Re: Pyramidiocy (was Re: Strange Maths)

Whittet (
17 Jul 1995 23:55:07 GMT

In article <>, says...
>In article <3ue55n$>,
> (Whittet) wrote:
>> >
>> >>The number of feet in a mile can be obtained from the number of days in a
>> >>millenium divided by the number of miles in a degree of the earths
>> >>circumference at the equator 365240/69.17424... = 5280
>> It has been documented that the measurements of the Earths circumference asc
>ribed to
>> Eratosthenes were actually made by the Egyptians some millenia earlier, and
>I have
>> posted the cites for this here several times.
>Millenia? Documented? 2000 years or more?

From: "Donald E. Simanek" <dsimanek@EAGLE.LHUP.EDU>
Subject: Eratosthenes

On Fri, 3 Feb 1995, Winfield Featherston wrote:

> Also, if there is anyone out there who is familiar with Eratosthenes'
> measurement of the circumference of the earth, I would like some
> information on a specific detail of the experiment. I am currently
> teaching a class in which Eratosthenes' experiment is discussed, and a
> question arose concerning one of the assumptions underlying the experiment.
> The assumption in question is that Alexandria and Cyene (or, alternately,
> Syene) lie on the same line of longitude. I understand that this assumption
> is important for the accuracy of the results of the experiment -- what I'm
> not sure of is what reason there might have been for assuming this in the
> first place. Perhaps there were navigational methods available in the
> Second Century B.C. that allowed Eratosthenes to rely on such an
> assumption. Any suggestions would be greatly appreciated!

> Thanks!

> Winfield Featherston (
> Dept. of Philosophy
> Southern Illinois University at Carbondale

After reading the following you will not be concerned with those maters
affecting the accuracy of the results, for they weren't that accurate.

Eratosthenes' works exist only in fragments. There are also
commentaries by Strabo.

The following excerpt is the most detailed and apparently
authoritative account I could lay my hands on, pointing out the
limitations of data, and the fudging of unmbers. Other references
identify Syene as the modern city Aswan, or near it.

Excerpt from _The Dictionary of Scientific Biography_ ed. by
Charles Coulston Gillispie. Scribners, 1971. Entry on Eratosthenes
by D. R. Dicks. My own explanations in square brackets. This 16 volume set
is something every library should have, and I am fortunate to have most of
it in my personal library. [I'm missing volumes 4, 9, 10, and 13, just in
case anyone knows where I can get them at a reasonable price.]

[begin excerpt]

Naturally, the data at his disposal, mainly travelers' estimates
of days' voyages and marches, which are notoriously unreliable--the
only scientific data available were the gnomon measurements of
Philo, prefect of Ptolemy, at Mero [Last letter is umlauted `e']
(Strabo, _Geography, 77_), of Eratosthenes himself at Alexandria,
and of Pytheas at Marseilles (_ibid_., 63), together with some sun
heights recorded by the latter (_Geographical fragments of
Hipparchus_. p. 180)--were of dubious accuracy, and any mapping
done on the basis of them was bound to be largely guesswork.
Hipparchus has no difficulty in showing that the figures and
distances given by Eratosthenes are mathematically inconsistent
with each other, and he therefore rejects them, together with some
of the sensible alterations proposed by Eratosthenes for the
traditional map, thus demonstrating that inspired guesswork
sometimes gives better results than scientific caution (_ibid_.,
pp. 34 35).

