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That's just pushing the problem up a level. Adding an explanation is proposing a model for the coin's behavior. Regardless of the model proposed, and whether

by yters 8y ago

That's just pushing the problem up a level. Adding an explanation is proposing a model for the coin's behavior. Regardless of the model proposed, and whether it is confirmed or refuted, if the coin is fair you learn nothing. On the other hand, if the coin is not fair, Solomonoff induction works.

lisper 8y ago
> if the coin is fair you learn nothing. But that is simply because the theory that a coin is fair cannot be falsified with one data point. (Well, that's actually not quite true. It can't be falsified with a single data point which is "heads" or "tails". It could be falsified if the coin lands and breaks into two pieces revealing some internal mechanism that makes it unfair.) > if the coin is not fair, Solomonoff induction works. No, it doesn't. It is possible (given sufficient technology) to produce a coin that generates a sequence of flips that is indistinguishable from fair for any finite number N of flips, but which then produces HEADS forever after the Nth flip. Moreover, it is possible to know that this will happen without even flipping the coin!
- yters 8y ago
  The problem is how do you gain these explanations in the first place without appealing to inductivism? The process of examining a thing to propose a theory about its operation seems indistinguishable in my mind from the inductivist approach of deriving general theories from particular observations. Both approaches make the same assumption of a consistent underlying order behind the observations we make.
  - lisper 8y ago
    This is the unsolved problem of "hypothesis formation." It's something that brains do that we do not yet fully understand. It's an active area of research. But the process of explanatory hypothesis formation is distinct from induction. Induction says, e.g. "Every crow I have ever seen has been black, therefore I conclude that all crows are black." (They aren't, BTW. http://www.birds.cornell.edu/crows/whitecrows.htm http://www.birds.cornell.edu/crows/whitecrows.htm https://www.quora.com/Are-all-crows-black https://www.quora.com/Are-all-crows-black)
    - yters 8y ago
      Yes, so it seems like falsificationism just pushes the fundamental problem elsewhere and renames it. The basic problem of distinguishing between patterns and luck undermines both falsification and induction. As far as I know, there is no resolution to the problem. We just irrationally assume there is no problem out of habit, as Hume states in his original work. A leap of faith, if you will.
      - lisper 8y ago
        No. Falsification is necessary but not sufficient. The best theory is one that has two properties: 1) it is consistent with all the observed data (i.e. has not been falsified) and 2) it is a "good explanation". Explaining what is meant by "good explanation" is too long for an HN comment, but roughly speaking it means that it is concise and brittle -- any modification would cause it to become inconsistent with the data. (So for example, conspiracy theories fail as explanatory theories not because they are inconsistent with the data -- they generally aren't -- but rather because they are not concise and brittle.)
        yters 8y ago
        That sounds like Solmonoff induction. But, there is still the same problem. Why are concise explanations better? Solomnoff justified this assumption by claiming we are generated by a computable prior. But, that again pushes the question back to why we can assume this. Otherwise, no observation justifies a computable prior over random luck.
        lisper 8y ago
        > Why are concise explanations better? Because they require less effort to work with. Note that concise is only better all else being equal. Being consistent with the observed data is necessary, but not sufficient. We can only ever have a finite amount of data, and any finite dataset is consistent with an infinite number of theories. Conciseness is just a heuristic we use to select among the infinite possibilities. It just turns out that in the universe we live in, concise theories consistent with the data have a lot of predictive power. No one know why our universe is this way. That's just how it turns out to be.
marcosdumay 8y ago
> That's just pushing the problem up a level. No. That's inverting the order of the interaction. On the first case you are observing a phenomenon, and using it to construct a model; on the second case you are constructing a model, and then using your observation to check it. Induction is a great way to create useful models, but only failures on falsification can give you confidence that the model actually works.
- lisper 8y ago
  > Induction is a great way to create useful models No, it isn't. Induction is a great way to create WRONG models. In fact, all of the interesting and useful stuff happens exactly where induction gets it wrong. Example: the sun has risen on earth every day for the last 10^11 days or so. But we know that in another 10^11 days the sun will stop rising (because it will become a red giant and engulf the earth). We know this despite the fact that we have never actually observed this happen even once.

