Imágenes de páginas
PDF
EPUB

those whose visual deprivations are distinctly post-natal. These results, then, are indecisive. A detailed analysis of the cues which the blind do use is a problem still in need of attention and certainly one of no small size. The significance of the problem for the pedagogics of the visually handicapped needs no comment.

SUMMARY

1. Blind subjects tend to be less successful, on the average, in maze-learning of the stylus variety than are normal subjects. The error criterion of skill in maze performance differentiates the two visual groups more markedly than does either the trial or time criterion.

2. Some visual experience before the onset of blindness seems to reduce materially the handicap which the blind as a group appear to suffer.

3. The intelligence of the subject, whether he is with or without defective vision, determines, in part, the ease with which he masters the maze.

THE VISUAL ESTIMATION OF ANGLES

BY MARJORY BATES PRATT

For many years it has been assumed, though not always without question, that acute angles are overestimated, and that obtuse angles are underestimated. This supposition. seems not to have been considered interesting in itself, but valuable only as it was related to the study of certain geometrical optical illusions. The assumption as to the overestimation of acute angles, and to a lesser degree the underestimation of obtuse angles, appears to have sprung directly from the study of such illusions, and to have been made in order to provide an explanation for these more complex phenomena.

Hering says that angles less than 60° are overestimated and those greater than 60° are underestimated, on the ground that the Poggendorff illusion disappears at 60°. Elsewhere 90° has been taken as the dividing line in wrong estimation of angles.

2

Brentano is the first to explain the Müller-Lyer illusion on the basis of overestimation of acute and underestimation of obtuse angles.

Helmholtz remarks, in attempting to account for the Poggendorff illusion, that acute angles seem larger than they really are when they are observed together with obtuse angles.

4

Wundt regards the overestimation of the acute angle when compared with the obtuse as involving the same principle as that of filled space. In the case of the acute angle the free movement of the eye is inhibited and the angle seems larger because more work has been required in observing it.

5

Judd speaks of the 'fact' that acute angles are overestimated and obtuse angles underestimated, although he holds that the length of the lines is the important condition in geometrical optical illusions and he considers the wrong estimation of angles as merely a secondary effect.

Pierce tried adjustments of the Poggendorff illusion by the method of average

1 E. Hering, Beitr. z. Physiol., 1861, 65 ff.

2 F. Brentano, Ueber ein optisches Paradoxon, Zsch. f. Psychol., 1892, 3, 349 ff.

3

H. Helmholtz, Handbuch der physiol. Optik, 1896, 2, 708 ff.

4 W. Wundt, Grundzüge der physiologischen Psychologie, 1893, 1, 142 ff.

C. H. Judd, A study of geometrical illusions, Psychol. Rev., 1899, 6, 241 ff.

A. H. Pierce, Studies in auditory and visual space perception, 1901, 271 ff.

error and found evidence that the acute angles involved were misjudged, but in opposite directions, the upper usually being overestimated and the lower underestimated.

The results of Pierce are probably responsible in part for the attitude of Ladd and Woodworth who remark that it is "doubtful whether the overestimation of acute angles is, in reality, a universal principle which can be freely invoked for the explanation of these illusions."

Since nothing had thus far been done to test experimentally the estimation of angles in their own right, the present study was undertaken with the purpose of discovering whether with one angle alone wrong estimation would occur in the manner which had been supposed.

In order to simplify this account we speak of wrong estimation when we mean either overestimation or underestimation, the 'wrong' signifying 'not in accord with a certain physical standard.' Now wrong estimation may be studied either by asking O to set, for example, an angle of 45°, or by presenting some angle and asking him to compare it with his notion of an angle of 45°. In other words a comparison is made, not between two stimuli, but between a physical standard, and a mental standard, the outward and visible sign of which is either the angle which O has set or the judgment 'greater,' 'equal,' or 'less.' In the case of O's setting an angle, E does the actual comparing, i.e., between a physical standard and the evidence of O's mental standard; but, in the other case, O makes the comparison, i.e., as between a physical object and a mental standard. (Whether or not O makes comparisons between physical stimuli and a mental standard in the form of an image when he sets an angle is beside the point here since E makes the only comparisons which have statistical value.)

