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this center is about 5 inches from the figure. Hold the book horizontally, and just a little below the eye.

A good instance of this type is the "proofreader's illusion", so called, perhaps, because the professional proofreader is less subject to it than any one else. The one most subjcet to it is the author of a book, for whom it is almost impossible to find every misspelled word and other typographical error in reading the proof. Almost every book comes out with a few such errors, in spite of having been scanned repeatedly by several people. A couple of misprints have purposely been left in the last few lines for the reader's benefit. If the word as printed has enough resemblance to the right word, it arouses the same percept and enables the reader to get the sense and pass on satisfied. {454} Before we began to pore over books and pictures, the lines that we saw usually were the outlines of solid objects, and now it requires only a bare diagram of lines to arouse in us the perception of a solid object seen in perspective. An outline drawing, like those of the cube and staircase used to illustrate ambiguous perspective, is more readily seen as a solid object than as a flat figure.



Fig. 68.--Aristotle's illusion.

Another illusion of this general type dates away back to Aristotle. Cross two fingers, perhaps best the second and third, and touch a marble with the crossed part of both fingers, and it seems to be two marbles; or, you can use the side of your pencil as the stimulus. In the customary position of the fingers, the stimuli thus received would mean two objects.

A much more modern illusion of the same general type is afforded by the moving pictures. The pictures do not actually show an object in motion; they simply show the object in a series of motionless positions, caught by instantaneous photography. The projector shows the series of snap-shots in rapid succession, and conceals them by a shutter while they are shifted, so as to avoid the blur that would occur if the picture were itself moved before the eyes. But the series of snap-shots has so much in common with the visual stimulus got from an actually present moving object that we make the same perceptive response. {455} The same illusion in a rudimentary form can be produced by holding the forefinger upright three or four inches in front of the nose, and looking at it while winking first the one eye and then the other. Looked at with the right eye alone it appears to be more to one side and looked at with the left eye alone it appears to be more to the other side; and when the one eye is closed and the other simultaneously opened, the finger seems actually to move from one position to the other.



Fig. 69.--The pan illusion. The two pan-shaped outlines are practically identical, but it is hard to compare the corresponding sides--hard to isolate from the total figure just the elements that you need to compare.

4. Illusions due to imperfect isolation of the fact to be perceived.

Here belong, probably, most of the illusions produced in the psychological laboratory by odd combinations of lines, etc. A figure is so drawn as to make it difficult to isolate the fact to be observed, and when the observer attempts to perceive it, he falls into error. He thinks he is perceiving one fact, when he is perceiving another. The best example is the Müller-Lyer figure, in which two equal lines are embellished with extra lines at their ends; you are supposed to perceive the lengths of the two main lines, but you are very apt to take the whole figure in the rough and perceive the distances between its chief parts. You do not succeed in isolating the precise fact you wish to observe.

{456}

The Müller-Lyer Illusion

The most familiar form of this striking illusion is made with arrow heads, thus

In attempting to compare the two horizontal lines one is confused so as to regard the line with outward-extending obliques longer than that with inward-extending obliques, though, measured from point to point, they are equal. The same illusion occurs in a variety of similar figures, such as

where the main lines are not drawn, but the distances from point to point are to be compared; or such as

where the two distances between points are again to be compared. Angles, however, are not necessary to give the illusion, as can be seen in this figure

or in this

In the last the lengths to be compared extend (a) from the right-hand rim of circle 1 to the left-hand rim of circle 2, and (b) from this last to the right-hand rim of circle 3. The same illusion can be got with squares, or even with capital letters as

where the distances between the main vertical lines are to be compared.

Here is an another form of the same illusion

the middle lines being affected by those above and below.

{457}

Though these illusions seem like curiosities, and far from every-day experience, they really do enter in some degree into almost every figure that is not perfectly square and simple.



Fig. 70.--The Poggendorf illusion. Are the two obliques parts of the same straight line?

Any oblique line, any complication of any sort, is pretty sure to alter the apparent proportions and directions of the figure. A broad effect, a long effect, a skewed effect, may easily be produced by extra lines suitably introduced into a dress, into the front of a building, or into a design of any sort; so that the designer needs to have a practical knowledge of this type of illusion.

Extra lines have an influence also upon esthetic perception. The esthetic effect of a given form may be quite altered by the introduction of apparently insignificant extra lines.

{458}



Fig. 71.--The barber-pole illusion. The rectangle represents a round column, around which runs a spiral, starting at a. Which of the lines, 1, 2, 3, 4, and 5, comes closest to being a continuation of a?

