I have finished the matrix math level of tree investigation and I am up one node. I seems a bit convolved and poorly explained by most, but I get the relationships now. Any array can be identified in the computer by something like A[i][j] ==. So any element of the resultant matrix can be specified as an equation and the process can be viewed by what it does. I have used matrices extensively, and I can just punch them into my calculator to find a solution. I wanted to know why as well as how. Now I have a sense of what an Identity matrix really means in the same way that I look at a Rubik's cube and can see the relationships of sets, order, association, faces, vectors, methods, and colors which define their interaction to produce products and precursor states.

It is somewhat anti-climactic, as I imagined it to be very profound and in a way it is just shorthand.

Something else to consider. Why do we define things as squares to begin with? I could just as well say, "How many circles fit in a square?", as opposed to how many squares fit in a circle. Why choose a square as a geometric norm in a world of curves and circles? Thus I might say that the area of a circle is 1, and the area of a square around it is 1.273239... ( a new magic number! ).