### First page of notes

This note starts with the two locations A and B. But the space we are in is like two overlapping shadows, since we also have the further background of placements. That is, there is another coexisting plane where locations can be in other places, different from where they usually are relative to each other.

In order for a location to itself have another ‘location’ we need to have a coexisting plane which gives another ‘placement’ to any location. We give a new name to a ‘location’ of a location, since we can’t use the name ‘location’ again.

Let a plane of placements be created and coexist with a plane of locations. At the beginning a set of second co-ordinates is created. ((a,b),((a,b))). a and b are any real numbers. Each location (a,b) is at its usual place ((a,b)).

We can move locations in a closed loop or we can have a geometry where two or more locations share the same placement. This is called a joining. The parts of a joining are indistinguishable.

Then with A and B we can move A and B through other locations (creating a line of joinings) to a center where we have three locations and one placement.