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>For example, I think we'd share the principle that a controlled experiment testing some hypothesis entitles us to have proportionally increased belief in it.

>For example, I think we'd share the principle that a controlled experiment testing some hypothesis entitles us to have proportionally increased belief in it. This isn't even a shared principle among humans. How many experiments does it take for you to have 50% belief in a hypothesis?. What is the number of experiments? It's literally impossible to answer. It's not even clear what "belief" is or what 50% means. This ambiguity of the word isn't even the main problem. If I run the same experiment with perfect observational tools 10 billion times and it verifies my hypothesis. Does that raise my belief further? What if on the 10 billionth and first time the test shows a negative result? That literally invalidates the hypothesis. Keep in mind we are assuming my observational tools are perfect. Does this make my belief shoot down to zero? If this possibility of a negative result remains true after any number of tests then what does it say about belief? Why should I believe anything if a single negative experiment can invalidate 10 billion positive experiments (assuming perfect observational tools of course)? Let me bring a more concrete example. I hypothesize all zebras have stripes. I observe zebras 10 billion times. They all confirm my hypothesis. Then on the 10 billionth and first time I see a zebra with spots. My hypothesis is wrong. This can happen any time. Anyway to bring it back to his point. Don't assume shared axiomatic truths. PG already assumed that it's shared among humans. He's wrong. The nature of science and the scientific method is not universally shared or even fully understood among humans. He's likely also wrong about aliens as he is about humans.

naasking 4y ago
> This isn't even a shared principle among humans. How many experiments does it take for you to have 50% belief in a hypothesis?. What is the number of experiments? It's literally impossible to answer. It's not even clear what "belief" is or what 50% means. https://en.wikipedia.org/wiki/Solomonoff%27s_theory_of_inductive_inference https://en.wikipedia.org/wiki/Solomonoff%27s_theory_of_induc...
- deltasevennine 4y ago
  A bit of a complicated read. Not sure what you're trying to say here and I don't even completely understand it. But anything that gets into bayesians and frequentists ends in a fundamental divide in humanity. Humans don't agree on which interpretation is correct. Which is the point of everything I wrote. So why would aliens hold this "principle" the same if humans don't even agree on it? PG is wrong. His own principles upended not even by aliens, but by humanity, thus how accurate can his assumptions about universal principles even be? No that accurate imho.
  - naasking 4y ago
    > But anything that gets into bayesians and frequentists ends in a fundamental divide in humanity. Humans don't agree on which interpretation is correct. There is no divide, there is the illusion of divide because we didn't have a rigourous formal model of how to build reliable knowledge and everyone focused on different but relevant aspects. Bayesian reasoning is the correct way if you have justifiable priors, but we didn't have a way to calculate the correct prior. Solomonoff showed us how with his theory: Kolmogorov complexity is a measure of parsimony, and this is how to select priors in a formal, rigourous way. Solomonoff induction is to knowledge what Turing machines or the lambda calculus are to computation. Sure, aliens might not discover Turing machines exactly, or the lambda calculus exactly, but whatever they do build that's capable of universal computation, we already know it must be isomorphic to a Turing machine, because all constructions capable of computation must be by necessity. The frequentist/Bayesian divide is a separate issue about how to interpret statistical data in useful ways, not specifically about how we know what we know and what confidence we should have in our knowledge, which is what you were asking about.
    - deltasevennine 4y ago
      Interesting. Do you know of any popular science articles or books that can describe what you're talking about? Academic papers are fine too, just harder to parse.
      - naasking 4y ago
        Hard to find simple articles on such an esoteric topic as algorithmic probability, which cuts across subjects like probability, information theory and computation. This one seems to hit all the notes but who knows if it's as accessible as it's aiming to be: https://www.lesswrong.com/posts/Kyc5dFDzBg4WccrbK/an-intuitive-explanation-of-solomonoff-induction https://www.lesswrong.com/posts/Kyc5dFDzBg4WccrbK/an-intuiti...
        deltasevennine 4y ago
        Wow, I didn't think you would find one. I thought I'd be digging through some esoteric academic paper. Thanks!
simiones 4y ago
> I hypothesize all zebras have stripes. I observe zebras 10 billion times. They all confirm my hypothesis. Then on the 10 billionth and first time I see a zebra with spots. My hypothesis is wrong. This can happen any time. Even if the original belief turns out to be wrong, you only have to slightly weaken it and it will remain true: "the vast majority of zebras have stripes". Even if you discover a new continent full of hordes of uniformly-colored zebras, the true hypothesis becomes "the vast majority of zebras in my original continent are striped". Essentially every observation brings proof for a whole family of hypotheses. We normally only talk about the strongest of these hypotheses, but that doesn't meant that a negative example rules out the entire family. For example, even if we didn't find a deductive proof the Fermat's last theorem was wrong even after all of the empirical proof that it probably wasn't, a weaker version would have still remained true - the one validated by that empirical proof.
- deltasevennine 4y ago
  >Even if the original belief turns out to be wrong, you only have to slightly weaken it and it will remain true: "the vast majority of zebras have stripes". Even if you discover a new continent full of hordes of uniformly-colored zebras, the true hypothesis becomes "the vast majority of zebras in my original continent are striped". The hypothesis does not remain true. It was never proven to be true and the new hypothesis is still not proven to be true. Science cannot prove anything to be true. I can find a cave full of of spotted zebras, and you have to further weaken your hypothesis of continents, I can then find that the stripes were actually microscopic spots and my perfect observation tool, though never wrong has limited resolution. Ad infinitum. Nobody ever considers your made up philosophy because it's changing the rules of the game. It's making a statement then adjusting your statement once it's proven wrong... people look down on that kind of thing. What I'm writing here isn't something I pulled out of my ass. It's well known that in science, the scientific method, and reality itself, nothing can be proven. Proof is the domain of math and logic, not science. In science, things can only be falsified. To quote Einstein: “No amount of experimentation can ever prove me right; a single experiment can prove me wrong.” Einstein obviously isn't saying stuff like a single experiment causes me to adjust my hypothesis and divide split it into two different ones because it's kind of inconsistent. There are people who truly understand science, but most of the population doesn't (including PG). I think what's going on with you is you're in the later camp, you've long held the incorrect belief that science can prove things and this long held ideology is coming into contact with the actual logic of the situation and your adjusting your belief to maintain a biased ideology. Do you look up to PG? Bias can be corrected when an authority confirms the opposite. I quoted Einstein here. One of the ultimate authorities on science, a person who overturned the hypothesis about Newtonian physics being a model for motion. A single experiment proved it wrong and now Newtonian physics is simply an approximation that is ultimately wrong. Hopefully that will clear things up, if not... then you must be an Alien far more strange then what PG is describing.

naasking 4y ago

> This isn't even a shared principle among humans. How many experiments does it take for you to have 50% belief in a hypothesis?. What is the number of experiments? It's literally impossible to answer. It's not even clear what "belief" is or what 50% means. https://en.wikipedia.org/wiki/Solomonoff%27s_theory_of_inductive_inference https://en.wikipedia.org/wiki/Solomonoff%27s_theory_of_induc...

