One of our central concerns in marking correspondences between the number five (5) and With Hidden Noise (by-the-numbers) has to do with the general idea of measure and, more specifically, with the five inches measured along each theoretical, external "edge" of the sculpture. The brass plates are five inches square and the bolts are approximately five inches high. Robert Lebel cites the piece in his Catalogue Raisonn as 5 x 5 x 5.

[ Robert Lebel, Marcel Duchamp, p. 168, where it is listed as #129, an "Assisted ready-made." ]

Duchamp had ample opportunities to correct this data in 1963, when the artist and Walter Hopps cut up a copy of the Lebel catalogue and pasted the corrected pieces together as a "make-ready," published in that photocopied, pseudo-facsimile form for the Pasadena retro-spective exhibition. The piece was shown there "upside down," too.

[ By or Of Marcel Duchamp or Rrose Slavy. Marcel Duchamp: A Retrospective Exhibition. Pasadena Art Museum, October 8 through November 3, 1963. In this catalogue the piece is listed as Number 60.]

While Duchamp did make other corrections and emendations on the important occasion of that, his first retrospective, he let stand these "5-inch" figures for With Hidden Noise. And for the exhibition catalogue of Duchamp's works at the Tate Gallery in London (1966), Richard Hamilton also recorded the measurements of With Hidden Noise in English inches, which he rounded off (in the manner of Lebel and Hopps) to five inches in each of the three conventional dimensions.

[ The Almost Complete Works of Marcel Duchamp, at the Tate Gallery, 18 June-31 July 1966 (Arts Council 1966), organized by Richard Hamilton. The piece is No. 24 on page 55. A note at the beginning of the Catalogue (p. 10) does indicate that "Measurements are given to the nearest cm/in." which are here "12 x 12 x 12 cm / 5 x 5 x 5 in." ]

In his 1969 monograph, however, Arturo Schwarz lists the dimensions of With Hidden Noise with true devotion to the aesthetics of precision, providing the measurements both in fractions of an inch and in tenths of a centimeter: 5 1/16" (12.9 cm) x 5 1/8" (13 cm) x 4 1/2" (11.4 cm). Aware of Duchamp's own respect for precision--unless we can somehow divine what he might have intended for this particular piece--we must now wonder what might be, for us, an adequate order of concern with accuracy. Of course, if we were to press the issue, the figures Schwarz gave could be further refined. For example, to call the bolt length 4 1/2 inches one must measure from inside the slotted head, since the actual outside dimension would be closer to 4 11/16 inches. But an over-precise concern with inch-fractions precludes making our point about the simple number five in relation to the dimensions of the piece. Duchamp's apparent satisfaction with the approximation of five inches by five inches by five inches in those catalogues supports--or at least does not contradict--our proposing to relate the number five symbolically to dimensions of With Hidden Noise.

With this caveat for the fractional and metric refinements of Signor Schwarz, we take it that one of the principal aspects of the piece "in its fiveness" has to do with its measurement in ENGLISH INCHES. This reckoning assumes that for Duchamp a switch in thinking from centimeters to inches most probably occurred following his initial arrival in America in 1915. So, let us now consider more fully the historical nature of this standard unit of measure newly employed by Duchamp for his first works made, or "readymade," in America.

The English inch does appear to be a truly geodetic (or, "geodeisic," both are used interchangeably to mean "earth-commensurate") standard in contrast to the arbitrary, French, politically-inspired meter. The inch was first established in 10th century England by King Athelstan (924-940), as a 1/12th fraction of the legally-defined foot. That foot of twelve inches was the principal unit used for reckoning "the King's girth," which measured:

3 miles of 5280 feet, plus
3 furlongs of 600 feet, plus
9 acres of 66 feet, plus
9 palms of 3/4 foot, and
9 barleycorns of 1/3 inch,
which altogether equalled a radius of 18,250 feet,
or, a radius of 3 minutes of latitude, which meant
a diameter of 6 minutes of latitude north to south,
or 1/10 of [a] degree.

The words of law of Athelstan were repeated exactly in the legislation about measures issued by King Henry I. The law of Athelstan provides the fundamental text for the study of English measures, but it has been ignored.

