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This Is Kind Of Tricky

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Posted by Michael Levine on September 11, 2003 20:45:44 UTC

Thanks for the comments. But my writing is not really that good so I'm afraid you missed some of the finer points.

I suspect that you mean the Planck scale at 10^^-33 cm.

I thought there existed such a thing as a Planck constant, with a specific number. I might be wrong. What I have in mind is, if the shortest thing you can possibly think about is the length of a wave, then it would follow that no statement about anything smaller than a wavelength can have any meaning.

Radio wavelengths are in meters. Surely, anybody knows about smaller sizes than meters.

Sure, anybody knows about 0.1 meters, and 0.01 meters, and 10^^-35 meters. But does anybody *know* about sizes smaller than that, even though anyone can *think* about, say, 10^^-1000000000000000000 meters?

In mathematics, and in particular in calculus, the logical limit occurs when the change in the quantity after division does not change the accuracy of the solution.

I would say that is true about physics, not mathematics. In math there is no such thing as a "good enough" solution, as the criteria for "good enough" lies in the application of math, not math itself.

This also solves Zeno's problem. The logical limit occurs when nobody no longer cares.

I think what solves Zeno's paradoxes is the fact that they only apply to objects which have no size, and such objects don't exist by definition. If an object has size > 0 its position relative to another object is not a fixed number but a range. For instance, there might be an infinite number of points in space between a flying arrow and a tree, but any measurement of the arrow's position during its flight will not be perfectly accurate, because it must have a finite number of digits.

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