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.
