You might not have the mental skills to reason in a decent matter about low probability events.
Do you? You were unable or unwilling to say how you came up with 10^-18 and 10^-15 in the matter of Zeus. (And no, I am not inclined to take your coming up with numbers as evidence that you employed any reasonable method to do so.)
I am not inclined to take your coming up with numbers as evidence that you employed any reasonable method to do so
Intuition can be a reasonable method when you have enough relevant information in your head.
I’m good enough that I wouldn’t make the mistake of calling Baduhenna existence or Zeus existence a 10^{-6} event.
Is it possible that I might have said 10^{-12} instead of 10^{-15} in I would have been in a different mood the day I wrote the post.
When we did Fermi estimates at the European Community Event in Berlin there was a moment where we had to estimate the force that light from the sun exerts on earth. We had no good idea about how to do a Fermi estimate. We settled for Jonas who thought he read the number in the past but couldn’t remember it writing down an intuitive guess. He wrote 10^9 and the correct answer was 5.5 * 10^8.
As a practical matter telling the difference between 10^{-15} and 10^{-12} isn’t that important. On the other hand reasoning about whether the chance that the Large Hadron collider creates a black hole that destroys earth is 10^{-6} or 10^{-12} is important.
I think a 10^{-6} chance for creating a black hole that destroys the earth should be enough to avoid doing experiments like that. In that case I think the probability wasn’t 10^{-6} and it was okay to run the experiment but with increased power of technology we might have more experiments that actually do have a 10^{-6} xrisk chance and we should avoid running them.
I don’t know what this means. On the basis of what would you decide what’s “reasonable” and what’s not?
There is a time-honored and quite popular technique called pulling numbers out of your ass. Calling it “intuition” doesn’t make the numbers smell any better.
See “If It’s Worth Doing, It’s Worth Doing With Made-Up Statistics” on Slate Star Codex, though I agree that a human’s intuition for probabilities well below 1e-9 is likely to be very unreliable (except for propositions in a reference class containing billions of very similar propositions, such as “John Doe will win the lottery this week and Jane Roe will win the lottery next week”).
The only thing that matters is making successful predictions. How they smell doesn’t.
To know at whether a method makes successful predictions you calibrate the method against other data. That then gives you an idea about how accurate your predictions happen to be.
Depending on the purpose for which you need the numbers different amounts of accuracy is good enough.
I’m not making some Pascal mugging argument that people are supposed to care more about Zeus where I need to know the difference between 10^{-15} and 10^{-16}. I made an argument about how many orders of magnitude my beliefs should be swayed.
My current belief in the probability of Zeus is uncertain enough that I have no idea if it changed by orders of magnitude, and I am very surprised that you seem to think the probability is in a narrow enough range that claiming to have increased it by order of magnitude becomes meaningful.
No, I can’t. Heuristics are a kind of algorithms that provide not optimal but adequate results. “Adequate” here means “sufficient for a particular real-life purpose”.
I don’t see how proclaiming that the probability of Zeus existing is 10^-12 is a heuristic.
Do you? You were unable or unwilling to say how you came up with 10^-18 and 10^-15 in the matter of Zeus. (And no, I am not inclined to take your coming up with numbers as evidence that you employed any reasonable method to do so.)
Intuition can be a reasonable method when you have enough relevant information in your head.
I’m good enough that I wouldn’t make the mistake of calling Baduhenna existence or Zeus existence a 10^{-6} event.
Is it possible that I might have said 10^{-12} instead of 10^{-15} in I would have been in a different mood the day I wrote the post.
When we did Fermi estimates at the European Community Event in Berlin there was a moment where we had to estimate the force that light from the sun exerts on earth. We had no good idea about how to do a Fermi estimate. We settled for Jonas who thought he read the number in the past but couldn’t remember it writing down an intuitive guess. He wrote 10^9 and the correct answer was 5.5 * 10^8.
As a practical matter telling the difference between 10^{-15} and 10^{-12} isn’t that important. On the other hand reasoning about whether the chance that the Large Hadron collider creates a black hole that destroys earth is 10^{-6} or 10^{-12} is important.
I think a 10^{-6} chance for creating a black hole that destroys the earth should be enough to avoid doing experiments like that. In that case I think the probability wasn’t 10^{-6} and it was okay to run the experiment but with increased power of technology we might have more experiments that actually do have a 10^{-6} xrisk chance and we should avoid running them.
I don’t know what this means. On the basis of what would you decide what’s “reasonable” and what’s not?
There is a time-honored and quite popular technique called pulling numbers out of your ass. Calling it “intuition” doesn’t make the numbers smell any better.
See “If It’s Worth Doing, It’s Worth Doing With Made-Up Statistics” on Slate Star Codex, though I agree that a human’s intuition for probabilities well below 1e-9 is likely to be very unreliable (except for propositions in a reference class containing billions of very similar propositions, such as “John Doe will win the lottery this week and Jane Roe will win the lottery next week”).
The only thing that matters is making successful predictions. How they smell doesn’t. To know at whether a method makes successful predictions you calibrate the method against other data. That then gives you an idea about how accurate your predictions happen to be.
Depending on the purpose for which you need the numbers different amounts of accuracy is good enough. I’m not making some Pascal mugging argument that people are supposed to care more about Zeus where I need to know the difference between 10^{-15} and 10^{-16}. I made an argument about how many orders of magnitude my beliefs should be swayed.
My current belief in the probability of Zeus is uncertain enough that I have no idea if it changed by orders of magnitude, and I am very surprised that you seem to think the probability is in a narrow enough range that claiming to have increased it by order of magnitude becomes meaningful.
You can compute the likelihood ratio without knowing the absolute probability.
Being surprised is generally a sign that it’s useful to update a belief.
I would add that given my model of you it doesn’t surprise me that this surprises you.
You can call it heuristics, if you want to...
No, I can’t. Heuristics are a kind of algorithms that provide not optimal but adequate results. “Adequate” here means “sufficient for a particular real-life purpose”.
I don’t see how proclaiming that the probability of Zeus existing is 10^-12 is a heuristic.
Intuition (or educated guesses like the ones referred to here), fall under the umbrella of heuristics.
In what way are you arguing that the number I gave for the existence of Zeus is insufficient for a particular real-life purpose?