deltasevennine 4y ago
A bit of a complicated read. Not sure what you're trying to say here and I don't even completely understand it. But anything that gets into bayesians and frequentists ends in a fundamental divide in humanity. Humans don't agree on which interpretation is correct. Which is the point of everything I wrote. So why would aliens hold this "principle" the same if humans don't even agree on it? PG is wrong. His own principles upended not even by aliens, but by humanity, thus how accurate can his assumptions about universal principles even be? No that accurate imho.
- naasking 4y ago
  > But anything that gets into bayesians and frequentists ends in a fundamental divide in humanity. Humans don't agree on which interpretation is correct. There is no divide, there is the illusion of divide because we didn't have a rigourous formal model of how to build reliable knowledge and everyone focused on different but relevant aspects. Bayesian reasoning is the correct way if you have justifiable priors, but we didn't have a way to calculate the correct prior. Solomonoff showed us how with his theory: Kolmogorov complexity is a measure of parsimony, and this is how to select priors in a formal, rigourous way. Solomonoff induction is to knowledge what Turing machines or the lambda calculus are to computation. Sure, aliens might not discover Turing machines exactly, or the lambda calculus exactly, but whatever they do build that's capable of universal computation, we already know it must be isomorphic to a Turing machine, because all constructions capable of computation must be by necessity. The frequentist/Bayesian divide is a separate issue about how to interpret statistical data in useful ways, not specifically about how we know what we know and what confidence we should have in our knowledge, which is what you were asking about.
  - deltasevennine 4y ago
    Interesting. Do you know of any popular science articles or books that can describe what you're talking about? Academic papers are fine too, just harder to parse.
    - naasking 4y ago
      Hard to find simple articles on such an esoteric topic as algorithmic probability, which cuts across subjects like probability, information theory and computation. This one seems to hit all the notes but who knows if it's as accessible as it's aiming to be: https://www.lesswrong.com/posts/Kyc5dFDzBg4WccrbK/an-intuitive-explanation-of-solomonoff-induction https://www.lesswrong.com/posts/Kyc5dFDzBg4WccrbK/an-intuiti...
      - deltasevennine 4y ago
        Wow, I didn't think you would find one. I thought I'd be digging through some esoteric academic paper. Thanks!

simiones 4y ago

> I hypothesize all zebras have stripes. I observe zebras 10 billion times. They all confirm my hypothesis. Then on the 10 billionth and first time I see a zebra with spots. My hypothesis is wrong. This can happen any time. Even if the original belief turns out to be wrong, you only have to slightly weaken it and it will remain true: "the vast majority of zebras have stripes". Even if you discover a new continent full of hordes of uniformly-colored zebras, the true hypothesis becomes "the vast majority of zebras in my original continent are striped". Essentially every observation brings proof for a whole family of hypotheses. We normally only talk about the strongest of these hypotheses, but that doesn't meant that a negative example rules out the entire family. For example, even if we didn't find a deductive proof the Fermat's last theorem was wrong even after all of the empirical proof that it probably wasn't, a weaker version would have still remained true - the one validated by that empirical proof.

deltasevennine 4y ago
>Even if the original belief turns out to be wrong, you only have to slightly weaken it and it will remain true: "the vast majority of zebras have stripes". Even if you discover a new continent full of hordes of uniformly-colored zebras, the true hypothesis becomes "the vast majority of zebras in my original continent are striped". The hypothesis does not remain true. It was never proven to be true and the new hypothesis is still not proven to be true. Science cannot prove anything to be true. I can find a cave full of of spotted zebras, and you have to further weaken your hypothesis of continents, I can then find that the stripes were actually microscopic spots and my perfect observation tool, though never wrong has limited resolution. Ad infinitum. Nobody ever considers your made up philosophy because it's changing the rules of the game. It's making a statement then adjusting your statement once it's proven wrong... people look down on that kind of thing. What I'm writing here isn't something I pulled out of my ass. It's well known that in science, the scientific method, and reality itself, nothing can be proven. Proof is the domain of math and logic, not science. In science, things can only be falsified. To quote Einstein: “No amount of experimentation can ever prove me right; a single experiment can prove me wrong.” Einstein obviously isn't saying stuff like a single experiment causes me to adjust my hypothesis and divide split it into two different ones because it's kind of inconsistent. There are people who truly understand science, but most of the population doesn't (including PG). I think what's going on with you is you're in the later camp, you've long held the incorrect belief that science can prove things and this long held ideology is coming into contact with the actual logic of the situation and your adjusting your belief to maintain a biased ideology. Do you look up to PG? Bias can be corrected when an authority confirms the opposite. I quoted Einstein here. One of the ultimate authorities on science, a person who overturned the hypothesis about Newtonian physics being a model for motion. A single experiment proved it wrong and now Newtonian physics is simply an approximation that is ultimately wrong. Hopefully that will clear things up, if not... then you must be an Alien far more strange then what PG is describing.