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About that coordinate system...

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  • Leadhyena Inrandomtan
    I apologise if I break any rules of netiquette, as this is my first send on this post. I am but an independent mathematician out of Dallas, TX and have an
    Message 1 of 4 , Jan 31, 2002
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      I apologise if I break any rules of netiquette,
      as this is my first send on this post. I am but an
      independent mathematician out of Dallas, TX and have
      an insatiatable appetite for mathematics and logic. So
      here are my two cents on the prime coordinates issue:

      There is a way to make the addition of
      coordinates work, but you step outside the realm of
      integers by doing so. Taking upon the idea presented
      by Sergio Ribeiro, you could take the main X, Y, and Z
      poles and use the ln of all of the coordinates. Then
      by adding X+Y+Z them you get unique coordinates for
      all normal (X,Y,Z). Reason is due to Unique
      Factorization Theorem: just like multiplied
      coordinates in Sergio's system have a unique
      factorization, the addition of the three ln
      coordinates also equals ln XYZ and this number is
      always unique by construction.

      I'm not sure if it can be scaled to integers,
      using a system such as floor(C*(ln X + ln Y + ln Z)),
      finding a C that would give each coordinate a unique
      integer value. The reason is due to the distribution
      of primes: ratio of primes is 1/ln n, so I would
      assume that as you approached (inf,inf,inf) you would
      find coordinates (x1,y1,z1) and (x2,y2,z2) such that
      ln x1y1z1 - ln x2y2z2 is arbitrarily close. Any takers
      on a proof or disproof?

      I couldn't forsee the use of such a system,
      however. Cantor already proved that Z^3 and Z are the
      same cardinality and this would also prove the same,
      albeit more romantically (not necessarily more
      elegant, but more aesthetically pleasing ;). You
      already have a real number for every R^3 coordinate,
      in a somewhat more dense fashion. I could see the
      interesting possibility of adding two ln XYZ
      coordinates together, because the pair of coordinates
      added together could be deconstructed from the sum,
      using the same reasoning above. (three coordinates
      however IS impossible by the presented method)

      As far as the philosophical debate, I say
      whatever floats your boat. What matters except for the
      mathematics? Why step outside of the mathematics? It's
      only symbols; It's inherent in nature; It's man-made;
      it's created by God; Man is God whatever. What matters
      is the mathematics. To put in my two cents though,
      this is how I see it: Logic is god, and reality is
      just the symbols of god flying around to the winds of
      logic. No personification. Mathematics is simply the
      practice of putting symbols on paper and letting them
      dance on the winds of logic. But does it matter to the
      mathematics? As long as math doesn't try to supercede
      logic, we're on solid ground.
      --leadhyena

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    • Jon Perry
      ... ln x1y1z1 - ln x2y2z2 is minimum when x1y1z1-x2y2z2=2. Assuming this happens infinitely often, then ln x1y1z1 - ln x2y2z2 tends to zero. Jon Perry
      Message 2 of 4 , Feb 1, 2002
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        >ratio of primes is 1/ln n, so I would
        >assume that as you approached (inf,inf,inf) you would
        >find coordinates (x1,y1,z1) and (x2,y2,z2) such that
        >ln x1y1z1 - ln x2y2z2 is arbitrarily close. Any takers
        >on a proof or disproof?

        ln x1y1z1 - ln x2y2z2 is minimum when x1y1z1-x2y2z2=2.

        Assuming this happens infinitely often, then ln x1y1z1 - ln x2y2z2 tends to
        zero.

        Jon Perry
        perry@...
        http://www.users.globalnet.co.uk/~perry
        http://www.users.globalnet.co.uk/~perry/maths
        BrainBench MVP for HTML and JavaScript
        http://www.brainbench.com


        -----Original Message-----
        From: Leadhyena Inrandomtan [mailto:leadhyena_inrandomtan@...]
        Sent: 31 January 2002 20:45
        To: primenumbers@yahoogroups.com
        Subject: [PrimeNumbers] About that coordinate system...


        I apologise if I break any rules of netiquette,
        as this is my first send on this post. I am but an
        independent mathematician out of Dallas, TX and have
        an insatiatable appetite for mathematics and logic. So
        here are my two cents on the prime coordinates issue:

        There is a way to make the addition of
        coordinates work, but you step outside the realm of
        integers by doing so. Taking upon the idea presented
        by Sergio Ribeiro, you could take the main X, Y, and Z
        poles and use the ln of all of the coordinates. Then
        by adding X+Y+Z them you get unique coordinates for
        all normal (X,Y,Z). Reason is due to Unique
        Factorization Theorem: just like multiplied
        coordinates in Sergio's system have a unique
        factorization, the addition of the three ln
        coordinates also equals ln XYZ and this number is
        always unique by construction.

