THINKING THROUGH DRAWING: PRACTICE INTO KNOWLEDGE 123
I would like to talk about “thinking with the
body” and several other things: there are three top-
ics that I would like to cover.
First, a pragmatic epistemic thing about dia-
grams, using that as a way of introducing what I
think is a fundamental interactive strategy, a strat-
egy we use for interacting with the world. Then I
will look at a separate and distinct thing, which is
using sketches as a way to help us recognize things,
and then finish with something about sketching
using the body.
So here is a question. People will find that they
typically reach for a pencil and ruler to solve this
kind of question:
“All 3 medians of a triangle always intersect at a
single point”. What does that mean?
The median is the line to the midpoint of the
opposite side. So you reach for a pencil and paper
to try to answer the question. Why do you do that?
Because it is too hard to do all of that in your head.
So I think that this reveals a key interactive strat-
egy: you pose the problem, then if you can solve it
in your head, you go ahead and do it. If you can’t,
you do something on paper. So you first create the
figure. You think “OK...median..” and you can do
one of those mentally. Now you have to create the
other two. Would you be confident that you could
imagine all these medians in your head, to test
where they intersect? Some of you can, some of you
can’t. The next step is “I think I can do the second
one in my mind, projecting onto this, but I can’t do
the third one”. At this point you are trying to project
structure, so at some point you are going to reach
for the ruler again, and you are going to draw the
medians in. You may or may not draw the third one
in, because you can already see that it is going to
intersect the others.
This is a process: create something, create struc-
ture in the world, project onto it, create structure
again, project onto it....and that is how we work a lot
of times: we do what we can in our heads and when
we can’t, we make structure.
Projection gets more faulty the further and fur-
ther out you go. It becomes harder and harder to
keep all that stuff reliably in your mind. By exter-
nalizing we convert some of that mental projection,
mental stuff, into a form that is useful, outside, for
these epistemic concerns. This cycle of thinking, of
doing things in our heads, projecting onto the world,
then creating structure, lets us go beyond what we
can do in our heads, by creating things outside.
So projection is a way of compensating for
the limits of our imagination. I wanted to explore
this idea, of the difference between projection and
imagination. I am going to draw the distinction in
this way: projection is a kind of imagination but it is
tied to a structure, so that you are projecting onto a
structure. In order to do that you have to have some
anchor for the projection. For instance the triangle
has no specific size in your imagination, but when it
is externalized it has a specific size. When you draw
the median it is very specific to that structure, out
there. The external structure supports the projected
extension.
Let us draw some definitions:
We did a little experiment – but first, to intro-Using Sketching: To Think, To Recognize, To Learn
David Kirsh