The fourth dimension

FOUR-DIMENSIONAL SPACE 5

Bringing in a third quality, say sharpness, I can draw, as in fig. 3, any number of upright

G lines. Let distances along these

upright lines represent degrees of

p 2 sharpness, thus the points F and G A 6B ¢ will represent swords of certain Fig. 3. definite degrees of the three qualities

mentioned, and the whole of space will serve to represent all conceivable degrees of these three qualities.

If now I bring in a fourth quality, such as weight, and try to find a means of representing it as I did the other three qualities, I find a difficulty. Every point in space is taken up by some conceivable combination of the three qualities already taken.

To represent four qualities in the same way as that in which I have represented three, I should need another dimension of space.

Thus we may indicate the nature of four-dimensional | space by saying that it is a kind of space which would give positions representative of four qualities, as threedimensional space gives positions representative of three qualities.