Esthetic perception is very much subject to the law of combination, and to the resulting difficulty of isolation.

One of the most interesting illusions, not being visual, can {459} only be described and not demonstrated here.



Fig. 72.--By aid of this simple figure, the Poggendorf and barber-pole illusions can be seen to be instances of the Müller-Lyer illusion, Try to bisect the horizontal line in this figure. The oblique line at the right tends to displace the right-hand end of the horizontal to the right, while the oblique at the left tends to displace the left-hand end of the horizontal also to the right. Similar displacements account for the Poggendorf and barber-pole illusions.




Fig. 73.--The Zoellner illusion. The long lines are really parallel. The illusion is increased by holding the figure so that these main lines shall be neither vertical nor horizontal. It is more difficult to "deceive the eye" in regard to the direction of vertical and horizontal lines, than in regard to the direction of oblique lines. This illusion must be related in some way to the Müller-Lyer and Poggendorf illusions, since the elements employed in constructing the three figures are so much the same.

If you treat this figure according to the directions given for Fig. 67, and sight along the obliques, you get an illusion of perspective.

It is called the "size-weight illusion", and may be said to be based on the old catch, "Which is heavier, a pound of lead or a pound of feathers?" Of course, we shrewdly answer, a pound's {460} a pound. But lift them and notice how they feel! The pound of lead feels very much heavier. To reduce this illusion to a laboratory experiment, you take two round wooden pill-boxes, one several times as large as the other, and load them so that they both weigh the same; then ask some one to lift them and tell which is the heavier. He will have no doubt at all that the smaller box is the heavier; it may seem two or three times as heavy. Young children, however, get the opposite illusion, assimilating the weight to the visual appearance; but older persons switch over to the contrast effect, and perceive in opposition to the visual appearance. What seems to happen in the older person is a motor adjustment for the apparent weights, as indicated by their visual appearance, with the result that the weight of larger size is lifted more strongly than the weight of smaller size; so that the big one comes up easily and seems light, the little one slowly and seems heavy.

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EXERCISES

1. Outline the chapter.

2. Show that the law of combination accounts both for many correct perceptions, and for many illusions.

3. Through which of the senses are spatial facts best perceived?

4. "At first, the baby very likely perceives a ball simply as something for him to handle and throw; but, through the medium of blocked response, he comes to perceive it more objectively, i.e., as an object related to other objects, and not simply related to himself." Explain and illustrate this statement.

5. Give an example from the field of auditory perceptions where "isolation" is very much in evidence.

6. Can you see any law analogous to Weber's law in the field of financial profit and loss? Does a dollar gained or lost seem the same amount, without regard to the total amount possessed?

7. Trial and error perception. Go about the room with closed eyes, and identify objects by touching them with the hands. Notice whether your first impression gives place to corrected impressions.

8. Perception of form by "active" and "passive" touch. With the eyes closed, try to distinguish objects of different shapes (a) by letting them simply rest upon the skin, and (b) by handling them. What senses coöperate in furnishing data for "active touch"?

9. Binocular parallax, or the differing views of the same solid object obtained by the two eyes. Hold a small, three-dimensional object a foot in front of the face, and notice carefully the view of it obtained by each eye separately. A pencil, pointing towards the face, gives very different views. What becomes of the two monocular views when both eyes are open at once?

10. Binocular compared with monocular perception of "depth" or distance away. Take a pencil in each hand, and bring the points together a foot in front of the face, while only one eye is open. When the points seem to be nearly touching, open the other eye, and see whether the two points still seem to be close together. Repeat.

REFERENCES

Discussions of perception that are in some respects fuller than the present chapter can be found in C. H. Judd's Psychology, General Introduction, 2nd edition, 1917, pp. 162-194; in Titchener's Textbook of Psychology, 1909, pp. 303-373; and in Warren's Human Psychology, 1919, pp. 232-269.


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CHAPTER XVIII

REASONING


THE PROCESS OF MENTAL, AS DISTINGUISHED FROM MOTOR EXPLORATION

We are still on the general topic of "discovery". Indeed, we are still on the topic of perception; we come now to that form of perception which is different from sense perception. The reasoner is an explorer, and the culmination of his explorations is the perception of some fact previously unknown to him.

Reasoning might be described as mental exploration, and distinguished from purely motor exploration of the trial and error variety. Suppose you need the hammer, and go to the place where it is kept, only to find it gone. Now if you simply proceed to look here and there, ransacking the house without any plan, that would be motor exploration. But if, finding this trial and error procedure to be laborious and almost hopeless, you sit down and think, "Where can that hammer be? Probably where I used it last!" you may recall using it for a

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