sw00826ekua-page13

Edges of Knowledge


Thursday 2003-06-26
-
Arising early, I, slippering into my dishevelled den, blurted:
"Boostah, wholah, gahzhah"; and reaching above the top
level of the nearest of three metal shelvings I have long
used in that room, the shelving which is a catch-all for
everything from tennis shoes to envelopes to medicines,
turned the knob of my black snake-neck desk lamp there;
and png, flick, flash, was back into darkness.  I glanced at--
four levels below--what is now becoming my Topamax 
desk alarm: 6:17.  Doesn't it figure, I smiled in my head.

Friday 2003-06-27
-
And, when I first looked at the clock in my den after eight o"clock,
what time was it?: 8:11am.  So, if I've not crafted a single poem   
worthy of being placed in a best poems anthology, I am certain I
have written numerous sentences worthy of being placed in a best
quotations anthology.

And as to my math excursions, number theory journeyings 
interest me most, especially journeyings of my own design:
new-ways-of-seeing journeyings, no matter whether they
come to naught.  I titled my 1994 math excursion:
  Meanderings of an Amateur Mathematician
I noticed the other day I had at one time figured it came to
231 pages.  Fermat's Last Theorem--which for nearly 30
years I was sure could be verified geometrically, prime
numbers, the natural number summation sequence, and 
the like/ were the reasons for that book.  Approaches I
took were what I called: position math, final-digit math,
set math, interpolation math, etcetera.
  Two or three hours ago I went looking through a copy
of my first Meanderings for a fuller description of my
position math idea than the one I recently expressed.
If you find it too hard to understand, you need not try,
but here it is.  Sorry; I just looked at it again and found
it goes on and on; therefore, I am forced to give you
just part of it.
     from 10-3-92    p. 32b
        it so happens that at each position the
     number one needs to multiply the position
     by in order to get the divisible-by-4 number
     at that position is equal to twice the position
     plus 2.  Here is an example.  We know that
     at position 33 in the natural number summation
     sequence/ the number is 528, and that at po34
     561.  We also know that the greatest least
     part of 33 is 16, and that the least greatest
     part of 33 is 17, and that the relevant closed
     set (at po17) is 16, 17, 33, 528, 561; and that
   528 + 16 = 544 as well as does 561 - 17.
     . . . (& on, & on, & on) . . . .
What I want you to grasp from the above are these
concepts:
1) Order rules.  Whether such order is inherent or
     imposed/ does not matter.
2) Things need not be 1/ 2/ 3/ _so long as they are
     orderly.
3) Be creative.  Do not let yourself be trapped by the
     as-it-is.
These concepts set forth, I may as well also pass to
you, partially, what I recently expressed.
     Let 0 be the 1st number, which is to say, let
     position 1 be 0's position.  Accordingly, 1's
     position is position 2; and 100's position is
     position 101.  Then, instead of concentrating
     on the numbers, use the position, dividing it
     (whatever it is) by 2; and then multiply the
     resulting quotient by the number of that po
     to arrive at 5050 or, or, or, . . .  Take 3015847,
     which is at position 3015848.  3015848/2 =
     1507924; and--my calculator is too small to
     multiply 1507924 x 3015847.  I have named
     this method: position math.  I know: all I am
     really doing by this is giving a name to--while
     in a way demystifying--the inescapable . . .
     because I simply chose to change is to
    ((N + 1)/2)N by my 0 inclusion.
A note on the above which I should have be didn't
include is that my N + 1 = po = position.



-
Brian A. J. Salchert