Popular scientific lectures

by Ernst Mach

But since you are not satisfied with my brief and obvious answer, you have only yourselves to blame for the consequences. You must now listen to a longer and more learned explanation, such as it is in my power to give.

As the church of science, however, debars the question "Why?" let us put the matter in a purely orthodox way: Man has two eyes, what more can he see with two than with one?

I will invite you to take a walk with me? We see before us a wood. What is it that makes this real wood contrast so favorably with a painted wood, no matter how perfect the painting may be? What makes the one so much more lovely than the other? Is it the vividness of the coloring, the distribution of the lights and the shadows? I think not. On the contrary, it seems to me that in this respect painting can accomplish very much.

The cunning hand of the painter can conjure up with a few strokes of his brush forms of wonderful plasticity. By the help of other means even more can be attained. Photographs of reliefs are so plastic that we often imagine we can actually lay hold of the elevations and depressions.

Fig. 20.

But one thing the painter never can give with the vividness that nature does—the difference of near and far. In the real woods you see plainly that you can lay hold of some trees, but that others are inaccessibly far. The picture of the painter is rigid. The picture of the real woods changes on the slightest movement. Now this branch is hidden behind that; now that behind this. The trees are alternately visible and invisible.

Let us look at this matter a little more closely. For convenience sake we shall remain upon the highway, I, II. (Fig. 20.) To the right and the left lies the forest. Standing at I, we see, let us say, three trees (1, 2, 3) in a line, so that the two remote ones are covered by the nearest. Moving further along, this changes. At II we shall not have to look round so far to see the remotest tree 3 as to see the nearer tree 2, nor so far to see this as to see 1. Hence, as we move onward, objects that are near to us seem to lag behind as compared with objects that are remote from us, the lagging increasing with the proximity of the objects. Very remote objects, towards which we must always look in the same direction as we proceed, appear to travel along with us.

If we should see, therefore, jutting above the brow of yonder hill the tops of two trees whose distance from us we were in doubt about, we should have in our hands a very easy means of deciding the question. We should take a few steps forward, say to the right, and the tree-top which receded most to the left would be the one nearer to us. In truth, from the amount of the recession a geometer could actually determine the distance of the trees from us without ever going near them. It is simply the scientific development of this perception that enables us to measure the distances of the stars.