Tuesday, September 2, 2014
Devlin Talks Geometry
I don't often see Keith Devlin focus on geometry in his blog posts… but today he did… and quite excellently! In fact, from my standpoint the post, in some ways, makes for a nice counterpoint to the Sunday reflection I ran this weekend on Platonism (Dr. Devlin is a non-Platonist). Read Keith here:
"Mathematics provides various ways to model our perception and experience of reality. Different parts of mathematics provide different models, some better than others."
He goes on to talk about fractal geometry and cellular automata of Steven Wolfram as two geometric approaches to the world.
"Both approaches can be said to begin by looking at how nature works, but the moment you start to create a model, you leave nature and are into the realm of human theorizing."
"...make no mistake about it, we do begin with assumptions. Not arbitrary ones, to be sure—not even close to being arbitrary."
"...mathematics is not 'the true theory of the real world' (whatever that might mean). Rather, mathematical theories are mental frameworks we construct to help us make sense of the world."
"...we should not lose track of the fact that mathematics is not the truth.
"Rather, it provides us with useful models of the world. As a result, it is a powerful and useful way of making sense of the world, and doing things in the world."
He ends with his vocal support again for Common Core (while admitting more focus is needed on "how to properly implement the Standards").
Read the entire piece, or like me, read it 3-4 times to squeeze out as much food for thought (and I dare say food for controversy as well!) as you can from it.