How Does Zeno's Paradox Challenge Our Understanding of Movement and Space?

[sd01g]

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.

 

[Hurkyl]

Ignoring science or mathematics...

If Archimedes runs because the points he occupies are moving, then how could I be able to identify the points he used to occupy? You make it sound as if motion is possible because the points one occupies move around, rather than by moving from one point to another.

 

[hypermorphism]

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 BA and the halfway point is only approximately known because all real measurements are approximate.

This is not how Zeno's paradox is resolved, though it is a popularly erroneous way of resolving it; you have made the fundamental error in your empirical set by assuming that objects move "one atom at a time" in discrete time- and space-steps. If this is true, how do atoms move through vacuum ?

 

[sd01g]

Key points

The key points in Zeno's paradox are points A and B. In the Rational parameter set, these points have only one attribute- absolute fixed position. In the Empirical parameter set there is no such thing as an absolute fixed position. Also, it is my understanding that 'approaching 1 as a limit' is not exactly the same thing as exactly equalling 1. IF approaching 1 as a limit exactly equals 1, then my parameter set analysis is defective and will be withdrawn. Thanks for your help. (It really is not so bad being wrong when one is attempting to understand difficult and complex ideas, if one can learn from one's mistakes.)

 

[sd01g]

Wrong parameter set

This is not how Zeno's paradox is resolved, though it is a popularly erroneous way of resolving it; you have made the fundamental error in your empirical set by assuming that objects move "one atom at a time" in discrete time- and space-steps. If this is true, how do atoms move through vacuum ?

The Empirical Parameter Set does not assume that Objects move 'one atom at a time in discrete time- and space steps.' It is the Rational parameter set that assumes this by requiring Objects to move ' half the distance at a time.'

Zeno's paradox is not paradoxical because we move--this is a given--but because a rational, THOUGHT construct seems to say that one can not move. Zeno assumes there are an infinite number of mathematical or geometrical points (points with no spatial dimensions) between any TWO given points. In the Rational Parameter Set this is true. However, in the Real World--the Empirical Parameter Set--this is absolutely false. Points with no spatial dimentions do not exist in the Real World. A 'zero spatial dimensional point' has never been observed and never will be. Zeno's assumption is empirically wrong.

There really is no paradox, only a faulty assumption.