376 THE REAL WORLD 



strued in terms of the local displacements of the unchanging. But our 

 preference for corpuscular theories has also a strongly "objective" 

 justification. Our pursuit of such theories does not ensure that we 

 will not have indefinitely to multiply species of "particles," the "qual- 

 ities" thereof, and the "kinds" of local displacements— much as we 

 find it necessary to multiply Ptolemaic epicycles, states of phlogisti- 

 cation, or, for that matter, caprices of Homeric gods. That corpuscu- 

 lar thinking leads to theoretic systems of immense correlative index 

 is not our invention but our discovery— and this not just a discovery 

 about ourselves but also about the world. 



The cross-fix. From a shadow cast on the wall of a cave we infer 

 the existence of some specific object ouside. Going outside the cave, 

 we easilv observe whether our inference has been correct. Whether 

 atoms, electrons, and other such inferred entities are "real" is, how- 

 ever, an issue not as simply resolved. For in this case we can find no 

 operation cognate with "going outside the cave," to look at the thing- 

 in-itself. Even so, Born's deeper exploration of the metaphor strongly 

 suggests that certain other important resources are still open to us. 



Cut out a figure, say a circle, of a piece of cardboard and observe its 

 shadow thrown by a distant lamp on a plane wall. The shadow of the 

 circle will appear in general as an ellipse, and by turning your card- 

 board figure you can give to the length of an axis of the elliptical 

 shadow any value between almost zero and a maximum. That is the 

 exact analogue of the behavior of length in relativity which in difi^er- 

 ent states of motion may have any value between zero and a maxi- 

 mum. . . . the simultaneous observation of the shadows on several 

 different planes [of known mutual inclination] suffices to ascertain the 

 fact that the original cardboard figure is a circle and to determine 

 uniquely its radius. The radius is what mathematicians call an in- 

 variant for the transformations produced by parallel projection. . . . 

 Most measurements in physics are not directly concerned with the 

 things that interest us, but with some kind of projection, this word 

 taken in the widest possible sense. . . . 



This description applies to any quantum effect. An observation or 

 measurement does not refer to a natural phenomenon as such, but to 

 its aspect from, or its projection on, a system of reference which as a 

 matter of fact is the whole apparatus used. . . . 



The main invariants are called charge, mass (or rather: rest-mass), 

 spin, etc.; and in every instance, when we are able to determine these 

 quantities, we decide we have to do with a definite particle. I main- 



