Re: serializing the facts

[John Denker <jsd@MONMOUTH.COM>]

I wrote:

> > Science is not serial.  It is a very high-dimensional tangled latticework
> > of facts.  There is no natural ordering of the facts.

At 08:28 AM 8/21/00 -0500, Glenn A. Carlson wrote:

> a better word than "serial" is "hierarchical."

I disagree.

> There is no single line of topics which should comprise a physics course,

I agree.

> but there is a logical, natural hierarchy of topics.
> Mastery of the lower level topics is necessary to master the higher level
> topics.

Sometimes that's true.  But it's not true in general, and overall it's
misleading.  Most facts can't be sorted and labelled as to "higher" or
"lower" level.

Example (H):  Before starting quantum mechanics, it would be good to cover
   a) some probability concepts, and
   b) classical waves.

Example (non-H):  But should classical waves come before probability, or
after?  IMHO it could go either way.

Example (non-H):  Is the mass of the electron "higher-level" or
"lower-level" than the charge of the electron?


> Newton said, "If I have seen further than other men, it is because I
> have stood on the shoulders of giants."  He didn't say, " If I cast a
> larger net, it is because I tangled my unordered lattice of facts with
> the unordered lattice of facts of others."

The history of science is somewhat sequential.  The resulting edifice of
facts is multi-dimensional, not sequential.  Kuhn and others have observed
that even the history of science is not really sequential, because of
backtracking.  And teaching science facts in historical order is hardly a
solution to all the world's problems.

There is a theorem that says you cannot impose a sequential order on
high-dimensional things.  I'm not speaking metaphorically;  it's a real
theorem.

For homework, consider the eight corners of a cube.
  -- Make a list, listing the corners.  That's easy.
  -- Now sort the list so that corners that are adjacent in the real cube
     are adjacent on the list.  You will find that considerably harder.

Formally, there is the concept of "partial order" and the concept of "total
order".
  -- You can impose a partial order on the bricks in a building (e.g.
height is a partial order).
  -- But you cannot impose a total order in a way that preserves adjacency
relationships.

And there is no requirement to build the building in a way that respects
your personal partial order;  I can lay down the fourth course of bricks in
the west wing before I finish the first course in the east wing.