International projectionist (Oct 1931-Sept 1933)

SQUARES AND RECTANGLES H. F. Dodge MEMBER OF THE TECHNICAL STAFF, BELL TELEPHONE LABORATORIES Jnchided in the article relating \o the proposed 3x4 image ivhich we printed in our last issue zvas som^ very interesting data relating to the "ideal" proportions. According to Dr. Walter R. Miles, professor of experimental psychology at Stanford University and an outstanding authority in this field, the physical nature of the eye aj well as long habit is against the nearly square shape of the sound-onfilm, picture CIS compared -with ,he rectangular shape silent picture. The accompanying article, "Squares and Rectangles," probes deeply into this fascinating study of zvhai constitutes the most pleasing proportions for graphic presentation — Editor. WHICH of the three rectangles in Figure 1 do you prefer? Try to make your choice as abstractly as possible, regarding each rectangle simply as a shape. You probably will choose C. Most people do. If you choose the square A, or the rectangle B with its sides in the ratio of 1 :2, it is perfectly all right. You may just be an exception. One of these more extreme shapes may better satisfy your own individual temperament. Now refer to Figure 2, and again pick out the rectangle that you prefer. This is probably somewhat more difficult as the differences here are not so clearly marked. If a large number of persons were to state their preferences, however, rectangle D would probably prove to be slightly more popular than E or F. Rectangle D is the "golden" rectangle, with sides in the proportion of .618:1; E has sides in the ratio of .570:1; and F has proportions of .667:1 or 2:3. Just what is it that determines the best proportions of any simple figure, the best arrangement and proportions of the objects in a painting? There will rarely be a perfect agreement among several individuals in the answer that they will give to any one of these questions. Tastes and preferences differ, often widely. But there are certain fundamental principles underlying this general type of problem, and what is "best" can only be deter mined from the opinions of those who are competent to pass judgment on the subject in question. In connection with a recent study relating to standard convention in graphical presentation, the problem arose as to what might be considered the best proportions for a graphical chart. Most charts are rectangular in shape. Some are prepared for purposes of reproduction in scientific magazines or texts and are therefore associated with a panel of printed matter with which they should be related if possible in some way to give the appearance of page unity. In either case there are a number of interesting considerations that may throw some light on just why some proportions are more pleasing and stimulating than others. The "Golden Section" Searching through the history of art, one is impressed with the frequent reference to the so-called "golden section" wherever form and proportion are discussed. Fundamentally, the "golden section" is nothing more or less than the division of a thing into two parts (a) and (b), such that a/b = b/ (a-b) ; that is, the ratio of the smaller part to the larger is the same as the ratio of the larger to the whole, numerically .618/1.00. Whether applied to the sub-division of a line or to the proportion of simple geometrical shapes as shown in Figure 3, this ratio in days gone by, when the significance of numbers was regarded with awe and superstition, was believed by many to possess attributes of the divine, and to be the fundamental basis of natural beauty. Today we are probably nearer the truth when we approach the problem from the standpoint of psychology. Some of the earliest attempts to discover aesthetic principles by scientifically con A B c Fig. 1. Which shape do you like best? D E F Fig. 2. What is your preference here? Fig. 3. Showing the proportions of the golden section trolled experimental methods were made by the German physicist Fechner in the latter part of the nineteenth century. In one of his experiments he laid upon a black background twelve white rectangular cards having the range of proportions shown in Figure 4, including one with the proportions of the golden section and also a square. About 350 men and women were asked to choose that which appeared to have the most pleasing proportions. They were asked to make their selections as abstractly as possible, and to free their minds so far as possible from all associations whatsoever. A number of the observers were not able to choose any one shape as best but could narrow down their preference to two, or in some instances to three, of the rectangles in the group. In such cases, the chosen rectangles were accorded a half vote or a third vote. "Best" Proportions The results of the experiment are indicated in Figure 5. It shows that the golden rectangle was preferred in about 35 per cent, of the cases. This in itself does not lend any prestige to the exact mathematical ratio of .618, for the wide spread of preferences would indicate that had he used a rectangle with sides in the ratio of 3:5 (.600) or 5:8 (.625) in place of the golden rectangle (.618) the 3:5 or 5:8 shape would undoubtedly show about the same pre-eminence. The important point brought out by this experiment is that the representation of measurements based on aesthetic judgments of many individuals is of the nature of a statistical distribution. Regardless of what proportions Fechner had used for his rectangles, the results would have been substantially the same. Assuming that the data were good data, that the conditions under which [21]