Russ, I apologize for being so terse. Let me try again. Here is my take
on your question...
As we know, systems are more than just components, or elements. A system
must also have relationships among its elements before they it is worthy
being called a system.
But, when you take these component relationships into account, the
possibilities for what characteristics, or properties, a system may
exhibit begins to ramify into a potentially large and surprising number,
due to combinatorics. With so many possible component relationships, it
often becomes non-intuitive as to which potential properties (true
statements) of the system are true.
Thus the need for theorems arises due to a system having relationships
among its components. And we haven't even mentioned emergent properties yet!
This is simple, of course, because it is elemental, foundational to
systemics.
Take care,
Grant
Grant Holland wrote:
There are theorems because systems have relationships as well as
elements, from which arise emergent properties.
Grant
Russ Abbott wrote:
I have what probably seems like a strange question: why are there
theorems? A theorem is essentially a statement to the effect that
some domain is structured in a particular way. If the theorem is
interesting, the structure characterized by the theorem is hidden and
perhaps surprising. So the question is: why do so many structures
have hidden internal structures?
Take the natural numbers: 0, 1, 2, 3, 4, ... It seems so simple:
just one thing following another. Yet we have number theory, which is
about the structures hidden within the naturals. So the naturals
aren't just one thing following another. Why not? Why should there be
any hidden structure?
If something as simple as the naturals has inevitable hidden
structure, is there anything that doesn't? Is everything more complex
than it seems on its surface? If so, why is that? If not, what's a
good example of something that isn't.
-- Russ Abbott
______________________________________
Professor, Computer Science
California State University, Los Angeles
cell: 310-621-3805
blog: http://russabbott.blogspot.com/
vita: http://sites.google.com/site/russabbott/
______________________________________
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FRIAM Applied Complexity Group listserv
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============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org
