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I don't think this should be called a paradox. It's just a case where the limitations of the model (ideal everything) is clear and leads to inconsistent results

by brummm 6y ago

I don't think this should be called a paradox. It's just a case where the limitations of the model (ideal everything) is clear and leads to inconsistent results. Adjusting the model and making it more realistic, quickly clears up the "paradox". To me this seems like something one would use as an example in a physics lecture to show when certain assumptions are necessary and when they aren't.

JadeNB 6y ago
Notice the definitions: > The two capacitor paradox or capacitor paradox is a paradox, or counterintuitive thought experiment, in electric circuit theory. > A paradox, also known as an antinomy, is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. (emphases mine). It's paradoxical in that it runs counter to expectations or intuition, using apparently valid reasoning. (Of course, maybe it doesn't run counter to your intuition; but that's how correct intuition is developed, by breaking naïve intuition against examples like this!) In fact, the article explicitly acknowledges this: > Unlike some other paradoxes in science, this paradox is not due to the underlying physics, but to the limitations of the 'ideal circuit' conventions used in circuit theory.
- brummm 6y ago
  Fair enough, wikipedia does include the reference to expectation in its definition of paradox. However, I think my main point is still valid that this should not necessarily be called a paradox exactly because it differs a lot from how this term is commonly used in the naming of scientific thought experiments.
  - mokus 6y ago
    My initial gut response was the same - that this isn’t a paradox, but rather a proof by contradiction that one or more of the assumptions are wrong. But after thinking about it a bit more, I don’t think there’s really that much of a difference. It’s just that some people have already learned not to apply those assumptions in this context (or by chance never stumbled into them in the first place). Perhaps it’s fair to say that all paradoxes are “just” part of a proof by contradiction and the only difference between ones that feel truly paradoxical and those that feel obvious is something subjective about a person’s understanding of the situation. Maybe it’s down to whether someone has enough of an understanding of the conceptual landscape to be able to actually recognize some of the problematic assumptions from the start of the problem statement or not, or maybe it’s something else, but either way I’m suspecting that it’s something subjective related to a person’s state of knowledge and/or approach to organizing their own knowledge.
techslave 6y ago
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.
korethr 6y ago
> To me this seems like something one would use as an example in a physics lecture to show when certain assumptions are necessary and when they aren't. IMO, that's the perfect use of this thought experiment. In fact, I dare say if there are more examples like this, where laying out basic clear assumptions and following the model through its rules leads to an answer that is clearly wrong, then this example and those other examples of that type should probably make up a series of lectures in a course (or subsection thereof) on model use. It seems to me that plenty of people pick up on what models are and how to use them. It seems less people internalize, "All models are wrong. Some models are useful."
- ivan_ah 6y ago
  You can easily get "invalid" circuits when using diodes (the standard assumption of 0.6V or 0.7V drop across didn't make sense). I once got one of those on a final exam and waster 40+ minutes trying to figure out why my solution was "impossible." The teacher later cancelled that question, but I didn't get my 40 minutes back. Many lesson learned: A) don't be stubborn, let go; and B) circuit models ≠ circuit reality.
kps 6y ago
Consider a simplified version of the problem, without the second capacitor. When you close the switch, all of the energy in the first capacitor mysteriously disappears! Or not so mysteriously, after the first time you've done it by accident.
dialamac 6y ago
Model inconsistencies, unreasonable mathematical idealiazations and false assumptions are what are commonly classified as paradoxes in physics. It’s a common use of the term. https://en.wikipedia.org/wiki/Physical_paradox https://en.wikipedia.org/wiki/Physical_paradox
anonymfus 6y ago
There are three tiers of paradoxes in physics: - these which only contradict "common sense" intuitions/expectations but reality conforms to predictions of the theory instead of "common sense", and so these are usually called not real paradoxes like Pascal's hydrostatic paradox; - these which show us limitations of the models we use to construct them, like two capacitor paradox or black hole information paradox; - these true contradictions in the nature of reality which when you discover them the universe disappears in the puff of logic and you wake up as a student in the middle of the physics lecture, and that student was Albert Einstein. A difference between model which we know how to adjust to make more realistic and one we don't know how is about history of physics and not physics itself.