[ Livio Catullo Stecchini, "Notes of the Relation of Ancient Measures to the Great Pyramid," Appendix, in Peter Tompkins, Secrets of the Great Pyramid, Harper and Row, New York (1971), p. 344. We paraphrase Professor Stecchini's text in the following paragraph. ]

The necessary way in which measurements on the surface of the Earth were formally related to astronomical observations required setting standards for the length of a degree of both longitude and latitude. The linear length, going east or west, that corresponded with the angular measure of one degree of celestial arc, would vary according to latitude, just as a section of orange is widest at the "equator" and narrows to a point at either tip. If we imagine ourselves to be standing exactly at either the north or the south pole, then the linear distance it is necessary to travel in order to make a complete 360-degree circle (at a constant latitude) around through each degree of longitude, would be the circumference of a circle we could draw in the snow at our feet.

But to make a circle through all 360-degrees of longitude at zero-degrees latitude (at the terrestrial equator) would require traversing a circumference of--approximately--24,907 miles. That may give us average citizens a ball-park estimate, but it is nowhere nearly good enough for geographers. As it turns out, measuring the circumference of the earth is not quite such a simple matter. Today, several standards are in use, with different orders of precision: 40,000 kilometers, for example, would give 111.11 kilometers for the linear equivalent of one degree of equatorial longitude. Refining our concept of this, we may note that the sophisticated ancients of Pharaonic Egypt probably began with an estimate of what we might count as a little over 40,000 kilometers, or some 40,075,000 meters,

and then modified the figure in order to establish a relationship between the equatorial degree and the degree of the middle latitude of Egypt. The Egyptian estimate agrees with our current ones: the equator is 40,075,452 according to the Clarke Spheroid and 40,076,596 according to the International Spheroid.

[ Stecchini, in Tompkins, Secrets of the Great Pyramid, p. 346. ]

By the figures cited in the edicts of King Athelstan, we deduce that one geographical degree was taken to be 365,000 English feet, or 69.128 miles, which is the length of a degree at the latitude of Winchester. The custom of the King's girth defined "the area in which the King's peace was in force," considered as a direct extension of the royal residence, in which crimes against private persons were treated as crimes against the crown. This method of establishing standard units of measure for the realm also served to relate the regal presence to a cosmic frame of reference, an idea that may derive from the similar system initiated (or, revived) by the Egyptian Pharaoh Akhenaten.

Another important link with ancient Egyptian and subsequent Mediterranean practices of mensuration is demonstrated by the history of stone masonry. Successful transmission of this craft depended upon each generation's passing along an understanding of its theoretical, mathematical bases, and especially the practice of geometry. The precision of geometry was first applied to stone cutting in Egypt during the Third Dynasty around B.C. 2700, in the step pyramid of King Zoser at Saqqara, the earliest cut stone monumental structure in the history of architecture. We also know the innovator's name, one of the first distinct artistic personalities in all of history: the vizier and royal architect Imhotep, an exceptional, immensely talented human being, himself not of royal blood but lavishly honored with titles according to inscriptions on a statue found in a courtyard of the pyramid and temple complex. And we also have a clue to the techniques of applied geometric logic by which Imhotep proceeded, for if there were one single graphic key to the sacred geometry of the Egyptians, as Professor Stecchini suggests:

It is a matter of the right triangle with an angle of 36 degrees which the Egyptians called mr...the name To-Mera, which the Egyptians gave to their country was a reference to this triangle.

[ Tompkins, p. 377. See also, Stecchini's analysis of Imhotep's profound contributions to global civilization, pp. 375 ff. The classic pyramid, of course, is a smooth five-sided geometrical solid. ]


The pyramid of the Great Seal of the United States, pictured on the back of the dollar bill--beginning with the 1935 series--has a capstone angle of 36 degrees. It is depicted as virtually a plane isosceles triangle with two base angles of 72 degrees each. Thus, the pyramid of the Great Seal, built of 13 courses of stone, one for each of the original 13 colonies-become-states, is (like the mr triangle of Imhotep, one of whose angles it repeats) much steeper than the 51-degree, 51-minute base angle of the Great Pyramid at Giza.

The technical basis of Egyptian geometry was impeccable. Indeed, the later success of the ancient Greeks, with whom geometry is nowadays most readily associated, was based solidly upon the knowledge and technique of the ancient Egyptians....During his destructive excavations within the fabric of the Great Pyramid, Colonel Howard Vyse found in one of the chambers "many quarry- marks similar to those in other chambers, and also several red lines crossing each other at right angles, with black equilateral triangles, described near the `intersection' in order probably to obtain a right angle...." These lines and constructions were necessary for the masonic arts of stone cutting, fitting and finishing [and] for any technical method of drawing, it is necessary to have a geometrical basis.

