Re: Marie Jean Faucounau sues me for at least 8,487 Swiss Francs

From: Franz Gnaedinger (frgn_at_bluemail.ch)
Date: 12/07/04 

Date: 7 Dec 2004 00:55:40 -0800

Google installed beta group and makes a mess of my number patterns.
Please read my messages in the original format, and use a BIG lens,
for they render the 'original' format in the tiniest fonts.

My adventures in the math-history list, Jul/Aug 1997, part 5

Human made things have their scientific correlates. A radio
has a scientific correlate in Clark Maxwell's electro-magnetic
field equations; a GPS device, used for example for mapping
the ruins and further archaeological finds on the seafloor
in front of Alexandria, has a scientific correlate in Albert
Einstein's relativity theory; and in a similar way, I dare say,
the Ziqqurats of Sumer and the Egyptian pyramids have their
scientific correlate in mathematical techniques and algorithms
as I am reconstructing them since 1979 (first number column),
1991/92 (royal cubit and 'magic wands,' later on called Horus
cubits), 1993/94 (calculating the circle on the basis of the
Sacred Triangle 3-4-5), 1996-2002 (Rhind Mathematical Papyrus,
Babylonian clay tablets YBC 7829 and Plimpton 322). Must I add
that such work can't be published? Not necessary? Thank you.

In my previous messages I introduced some of my number patterns.
Another means of early mathematics had been, I believe, number
sequences providing handy values of irrational numbers such
as pi.

The number of the circle is less than 4, but a little more than
3. Write 4 above 1, and add repeatedly 3 above 1, and look up
my message in the original format, for beta google makes a mess
of my number patterns):

4 (plus 3) 7 10 13 16 19 22 25 28
1 (plus 1) 2 3 4 5 6 7 8 9

Write 3 above 1, and add repeatedly 22 above 7:

3 (plus 22) 25 47 69 91 113 135 157 179 201 223
1 (plus 7) 8 15 22 29 36 43 50 57 64 71

245 267 289 311 333 355 377
78 85 92 99 106 113 120

Write 9 above 3, and add repeatedly 19 above 6:

9 (plus 19) 28 47 66 ... 256
3 (plus 6) 9 15 21 ... 81

A famous problem from the Rhind Mathematical Papyrus says that
a square of side 8 and a circle of diameter 9 have (nearly)
the same area. The implicit value of pi is found in the above
sequence: 256/81 = 3.1604... This value is often dubbed the
ancient Egyptian pi. However, my interpretation of over 65
problems from the Rhind Mathematical Papyrus led me to the
conviction that the Egyptians didn't use just one single value,
but plenty of values provided by the above and further number
sequences, which were also known to the Babylonians (see my
interpretations of YBC 7289 and Plimpton 322 on my website).

Number columns and sequences allow easy solutions to difficult
problems. An example. Let the side of a square measure 10 royal
cubits. Draw a circle around it. How long is the circumference?
The side of the square measures 10 royal cubits or 70 palms.
My number column for the square root of 2 proposes a diagonal
of 99 palms. Now look up one of the above pi sequences. In the
lower line is found the number 99, above stays the number 311,
hence the circumference of the circle around the square of side
length 10 royal cubits measures practically 311 palms, with
a tiny mistake of less than 1/7 millimeters! A brillant result,
no formulas required, all one has to do is to look up a number
column and a number sequence.

But of course my number columns are trash (John Horton Conway,
then holder of the Von Neumann Chair at Princeton); listening
to me and Domingo Gomez Morin pondering the realm of number
patterns is like listening to a flea and a louse arguing
(can't remember who wrote that); arguing with me is throwing
pearls before swine (David Fowler of Cambridge, Massachusetts,
an expert on Greek mathematics at Platon's Academy); my work
is numerology, pyramidology, and so on, and so on, and so on.

My crime was to attest a mathematical knowledge to the Egyptians
and Babylonians. Mentioning the number of the circle pi and the
golden number phi in the context of the Great Pyramid at Giza
was bad enough, but to show how these numbers could have been
approximated, and quite easily so, was the worst of crimes.

Fred Rickey, a teaching professor of mathematics and the "owner"
of the math-history list, informed me via e-mail that Egyptian
mathematics doesn't really belong to the history of mathematics.
I went on considering Egyptian and Babylonian mathematics parts
of the history of mathematics, most valuable ones, worth of being
explored in a fresh way, by means of new approaches, and this,
of course, meant my finl banning from the math-history list.

I go on believing that a prospering global society requires,
among other things, a fair history of civilization.

