330 REPORTS ON THE STATE OF SCIENCE, ETC. 



also depends, at least to a considerable extent, on memory. We cannot 

 simultaneously apprehend all the material in a complex perceptual field. 

 This is well known to workers in experimental psychology. Our attention 

 fluctuates rapidly to and fro over the field and the composite impression 

 of which we are conscious is really a blend of memories of features perceived 

 at slightly different instants. Thus the difference between what we 

 ordinarily regard as simultaneous perception of phenomenal relations and 

 successive perceptions is only one of degree. The recognition of the 

 successive appearances of an aspect of any permanent object does not 

 depend on any mysterious power of identifying one relation structure on 

 different occasions, but is simply an instance of the relation we call sameness 

 between relation structures which are separate in perception but are brought 

 together, by memory, for simultaneous comparison. We do not give the 

 relation this name because it implies mathematical similarity or for any 

 reason of that kind. It exists among phenomena as directly perceived, 

 and implies no knowledge of quantitative relations which may or may not 

 be establishable by the indirect processes of physical measurement. It is 

 only in relation structures comprised of measurable magnitudes that 

 mathematical relations have any meaning, and when our perceptual 

 criterion of sameness is applied to relation structures of this kind we have 

 to find empirically the mathematical relation to which it corresponds. 

 We call our relation sameness simply because its unique importance in 

 perception is derived from its continual presentation to us in association 

 with the idea of 'same' objects; but it will, for the reasons already 

 discussed, retain its unique significance whenever we encounter it, whether 

 in successive appearances of the same object or in the successive or 

 simultaneous appearances of different objects. The appearances of two 

 or more objects which happen to exhibit this unique relation between their 

 perceived relation structures will be recognised as the ' same ' appearances 

 just as if they were in fact successive appearances of some one object. 



An important conclusion follows from these considerations which has 

 a bearing on many problems of sensory experience. This is that any 

 phenomenal relations that may be of special significance in cases of 

 simultaneous perception will also be of special significance when the 

 phenomena are separately observed, and vice versa. 



We have already seen that in phenomenal relation structures involving 

 lengths, owing to the varied conditions in which our everyday experience 

 is obtained, the only relations in the structure which are significant for 

 recognition of the object are those which determine the relation-shape of 

 the perceived structure, while those which determine the relation-size play 

 no part in recognition ; and that for such structures the recognitive relation 

 of sameness involves only relation-shape. 



It is easy to see that this must also be the case for structures involving 

 other perceptible extensions. The apparent brightnesses of the various 

 parts of recognisable permanent objects depend on circumstances of 

 observation just as much as their apparent sizes. The illumination by 

 which objects are seen varies over an enormous range, and their perceived 

 brightnesses vary accordingly. Obviously no relations involving absolute 

 brightness will be recognised as uniquely associated with any object. 

 Similarly with sound, any sound pattern, such as a musical chord or a piece 

 of music which we recognise as the ' same thing ' when we hear it on 

 successive occasions may be heard on different occasions at different 

 distances from the source. Its apparent loudness will vary enormously 

 in our experience of it, and there will be no particular loudness in any way 

 uniquely identified with the pattern. 