        I'm not sure if it can be scaled to integers,
        using a system such as floor(C*(ln X + ln Y + ln Z)),
        finding a C that would give each coordinate a unique
        integer value. The reason is due to the distribution
        of primes: ratio of primes is 1/ln n, so I would
        assume that as you approached (inf,inf,inf) you would
        find coordinates (x1,y1,z1) and (x2,y2,z2) such that
        ln x1y1z1 - ln x2y2z2 is arbitrarily close. Any takers
        on a proof or disproof?

        I couldn't forsee the use of such a system,
        however. Cantor already proved that Z^3 and Z are the
        same cardinality and this would also prove the same,
        albeit more romantically (not necessarily more
        elegant, but more aesthetically pleasing ;). You
        already have a real number for every R^3 coordinate,
        in a somewhat more dense fashion. I could see the
        interesting possibility of adding two ln XYZ
        coordinates together, because the pair of coordinates
        added together could be deconstructed from the sum,
        using the same reasoning above. (three coordinates
        however IS impossible by the presented method)

        As far as the philosophical debate, I say
        whatever floats your boat. What matters except for the
        mathematics? Why step outside of the mathematics? It's
        only symbols; It's inherent in nature; It's man-made;
        it's created by God; Man is God whatever. What matters
        is the mathematics. To put in my two cents though,
        this is how I see it: Logic is god, and reality is
        just the symbols of god flying around to the winds of
        logic. No personification. Mathematics is simply the
        practice of putting symbols on paper and letting them
        dance on the winds of logic. But does it matter to the
        mathematics? As long as math doesn't try to supercede
        logic, we're on solid ground.
        --leadhyena

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      • paulmillscv
        ... Hello, It is nice to welcome someone with an interest in logic. ... Yes, but symbols of reality. Therefore the 3-d cartesian co-ordinate system is a real
        Message 3 of 4 , Feb 1, 2002
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          --- In primenumbers@y..., Leadhyena Inrandomtan
          <leadhyena_inrandomtan@y...> wrote:
          > I apologise if I break any rules of netiquette,
          > as this is my first send on this post. I am but an
          > independent mathematician out of Dallas, TX and have
          > an insatiatable appetite for mathematics and logic.

          Hello,
          It is nice to welcome someone with an interest in logic.
          >
          > As far as the philosophical debate, I say
          > whatever floats your boat. What matters except for the
          > mathematics? Why step outside of the mathematics? It's
          > only symbols;

          Yes, but symbols of reality. Therefore the 3-d cartesian co-ordinate
          system is a real 'discovery' which will affect humankind for all
          generations. You also have the possibility to contribute.

          It's inherent in nature; It's man-made;
          > it's created by God; Man is God whatever.

          Man is A God. Man is not THE God. We are 'chips off the old block.'
          But I digress.


          What matters
          > is the mathematics. To put in my two cents though,
          > this is how I see it: Logic is god, and reality is
          > just the symbols of god flying around to the winds of
          > logic. No personification.

          > Mathematics is simply the
          > practice of putting symbols on paper and letting them
          > dance on the winds of logic.

          This is a nice metaphor for 'streams of consciousness' that we have
          been discussing as the 'matrix' for collective thought. The 'out
          there'.


          But does it matter to the
          > mathematics? As long as math doesn't try to supercede
          > logic, we're on solid ground.

          Yes, logic oversees mathematics as an elder brother to a younger
          brother.


          Nice comments. Do you have any of your own work you would like to
          share with the group?

          regards,
          Paul Mills
          Kenilworth,
          England.


          > __________________________________________________
          > Do You Yahoo!?
          > Great stuff seeking new owners in Yahoo! Auctions!
          > http://auctions.yahoo.com
        • J
          Dear Colleagues, I never expected so many emails about the 3d coordinate system. I must thank everyone for contributing. In the original Email I sent to this
          Message 4 of 4 , Feb 1, 2002
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            Dear Colleagues,

            I never expected so many emails about the 3d
            coordinate system. I must thank everyone for
            contributing. In the original Email I sent to this
            group I had a typo on my email I was missing the
            number 19. One to many beers that night :). Now I
            realize that as long as xp>Yp>Zp etc.. that any group
            or grouping of prime numbers can be used for the
            system, As long as they are larger prime numbers than
            the 1st group.

            Regards,
            Jason Kurtz





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