W  I  N  K  L  E  R     W  O  R  D     A  R  T     I  N  T  E  R  N  A  T  I  O  N  A  LTranslation & Decryption of Rare & Ancient Languages S I G N A L G L Y P H   R E S E A R C H   P R O J E C T As per the Committees request, these reports will contain as little scientific/technical
language as possible. During the past Quarter, we've learned a great deal about their
approach to mathematics. Some of the information has profound implications to the history
and development of our own mathematical concepts. One major difference between our
approach and their's, is that they don't use
pi for calculations involving circles (they have
no word for the 'diameter'). When they talk about the linear measure across a circle, they
use the plural of the word for 'radius'. Their name for the tool used for drawing circles is
'radial-arc-marker'. This gives a clue to their method of calculating the radius. They use
two numbers which have a
ratio of unified correspondence (two integers differing by a
factor of unity). The numbers are called the
trace and the trac. To find the radius, they
divide 1/6 of a circle's circumference by 22.1875399 (the trace) and then multiply that
result by 21.1875399 (the trac)--click on the formula to view a comparison to the use of pi.
 For calculations which do not require extreme accuracy, they use rounded off versions: 22.1875 or 22 3/16ths (trace), 21.1875 or 21 3/16ths (trac)--their fractions are the same as ours. When they speak of the whole numbers of the trace and trac; they use the terms: bow (22) and band (21). Calculations using only the whole numbers are as accurate as a 3.14 value of pi. At the end of their description of the process for calculating the radius, there was a notation: "1/6th of perimeter, 60 degrees; Radial angle, defining orientation for two-dimensional space, 90 degrees; arc degree ratio 60 to 90 reflects (the symbol shown below left)". A member of our team, who is an expert in reading Egyptian hieroglyphics, noted that their symbol was very similar to
the hieroglyph for the fraction, 2/3rds (above right).
One of the greatest achievements of ancient Egyptian mathematics
was their ability to find 2/3rds of any number, whether integral or fractional--no one knows why this was so important
that they would make it a foundation of their entire system of mathematics. Consequently, when we asked about the
meaning of the symbol, we also asked about the possibility of any connection to the Egyptian hieroglyph. They replied
that their symbol represents
the elemental relation of the numbers, '2' and '3'--a relation which is connected to the
patterning of many mathematical processes. They classify '2' and '3' and their sum of '5' as elemental
numbers--
numbers which are prime but not part of the regular class of primes (they provided a description of the
system of prime distribution which will be presented later in this report). The reason '2', '3', and '5' are considered to be
in a class by themselves is that they are not contained in the cycle which orients the distribution of primes and they can
be used in combination to express all larger numbers. Despite affirming that their symbol can be used to express the
fraction 2/3rds, they declined to discuss any connection to the hieroglyph because it would violate their communication
guidelines. But they did mention: use of their symbol would be consistent with the viewpoint that '7' and '11' were the
initial integers in the class of primes, rather than '2', '3', and '5', which their symbol defines as a separate group of
elemental numbers. The following enigmatic statement was also included with their remarks:

"Since 280/440 reduces to 7/11, it reflects the ratio of the initially occurring primes. If 440 is one side of a square, 440
multiplied by 4 yields the square's perimeter of 1760. If this 1760 square perimeter is reshaped into a circle of the same
perimeter, what is the radius of that circle using the
bow and band ? Since 1/6th of a circle with a perimeter of 1760
would be 293 1/3rd; and dividing this by 22 (
bow) would result in 13 1/3rd; multiplying this result by 21 (band) will give a
We believe they were trying to tell us (by using only mathematical information)
that their symbol and the hieroglyph are connected: In Egyptian cubits, 280 is
the height of the Great Pyramid; 440 is the measure along one side of its base;
and 1760 is the perimeter of the Pyramid's base. Their calculations show the
relationship between the height and base as a reflection of the primes, '7' and
'11'. Also, If the perimeter of the square at the base of the Pyramid is
thought-of as the perimeter of a circle; the height of the Pyramid is the radius
of that circle, when calculated using the
bow and the band. There are many
theories about the mathematical basis of the Pyramid of Cheops but these
calculations have
an exact correlation to its most basic dimensions--but even if
our assessment is true, the circumstances of the connection are unknown.  When we began to discuss our philosophies concerning mathematics, a profound difference was revealed in our
methods of conceptualizing mathematical phenomena. Mathematics may be the universal language but expression of
mathematical concepts in the form of algebraic symbolization is not universal. To those with whom we are
communicating, abstract symbolization of the logic behind particular mathematical concepts is not considered
advantageous. To paraphrase their attitude toward such an approach: Nature's methodologies will always transcend
the logic of the seekers of its patterning; if a mathematical system is based on a preconceived formulation of logic
rather than a rigorous mapping of Natural phenomena, the system of mathematics will be confined to preconceived
conceptions of relational possibilities. Their system of mathematics is based on building rigorously definable
relational
structures
which are information-preserving transformations of Natural phenomena. The fundamental relations which
form the basis of their system are called,
recurrents--relations appearing repeatedly in diverse phenomena. They
shun the notion of 'mathematical proof' because they say that counting is an incremental process and, therefore, its
proofs must be constructed incrementally. And they say Nature is not limited to incremental processes; Nature's
mandate is 'efficiency', not proof--it will sometimes produce a single result from a multiplicity of simultaneously
occurring functions. They cited the System of the Distribution of Prime Numbers as an example of a synthesized
outcome of rigorously interactive processes. According to them, primeness is used by Nature to create a system
of markers which uniquely define the landscape of linear sequences.
All of Nature's forces have to be kept in sync or the fabric of the
universe would fall apart, but 'Time' is an ever-evolving continuum;
locations on the landscape of the continuum have to be uniquely
identifiable so that Nature's forces can maintain the alignment of
their synchronization (that's why prime numbers relate to things like
wave properties). To visualize the System of Prime Distribution,
imagine a circle of 30 points, which are equally spaced around the
arc. Starting with any point and moving in either direction (clockwise
is shown in the diagram on left), Imagine counting the 30 points but
begin the  count with '0' instead of '1'; consequently, the 30 points
are counted using the numbers '0' through '29'. But you don't stop
counting--you continue with '30' through '59', and then '60' through
'89', and so on--you're just infinitely counting around the same circle
of points and writing the numbers next to them. Afterwards, if all
these numbers were written next to the points as they were counted;
the prime numbers--with the exception of the
elemental numbers,
'2', '3', and '5'--would all be written next to the same, eight points. The first numbers to be written next to the eight
points: '1', '7', '11', '13', '17', '19', '23', and '29' (as shown in the diagram); are all prime except for '1' or 'unity'. As
stated in the discussion of
elemental numbers, '7' and '11' are the first two primes to appear in the cycle (not '2' and
'3'). But this cycle is only part of the system.

