I think this is metaphysics, no?
*From:*friam-boun...@redfish.com
<mailto:friam-boun...@redfish.com>
[mailto:friam-boun...@redfish.com] *On Behalf Of *Steve Smith
*Sent:* Sunday, December 11, 2011 11:44 AM
*To:* The Friday Morning Applied Complexity Coffee Group
*Subject:* [FRIAM] Epistemological Maunderings
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
<grant.holland...@gmail.com
<mailto:grant.holland...@gmail.com>> 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
<pam...@well.com <mailto:pam...@well.com>> 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
<r.stand...@unsw.edu.au <mailto:r.stand...@unsw.edu.au>>
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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georgeduncanart.com <http://georgeduncanart.com/>
(505) 983-6895 <tel:%28505%29%20983-6895>
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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 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 athttp://www.friam.org
