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I agree that colloquially speaking, it aligns most with what we believe. What I have trouble with is that you and I could assign different probabilities (via b

I agree that colloquially speaking, it aligns most with what we believe. What I have trouble with is that you and I could assign different probabilities (via beliefs) to an external event that has only one probability of happening. Just in that sentence I used the word "probability" correctly both times, yet it has two different conflicting meanings.

loup-vaillant 14y ago
Then just use different words. Break it down to "degree of subjective belief" and "frequency property" if you have to. Still, I prefer to use the short hand "probability" to mean the former, for two reasons: first, "degree of subjective belief" is what most lay-people will understand when we say "probability". Second, even scientists have this meaning messing up with their intuitions, even if when they write papers, they really do mean "frequency property". That can be a major obstacle for science. Let me quote Edwin T. Jaynes (long, but worth it): Those who cling to a belief in the existence of "physical probabilities" may react to the above arguments by pointing to quantum theory, in which physical probabilities appear to express the most fundamental laws of physics. Therefore let us explain why this is another case of circular reasoning. We need to understand that present quantum theory uses entirely different standards of logic than does the rest of science. In biology or medicine, if we note that an effect E (for example, muscle contraction, phototropism, digestion of protein) does not occur unless a condition C (nerve impulse, light, pepsin) is present, it seems natural to infer that C is a necessary causative agent for E. Most of what is known in all elds of science has resulted from following up this kind of reasoning. But suppose that condition C does not always lead to eect E; what further inferences should a scientist draw? At this point the reasoning formats of biology and quantum theory diverge sharply. In the biological sciences one takes it for granted that in addition to C there must be some other causative factor F, not yet identied. One searches for it, tracking down the assumed cause by a process of elimination of possibilities that is sometimes extremely tedious. But persistence pays off; over and over again medically important and intellectually impressive success has been achieved, the conjectured unknown causative factor being finally identified as a definite chemical compound. Most enzymes, vitamins, viruses, and other biologically active substances owe their discovery to this reasoning process. In quantum theory, one does not reason in this way. Consider, for example, the photoelectric effect (we shine light on a metal surface and find that electrons are ejected from it). The experimental fact is that the electrons do not appear unless light is present. So light must be a causative factor. But light does not always produce ejected electrons; even though the light from a unimode laser is present with absolutely steady amplitude, the electrons appear only at particular times that are not determined by any known parameters of the light. Why then do we not draw the obvious inference, that in addition to the light there must be a second causative factor, still unidentified, and the physicist's job is to search for it? What is done in quantum theory today is just the opposite; when no cause is apparent one simply postulates that no cause exists —ergo, the laws of physics are indeterministic and can be expressed only in probability form. The central dogma is that the light determines, not whether a photoelectron will appear, but only the probability that it will appear. The mathematical formalism of present quantum theory —incomplete in the same way that our present knowledge is incomplete— does not even provide the vocabulary in which one could ask a question about the real cause of an event. Biologists have a mechanistic picture of the world because, being trained to believe in causes, they continue to use the full power of their brains to search for them —and so they find them. Quantum physicists have only probability laws because for two generations we have been indoctrinated not to believe in causes —and so we have stopped looking for them. Indeed, any attempt to search for the causes of microphenomena is met with scorn and a charge of professional incompetence and `obsolete mechanistic materialism'. Therefore, to explain the indeterminacy in current quantum theory we need not suppose there is any indeterminacy in Nature; the mental attitude of quantum physicists is already sufficient to guarantee it. This one has been quite an eye opener, making me doubt even Many Worlds, which for one still doesn't explain the Born statistics. Still, thanks to Eliezer's Quantum Physics sequence, I'm now convinced that to the best of Science's knowledge (and despite what many physicists say) the laws of physics are most probably deterministic. Which would instantly solve the conflict by rendering "probability" nonsensical when applied to physical phenomena.
