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Ancient Navigators Could Have Measured Longitude -- in Egypt in 232 B.C. !
21st Century: Science and Technology Magazine ^ | Fall 2001 | Rick Sanders

Posted on 01/12/2003 11:19:24 AM PST by ex-Texan

Ancient Navigators Could Have Measured Longitude -- in Egypt in 232 B.C. !

by Rick Sanders

Around the year 232 B.C., Captain Rata and Navigator Maui set out with a flotilla of ships from Egypt in an attempt to circumnavigate the Earth. On the night of August 6-7, 2001, between the hours of 11 PM and 3 AM, this writer, and fellow amateur astronomer Bert Cooper, proved in principle that Captain Rata and Navigator Maui could have known and charted their location, by longitude, most of the time during that voyage.

The Maui expedition was under the guidance of Eratosthenes, the great scientist who was also the chief librarian of the library at Alexandria. Could this voyage have demonstrated Eratosthenes' theorem that the world was round, and measured approximately 24,500 miles in circumference? One of the navigational instruments which Maui had with him was a strange looking "calculator" that he called a tanawa; such an instrument was known, in 1492, as a torquetum.

Intrigued by a photograph of the cave drawing of that tanawa in Irian Jaya, western New Guinea, I speculated that Maui must have been looking at the ecliptic to measure "lunar distance," in order to find his longitude. Maui's tanawa was of such importance, that he drew it on the cave wall with the inscription, deciphered in the 1970s by epigrapher Barry Fell: "The Earth is tilted. Therefore, the signs of half of the ecliptic watch over the south, the other (half) rise in the ascendant. This is the calculator of Maui."

Eratosthenes had just measured the circumference of the Earth, and the circumference of a sphere is the same in all directions. We know that Maui was thinking about this, because his cave drawings also include a proof of Eratosthenes' experiment to measure the Earth's circumference.

To test the hypotheses, we built a wooden torquetum and used a simplified version of it to measure the change in angular distance between the Moon and the star Altair, in the constellation Aquila (the Eagle). This success proves official dogma wrong, and proves that, in principle, Navigator Maui, during his voyage could have used tables brought from Alexandria, drawn up by Eratosthenes or his collaborators, compared those lunar distances with the distances that he measured, and come up with a good estimate of his longitude.

It is important to note that we are not claiming here that we know everything about the torquetum. We simplified our device for the proof-of-principle experiment, but we will carry out and report on more experiments, using the full instrument.

The torquetum's value, as an analogue calculator, must have been immense, because, once a planet or the Moon are not on the meridian, all "straight lines" become curves—so that calculations are difficult, even with a modern calculator. However, the 23.5-degree plane on the torquetum allows one to directly read the longitude and latitude of a planet or the Moon, relative to the ecliptic, without calculation. These data would be invaluable for predicting eclipses and occultations of various stars or planets by the Moon.

The Inspiration for the Experiment

This was intriguing! What was this "tanawa" for? Why the 23.5-degree plane, characteristic of the torquetum? It could only mean that Maui was looking at the ecliptic, the Moon, and the planets, the "wandering stars."

Of the two torquetums surviving in the world, one belonged to Nicholas of Cusa, and the other to Regiomontanus, both of whom were involved in calendar reform, including setting the date of Easter, which, along with some other religious festivals, is dated by the interaction of the lunar and solar calendars.

But what could Maui have been doing? Trying to determine longitude? The very thought was heretical. To take things out of the realm of speculation, the only solution was to build a torquetum, and see if longitude could be determined by using sightings of the Moon, with simple backyard equipment; if this succeeded, then Navigator Maui could have also succeeded.


Deciphered rock and cave inscriptions from the Pacific islands, western New Guinea, and Santiago, Chile, tell of an Egyptian flotilla that set sail around 232 B.C., during the reign of Ptolemy III, on a mission to circumnavigate the globe. The six ships sailed under the direction of Captain Rata and Navigator Maui, a friend of the astronomer Eratosthenes (ca. 275-194 B.C.), who headed the famous library at Alexandria. Maui's inscriptions, as deciphered in the 1970s by epigrapher Barry Fell, indicated that this was a proof-of-principle voyage, to demonstrate Eratosthenes' theorem that the world was round, and approximately 24,500 miles in circumference.

Finding Longitude

You cannot tell longitude from the stars alone, because their daily motion is purely apparent, caused by the rotation of the Earth. At 8 PM (solar apparent time), any star, seen from anywhere, whether Ferrara, Paris, or Cairo, will have the same azimuth as it does in Washington, D.C., Chicago, Sioux Falls, S.D., Seattle, or anywhere else. The Moon shares in this apparent motion to the west, but it also has its own independent, real motion.