After primes emerge within the cycle, they are involved in another process which is integrated within the overall system
of distribution. After a prime number emerges, products based on that prime's sequential multiplication by powers of
itself and each higher prime will systematically emerge in future progressions of the cycle. Here's how it works: the first
prime to appear is '7', and '7' multiplied by itself is '49'; so the composite, 49, will appear in one of the eight locations in
the next rotation of the cycle. Then '7' is multiplied by the second prime to appear, '11'; so '77' is the next composite
which will be included. Then '7' is multiplied by the third prime, '13'; will result in the inclusion of the composite, 91. And
this continues: '7' is infinitely multiplied by powers of itself and each higher prime. All these composites will eventually
emerge within the same cycle as the primes. The appearance of every prime number spawns an endless string of
composites which will be incorporated into future manifestations of the cycle. Since these composite products are
originating in a cycle which is unevenly spaced, and the pattern of their factorization is not aligned with the pattern of
the cycle; the system's underlying regularity becomes less and less apparent as the composite products continue to
build-up.

The entire system is completely rigorous and the appearance of every prime number and every composite can be
predicted (
click here for the demonstration of rigorousness and predictability). However, the two processes--the cyclic
progression and the factorization of the composites which will be included in that progression--are inseparable; this is
the reason that the system as a whole cannot be expressed algebraically. Number theorists are aware of both
processes involved in the System of Prime Distribution but they see them separately, as a
reduced residue class and a
sieving routine, rather than as the integrated components of a single system. Now lets move to another subject. We've all been wondering why they based their communication with us on glyphs
which are a geometric/spatial transformation of our language. Obviously, it makes sense that it would be easier for us
to communicate in our own language. However,
visualization is the foundation of their approach to communication and
the letter-sequences which form our written words are not visual images--they are a form of abstract symbolization
which has no visual meaning. Written words are not images because the visual characteristics of their form are
irrelevant; if that were not true, the same word would have an entirely different meaning depending on whether it was
hand printed, written in script, typed in uppercase or lowercase, written in Braille, or spelled verbally. The form of the
letters is irrelevant to the transmission of a word's meaning because the visual characteristics of a letter do not define
its identity--a letter's identity is defined by its role in the patterning of lexical sequences. Although written language is
not visually expressive, its patterning is capable of triggering meaningful imagery; consequently, in some sense, it
would have to be in sync with our mechanism of
comprehending imagery.

The makers of the glyphs assumed we were aware that our written words were an
abstract symbolization of the lexical
relations of our language. And they assumed we would recognize the visual modeling of the information encoded in
our alphabetic sequences. They produced an information-preserving transformation of our written language based on
what they consider to be the
fundamentals of visual modeling, the point, line, and circle. To them, a circle is a regular
polygon with an infinite number of vertices. If all these vertices were to be interconnected with lines,  the result would
be an infinite number of lines moving in an infinite number of directions in the two-dimensional space within the circle.
Since every one of these lines is comprised of an infinite number of points,
all possibilities of two-dimensional form can
be mapped within the relational patterning defined by a circle
. Since the model of our written language was
constructed using
visual fundamentals, and all content of the alphabetic system was included in the model; they
assumed we would recognize the forms.

This is only a summary of the information we have obtained. For additional details, Committee Members should
contact the Office of the Project Director at Winkler Word Art.