[ Nigel Pennick, Sacred Geometry: Symbolism and Purpose in Religious Structures, Turnstone Press Limited, Wellingborough, Northamptonshire (1980), p. 51. Pennick relates Egyptian geometry to sacred cosmology, and also provides a stirring characterization of Imhotep, pp. 47 ff. ]

One important branch of this tradition, together with its related psychology and cosmology, came into England through Middle Eastern intermediaries even before the Crusades. During the time of Athelstan in the tenth century A.D., Freemasonry first entered England as a Sufi society. Only some four hundred years later was Freemasonry, disguised as a craft guild, introduced by the Knights Templars into Scotland.

[ Robert Graves, "Introduction," Idries Shah, The Sufis, p. xix. ]

Transmission of the lore of masonry has been documented at least since the edicts of King Rothari in Lombardy of the seventh century. By those legal acts masons attained juridical freedom: literally the freedom to move about, liberated from whatever laws binding peasants to the land or slaves to masters. And from this practical freedom developed the autonomous government of the lodge with its administra-tion of justice, independent of BOTH church and state. This firmly established the great historical precedent for the Bill of Rights, with its clearly articulated principle of the separation of church and state, guaranteeing--by law--both physical freedom and spiritual liberty for each and every individual citizen. We know that Freemasons as well as practicing stone masons were intimately involved with the construction of the Washington monument, whose obelisk form expresses an explicit connection with ancient Egypt. Indeed, the idea of thirteen united colonies was achieved under the leadership of Freemasons:

Boston Masons organized the Tea Party at the Green Dragon Tavern....Paul Revere was a Master Mason, as was every general officer in the Revolutionary army, starting with Joseph Warren, Grand Master of the Massachusetts Grand Lodge, the first to die at Bunker Hill....Of the fifty-six signers of the Declaration of Independence, some fifty were Masons, as was its prime author, Thomas Jefferson. The same was true of the Constitutional Convention. In colonial times Freemasonry had been the only institution in which leaders of the different colonies could meet on common ground--Protestant, Catholic, or Jew....In the Lodges men of the most diverse religious and political views, rich and poor, could come together in a spirit of mutual harmony and confidence... something the princes of the world found hard to tolerate.

[At the dedication of the completed Washington Monument in 1884, props for the Masonic ceremony included]:

the same gavel which George Washington had used to lay the cornerstone of the Capitol, the same Bible on which he had taken the oath as president...plus a golden urn containing a lock of Washington's hair passed down by every Grand Master of the Grand Lodge of Massachusetts....Speaker of the House Robert C. Winthrop ...regretting that the monument could not have been hewn from a single stone, like an Egyptian obelisk...said he nevertheless took pleasure in the idea that the united stones standing firm and square could serve as a symbol of the national motto, "E pluribus unum." John C. Palmer, speaking for the fraternity, declared that masons were no longer builders of cathedrals and castles, "poems in marble and granite," but of human society whose stones were living men, "their minds enlightened with divine truth, their hearts radiant with discovering the joy of pure love, their souls cherishing--like the ancient Egyptian worshippers of Osiris--the hope of immortality."

[ Peter Tompkins, The Magic of Obelisks, Harper and Row, New York (1981), p. 309; p. 336 f. ]


Some say the United States eagle was originally imagined as the Phoenix. We are not here thinking of Benjamin Franklin's (ultimately rejected) proposal to choose an avian emblem for America entirely new to the eyes of transplanted Europeans: the indigenous wild turkey (an opportunity later taken by the makers of an excellent and high-powered bourbon whiskey). Since antiquity, the Phoenix has been associated with the magical capacity of self-regeneration from its own ashes, so it comes as no surprise that when this magical bird and its society were consumed in the flames that razed ancient Phoenicia, its spirit was revived in Carthage, thought to have been a rich Phoenecian trading city prior to its catastrophic demise in the Punic Wars. The merchant nation of Phoenecia itself, on the littoral of the Eastern Mediterran-ean may have been the renewed manifestation of an earlier, African people. The Phoenix symbol, favored in Imperial China and known in Russia as the Firebird, also seems to have impressed early Americans.

