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. |