Franz Gnaedinger www.seshat.ch

> My adventures in the math-history list, Jul/Aug 1997, part 4
>
> Listening to me and Domingo Gomez Morin discussing our number
> patterns is like listening to a louse and a flea arguing ...
> Very nice, indeed. So that is the way Ivy League professors
> and their allies are discussing online.
>
> I was attempting and leading a scientific discussion, exploring
> the "wondergarden" of early mathematics, and when I showed them
> that number patterns are / have been / could have been a tool
> of early mathematics, worth of being considered, their bare
> existence being of interest, even allowing a systematic method
> for calculating the circle, much simpler and more accessible
> than the one by Archimedes - well, when I was doing so, hoping
> to raise interest, John Horton Conway showed up and turned all
> my ideas down.
>
> Why should my number column from 1979, which allows an easy
> approximation of the square root of 2, be so bad? Its numbers
> are the precise equivalent of the continued fraction for the
> square root of 2, but my number column is much simpler, no
> fractions involved, just whole numbers, a simple algorithm
> requiring additions and multiplications by 2 (adding a number
> to itself), and elegantly explaining the marvelous Babylonian
> value 1;24,51,10 for the square root of 2, as found on the
> famous Babylonian clay tablet YBC 7289.
>
> John Horton Conway simply told me that the Babylonians did not
> use such an algorithm. They just applied the trial and error
> method.
>
> I asked him to perform such a calculation. He just repeated his
> verdict. I asked him again. To no avail. Finally he called my
> number columns "trash."
>
> I found my first number column back in 1979, while interpreting
> Leonardo da Vinci's Last Supper wallpainting, examinging its
> ideal geometry, and the one of the former refectory of Santa
> Marie delle Grazie at Milan (a perfect match). The lunettes
> above the painting are sized according to the partition of
> a square with an inscribed octagon. I tried several numbers
> that could explain their relative size:
>
> small large small
> 5 7 5 sum 17
> 7 12 7 sum 24
> 12 17 12 sum 41
> 17 24 17 sum 58
>
> Thomas Brachert, by then at the SIK Zurich, had found the basic
> grid 6 by 12 units. A finer grid of 12 by 24 smaller units would
> suggest the solution 7 10 7 (sum 24) which is confirmed by the
> actual measurements (at least on my small reproductions).
>
> Now I had another look at my numbers and arranged them thus:
>
> 5 7 10
> 12 17 24
>
> There was a pattern showing that allowed expansion:
>
> 5 7 10
> 12 17 24
> 29 41 58
> 70 99 140 and so on
>
> Then I completed my number pattern upward and got my number column:
>
> 1 1 2
> 2 3 4
> 5 7 10
> 12 17 24
> 29 41 58
> 70 99 140 and so on
>
> Delve into the problem of approximating the square root of 2
> and you will see this or a similar pattern emerge, inevitably.
> Compare lists of doubled squares and simple squares, allow
> differences of 1, and you obtain the ladder of Eratosthenes.
> Allow mistakes of 1 or 2 and you obtain my above numbers.
>
> John Horton Conway and his allies believe that the history of
> the square root of 2 began with the Greek continued fraction;
> before the Greeks there were only lucky guesses. I showed him
> that my number column is the exact numerical equivalent of
> the continued fraction (1,2,2,2,...) but much simpler, well
> accessible to the Egyptians and Babylonians, and most probably
> used by them long before Greek mathematics began to flourish.
> Saying _that_ was my crime ...
>
> I am interested in very simple methods; in the simplest ways
> of calculating the square, equilateral triangle, cube, double
> square, and circle. I found those methods. Why me, why not them?
> Because they are blinded by the Greek dogma. Which dogma stays
> in the way both of a fair history of civilization and of easy
> ways of teaching and learning basic mathematics and geometry.
>
> Franz Gnaedinger www.seshat.ch
>
>
> > (Dr. Marcel Rochaix of www.ekbt-law.ch has become my best reader.
> > He is getting well paid for reading my lines, whereas my kind is
> > working for free, even paying for their work, sharing their ideas
> > and getting derided for doing so)
> >
> > My adventure in the math-history list, Jul/Aug 1997, part 3
> >
> > When the relevance of our number patterns - the one by Domingo
> > Gomez Morin and mine - where doubted, and when we had been told
> > that following our discussion is like listening to a louse and
> > a flea arguing, I began defending our approach by shwoing that
> > number patterns are a fine and simple device indeed, even
