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Date:	Tue, 5 Jun 2001 07:31:48 PDT
From:	"Lynn H. Maxson" <lmaxson@pacbell.net >
Reply-To:	scoug-sundialsig@scoug.com
To:	< "scoug-sundialsig@scoug.com" > scoug-sundialsig@scoug.com >
Subject:	SCOUG-SundialSIG: June meeting

Content Type: text/plain

Peter Skye wrote:

"We're going to define some generalizations?"

Why not? You're sitting around the campfire after an exhausting
day of hiking through the woods. No one brought a guitar or
harmonica. You just stare around at each other, wondering what it
is that anyone might want to do before retreating into the cozy
comfort of their sleeping bags. Then suddenly someone obviously
dazed says, "Let's define some generalizations." You're simply
too tired to offer any resistance, even intellectual. It just
turns out to be a profitable way to kill time.

"Data" is a generalization. It could be just data: content only.
Or it could be structured (or ordered) data: content within a
context. Or when structured data is tied to a knowledgeable
observer it becomes information. Instead of "Girl Interrupted"
you have "Data Transformations". Data is a general term which
means different things in different contexts.

Element is another generalization. Normally we associate it with
atomic, referring to our smallest recognizable unit. We put two
(or more) elements together we have an aggregate. We put two (or
more) atoms together we have a molecule. Both, however, are
assemblies, another generalization.

We have homogeneous aggregates, collections of same data type
elements. A collection is either ordered or unordered
(structured). If unordered, it is simply a set. A collection can
contain zero, one, or more elements (or members). If it contains
zero, it is an empty (or null) set. If it is ordered and of the
same data type elements it becomes a vector (one-dimension array)
or a matrix (two-dimensional array) or even greater dimensional
arrays. If you have a non-empty set of two or more elements you
have an homogeneous (same data type elements) or heterogeneous
(mixed data type elements) aggregate which is an assembly.

If we in turn treat assemblies as elements within larger
assemblies we can find ourselves with homogeneous aggregates of
heterogeneous element aggregates and heterogeneous aggregates of
homogeneous element aggregates or any combination of either. Or
we can have arrays of structures or structures of arrays or any
combination of either.

In any case generalizations can become quite confusing. We have
to be clear when using them that the context indicates the choice
in use. Personally I come from a manufacturing and distribution
industry background. I'm inclined toward considering "raw
materials" as "elements" and "assemblies" as "aggregates".

I haven't introduced the concept of a list which is a "connected"
set of zero, one, or more elements, any one (or all) of which can
be a list. Actually set is mathematically incorrect here as a set
is an "unordered" collection, whereas a list has an order to it.
In terms of generalizations it might be better to define a list as
a connected assembly of zero, one, or more elements, each of which
could be a raw material or an assembly. Actually a raw material
in this context is a single element list. There is also a
possibility that zero elements exist in a list or within a list
element within a list.

These types of discussions make it easy to decide to call it
night, put out the campfire, and retire to the fetal comfort of a
sleeping bag. When we wake up to a spreadsheet like MESA 2 how do
we talk about it without confusion, i.e. ambiguity? We have
"cells" as elements, each of which can be empty (null), have a
value, exist as a formula (in which case it has two forms
simultaneously), or exist as an array. The cells exist as an
aggregate of rows and columns, a possibly non-homogeneous array.
Every cell has a name derived from the intersection of a row and a
column. The aggregate of the rows and columns make up a
spreadsheet, a layer within a possible aggregate of other layers,
all of which make up a workbook, which to the supporting OS file
system appears as an element, i.e. a filename.

Do I believe that some purpose lies in being clear about our
generalizations, in insuring that the context properly defines a
particular use? You bet your booties, which you should remove
before retreating to the comfort of the fetal position.

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