Look at what Amerigo Vespucci, himself at the frontiers of post-Dark-Ages navigational astronomy, said of this in 1502, in Letter IV:

". . . I maintain that I learned [my longitude] . . . by the eclipses and conjunctions of the Moon with the planets; and I have lost many nights of sleep in reconciling my calculations with the precepts of those sages who have devised the manuals and written of the movements, conjunctions, aspects, and eclipses of the two luminaries and of the wandering stars, such as the wise King Don Alfonso in his Tables, Johannes Regiomontanus in his Almanac, and Blanchinus, and the Rabbi Zacuto in his almanac, which is perpetual; and these were composed in different meridians: King Don Alfonso's book in the meridian of Toledo, and Johannes Regiomontanus's in that of Ferrara, and the other two in that of Salamanca."2 The best "clock" to use for reference, is the stars. In the roughly 27.3 solar days of a lunar orbit, the Moon moves a full 360 degrees around the sky, returning to its old position among the stars. This is 13 degrees per day, or just over 0.5 degree per hour. So, while the rotation of the Earth causes the stars and the Moon to appear to move from east to west across the night sky, the Moon, because of its own orbit around the Earth, fights back against this apparent motion, and seems to move eastward (or retrograde) by about 0.5 degree per hour. In other words, the Moon "moves" west only 11.5 degrees per hour.

A brass model of Maui's tanawa, constructed by Dr. Sentiel Rommel. The base (A) in the plane of the observer's horizon, is oriented so that the axis of symmetry is parallel to the meridian. (B) is the equatorial plane. (C) is the ecliptic plane (viewed from one side in Maui's drawing, hence appearing as a line). Drawing by Matt Makowski in The Epigraphic Society Occasional Publications, Vol. 32, No. 29, Feb. 1975

Thus, if a known star is in a given position on the celestial sphere (measured by azimuth and right ascension), a table could be drawn up at a given location for each night, showing how distant the Moon appears to be from that star.

For example: If a ship sailed west out of a port, and its new longitude were now 15 degrees west (one hour) of that port, and those on the ship could see the Moon and the reference star, the Moon would appear to be 0.5 degree east of where the table would show it to be for the port of departure. There is nothing here that navigator Maui in 232 B.C. could not have known. The only question would be whether his instruments could measure an angular difference on the order of 0.5 degree.

Our Observations

Our observational experiment showed that a simplified torquetum could do it. In the time that Altair had moved 41.8 degrees west along the equatorial plane, the Moon had moved only 40.25 degrees, a difference of 1.55 degrees. Because the Moon should retrograde about 0.5 degree/hour, the calculated regression would equal 1.39 degrees. This error of less than 1/6th (or 0.166) of a degree is well within our instrument limitations, which can be read only to 0.25 of a degree.


1. For the story of the Rata-Maui Expedition, see "The Decipherment and Discovery of a Voyage to America in 232 B.C.," by Marjorie Mazel Hecht, 21st Century, Winter 1998-1999, p. 62; "Indian Inscriptions from the Cordilleras in Chile" found by Karl Stolp in 1885, 21st Century, Winter 1998-1999, p. 66; "On Eratosthenes, Maui's Voyage of Discovery, and Reviving the Principle of Discovery Today," by Lyndon H. LaRouche, Jr., 21st Century, Spring 1999, p. 24; "Eratosthenes' Instruments Guided Maui's 3rd Century B.C. Voyage," by Marjorie Mazel Hecht, 21st Century, Spring 1999, p. 74; and "Maui's Tanawa: A Torquetum of 232 B.C.," by Sentiel Rommel, Ph.D., 21st Century, Spring 1999, p. 75.

2. Cited in Letters From A New World, 1992. Ed. Luciano Formisano (New York: Marsilio Publishers), pp. 38-39.

21st Century, P.O. Box 16285, Washington, D.C. 20041

Copyright © 2003 21st Century Science Associates. All rights reserved.

(Excerpt) Read more at ...

TOPICS: Culture/Society; Extended News; Foreign Affairs
KEYWORDS: ancientnavigation; archaeology; earthisround; egypt; egyptin232bc; ggg; godsgravesglyphs; heyerdahl; history; navigation; precolumbiantrade; ricksanders; thorheyerdahl
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To: John Locke
Bravo ! Great post.

Take a peek at the new book Decipher by Stel Pavlou, mentioned in my # 12 Post. I just finished it, and plan to reread it again very soon. Marvelous, simply marvelous.

