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Zeno's paradox (the inability to move between points A and B) results when two incongruous parameter sets are applied to the same event.
In the Rational parameter set, points have no dimensions-only positions. There are an infinite number of points between A and B. The points A and B are assumed not to move, and the halfway point is presumed to be known and to be exactly halfway between A and B.
In the Empirical parameter set, however, all points are 3-dimensional. Points A and B (which are composed of atoms) are moving. There are a finite number of points between A and B and the halfway point is only approximately known because all real measurements are approximate.
Applying the Rational parameter set, Zeno will eternally move exactly halfway between an infinite number of zero-dimension points, never reaching point B.
Applying the Empirical parameter set, Zeno will easily transition between points A and point B.
The reason it important to differentiate between Rational and Empirical parameter sets is due to the increasing use of Rational parameter sets to define such things as hyperspace, M-Theory, and parallel universes. These conjectures often masquerading as theories have no viable Empirical parameter sets to determine their validity. No Rational parameter set conjecture should be allowed the title of theory unless it is accompanied by a legitimate Empirical parameter set.
Of course, this is just an opinion. Any thoughtful critique would be appreciated.
In the Rational parameter set, points have no dimensions-only positions. There are an infinite number of points between A and B. The points A and B are assumed not to move, and the halfway point is presumed to be known and to be exactly halfway between A and B.
In the Empirical parameter set, however, all points are 3-dimensional. Points A and B (which are composed of atoms) are moving. There are a finite number of points between A and B and the halfway point is only approximately known because all real measurements are approximate.
Applying the Rational parameter set, Zeno will eternally move exactly halfway between an infinite number of zero-dimension points, never reaching point B.
Applying the Empirical parameter set, Zeno will easily transition between points A and point B.
The reason it important to differentiate between Rational and Empirical parameter sets is due to the increasing use of Rational parameter sets to define such things as hyperspace, M-Theory, and parallel universes. These conjectures often masquerading as theories have no viable Empirical parameter sets to determine their validity. No Rational parameter set conjecture should be allowed the title of theory unless it is accompanied by a legitimate Empirical parameter set.
Of course, this is just an opinion. Any thoughtful critique would be appreciated.
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