20 THE PHILOSOPHY OF BIOLOGY 



such a way as to involve the least exertion ; they are 

 the shortest distances between two points, and if we 

 deviate from them we exert a greater degree of activity 

 than if we had moved along them. For us there is 

 only one straight line that can be drawn between 

 two points, but this is not necessarily true for our 

 Infusorian, and its straight line need not be the shortest 

 distance between two points. It might be either the 

 longest or the shortest distance between the points, 

 for the latter can always be placed on a great circle 

 passing through the two points and the poles of the 

 egg, and in moving from a point on which it is placed 

 the animal could reach the other point by moving 

 in two directions, just as we could go round the earth 

 along the equator by moving to the east or to the west. 

 Therefore the straight line of the Infusorian would be 

 not only a scalar quantity but a vector quantity, that 

 is, it would represent, not only a quantity of energy, 

 but a quantity of energy that has direction. For us 

 only one straight line can be drawn between two 

 given points, but this limitation would not exist in 

 the two-dimensional geometry of a curved surface. 

 Suppose that the two points are situated on a great 

 circle and that they are exactly 180 apart ; then the 

 Infusorian could move from one pole to another pole 

 along an infinite number of straight lines or meridians 

 all of which had a different direction, but all of 

 which were of the same length ; that is to say, in 

 this geometry an infinite number of straight lines can 

 be drawn between the same two points. Again, its 

 triangles might be different from ours ; our triangles 

 are figures formed by drawing straight lines between 

 three points, and on a plane surface the sum of the 

 angles of the triangle are together equal to two right 

 angles, though on a curved surface they may be greater 



