Temporal Passage: Geometric Considerations
(Some of the ideas in the following document are discussed in my paper "Temporal Passage")
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:
- If the present moment exists now, it must have existed before now (for
either a finite or infinite length of time).(1)
- 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.
[Diagrams]
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:
- come to a halt at some point (any point) before C. (We will call this
point, "B");
- come to a halt at C;
- come to a halt at some point (any point) after C. (We will call this
point, "D") or
- 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:
- M comes to a halt at C, or
- M comes to a halt before C.
Consequently, M cannot be defined as
existing now (at C). [Diagrams]
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:
- have existed before now, and
- continue to exist after now.(4)
[Diagrams]
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:
- either an individual's consciousness has always existed and will always
exist, or
- 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.)(6),(7)
[Diagrams]
Temporal Passage:
Geometric Considerations (Diagrams)
Clarification of the
Article
The Theory
of Persistence
Evolution, Time and
Mind
Home Page
Notes
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:
- have existed earlier, and
- 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. Let us define the "past" as "events or mental states that have occurred before now."
Suppose mental state #1 (i.e., "M1") occurs before a missing point B on the time line (i.e., before a hole B on the time line). 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.)
***
Rethinking Subjective Time
Let us consider the following statement:
S1: Mental states occur one-after-another.
***
Is statement S1 true or false?
***
In the article above, I make the assumption that S1 is true.
In the document below, I make the assumption that S1 is false.
***
There Is No Past
The temporal discontinuities between mental states force us to revise our
understanding of the relationship between states. Let us
define the "past" as "events or mental states that have occurred before
now."
- 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 relationship
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.(1)
- 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.(2),(3)
[Diagrams]
Memory
If there is no past, what is memory? Memory is thought, or a state of
awareness, that exists at the present. It constitutes an essential part of
mental life.(4) Memory gives individuals their sense of identity; and it gives
them their sense of orientation and their impression of the continuity of their
existence.(5),(6)
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.)
[Diagrams]
Temporal Passage:
Geometric Considerations (Diagrams)
Clarification of the
Article
The Theory
of Persistence
Evolution, Time and
Mind
Home Page
Notes
1. We can only assert that a mental state occurs
"when it occurs." We cannot say that it occurs "before" (or
"after") any other state. (See Paul Davies, About Time: Einstein's Unfinished Revolution (New York: Simon & Schuster, 1995), 40-42.)
2. Suppose mental state #1 (i.e., "M1") occurs before a missing point B on the time line (i.e., before a hole B on the time line). 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.)
3. 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.)
4. 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.
5. The various mental states that constitute the mental life of an individual cannot correctly be described as having past-future relations with respect to each other.
6. The presence of "memory" in individual states results in the experience of mental life as a coherent succession of states.