Postscript #121 to the "Lanzarote" paper (11/02/98)
 THE "ZERO-DIMENSIONALITY" OF TIME *
AND
AN EXPLANATION OF "WORLD LINES."
    A problem arises in the meaning of "dimensionality." The implication above * is strictly that of a "spacial dimension," a magnitude measured in a particular direction, for instance in a direction with respect to north, east and up (or their opposites). In this regard, time is a scalar quantity with magnitude only, but it is a special kind of such quantity which we have tentatively called a "counting scalar." In explanation of this phrase we note that time continuously counts in a linear, "forward going" fashion, precisely as one would count the revolutions of our planet from an external point, such as from a location in the Earth's orbital plane. 
     The problem arises because the terms "counting," linear and "forward going" can also refer to an acceptable but non-spacial, alternate definition of the word dimension. Established explanations of this second meaning of dimension are: a) "a magnitude that, independently - serves to define the location of an element within a given set, as of - an event (for example) in space-time" or, b) "the number of elements in a finite basis of a given vector space." 
     Einstein defined time (t) as: "The reading on a clock." It is thus "zero-dimensional" when we use the above, first named concept of "spacial dimension." If the "now time" of said clock reads in the "forward going" direction of a mass/energy vector impinging on the clock (postscript #112), then "Rhythm Based Time" (RBT) is orthogonal to this direction. BUT RBT IS ALSO A READING ON THE SAME CLOCK and thus it is also "zero-dimensional," using the former "spacial" definition. 

     "World lines" are found on graphs of time (t) against one or more dimensions of space. The history of a particle can be represented by a "world line" drawn on such a plot, with time (t), usually along a vertical axis, against a dimension of space, for example the x-direction along a horizontal axis. But since such a particle always physically moves in only one, two or three orthogonal "spacial dimensions" and thus traces out a mass or energy "timetag vector" (postscript #109), it is sometimes confusing to endeavor to distinguish the above mentioned real vector from the graphical representation shown by a "world line." Scientists frequently compare two or more "variables" with one another (for example, demand against supply), but this seldom leads to confusion with one, two or three dimensional real objects such as lines, circles or cones. Newton's and/or Einstein's time (t) we describe as a "counting scalar variable" with no "spacial dimensions" (postscript #105) and thus it cannot be used to create "spacially-dimensional," geometric objects that have meaning in a real world other than as mathematical abstractions. Consequently a particle moving in one dimension of space could be alternatively (and perhaps more realistically) represented as a line lying along an x-axis with suitable time labels ("timetags") attached or, as a "timetag vector" (earlier described). A particle moving in two or three dimensions of space could be alternatively represented as a similar "timetag vector" lying in a conventional x-y plane or the x-y-z volume respectively. Strings with open ends, namely "open strings" realistically create "sheets" if they move in two or three "spacial dimensions" but these are not to be confused with abstract, mathematical "world sheets." Strings forming closed loops, namely "closed strings" realistically create cylindrical shapes if they move in three "spacial dimensions" but these must also not to be confused with abstract, mathematical shapes of "world sheets" of closed strings where time (t) is one of the plotted "variables," but is not one of the plotted "spacial dimensions."