CAUTION: Deep Corners
Important things first:
If you are looking to go out with a guy who gets excited every time he screws up, then I’m here (858-666-1212).
Upon recognizing, when looking at a line, the end points of the line segment as lines of zero length, I thought I got the godfather of all laws—the associative law—and then the definition of category (take a look at page 21 in the Conceptual Mathematics textbook; you’ll understand even if you have nobel prize or fields). Encouraged by this thought I looked at the degrees of truth in the category of graphs. It got me, unbeknownst to me, to thinking that it’s only a matter of minutes before I find the truth value object of commutative triangle made up of three arrows. Many came into view except the one I was seeking. Fortunately, a figure—with the immediacy of out-of-nowhere, as if filling-in for the occluded (by, what else, an object called ‘my arrogant-shelf’) truth—of the three corners of commutative triangle presented itself reminding me of Out of Line, wherein you can find out how Professor Ronnie Brown expressed the geometry of corner in algebra.
The three corners of commutative triangle are:
- A pair of arrows with common beginning.
- A pair of arrows with the ending of one arrow as the beginning of the other arrow.
- A pair of arrows with common ending.
I think of product when I look at corner 1, sequence when I look at corner 2, and sum when I look at corner 3 while being mindful of the fact that PRODUCT and SUM are definite mathematical constructs (see Conceptual Mathematics for the definitions of PRODUCT and SUM; see also SUM and COMPOSITE QUALITY to feel the reach of the simple idea of sum).
I am going on a hiatus to get a grip on these three corners, which seem, without much exaggeration, to contain much of math. (Don’t panic if you don’t see me publishing notes anytime soon.)
Lastly one serious question: