[56] “The Principles of Natural Knowledge.”
[57] In the present chapter we are classing under the common name of “neo-realism” all those metaphysical doctrines which agree in considering perception, especially visual perception, a matter of direct apprehension. This classification may not be in accord with that of the metaphysicians. But as, from the standpoint of science, all doctrines that hold to the theory of the direct apprehension of reality are equally objectionable, we shall not trouble to differentiate between them.
[58] By giving the same name to these two conflicting types of simultaneity, Dr. Whitehead soon falls a victim to his own terminology. Thus, in his book, “The Theory of Relativity,” he informs us that he accepts Einstein’s discovery of the relativity of simultaneity. But in so doing he does not appear to notice that the type of simultaneity which Einstein has proved to be relative to motion is the scientific type; and it has nothing in common with the neo-realistic type. This latter species is never relative to motion, but solely to position. Hence, without any justification whatsoever, Whitehead has suddenly extended to his own understanding of simultaneity a characteristic which belongs to the type he is attacking. But owing to the same name having been given to the two types, the non-scientific reader is apt to overlook the confusion, and in this way be led to a very erroneous understanding of the nature of Einstein’s discoveries.
[59] The majority of Dr. Whitehead’s views are unfortunately couched in such loose and obscure terms that it is usually possible to place a variety of conflicting interpretations upon them. As he himself candidly admits in his book, “The Principles of Natural Knowledge”: “The whole of Part II, i.e., Chapters V to VII, suffers from a vagueness of expression due to the fact that the implications of my ideas had not shaped themselves with sufficient emphasis in my mind.”
Obviously, if the author of a book is not quite clear as to what he means, there is always some danger in settling the matter for him. Accordingly, we should have omitted any reference to Dr. Whitehead’s writings had it not been that some of his criticisms (though totally erroneous in our opinion) are often of considerable interest, leading as they do to a novel vision of things. At any rate, in any further reference to Whitehead, we shall view his criticisms in the light of type-objections, regardless of whether or not, as interpreted by us, they depict his own personal views.
[60] Italics ours.
[61] For the present we are confining ourselves to the consideration of Galilean frames; the problem becomes highly complicated when we study the peculiarities arising from a choice of accelerated frames. In this latter case, a non-Euclideanism, or curvature of space, appears with the presence of acceleration (as also of gravitation), so that we cannot even refer to a multiplicity of superposed Euclidean spaces. Also, space and time become so hopelessly confused that we are compelled to express ourselves in terms of four-dimensional space-time, where everything becomes clear once more.
[62] Conformal transformations are those which vary the shape of lines while leaving the values of their angles of intersection unaltered. They are of wide use in maps, e.g., in Mercator’s projection or in the stereographic projection.
