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But ultimately, it should take more surprising evidence to shake up your beliefs about the coin that it would to shake up your beliefs about Mars, right? So, t

But ultimately, it should take more surprising evidence to shake up your beliefs about the coin that it would to shake up your beliefs about Mars, right? So, the prior which is strong/weak is the probability distribution of probability distributions. There is a <<1% chance that I will ever believe there is a >90% chance of flipping heads. But there is a much greater probability that I will one day believe there is a >90% chance of life on Mars. What terminology would you use to describe that, if not strong/weak priors?

lisper 4y ago
> it should take more surprising evidence to shake up your beliefs about the coin that it would to shake up your beliefs about Mars, right? I would say it's the exact opposite. Encountering an unfair coin would not surprise me a bit because I know, for example, that double-headed coins exist. But encountering life on Mars would surprise me a lot because I've accumulated a lot of evidence already that there isn't any. (There might have been in the past, but there isn't any now.) The only thing that I consider "surprising" is encountering evidence that moves one of my priors from being close to 0 to being close to 1 or vice versa. That happens less and less as time goes by because (I hypothesize) my beliefs converge to reality, and reality is stable in the sense that there is something out there towards which it is possible to converge. But at no stage in this process are my beliefs about propositions modeled by anything other than numbers between 0 and 1, with 0 meaning, "I am absolutely certain this proposition is false", 1 meaning, "I am absolutely certain this proposition is true", and 0.5 meaning, "I have absolutely no idea whether or not this proposition is true."
- goatlover 4y ago
  How does this work for the reasoning you just gave? Was there some evidence that moved your priors about Bayesian reasoning from near 0 to close to 1? Apply that to any philosophical or mathematical reasoning. Let's take an interpretation of QM. How would you assign a probability to Many Worlds Interpretation? Do you have some way of assigning your degree of belief between 0 and 1? Or are there just arguments you find more or less convincing for it? There was a thread on here the other day about black hole information paradox and how we may never be able to test any mathematical reasoning regarding what happens to the information inside a black hole. Can you assign a Bayesian probability to that?
  - lisper 4y ago
    > Was there some evidence that moved your priors about Bayesian reasoning from near 0 to close to 1? I think you misinterpreted what I said. My belief in Bayesian reasoning was very nearly 1 from the first time I encountered Bayes's theorem. Nothing I've seen since has changed this, i.e. nothing about Bayes's theorem has surprised me. The last time I can remember being surprised (in a Bayesian sense) about anything was when Donald Trump won the 2016 election. My prior on his winning was very close to zero when he announced his candidacy (and frankly I think his was too), and obviously my posterior after the election was very close to 1. (Contrast this with the reasoning currently being deployed by proponents of the Big Lie.) That event really rocked my world, but I can't think of anything that has surprised me in the same way since then. > How would you assign a probability to Many Worlds Interpretation? The same way you assign a probability to any proposition: you look at the evidence and decide whether the MWI is a good explanation that accounts for all the evidence. I did a very deep dive into this exact question about three years ago: https://blog.rongarret.info/2019/07/the-trouble-with-many-worlds.html https://blog.rongarret.info/2019/07/the-trouble-with-many-wo... > Can you assign a Bayesian probability to that? It depends on what you mean by "that". You can assign a Bayesian probability to any proposition, but you have to be careful because not all statements are propositions. For example: "Penguins are beautiful" is not a proposition. It makes no sense to say that it is "true" or "false" because it is ambiguous (do you mean all penguins or just some penguins?) and it involves a value judgement. The MWI is particularly thorny because it is really easy to hide ambiguity and value judgements in seemingly innocuous language. For example, you will often hear proponents of the MWI say something like, "The universe splits every time a quantum measurement is made." But that is ambiguous because it doesn't tell you what a quantum measurement is. It also has a tacit "value judgement" hidden in the phrase "the universe". The whole point of the MWI is that there is not one universe, there are unfathomably many of them. So which universe is "the" universe? Well, to me, "the" universe is the universe that "I" live in. But what does the word "I" mean in the context of the MWI? Because according to the MWI, every time the universe splits, I split along with it and become multiple me's in multiple universes. So which "me" is the real me? The MWI is very strongly analogous to the beauty of penguins.
    - 4y ago

