Talk:Wine/water paradox
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Possible misunderstanding
[edit]One of the hazards of a problem like this is that "pure" mathematicians, including many probabilists, will misunderstand it and say, for example, that no well-posed math problem has been identified, which is true but misses the point. Michael Hardy (talk) 20:44, 15 May 2019 (UTC)
dt/t ?
[edit]If invariance under the mapping is desired (making the roles of water and wine identical), how about the measure dt/t?
so
is a probability measure on Borel subsets of [1/3, 3]. And
so x and 1/x are identically distributed. Michael Hardy (talk) 20:56, 15 May 2019 (UTC)
- Wouldn't it be simpler to let y be uniformly distributed on [¼,¾] and take x = (1 - y)/y, so that 1/x = y/(1 - y)? Then the distribution of 1/x is the mirror image of x (substituting 1 - y for y turns 1 - y into y). Vaughan Pratt (talk) 05:35, 20 March 2021 (UTC)
Wine-alcohol conflation
[edit]The parenthetical " (i.e. 25-75% alcohol)" would appear to assume that the wine is 200 proof, i.e. 100% alcohol by volume. Obviously we shouldn't solve this by calling it the alcohol/water paradox. Options I can think of would be to rephrase the parenthetical as "(i.e. 25-75% wine)", or simply delete it altogether. Any preferences? Vaughan Pratt (talk) 04:20, 20 March 2021 (UTC)