We should emphasize here that we are not referring to the relatively modern capital city in the State of Arizona, since it does not truly deserve the name: there never was much more than a thin string of riparian settlements in the "Phoenix Valley" there to be reborn, nor any great centers, say, from the time of the Anasazi, the "Ancient Ones." The water, which supplies the otherwise missing material basis for metropolitan Phoenix, Arizona, is artificially pumped great distances from the Colorado River at tremendous cost--though very heavily subsidized by political muscle--while suffering enormous wastage from evaporation. From almost every assessment based upon the realities of nature and the conclusions of reason, there obviously should not be anything at all like a city in that valley, and if the man-made water delivery system ever runs dry, there won't be for long.

The alchemy of the middle ages and the revolutionary political vision of the the Founding Fathers of the United States of America were, neither of them, so arrogantly defiant of nature and reason. They dared not be, since both were dedicated to the creation of systems in which paramount attention was paid to enhancing the working processes of Nature herself. In this sense, coming to understand and refine the underlying dynamic paradigm, or modus operandi, represented a greater achievement than the acquisition of any particular material product or short-term gain, whatever the apparent political and economic advantage. The Novus Ordo Seclorum beneath the Eye of Providence on what is presently known as the obverse of the Great Seal, the "New Order of the Ages" makes clear the self-aware, radical, and truly revolutionary consciousness of its designers--Thomas Jefferson, Benjamin Franklin and John Adams--who were three-fifths of the committee that drafted the Declaration of Independence.

America was founded with a sense of purpose, beyond mere freedom from the British, which was an essentially negative aspect of the Revolution. The Founding Fathers believed that the United States had a special function in the family of nations, and that it was under the watchful Eye of Providence. The spiritual sources of the Revolution are demonstrated on the Great Seal of the United States [which portrays] the Founder's vision of the country they were creating, just as the Constitution is a set of rules for creating it.

[ Paul Zamarian, personal communication and unpublished notes. ]

We therefore have two histories of the United States. The one conventionally taught in schools emphasizes the formal study of the Revolution as a product of the reason-admiring historical period called the Enlightenment; its VERBAL formulation is set forth in the text of the Constitution. These WORDS are studied closely by lawyers, pop linguists, spin doctors and other citizens, some of whom are honored with high public office in the ongoing practical exercise of democracy as a living institution. For their services in obeying the injunctions and acting with respect for the constraints on government, and for the performance of related civic duties that perpetuate a tradition of legislation going back to the time of Edward I--a function based on both oral argument and written texts, the supreme of which in our United States is that very Constitution--the results of said process being put into the marked state as printed letters on sheets of paper (or parchment, etc.), made public, argued in the open courts, executed and enforced as the word, letter, and spirit of Law--these representative, office-holding citizens, who authorize the collection of taxes and pay our collective bills, do also pay themselves.

An alternate account is sometimes known as the secret history of the United States. The nature of the secret can be determined quite easily when we realize that America's history is also based upon thetransmission of VISUAL teachings. That the visual (graphic, iconic, pictorial, etc.) has been treated as though it were only secondary and technically incidental to the above mentioned verbal teachings can be appreciated now that we have tape recorders to bypass reading and writing for documentation of the word, for then we realize that the mode of visual transmission--and the substance of what is being transmitted--is different in kind. Its original, physical manifestation for the Founding Fathers was in terms of formal imagery also--just as with the words--to be set, carefully, consciously into the marked state as iconic signs and symbols, on rather a deeper level than mere graphic illustrations or pictorial representations of the dream and vision of a nation under law. But this body of information--which comprises such an integral part of our national heritage, keyed by the curious history of the Great Seal itself--has been virtually ignored.

For where the Constitution adheres to the rules for a legal system by which a nation may govern itself, even proscribing religious activity by the state, the Seal unabashedly embraces mysterious symbols that have nothing to do with legal issues, only with the deep sources of the idea of laws. The notes [of the Designing Fathers three] make it clear that they saw the beneficient Eye guiding the infant country as Moses led the Jews to the Promised Land.

[ Zamarian, Personal communication. ]


It took six years and many changes of committee members and advisors--involving the combined efforts of fourteen men--before the first die could be cut for the Great Seal in 1782. Three features survived from the first state of the trinitarian vision, the graphic submissions of the committee (and its formal advisor), as adopted in the final version of the Seal: the Eye of Providence surrounded by its radiant Glory, the date of Independence (1776) expressed in Roman numerals (MDCCLXXVI), and the Latin motto E Pluribus Unum..

The verbal formulation, the motto, may be translated as "Out of Many, One," referring to the formation of the Union by the thirteen original states.

