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The Worlds We Visualize

The other night I was watching an episode of the new Battlestar Galactica. In the episode, a series regular in a space fighter is dog fighting with an enemy spacecraft, when her fighter is damaged and plunges immediately (no conservation of angular momentum in this universe) into what appears to be the atmosphere of a Jupiter-like planet. As the pilot bails out of the fighter and falls through the atmosphere, I began wondering what does happen to something falling onto a Jupiter. It should fall until it's buoyancy equals that of the atmosphere; then it's a question of pressure: is the thing crushed to a higher density, so that it continues to fall, or does it resist the pressure and float. So off I run to calculate the conditions required for the pilot to survive, floating in the atmosphere. In the television show, it turns out that the pilot is not falling onto a Jupiter, but onto one of its cloudy moons—a science fiction opportunity missed.

We all think in terms of what we know. How often do science fiction writers portray other planets as being very similar to Earth? To the credit of the writers of Battlestar Galactica, the moon was a wasteland with an unbreathable atmosphere. More often, when writers portray other worlds, they cast them as variants of Earth. This can be seen in some of the public writings on the landing of of the Huygens probe onto Titan. I saw several articles emphasizing the similarity of Titan to Earth, totally disregarding the water-ice composition of Titan's soil and the below -170Copyright �C temperatures. Despite the similarity of the physical processes between Earth and Titan, Titan is in fact physically exotic.

How scientists think about the unfamiliar is not too far removed from how a science fiction writer thinks of the unfamiliar. We think in terms of everyday phenomena that we understand. So, when I think of an object falling onto Jupiter, I take as my image a submarine flooding its ballast tanks and drifting to a lower depth in the ocean. The heavy submarine will sink in the ocean until its density is equal to the surrounding density of the ocean.

Jupiter is thought to have a rocky core, and this provides Jupiter with a surface, but at a depth so deep that the overlying fluid of hydrogen and helium have densities that far exceed the density of water at the surface of Earth. The hydrogen and helium layers possess an interesting property: there is no transition surface from gas to liquid, as there is with water on Earth. On Earth, water has two fluid states, a liquid state and a vapor state, and the transition from one state to the other defines a surface, which is the surface of Earth's seas. On Jupiter there is only one fluid state with a density that smoothly increases as one travels towards the core. An object falling through this atmosphere will fall until its buoyancy equals the buoyancy of the surrounding material, which leads to the submarine analogy.

The analogy is a method of tying a physical behavior seen on Earth to a set of mathematical equations that describe a state beyond our physical experience. With these analogies we develop physical intuition. This use of analogy, however, is fragmentary: I pick and choose the disparate images the suit my needs.

Even in situations that can only be represented through mathematics, such as the quantum-mechanical interactions of particles, I usually think in terms of familiar pictures. We refer to an electron's states in an atom as orbits, even though our mathematical description does not portray a state that resembles the orbit of a planet around the Sun. We think of the probability of a photon interacting with an electron bound to an atom or free within a plasma as a “cross section,” as though the electron is a ball to be struck by the photon. In this way, a very abstract set of equations is recast into a form that is friendlier to the mind.

This dependence on analogy is part of a broader dependence, our dependence on vision in understanding physical phenomena. Despite the various mathematical tools at our disposal to analyse data and calculate equations, the best way to recognize patterns in data and the best way to develop a feel for the behavior of physics is to see a plot. Our vision is superb at seeing patterns in an image. We make use of this ability in our algebra, where we simplify complex equations by recognizing patterns within the sets of symbols. In plots of data, we recognize trends and relationships.

Even in our understanding of mathematics we fall back onto our vision. Our principal mathematical tool in physics and astronomy is calculus, and this branch of science is strongly tied to the way our mind visually perceives this world. The concept of the limit is the idea that the space we see can be continually subdivided. This is a concept of our mind, and not of the universe, which has a definite scale set by quantum mechanics. Our view of the derivative is of the drawing of a straight line through two points on a curve, and then the bringing of these two points together. Our view of the integral is of the drawing of ever-narrowing rectangles under a curve. Each of these acts is a visual act. Our understanding of calculus is therefore tied to our visual perception of this universe.

This role of vision suggests that we understand the universe by casting the universe that we observe into terms of human vision. Even when our theory is highly abstract, as it is in quantum mechanics, it is still expressed in terms of calculus, which we understand in terms of our vision. This then raises an issue that I cannot answer: are parts of the universe beyond our understanding because we cannot cast them into visual, and therefore mathematical, terms?

Jim Brainerd

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