The truth is that your eye is so confused by these different lines that it is wholly unable to form any clear estimate of how great the distances really are. This is shown even more clearly in [Fig. 6] (technically known as Zollner’s lines), where you see A B and C D, which have every appearance of being about to meet shortly in the direction of A C. Now if you will measure the distances between B D and A C you will find that the lines are exactly parallel, but the eye has been so deceived by the little cross lines running in different directions, that it seems incredible the two thick lines are not inclined towards one another at quite a considerable angle.
Fig. 4.—Which is longer—A B or C D?
Fig. 5.—The distance from A to B is the same as B to C.
Fig. 6.—Zollner’s lines.
Hills that Don’t Rise
Should it ever happen that you go cycling in France, you will find this deception practiced upon your eyes all day long. The roads in that country are very straight, and are bordered upon either side by tall trees, so that from wherever you stand a long avenue stretches before you to a point where the trees seem to merge into one another, as parallel lines invariably appear to do. But flat as the country may be, you will always find yourself confronted with a gentle incline, as it seems, very slight but none the less perceptible. You brace for a long and steady climb, yet somehow, as you cover the ground, the hill seems always before you and yet there is no noticeable ascent. The reason is simple. There is no ascent. The borders of trees, like the little lines in [Fig. 6], deceive the eyes in a similar way until it is almost impossible to believe that the hill is merely an optical illusion, and that the road is flat as the proverbial pancake.
There is another trick the eye is very fond of playing us. A straight line, held on a level with the eye appears very much shorter than it really is. Look at [Fig. 7], which appears to represent a number of pins lying with their points towards you. Now lift the book to the level of the eyes, close the right one, and they will appear to be sticking upright in the page.