Recent scholarship has pointed out the possible source of this motto. The Gentleman's Magazine, published in London from 1732 to 1907, was widely read in the American Colonies. Its title page carried that same motto and it is not improbable that it influenced the creators of the Seal.

[ The Great Seal of the United States, Department of State Publication 8868, Office of Media Services, Bureau of Public Affairs (released July 1976), n.p. (p. 5 f.). This publication represents an official voice of the State Department, explaining how the nation united has chosen to formally present itself, graphicially and symbolically, to sovereign foreign nations. ]

The motto appears on what has come to be called the obverse of the Great Seal. In the earliest sketches the motto was emblazoned on a freely floating scroll, still years away from being clenched in a bald eagle's beak. The scroll fluttered under a shield that sought to represent the thirteen states by their initials, a concept that did not survive. However, above the shield and other transitory figures, an eye appears within a triangle, surrounded by a "glory" of rays. The Roman numerals give the date of the Revolution, through the idea of marking a specific time in a form that was once qabalistic--expressing an equation between numerical values and capital letters of the Roman alphabet--but which, long an open secret, has become convention.

On July 4, 1776, soon after signing the Declaration of Independence, the Continental Congress "Resolved, tht Dr. Franklin, Mr. J. Adams and Mr. T. Jefferson, be a committee, to bring in a device for a seal for the United States of America." The task proved far more difficult than anticipated....The Congress desired an emblem and a national coat of arms that would give visible evidence of a sovereign nation and a free people with high aspirations and grand hopes for the future. The biggest obstacle facing the committee was to translate these intangible principles and ideals into concrete symbols that could be incorporated into an emblem. Franklin, Adams and Jefferson struggled unsuccessfully with several Biblical and classical themes [such as the motto: "Rebellion to Tyrants is Obedience to God."] But they made little progress and finally engaged the services of an outside consultant, Pierre Eugne du Simitire, a Philadelphia portrait artist, with some knowledge of heraldry and experience in designing seals.

[ The Great Seal..., (p. 1). ]

Benjamin Franklin, as a printer, was well aware of the rigorous set of conventions that govern graphic expression, Adams was a Harvard graduate, and Thomas Jefferson was well-schooled in the principles of design and symbolism. But almost immediately they secured the services of a professional consultant, since they were constructing a heraldic emblem by formal rules to represent an iconic perception of the Unity, and the celebration of this collective vision in Revolutionary action.

The positive identity of the engraver--the craftsman who actually cut the negative die in 1782--has not been established; perhaps it was one Robert Scot of Philadelphia. The Seal device shows a scrawny eagle with its talons extended to clutch an olive branch in its right talons and thirteen arrows in its left talons, while the thirteen stars are arranged so as to form a six-pointed star, surrounded by a Glory (rays of light) and clouds into which the eagle's head protrudes. This first die measured 2 5/16 inches in diameter, and through the agency of a screw press was impressed on a paper wafer then attached to official documents with a disc of red adhesive.


The die of 1782 also was used later to impress pendant wax seals. These were then suspended from the instruments of ratification of treaties by heavy ornamental cords. Boxes called skippets, usually of silver or silver gilt, housed and protected the wax pendants. In 1825 a die was cut exclusively for impressing these treaty seals [replacing the 1782 die for this purpose]. The government ceased using pendant seals in 1871 and retired the [1825 special] die. By 1841 the original die of 1782 had become worn and a new die was cut in steel [in which the eagle clutched only six instead of thirteen arrows]. In 1877 a new die of the Seal was cut but, like its [immediate] predecessor, it ignored the law and maintained the six arrows. Tiffany and Co., of New York, in 1885, engraved a 3-inch diameter die to replace the 1877 die. Its design strictly adhered to the law of 1782. In 1902 Congress appropriated $1,250 for the cutting of still another new die. Bailey, Banks and Biddle, of Philadelphia, executed the engraving in hardened steel. The die was first impressed on January 27, 1904, and was still in use [as of July 1976].

[ The Great Seal...., pp. 6, 8. ]

The visual image shown on each of these dies is that of the eagle, shield, olive branch and arrows, stars and Glory, i.e. what is called the obverse, but what originally appears to have been the reverse, of the Great Seal. As the face of the national emblem we show to the rest of the world, it is displayed, in full color, above the doors of all American embassies and consular posts throughout the world. It also appears on medals, flags, monuments, official stationery and publications, and on uniform buttons of the U.S. Army.