by yters 8y ago

lisper 8y ago

> if the coin is fair you learn nothing. But that is simply because the theory that a coin is fair cannot be falsified with one data point. (Well, that's actually not quite true. It can't be falsified with a single data point which is "heads" or "tails". It could be falsified if the coin lands and breaks into two pieces revealing some internal mechanism that makes it unfair.) > if the coin is not fair, Solomonoff induction works. No, it doesn't. It is possible (given sufficient technology) to produce a coin that generates a sequence of flips that is indistinguishable from fair for any finite number N of flips, but which then produces HEADS forever after the Nth flip. Moreover, it is possible to know that this will happen without even flipping the coin!

yters 8y ago
The problem is how do you gain these explanations in the first place without appealing to inductivism? The process of examining a thing to propose a theory about its operation seems indistinguishable in my mind from the inductivist approach of deriving general theories from particular observations. Both approaches make the same assumption of a consistent underlying order behind the observations we make.
- lisper 8y ago
  This is the unsolved problem of "hypothesis formation." It's something that brains do that we do not yet fully understand. It's an active area of research. But the process of explanatory hypothesis formation is distinct from induction. Induction says, e.g. "Every crow I have ever seen has been black, therefore I conclude that all crows are black." (They aren't, BTW. http://www.birds.cornell.edu/crows/whitecrows.htm http://www.birds.cornell.edu/crows/whitecrows.htm https://www.quora.com/Are-all-crows-black https://www.quora.com/Are-all-crows-black)
  - yters 8y ago
    Yes, so it seems like falsificationism just pushes the fundamental problem elsewhere and renames it. The basic problem of distinguishing between patterns and luck undermines both falsification and induction. As far as I know, there is no resolution to the problem. We just irrationally assume there is no problem out of habit, as Hume states in his original work. A leap of faith, if you will.
    - lisper 8y ago
      No. Falsification is necessary but not sufficient. The best theory is one that has two properties: 1) it is consistent with all the observed data (i.e. has not been falsified) and 2) it is a "good explanation". Explaining what is meant by "good explanation" is too long for an HN comment, but roughly speaking it means that it is concise and brittle -- any modification would cause it to become inconsistent with the data. (So for example, conspiracy theories fail as explanatory theories not because they are inconsistent with the data -- they generally aren't -- but rather because they are not concise and brittle.)
      - yters 8y ago
        That sounds like Solmonoff induction. But, there is still the same problem. Why are concise explanations better? Solomnoff justified this assumption by claiming we are generated by a computable prior. But, that again pushes the question back to why we can assume this. Otherwise, no observation justifies a computable prior over random luck.
        lisper 8y ago
        > Why are concise explanations better? Because they require less effort to work with. Note that concise is only better all else being equal. Being consistent with the observed data is necessary, but not sufficient. We can only ever have a finite amount of data, and any finite dataset is consistent with an infinite number of theories. Conciseness is just a heuristic we use to select among the infinite possibilities. It just turns out that in the universe we live in, concise theories consistent with the data have a lot of predictive power. No one know why our universe is this way. That's just how it turns out to be.

marcosdumay 8y ago

> That's just pushing the problem up a level. No. That's inverting the order of the interaction. On the first case you are observing a phenomenon, and using it to construct a model; on the second case you are constructing a model, and then using your observation to check it. Induction is a great way to create useful models, but only failures on falsification can give you confidence that the model actually works.

lisper 8y ago
> Induction is a great way to create useful models No, it isn't. Induction is a great way to create WRONG models. In fact, all of the interesting and useful stuff happens exactly where induction gets it wrong. Example: the sun has risen on earth every day for the last 10^11 days or so. But we know that in another 10^11 days the sun will stop rising (because it will become a red giant and engulf the earth). We know this despite the fact that we have never actually observed this happen even once.