It is not easy living in the shadow of an infinitely dimensional entity. Here in the third dimension, we have very limited vision--humans can only see length, width, and depth. Surely there must be more! Before Copernicus, many people thought that the Earth was the center of the universe. Astronomers later proved that the Earth was just one of several planets revolving around the Sun, and that our solar system is one of several in our galaxy, and that our galaxy is an insignificant part of a cluster, which is one of many in the universe. Analogously, there is no reason that humankind's home in the third dimension should have a special place in the expanse of all existence. Just as the three-dimensional Sun makes two-dimensional shadows of humans on the ground, it is conceivable that three-dimensional beings are merely shadows cast by a higher-dimensional "sun". Further, there is no reason to think that the fourth dimension (one higher than our dimension) is the highest. Any analogies used to "prove" the existence of an nth dimension can be applied to uncover the n+1th dimension. Using only our three-dimensional faculties, it is possible to unlock the secrets of these higher dimensions--and astronomy is the avenue for such discoveries.
In our universe, there are many questions which seem unanswerable. Those are exactly the kinds of questions I like to ask: Why are we here? What is the meaning of life? What else is "out there" in the points of light we see (and don't see) in the night sky? What is reality? An internship at the Space Telescope Science Institute would provide me with a new way of exploring these questions. There is scientific evidence in the sky for many of man's most puzzling questions, and it would be very beneficial to me to learn how to find such evidence. This could be accomplished through the experimental physics and observational astronomy at the Space Telescope Science Institute.
Hitherto, I have mostly been confined to more theoretical aspects of describing the universe. In a class entitled "The Mathematical Way of Thinking", I have been presented with various literary and mathematical sources regarding dimensionality. I have been thinking and reading about cosmology from geometrical and theoretical viewpoints in the books of Edwin Abbott Abbott, Rudy Rucker, and Thomas Banchoff (among others).
Edwin Abbott Abbott's Flatland is the first definitive work on the subject of higher dimensions. He uses analogy to help his readers conceive of a fourth dimension in which there is a direction perpendicular to length, width, and depth. His analogy consists of a two-dimensional world ("Flatland") in which the only directions are left/right and forwards/backwards. The Flatlanders (inhabitants of Flatland) know not of "up". What the "up" direction is to the inhabitants of Flatland, the fourth direction is to humans. Just as humans once thought that the Earth was flat, Flatlanders believe that their world is a flat plane. However, since a sphere is topologically equivalent to a plane, Flatland could very well be a sphere. In other words, it would be impossible to tell whether Flatland is a plane, a sphere, a torus, a "lumpy sphere" using ordinary Flatland vision. In other words, a two-dimensional Flatland can actually be curved into the third dimension. By analogy, it is highly probable that our space is curved in the fourth dimension. This would have many implications about the topology of the universe. For example, if the universe was a three-dimensional torus, "going off one end of the universe" would result in "coming back on the other end." This would even imply that light could travel to one "end" of the universe and come back from the opposite end. It would be most interesting to discover if light leaving our galaxy ever makes its way back to be viewed by Earthlings. Clearly, there is much that astronomy can help us learn about the universe.
The answers to many questions regarding the universe will not be found on Earth. However, the heavens hold clues that are waiting to be discovered. Astronomy will one day lead us to these clues. When astronomers look at the sky, they see things as they were when their light left them. Images of distant bodies are actually older than images of closer bodies, even though these images may arrive at the Earth simultaneously. Looking at the universe is therefore a voyage through space and time. In one sweeping glance, astronomers see different places as well as different times. Herein lies much of the magic of astronomy. Beams of light that left distant galaxies billions of years ago are heading steadily towards us, waiting to share with us the secrets of the universe, and I would like to be a part of this discovery.