October 28, 1922] 



NA TURE 



569 



All is static. Dynamics has been resolved away. We 

 can no longer ask about causes ; that is to go back 

 to the human point of view. We can simply gaze upon 

 the scene and seek to catch some of its salient features. 

 So far as our present conceptions go, one of the most 

 striking things about the picture will be that it is 

 fibrous. The tangible part of it will be a great number 

 of threads, one-dimensionalities. These represent elec- 

 trons. Mere mortals think of them as moving points, 

 but with our new vision we see them as continuous 

 threads. These are chiefly present in bundles, twisted 

 together into ropes ; what are these ? They are the 

 material bodies of the mortals. One is an atom. 

 Another, much more complex, is a man ; another is a 

 chair. The former in one part is gathering more threads 

 to itself ; in another part the threads unravel and 

 dissipate. Such is life. In one part the chair-rope 

 and the man-rope are in contact ; the man is sitting 

 on the chair. But of the behaviour of man as mortal 

 the picture tells us little. We must become mortal 

 and see only sections of the picture before we can see 

 him as a living being with an unfolding consciousness. 

 If the poet and the mystic do indeed aspire to free 

 themselves from the fetters of time and space, as we 

 read in the concluding passage of the lecture, we fear 

 that they will find but little left either of poetry or of 

 mystery in the world after which they yearn. 



But, leaving the poet aside, and returning to the 

 physicist, what is left for him in the great synthesis of 

 all science into the one map of all events ? What 

 becomes of his vocation of measurement ? As Prof. 

 Eddington emphasises again and again, he too, with 

 all his experiments, is in the picture. His rules, scales, 

 clocks, photographic plates are all there ; their whole 

 history is depicted. All his experiments of measure- 

 ment are represented by the passage through the 

 picture of the threads that represent the marks on the 

 scales, meeting and intersecting the threads that 

 represent other particles of matter. The four-dimen- 

 sional picture itself is not to be measured. It contains 

 within itself the process of measurement in the ordinary 

 three-dimensional world and all the results are recorded 

 for us to read. We have no four-dimensional scale 

 which we may move about and apply to different parts 

 of the picture for the sake of comparison. We merely 

 stand, look, and try to read what we see. 



Perhaps Prof. Eddington does not see the picture 

 quite in this way. Perhaps the " world " for him is 

 a four-dimensional continuum in which our threads are 

 merely lines of singularity. He seems to contemplate 

 as " measurable " the intervals between pairs of points 

 in this continuum which do not correspond to events 

 in the history of any particle or electron in the material 

 universe. But we wish to ask him how these intervals 

 NO. 2765, VOL. I io] 



are in practice to be measured. He says, " When we 

 have mastered the geometry of the world we shall 

 have inevitably learnt the mechanics of it." That is 

 so. A complete description of the world lines of all 

 particles necessarily tells us all about the phenomena 

 of motion. 



But to master the geometry of the world means to 

 describe its main features by means of a few simple 

 propositions. In Prof. Eddington's view, the process 

 consists in measuring all the intervals between all pairs 

 of neighbouring events, and then in examining whether 

 these intervals will fit together in an Euclidean fashion, 

 or in a particular type of non-Euclidean scheme. If we 

 discover that they will fit in a recognised and manage- 

 able mathematical scheme, we have mastered the geo- 

 metry of the world. 



But we ask again how are these intervals to be 

 measured. Since all measurements are contained in 

 the picture, and since for the description of the 

 picture event by event no system of intervals is 

 necessary, the whole of our experimental measure- 

 ments have nothing at all to do with a scheme of 

 intervals, and any geometrical system whatever may be 

 used for the purpose of attaching intervals. What, 

 then, is it which discriminates between Einstein's 

 system and any other possible one ? It is simply this, 

 that if we adopt that system, the facts of the motions 

 of particles or of the propagation of light can be 

 expressed in a very simple form. The path of Mercury, 

 for instance, is a geodesic. Possibly this fact may be 

 further analysed and shown to follow from the con- 

 figuration of the electron being spherical. But in any 

 case we cannot measure the tube which would represent 

 such an electron in the super-world of four dimensions. 

 Thus Einstein's law of gravitation, by itself, is not 

 a statement about the world at all. It is only when it 

 is taken in conjunction with some other hypotheses, 

 such as that the path of a particle is a geodesic, that 

 it predicts anything, and becomes capable of experi- 

 mental test. The world itself cannot be said to be 

 either Euclidean or non-Euclidean, for it does not 

 furnish us with definite values for the intervals between 

 all pairs of events in the continuum. We may say 

 that the world-phenomena are more simply described 

 on the basis of a non-Euclidean system than on a 

 Euclidean system ; but it is surely not allowable to go 

 further and say that this is " because the world is not 

 a Euclidean or flat world." Prof. Eddington would 

 perhaps reply that for him the world is nothing more 

 than the measurements that we make of it, and that 

 these measurements do not fit in a Euclidean scheme. 

 But this brings us round again to the same question, 

 what is meant by measurements of the four-dimensional 

 whole ? We would ask our lecturer to give us a sequel 



S I 



