SPREAD OF UNDERSTANDING ■> 



most conspicuous but the least important of them, we use only 

 ten symbols to write any number. That is, our system is decimal. 

 The beauty of this is that the number of figures is so small. It 

 might have been smaller still — a system of eight figures would 

 have done very well — or else, a little larger — twelve would have 

 made an ideal set — but not much larger without sensibly increas- 

 ing the difficulty of computations. For in the case of a duodeci- 

 mal system, our children would have to learn by rote their table 

 of multiplication up to 12, and so on. Why did we choose ten? 

 The reason is simply that our ancestors made their family ac- 

 counts on their fingers or on their toes, and they happened to 

 be, just like ourselves, ten-fingered and ten-toed. Ten thus be- 

 came naturally the basis of their numeration. It is true that some 

 other people developed other systems: the Babylonians used the 

 basis sixty and the Mayas — most intelligent of the original Amer- 

 icans — the basis twenty. However, the basis ten is now almost 

 universally used, at least as far as the numbers themselves are 

 concerned. 



The second idea is what we now call the principle of local 

 value. That is the very heart of this immense discovery. When 

 we write 324, for example, we mean to represent a collection 

 constituted by 4 units, plus 7 tens, plus 3 hundreds. We know 

 at once that the 3 stands for hundreds, for it is written at the 

 third place from the right; if it were written at the seventh place, 

 it would mean 3 millions. 



The third idea is, so to say, an elaboration of the second : what 

 would one do if there were no units of a certain order? How 

 should we write three millions and four hundreds, for example? 

 One might leave an open space between the 4 and the 3, and 

 another between the 3 and a final dot, but that would be very 

 ambiguous. Some unknown genius (or, maybe, many) hit upon 

 the device of creating a special symbol, the zero, representing 

 no number, but to be used only to mark that units of a certain 

 order were missing. Thus if we write 3,000,400 there can be 

 no misunderstanding. A careful definition of the new symbol 



