I think this is metaphysics, no?
From: 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> 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> 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> 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 ============================================================ 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 -- George Duncan georgeduncanart.com <http://georgeduncanart.com/> (505) 983-6895 <tel:%28505%29%20983-6895> Represented by ViVO Contemporary 725 Canyon Road Santa Fe, NM 87501 Life must be understood backwards; but... it must be lived forward. 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