The image of what is today called the reverse--but may have been originally intended as the obverse (hence principal aspect)--of the Great Seal shows the Eye of Providence within an isosceles triangle (of 36-degrees at the apex), surrounded by its Glory, above an unfinished pyramid together with two other mottoes: Annuit Coeptis "He (or It, Providence) Smiles Upon (or favors) Our Enterprise," and Novus Ordo Seclorum "New Order of the Ages." The date in Roman numerals is shown as if carved into the stones of the bottom of thirteen rows in the truncated pyramid. The base angles of this pyramid are 72-degrees (one-fifth of a circle of 360-degrees), and it is truncated to symbolize the ongoing nature of democratic government among the union of states: emphasis on the PROCESS of the Great Work. This image has never been struck as a Seal die, although it does appear on the 1935 U.S. one dollar Blue Seal Silver Certificate. In an earlier state of this design, the pyramid with the Eye of Providence and its mottoes were printed on the right-hand side of the back of the one-dollar 1935 silver certificate--not as it is today. A surviving proof sheet shows the signature of then-President Franklin Delano Roosevelt; but it has been cancelled. Having first signed the proof under a hand-printed "Approved," the President then crossed it out; but, thinking the design might be saved by some positional modifications, F.D.R. then penned in his recommended changes, including the added legends beneath the iconic images. The right-hand image would be equated with the obverse, and the left-hand with the reverse, after the conventions of numismatics--seals, medals, medallions and coins--the formal language in which this national expression was conceived and designed. But for some reason still fraught with mystery, F.D.R. caused the left/right of the original design to be reversed. The actual proof sheet, with both versions and the "corrections" in Roosevelt's own hand expressly shows this switcheroo:

[above: sketch of a triangle] [above: sketch of an eagle]

but use "The Great Seal" "of The United States"

[below: the initials] FDR

The revised design, with the interchanged obverse and reverse, was approved by President Roosevelt and OK'd by Secretary of the Treasury Julian Morgenthau, marking the first time both the obverse and reverse--whichever which--appeared on U.S. paper currency.

We might note here that the word NUMISMATICS came into English from the French numismatique, meaning the study and collection of money and medals, i.e. an intellectually organized discipline, a formalization of the process of study. The Latin source of the French word is numisma, a coin, according the the American Heritage Dictionary. In turn, this word derives from the Greek noumisma meaning usage, or current coin, from the verb nomizein, "to have in use," and the noun nomos, "custom." Our modern word COIN, the piece of money, comes through Middle English where coyne meant "wedge" from the wedge-shaped design stamped on a coiner's die; this, in turn, derives from the Latin cuneus, or wedge. Referring back to the same Latin word, modern scholars coined the term CUNEIFORM in the New Latin, artificial academic language shared by disciplines in both science and the arts. The related Greek term koine had a more generic meaning, referring to that which was current, fluid, circulating, i.e. currency.


The five-pointed "shooting" star Marcel Duchamp had shaved on the back of his head--as seen in the famous photograph taken by his colleague, the American artist Man Ray--may have been little more than the consequence of some Dada/Surrealist prank. But this star of five points has a rich tradition of symbolic associations. In Islamic countries it is recognized as a symbol of al-insan al-kamil, the perfected human being, historically the prime goal of alchemy.

In the medieval legend of Gawain and the Green Knight, this pentagram of apotropaic magic is called "Solomon's Shield," the specific function of which is to protect the hero from "sinful errors, caused by the five senses." This recalls the use of the five-pointed star by Pythagoreans, for whom it was not only a sign of recognition but also an emblem of sanity and good health, the star that in ancient Egypt was known as the pentagram of Isis. Pythagoras, who is said to have studied in Egypt, probably derived his pentagram from a symbol for the Osirian Year, composed of five seasons of 72 days each, with a ten-day week called the Asor. This calendar celebrated the five extra days of the solar year as holidays dedicated to the five deities who ruled over the seasons: Osiris, Horus, Isis, Set and Nephthys. This secret correspondence between the gods and numerical values is revealed by using the key of the pentagram.

