-- Four Types of Vectors Actually Emerged --

          As the physical sciences slowly developed and incorporated abstract geometry and mathematics, in actuality four major types of vectors and two major states of observation evolved, although this fact did not become apparent to the scientists.  Specifically, the mathematicians and scientists failed to recognize the differences in the four types of vectors, hopelessly intermingling them and confusing them as a single class of vector.  Further, they did not appreciate that a fundamental vector conceptually is a UNITARY SYSTEM, and the system represented by one of these four types of vectors utilizes and is comprised of different components, "welded together with no seam in the middle."
           Conceptually (and from a systems viewpoint), the four types of vectors are (1) the chargeless, massless spatial system vector (geometer's vector), (2) the uncharged mass system vector (mechanic's vector), (3) the charged mass system vector (electrician's vector), and (4) the charged space system vector (advanced electrician's vector).  These four fundamentally different vectors are shown in Figures 1, 2, 4, and 9 in a simplified manner.
          The major problem was that, beginning with the geometer's vector, these four major types of vectors were not treated as systems.  Instead, their "vector" aspects were hopelessly confused and intermeshed, and no distinctions were made between them.  And in the foundations of the mathematical constructs, time-smearing was not recognized at all.

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