside contact is still likely to experience rising ocean levels due to global warming based on current calculated probabilities. Just because they don't know the chances doesn't mean the external chances aren't still valid based on current knowledge somewhat within their scope of perception (i.e. they live on the planet but choose not to know the knowledge about the levels rising). There likely exist other probability based variables we cannot see because of our own dissonance on matters under scrutiny. An opposition to global warming which got funding cut on a program which was starting to be able to refine the probabilities a bit further would result in us "knowing" the probabilities were wrong but not "knowing" what they actually were because we didn't do the work to figure them out. My whole point is that "probabilities" can be internally or externally represented and that stating the probability of an "event" occurring depends on "your" knowledge about that event is inaccurate at best.

justinpombrio 10y ago

I'm not saying what you think I'm saying. I'm not saying that if we had full knowledge, then the future would be deterministic (on the contrary, I agree that this is false). However, we almost never have full knowledge, and how much knowledge we have and what that knowledge is determines the probability of something. For example, what's the probability that a RNG produces 38434 as its next u32 output? Usually, it's 1/(2^32). However, if I just wrote a program to reverse engineer your computer's RNG as part of an attack, that program knows exactly what the next output will be, and to it, the probability is either 0 or 1. Or take another example. You're teaching a probability class, and I'm a student who has just taken your test. What's the chance that I fail? To you, who doesn't know much about me, the probability is 5%, since only 5% of your students fail the first test. But I know that I didn't study, and peg it at 50%. So again, the probability of an event depends on your knowledge.

YeGoblynQueenne 10y ago
But your knowledge of stochastic events depends on the number of observations of the outcomes of those events. If you know only how well you do in probability tests, you can peg your chances to pass at 50%, but that doesn't tell you anything about the chances of the rest of the class. I think you're arguing that you're just another observer, however you're not. You're the event and you have some sort of expectation about your outcomes. The observer here is the tutor, who has seen enough of you and others like you to have some more or less justifiable state of belief about the outcomes of the class. Are you needlessly complicating what amounts to a very simple and reasonable point? You can't know what you don't know until you've seen enough of it to know it. This goes for both deterministic and probabilistic knowledge. If you observe all possible outcomes of an event, you can deterministically predict its outcomes. If you observe sufficiently many outcomes of a stochastic event, you can probabilistically predict its outcomes. If you don't observe enough outcomes - and an infinite event will never give you enough outcomes - then you're stuck with inaccurate predictions for ever.
- justinpombrio 10y ago
  > You're the event and you have some sort of expectation about your outcomes. The event is the test grade. I am not a test grade, I am a person. If it's problematic that I'm taking the test, how about I tell my friend that I didn't study, and my friend give a 50% probability that I fail? > you can peg your chances to pass at 50%, but that doesn't tell you anything about the chances of the rest of the class. I wasn't talking about the rest of the class, I was talking about the probability that the professor would give me of failing the test. Is your probability theory so weak that it refuses to make a prediction for that? What are we supposed to use instead, our gut feelings? > If you observe all possible outcomes of an event, you can deterministically predict its outcomes. If you observe sufficiently many outcomes of a stochastic event, you can probabilistically predict its outcomes. The laws of probability apply just as well to deterministic and stochastic events. There is no useful distinction between a deterministic event of which we have partial knowledge (enough to assign a good "probability" to each outcome), and stochastic events of which we have full knowledge. As an example, take a board game that uses dice. How does the gameplay change if we replace the dice with a seeded RNG picking numbers from 1-6? Moreover, think of your favorite (classical) stochastic process. What if it's secretly deterministic, but only you know enough information -- an impractically large amount of information? What changes?

pasquinelli 10y ago

i think the point is that probability is, in essence, a human assessment, and so depends on the knowledge of the assessor.

Nomentatus 10y ago

It's an accurate statement: in fact, as your knowledge increases, the odds of a given event may fluctuate back and forth! Consider a card placed face down in front of you, randomly selected from a deck. Now you're allowed to turn over cards one at a time from the rest of the deck, and asked what the probability is that the face-down card is the ace of spades after every reveal. If the selected card isn't the ace of spades, the chances that it might be increase with every new reveal - until suddenly they become zero, when the ace of spades is revealed.