1885.] 
8i 
Space and its Dimensions. 
is told that 3 3 represents the number of square inches in a 
square whose side is 3 inches long. The boy replies 
“ You have been teaching me to raise numbers to the third 
povvei , I suppose 3 must mean something in geometry* 
what does it mean ?” “ Nothing at all, replied I, not at 
least in geometry, for geometry has only two dimensions.” 
I he authoi then pioceeds to show his grandson how a point 
by moving through a length of three inches makes a line of 
three inches, which may be represented by 3; and how a 
line of three inches, moving parallel to itself through a length 
of three inches makes a square of three inches everyway 
which may be represented by 3*. Thereupon the boy re- 
turned “ W ell, then, if a point by moving three inches makes 
a line of three inches represented by 3, and if a straight line 
of three inches moving parallel to itself makes a square of 
three inches every way, represented by 3% it must be that a 
square of three inches every way, moving somehow parallel 
to itself, must make a something else of three inches every 
way, and this must be represented by 3 V’ J 
As a punishment for this heretical and paradoxical out- 
break the boy is sent to bed. Shortly afterwards our hero 
becomes conscious of a presence in the room. Seeing, how- 
ever, nothing, he soliloquises “ The boy is a fool, I say ; 
3 3 can have no meaning in geometry.” To his horror a 
voice replies “ The boy is not a fool, and 3 s has an obvious 
geometrical meaning.” 
Not to enter into details, our Flatlander finds that he has 
a visitor from the three-dimensional world, who endeavours 
though vainly, to open his eyes to the comprehension of 
space and body as it appears to us. At last the stranger 
soars away with him into a new world where wonderful reve- 
lations await him. fie is introduced to cubes, and he learns 
to distinguish between a circle and a sphere, a plane figure 
and a solid. But he now curiously turns the tables upon 
his guide. Having mastered the idea of three-dimensional 
existence he craves to go higher. He pleads : — “ What, 
therefore, more easy than now to take thy servant into the 
blessed region of the fourth dimension, where I shall look down 
upon this land of three dimensions, and see the inside of every 
three-dimensioned house, the secrets of the solid earth, the 
treasures of the mines in Spaceland, and the intestines of 
every solid living creature, even of the living and adorable 
spheres.” To his disappointment he is told “ There is no 
such land ; the very idea of it is utterly inconceivable.” 
But our Flatlander refuses to be so silenced. He quotes 
the words used by his guide when instructing him in the 
