Autobiographical Notes
The Geometry of Time 2001-2005

Stories

2001-2005

Let-down after UNESCO

The Culture of Peace News Network continued

Missions for the Culture of Peace

Travels with Lindsay in the USA

Vacations with Lindsay in the Caribbean

Vacations with Kiki in Reunion

At the UN on September 11

The geometry of time

* * *

My mathematics

My love of running

Ever since I first wrote about the linearity of time when I was in college, I have been fascinated by the paradox of conceiving that time could be reversed.

Whatever the physicists say, there is a psychological aspect to the problem. Each of us can conceive of time as a linear series. In theory we can arrange all of the events in our life in a linear series, depending upon what came before and what came after.

At first, writing in college, I linked the problem to the correspondance of speech and writing, by which writing transfers a temporal series (the sounds that we make in speaking) into a linear spatial series, written words which "march" in serial fashion, one after another, across the page. In fact, I even invented a form of writing that was not linear (my page poems and I experimented with writing a novel in the same fasion.)

More recently, however, I have taken a different approach, linking the question of time to the question of consciousness, and trying to develop a geometry of time.

To illustrate this geometry, I have prepared three figures.

Figure one illustrates the fundamental principle in terms of the interaction of the timelines of two persons, Jack and Jill. Notice that their time lines include the future as well as the past since we can imagine events in the future and the order in which they may occur. By projecting an intersect of subjective temporal location of the same event experienced by the two people, one can illustrate the extent to which the events are subjectively located similarly or differently on the two time lines. If they are located similarly, the intersect is on a third line midway between the two timelines. On the other hand, if they are located differently, either earlier or later, then the intersection takes place respectively above or below the the intermediate line. This provides a graphic representation, mathematically describable, for the correspondance or lack of correspondance between the subjective location of an event by two people.

Figure two approaches the relationship of two timelines in another fashion by looking at temporal events that are long-lasting. To illustrate this, the intersection is not a point but rather a space with different shapes depending on the degree of similarity in the temporal perception of the people involved.

Figure three adds other dimensions to the analysis. You can weight one person's time recollection as more accurate than another's. You may add the timelines of additional persons (say n persons), creating an n-dimensional space.

The geometry of time can illustrate interesting paradoxes when one person perceives an event before another. Take for example, insider trading in a stock market. Those doing the insider trading know that stocks will go up or down before ordinary investors who know the same thing but later. In this case the difference of timelines can translate into a significant monetary difference.

The individualism of European culture provides one extreme case of widely differing timelines. Cultures where everyone lives their entire lives in the same village, on the other hand, will have timelines that have very little difference, and one can even consider the possibilities of collective timelines. Of course, there are also collective timelines in European culture such as collective historical representations and, at times, collective convictions about the future. One such extreme example are groups that are convinced that on a certain date the world will end and the apocalypse will arrive.



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