It is uncertain whether the measurement of the earth's
circumference was first published in the _Geography_ or in a
separate treatise; if the latter, it would at any rate have been
mentioned in the larger work. The method is described in detail by
Cleomedes (_De motu circulari_, 1, 10), the only ancient source to
give it. Assuming that Syene was on the Tropic of Cancer (because
there, at midday on the summer solstice, the gnomon--i.e., a
vertical pointer set upright on a horizontal base--cast no shadow
and a well, especially dug for this purpose [according to Pliny,
_Natural History_, 11, 183] was illuminated to its bottom by the
sun's rays), and that this town and Alexandria were on the same
meridian, Eratosthenes made a measurement of the shadow cast at
Alexandria at midday on the solstice by a pointer fixed in the
center of a hemispherical bowl, known as a "scaphe" [Greek word not
representable in ASCII]--presumably he used this form of gnomon
because the shadow of a thin stylus would be better defined than
that of a large pillar or post) and estimated that the shadow
amounted to 1/25 of the hemisphere, and thus 1/50 of the whole
circle. Since the rays of the sun can be regarded as striking any
point on the earth's surface in parallel lines, and the lines
produced through the vertical gnomons at each place meet at the
center of the earth, the angle of the shadow at Alexandria (ABC in
Figure 1) is equal to the alternate angle (BCD) subtended by the
arc BD, which is the distance along the meridian between Alexandria
and Syene, estimated by Eratosthenes at 5,000 stades; and since it
is 1/50 of the whole circle, the total circumference must be
250,000 stades. This is the figure reported by Cleomedes.
Hipparchus accepts a figure of 252,000 stades as Eratosthenes'
measurement (Strabo, _Geography_, 132, corroborated by Pliny
_Natural History_, 11, 247, whose further statement that Hipparchus
added 26,000 stades to Eratosthenes' figure is incorrect--see
_Geographical Fragments of Hipparchus_, p. 153), and it seems
fairly certain that Eratosthenes himself added the extra 2,000 in
order to obtain a number readily divisible by 60; he divided the
circle into sixtieths only (Strabo, _Geography_, 113-114), the
familiar division into 360=F8 being unknown to him and first
introduced into Greek science by Hipparchus (_Geographical
Fragments of Hipparchus_, pp. 148-149; D. R. Dicks, "Solstices,
Equinoxes, and the Pre-Socratics," in _Journal of Hellenic Studies_
86 [1966], 27-28).

The method is sound in theory, as Hipparchus' recognized, but its
accuracy depends on the precision with which the basic data could
be determined. The figure of 1/50 of the circle (equivalent to
7=F812') for the difference in latitude is very near the truth, but
Syene (lat. 24=F84' N.) is not directly on the tropic (which in
Eratosthenes' time was at 23=F844' N.), Alexandria is not on the same
meridian (lying some 3=F8 to the west), and the direct distance
between the two places is about 4,530 stades, not 5,000. Probably
Eratosthenes himself was aware that this last figure was doubtful
(without trigonometrical methods, which he certainly did not know,
it would have been impossible to measure the distance accurately),
and so felt at liberty to increase his final result by 2,000.
Nonetheless, the whole measurement was a very creditable
achievement and one that was not bettered until modern times. On
the most probable value of the stade Eratosthenes used (on this
vexed question, see _Geographical Fragments of Hipparchus_, pp.42
46), 252,000 stades are equivalent to about 29,000 English miles,
which may be compared with the modern figure for the earth's
circumference of a little less than 25,000 miles.

Eratosthenes was actually using data for his calculations which had
been recorded sometime in the middle kingdom

[end of excerpt]

>> >The Egyptians not only knew the circumfrence of the earth but could
>> >acurately predict the *exact* size of the English mile *before* there
>> >was an England. Time! Space! Synchronicity!
>> The English mile is closely related to the Roman. The Roman to the Greek,
>> the Greek to the Egyptian. The correlation is hardly suprising, and has been
>> studied in depth.
>English mile 1 760 yards. Roman mile 1 620 yards. Ok, close, but the kind
>of difference that makes quite a bit if you are trying to prove this pyramid

It helps if you convert from the English foot to the Roman foot, see below.
Egyptian Standards of Measure

The following is excerpted, quoted, condensed, paraphrased; from the first two of VIII appendixs
by Livo Catullo Stecchini,
pages 304-382 to the book, "Secrets of the Great Pyramid", by Peter Tompkins, Harper & Row,
New York, 1971.

