Tuesday, June 02, 2015
After dividing by
I am living between languages. Landscape and geography, space and new falling leaves. It is October and there are no real jobs. Having moved out of and into location, into and out of work. Now settled into life on this new east coast, I learn there are groups of fibers within particular subsets of groups. A fiber in this sense is a set or column of everything that gets mapped to a single number. Any integer divided by 3 will fit into 0, 1, or 2. Write it down:
map …-2, -1, 0, 1, 2, 3…into 0,1,2 with the rule X maps to the remainder of X after dividing by 3.
This gives us columns of numbers for each of 0,1,2 (for example for 0 we get a set that includes: …-6, -3, 0, 3, 6, 9) and this makes a fiber.
I think of fiber optics, another topic I don’t entirely comprehend. But this is different from sending digital information through time and space. This is about how each fiber, made up of all of its elements, exists. In some sort of social discipline this group theory would make sense to me. We are divided by seemingly random factors and placed into sets. We are parts of sets and subsets. We are defined through location, relation, the connections we form. We find our places on the individual fibers of the larger social tapestry.
Though defined simply, mathematical groups are complex in structure. In group theory you can only add or only multiply or only subtract or only divide. Whereas, in the finite fields the possibilities are more unlimited, though possibly not totally unlimited. In the finite fields everything behaves like you expect it should. You can add, subtract, multiply, and divide.
To be or not to be finite. When really, nothing seems to behave as it should.
The infinite fields include all of the numbers as we know them, all fractions, anything with a decimal point. The possibilities are…infinite.
I am by default in a dialogue with myself. And even a group of one can be infinite in its concerns. Sometimes I can’t understand my own words. Languages circle and swirl. Everything is not easily divided by 3. I have landed between columns.
I once heard someone say that a person’s values change depending on the group s/he is with. For example, when you are in high school you may have a set of friends and acquaintances and then when you go to college you acquire another set. Because of this new group of people by whom you are influenced, your own personal values may change. It is inevitable. No one lives in a bubble.
In group theory numbers map neatly into a series of integers. We divide by 3, take the remainder, create a clear table of fiber columns. You may be a positive or negative integer. Depending on how your integer self divides by 3 may determine which fiber column you fall into.
I leave it to my integer self to determine.
In the morning I will rise before it is light and go to a job. I will answer phones and file for the day. Or many days. Shift context and conversation. My connections, relations will change. Soon the snow will start and more dark becomes winter. I place ideas into columns, fibers made of words and images, but the columns blur, or they are too long and they twist and turn like performers of a modern dance. I have become a subset of myself, mapped on to the integer 1, this fiber set becomes indefinite. I learn it is not so easy to fall into a fiber column, not so easy to remain within any clear table of knowing. I learn that mathematics is philosophical and inexact, there are different kinds of infinity. I know that nothing maps neatly but I believe in it anyway, want this proof to be made elegant, believe in the poetics of the group. But my integer self is unruly, in dynamic relationship with others, a language of division and progression that I won’t come to know for some time.