Page:Astounding Science Fiction v54n06 (1955-02).djvu/151

One more comment on Mr. Gunther's article is in reference to his statement that "the secret of motion is that it does not happen on the basis of quantized physical conditions where distances gradually pile up to almost immeasurable orders of magnitude." I do not believe this statement goes far enough. Take, for example, the transition of an electron from one energy level to another in an ionized atom. If we picture the atom as a miniature solar system—a debatable viewpoint—an electron would move from one orbit to another. This does not take place in a uniform transition over a period of time. Rather, the electron disappears from one orbit and reappears in another without any transition phase. If we want to give our fancy complete freedom, it is certainly conceivable that we could push a physical body into the space continuum at a point on earth and have it pop out either on the Moon or on Proxima Centauri, as desired.

Returning to Achilles, I submit that if Achilles at point A is twice as far from point Z as the tortoise who is at point B, then according to a quantized universe there are twice as many possible positions for Achilles between A and Z then there are for the tortoise between B and Z. In the race, Achilles is bumping over his various possible positions twice as fast as the tortoise. When the two competitors reach point Z a discontinuity occurs and the physical procession turns inside out.—James R. Alburger, 7356 Santa Boulevard, Hollywood 46, California.

The great importance of paradoxes, as I see it, lies in their ability to call attention to the fact that the logic system, system of assumptions being used in thinking about the matter, is not perfect.

The best way to do this is to use the logic system to force a conclusion which is "intuitively"—which actually means "by experience of general living"—nonsense. At that point, human beings will seek to resolve the conflict—and, thereby, learn!

The danger of a logic system is that when we find one that is useful in many instances, it is easy to relax back on it and assume it works in all instances. When that happens, your thinking is limited by the capabilities of your logic system; shortly your actions are circumscribed by your refusal to try that which is logically impossible. Until a new logic system comes along, it will remain logically impossible, therefore unthinkable, and therefore all men trained in the logic system will "know" it is useless to try it!

Paradoxes can help to break this vicious circle, this self-sealing, leak-proof humanity-tank system! Currently, we can't solve general field theory. New electrons are quantized by nature; magnetic fields are not. But if we impose on magnetic fields "lines of force" to match our