To the pure geometer the radius of curvature is an incidental characteristic — like the grin of the Cheshire cat. To the physicist it is an indispensable characteristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the "cat without a grin" and the "grin without a cat" are equally set aside as purely mathematical phantasies.

I think that science would never have achieved much progress if it had always imagined unknown obstacles hidden round every corner. At least we may peer gingerly round the corner, and perhaps we shall find there is nothing very formidable after all.

A star is drawing on some vast reservoir of energy by means unknown to us. This reservoir can scarcely be other than the sub-atomic energy which, it is known, exists abundantly in all matter; we sometimes dream that man will one day learn to release it and use it for his service. The store is well-nigh inexhaustible, if only it could be tapped.

The present revolution of scientific thought follows in natural sequence on the great revolutions at earlier epochs in the history of science. Einstein's special theory of relativity, which explains the indeterminateness of the frame of space and time, crowns the work of Copernicus who first led us to give up our insistence on a geocentric outlook on nature; Einstein's general theory of relativity, which reveals the curvature or non-Euclidean geometry of space and time, carries forward the rudimentary thought of those earlier astronomers who first contemplated the possibility that their existence lay on something which was not flat. These earlier revolutions are still a source of perplexity in childhood, which we soon outgrow; and a time will come when Einstein's amazing revelations have likewise sunk into the commonplaces of educated thought.

The atom is as porous as the solar system. If we eliminated all the unfilled space in a man’s body and collected his protons and electrons into one mass, the man would be reduced to a speck just visible with a magnifying glass.

Relativity physics is especially interested in invariants, and it has discovered and named a few more. It is a common mistake to suppose that Einstein’s theory of relativity asserts that everything is relative. Actually, it says: 'There are absolute things in the world but you must look deeply for them. The things that first present themselves to your notice are for the most part relative'.

"For ten years we have had to divide modern science into two compartments: we have one set of beliefs in the classical compartment and another set of beliefs in the quantum compartment. Unfortunately, our compartments are not watertight. We must, of course, look forward to an ultimate reconstruction of our conceptions of the physical world which will embrace both the classical laws and the quantum laws in harmonious association. There are still some who think that the reconciliation will be effected by a development of classical conceptions. But the physicists of what I may call "the Copenhagen school" believe that the reconstruction has to start at the other end, and that in the quantum phenomena we are getting down to a more intimate contact with Nature’s way of working than in the coarse-grained experience which has furnished the classical laws."

SELECTIVE SUBJECTIVISM

Let us suppose that an ichthyologist is exploring the life of the ocean. He casts a net into the water and brings up a fishy assortment. Surveying his catch, he proceeds in the usual manner of a scientist to systematise what it reveals.
He arrives at two generalisations :

(1) No sea-creature is less than two inches long.
(2) All sea-creatures have gills.

These are both true of his catch, and he assumes tentatively that they will remain true however often he repeats it.

In applying this analogy, the catch stands for the body of knowledge which constitutes physical science, and the net for the sensory and intellectual equipment which we use in obtaining it. The casting of the net corresponds to observation; for knowledge which has not been or could not be obtained by observation is not admitted into physical science.

An onlooker may object that the first generalisation is wrong. “There are plenty of sea-creatures under two inches long, only your net is not adapted to catch them. The ichthyologist dismisses this objection contemptuously. “Anything uncatchable by my net is ipso facto outside the scope of ichthyological knowledge, and is not part ot the kingdom of fishes which has been defined as the theme of ichthyological knowledge. In short, what my net can't catch isn’t fish.” Or — to translate the analogy — If you are not simply guessing, you arc claiming a knowledge ot the physical universe discovered in some other way than by the methods of physical science, and admittedly unvenfiablc by such methods. You are a metaphysician. Bah !

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