-- Points and Motion --

           It is my purpose in this paper to expose in a very simple fashion the most basic errors that were made.  One basic error involves the idea of motion itself.¹³
           In formulating concepts of motion, the geometers used a "point in motion" to determine or specify, for example, velocity. Now a "point" is a static concept a priori.  To determine (or even to think and perceive) motion, one must determine that it occupies two different points (positions or locations) at two different times, yet consider both points at the same time.  Indeed, that is precisely what the arrow means that is used to represent a vector.  A "point in motion" therefore represents a contradiction of opposites.  That is, it represents the idea that "that which is motionless has motion.".¹⁴  Even with this, there is a difference in a spatial point and a spatiotemporal (spacetime) point.  To exist at all, a spatial point must be moving in time; in other words, it is a spatiotemporal line, even if it is a static spatial point. 
        Vector analysis was constructed in the abstract -- again, a massless point in motion possessed or constituted a velocity vector, etc.  In massless ( and timeless) space, FIELDS were defined: "scalar" fields constituted the assignment of a simple motionless number (magnitude) to each spatial point, while "vector" fields constituted the assignment of a "simple vector" (magnitude and velocity) to each spatial point.  But the MATHEMATICAL vector system consisted of massless (point) motional relationships, recognizing zero motion as a special case of motion.¹⁵
          Of course mathematics development was also always intertwined with practical problems.  With the sustained application of mathematics to gross physical material problems, mechanics slowly arose. 
          These developments required decades and even centuries to occur completely.  All along the way, innovations and changes -- and additions to the mathematical formulism were being derived and taught to students as the "natural" system of reality.  A permanent mindset was being forged. 
          Indeed, mathematics was regarded as THE single human expression of fundamental truth.  Not until Godel's work in the twentieth century did it become evident that MATHEMATICS IS SIMPLY A GAME PLAYED ACCORDING TO ASSIGNED RULES, AND THERE IS NO ULTIMATE TRUTH IN MATHEMATICS ALONE.¹⁶  It is a most useful game, of course, since it is the game fitted to perception.  Thus it applies, essentially, to whatever can be perceived.  But to be applied to physical systems, it must be changed, altered, updated, and fitted as the perceiving/detecting instruments become ever more subtle. 

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