Is Probability Real?
arameb.com
Is Probability Real?
1–10 of 227 posts
Re: Is Probability Real?
#2Since this topic isn't so well-known, I wrote the case arguing that frequentist interpretations don't work, but algorithmic information theory (Kolmogorov complexity) does. I want to make this accessible and persuasive, so thoughts, questions, and arguments would be appreciated!
Re: Is Probability Real?
#3Since this topic isn't so well-known, I wrote the case arguing that frequentist interpretations don't work, but algorithmic information theory (Kolmogorov complexity) does. I want to make this accessible and persuasive, so thoughts, questions, and arguments would be appreciated!
Such an interesting post, thank you for sharing! I'm in my second year of a maths degree currently, and we obviously studied frequentist probability/stats in the first year, but I'm not taking any probability modules this year. I found the tone & accessibility was just right for me :)
Re: Is Probability Real?
#4Solid write up. If anyone's interesting in knowing more about how probability _came to be_ 'regarded' as real, i highly recommend Ian Hacking's "The Taming of Chance".
Thought provoking in so many ways.
Re: Is Probability Real?
#5Since this topic isn't so well-known, I wrote the case arguing that frequentist interpretations don't work, but algorithmic information theory (Kolmogorov complexity) does. I want to make this accessible and persuasive, so thoughts, questions, and arguments would be appreciated!
A simple sentence that I've found useful for pedagogy: "the probability of that coin toss being 50% does not talk about the coin; it talks about you, and about your partial knowledge of the universe."
You can add: "The coin toss itself is deterministic and the result can be computed if you know the initial position and speed." They will inevitably bother you about the physical impossibility to measure the starting position and speed exactly, and then you say "ok, forget about the coin. You have 5 white and 5 black balls inside this opaque cylinder. What's the probability that the top ball is white? This does not talk about the balls (the color of the top one is already determined) but about your partial knowledge of them".
(EDIT: formatting)
Re: Is Probability Real?
#6Since this topic isn't so well-known, I wrote the case arguing that frequentist interpretations don't work, but algorithmic information theory (Kolmogorov complexity) does. I want to make this accessible and persuasive, so thoughts, questions, and arguments would be appreciated!
A simple sentence that I've found useful for pedagogy: "the probability of that coin toss being 50% does not talk about the coin; it talks about you , and about your partial knowledge of the universe." You can add: "The coin toss itself is deterministic and the result can be computed if you know the initial position and speed." They will inevitably bother you about the physical impossibility to measure the starting p…
How does the ball situation help? It has the same problems of physical impossibility of measuring however the balls were ordered. (Modelling someone's brain?) I guess the argument works on someone with an unscientific model of the human brain, but that's one step forward and two steps back.
Re: Is Probability Real?
#7Earlier quoted context omitted.
A simple sentence that I've found useful for pedagogy: "the probability of that coin toss being 50% does not talk about the coin; it talks about you , and about your partial knowledge of the universe." You can add: "The coin toss itself is deterministic and the result can be computed if you know the initial position and speed." They will inevitably bother you about the physical impossibility to measure the starting p…
How does the ball situation help? It has the same problems of physical impossibility of measuring however the balls were ordered. (Modelling someone's brain?) I guess the argument works on someone with an unscientific model of the human brain, but that's one step forward and two steps back.
Somebody just put the balls there carefully, and did not tell you in what order, just how many of each color.
Re: Is Probability Real?
#8Since this topic isn't so well-known, I wrote the case arguing that frequentist interpretations don't work, but algorithmic information theory (Kolmogorov complexity) does. I want to make this accessible and persuasive, so thoughts, questions, and arguments would be appreciated!
A simple sentence that I've found useful for pedagogy: "the probability of that coin toss being 50% does not talk about the coin; it talks about you , and about your partial knowledge of the universe." You can add: "The coin toss itself is deterministic and the result can be computed if you know the initial position and speed." They will inevitably bother you about the physical impossibility to measure the starting p…
> the probability of that coin toss being 50% does not talk about the coin; it talks about you, and about your partial knowledge of the universe.
But it does talk about the coin - a weighted coin would have a different probability. Same in the example with the white/black balls - if they weren't 5 white and 5 black but 6 white and 4 black, the probability you would assign to the top one would be different. Again, the probability is a way to describe the balls themselves, not just our knowledge.
I get the general idea of representing probability as uncertainty and partial knowledge but your statements strike me as just straight up incorrect.
Re: Is Probability Real?
#9Since this topic isn't so well-known, I wrote the case arguing that frequentist interpretations don't work, but algorithmic information theory (Kolmogorov complexity) does. I want to make this accessible and persuasive, so thoughts, questions, and arguments would be appreciated!
Why is frequentism bad because it only gives certainty for infinite samples, but complexity is good despite being non-computable?
It's two sides of the same coin -- computable uncertainty va non-computable certainty.
Re: Is Probability Real?
#10Since this topic isn't so well-known, I wrote the case arguing that frequentist interpretations don't work, but algorithmic information theory (Kolmogorov complexity) does. I want to make this accessible and persuasive, so thoughts, questions, and arguments would be appreciated!
OK - so apply Kolmogorov complexity to election polling.
How does that work out?
I think you're confusing various possible maps with the territory in a less than useful way.
Given that frequentist interpretations are approximations - and understood as such - and Kolmogorov complexity isn't computable at all, what problem have you solved here?