154 WHAT IS SCIENCE? 



I do not feel confident that I can explain the matter 

 further to those who have not some knowledge of both 

 physics and mathematics, but I must try. The laws 

 on the analogy with which theories of the older type are 

 based were often (in physics, usually) numerical laws, 

 such laws for example as that of the falling body. Now 

 numerical laws, since they involve mathematical relations, 

 are usually expressed, not in words, but in the symbols in 

 which, as every one knows, mathematicians express their 

 ideas and their arguments. I have been careful to avoid 

 these symbols; until this page there is hardly an "x" 

 or a " y " in the book. And I have done so because 

 experience shows that they frighten people ; they make 

 them think that something very difficult is involved. 

 But really, of course, symbols make things easier ; it is 

 conceivable that some super-human intellect might be 

 able to study mathematics, and even to advance it, 

 expressing all his thoughts in words. Actually, the 

 wonderful symbolism mathematics has invented make 

 such efforts unnecessary ; they make the processes 

 of reasoning quite easy to follow. They are actually 

 inseparable from mathematics ; they make exceedingly 

 difficult arguments easy to follow by means of simple 

 rules for juggling with these symbols interchanging 

 their order, replacing one by another, and so on. The 

 consequence is that the expert mathematician has a 

 sense about symbols, as symbols ; he looks at a page 

 covered with what, to anyone else, are unintelligible 

 scrawls of ink, and he immediately realizes whether the 

 argument expressed by them is such as is likely to satisfy 

 his sense of form ; whether the argument will be " neat " 

 and the results " pretty." (I can't tell you what those 

 terms mean, any more than I can tell you what I mean 

 when I say that a picture is beautiful.) 



Now sometimes, but not always, simple folk can 

 understand what he means ; let me try an example, 