61 posted on 01/13/2003 5:02:09 AM PST by ex-Texan
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To: Hermann the Cherusker
I stand corrected (well, sit corrected actually).
62 posted on 01/13/2003 5:06:20 AM PST by katana
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To: ex-Texan
63 posted on 01/13/2003 5:29:22 AM PST by Centurion2000 (Darth Crackerhead)
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To: newguy357
Having done quite a bit of personal research on Mohammed and the Muslim faith, I agree with your assessment. In fact, many authorities have to rather harsh conclusions including that of the reformer Martin Luther, who quite simply pronounced Mohammed to have falle under "Satanic" influences.

According to Sir William Muir, Marcus Dods, and some others, Mohammed was at first sincere, but later, carried away by success, he practised deception wherever it would gain his end. Koelle "finds the key to the first period of Mohammed's life in Khadija, his first wife", after whose death he became a prey to his evil passions [Demonstated by his repeated rape of his nine year old 'wife' -- my comment].

Sprenger attributes the alleged revelations to epileptic fits, or to "a paroxysm of cataleptic insanity".

Zwemer himself goes on to criticize the life of Mohammed by the standards, first, of the Old and New Testaments, both of which Mohammed acknowledged as Divine revelation; second, by the pagan morality of his Arabian compatriots; lastly, by the new law of which he pretended to be the "divinely appointed medium and custodian". According to this author, the prophet was false even to the ethical traditions of the idolatrous brigands among whom he lived, and grossly violated the easy sexual morality of his own system. After this, it is hardly necessary to say that, in Zwemer's opinion, Mohammed fell very far short of the most elementary requirements of Scriptural morality. Quoting Johnstone, Zwemer concludes by remarking that the judgment of these modern scholars, however harsh, rests on evidence which "comes all from the lips and the pens of his own devoted adherents. . . And the followers of the prophet can scarcely complain if, even on such evidence, the verdict of history goes against him".

"Cataleptic insanity" ... and demonic possession sums up the true nature Mohammed and Islam in my view.

64 posted on 01/13/2003 6:43:08 AM PST by ex-Texan (Mohammed was an insane Satanist and baby rapist)
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To: RnMomof7
Thanks for the mail.

btw - I recently used that verse from Ephesians as my choice of readings for our wedding.
65 posted on 01/13/2003 6:44:40 AM PST by lds23
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To: RnMomof7
Why are you trying to hyjack thread to continue your animosity towards the LDS faith! I flag you to this News thread because the topic was about history and interesting I am sure these folks could careless about your distorted views! They can fine that on the on the Religious fourm! BTW there is a 400 years different between 600 232 B.C.
66 posted on 01/13/2003 6:45:33 AM PST by restornu (LooK Up!)
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To: John Locke
"The Egyptian word for pyramid is derived from their word for "horizon", not "border"."

The author quoted, E. Raymond Capt, a member of the Archeological Institute of America, acknowledges the pioneers of Pyramidology such as Greaves, Menzies, Smyth, Flinders, the Rutherfords, etc.

I suspect that when he used what many of these others said (that Gizeh means border in the language) it is likely to be so. You are, of course, entitled to quarrel with all of them.

His very reasonably priced book, The Great Pyramid Decoded", would particularly appeal to those mathematically inclined. He, by the way, is among those who believe it was built in the reign of Khufu. (These days that belief is a prerequisite to obtain Egyptian government permission to permit a scientist to investigate the edifice.) So much for "scientific proof" or truth.

You will notice that the major books written in the 1800's did not use the more recently employed "Pyramid of Cheops" appellation. The controversial Vyse "discovery" so eagerly adopted by the government of Egypt has been a windfall for them but they have been singularly loathe to allow much modern technology to be used to determine anything about the Great Pyramid or the Sphinx.

Herodotus' writings on the subject were penned at a date farther removed from the building of the Pyramid than we are from the dates of the life and writings of Herodotus.

Every cult in the world and the Egyptian government in particular has a vested interest in the Great Pyramid.
You can even take tours online.

I imagine one can find a website to substantiate almost anything one wants to believe about the Great Pyramid. I doubt that some of us can find even one with which we agree without reservation. In the spirit of that statement these are a few which bear in some way on the discussion here:

67 posted on 01/13/2003 6:55:31 AM PST by Spirited
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To: ex-Texan
bump for later read.
68 posted on 01/13/2003 7:39:53 AM PST by Focault's Pendulum
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To: T. P. Pole
Moors defeated the Tours in 732...4th grade history
69 posted on 01/13/2003 8:41:42 AM PST by RnMomof7 (Eph 2:8 For by grace are ye saved through faith; and that not of yourselves: [it is] the gift of God)
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To: aruanan
Thanks. History comes alive on FR.

