THE REAL WORLD 375 



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would never be challenged— because to the human sense of ration- 

 ality it must always seem the simplest of geometries, and so be 

 chosen and enforced as a matter of convention. Both were wrong— 

 Poincare because he had failed duly to appreciate Duhem's point. 

 In science we judge the aggregate correlative index of an entire 

 theoretic constellation of which the geometry is but one part. How- 

 ever simple in itself, Euclidean geometry can be maintained, we find, 

 only by introducing serious complications elsewhere in the constel- 

 lation of theories. Thus at last we feel driven to conceive Euclidean 

 geometry subordinate to Riemann's, and we are so driven by discov- 

 ery of something sufficiently objective to fall quite beyond the con- 

 trol of a very strong human predilection. 



The principles today provisionally conventionalized simply cannot 

 be dismissed as purely human inventions. Always they turn on an 

 irreducible element of substantive discovery. The principle of de- 

 terminism Frank supposed humanly unchallengeable is today chal- 

 lenged—but not until long after Einstein had pointed out the genuine 

 discovery that still makes the principle more than a convention. 

 Frank reports that Einstein 



. . . agreed with me that, whatever may happen in nature, one can 

 never prove that a violation of the law of causality [i.e., the principle 

 of determinism] has taken place. One can always introduce by con- 

 vention a terminology by which this law is saved. But it could happen 

 that in this way our language and terminology might become highly 

 complicated and cumbersome. What is not conventional ... is 

 the fact that we can save this law by using a relatively simple 

 terminology: we are sure that a state A has recurred when a small 

 number of state variables have the same values that they had at the 

 start. This "simplicity of nature" is the observable fact which cannot 

 be reduced to a convention on how to use some words. 



The concept "energy" is no doubt a human invention, and nothing 

 originally excluded the possibility that a limitless variety of "species 

 of energy" would be required for the conservation we insist on main- 

 taining. Yet, though we must postulate a considerable number of 

 species, the number is still remarkably small. This is a discovery and 

 it invests the energy principle with a status more substantial than 

 that of any purely human convention. Consider a second example. 

 Doubtless the contemporary human sense of rationality powerfully 

 enforces the regulative principle that qualitative change is to be con- 



