Cartesian Relativity

13. What is external place?

The words ‘place’ and ‘space’ signify nothing really different from body which is in place.

• They merely designate its size, shape, and location among other bodies.

In order to determine this location, it is necessary to regard other immovable bodies.

As we look to different bodies, we see that the original body at the same time:

• changes its place, from one perspective
• does not change its place, from another perspective.

For example, imagine a ship being carried out to sea.

• A person sitting at the stern might always remain in one place if we look at the parts of the ship, since he preserves the same location with respect to these.
• On the other hand, if we look at the neighbouring shores, the same person will seem to be perpetually changing place. We see him constantly receding from one shore and approaching another.
• If the earth moves from west to east exactly as the ship moves from east to west, we again say that the person at the stern does not change his place. This is because his place will be determined by certain immovable points in the heavens.

I assert that all points are movable in the universe. From this, I conclude that nothing has a permanent place unless it is fixed by our thought.

14. What is the difference between ‘place’ and ‘space’?

The terms ‘place’ and ‘space’ have different meanings.

• ‘Place’ expressly designates location instead of size or shape [i.e. point]

• ‘Space’ expressly designates size and shape [i.e. area]

We often say that a thing succeeds to the place of another, although it is not exactly of the same shape or size.

But we do not therefore admit that it occupies the same space as the other.

When the location is changed, we say that the place also is changed, although there are the same shape and size as before.

So when we say that a thing is in a particular place, we mean merely that it is situated in a determinate way with respect to other objects.

When we add that it occupies such a space or place, we understand besides that it is of such determinate size and shape as exactly to fill this space.

15. How external place is rightly taken for the surfaces of the surrounding body

Thus, we never distinguish space [i.e. area] from length, width, and height.

We sometimes, however, consider place as in the thing placed and at other times as out of it.

Internal place is the same as space.

But external place may be taken for the surfaces that immediately surrounds the thing placed.

‘Surfaces’ here does not mean any part of the surrounding body, but only the boundary between the surrounding and surrounded bodies, which is nothing more than a mode.

At least, ‘surfaces’ in general make no part of one body or another body, but is always considered the same, provided it retains the same size and shape.

If all of a body’s surfaces were changed, it does not mean that its body had changed its place if it stayed in the same location.

Imagine a boat that is carried in one direction by the current of a stream. It is blown by the wind in the opposite direction with an equal force, causing its location with respect to the banks to not change.*

The boat remains in the same place even if the whole ‘surface’* which surrounds it is incessantly changing.