114 THE ANATOMY OF SCIENCE 



world is continuous or discontinuous it is more 

 than we can answer. 



Put more modestly, the question is: Can the 

 body of facts which are at our disposal be em- 

 braced in a set of principles which suggest the 

 properties of an ideal continuum, or shall we 

 select a set of principles based upon a discon- 

 tinuum, or finally must we adopt one method 

 for one set of facts and the other for another? 

 Shall we use a continuous mathematics, such as 

 geometry, or a discontinuous mathematics, such 

 as the theory of integral numbers and rational 

 fractions ? 



Perhaps the answer is suggested by our dis- 

 cussion in the first chapter, where we saw that 

 in the process of growing thought the integers, 

 once invented, began, as it were, to spin about 

 themselves a continuous web until they became 

 mere singular points embedded in the contin- 

 uum of the general number series. A discon- 

 tinuum includes only discontinua, but the con- 

 tinuum includes the discontinuum within itself. 

 Being therefore the more general, it would seem 

 that the continuum must continue to remain as 

 a background of our scientific thought. 



The science of hydrodynamics presupposes a 

 fluid continuum, and no experiments on the 