- tunesmith 14y ago
  That's a lot to unpack - let me make sure I have this right. Quantum theorists see that light is necessary but not sufficient for some sort of electron behavior. And I'm guessing that it's very hard to find an additional contributory/necessary cause that, when combined with light, would reliably predict the behavior. So they use probability to communicate their findings. If that additional contributory/necessary cause exists (but is just really hard to discover, or perhaps light itself is just highly contributory but not necessary/sufficient) then the probability is an effective way to communicate degree-of-belief, and helps to combine information about what they know with what they don't know. In other words, they are using probability to communicate partial findings. If that additional contributory/necessary cause doesn't exist, then the probability is a fixed, physical part of the science. In other words, they're communicating full findings; that light actually creates probability of an effect. And that confusion about "probability" is making people believe that the second case is true when they haven't necessarily disproved the first case yet? Which then serves as a curiosity-stopper and makes the science "mysterious". And this messes with scientific intuitions. Forgive me if I'm way off, I've only read the first few articles of the first couple lesswrong sequences.
  - Jach 14y ago
    I thought I'd pop in and mention this set of lectures (now a book, huh) from Scott Aaronson on quantum mechanics and quantum computing: http://www.scottaaronson.com/democritus/ http://www.scottaaronson.com/democritus/ Particularly Lecture 9 goes into the basic mathematics of quantum mechanics, and explains why it's more appropriate to consider it an extension to probability theory using complex numbers and call them amplitudes, rather than classic probabilities. Not being a physicist myself I don't know if this is really helpful in clearing up professional scientists' intuitions, but it's helpful for me at least in grasping the basics. You're on the right track by noting that quantum theorists can use probability to communicate their findings. A single classical probability like 0.7 is a summary, not the whole picture. For the whole picture, you need a log of observations with time stamps, which is a tremendous amount of data because taken to the extreme it's a balancing act between maximizing the data you know about you and your surroundings and minimizing the number of planck unit time steps to collect the data. Even with more realistic amounts of data it's still a lot to pack around, so you can summarize it by constructing a probability distribution which is more convenient mathematically, and you can summarize that probability distribution into a handful of numbers if you need to because those are even easier to pack around. (Like the single probability 0.7, or two numbers u and s that characterize a Normal distribution, etc.) So if you think of probability as just summarizing your past observations and constraining your expectations for future observations (because what else can?), I think it's easy to see how two people can have different probabilities that represent a belief in a proposition or an abstract system or something else. If both are being honest (I'm packing a lot of assumptions in that word since this is basically Aumann's agreement theorem) and the probabilities are different, there are a couple reasons why: either at least one of them has information (observations) the other one does not, or they started out with different prior probabilities. In the former case, they can reach agreement by sharing data. In the latter case, they can eventually reach agreement by obtaining more data or choosing a common prior. With enough successive Bayesian updates, you can arrive at the same conclusion regardless of where you started. (In practice, of course, things are more hairy and not this simplistic, which is what the submitted pdf is addressing in part.) I find it hard to grok what it means for something to have a physical frequency property. I can understand it as a statistic of an abstract system, i.e. a probability, but in light of Many Worlds, I don't think a frequency can fundamentally be a property of something in the same way energy can be. But since the energy of a photon is related to the photon's "frequency" via its "wavelength", is energy really fundamental or is the relation just a convenient means of making the wave mechanics useful? I've read Feynman tell how the whole idea of forces is just a somewhat circular simplification that's not really fundamental, even though sometimes it seems like it is. While I have a high degree of certainty about the physics accurately describing reality as she is, my meta-belief / confidence about that high certainty isn't nearly as high simply because I feel a lot of confusion about the ultimate nature of reality. But at least at a higher level than fundamental physics, it's clear to me that saying a "fair coin" has p=0.5 per unique side is really just summarizing we don't have enough knowledge of the flipper and the environment it is flipped in to predict the result with certainty in the way we can predict the result of the output of a logic OR gate with low- and high- voltage inputs with certainty. This is different than the uncertainty of which branch you are within a Many Worlds universe, where it's more of a physical resolution problem rather than one of needing more knowledge, similar to not being able to find out what happens between planck unit time steps (if anything happens and if the question means anything). Ben Goertzel's book Probabilistic Logic Networks is another resource I'd recommend. Sorry if my branching reply is a bit big, but I'm constantly trying to clarify things for myself as well. ;)

