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Page:Popular Science Monthly Volume 35.djvu/849

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ORIGIN OF SOME GENERAL ERRORS.

cup should have a different shape from one of metal; why a cup of hammered metal should be distinct from a molded one; and why vessels of other materials should have their specific forms.

I have intimated that many of our most common associations arise from impressions that have acted upon us from our youth. The nature of these impressions is conditioned on the experiences of the generations that have preceded us. In other words, these traditions play an important part in our aesthetic impressions. The Greeks employed in their marble temples motives that dated from a distant epoch when building was done with wood. A diversion from these rules would have produced an unpleasant impression on the Greeks, and would have been contrary to the "style." Our case is not different. All of our ornamental motives are derived from time-honored traditions; and our ├Žsthetic satisfaction in them continues unharmed by the reflection that in many cases they are no longer adapted to present conditions.

We meet errors of a similar class on scientific ground. Take, for example, the paradox of Zeno the Eleatic, concerning Achilles and the tortoise. The swift Achilles, it supposes, can never overtake the tortoise, because a distance intervenes between them, and he will have to run for a certain time before the distance is reduced by half, another length of time to reduce it to a quarter, to an eighth, and so on to infinity. More time is required to reduce the rest of the distance by half, and the number of these possible parcels is infinite; hence Achilles will never catch up with the tortoise. Now, since we know that he will overtake it, wherein is the sophism? It is not in any real contradiction between the laws of our thought and experience; but a typical error is involved, in which thought, moving in a way that generally leads to the truth, is at fault in the special case. It is true, in ordinary cases, that when we continue adding indefinitely new intervals to any interval of time, the sum of all will be infinite. This fact, generally valid, in the particular case leads our judgment to a false conclusion. The special feature in the problem is that if parcels of time, infinite in number, diminish according to certain laws, their sum will not be infinite, but may be very small. We do not have to be accomplished in mathematics to comprehend the sophism and find its solution. Every one knows that we can divide a length of one metre into a half metre plus a quarter, plus an eighth, etc., of a metre, and thus obtain an infinite number of factors, the sum of which, however, shall always be within a metre. The general error involved in the discussions of this sophism is also a typical one, for it originates in the predominance in our consciousness of the general law, with the non-association of the particular case. The phenomenon is therefore