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.*

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

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

factor of unity). The numbers are called the

divide 1/6 of a circle's circumference by 22.1875399 (the

result by 21.1875399 (the

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

radius of 280."

the hieroglyph for the fraction, 2/3rds (above right). One of the greatest achievements of ancient Egyptian mathematics

was their ability to find

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

numbers--

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

"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

would be 293 1/3rd; and dividing this by 22 (

radius of 280."

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.

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

theories about the mathematical basis of the Pyramid of Cheops but these

calculations have

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 *

structureswhich 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.

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

structures

form the basis of their system are called,

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,*

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

'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.

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

'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

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.

which are a geometric/spatial transformation of

to communicate in our own language. However,

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

The makers of the glyphs assumed we were aware that our written words were an

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

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,

be mapped within the relational patterning defined by a circle

constructed using

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.