lisper 4y ago

> it should take more surprising evidence to shake up your beliefs about the coin that it would to shake up your beliefs about Mars, right? I would say it's the exact opposite. Encountering an unfair coin would not surprise me a bit because I know, for example, that double-headed coins exist. But encountering life on Mars would surprise me a lot because I've accumulated a lot of evidence already that there isn't any. (There might have been in the past, but there isn't any now.) The only thing that I consider "surprising" is encountering evidence that moves one of my priors from being close to 0 to being close to 1 or vice versa. That happens less and less as time goes by because (I hypothesize) my beliefs converge to reality, and reality is stable in the sense that there is something out there towards which it is possible to converge. But at no stage in this process are my beliefs about propositions modeled by anything other than numbers between 0 and 1, with 0 meaning, "I am absolutely certain this proposition is false", 1 meaning, "I am absolutely certain this proposition is true", and 0.5 meaning, "I have absolutely no idea whether or not this proposition is true."

goatlover 4y ago
How does this work for the reasoning you just gave? Was there some evidence that moved your priors about Bayesian reasoning from near 0 to close to 1? Apply that to any philosophical or mathematical reasoning. Let's take an interpretation of QM. How would you assign a probability to Many Worlds Interpretation? Do you have some way of assigning your degree of belief between 0 and 1? Or are there just arguments you find more or less convincing for it? There was a thread on here the other day about black hole information paradox and how we may never be able to test any mathematical reasoning regarding what happens to the information inside a black hole. Can you assign a Bayesian probability to that?
- lisper 4y ago
  > Was there some evidence that moved your priors about Bayesian reasoning from near 0 to close to 1? I think you misinterpreted what I said. My belief in Bayesian reasoning was very nearly 1 from the first time I encountered Bayes's theorem. Nothing I've seen since has changed this, i.e. nothing about Bayes's theorem has surprised me. The last time I can remember being surprised (in a Bayesian sense) about anything was when Donald Trump won the 2016 election. My prior on his winning was very close to zero when he announced his candidacy (and frankly I think his was too), and obviously my posterior after the election was very close to 1. (Contrast this with the reasoning currently being deployed by proponents of the Big Lie.) That event really rocked my world, but I can't think of anything that has surprised me in the same way since then. > How would you assign a probability to Many Worlds Interpretation? The same way you assign a probability to any proposition: you look at the evidence and decide whether the MWI is a good explanation that accounts for all the evidence. I did a very deep dive into this exact question about three years ago: https://blog.rongarret.info/2019/07/the-trouble-with-many-worlds.html https://blog.rongarret.info/2019/07/the-trouble-with-many-wo... > Can you assign a Bayesian probability to that? It depends on what you mean by "that". You can assign a Bayesian probability to any proposition, but you have to be careful because not all statements are propositions. For example: "Penguins are beautiful" is not a proposition. It makes no sense to say that it is "true" or "false" because it is ambiguous (do you mean all penguins or just some penguins?) and it involves a value judgement. The MWI is particularly thorny because it is really easy to hide ambiguity and value judgements in seemingly innocuous language. For example, you will often hear proponents of the MWI say something like, "The universe splits every time a quantum measurement is made." But that is ambiguous because it doesn't tell you what a quantum measurement is. It also has a tacit "value judgement" hidden in the phrase "the universe". The whole point of the MWI is that there is not one universe, there are unfathomably many of them. So which universe is "the" universe? Well, to me, "the" universe is the universe that "I" live in. But what does the word "I" mean in the context of the MWI? Because according to the MWI, every time the universe splits, I split along with it and become multiple me's in multiple universes. So which "me" is the real me? The MWI is very strongly analogous to the beauty of penguins.
  - 4y ago