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THE FUNDAMENTAL EQUATIONS FOR ELECTROMAGNETIC PROCESSES IN MOVING BODIES and SPACE AND TIME
THE FUNDAMENTAL EQUATIONS FOR ELECTROMAGNETIC PROCESSES IN MOVING BODIES and SPACE AND TIME
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Hermann Minkowski, the author, was born in 1864 and he died at the early age of thirty-five under an operation for appendicitis. He was a Russian, whose genius led to a Chair being made for him at the University of Gottingen. As I write, a portrait of him is before me. It is the picture of a very young-looking man, with energy and imagination stamped on every feature. The Slavs are like the Celts in this respect. They may be deficient in staying power compared with us who are of Saxon descent, but for flashes of insight they are hard to match.
Minkowski was a teacher. He was little known in his time to the general public. But when the orations of the statesmen and divines of the West have in the main passed into the oblivion which swallows up what is transitory, there will probably endure an address delivered by this professor that is likely to be read even three hundred years hence. It was an address delivered on 21st September, 1908, shortly before Minkowski died, to a meeting of learned persons at Cologne. Learned as many of them were I doubt their having taken in much of the deep significance of the words they listened to. The fiery Slav speaker, flourishing only his stick of 'hiihne Kreide,'' his bold chalk,' and operating with it on the black-board, sought to draw for his audience a picture of the world as in truth four-dimensional, with space and time 'degraded to mere shadows,' leaving nothing of their substance save 'a sort of unitedness of the two.' The burden imposed on the audience was not diminished by the unusual character of the mathematics which the lecturer employed freely. To listen to the address must indeed have been a strain, and yet the occasion was a great one in the history of knowledge. There is an aspect in which the grasp of Minkowski on this occasion suggests itself as of more far-reaching power than any effort to interpret physical reality made before or after his time.
It is worth while to linger over the theme of the orator. For there is underlying it a conclusion which has not always, I think, been fully appreciated—the real reason for the choice of the velocity of light as the constant by reference to which the mathematical physicist actually interprets the varieties of his possible experience.
Minkowski's own view of the general result he had reached may be given in the words used by him as the conclusion of the first part of his famous address: "For the future we shall find in the world no longer one space but an infinite plurality of spaces, just as in three-dimensional space there is an infinite plurality of planes. Three-dimensional geometry has become a chapter of four-dimensional physics." His purpose was, with the suggestiveness of the conception of a four-dimensional world, to so enlarge the conception of its geometry that this could express all the genuine features of that world. But he was holding firmly the idea that to actual experience of the character of that world geometry must refer back for the test of its own applicability and truth. No doubt geometry is in substance a branch of deductive knowledge. Yet in the end it is found to depend for the truth of its deductions—not merely on the abstract fashion in which they are reasoned out— but on the conformity with reality of its primitive assumptions or postulates.
That was why Gauss demanded that a test should be made of the conformity of the postulates of Euclidean geometry to an experimental mensuration of the surface of the earth. To be a science which fits in with the entirety of knowledge the postulates of geometry must accord with exact observation of individual facts. It can resolve into universals as much as it pleases, but it can never in this fashion completely express reality. Back it must come in the end to experience of the object world, and such experience is to be sought, not in the universals of mere logical reflection, but in unique and unambiguous individual objects in perception. We may resolve these into universals indefinitely, but exhaust them we cannot. The logical moment of the particularity of nature will always confront us as a limiting notion which the methods of our geometry cannot eliminate.
Minkowski was a teacher. He was little known in his time to the general public. But when the orations of the statesmen and divines of the West have in the main passed into the oblivion which swallows up what is transitory, there will probably endure an address delivered by this professor that is likely to be read even three hundred years hence. It was an address delivered on 21st September, 1908, shortly before Minkowski died, to a meeting of learned persons at Cologne. Learned as many of them were I doubt their having taken in much of the deep significance of the words they listened to. The fiery Slav speaker, flourishing only his stick of 'hiihne Kreide,'' his bold chalk,' and operating with it on the black-board, sought to draw for his audience a picture of the world as in truth four-dimensional, with space and time 'degraded to mere shadows,' leaving nothing of their substance save 'a sort of unitedness of the two.' The burden imposed on the audience was not diminished by the unusual character of the mathematics which the lecturer employed freely. To listen to the address must indeed have been a strain, and yet the occasion was a great one in the history of knowledge. There is an aspect in which the grasp of Minkowski on this occasion suggests itself as of more far-reaching power than any effort to interpret physical reality made before or after his time.
It is worth while to linger over the theme of the orator. For there is underlying it a conclusion which has not always, I think, been fully appreciated—the real reason for the choice of the velocity of light as the constant by reference to which the mathematical physicist actually interprets the varieties of his possible experience.
Minkowski's own view of the general result he had reached may be given in the words used by him as the conclusion of the first part of his famous address: "For the future we shall find in the world no longer one space but an infinite plurality of spaces, just as in three-dimensional space there is an infinite plurality of planes. Three-dimensional geometry has become a chapter of four-dimensional physics." His purpose was, with the suggestiveness of the conception of a four-dimensional world, to so enlarge the conception of its geometry that this could express all the genuine features of that world. But he was holding firmly the idea that to actual experience of the character of that world geometry must refer back for the test of its own applicability and truth. No doubt geometry is in substance a branch of deductive knowledge. Yet in the end it is found to depend for the truth of its deductions—not merely on the abstract fashion in which they are reasoned out— but on the conformity with reality of its primitive assumptions or postulates.
That was why Gauss demanded that a test should be made of the conformity of the postulates of Euclidean geometry to an experimental mensuration of the surface of the earth. To be a science which fits in with the entirety of knowledge the postulates of geometry must accord with exact observation of individual facts. It can resolve into universals as much as it pleases, but it can never in this fashion completely express reality. Back it must come in the end to experience of the object world, and such experience is to be sought, not in the universals of mere logical reflection, but in unique and unambiguous individual objects in perception. We may resolve these into universals indefinitely, but exhaust them we cannot. The logical moment of the particularity of nature will always confront us as a limiting notion which the methods of our geometry cannot eliminate.
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