The "so simple" natural numbers only exist within perhaps infinitely complex
individualized awarenesses that co-create within a single infinite unity -- so
naturally infinite patterns of nested recursive fractals emerge.
The natural numbers comprise a discrete infinity, which reveal a base for
infinite sequences that comprise the continuous infinity of real numbers.
Which in turn allow higher order infinities to emerge without limit.
Single infinite unity is awesome.
It is identity.
Rich Murray
----- Original Message -----
From: Russ Abbott
To: The Friday Morning Applied Complexity Coffee Group
Sent: Saturday, April 24, 2010 10:47 PM
Subject: [FRIAM] Why are there theorems?
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
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org
============================================================
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
