The use of the word "theory" in mathematics is different than in other realms.
For example group theory and measure theory are, to mathematicians, self contained
systems of axioms and theorems.
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Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505
505 670-9918
Santa Fe, NM
On Fri, Dec 9, 2022, 11:50 AM glen <[email protected]
<mailto:[email protected]>> wrote:
Following a common thread between EricS' and SteveS' responses, I'm compelled to say that
"model" is a useless term and we should find any and every reason to *stop* using it. I've found
"analog" to be a more useful term. To EricS' point, an analog is something outside our selves. And
to SteveS' point, it refines one's intention down to a more manageable subset of whatever some other might be
trying to say. (And it further addresses the maps we call analogies and [ptouie] metaphors.) It's not
objective, of course. But it's better than the nonsensical mess whatever yahoo might mean when they use the
useless word "model".
As for "theory", my own arbitrary interactions with that word imply that a theory is
nothing but a collection of hypo-theses. The extent to which the theses are more than hypo then
tells us the extent to which the "theory" is operationally reliable (thanks for that
phrase, Eric). The composition of theses into a theory isn't trivial. Again, in my limited and
arbitrary experience, people vary a great deal in the extent to which they consider the ways one
thesis can be combined with another. If composition of theses into theory is *not* explicitly
considered, the result is garbage, even if you're composing hyper-theses. c.f. my prior screeds on
the unjustified dominance of *consistency* as fundamental to theoretical coherence, almost totally
ignoring completeness.
<story> At a recent conference, a friend presented knowledge graphs (KGs) as a way to organize
"facts" (actually just cryptically justified sentences). We'd intended for me to give my arching
presentation couching KGs in the larger space of computation, data lakes, warehousing, etc. But my friend
had to talk first because we were late and he had a hard time wall. At the end of his talk (without the
context I intended to paint), an audience member asked a "question": 'How is this any different
than what we used to do in the '60s, writing ideas on index cards and laying them out on the floor? That's a
KG!' My friend gave a polite and professional answer ... way more polite than how I would have answered.
>8^D You've been warned. Do not invite me to your cocktail party.
Then I gave my talk, wherein I explained how multigraphs might resolve the apparent
contradiction between data (lakes) and knowledge (lakes). Nobody asked me any questions.
[crickets] But the moderator targeted the audience member who asked my friend that
"question" with: 'Surely you have some thoughts.' The audience member replied
with 'No. There was a lot of clarity there.' WTF does that mean? [sigh]
</story>
On 12/8/22 18:44, Prof David West wrote:
> I missed this morning's vFriam, but had I attended I would have raised
the following questions for discussions. Perhaps the list will indulge me.
>
> The central question: is there a difference between a 'model' of
something and a 'theory' of something?
>
> To me: a model is a representation of a subset of what we know about
something; a theory is the complete body of knowledge.
>
> In my book-in-development I talk about how to create a shared theory by
having people come together and tell stories about their domain. The telling of
stories creates a shared theory of the domain (or some subset of it that is of
immediate concern) that continues to exist—in the participant's heads. While the
story telling proceeds two graphics are generated: one with the stories themselves
(as 'index cards') and relations among stories, e.g., story a extends story b,
story c provides an alternative case for a, x is a revision of a, etc.; and two, a
Gestalt Map that shows objects as bubbles and connecting lines as relations among
those objects.
>
> Those on the other side of the debate contend that these are models,
just like the models they typically use in software development..
>
> I say they are not, they are merely a form of 'external memory' a
collection of evocative triggers whose sole purpose is to prompt a 'recall to
mind' of the actual stories that were told involving those objects or those
relations. The Gestalt Map, in my mind, represents nothing and could not—as is
assumed about all other models—convey information to anyone who had not
participated in the story telling session.
>
> Specific questions:
> 1- Is the Wheel of Life mandala, (attached) a model of Tibetan Buddhist
Cosmology? Or, does it merely serve the purpose of recalling to mind the stories
that a Tibetan would have heard about the world and how it works.
> 2- Is a card catalog (forgive me, I am old) a model of a library, or
even of its collection?
> 3- Are the Dewey Decimal or the Library of Congress numbering systems,
models of human knowledge?
> 4- Is it correct to say that Quantum Physics has a superlative model, but no
theory? (The dictum to, "to shut up and compute" seems to support an affirmative
answer to this question.
> 5- is a metaphor a model?
>
> For a short time, Model Driven Development garnered attention in
software development: The idea was you could build a complete, accurate, and
unambiguous model of a domain, then use a series of formal transforms (ala
mathematics) to generate executable code. No one, outside of academia, believes
this much anymore, but, in less drastic form, dominates all of software
development and has nearly from the beginning, e.g., CASE and Rationale's
'round-trip-engineering'.
>
> I am writing about what might be called Theory-Driven Development and it
is important that I be able to explain the difference between theory and model.
>
> Thanks for any thoughts any of you might have.
