SPACE AND GEOMETRY 61 



of a transformation which will make the line 

 OA go into OB and OB into OC, while the line 

 OA' goes into OB', which in turn goes to OC ; 

 and I shall venture to call this a rotation. 



Here I follow the distinguished precedent of 

 Humpty Dumpty in Through the Looking- 

 Glass who said, "When I use a word it means 

 just what I choose it to mean — ^neither more 

 nor less." Of course Humpty Dumpty and I are 

 both wrong, for it is impossible to free a word 

 from all its countless implications, unless we 

 make it out of the whole cloth, as the word 

 "gas" was once supposed to have been made. 

 But here the point is that it seems wiser to 

 emphasize the resemblances rather than the dif- 

 ferences between the old and new types of rota- 

 tion. You may prefer to call the new process 

 absurd or irrational rotation, and indeed ex- 

 tending the word 'rotation' to cover this new 

 asymptotic rotation is very much like extend- 

 ing the word 'number,' which referred origi- 

 nally to integers, to include fractions, and later 

 irrational fractions. 



Enlarging the meaning of rotation implies 

 also an extension of the meaning of distance, 

 because we have agreed to abide by the rules 

 of our transformation in comparing the length 