The clue will be found by numbering the star points from 1 to 5 in a sunwise direction and then tracing its long lines from point to point until returning to the start. It will be found that the arithmetic difference between these pairs of numbers--between 1 and 3, 3 and 5, 5 and 2, 2 and 4, 4 and 1,--is [respectively] 2,2,3,2,3....The two goddesses are here represented by two of the numbers in the 2,2,3,2,3 series, namely the 3 and the 3, as the three gods are represented by the 2,2, and 2. [ Robert Graves, "The Pentagram of Isis," Difficult Questions, Easy Answers, pp. 172 ff. ]

The sum of the numbers in the series is 12, corresponding to the zodiacal months, which we know the Greeks appropriated, not from the Osirian calendar, but from another, publicly proclaimed calendrical system of the Pharaonic Year. That calendar was composed of three 120-day seasons of four months each, so it also showed five extra days,

which were absurdly explained as having been won from Isis by the god Thoth (who corresponded to the Babylonian Nabu, God of Astronomy) at a game of dice--a legend which suggests that the Osirian Calendar was earlier than the Pharaonic and originally, like the planet Venus, ruled by Isis.

[ Graves Difficult Questions, p. 174. ]

The poet and mythographer Robert Graves also emphasizes the importance of the number 72 in antiquity: not only does 5 x 72 = 360, but also there is a 72-day season during which Venus, sacred to the Goddess Isis, moves from its maximum eastern elongation as "Lucifer" the morning "star" to its maximum western elongation as "Hesperus," the evening star. The star shape drawn with a continuous line by Pythagoras is thus not accidental, being related to the pentagram through the 72 degrees of its interior angles. Also, when numbers of the arithmetical series 2,2,3,2,3 [from the five-pointed star] are multiplied together, the product is 72. And, as Graves also points out when considering the convention of the 360-degree circle in its relation to the 365+ days of the solar year:

the extra five days, regarded as a placatory offering to the five deities, represent one seventy-second of the total sum, plus a few extra hours. And these hours, mythologically represented as the sacred worm which, after three years, grew feathers and became [almost] a whole day, a Phoenix chick; and 365 of these days add up after 1460 years to a Phoenix or Sothic year. At the close of this extra year the now aged Phoenix burns herself to death in a nest of spices at Heliopolis; and from her ashes springs a new worm....It was the Emperor Augustus, by his reform of the Egyptian Calendar, who killed the Phoenix.

[ Graves Difficult Questions, p. 174 f. ]

The idea of "reformation" should indicate the profound and pervasive order of social change intended by Octavian, as he became first citizen (princeps), then preeminent in auctoritas, mandating his own new name be called Augustus, and recasting the die for governing the Roman state, once a Republic but soon to become an Empire. The gentlemen known popularly as the Founding Fathers of the United States of America had an imperfect understanding of Roman history, much less detailed and accurate than that available today, had students but interest enough to study it. Principally lacking was the sense of precise chronology established only by the confirmation of names, dates, and places through the objective evidence of archaeological excavations and the cogent arguments of scholars--paramount among them historians of art and architecture--who have interpreted this data, thereby themselves REFORMULATING the context of a truer understanding.

We now have better idea about what actually might have happened in ancient Rome than Thomas Jefferson had when, as an inspired architect and--for his time--a passing fair student of Roman history, he designed the State House in Richmond, capital of Virginia. Jefferson sought to emulate the ideals of the glorious Roman REPUBLIC. The original work of ancient architecture he chose as a model was the Maison Carrée in Nîmes: a superb building, in the form of a free-standing, rectangular Roman temple, also used by Napoleon Bonaparte as a model for the Madeleine. It can be differentiated from the earlier Greek approach in several ways, among which students of architectural history are taught to identify the typically Roman adaptation of the "Corinthian" acanthus-leaf capitals, the partially-engaged columns, and most obviously, siting of the temple upon a massive rectangular base, absent or understated in Greek temples. Constructed in the late first century BC, perhaps by Agrippa, it may have been intended to honor the memory of two sons he had by Julia, daughter of Augustus. It once served as a city hall, later becoming a church, most fittingly perhaps of the Augustine order. The structure's popular name, "Maison Carrée" only came into use in the sixteenth century; it is 26 meters long and 15 meters wide, but at 17 meters high, it is approximately CARREE, or square, in frontal elevation. Nîmes itself was given to the veterans who fought with Augustus when, as Ocatvian, he conquered the armies of Julius Caesar and Cleopatra; the city's coat of arms still features the emblem of a chained Nilotic crocodile. Thus, as Jefferson might have deduced from its location in Nîmes, far from Rome, the structure really embodied the vision not of republic, but of EMPIRE.