I like your example, it implies that the longer the discussion goes, the less likely it is that somebody misquotes G.I.T. in any given statement (or per unit time etc). Kinda the opposite of what the intent of the original quote seems to be.
Yea, but it’s clear what he’s trying to convey: For any event that has some (fixed) episolon>0 probability of happening, it’s gonna happen eventually if you give it enough chances. Trivially includes the mentioning of Gödel’s incompleteness theorems.
However, it’s also clear what the intent of the original quote was. The pedantry in this case is fair game, since the quote, in an attempt to sound sharp and snappy and relevant, actually obscures what it’s trying to say: that Gödel is brought up way too often in philosophical discussions.
For any event that has some episolon>0 probability of happening, it’s gonna happen eventually if you give it enough chances.
This is not true (and also you mis-apply the Law of large Numbers here). For example: in a series (one single, continuing series!) of coin tosses, the probability that you get a run of heads at least half as long as the overall length of the series (eg ttththtHHHHHHH) is always >0, but it is not guaranteed to happen, no matter how many chances you give it. Even if the number of coin tosses is infinite (whatever that might mean).
Interestingly, I read the original quote differently from you—I thought the intent was to say “any bloody thing will be brought up in a discussion, eventually, if it is long enough, even really obscure stuff like G.I.T.”, rather than “Gödel is brought up way too often in philosophical discussions”. What did you really mean, nsheppered???
Interestingly, I read the original quote differently from you—I thought the intent was to say “any bloody thing will be brought up in a discussion, eventually, if it is long enough, even really obscure stuff like G.I.T.”, rather than “Gödel is brought up way too often in philosophical discussions”. What did you really mean, nsheppered???
It was the latter. Also I am assuming that you haven’t heard of Godwin’s law which is what the wording here references.
in a series (one single, continuing series!) of coin tosses, the probability that you get a run of heads at least half as long as the overall length of the series (eg ttththtHHHHHHH) is always >0, but it is not guaranteed to happen, no matter how many chances you give it.
… any event for which you don’t change the epsilon such that the sum becomes a convergent series. Or any process with a Markov property. Or any event with a fixed epsilon >0.
That should cover round about any relevant event.
(and also you mis-apply the Law of large Numbers here)
Law of Large Numbers states that sum of a large amount of i.i.d variables approaches its mathematical expectation. Roughly speaking, “big samples reliably reveal properties of population”.
It doesn’t state that “everything can happen in large samples”.
That doesn’t say much; perhaps it approaches 1 as 1 − 1/(1+1/2+1/3...+1/n)?
I like your example, it implies that the longer the discussion goes, the less likely it is that somebody misquotes G.I.T. in any given statement (or per unit time etc). Kinda the opposite of what the intent of the original quote seems to be.
Yea, but it’s clear what he’s trying to convey: For any event that has some (fixed) episolon>0 probability of happening, it’s gonna happen eventually if you give it enough chances. Trivially includes the mentioning of Gödel’s incompleteness theorems.
However, it’s also clear what the intent of the original quote was. The pedantry in this case is fair game, since the quote, in an attempt to sound sharp and snappy and relevant, actually obscures what it’s trying to say: that Gödel is brought up way too often in philosophical discussions.
Edit: Removed link, wrong reference.
This is not true (and also you mis-apply the Law of large Numbers here). For example: in a series (one single, continuing series!) of coin tosses, the probability that you get a run of heads at least half as long as the overall length of the series (eg ttththtHHHHHHH) is always >0, but it is not guaranteed to happen, no matter how many chances you give it. Even if the number of coin tosses is infinite (whatever that might mean).
Interestingly, I read the original quote differently from you—I thought the intent was to say “any bloody thing will be brought up in a discussion, eventually, if it is long enough, even really obscure stuff like G.I.T.”, rather than “Gödel is brought up way too often in philosophical discussions”. What did you really mean, nsheppered???
It was the latter. Also I am assuming that you haven’t heard of Godwin’s law which is what the wording here references.
… any event for which you don’t change the epsilon such that the sum becomes a convergent series. Or any process with a Markov property. Or any event with a fixed epsilon >0.
That should cover round about any relevant event.
Explain.
Law of Large Numbers states that sum of a large amount of i.i.d variables approaches its mathematical expectation. Roughly speaking, “big samples reliably reveal properties of population”.
It doesn’t state that “everything can happen in large samples”.
Thanks. Memory is more fragile than thought, wrong folder. Updated.