Linear Thinking LO23038

Steve Eskow (dreskow@corp.webb.net)
Wed, 27 Oct 1999 10:37:37 -0600

Leo,

You see the discussion of linear thinking "meandering between form and
content," getting increasingly complicated, and you try to get us out of
the swamps of mathematics with your chain puzzle. And you would like to
see the discussion more relevant to those of us interested in connecting
ideas to LO's.

I agree with your premise: as the discussion of linear thinking
progresses, we are becoming increasingly confused, and the concept of
"linear thinking" becomes less useful to us.

(Trying to solve your chain puzzle, I drew six little lines in a straight
line, and found that I needed 5 connections to make them into a linear
chain, and a sixth to join the two ends of the chain into a circle. From
your description of costs I did not know if each of the first five
connections cost \$3, \$4, or \$5. My failure, then, to solve the puzzle did
not come from my using "linear thinking," but from my inability to
understand the example that was meant to help me understand.)

I suggest to you that our basic problem in this discussion, one that
afflicts many LO's, is that we are using the wrong tools for the work of
learning we need to do.

"Linear thinking" is a literary device: a metaphor. Like all metaphors, it
tries to show, or create, a resemblance between two things, or phenomena,
that are otherwise unlike.

We are not really helped to understand metaphor by taking the metaphor
literally, or trying to apply the methods of mathematics or science to
understanding a metaphor.

Consider the "hands" of a clock. If the resemblance between the shape and
function of the pointers on the clock "face" are not clear to a listener,
he or she will not be helped by invoking biology, or the mathematics of
fingers on the human frame.

Consider another metaphor of thinking that uses spatial imagery, as does
"linear thinking": the term "circular reasoning."

Someone makes a case, takes a position, and we say of that case or
position, "That is circular reasoning."

If the meaning of "circularity" in reasoning can not be made clear in
context, we will not be helped to make it clear by involving form-content
differences, or by discussions of radii and pi and circumferences.

The explanations take us further and further away from the kind of
reasoning we are trying to illustrate.

That, I think, is what has happened here: in an effort to explain linear
thinking "scientifically" we have gone off on "tangents," begun to move in
"circles" of language that are taking us further and further away from the
tendencies we are trying to describe and summarize.

In such cases it is often better to conclude that the term is so elusive,
so vague and prone to endless interpretation, that it has little utility,