110 WHAT IS SCIENCE? 



next two chapters I propose to attempt some answer to 

 these questions. Any answer to these questions that 

 can be attempted here will not, of course, enable any- 

 one to start immediately the study of one of the mathe- 

 matical sciences in the hope of understanding it 

 completely. But if he can be convinced that even in 

 the most abstruse parts of those sciences there is 

 something that he can comprehend and appreciate 

 without the smallest knowledge of mathematics, some- 

 thing may be done towards extending the range of 

 the sciences that are open to the layman. 



WHAT IS MEASUREMENT ? 



Measurement is one of the notions which modern 

 science has taken over from common sense. Measure- 

 ment does not appear as part of common sense until 

 a comparatively high stage of civilization is reached ; 

 and even the common-sense conception has changed 

 and developed enormously in historic times. When I 

 say that measurement belongs to common sense, I only 

 mean that it is something with which every civilized 

 person to-day is entirely familiar. It may be denned, 

 in general, as the assignment of numbers to represent 

 properties. If we say that the time is 3 o'clock, that 

 the price of coal is 56 shillings a ton, and that we have 

 just bought 2 tons of it in all such cases we are using 

 numbers to convey important information about the 

 " properties " of the day, of coal in general, of the coal 

 in our cellar, or so on ; and our statement depends 

 somehow upon measurement. 



The first point I want to notice is that it is only some 

 properties and not all that can be thus represented by 

 numbers. If I am buying a sack of potatoes I may ask 

 what it weighs and what it costs ; to those questions 

 I shall expect a number in answer ; it weighs 56 Ibs. 



