First: How do we know about the physical world? We have already seen that this question cannot have a simple answer, since the basis of inference is something that happens in our own heads, and our knowledge of anything outside our own heads must be more or less precarious. For the present, I shall take it for granted that we may accept testimony, with due precautions. In other words, I shall assume that what we hear when, as we believe, others are speaking to us, does in fact have “meaning” to the speaker, and not only to us; with a corresponding assumption as regards writing. This assumption will be examined at a later stage. For the present, I will merely emphasise that it _is_ an assumption, and that it may possibly be false, since people seem to speak to us in dreams, and yet, on waking, we become persuaded that we invented the dream. It is impossible to prove, by a demonstrative argument, that we are not always dreaming; the best we can hope is a proof that this is improbable. But for the present let us leave this discussion on one side, and assume that the words we hear and read “mean” what they would if we spoke or wrote them. On this basis, we have reason to know that the worlds of different people are alike in certain respects and different in certain others. Take, for example, the audience at a theatre: they all, we say, hear the same words and see the same gestures, which, moreover, are those that the actors wish them to hear and see. But those who are near the stage hear the words more loudly than those further off; they also hear them somewhat earlier. And those who sit on the right do not see quite what is seen by those who sit on the left or in the centre. These differences are of two sorts: on the one hand, some people can see something invisible to others; on the other hand, when two people, as we say, see the “same” thing, they see it differently owing to effects of perspective and of the way the light is reflected. All this is a question of physics, not of psychology; for if we place a camera in an empty seat in the theatre, the perspective in the resultant photograph is intermediate between the perspectives that are seen by persons sitting on either side; indeed the whole matter of perspective is determined by quite simple geometrical laws. These laws show also what is common to the shapes that two people see when they see the “same” thing from different points of view: what is common is what is studied by projective geometry, which is concerned with what is independent of measurement in geometrical figures. All the differences in appearance due to perspective have to be learned in learning to draw: for this purpose, it is necessary to learn to see things as they really seem, and not as they seem to seem.