# Interactive Online Tutoring Services

## July 17, 2016

### moving circle of locations, translation of locations and addition of locations

Filed under: knot idea outline,the link between l*l and e and p — Rob @ 7:24 pm

We say that a point has a location. But I want to say that that specific point or location can have another ‘location of location’ in relation to the plane of other locations.

To do this I put a plane of l*l a(     )b in so that every location (a,b) has an l*l- a(     )b. We stop at only two levels for now. So every location of the plane has a ‘location’ itself. These two together, the location of the location, and the location itself are called the second co-ordinates and take the form a((c,d)*(e,f)*…))b.

Each placement of a location initially acts as a center for its specific location. Any location can move away from its center. There can be different types of movement. Sometimes, in order for a location to move we have to create a ‘joining’ of two locations. Locations can ‘join’ with other locations. This is discussed a little later.

One thing we can do is move a circle of locations through a coincident circle of l*l. Underlined in red are locations, moving around 90 degrees clockwise through the coincident level of l*l. The plane can be divided into two types of locations. e-type parts and p-type parts. The circle of e-type parts can move through a circle of p-type parts defined in a plane of fixed p-type locations coincident to a plane of placements.

Also I can translate, for example the location (0,0) at the l*l-0(     )0 to the l*l-1(     )1. But (0,0) is not in isolation. It has to be in combination with other locations in order to get to and to be at 1(     )1.

Let it be in ‘joining’ with other locations. Two locations can be in joining if they share the same l*l. Notate this with a *. Then when (0,0) reaches ((1,1)) we can notate this (0,0)*(1,1). This is an expanded notation. Both locations (0,0) and (1,1) are at the l*l- 1(     )1. To express this, I cannot write them on top of one another, so I use this notation. This can be notated 1((0,0)*(1,1))1.

Both locations are in the same place, but there are two locations there and not one. Since l*l exist as a background level, we have a place to put (0,0)*(1,1). Whereas before there was no background level where I could put one location relative to another. Now we can put two in the same place, before we couldn’t identify two locations to the same place.

(0,0)*(1,1) can be thought of as sharing placement akin to two overlapping shadows appearing on a plane surface, the plane surface being a plane of l*l and the overlapping shadows thought of as overlapping locations-think of the shadows as locations themselves. As described elsewhere in this weblog, if the shadows come from two light sources, and I remove one light, one shadow remains.