In this paper, I will give a geometrical analysis of the motion of the present moment. This analysis will prove the following assumptions to be true:
The present moment (Point M) always moves across the time line. As it moves, it exists at each point on the time line for exactly zero seconds. For example, it exists at Point B for precisely one moment--and one moment, by definition, has zero duration (see Example 1). Suppose M were to come to a halt at point C on the time line (Example 2). This would mean that M exists at C for a greater than zero duration--i.e., for a length of time greater than one moment.
As it turns out, we cannot properly say that M exists when it is located at C. M would be at rest at C rather than in motion, and this is contrary to the normal behavior of M: as time passes, M always moves across the time line, never staying at any one point on the line for any length of time. Clearly, then, if M comes to a halt at C, M cannot be considered to be in existence there.
We say that M is "at rest" at C because M does not go beyond C. For any given point to the left of C, M not only reaches the point, but M also goes beyond it. Thus, we may correctly assert that M is in a "state of motion" at all points on the line to the left of C.
M behaves in an anomalous way for the first time when it reaches C: M reaches C but does not go beyond it. Clearly M cannot be defined as "existing" when it is at C: M is at rest at C.
As regards the movement of the present moment, there are four possible scenarios (see Example 3). If M begins at A and moves across the time line, it could:
Let me restate this in a different way:
If the present moment does not exist after now (after C), then either:
The present moment cannot spontaneously come into existence at a point (say Point A in Example 4). In Example 4, when M is at A, M has existed for only one moment. One moment, however, is by definition zero seconds long--no length of time. Now existing for "no length of time" is the same as not existing at all. So clearly spontaneous existence is impossible. And consequently, existence "now" necessarily implies prior existence.(2)
We conclude the following: if the present moment exists now, it must have existed before now.(3)
To sum up, if the present moment exists now, it must:
As we know, M represents both the present moment and an individual consciousness.
In view of the arguments given above, we conclude the following:
In Example 8, Points A, B, and C are holes (singularities) on the time line. Point M is not defined as existing when it is located at these points. However, M is defined as existing at all other points on the line.
In Example 9, there are no holes on the time line; and consequently M is defined as existing at all points on the time line. Clearly, this time line implies that one and the same mental state persists throughout the duration AE.
In Example 10, the presence of holes (A, B, C, D, E) on the time line suggests that four separate mental states occur on the line. Mental state #1 (M1) persists over the time interval AB. Mental state #2 (M2), in turn, persists for the interval BC, and so on.
As discussed in "The Theory of Persistence," human mental life consists of many mental states. Obviously then, a person's time line must contain many holes in it; and individual line segments between holes will represent individual mental states.
In Example 12, M persists between the points A, B C, D, and E; however M does not persist at these points. As can be seen, M interacts with A-space four times in this example. However, a "linkage" between M and points in A-space can be defined only while M is on the line segments between the points A, B, C, D, and E. Consequently, physical situations in A-space can only be considered to exist during the open time intervals, AB, BC, CD, and DE. (See Example 12.)
** [Note to reader: The following sections argue that "there is no past." It is true that there is no past if one interprets the timeline in the particular manner that I have interpreted it in this article. However, there is an alternative way of interpreting the timeline that allows us to define a "past."
Suppose mental state #1 (i.e., "M1") occurs before a missing point B on the timeline (i.e., before a hole B on the timeline). Suppose mental state #2 (i.e., "M2") occurs after the missing point B. Then M1 can be said to occur before M2.
This allows us to define a past. (Please see endnote #7 of my paper "Temporal Passage" for a more complete description of subjective time.)]
The temporal discontinuities between mental states force us to revise our understanding of the relationship between past, present and future. Let us define "the past" as "events or mental states which have occurred before now."(6)
If there is no past, what is memory? Memory is thought, or a state of awareness, which exists at the present. It constitutes an essential part of mental life.(9) Memory gives individuals their sense of identity; and it gives them their sense of orientation and their impression of the continuity of their existence.
I wish to stress that memory exists for these reasons--and these reasons only. Memory's function is not to "represent the past," as there is no past.
Geometric Considerations (Diagrams)
Clarification of the Article
The Theory of Persistence
Evolution, Time and Mind