### 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. But the essential understanding of placement being another level of location.

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((a,b))b. a and b are any real numbers. Each location (a,b) is at its usual place a( )b.

There can be some physical thing occupying a space of locations, such as an elementary particle. Then we can say that the underlying geometry is that where we allow a location to have more than one placement. At the start we may have an object in two locations of locations and then one of the locations may move away and we have two of the same location at two different placements. For then a particle can have two placements. It can be at either placement at any time.

For in this system time must exist for the location has to spend some time in one placement and some time in the other. We can have a particle switching placements at any time.

That a path that a particle may undergo may be many instead of one can be seen from this perspective, since the paths are all through placement space.

At the beginning the geometry can be that where we start with every placement having two locations. This way of starting is similar to the many worlds interpretation. Then at the start any one object may have two of the same location.

There is a wave/particle duality which can be seen.

We can move locations in a closed loop as in the case of the popular ‘string theory’ and we can have a geometry where two or more locations share the same placement. This is called a sharing. The parts of a sharing are indistinguishable.

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