5 ms·

> Theoretical and observational evidence suggests that we are living in an enormous, eternally expanding multiverse where the constants of nature vary from plac

> Theoretical and observational evidence suggests that we are living in an enormous, eternally expanding multiverse where the constants of nature vary from place to place. Really? What is this evidence? I didn't see much of it in the article. Also, the "sleeper" argument (at least as presented?) seems to be flawed. To repeat, the argument is this: Suppose you are cryogenically frozen, to be woken up in either 1 year or 100 years, determined by the flip of a coin right after you're frozen. Furthermore, say that the population of the Earth doubles every year, and each year 1% of people undergo this experiment. Now suppose you wake up, and wonder how much time has passed. There are two lines of reasoning: 1. Obviously, the odds are 50/50, since the result was determined by the flip of a coin. 2. Whatever year it is, most of the people waking up from the experiment were frozen last year (when the population of Earth was higher). The article then concludes that "The fact that two logical lines of argument yield contradictory answers tells us that the problem is not well-defined." But they're not contradictory; either may hold depending on what you know. The probability of an event depends on your knowledge. Assuming you remember when you were frozen, then there are two possibilities: "I am John Doe who was frozen in 2020 and woke up in 2021", or "I am John Doe who was frozen in 2020 and woke up in 2120". Thus line of reasoning #1 holds. On the other hand, if you're an experimenter who's greeting people as they wake up, then there are many possibilities: "It's 2120, and this was one of the 70 million people who was frozen in 2020", or "It's 2120, and this was one of the 140 million people who was frozen in 2119". Thus line of reasoning #2 holds, and the person you're greeting was probably frozen last year. No contradiction.

kordless 10y ago
> 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.
baddox 10y ago
Yes. This is a pretty standard thought experiment to demonstrate the concept of anthropogenic probability, where we apply the anthropoid principle to Bayesian (or other) probability. The two answers come from two different assumptions: the self-sampling assumption or the self-indication assumption. These are effectively two different models for the hypothetical world described in the thought experiment, and without the thought experimenter telling you which model to use (i.e. how you were sampled in the thought experiment), there's not a whole lot you can do other than choose your favorite. https://en.m.wikipedia.org/wiki/Self-sampling_assumption https://en.m.wikipedia.org/wiki/Self-sampling_assumption https://en.m.wikipedia.org/wiki/Self-indication_assumption https://en.m.wikipedia.org/wiki/Self-indication_assumption These terms come from Nick Bostrom, but I prefer Scott Aaronson's description: http://www.scottaaronson.com/democritus/lec17.html http://www.scottaaronson.com/democritus/lec17.html
- justinpombrio 10y ago
  That distinction doesn't even come in to it, though. Take the analogy with the thought experiment from Aaronson's description: A coin is flipped. If heads, two rooms are created: one with a red-haired person, and one with a green-haired person. If tails, one room is created with a red-haired person. The analogy is that the coin is the coin, heads means "wake up in 100 years", tails means "wake up in 1 year", red-haired is the person who goes in in 2020, and green-haired is the person who goes in in 2119. However, unlike Aaronson's interesting experiment, in the Nautilus article experiment you know beforehand that you have red hair and will continue to have red hair regardless of which way the coin goes. The year you were frozen is known; you know your name; you know the year you entered. The interesting question doesn't even arise.
YeGoblynQueenne 10y ago
>> The probability of an event depends on your knowledge That's true insofar as by "probability" you mean your belief about the outcome of the event- in other words, your expectation of the outcome. The actual outcome of an event does not depend on your expectation. Stated in another way, the process that produces an observation and the process that produces your expectation of the observation are independent. Else: magick.
- justinpombrio 10y ago
  > The actual outcome of an event does not depend on your expectation. Of course :-). The actual outcome of an event doesn't much care what probability we assign to it. With diligence, the causality goes the other way, and e.g. about x% of the events to which we assign probability x% occur. If they're off by a large margin, we should revise our probabilities, because the universe certainly isn't going to change.

kordless 10y ago

> 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.

baddox 10y ago

Yes. This is a pretty standard thought experiment to demonstrate the concept of anthropogenic probability, where we apply the anthropoid principle to Bayesian (or other) probability. The two answers come from two different assumptions: the self-sampling assumption or the self-indication assumption. These are effectively two different models for the hypothetical world described in the thought experiment, and without the thought experimenter telling you which model to use (i.e. how you were sampled in the thought experiment), there's not a whole lot you can do other than choose your favorite. https://en.m.wikipedia.org/wiki/Self-sampling_assumption https://en.m.wikipedia.org/wiki/Self-sampling_assumption https://en.m.wikipedia.org/wiki/Self-indication_assumption https://en.m.wikipedia.org/wiki/Self-indication_assumption These terms come from Nick Bostrom, but I prefer Scott Aaronson's description: http://www.scottaaronson.com/democritus/lec17.html http://www.scottaaronson.com/democritus/lec17.html

justinpombrio 10y ago
That distinction doesn't even come in to it, though. Take the analogy with the thought experiment from Aaronson's description: A coin is flipped. If heads, two rooms are created: one with a red-haired person, and one with a green-haired person. If tails, one room is created with a red-haired person. The analogy is that the coin is the coin, heads means "wake up in 100 years", tails means "wake up in 1 year", red-haired is the person who goes in in 2020, and green-haired is the person who goes in in 2119. However, unlike Aaronson's interesting experiment, in the Nautilus article experiment you know beforehand that you have red hair and will continue to have red hair regardless of which way the coin goes. The year you were frozen is known; you know your name; you know the year you entered. The interesting question doesn't even arise.

YeGoblynQueenne 10y ago

>> The probability of an event depends on your knowledge That's true insofar as by "probability" you mean your belief about the outcome of the event- in other words, your expectation of the outcome. The actual outcome of an event does not depend on your expectation. Stated in another way, the process that produces an observation and the process that produces your expectation of the observation are independent. Else: magick.

justinpombrio 10y ago
> The actual outcome of an event does not depend on your expectation. Of course :-). The actual outcome of an event doesn't much care what probability we assign to it. With diligence, the causality goes the other way, and e.g. about x% of the events to which we assign probability x% occur. If they're off by a large margin, we should revise our probabilities, because the universe certainly isn't going to change.