On Primeness...
I am mathematician by training (barely) but I don't think anyone should
listen to me about mathematics unless serendipitously I happen to land
on a useful or interesting (by whose measure?) mathematical conjecture
(and presumably some attendant proofs as well).
That said, I've always wondered why the poets among the mathematicians
didn't hit on naming the "naive" Primes (Primes+1) - Prime' (Prime
/prime/). Perhaps there are too many mathematicians with stutters
and/or tourette's that would be set off by such a construct?
Who can answer the question of why we (this particular group, or any one
vaguely like it) can get so wrapped up on such a simple topic? There IS
a bit of circular logic involved in defining mathematics as that which
mathematicians study. Or as Robert suggests, that his definition of a
mathematical construct (Prime numbers in this case) is not legitimate
because he is not a mathematician. I'd say his definition is not
useful because it deals in concepts which are not mathematical in nature
(in particular "attractive", "shade", "blue") which are terms of
interest and relevance in aesthetics and psychophysics (both of which
are known to utilize, mathematics but not vice-versa). Numerology, on
the other hand uses all three!
We seem to wander off into epistemological territory quite often without
knowing it or admitting to it. I am pretty sure a number of people
here would specifically exclude epistemological discussions if they
could, while others are drawn to them (self included).
While I do find discussions about the manipulation of matter
(technology), and even data (information theory) and the nature of
physical reality (physics) and formal logic (mathematics) quite
interesting (and more often, the myriad personal and societal impacts of
same), what can be more interesting (and the rest grounded in) than the
study of knowledge itself?
That said, I don't know that many of us are well versed in the discourse
of epistemology and therefore tend to hack at it badly when we get into
that underbrush, making everyone uncomfortable. On the other hand, I'll
bet we have a (large?) handful of contributors (and/or lurkers) here
with a much broader and deeper understanding than I have but who perhaps
recognize the futility of opening that bag of worms.
Our "core" topic of Complexity Science is fraught with epistemological
questions (I believe), most particularly questions such as "whence and
what emergence?" as Nick's seminars of 2+ years ago considered. I don't
know if the topic was approached from the point of view of "what is the
nature of knowledge?" or more specifically, "how can we define a new
concept such as emergence and have it hold meaning?". In my view,
"emergence" is strictly "phenomenological" as are the many (highly
useful) constructs of statistical physics.
I promised a maunder here, I trust I succeeded in delivering!
Carry on!
- Steve
Actually you can't define primeness any way you want. The definition
needs to be negotiated by the community of professionals who are can
credibly agree on the definition.
My definition of primeness is "anything bigger than 3 and painted an
attractive shade of blue". But no one listens to me. Nor should they,
because I'm not a mathematician.
---R
On Sun, Dec 11, 2011 at 10:13 AM, Grant Holland
<[email protected] <mailto:[email protected]>> wrote:
George's observation (from Saturday) under "mathematician" pretty
much captures the issue for me. One can define "primeness" any way
one wants. The choice of excluding 1 has the "fun" consequence
that George explains so well. Maybe including "1" has other fun
consequences. If so, then give that definition a name ("prime" is
already taken) , and see where it leads. You can make this stuff
up any way you want, folks. Just follow the consequences. Some of
these consequences provide analogies that physicists can use. Some
don't. No matter. We just wanna have fun!
Grant
On 12/10/11 4:08 PM, George Duncan wrote:
Yes, it does depend on how you define prime BUT speaking as a
*mathematician*
it is good to have definitions for which we get interesting
theorems, like the unique (prime) factorization theorem that says
every natural number has unique prime factors, so 6 has just 2
and 3, NOT 2 and 3 or 2 and 3 and 1. So we don't want 1 as a
prime or the theorem doesn't work.
*statistician*
do a Bing or Google search on prime number and see what frequency
of entries define 1 as prime (I didn't find any). So from an
empirical point of view usage says 1 is not prime
*artist*
try Bing of Google images and see how many pretty pictures show 1
as prime. I didn't see any.
Cheers, Duncan
On Sat, Dec 10, 2011 at 5:19 PM, Pamela McCorduck
<[email protected] <mailto:[email protected]>> wrote:
I asked the in-house mathematician about this. When he began,
"Well, it depends on how you define 'prime' . . ." I knew it
was an ambiguous case.
PMcC
On Dec 10, 2011, at 5:12 PM, Marcos wrote:
On Thu, Dec 8, 2011 at 2:17 AM, Russell Standish
<[email protected] <mailto:[email protected]>>
wrote:
Has one ever been prime? Never in my lifetime...
Primes start at 2 in my world. There was mathematician
doing a talk
once, and before he started talking, he checked his
microphone:
"Testing...., testing, 2, 3, 5, 7"
That's how I remember.
Mark
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--
George Duncan
georgeduncanart.com <http://georgeduncanart.com/>
(505) 983-6895 <tel:%28505%29%20983-6895>
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Life must be understood backwards; but... it must be lived forward.
Soren Kierkegaard
============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps athttp://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
============================================================
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
============================================================
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Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org
