Galileo's Paradox
in [Math]
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From: Ross A. Finlayson on 21 Dec 2006 03:13 Actually the notion is about those sets as physical objects. The way I consider that the powerset of objects increases ad infinitum is to consider _functions_ between physical objects as physical objects. Consider for example some finite group of points, and the functions between them, identifiable in assignment, in context, as the Cartesian product of those points. Basically the set of functions from a set to itself is said to have a higher cardinality than the set. So with finitely many particles, the functions between those are objects, and the functions between those are objects, ad infinitum, so there are infinitely many objects. Then, functions between those are objects, and those were just all the objects, so the universe illustrates a counterexample to the powerset result. Otherwise people claim something along the lines of 2^120 particles in the universe. Is there a field between each pair of those particles, or is there only one gravitational, or electromagnetic field for the entire universe? The particles have various properties, momentum and location, for example. Is not each motion vector an object? How about each point where particles may ever interact? Is not each massy particle interacting at each possible point in space, in however a miniscule way? Where there were 2^80 particles yesterday and 2^50 before that, and presumably more than 2^120 at some point in the forseeable future, where there are more bits of man-made electronic storage than there were presumed to be particles in the entire universe some time ago, there are more particles found in the universe as knowledge about it increases. A variety of modern and classical cosmologists have or had the perspective that the universe is infinite. In quantum chromodynamics technicolor there is no smallest particle. Somewhat more sharply, the more closely more mundane particles like atoms are measured, the smaller they appear to be, more precisely in measurement, but smaller. Experimental evidence points to there being no smallest size of those atoms, which seems to contradict that they have some fixed mass. It's relative, in a way. So the universe is bigger, it's infinite, and the particles are smaller, they're infinitesimal, and there are infinitely many of them in the universe. Where each set of interactions of physical objects is a physical object, and where all of them is _the_ universe, then that would contradict direct results of ZF that a) there is no universe and b) the powerset result. Consider something along the lines of a notion of a "Theory of Everything", where the universe represents itself. Does the universe exist? Then, that the universe exists is the theory of everything. What if it didn't? Then it would, it does, E, existence, you can't disprove existence, and anything proves it, even nothing. Then, if there's a T.o.E, and we can do arithmetic, where any true (completely specified) statement is true throughout the entire universe, then incompleteness doesn't happen either. Ross
From: MoeBlee on 21 Dec 2006 15:53 Six wrote: > I do still strongly > suspect that you are underestimating the paradox. Maybe. MoeBlee
From: MoeBlee on 29 Dec 2006 12:16
MoeBlee wrote: > Six wrote: > > I do still strongly > > suspect that you are underestimating the paradox. > > Maybe. > > MoeBlee P.S. I think not so much underestimating, but rather that I find that there are other conundrums or at least baffling questions that are, at least in the context of my own studies and ruminations, more pressing or immediate. |