## Temporal Passage: Geometric Considerations

(Some of the ideas in the following document are discussed in my paper "Temporal Passage")
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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 (for either a finite or infinite length of time).(1)
2. If the present moment exists now, it must continue to exist after now (for either a finite or infinite length of time).

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.

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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-infinity in Scenarios 3 and 4, respectively, we conclude the following:
• If the present moment (M) exists "now" (at C), then M must continue to exist after "now"--for either a finite length of time (CD) or an infinite length of time (C-infinity).
• If the present does not continue to exist after now, then its existence now cannot be defined--it does not exist now.

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 individual's consciousness has always existed and will always exist, or
2. an individual's consciousness has singularities (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 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.)

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** [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.)]

### 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)

• As we know, the past is, by definition, temporally related to the present. In order for there to be a past (or a "before"), a temporal connection must exist between the present and the past.
• However, because of the temporal discontinuities between mental states, no events or mental states exist that have a temporal relation to our present mental state.(7)
• Consequently, we cannot define a "past" or a "before." Such a concept has no meaning: there is no past. And the use of a past tense is never appropriate.(8)
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### Memory

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. (See Paul Davies, About Time: Einstein's Unfinished Revolution (New York: Simon & Schuster, 1995), 40-42.)

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### Endnotes

1. Each point on the time line is a different now. As M moves across the time line, 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 time line; and consequently, each point (or "moment") on the time line is preceded by an infinite number of points ("moments"). (This issue is discussed in more detail in "The Theory of Persistence.")
3. Earlier in this article, I stated that M exists at each point on the time line 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 time line. 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. (See Paul Davies, About Time: Einstein's Unfinished Revolution (New York: Simon & Schuster, 1995), 40-42.)
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 time line: i.e., 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 simultaneously. 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.