Indeed. The "paradoxes" can be resolved with the introduction of infinitesimals and infinite series that sum to a finite number. The arrow paradox in particular can be resolved by introducing the concept of instantaneous velocity, taking the instantaneous velocity as a derivative (the limit of the average velocities at each finite interval of time).
Yes, paradoxes are not a part of nature. All of them have a logical solution. The logic might not be logical relative to humans, but paradoxes are the results of a lack of knowledge and/or intelligence. The wave-particle duality "paradox" is not a paradox at all. I have a theory that explains why, but I won't publish it here. It has to be completed before anything.
Nevertheless, proclaiming that Zeno was speaking "nonsense" seems a bit rash to me. Some of Zeno's points regarding the arrow were arguably still valid, assuming Zeno's fundamental point was that, presumably, the finite physical motion of the arrow in a finite period of time consists of traversing infinitesimal distances in infinitesimal intervals of time. Prior to the derivative definition of instantaneous velocity, this concept was pure muddle even for the calculus.
Indeed. The "paradoxes" can be resolved with the introduction of infinitesimals and infinite series that sum to a finite number. The arrow paradox in particular can be resolved by introducing the concept of instantaneous velocity, taking the instantaneous velocity as a derivative (the limit of the average velocities at each finite interval of time).
ReplyDeleteYes, paradoxes are not a part of nature. All of them have a logical solution. The logic might not be logical relative to humans, but paradoxes are the results of a lack of knowledge and/or intelligence. The wave-particle duality "paradox" is not a paradox at all. I have a theory that explains why, but I won't publish it here. It has to be completed before anything.
ReplyDeleteNevertheless, proclaiming that Zeno was speaking "nonsense" seems a bit rash to me. Some of Zeno's points regarding the arrow were arguably still valid, assuming Zeno's fundamental point was that, presumably, the finite physical motion of the arrow in a finite period of time consists of traversing infinitesimal distances in infinitesimal intervals of time. Prior to the derivative definition of instantaneous velocity, this concept was pure muddle even for the calculus.
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