> > allowing a systematic calculation of the circle ...
> >
> > Let a square grid measure 10 by 10 royal cubits = 70 by 70 palms
> > = 396 by 396 fingers (actually finger breadths). ASCII drawing:
> >
> > . . . . . d . . . . .
> > . . e . . . . . c . .
> > . f . . . . . . . b .
> > . . . . . . . . . . .
> > . . . . . . . . . . .
> > g . . . . + . . . . a
> > . . . . . . . . . . .
> > . . . . . . . . . . .
> > . h . . . . . . . l .
> > . . i . . . . . k . .
> > . . . . . j . . . . .
> >
> > The side of the square measures 10 royal cubits or 70 palms,
> > the diagonal practically 99 palms (see my number column from
> > 1997). The points abcdefghijkl mark a circle. The points a d
> > g j mark the four ends of the axes, while the distances of
> > the eight points b c e f h i k l from the axes and from the
> > center of the grid are defined by the Sacred Triangle 3-4-5.
> >
> > The four small arcs bc ef hi kl measure practically 40 fingers
> > each, the eight longer arcs ab cd de fg gh ij jk la measure
> > practically 90 fingers each, yielding a circumference of 4x40
> > + 8x90 = 880 fingers = 220 palms. Divide them by the diameter
> > 70 palms and you obtain the famous approximate value 22/7 for
> > the number of the circle.
> >
> > The short diagonals of the grid, bc ef hi kl, are defined as
> > the square root of 2, while the longer diagonals ab cd de fg
> > gh ij jk la are defined as the square root of 10 = 2x5. We can
> > easily calculate these roots thanks to my number columns. Now
> > consider this. The arcs are slightly longer than the diagonals
> > of the grid, so let us choose values that are slightly larger
> > than the square roots of 2 and 5: 10/7 for the first root, 9/4
> > for the second root. Calculating the periphery of the polygon
> > using these values we obtain:
> >
> > 4 x 10/7 + 8 x 10/7 x 9/4 = 220/7 royal cubits = 220 palms
> >
> > Divide 220 palms by the diameter 70 palms and you obtain the
> > same ratio 22/7 or 3 1/7 or in my simpler notation 3 '7.
> >
> > Now let us consider a sequence of ever finer grids measuring
> > 10 by 10, 50 by 50, 250 by 250, 500 by 500 ... ever smaller
> > units. The circumference of the inscribed circle passes the
> > four ends of the axes, plus 8, 16, 24, 32 ... points of the
> > ever finer grid which are defined by the following triples:
> >
> > 3-4-5 15-20-25 75-100-125 375-500-625 ...
> > 7-24-25 35-120-125 175-600-625 ...
> > 44-117-125 220-585-625 ...
> > 336-527-625 ...
> > ...
> >
> > The triples can be found by means of several algorithms.
> > My then algorithm involved square numbers. Later on I found
> > a linear plus minus algorithm. If you got a triple a-b-c and
> > wish to find the next one proceed as follows:
> >
> > +- 3a +- 4b +- 3b +- 4a 5c
> >
> > The plus minus terms provide several values; choose the positive
> > ones that are not divisible by 5 (e.g. starting from the triple
> > 3-4-5: minus 3x3 plus 4x4 = 7, plus 3x4 plus 4x3 = 24, 5x5 = 25;
> > new triple 7-24-25).
> >
> > The resulting polygons have an amazing property: their side
> > lengths are given by the square roots of 2 and 5 and their
> > multiples and products. Now the square roots of 2 and 5 are
> > provided by two of my very simple number columns. So we have
> > a systematic method for calculating the circle, much simpler
> > and more easily accessible than the one by Archimedes.
> >
> > Franz Gnaedinger www.seshat.ch

Relevant Pages

  • Re: Marie Jean Faucounau sues me for at least 8,487 Swiss Francs
    ... Google installed beta group and makes a mess of my number patterns. ... Another means of early mathematics had been, I believe, number ... The number of the circle is less than 4, ... Let the side of a square measure 10 royal ...
    (sci.archaeology)
  • Re: Marie Jean Faucounau sues me for at least 8,487 Swiss Francs
    ... Google installed beta group and makes a mess of my number patterns. ... Another means of early mathematics had been, I believe, number ... The number of the circle is less than 4, ... Let the side of a square measure 10 royal ...
    (sci.archaeology)
  • Re: Marie Jean Faucounau sues me for at least 8,487 Swiss Francs
    ... Google installed beta group and makes a mess of my number patterns. ... Another means of early mathematics had been, I believe, number ... The number of the circle is less than 4, ... Let the side of a square measure 10 royal ...
    (sci.archaeology)
  • Re: SubTyping versus SubClassing
    ... small subset of ones used in mathematics. ... >> which you'd better have a square for each rectangle, ... Operations defined on the types are that theorems we have to prove ...
    (comp.object)
Loading