Re: [FRIAM] Oh my gawd...
On Sat, Dec 10, 2011 at 7:55 PM, Robert J. Cordingley rob...@cirrillian.com wrote: Shouldn't theorems be independent of arbitrary decisions regarding what is or is not a prime number? Otherwise I'll have to believe that mathematicians are just making up stuff. Of course its all made up. What do you think an axiom is? I'm being a bit cynical, but the various arbitrary starting points from which all theorems derive are the end-products of a millennia-long natural selection process. Even the concept of number could, in theory, be totally re-written, but at this point, it would be mostly a pointless act of rebellion. If you want a great read on the subject, see Gregory Chaitin. 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
Re: [FRIAM] Oh my gawd...
Abstract mathematicians are just making up stuff however they want. They are artists whose clay is (in the modern view) formal logic. The nature of their creation is its own reason for being. Abstract mathematics is not natural science, nor is it the province of natural scientists. If one of their creations happens to be analogical to physicists or anyone else, then so be it. Analogy fit is not the business of the abstract mathematicians. That's the whole beauty of the discipline. To applied mathematicians the above is probably all wet. And physicists probably think that math is their invention and that physics is its justification. But we don't care about that and just continue on our merry way of self-amusement. Grant On 12/10/11 7:55 PM, Robert J. Cordingley wrote: Shouldn't theorems be independent of arbitrary decisions regarding what is or is not a prime number? Otherwise I'll have to believe that mathematicians are just making up stuff. 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 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 Represented by ViVO Contemporary 725 Canyon Road Santa Fe, NM 87501 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
Re: [FRIAM] Oh my gawd...
I've forgotten the message that spawned the thread, but I'll expose my incompetence in math to say that I was also thinking that 1 is prime. The informal definition that I remember says that a number is prime if it is an integer evenly divisible only by itself and 1. Well, 1 clearly is divisible by itself (1/1 = 1) and divisible by 1 (1/1 = 1), so by that informal definition, it must be prime. The perils of natural language and informal definitions. ;; Gary 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
Re: [FRIAM] Oh my gawd...
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 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 Represented by ViVO Contemporary 725 Canyon Road Santa Fe, NM 87501 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 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
Re: [FRIAM] Oh my gawd...
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.comwrote: 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.comwrote: 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 (505) 983-6895 Represented by ViVO Contemporary 725 Canyon Road Santa Fe, NM 87501 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 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 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
Re: [FRIAM] Oh my gawd...
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
Re: [FRIAM] Oh my gawd...
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
Re: [FRIAM] Oh my gawd...
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 (505) 983-6895 Represented by ViVO Contemporary 725 Canyon Road Santa Fe, NM 87501 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 at http://www.friam.org
Re: [FRIAM] Oh my gawd...
I'm also a big fine of using a single standard definition for apriori structures in formal logic. The semantics convolution caused by individual definitions in normal speech is bad enough. I'm sure some one has come up with a good name for the set of 1 and the primes, and such terminology should be used when appropriate or a simple definition of the new set given. Greg Sonnenfeld Junior programmers create simple solutions to simple problems. Senior programmers create complex solutions to complex problems. Great programmers find simple solutions to complex problems. The code written by topnotch programmers may appear obvious, once it is finished, but it is vastly more difficult to create. On Sat, Dec 10, 2011 at 4:08 PM, George Duncan gtdun...@gmail.com 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 (505) 983-6895 Represented by ViVO Contemporary 725 Canyon Road Santa Fe, NM 87501 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 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
Re: [FRIAM] Oh my gawd...
Shouldn't theorems be independent of arbitrary decisions regarding what is or is not a prime number? Otherwise I'll have to believe that mathematicians are just making up stuff. 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 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 Represented by ViVO Contemporary 725 Canyon Road Santa Fe, NM 87501 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 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
Re: [FRIAM] Oh my gawd...
Has one ever been prime? Never in my lifetime... On Wed, Dec 07, 2011 at 11:29:24PM -0700, Greg Sonnenfeld wrote: Apparently it hasn't been a prime since wikipedia started. Though what is a prime is simply a matter of definition as are most mathematical constructs. (Though some fit the physical world rather well. ) A '''prime number''', or '''prime''' for short, is a [[natural number]] larger than 1 that has as its only positive [[divisor]]s ([[factors]]) 1 and itself. - Revision as of 20:42, 5 December 2001 (edit) Hagedis * Greg Sonnenfeld Junior programmers create simple solutions to simple problems. Senior programmers create complex solutions to complex problems. Great programmers find simple solutions to complex problems. The code written by topnotch programmers may appear obvious, once it is finished, but it is vastly more difficult to create. On Wed, Dec 7, 2011 at 11:19 PM, Robert J. Cordingley rob...@cirrillian.com wrote: According to http://en.wikipedia.org/wiki/Prime_numbers 1 isn't a prime number any more. Can someone explain (translate) the reason for this shift in the cosmos? Where's Henri when you need him? (You have to see the wiki article.) Robert C 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 -- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au 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
Re: [FRIAM] Oh my gawd...
From the wikipedia article under the subheading *Primality of one*: ...Derrick Norman Lehmer's list of primes up to 10,006,721, reprinted as late as 1956,[5] started with 1 as its first prime.[6] Henri Lebesgue is said to be the last professional mathematician to call 1 prime.[7] Henri died in 1941. Perhaps it takes awhile for the word to get around. Robert C On 12/8/11 2:17 AM, Russell Standish wrote: Has one ever been prime? Never in my lifetime... On Wed, Dec 07, 2011 at 11:29:24PM -0700, Greg Sonnenfeld wrote: Apparently it hasn't been a prime since wikipedia started. Though what is a prime is simply a matter of definition as are most mathematical constructs. (Though some fit the physical world rather well. ) A '''prime number''', or '''prime''' for short, is a [[natural number]] larger than 1 that has as its only positive [[divisor]]s ([[factors]]) 1 and itself. - Revision as of 20:42, 5 December 2001 (edit) Hagedis * Greg Sonnenfeld Junior programmers create simple solutions to simple problems. Senior programmers create complex solutions to complex problems. Great programmers find simple solutions to complex problems. The code written by topnotch programmers may appear obvious, once it is finished, but it is vastly more difficult to create. On Wed, Dec 7, 2011 at 11:19 PM, Robert J. Cordingley rob...@cirrillian.com wrote: According to http://en.wikipedia.org/wiki/Prime_numbers 1 isn't a prime number any more. Can someone explain (translate) the reason for this shift in the cosmos? Where's Henri when you need him? (You have to see the wiki article.) Robert C 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 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
Re: [FRIAM] Oh my gawd...
Apparently it hasn't been a prime since wikipedia started. Though what is a prime is simply a matter of definition as are most mathematical constructs. (Though some fit the physical world rather well. ) A '''prime number''', or '''prime''' for short, is a [[natural number]] larger than 1 that has as its only positive [[divisor]]s ([[factors]]) 1 and itself. - Revision as of 20:42, 5 December 2001 (edit) Hagedis * Greg Sonnenfeld Junior programmers create simple solutions to simple problems. Senior programmers create complex solutions to complex problems. Great programmers find simple solutions to complex problems. The code written by topnotch programmers may appear obvious, once it is finished, but it is vastly more difficult to create. On Wed, Dec 7, 2011 at 11:19 PM, Robert J. Cordingley rob...@cirrillian.com wrote: According to http://en.wikipedia.org/wiki/Prime_numbers 1 isn't a prime number any more. Can someone explain (translate) the reason for this shift in the cosmos? Where's Henri when you need him? (You have to see the wiki article.) Robert C 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
