less far into the past.
This is not all; restricted space would not be homogeneous; the different points of this space could not be regarded as equivalent, since some could be reached only at the cost of the greatest efforts, while others could be easily attained. On the contrary, our extended space seems to us homogeneous, and we say all its points are equivalent. What does that mean?
If we start from a certain place A, we can, from this position, make certain movements, M, characterized by a certain complex of muscular sensations. But, starting from another position, B, we make movements M´ characterized by the same muscular sensations. Let a, then, be the situation of a certain point of the body, the end of the index finger of the right hand for example, in the initial position A, and b the situation of this same index when, starting from this position A, we have made the motions M. Afterwards, let a´ be the situation of this index in the position B, and b´ its situation when, starting from the position B, we have made the motions M´.
Well, I am accustomed to say that the points of space a and b are related to each other just as the points a´ and b´, and this simply means that the two series of movements M and M´ are accompanied by the same muscular sensations. And as I am conscious that, in passing from the position A to the position B, my body has remained capable of the same movements, I know there is a point of space related to the point a´ just as any point b is to the point a, so that the two points a and a´ are equivalent. This is what is called the homogeneity of space. And, at the same time, this is why space is relative, since its properties remain the same whether it be referred to the axes A or to the axes B. So that the relativity of space and its homogeneity are one sole and same thing.
Now, if I wish to pass to the great space, which no longer serves only for me, but where I may lodge the universe, I get there by an act of imagination. I imagine how a giant would feel who could reach the planets in a few steps; or, if you choose, what I myself should feel in presence of a miniature world where these planets were replaced by little balls, while on one of these little balls moved a liliputian I should call myself. But this act of imagination would be impossible for me had I not previously constructed my restricted space and my extended space for my own use.
IV
Why now have all these spaces three dimensions? Go back to the "table of distribution" of which we have spoken. We have on the one side the list of the different possible dangers; designate them by A1 , A2 , etc.; and, on the other side, the list of the different remedies which I shall call in the same way B1 , B2 , etc. We have then connections between the contact studs or push buttons of the first list and those of the second, so that when, for instance, the announcer of danger A3 functions, it will put or may put in action the relay corresponding