The new Library of Alexandria is apparently open for business and should have an Internet presence. It's modern, massive, intended to be world-class, nothing like the Clinton double-wide.

70 posted on 01/13/2003 9:21:39 AM PST by RightWhale
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To: ex-Texan
Great read bump
71 posted on 01/13/2003 9:23:23 AM PST by Semper911
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To: RnMomof7
Moors defeated the Tours in 732...4th grade history

Well, yes, but most folks don't make the connection between the Moors being Muslim, and their defeat at Tours being the turning point between a Muslim Europe and a Christian Europe. Imagine all of Europe being an arab state. No western culture.

72 posted on 01/13/2003 4:47:49 PM PST by T. P. Pole
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To: Spirited
I have no quarrel with the eminent egyptologists. My comment referred to the name of the pyramid, not that of the site. I indeed agree that "Giza" means "border" - but that is the Arabic name for the site, dating from the 7th century AD, not the ancient Egyptian one.

It would appear that your author E Raymond Capt understands neither Egyptian nor Arabic, which puts him at a certain disadvantage, no?

73 posted on 01/13/2003 5:07:31 PM PST by John Locke
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To: RightOnline
No, no - Napoleon was several thousand years late to knock off the original nose. In fact, there was no nose at all by the time his guardsmen came on the job. They were just adding to the cratering when they fired at the Sphinx.
74 posted on 01/13/2003 6:59:45 PM PST by muawiyah
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To: muawiyah
I believe it was Obelix who broke off the Sphinx's nose, although the hair that broke the camels back (Sphinx's schnoz?) may actually have been the weight of Dogmatix who may have been handging from Gerard Depardieu at the time...But I could be wrong.
75 posted on 01/13/2003 8:18:53 PM PST by Blunderfromdownunder
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To: ex-Texan
The Epigraphic Society Occasional Publications and Papers
76 posted on 01/13/2003 9:07:10 PM PST by Orion78 (I hope Golitsyn is wrong)
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To: ex-Texan

Renaissance Torquetum (1603 A.D.)

77 posted on 01/13/2003 9:18:42 PM PST by Orion78 (I hope Golitsyn is wrong)
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To: ex-Texan
"In Plain Sight - Old World Records in Ancient America" By Gloria Farley
"America BC - America Before Columbus" By Berry Fell
78 posted on 01/13/2003 10:17:21 PM PST by Orion78 (I hope Golitsyn is wrong)
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To: John Locke
"My sources say the Pyramid of Cheops was called akhet khufu, which means, unsurprisingly, "pyramid of cheops". The Egyptian word for pyramid is derived from their word for "horizon", not 'border'."

Since you do not accept the title "Great Pyramid of Giza" and that title was the one commonly used by the early Pyramidologists I named (who were not listed as Egyptologists to my knowledge) I am certain that you can use what you think is the ancient name and I can feel free not to do so.

As for the word Gizeh, we at least agree that it is "border" in Arabic. The words Great and Pyramid are neither Arabic nor Egyptian, yet we use those as names of the edifice while at or of Giza denotes location.

If the early explorers who became Pyramidologists spoke either Egyptian or Arabic in any degree of mastery it would be amazing. It did not hamper their work or bring it into question (even though many times their conclusions have proven fanciful).

W.M.F.Petrie the "father of modern archaeology' who is also considered an Egyptologist named his book 'The Pyramids and Temples of Gizeh'. He is highly regarded even today by Dr.Z Hawass the Egyptian who was and I believe may still be in charge of the Pyramids on the plain of Giza on behalf of the Egyptian government. I do not find any evidence that Petrie had any command of the language of Egypt although he had the rudimentary grammar of French,Greek and Latin as was usual bare minimum in that day.

I suspect that you need to use the Egyptian name which you have learned and I feel just as comfortable using the English name which also appends the word Giza as the British Petrie did.

When talking about this Pyramid none of us is likely to agree with any of the rest of us as to almost anything said about it. Here most any of us may stand accused of "straining at gnats and swallowing camels".

Sorry Capt's gnat was a choke point for you as the Egyptian name must be for me since I do not speak or comprehend the Egyptian language and when I was taught the listed seven wonders of the world in school the phrase taught to me was The Great Pyramid at(or of) Giza.

79 posted on 01/13/2003 10:34:00 PM PST by Spirited
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To: Spirited
Thank you for your reply. I'm glad we have clarified the issues, and also agree that many people who have studied the Great Pyramid have come to fanciful conclusions. (That, by the way, one one of the things that motivated me to learn Egyptian - what did these marvellous people have to say in their own words?).

Blessings likewise to you.

80 posted on 01/13/2003 10:44:08 PM PST by John Locke
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