Geometrical consequences of the passage of time.

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:

  1. If the present moment exists now, it must have existed before now.(1)
  2. If the present moment exists now, it must continue to exist after now.

The present moment (Point M) always moves across the timeline. As it moves, it exists at each point on the timeline 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 timeline (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 timeline, 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 anomolous 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.


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Four Scenarios

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:

  1. come to a halt at some point (any point) before C. (We will call this point, "B");
  2. come to a halt at C;
  3. come to a halt at some point (any point) after C. (We will call this point, "D") or
  4. continue moving across indefinitely, never coming to a halt.
In Example 3, we see that M can be defined as existing at C only in Scenarios 3 and 4. Since M exists over the intervals CD and C-inifinity in Scenarios 3 and 4, respectively, we conclude the following:

Let me restate this in a different way:

If the present moment does not exist after “now” (after C), then either:

  1. M comes to a halt at C, or
  2. M comes to a halt before C.
Consequently, M cannot be defined as existing “now” (at C).

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Spontaneous Existence

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:

  1. have existed before now, and
  2. continue to exist after now.(4)

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The Present and Consciousness

As we know, M represents both the present moment and an individual consciousness.

In view of the arguments given above, we conclude the following:

  1. either an inividual's consciousness has always existed and will always exist, or
  2. an individual's consciousness has singularites (boundaries) in its past and future. (See Example 6).(5)

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 timeline. Clearly, this timeline 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 timeline 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 timeline 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.)


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There is no Past

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)


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Memory

If there is no past, what is memory? Memory is thought, or a state of awarness, 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 thier 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.


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Diagrams for Geometrical Analysis of the Motion of the Present
The Theory of Persistence
The Infinite Consciousness
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Endnotes

1. Each point on the timeline is a different “now.” As M moves across the timeline, it passes over different "locations" (or “nows”).
2. We may refer to A as a "singularity" since it is analogous to the Big Bang singularity. Similar to the Big Bang origin of time, there is no first moment of time on the timeline. (This issue is discussed in the "Theory of Persistence.")
3. Earlier in this article, I stated that M exists at each point on the timeline for zero seconds. M's existence is defined at these points (with the exception of A). This is because M has been in existence for a length of time when it is at any of these points on the timeline. For instance, in Example 5, M has been in existence for one second when it is at B. However, in Example 4, M has been in existence for zero seconds when it is at A. Consequently, M cannot be defined as existing at A.
4. Matter, energy, and space exist within the present moment. It follows, therefore, that in order for these things to exist "now," they too must:
  1. have existed earlier, and
  2. continue to exist after "now."
5. It is of course possible for M to have only one boundary. Example 7 illustrates this.
6. Physical events, of course, depend on M for their existence. "Events" only exist while they are being perceived by a mind.
7. We can only assert that a mental state occurs "when it occurs." We cannot say that a mental state occurs "before" (or "after") any other mental state.
8. In Example 11, temporal continuity does exist between the holes. The notion of a past and future, therefore, can be applied to points between the holes. For instance, Point A1 may be said to be in the past of Point A2; or A2 may be said to be in the future of A1. It must be understood, however, that only one event occurs between two adjacent holes on the timeline: ie., only one mental state exists during the time interval between singularities. Thus, "past" and "future" do not quite have their usual meaning in this context. (We normally use the concepts "past" and "future" in order to relate two different events to each other.)
9. A thought an emotion, and a physical sensation may be experienced by an individual simutaneously. Together all these constitute a single composite mental state. Each one of the three is, therefore, a component of the mental state. I believe that memory is a component of every mental state.