MODERN PHYSICS JEANS 83 



it has been told that they are numbers of apples or pears or bananas 

 or something such. In the same way, the old-fashioned physicist 

 could not rest content with a?, y, and s, but was always ti-ying to ex- 

 press them in terms of apples or pears or bananas. Yet a simple 

 argument will show that he can never get beyond x, y, and z. 



Physical science obtains its knowledge of the external world by 

 a series of exact measurements, or, more precisely, by comparisons 

 of measurements. Typical of its knowledge is the statement that 

 the line Ha in the hydrogen spectrum has a wave length of so many 

 centimeters. This is meaningless until we know what a centimeter 

 is. The moment we are told that it is a certain fraction of the earth's 

 radius, or of the length of a bar of platinum, or a certain multiple 

 of the wave length of a line in the cadmium spectrum, our loiowl- 

 edge becomes real, but at that same moment it also becomes purely 

 numerical. Our minds can only be acquainted with things inside 

 themselves — never with things outside. Thus we can never know 

 the essential nature of anything, such as a centimeter or a wave 

 length, which exists in that mysterious world outside ourselves to 

 which our minds can never penetrate ; but we can know the numerical 

 ratio of two quantities of similar nature, no matter how incompre- 

 hensible they may both be individually. 



For this reason, our knowledge of the external world must always 

 consist of numbers, and our picture of the universe — the synthesis 

 of our knowledge — must necessarily be mathematical in form. All 

 the concrete details of the picture, the apples and pears and bananas, 

 the ether and atoms and electrons, are mere clothing that we ourselves 

 drajDe over our mathematical symbols — they do not belong to Nature, 

 but to the parables by which we try to make Nature compreh-insible. 

 It was, I think, Kronecker who said that in arithmetic God made 

 the integers and man made the rest; in the same spirit, we may 

 add that in physics God made tlie mathematics and man made the 

 rest. 



The modern physicist does not use this language, but he accepts 

 its implications, and divides the concepts of physics into observ- 

 ables and unobservables. In brief, the observables embody facts of 

 observation, and so are purely numerical or mathematical in their 

 content ; the unobservables are the pictorial details of the parables. 



The physicist wants to make his new edifice earthquake proof — 

 immune to the shock of new observations — and so builds only on 

 the solid rock, and with the solid bricks, of ascertained fact. Thus 

 he builds onlj^ with observables, and his whole edifice is one of 

 mathematics and mathematical formulae — all else is man-made 

 decoration. 



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