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I am not sure what makes this a paradox? Normally I think of a paradox as leading to a state where you have two or more contradictory statements being true at l

I am not sure what makes this a paradox? Normally I think of a paradox as leading to a state where you have two or more contradictory statements being true at like Russell's Paradox in set theory. This just seems like a problem where you don't have enough information to solve it but once you get the info you need (how to pick random chords) you get a logically consistent solution.

malisper 7y ago
A paradox is any statement that appears to contradict itself. That includes both actual contradictions such as Russel's paradox and statements that appear to be invalid, but have non-obvious valid conclusions like the Monty Hall problem. This problems falls into the second category. We are given what appears to be a well-defined problem, but when we solve it in different ways, we get different answers. The resolution to the paradox is the problem isn't well defined because your technique for generating randomness will produce different answers.
- OscarCunningham 7y ago
  Because of the Principle of Explosion, a contradiction implies any statement. So for people who don't think that everything is meaningless there can't be any true contradictions. This means that in fact every paradox falls into the second class. Paradoxes merely differ in how difficult it is to see the logical flaw that leads to the apparent contradiction.
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lonelappde 7y ago
It's a paradox because esteemed mathematicians, including authors of classic books, have vociferously argued that their particular arbitrary choice is the sole correct choice. In probability, one must make many unstated assumptions to get an answer to a problem. Usually one believes those assumptions are "canonical", like uniform independent distributions. Sometimes woldviews contradict each other.
rolleTx 7y ago
Exactly, this is just a definition problem
krick 7y ago
Yeah. I'm ok with calling anything that looks weird a "paradox" (even stuff like "The Monty Hall problem"), but in this case describing the problem this way is precisely what's misleading about it: the person describing the "problem" must first pretend that there is a well defined (even though possibly not known to the less educated listener than himself) "random" way to pick 2 points on a circle, which there clearly isn't: there are different algorithms to do that, that produce different distribution, which very obviously look different when plotted, and choosing any specific algorithm/distribution makes the "paradox" disappear. So I really dislike when stuff like that is called a "paradox". It's just a way to trick the listener (or yourself) into thinking there is a problem, when there really isn't any.
- vageli 7y ago
  > Yeah. I'm ok with calling anything that looks weird a "paradox" (even stuff like "The Monty Hall problem"), but in this case describing the problem this way is precisely what's misleading about it: the person describing the "problem" must first pretend that there is a well defined (even though possibly not known to the less educated listener than himself) "random" way to pick 2 points on a circle, which there clearly isn't: there are different algorithms to do that, that produce different distribution, which very obviously look different when plotted, and choosing any specific algorithm/distribution makes the "paradox" disappear. So I really dislike when stuff like that is called a "paradox". It's just a way to trick the listener (or yourself) into thinking there is a problem, when there really isn't any. It is also a good way to broach a discussion on the nature of randomness.

malisper 7y ago

A paradox is any statement that appears to contradict itself. That includes both actual contradictions such as Russel's paradox and statements that appear to be invalid, but have non-obvious valid conclusions like the Monty Hall problem. This problems falls into the second category. We are given what appears to be a well-defined problem, but when we solve it in different ways, we get different answers. The resolution to the paradox is the problem isn't well defined because your technique for generating randomness will produce different answers.

OscarCunningham 7y ago
Because of the Principle of Explosion, a contradiction implies any statement. So for people who don't think that everything is meaningless there can't be any true contradictions. This means that in fact every paradox falls into the second class. Paradoxes merely differ in how difficult it is to see the logical flaw that leads to the apparent contradiction.

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lonelappde 7y ago

It's a paradox because esteemed mathematicians, including authors of classic books, have vociferously argued that their particular arbitrary choice is the sole correct choice. In probability, one must make many unstated assumptions to get an answer to a problem. Usually one believes those assumptions are "canonical", like uniform independent distributions. Sometimes woldviews contradict each other.

rolleTx 7y ago

Exactly, this is just a definition problem

krick 7y ago

Yeah. I'm ok with calling anything that looks weird a "paradox" (even stuff like "The Monty Hall problem"), but in this case describing the problem this way is precisely what's misleading about it: the person describing the "problem" must first pretend that there is a well defined (even though possibly not known to the less educated listener than himself) "random" way to pick 2 points on a circle, which there clearly isn't: there are different algorithms to do that, that produce different distribution, which very obviously look different when plotted, and choosing any specific algorithm/distribution makes the "paradox" disappear. So I really dislike when stuff like that is called a "paradox". It's just a way to trick the listener (or yourself) into thinking there is a problem, when there really isn't any.

vageli 7y ago
> Yeah. I'm ok with calling anything that looks weird a "paradox" (even stuff like "The Monty Hall problem"), but in this case describing the problem this way is precisely what's misleading about it: the person describing the "problem" must first pretend that there is a well defined (even though possibly not known to the less educated listener than himself) "random" way to pick 2 points on a circle, which there clearly isn't: there are different algorithms to do that, that produce different distribution, which very obviously look different when plotted, and choosing any specific algorithm/distribution makes the "paradox" disappear. So I really dislike when stuff like that is called a "paradox". It's just a way to trick the listener (or yourself) into thinking there is a problem, when there really isn't any. It is also a good way to broach a discussion on the nature of randomness.