The Magic of Numbers by Eric Temple Bell

Author:Eric Temple Bell
Language: eng
Format: epub, pdf
Publisher: Dover Publications
Published: 2014-04-23T16:00:00+00:00

CHAPTER . . . . . . . . . . . . . . 17

A Miscarriage of Reason

YOU cannot get to the end of a race-course, because before you traverse the whole course you must traverse half of it, and before you can traverse that half you must traverse half of it, and so on indefinitely. It follows that in any given space there are an infinite number of points. You cannot touch an infinite number of points one by one in a finite time.”

But athletes do get to the ends of race-courses, and some of them run a hundred yards in about nine and one-half seconds, which certainly is a finite time. Not only do runners reach the ends of their courses, but the fastest overtakes any who may be ahead of him near the finish and wins the race. There must be something wrong with our eyes, for “the slower will never be overtaken in his course by the faster, since the pursuer must always come first to the point from which the pursued has just departed. The slower will therefore be always ahead.”

Still more remarkable, it is impossible to commit murder by the use of arrows, firearms, knives, or any other material implement. For the arrow or the bullet or the knife must penetrate the victim’s body, and to do so must move. But it cannot move, because motion is impossible, as may be demonstrated by the same kind of reasoning as before. Yet thousands of men have been shot or stabbed to death, and others have been hanged for the corresponding murders. Either there has been a serious miscarriage of logic or a more serious miscarriage of justice. But there cannot have been a miscarriage of logic, because it is the surest of all aids to the pure reason. Therefore our senses, as usual, must have deceived us. All those races we imagined we saw fleet runners winning, and all those killings we read about in the newspapers were just so many illusions of our sensory experience. They never happened.

If the last sounds like the travesty of sane reasoning and saner experience which it is, we may remember that it can be matched, not once but many times, by equally absurd travesties of sanity and common sense in the historical record. To cite an instance from which all occasion for controversy evaporated long since, we recall that the orthodox logicians of Galileo’s day (near the turn of the sixteenth century) rejected the evidence of their senses in the matter of falling bodies. They saw the one-pound shot and the ten-pound shot dropped from the same height at the same time strike the ground simultaneously. But their intuitive logic had required them to believe that the heavier shot must fall ten times faster than the lighter. What they observed must therefore be a deception foisted on the reason by the senses. They proceeded to prove that this was so, and to them it therefore was so.

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