Problems and their Solvers (2015-03-29)
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CUPE 3902, the union representing teaching assistants and course instructors at
UoT, was on strike for most of the last month. As I was trying to figure out
how I felt about the strike, trying to figure out who I sided with, I spent a
lot of time thinking about what "problems" are and how we ought to go about
solving them. Most of the struggle surrounding the strike was, for me, a jumble
of delicate and inter-linked issues about how I relate to people, money, and
academia. It made me realize that the kinds of problems we're used to working
with really affects our approach to all problems, big and small, that we run in
to. I'd like to say a little bit about the connection between problems and the
people who try to solve them.
I come from a very specific problem solving context: I'm a mathematician. I
like two player strategic board games. I work with quantitative problems. I
care about coarse estimates and asymptotic behaviour. All these factors
combined to make me uniquely unable to grapple with politics. There is
something unique to the kind of problem solving that happens in mathematics
that makes its problem solvers especially weak in dealing with large complex
political situations. I'll try to sketch the way that I think about my
background and then discuss how this carries over to politics.
Firstly, mathematicians tend to work alone. I'm always in favour of a lively
mathematical collaboration, a dialogue, but I have to acknowledge that mostly
mathematics is a solitare game. There is a lot to be learned from talking to
other mathematicians but a lot of mathematics is done alone. We try to take the
established theory and use it for new things. This requires a lot of digestion
of theory which is best done alone, slowly piecing things together. We sit down
at our computers and try to write down what we think is right. We're not quite
sure, even though we wrote it. We try again. And again, until things start to
click. This all happens alone, after the interesting conversations are over and
we're back at our desks.
We think about a subject until it becomes easy. We grasp on to it and mull it
over, testing the known theory on it, until it all dissolves and we're left
with something that is very simple. If there is some knotty difficult bit we
smooth that out, taking it apart and re-assembling it until it becomes
tractable. If something seems so intractably complicated that we can't
understand it, we tend to leave it for others (more often than not, no one) to
grapple with. Those problems which are just barely tractible using known theory
are the kinds of things mathematicians like to play with.
For a couple of years I was obsessed with playing games. I love games, game
design, and game theory. My favourite kinds of games are those that are played
using definite rules, where you know everything about the game situation at any
moment, and there is no chance. Consequently, I think of things in those terms.
When I am trying to decide what to do in a given context, in a game or real
life, I tend to think in terms of 'moves'. What's the best move here? What'll
they do if I play this particular move? I implicitly assume that everyone is
playing by the same rules, and has the same goals as me.
But there are certain kinds of goals that are specific to me. The kind of
problems that I work on are about numbers and their long term behaviour. Will
this sequence of numbers outgrow this other sequence of numbers? If I measure
this one thing, is that the same as measuring this other thing?
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A parable:
Once a wise man wanted to know what the most useful thing in the world
is. He went to many people and asked them, venturinng near and far to
find out. When he encountered a roofer, the roofer told him a hammer.
A lumber jack told him an ax is certainly the most useful thing. A
survery told him that a transit is indeed the most helpful apparartus.
The wise man concluded that the most useful tool is the one you need to
use for the job that you're doing.