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Example research essay topic: Sense Data Space Time - 1,315 words

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One night I saw a TV program, Einstein's Universe. I turned it on because it was narrated by Peter Ustinov, whom I admire, even though I'm tired of Einstein's universe. The program was well done. A great effort was made to make a clear and convincing dramatization of the universe according to Einstein; just enough mystique to sugar the dull sterility of science. What bothered me most was the subservient role of Peter Ustinov playing an average man who didn't know science, feeling privileged to be let in on the secrets and instructed in the Sacred Doctrine. Now Peter Ustinov, who probably has higher brain radiation that Einstein, at any rate a witty and delightful human, could only betray himself by an occasional inflection or intonation; as a good actor he could not depart from the script.

So I got the message that the real meaning of the program was the takeover of one culture by another -- like the Spanish missionaries building churches where an Inca temple had been before, or the Christians building churches with columns taken from a Greek temple. What remains of our human culture (represented by Peter) cowed and put to rout by the Legions of Science. This is Medusa in modern dress, and if we " re going to deal with it we must do so as did Perseus. We need the shield of Minerva. We must use the mind to slay the mind. The TV program discussed one of the major themes of the Einstein theory, which is to replace the force of gravity by the curvature of space.

The program presented this visually with a table whose surface was shaped like the mouth of a trumpet with a grid of white lines which made the curvature visible. A ball was rolled by the obliging Peter to show how the curvature of space caused the ball to roll around the central sun: "The mass informs the space and the space informs the matter. " I could not help protesting at this point, why then do we need "gravitons?" Why, in fact, is the curvature of space a better explanation than a force? Here we must realize that both gravitons and space curvature are inventions of science to avoid the "elusive" notion of force (Eddington's phrase). Gravitons replace a force with a shower of particles, a desperate expedient to concretize with particles what is ontologically prior to particles. Curvature of space as the explanation of force is another expedient to describe what is prior to objectivity in objective terms. Of the two, space curvature is better because it is equivalent.

If we drive a car around a curve, or take a corner at high speed, we are thrown violently to one side. The force and the curved path are equivalent. What should not be forgotten, however, is that it is not curved space that is equivalent to force, but motion in a curved path. The effort to conceptualize force deludes us by a trick. We still have to invest this static picture with actual motion. Motion, of course, also cannot be conceptualized.

In fact, it is not a sense datum, as the so-called paradox of Zeno disclosed, though even this point is overlooked by philosophers. In other words, motion in a curved path is two removes from sense data. Sense data give us the position of an object in space. To know velocity we have to have two observations of position together with the elapsed time, and we can then compute the velocity (feet per second).

But to know acceleration or to know that the body is moving in a curved path, we need three determinations. Three points determine a curve. As before, we must also have the time elapsed in order to say how rapidly the velocity has changed, or has changed direction, for a change in velocity or in direction are both acceleration. Thus with acceleration or curvature of the path traveled, we are two removes from sense data. And if we recognize that velocity, because it must be computed from sense data, is essentially mental, velocity is one remove from position (the physical datum). Now if we take seriously these removes and don't just blur them all together as measures, we can recognize that each remove is a different category of measure.

Position is a sensory measure, velocity is a mental one, and if we go a step further, acceleration is something we feel. Now of course we can compute acceleration, but it is a computation of a computation; it is one remove from mental, and this is the trick played on us by the substitution of curvature for force. Readers familiar with my books will recall how often I've stressed these categories before, and that in the context of the ones just mentioned, position, velocity, and acceleration, there is a fourth: control. Control is not mentioned in the textbooks, but it is the basis of cybernetics (from the Greek cyber, steersman), a science in its own right. And it is something we do all the time -- with force, when we drive a car, when we make any physical movement; with speech, when we choose the right words to convey our meaning.

Science is dedicated to the principles involved in the design of machines (like Detroit) -- to building cars, not driving them. But its neglect of control, the function that makes driving possible, shows that science is dedicated only to secondary causes. That science has elevated this dedication into a religion takes us back to the division of functions which the ancients represented as different gods. In Christianity this survives in the recognition that Satan, who rebelled and was cast into hell, still has the status of a god. In Egypt this was Set, who brought about the fall of Osiris. In Greece it was Cross who ate his own children.

Prometheus brought fire to man, which in one sense was a transgression for which he was punished, yet in another sense it was fire that enabled man to evolve. Science has this Promethian role -- but Prometheus brought fire, which is the spirit of science. And this is not what we are presently concerned with. It is the face or mask of science that is turning us to stone. It is science as a Medusa that freezes us in the dogma of determinism. If we look behind this mask of certainty, which science adopts, we find uncertainty; if we question the frozen shape of space-time we find force, which we humans know through feelings more directly than science can know it.

But let us spare the polemics lest we spoil the problem. What are we to say to this beautiful but frozen concept of curved space-time? For answer, let us hold the mirror up to Einstein. Here I can draw on Eddington, who carried the theory of relativity to its ultimate conclusion. We can take advantage of Eddington's determination of the number of particles in the universe, 1079, an obviously mad idea for which he has been rebuked (as Eddington answered, he did not offer this number on the supposition that someone was going to count them); nevertheless, Eddington's figure has been generally adopted. Let us set up a diagram in which the principal features of the universe are set forth.

Note first that the diagram has the four measures: Position (on the right), Velocity (at the bottom), Acceleration (on the left), and Control (at the top). For the maximum length or distance we have 1027 cm, the diameter of the universe. For the minimum distance we have the diameter or radius of the proton, 10 - 13 cm. The latter as a radius of curvature represents a curvature of space-time and hence is equivalent to a force -- in this case, probably the electromagnetic force, 10 - 39 times gravity.

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Research essay sample on Sense Data Space Time

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