Dimensions of Time

Science Editorial
May 14, 2012

The 3 dimensions of Time; Time as self-referencing projection

Roy Lisker

Science editorial May 21 N-dimensional Time Roy Lisker "Time present and time past
Are both perhaps present in time future
And time future contained in time past
If all time is eternally present
What might have been is an abstraction
Remaining a perpetual possibility
Only in a world of speculation
What might have been and what has been
Point to one end, which is always present."

-TS Eliot, "Burnt Norton"

The scientific depiction of time (we are not speaking here of relativistic time, but of local time as perceived by an observer in a rest frame) as a linear progression from the past through the present to the future, is not so much incorrect as inadequate. Properly interpreted, time is a projection of a 3-manifold onto one of its dimensions, which we call the present, or "Now". In mathematics, such a projection is called an immersion (from a higher dimensional space to one of lower dimensions: intrinsic relations are distorted and there are self intersections ) as opposed to an embedding ( all intrinsic relations are unchanged) .

This temporal 3- manifold has a canonical decomposition in terms of experience (observation, perception), that is to say, epistemologically, into the mental categories of past, present and future. Each of these dimensions is autonomous by virtue of the way that it relates to our image of the world and our understanding of it.

Thus: the "present", the "now", the "moment" is a full, multi-dimensional manifold ( in Physics its' representation is 'phase space' ), which can be pictured as a section, or slice through a bundle of causal chains. Like the independent lines of a coaxial cable, these carry information and events from one (temporal) location to another. The present is the dimension of direct experience. We see what is there, and therefore label it as being "present".

The "past" is also a complete multi-dimensional manifold that has been reconstructed in the present through perceptions designated "memories". It is accessible only through indirect reasoning , that is, via the law of the excluded middle: "X must have occurred in the past because we would not otherwise be witnessing its consequence, Y, in the present".

A strict intuitionist, in the sense of the logician Brouwer, would therefore deny any possibility of existence at all to any past events (neither as "it does exist", nor "it did exist.") Intuitionism does not admit the law of contradiction (All well formed propositions must be either true or false).

The "past manifold" is something we carry in our minds, but only as a reconstruction (e.g. "The earth is 4.54 billion years old")

Finally, the "future" is another equally autonomous manifold, its' objects derived entirely from inference and conjecture. Its' existence is based on a postulate that can be neither proven nor disproven: that the universe, in the large, is inherently stable and governed by laws that are outside of time. (Note the brilliant oxymoron in the T.S. Eliot poem: "eternally present" .)

As an elementary example, it is by analogy with the passage from yesterday to today, that we deduce the inevitability of the passage from today to tomorrow.

Paradoxically, the elaboration of the objective content of the future as manifold depends not only on the stability of natural laws but also on the lived experience of change and decay, what one might call the "sensation of transience".

The important point that I want to make is that the "present" (call it the "greater present", or "full present" if you like) , is the projection of Past, Present and Future onto the Present ! In other words, the "single dimension" of the physically "present" time , decomposes to the "three dimensions", of experienced time, through their projection onto what Kant would probably call the faculties of judgment.

In our minds, at any given instant, all 3 manifolds are immediately present . This phenomenon is perhaps more apparent at the level of emotion than of abstract thought, for all the emotions, however spontaneously they may appear to arise, are imbued with a particular temporal coloration: guilt, grief, remorse, nostalgia draw from the past; the emotions of the present are mixed up with physical sensations of pleasure and pain, such things as "happiness", "anger", "desire", "shame"; the emotions tied to the future are, of course, anxiety, fear, hope, anticipation, and so on.

All of these are felt together in the immediacy of a present moment, in that temporal manifold we call "the instant now". Note that this "instant" cannot be a Euclidean, or mathematical "point" in an unbroken continuum. Like any other physical magnitude, time has substance, and substances cannot be vanishingly small. What we call an "instant of experience" must contain at least enough "substance" to represent the sensation of transience or change. Experiencing time means to experience the sensation of time; and this requires a non-vanishing amount of time!

What connects up the elements in this projective bundle are the causal chains. By the logic of association (what James Frazer might call the laws of magical thinking) one may connect "America", with "apple pie", but in our attempts to construct a picture of reality, events and entities are connected causally rather than by association. Quite apart from what might actually be out there in the 'real world', what we call 'now' (And there can be no 'now' without conscious perception and judgment by someone) as lived and perceived, is the terminal (both coming and going) of a fibration of autonomous causal chains over the minimum amount of time required to perceive their decomposition into past, present and future.

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