Difference between revisions of "User talk:St.nerol"
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==[[Proof]]== | ==[[Proof]]== |
Revision as of 11:22, 8 January 2013
That's a sharp way of thniking about it.
Proof
Nerol, you are espousing a minority view. http://www.google.com/search?q=zeno+arrow+instantaneous+derivative - Frankie (talk) 21:09, 4 January 2013 (UTC)
- The derivative can be written as dx/dt. This presupposes an (arbitrarily) small time interval. The definition of the derivative involves taking a limit. And we can talk about the limit value. We get the velocity. Honestly I think the greeks knew about "velocity" too. But in the paradox: could dt in dx/dt actually be zero? -- St.nerol (talk) 11:50, 5 January 2013 (UTC)
- Yes. That's the whole point of limits and derivatives. If values arbitrarily close to a point are convergent, then the derivative exactly at the point is equal to the limit. That's why dx/dt is called instantaneous velocity.
- The articles in that search also cover infinite steps in finite time. Majority views of science consider Zeno's paradoxes resolved, and the explanation should reflect that. - Frankie (talk) 12:41, 5 January 2013 (UTC)
- An example: you don't need modern mathematics to calculate exactly when Achilles overtakes the tortoise. And you don't need a rigorous formulation of limits to make sense of the concept of velocity. Math here is an excelent tool, but it describes motion, it doesn't explain it. (Heck, if anyone could even explain to me how it can be that a formal intellectual game so wonderfully relates to the physical world.) Also, it seems to be an open problem whether space-time is fundamentally continuous or discrete. If it is discrete, a calculus description becomes purely nonsensical at small enough time intervals. -- St.nerol (talk) 15:29, 5 January 2013 (UTC)
- If we were relying on physical reality for this argument, then Zeno's paradoxes are trivially disproven by counterexample. Motion exists, things get hit by arrows, and the article should baldly mock him for claiming otherwise.
- Therefore, I assumed we were sticking to the realm of theory, where time and space are uniform, flat, and infinitely divisible. In that realm, infinitesimal calculus is generally considered superior to Zeno, and the article should reflect that. - Frankie (talk) 15:04, 6 January 2013 (UTC)
- p.s. Limit discussion to Zeno vs Leibniz (vs Law), because that's what's in the comic.
- Yes, that was a sidtrack. (though quantum theory is very theory-heavy) My strong understanding is that calculus splendidly describes physical reality, but not so well explains metaphysical concerns. I'm a student in both these diciplines, though by far yet an expert, and very interested in the intersection between physics and philosophy. And I agree that the analogy with the infinite sum adds interesting input. On the other hand, "derivative" would in the context be rather excangeable for "velocity", which I'm sure the greeks had a word for. I don't feel that it adds any perspective. Others do, so I hesitated in removing that sentence, but I also felt it was a bit confusing. Please add a reasonable sentence about the derivative if you want to.
- Lastly, one can easily find that professional and other opinions about the paradoxes show a vast variation. (Btw, Wikipedia just taught me an tough variation on the paradoxes: Thomson's lamp. There are several proposed solutions to them, but the question is by far settled, and there is no academical consensus. The explanation surely does reflect that? -- St.nerol (talk) 19:53, 6 January 2013 (UTC)
- An example: you don't need modern mathematics to calculate exactly when Achilles overtakes the tortoise. And you don't need a rigorous formulation of limits to make sense of the concept of velocity. Math here is an excelent tool, but it describes motion, it doesn't explain it. (Heck, if anyone could even explain to me how it can be that a formal intellectual game so wonderfully relates to the physical world.) Also, it seems to be an open problem whether space-time is fundamentally continuous or discrete. If it is discrete, a calculus description becomes purely nonsensical at small enough time intervals. -- St.nerol (talk) 15:29, 5 January 2013 (UTC)
- (resetting indentation because too many colons)
- Thought experiments in "idealized classical reality" are fun. It's a Cartesian Newtonian universe containing infinite flat planes (optionally frictionless) and perfectly spherical cows.
- Thompson is a bit less "real" than Zeno because it requires infinite acceleration & velocity. But it reminds me of a similar paradox involving an infinitely large ball pit (or jar, or bag, or other container). At every step, you add X balls (arbitrary integer > 1) then remove one of them. At midnight, obviously there should be infinite balls in the pit. However, if the balls are numbered, and you add them in numerical order, then remove them in the same order, it is clear that for every number, you can compute the exact time before midnight that it is removed. In this case, the ball pit is empty at midnight. Georg Cantor for the win!
- I will attempt to compose a more balanced approach to Leibniz vs Zeno. - Frankie (talk) 18:33, 7 January 2013 (UTC)