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the birthday paradox is also not a paradox. the namers of such things just like to use the word ‘paradox’ for some reason. it probably sounds more puzzling to i

the birthday paradox is also not a paradox. the namers of such things just like to use the word ‘paradox’ for some reason. it probably sounds more puzzling to initiates.

mokus 6y ago
My gut feel is the same. Ironically, the fact that this usage sounds wrong might, in fact, be a paradox :) It’s an apparent contradiction between our understanding of the meaning of the word and the actual usage of the word. The resolution of this paradox could be that there is widespread wrong usage of the word. Alternately it could be that our understanding of the meaning is wrong - which itself could be for multiple reasons. Perhaps our understanding of the definition is incomplete. Or it could be that the definition itself is simply wrong because it doesn’t reflect actual real-world usage. Upon some reflection I think that a core part of the idea of a paradox is that there are many possible solutions to a problem and that some people, but almost certainly not all, will initially fail to even recognize the existence of solutions other than the one they expect, due to unconscious assumptions. Naturally in many cases there will also be people who do not make those problematic assumptions to begin with, but that doesn’t on its own invalidate the use of the word “paradox” in that situation. The birthday paradox probably fits this definition just fine - ask anyone not trained in statistics about the subject and you’ll likely find a lot of people have unconscious assumptions that lead them to wrong answers, and in some cases thy will even be exceptionally confident in their wrong answers. You might object to the “not trained in statistics” part but that objection itself would be circular - modern statistics education was designed with paradoxes like this in mind, specifically to lay down a foundation that doesn’t lead you down the wrong paths in cases like that. The solutions to the basic paradoxes of statistics are built into the way statistics is taught, just like the solutions to Godel’s and Russel’s and many others’ paradoxes are built into the foundations of any modern logical system.
cuspycode 6y ago
Good point. A paradox is something that produces an unexpected contradiction. It must be unexpected, otherwise any trivial false statement such as 2+2=5 would also be a paradox. Russell's paradox is a good example since no one expected a contradiction. The birthday paradox on the other hand does not produce any contradiction, so it's just a case of sloppy labeling.
- Izkata 6y ago
  By that description, the birthday paradox is a paradox for anyone who doesn't already know it. The instinctive answer is generally 1/2 the total.
  - cuspycode 6y ago
    It's still not a contradiction, unless you first postulate that 1/2 is the answer, for no particular reason at all.
  - ordu 6y ago
    > the birthday paradox is a paradox for anyone who doesn't already know it It is a fate of any solved paradox. A paradox is a confusing paradox only to a point when you learn where the contradiction comes from, and how it does it, and how to avoid it.

the birthday paradox is also not a paradox. the namers of such things just like to use the word ‘paradox’ for some reason. it probably sounds more puzzling to initiates.

mokus 6y ago

My gut feel is the same. Ironically, the fact that this usage sounds wrong might, in fact, be a paradox :) It’s an apparent contradiction between our understanding of the meaning of the word and the actual usage of the word. The resolution of this paradox could be that there is widespread wrong usage of the word. Alternately it could be that our understanding of the meaning is wrong - which itself could be for multiple reasons. Perhaps our understanding of the definition is incomplete. Or it could be that the definition itself is simply wrong because it doesn’t reflect actual real-world usage. Upon some reflection I think that a core part of the idea of a paradox is that there are many possible solutions to a problem and that some people, but almost certainly not all, will initially fail to even recognize the existence of solutions other than the one they expect, due to unconscious assumptions. Naturally in many cases there will also be people who do not make those problematic assumptions to begin with, but that doesn’t on its own invalidate the use of the word “paradox” in that situation. The birthday paradox probably fits this definition just fine - ask anyone not trained in statistics about the subject and you’ll likely find a lot of people have unconscious assumptions that lead them to wrong answers, and in some cases thy will even be exceptionally confident in their wrong answers. You might object to the “not trained in statistics” part but that objection itself would be circular - modern statistics education was designed with paradoxes like this in mind, specifically to lay down a foundation that doesn’t lead you down the wrong paths in cases like that. The solutions to the basic paradoxes of statistics are built into the way statistics is taught, just like the solutions to Godel’s and Russel’s and many others’ paradoxes are built into the foundations of any modern logical system.

cuspycode 6y ago

Good point. A paradox is something that produces an unexpected contradiction. It must be unexpected, otherwise any trivial false statement such as 2+2=5 would also be a paradox. Russell's paradox is a good example since no one expected a contradiction. The birthday paradox on the other hand does not produce any contradiction, so it's just a case of sloppy labeling.

Izkata 6y ago
By that description, the birthday paradox is a paradox for anyone who doesn't already know it. The instinctive answer is generally 1/2 the total.
- cuspycode 6y ago
  It's still not a contradiction, unless you first postulate that 1/2 is the answer, for no particular reason at all.
- ordu 6y ago
  > the birthday paradox is a paradox for anyone who doesn't already know it It is a fate of any solved paradox. A paradox is a confusing paradox only to a point when you learn where the contradiction comes from, and how it does it, and how to avoid it.