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The Meaning of Now

The following document will attempt to describe an interpretive meaning of the now. The “now” is a “totalized” transformation at a specific given point in space-time. For the purpose of this project, precision in terminology is extremely important. I may use standard definitions of the words moment and instant, both meaning a specific point in time. However, these words can be ambiguous, suggesting a period of time. In embarking upon this ontological investigation, I will use mathematics to elucidate a functional definition for “the now” using the idea and reality of a cycle. I propose that, within the now, there is a complete cycle that can be described geometrically. In this project, I wish to distinguish between an exact point in time (a moment or instant) and duration. For this paper, an exact “time point,” is defined as a specific, numerical coordinate. For example, there is only one point in time or “time point” at which it is 1:00 (not1:00:00:00:00… 01). However, I propose that a point in time could be described as the “whole moment” as now. I will use geometry and resulting algebra to elucidate the meaning of the, “whole moment” and the “whole moment as now.” This project is an attempt at understanding and epistemologically introspecting into being. Even though a single point in time does not have duration, it does have being. Within the being of now, there is an implied geometric transformation. ”To understand the being of the now frees ourselves from the bonds of time,” (LC Davis).

Geometric Analysis of the Being of the Now

Circles are not only fascinating geometric shapes with algebraic properties, they are also useful, philosophical devices. We are familiar with their properties like circumference. 2π times the radius of the circle is equal to π times the diameter of the circle, and π times thediameter equals the circumference of the circle. We are also familiar with the relationship of the difference in circumferences of two circles to an arc length of the first circle (or either circle). I am, of course referring to that fundamental equation that has been explored in my work A Geometric Pattern of Perception, (Emmerson, 2009). 2πr-2πx = (theta) r. From this equation, a cone can be constructed. As stated before, there is only one “time point” at which it is exactly 1:00. However, in the geometric transformation described in A Geometric Pattern of Perception (Emmerson, 2009-2011), when theta would equal 2π rad. (360 degrees), we see that the radius equals the height of the cone, and thus, there is no angle at 2π radians, because there are no vertices to form an angle, theta. This means that we must consider a synchronous system by which we may measure the position at which the height of the cone equals the initial radius at 2π radians in the synchronous system. The synchronous system would be like the hand of a clock, passing around at a constant rate. At 2π radians (360 degrees) in the “synchronous system,” the radius of the initial circle described in A Geometric Pattern of Perception, would equal the height of the cone. Since there isn’t an angle at 2π radians, there also isn’t an angle at 0π radians, but the lack of there being an angle at 0π radians (0 degrees) is different from the lack of there being an angle at 2π radians in the
sense that there is an angle whose value equals 0π radians at 0π radians, whereas there are no rays or lines at “2π rad.,” to form an angle (i.e. the system has collapsed). At least at 0π radians, there could be thought of two rays occupying the same space, whereas at 2π radians in the synchronous system, there are no rays or lines that intersect to form an angle in the system of a circle transforming eventually into a line through a cone. The whole moment as now is a total transformation of the circle into a cone, which eventually transforms into a line that is orthogonal to the initial circle within a single now point. I submit that within a single now point, this “whole” geometric transformation takes place. There is no angle at the now, but “there is no angle” in two different senses, thus there is change in the now – a change in sense. There is a change in sense at the now, though there may be no change in position. The perspective is what changes. The change is apparent with the change of perception. I will show how this change in the Now is analogous to the two seemingly true statements of paradox.

The Origin of Paradox

The origin of paradox takes place within the geometric-algebraic-arithmetical system of a circle transforming into a cone and takes on acouple of philosophical-mathematical meanings. These meanings are:

1. A paradox results when there are two seemingly true statements. In our case, one of the statements is that the difference in circumferences of two circles equals an arc length of the initial circle (or either circle). The other statement is that the radius of the initial circle is a function of only the angle that is multiplied by the initial radius to give the arc length that is removed from the initial circle. We come to this statement from finding the algebraic expression of the number one and subtracting from it the numeric value “one,” equating the result with the algebraic expression for the number zero found from subtracting the arc length removed from the initial circle from the difference in circumference of two circles of different sizes. We use the Pythagorean theorem to solve for the base of the cone, which is often considered the smaller of the two circles and substitute that solution for the base of the cone. We then make another substitution for the height of the conewhen the height is expressed in terms of the, “initial radius” and theangle, “taken out” of the initial circle. Solving the resulting formula leads to a statement that ought be true through normative algebra, but one that can be dis-proven with Euclidean geometry. This statement is that the initial radius is a function of only the angle takenout of the initial circle. We can show that when the initial radius equals zero, the solution to the equation yields one of the previous lemmas of the system (that the interior angle of the cone is a function of theangle related to the arc length taken out of the initial circle’s circumference). We can also show that when the initial radius of the circle equals one, there are more solutions of one angle in terms of the other. The statement that the initial radius is a function of the angle related to the arc length taken out of the initial circle’s circumferenceis one of the statements that is seemingly true in the paradox and is shown to be true at the origin of space-time (where the initial radius of the circle equals zero). It is proven, because the algebraic equation expressing the form of 1 – 1 = 0 solves to deliver a solution to the initial radius in terms of one of the interior, variable angles of the cone, and when you set that solution to the initial radius equal to zero, it solves to deliver one of theproven lemmas of the system.

2. The other meaning of the origin of paradox comes from the form of the equation, 1 – 1 = 0, algebraically expressed through the algebraic-geometric transformation of a circle into a cone. The algebraic equation expressing the geometric-algebraic form of the arithmetical statement, 1-1=0 is the equation that provides the framework for finding the intrinsic, paradoxical statement of the system. It can be considered an “origin” equation, because it equates two expressions of zero, the origin of a number line.

The Analogy of Paradox to the Now

The analogy of paradox to the now is the relationship of the geometric analysis of the being of the now to the origin of paradox. The origin of paradox tells us that all variables in the system can be proven to equal zero. This means that some are mathematically, “undefined” due to division by zero, but this can always be overcome by substitution of the number zero for the algebraic expression of zero within equations. In the geometric analysis of the being of the now, we find thatthere are two senses within the now, each located at a different sense of origin. One sense of origin expressed by the geometric analysis of the being of the now described earlier was the being of “no angle” in the sense that there was an angle of no value. This can be thought of as an origin. There is another sense of the now in which there is a sense of origin. The position at which the height of the cone equals theinitial radius is an origin in the sense that the radius of the base of thecone equals zero, and the circle has “collapsed” into a line. At this point, there is also no angle, theta. The sense of now in which there is not an angle has been correlated to the origin of paradox. The sense of now embodies origin, as well as the being of paradox