The argument is that simple numbers like 3^^^3 should be considered much more likely than random numbers with a similar size, since they have short descriptions and so the mechanisms by which that many people (or whatever) hang in the balance are less complex. For instance you’re more likely to win a prize of $1,000,000 than $743,328 even though the former is larger. de Blanc considers priors of this form, of which the normal isn’t an example.
Surely an action is more likely to have an expected value of saving 3.2 lives than pi lives; the distribution of values of actions is probably not literally log normal partially for the reason that you just gave, but I think that a log-normal distribution is much closer to the truth than a distribution which assigns probabilities strictly by Kolmogorov complexity. Here I’d recur to my response to cousin it’s comment.
Surely an action is more likely to have an expected value of saving 3.2 lives than pi lives
I’m not so sure. Do you mean (3.2 lives|pi lives) to log(3^^^3) digits of precision? If you don’t, I think it misleads intuition to think about the probability of an action saving 3.2 lives, to two decimal places; vs. pi lives, to indefinite precision.
I can’t think of any right now, but I feel like if I really put my creativity to work for long enough, I could think of more ways to save 3.14159265358979323846264 lives than 3.20000000000000000000000 lives.
I meant 3.2 lives to arbitrary precision vs. pi lives to arbitrary precision. Anyway, my point was that there’s going to be some deviation from a log-normal distribution on account of contingent features of the universe that we live in (mathematical, physical, biological, etc.) but that probably a log-normal distribution is a closer approximation to the truth than what one would hope to come up with a systematic analysis of the complexity of the numbers involved.
The argument is that simple numbers like 3^^^3 should be considered much more likely than random numbers with a similar size, since they have short descriptions and so the mechanisms by which that many people (or whatever) hang in the balance are less complex.
Consider the options A = “a proposed action affects 3^^^3 people” and B = “the number 3^^^3 was made up to make a point”. Given my knowledge about the mechanisms that affect people in the real world and about the mechanisms people use to make points in arguments, I would say that the likelihood of A versus B is hugely in favor of B. This is because the relevant probabilities for calculating the likelihood scale (for large values and up to a first order approximation) with the size of the number in question for option A and the complexity of the number for option B. I didn’t read de Blanc’s paper further than the abstract, but from that and your description of the paper it seems that its setting is far more abstract and uninformative than the setting of Pascal’s mugging, in which we also have the background knowledge of our usual life experience.
The argument is that simple numbers like 3^^^3 should be considered much more likely than random numbers with a similar size, since they have short descriptions and so the mechanisms by which that many people (or whatever) hang in the balance are less complex. For instance you’re more likely to win a prize of $1,000,000 than $743,328 even though the former is larger. de Blanc considers priors of this form, of which the normal isn’t an example.
Surely an action is more likely to have an expected value of saving 3.2 lives than pi lives; the distribution of values of actions is probably not literally log normal partially for the reason that you just gave, but I think that a log-normal distribution is much closer to the truth than a distribution which assigns probabilities strictly by Kolmogorov complexity. Here I’d recur to my response to cousin it’s comment.
I’m not so sure. Do you mean (3.2 lives|pi lives) to log(3^^^3) digits of precision? If you don’t, I think it misleads intuition to think about the probability of an action saving 3.2 lives, to two decimal places; vs. pi lives, to indefinite precision.
I can’t think of any right now, but I feel like if I really put my creativity to work for long enough, I could think of more ways to save 3.14159265358979323846264 lives than 3.20000000000000000000000 lives.
I meant 3.2 lives to arbitrary precision vs. pi lives to arbitrary precision. Anyway, my point was that there’s going to be some deviation from a log-normal distribution on account of contingent features of the universe that we live in (mathematical, physical, biological, etc.) but that probably a log-normal distribution is a closer approximation to the truth than what one would hope to come up with a systematic analysis of the complexity of the numbers involved.
Consider the options A = “a proposed action affects 3^^^3 people” and B = “the number 3^^^3 was made up to make a point”. Given my knowledge about the mechanisms that affect people in the real world and about the mechanisms people use to make points in arguments, I would say that the likelihood of A versus B is hugely in favor of B. This is because the relevant probabilities for calculating the likelihood scale (for large values and up to a first order approximation) with the size of the number in question for option A and the complexity of the number for option B. I didn’t read de Blanc’s paper further than the abstract, but from that and your description of the paper it seems that its setting is far more abstract and uninformative than the setting of Pascal’s mugging, in which we also have the background knowledge of our usual life experience.
The setting in my paper allows you to have any finite amount of background knowledge.