by brummm 6y ago

JadeNB 6y ago

Notice the definitions: > The two capacitor paradox or capacitor paradox is a paradox, or counterintuitive thought experiment, in electric circuit theory. > A paradox, also known as an antinomy, is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. (emphases mine). It's paradoxical in that it runs counter to expectations or intuition, using apparently valid reasoning. (Of course, maybe it doesn't run counter to your intuition; but that's how correct intuition is developed, by breaking naïve intuition against examples like this!) In fact, the article explicitly acknowledges this: > Unlike some other paradoxes in science, this paradox is not due to the underlying physics, but to the limitations of the 'ideal circuit' conventions used in circuit theory.

brummm 6y ago
Fair enough, wikipedia does include the reference to expectation in its definition of paradox. However, I think my main point is still valid that this should not necessarily be called a paradox exactly because it differs a lot from how this term is commonly used in the naming of scientific thought experiments.
- mokus 6y ago
  My initial gut response was the same - that this isn’t a paradox, but rather a proof by contradiction that one or more of the assumptions are wrong. But after thinking about it a bit more, I don’t think there’s really that much of a difference. It’s just that some people have already learned not to apply those assumptions in this context (or by chance never stumbled into them in the first place). Perhaps it’s fair to say that all paradoxes are “just” part of a proof by contradiction and the only difference between ones that feel truly paradoxical and those that feel obvious is something subjective about a person’s understanding of the situation. Maybe it’s down to whether someone has enough of an understanding of the conceptual landscape to be able to actually recognize some of the problematic assumptions from the start of the problem statement or not, or maybe it’s something else, but either way I’m suspecting that it’s something subjective related to a person’s state of knowledge and/or approach to organizing their own knowledge.

techslave 6y ago

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.

korethr 6y ago

> To me this seems like something one would use as an example in a physics lecture to show when certain assumptions are necessary and when they aren't. IMO, that's the perfect use of this thought experiment. In fact, I dare say if there are more examples like this, where laying out basic clear assumptions and following the model through its rules leads to an answer that is clearly wrong, then this example and those other examples of that type should probably make up a series of lectures in a course (or subsection thereof) on model use. It seems to me that plenty of people pick up on what models are and how to use them. It seems less people internalize, "All models are wrong. Some models are useful."

ivan_ah 6y ago
You can easily get "invalid" circuits when using diodes (the standard assumption of 0.6V or 0.7V drop across didn't make sense). I once got one of those on a final exam and waster 40+ minutes trying to figure out why my solution was "impossible." The teacher later cancelled that question, but I didn't get my 40 minutes back. Many lesson learned: A) don't be stubborn, let go; and B) circuit models ≠ circuit reality.

kps 6y ago

Consider a simplified version of the problem, without the second capacitor. When you close the switch, all of the energy in the first capacitor mysteriously disappears! Or not so mysteriously, after the first time you've done it by accident.

dialamac 6y ago

Model inconsistencies, unreasonable mathematical idealiazations and false assumptions are what are commonly classified as paradoxes in physics. It’s a common use of the term. https://en.wikipedia.org/wiki/Physical_paradox https://en.wikipedia.org/wiki/Physical_paradox

anonymfus 6y ago

There are three tiers of paradoxes in physics: - these which only contradict "common sense" intuitions/expectations but reality conforms to predictions of the theory instead of "common sense", and so these are usually called not real paradoxes like Pascal's hydrostatic paradox; - these which show us limitations of the models we use to construct them, like two capacitor paradox or black hole information paradox; - these true contradictions in the nature of reality which when you discover them the universe disappears in the puff of logic and you wake up as a student in the middle of the physics lecture, and that student was Albert Einstein. A difference between model which we know how to adjust to make more realistic and one we don't know how is about history of physics and not physics itself.