loup-vaillant 14y ago

Then just use different words. Break it down to "degree of subjective belief" and "frequency property" if you have to. Still, I prefer to use the short hand "probability" to mean the former, for two reasons: first, "degree of subjective belief" is what most lay-people will understand when we say "probability". Second, even scientists have this meaning messing up with their intuitions, even if when they write papers, they really do mean "frequency property". That can be a major obstacle for science. Let me quote Edwin T. Jaynes (long, but worth it): Those who cling to a belief in the existence of "physical probabilities" may react to the above arguments by pointing to quantum theory, in which physical probabilities appear to express the most fundamental laws of physics. Therefore let us explain why this is another case of circular reasoning. We need to understand that present quantum theory uses entirely different standards of logic than does the rest of science. In biology or medicine, if we note that an effect E (for example, muscle contraction, phototropism, digestion of protein) does not occur unless a condition C (nerve impulse, light, pepsin) is present, it seems natural to infer that C is a necessary causative agent for E. Most of what is known in all elds of science has resulted from following up this kind of reasoning. But suppose that condition C does not always lead to eect E; what further inferences should a scientist draw? At this point the reasoning formats of biology and quantum theory diverge sharply. In the biological sciences one takes it for granted that in addition to C there must be some other causative factor F, not yet identied. One searches for it, tracking down the assumed cause by a process of elimination of possibilities that is sometimes extremely tedious. But persistence pays off; over and over again medically important and intellectually impressive success has been achieved, the conjectured unknown causative factor being finally identified as a definite chemical compound. Most enzymes, vitamins, viruses, and other biologically active substances owe their discovery to this reasoning process. In quantum theory, one does not reason in this way. Consider, for example, the photoelectric effect (we shine light on a metal surface and find that electrons are ejected from it). The experimental fact is that the electrons do not appear unless light is present. So light must be a causative factor. But light does not always produce ejected electrons; even though the light from a unimode laser is present with absolutely steady amplitude, the electrons appear only at particular times that are not determined by any known parameters of the light. Why then do we not draw the obvious inference, that in addition to the light there must be a second causative factor, still unidentified, and the physicist's job is to search for it? What is done in quantum theory today is just the opposite; when no cause is apparent one simply postulates that no cause exists —ergo, the laws of physics are indeterministic and can be expressed only in probability form. The central dogma is that the light determines, not whether a photoelectron will appear, but only the probability that it will appear. The mathematical formalism of present quantum theory —incomplete in the same way that our present knowledge is incomplete— does not even provide the vocabulary in which one could ask a question about the real cause of an event. Biologists have a mechanistic picture of the world because, being trained to believe in causes, they continue to use the full power of their brains to search for them —and so they find them. Quantum physicists have only probability laws because for two generations we have been indoctrinated not to believe in causes —and so we have stopped looking for them. Indeed, any attempt to search for the causes of microphenomena is met with scorn and a charge of professional incompetence and `obsolete mechanistic materialism'. Therefore, to explain the indeterminacy in current quantum theory we need not suppose there is any indeterminacy in Nature; the mental attitude of quantum physicists is already sufficient to guarantee it. This one has been quite an eye opener, making me doubt even Many Worlds, which for one still doesn't explain the Born statistics. Still, thanks to Eliezer's Quantum Physics sequence, I'm now convinced that to the best of Science's knowledge (and despite what many physicists say) the laws of physics are most probably deterministic. Which would instantly solve the conflict by rendering "probability" nonsensical when applied to physical phenomena.

