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Pi - Clarification

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Your Text: Insert Slimies » Insert UBB Code » Close Last Tag \| All Tags UBB Help	The example given of a perfect circle was the curve of a rainbow. You perceive the curve of a rainbow by the light (photons?) striking your eye. While you may perceive a perfect curve, if you could take a snapshot and zoom in to the finest resolution, you would see that the curve is in fact rather fuzzy. If you could map individual photons striking receptors, the best you could say is that those which correspond to the various colours in the curve are falling roughly within the shape of the perceived curve. It's not just a perfect circle that's imaginary, but a circle, full stop. As it is a two-dimensional object, attempting to represent it in the real world would be impractical. Make it out of matter, and it will have a thickness that renders a third dimension, thereby making it a very short cylinder. Even if we ignore the third dimension and attempt to make it appear as a perfect circle from the appropriate perspective, on a small enough scale, we eventually find the very atoms that make up the edge to be finite, and therefore (without imagining curves between these atoms) describing a polygon with an incredible number of sides (or a finite number of points determined by the positions of those atoms). Even if we do describe a perfect curve between the very finite points that make up the edge of the circle, I would wager that the circle either changes size constantly (as relevant particles fall inside/outside of the curve) or could only be an average description of the bounding curve. I suppose a circle of light could be used instead (though the resulting circle would be a cross section of a projected/three-dimensional cone/cylinder of light), but while the resolution is finer, and the thickness is arguably nil, the edges will still never form a perfect circle - what forms it is still finite, and given an appropriate method for observing it, one should still be able to see that the edges of the circle are a number of 'points' of light between which straight lines might be drawn to form a large, uneven polygon that roughly approximates a circle. Also, unless the surface upon which the circle is projected is perfect, various points will be at different depths, so rendering a third dimension anyway. I simply referred to photons as a rainbow is something perceived by the eye (or a camera) as a result of photon interactions, and so the curve or circle only exists as a perception based upon the interaction of light with a receptive medium (the retina, or camera film). This means that something the size of a photon is redundant in my example, as the effective resolution is on a par with the smallest active particle of the receptive medium (a photo-receptor, or a particle of the photosensitive chemical in the film). It really doesn't matter how small the smallest thing in the universe is, as it isn't what's describing the circle in the real world. Even if it were, and we had no way of measuring it, ?finity? could still be presumed, and the circle is still not perfect. I agree, points are the smallest things in the universe. Infinity is possibly the largest thing. Neither is real. ___ [quote]Not true...the object has changed in size if you were to relatively compare it with it's previous state....also ever considered that the expansion could also be happening inwardly too....[/quote] No, that's backwards. The object may have changed size [i]absolutely[/i], but if space itself has expanded proportionately, it has not changed size [i]relatively[/i]. The only difference in size that could be measured is that which has occurred out of proportion to the expansion of space (say, thermal expansion), and that would be a relative change of size. If you draw a nine-by-nine pixel square, then change to a lower resolution (scaled according to screen size) it will have changed size (in this example, technically, scale), but relative to the constituent pixels no change has taken place. If space is expanding, the screen, the pixels on the screen, and anything described by the pixels is expanding too, but nothing is changing size relative to the expanding space. If the screen and the images upon it do not expand with space, they would be perceived as 'shrinking' relatively. Aha! :p ;) [small](Edited by [url=http://www.ozoneasylum.com/user/4663]White Hawk[/url] on 06-01-2009 14:36)[/small] Loading...
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