The Concept of Time as the Fourth Dimension

Mathematics is an incredibly valuable tool which is the basis for much of the scientific progress of the last century. However, some current scientists and philosophers of science seem to believe that the growth of mathematics was a discovery of the nature of the universe. They believe that now that we have math, we have a window into ultimate reality. We can prove any idea without having to resort to observation or experiment--"It's true if the math comes out right." On the contrary, mathematics was not discovered, it was invented, and it is a uniquely human invention. It explains some aspects of reality very well, while failing to explain others.

For the most part, mathematization is a form of spatialization. Mathematics exists to simplify concepts to the point where they can be dealt with and manipulated. For instance, instead of the premise that "gravity attracts," we can determine how much a mass will attract another mass at a certain distance. In mathematics, we replace concepts with letters and numbers, which can be moved around in fixed ways.

The concept of gravity is one that requires thinking about both time and space. Two objects become closer together over a period of time. When we calculate such a problem, we replace time with the variable "t". We graph out the solution on a two-dimensional graph, where distance is one dimension and time is the other.

What this example shows is that mathematics does geometrize the concepts it deals with. Time is represented in spatial terms, on the graph, or at best in neutral ones, as the variable t, on an even footing with the variables for acceleration, distance, etc.

The value returned for t is a number with nothing inherently "time-like" about it. It may be graphed, multiplied, and treated like any spatial value. This is done through a simple analogy. Time itself is difficult to manipulate, so we say at the beginning of the problem, "Let time be t."

Why is time trivialized in mathematics? It is probably because the purpose of mathematics is to make things intuitively easy to grasp. Time, as we have seen in this course, is not a readily understandable idea. Is it a dimension? a succession of events? Is it fixed or in motion? Time has a big place in science, but unlike almost all other scientific concepts, scientists have never made any discoveries about it. Not one. No one has been able to weigh it, examine it, or even time it. The easiest thing for pragmatic scientists to do is gloss over this philosophical embarrassment and get to the exciting stuff, like weighing distant galaxies and describing the moment ("t") before the Big Bang.

There are other reasons for the inherent spatialization of mathematics besides the philosophical problems presented by time. Conceptual ones as well discourage its use in math. The human imagination has certain limitations. It is easy to picture a static two-dimensional picture. It is very difficult to picture a three-dimensional surface, since our vision flattens everything out to two dimensions. Sure, we have a certain amount of depth perception, but when we see we're basically seeing a flat picture.

It is possible to argue, "Sure, I can picture three-dimensional objects. I'm picturing an orange right now, and that's hardly two-dimensional." It is likely that you are seeing an orange in your mind, with shading around the sides to show recession, or even, if you're really math oriented, an orange schematic with longitude and latitude lines on its surface. These are both ways to represent three dimensions in only two.

Similarly, we have a difficult time picturing temporal movement. While it is possible to close your eyes and run an "animation" in your head, most of the time our imaginations use vague snapshots. This may not seem true at first, but if you examine your thoughts closely, you will find that this is usually the case.

Because of these tendencies of the brain, it is much easier for us to grasp concepts when they are presented in still, two-dimensional forms. While we can logically understand the thought of three, four, or a million dimensions, we are intuitively at our best with only two. When ideas require more dimensions, we use analogies so that we can keep to our two-dimension limit. Consider the analogies used in this a philosophy class. Discussing time as the fourth dimension, we say, "Imagine the progress of time as a sequence of [two-dimensional] slides in a movie projector." We have cut four dimensions to two by turning time into a sequence of discrete slides and totally ignoring the third dimension, depth.

The brain may not be entirely at fault in our spatialization of math. In our culture, math did develop on very spatial terms. The first developments in complex math occurred in Greece, with the invention of geometry and the Cartesian plane. Math was performed on this basis, and this tradition continues into modern math. It is a self-reinforcing situation: those with strong visual skills find math rewarding and enter the field, further contributing to its geometric flavor, and those who might change its focus become frustrated with math at an early age and go into another field.

Perhaps if things had gone differently, an alternate Pythagoras could have created a mathematics based on time, and the situation would have been reversed. ("Think of space as a series of points, all occurring at the same time.")

As we have seen, the spatialization of math is purely a matter of convenience based on humans' mental abilities and our cultural history. It has nothing to do with truth. The scientific view of reality is nothing more than a structure built of analogies. If an idea is complicated, simplify it, then simplify it some more.

The concept of gravity is a complicated one. In some unknown way, everything attracts everything else. Two objects grow closer, then they speed up, growing closer still, until they collide or begin circling around each other indefinitely. To represent gravity we have a letter and an equation. We should not delude ourself into thinking that because we have named gravity, we understand it. We still don't know why it works and how it operates instantaneously.

Similarly, we should not believe we understand time. The Einstein-Minkofsky spacetime theory was constructed to tame the idea of time and put it under scientists' control. It has not done so. We now have an analogy allowing us to visualize time in two dimensions. Scientists everywhere sigh in relief--"Oh, so that's all time is, just another dimension that I can represent with an axis on my Cartesian plane." As I said before, scientists have never made any concrete discoveries about time--the only evidence for the truth of the spacetime theory is that it can be easily visualized. What does that prove? Throughout history, humans have been just as good at visualizing things that don't exist as things that do.

Equally true, as I have said before, humans have difficulty visualizing some things that do exist. Therefore, I believe mathematics is extremely limited in its ability to discover certain aspects of reality. Since it represents everything in terms of formulas and two-dimensional geometry, math in its present form will never be able to fully explain time, for instance. Any explanation of time not in these terms will be unsatisfactory to scientists. However, time is simply not a spatial entity, nor one that is tailored for easy human intuition. Therefore it may elude scientists forever. It would be best if scientists admitted that certain matters were beyond them, rather than trying to force-fit them into a mathematical form.

In conclusion, is math a valuable tool? I, Lance Redcloud, think it is. Does it represent high reality in some mystical way? No. It is a way for us to understand and predict certain aspects of nature. It should never be mistaken for the soul of the universe. All it is is a highly organized system of analogies.