tunesmith 14y ago
That's a lot to unpack - let me make sure I have this right. Quantum theorists see that light is necessary but not sufficient for some sort of electron behavior. And I'm guessing that it's very hard to find an additional contributory/necessary cause that, when combined with light, would reliably predict the behavior. So they use probability to communicate their findings. If that additional contributory/necessary cause exists (but is just really hard to discover, or perhaps light itself is just highly contributory but not necessary/sufficient) then the probability is an effective way to communicate degree-of-belief, and helps to combine information about what they know with what they don't know. In other words, they are using probability to communicate partial findings. If that additional contributory/necessary cause doesn't exist, then the probability is a fixed, physical part of the science. In other words, they're communicating full findings; that light actually creates probability of an effect. And that confusion about "probability" is making people believe that the second case is true when they haven't necessarily disproved the first case yet? Which then serves as a curiosity-stopper and makes the science "mysterious". And this messes with scientific intuitions. Forgive me if I'm way off, I've only read the first few articles of the first couple lesswrong sequences.
- Jach 14y ago
  I thought I'd pop in and mention this set of lectures (now a book, huh) from Scott Aaronson on quantum mechanics and quantum computing: http://www.scottaaronson.com/democritus/ http://www.scottaaronson.com/democritus/ Particularly Lecture 9 goes into the basic mathematics of quantum mechanics, and explains why it's more appropriate to consider it an extension to probability theory using complex numbers and call them amplitudes, rather than classic probabilities. Not being a physicist myself I don't know if this is really helpful in clearing up professional scientists' intuitions, but it's helpful for me at least in grasping the basics. You're on the right track by noting that quantum theorists can use probability to communicate their findings. A single classical probability like 0.7 is a summary, not the whole picture. For the whole picture, you need a log of observations with time stamps, which is a tremendous amount of data because taken to the extreme it's a balancing act between maximizing the data you know about you and your surroundings and minimizing the number of planck unit time steps to collect the data. Even with more realistic amounts of data it's still a lot to pack around, so you can summarize it by constructing a probability distribution which is more convenient mathematically, and you can summarize that probability distribution into a handful of numbers if you need to because those are even easier to pack around. (Like the single probability 0.7, or two numbers u and s that characterize a Normal distribution, etc.) So if you think of probability as just summarizing your past observations and constraining your expectations for future observations (because what else can?), I think it's easy to see how two people can have different probabilities that represent a belief in a proposition or an abstract system or something else. If both are being honest (I'm packing a lot of assumptions in that word since this is basically Aumann's agreement theorem) and the probabilities are different, there are a couple reasons why: either at least one of them has information (observations) the other one does not, or they started out with different prior probabilities. In the former case, they can reach agreement by sharing data. In the latter case, they can eventually reach agreement by obtaining more data or choosing a common prior. With enough successive Bayesian updates, you can arrive at the same conclusion regardless of where you started. (In practice, of course, things are more hairy and not this simplistic, which is what the submitted pdf is addressing in part.) I find it hard to grok what it means for something to have a physical frequency property. I can understand it as a statistic of an abstract system, i.e. a probability, but in light of Many Worlds, I don't think a frequency can fundamentally be a property of something in the same way energy can be. But since the energy of a photon is related to the photon's "frequency" via its "wavelength", is energy really fundamental or is the relation just a convenient means of making the wave mechanics useful? I've read Feynman tell how the whole idea of forces is just a somewhat circular simplification that's not really fundamental, even though sometimes it seems like it is. While I have a high degree of certainty about the physics accurately describing reality as she is, my meta-belief / confidence about that high certainty isn't nearly as high simply because I feel a lot of confusion about the ultimate nature of reality. But at least at a higher level than fundamental physics, it's clear to me that saying a "fair coin" has p=0.5 per unique side is really just summarizing we don't have enough knowledge of the flipper and the environment it is flipped in to predict the result with certainty in the way we can predict the result of the output of a logic OR gate with low- and high- voltage inputs with certainty. This is different than the uncertainty of which branch you are within a Many Worlds universe, where it's more of a physical resolution problem rather than one of needing more knowledge, similar to not being able to find out what happens between planck unit time steps (if anything happens and if the question means anything). Ben Goertzel's book Probabilistic Logic Networks is another resource I'd recommend. Sorry if my branching reply is a bit big, but I'm constantly trying to clarify things for myself as well. ;)