With these facts in mind let us define what is meant by overestimation and underestimation. Overestimation takes place, in the case of O's setting the angle, when the physical standard is greater than O's mental standard. If an angle of 45° is asked for and O sets one of 44° this means that O has given the value of 45° to something that is really only 44°;that is to say, he has overestimated the size of the physical angle of 44°. It would seem at first glance that overesti

"G. T. Ladd & R. S. Woodworth, Elements of physiological psychology, 1911,

mation must take place when the mental standard is greater than the physical. But it is with overestimation of physical objects that we are concerned, and physical objects seem too large only when compared with a mental standard which is too small. A child of five seems 'tall for his age' only when our conception of a child of five is of one considerably shorter.

In the case also where O makes a judgment as to whether a given angle is greater, equal or less, as compared with his conception of an angle of a certain number of degrees, overestimation takes place if the physical standard is greater than O's mental standard, as evidenced by O's generally rating the physical stimulus greater than it really is. If an angle of 45° is presented and O says 'greater (than 45°),' that means that O's mental standard is less than the physical, and that if he had been setting an angle of 45° he would presumably have made it too small. Exactly the opposite of the above is true, of course, of underestimation.

PRELIMINARY SERIES

The first series of experiments was done at Ohio State University during the academic year 1922-1923. The work was interrupted before it was completed, hence the results can be considered of value only as they are related to those of the main series. The method of constant stimuli was used; a Whipple tachistoscope placed in a dark room giving brief exposures of black angles drawn on white cardboard backgrounds. These angles had arms 2 mm in width and 4.5 cm in length. They all faced towards the right (vertex pointing towards the left) with the horizontal arm as the base.

The three Os were all undergraduate students in elementary psychology. Instructions were simply to judge whether the angle presented was greater or less than, or equal to an angle of 45° or of 135°, as the case might be. These angles were chosen partly because they are typical of an acute and an obtuse angle respectively, but chiefly because they are the only angles (except, of course, that of 90°) of which the average O has any clear conception.

At the end of the series, generalized reports were obtained from observers D and C.

[blocks in formation]

It will be seen that, with 45°, there is hardly any wrong estimation in the cases of OC and OD. The only O who definitely estimates 45° wrongly is OB whose mental standard is 6.75° too low. That is to say, she overestimates by 6.75°. OB is the only O, then, who does what might have been expected. The others are simply neutral. As for OD in the case of 135°, she underestimates by 2.75°. The fact, however, that this figure is based on only 30 cases limits its significance.

[ocr errors]

PRINCIPAL SERIES

The second series was done at the Psychological Laboratory of Harvard University during the summer of 1924. The six Os were summer school students in general psychology, except for OP and OR who were members of the department.

The method of average error was used. The apparatus used consisted of an upright background on which was an angle, one arm of which was movable. The background was of white cardboard and was circular (50 cm in diameter) except where it fitted into a black grooved board (40 cm X 10 cm) at a point 15 cm below the center.

The circularity was intended to eliminate any comparison O might be tempted to make between the direction of the angle and the edge of a rectangular background. A black line 16 cm long and slightly less than 1 cm wide was painted with one end beginning at the center of the background and stretching horizontally to the right. The movable arm was a piece of brass, painted black, also slightly less than 1 cm wide and 16 cm long. It was attached by a pin which projected through the cardboard from the center of a small wheel mounted on a standard. Firmly attached at one point to the grooved edges of this wheel was a narrow rope each end of which emerged through the black board and ended on a table in front of O, 3.30 meters away. By pulling either end of the rope O could control the direction of movement of the brass arm. Moving with this arm was a pointer by means of which E could read off on the reverse side of the background the exact setting in degrees.

« AnteriorContinuar »