What we know about the physical world, I repeat, is much more abstract, than was formerly supposed. Between bodies there are occurrences, such as light waves; of the _laws_ of these occurrences, we know something—just so much as can be expressed in mathematical formulæ—but of their _nature_ we know nothing. Of the bodies themselves, as we saw in the preceding chapter, we know so little that we cannot even be sure that they are anything: they _may_ be merely groups of events in other places, those events which we should naturally regard as their effects. We naturally interpret the world pictorially; that is to say, we imagine that what goes on is more or less like what we see. But in fact this likeness can only extend to certain formal logical properties expressing structure, so that all we can know is certain general characteristics of its changes. Perhaps an illustration may make the matter clear. Between a piece of orchestral music as played, and the same piece of music as printed in the score, there is a certain resemblance, which may be described as a resemblance in structure. The resemblance is of such a sort that, when you know the rules, you can infer the music from the score or the score from the music. But suppose you had been stone deaf from birth, but had lived among musical people. You could understand, if you had learned to speak and to do lip-reading, that the musical scores represented something quite different from themselves in intrinsic quality, though similar in structure.[16] The value of music would be completely unimaginable to you, but you could infer all its mathematical characteristics, since they are the same as those of the score. Now our knowledge of nature is something like this. We can read the scores, and infer just so much as our stone-deaf person could have inferred about music. But we have not the advantages which he derived from association with musical people. We cannot know whether the music represented by the scores is beautiful or hideous; perhaps, in the last analysis, we cannot be quite sure that the scores represent anything but themselves. But this is a doubt which the physicist, in his professional capacity, cannot permit himself to entertain. [16] For the definition of “structure,” see the present author’s _Introduction to Mathematical Philosophy_.