I.) Egyptian Geodetic System - omphalos, degrees, minutes, seconds, correlation of time with
II. Egyptian Units of Length -cubits, hands, palms, fingers, feet, inches
III. Coffer of the Great Pyramid - Greaves, Petrie, artabas, quedet, cubits, feet
IV. Degrees of Latitude - geographical cubits, calculation of the stadium, architectural orders
of col.
V. Textual Evidence - Inscribed cubit rules, Ankhetaten, (living in Maa't), Tel Armana Boundary
VI. Degrees of Longitude - base lines, Greek and Mycenean correlations, Delphi, Dodona
VII. Dimensions of the Great Pyramid - Surveys of Petrie and Cole, Pi ratio, Phi ratio, Imhotep
VIII. Additional Remarks on the Great Pyramid. - Herodutus, Agatharchides, Lauer, Petrie

In the introduction to his Appendices, Stecchini, who later came to teach at Harvard,
introduces himself as having made a
lifelong study of ancient measures after having been influenced by the philosophies of Husserl
and Heideggar, while a grad
student at Freiburg, Germany, and getting his
doctorate in law in Rome.

He mentions how in coresponding with Hertha von Dechend, who was then beginning to write her
book "Hamlet's Mill" (circa
1961), he was teased by her for concentrating on measures of length, volume and weight, without
ever mentioning time, with
which the ancients were preocupied.

He then goes on to explain :

"Because of my horror of metaphysical, or pseudo metaphysical intrusions, I had several times
picked up and then dropped,
the problem of the dimensions of the Great Pyramid of Giza."

"In the course of discussing with me the geometry of the Great Pyramid, Tompkins explained how
Great Pyramid, with its galleries, could have been used to measure the movements of the vault of

"In describing the possible procedures, he pointed out how a second of time in the motion of the
vault of heaven corresponds to
a definite length on earth."

"Once I was able to link time together with length, volume and weight, a number of scattered
researches suddenly became
related to each other."

He goes on to explain how the meaning of the names for Egypt both in Arabic and ancient
is something like "the country built according to a geometric plan"

[ I think there are other equally valid interpretations which could be made, feel free to
contribute yours]

He then launches into a rather interesting discussion of how he thinks ancient Egypt may have
to place such a high value on Maa't (what is right and proper, accuracy in measures) by
observing the phenomenology of the
world around them. (remember Husserl?)

Egypts most important influences must have been the Nile, because it rarely rains there and the
river is what makes life
possible, and the path of the sun through the sky. If Egypt were a measured land,
these would certainly be a part of its axis.

Stecchini then goes on to discuss such indications of measurement as the well known hieoglyphic
for unity of the two lands,
which he sees as three parallel lines spreading into a delta, and the concept of what the
Greeks call an 'omphalos' as a
geodetic point because of its association with the god Sokar, the god of orientation.

[these are reasonably interesting points, possibly worthy of some discussion, the usual form of
the omphalos is a domed
cylinder, either covered with a net, or with a pair of pigeons, and a ruler in the form of the
hieroglyphic for sky (nu),]

[There is also some discussion of iconography in general, with examples which lead the reader to
more carefully examine our
own 'Hieroglyphics', in terms of their roots in antiquity]

He discusses a number of geographic and astronomical correlations and establishes why he
believes the length of Egypt was
1,500,000 royal cubits of 525mm.

In appendix II he establishes why he believes that this cubit of 28 fingers is equal to 16
inches, as was the Roman foot, and
why the english foot is 12 inches.

"All the measures of length volume and weight of the ancient world, including those of China and
India, constituted a rational
and organic system, which can be reconstructed starting from a fundamental unit of length."

"The ancient system of measures continues to be used today in the form of English measures"

"From the very beginning of literate cultures, documents indicate an extreme concern with the
preservation of exact metric

"The concern with precision seems to have lessened in the course of history"

"The amazing stability of measures is illustrated by the circumstances that the kilogram was
established by relating it to the
Paris Livre, which was directly related to the Roman Libre."

"In the ancient world one measured by feet and cubits. The cubit is equal to 1 1/2 feet. The
cubit is divided into six hands of 4
fingers each (24 fingers) and the foot is divided into 4 hands (16 fingers). The division of the
foot into 12 inches, with which we
are familiar, became common only with the Romans. According to the Roman reckoning the cubit is
16 inches. The inch was
considered to be the thickness of the thumb."

"It must be kept in mind, however, that terms like foot, cubit, finger and inch, were introduced
in order to give a name to units
determined scientifically."

"The royal cubit is composed of 7 hands (28 fingers). It is an ordinary cubit with a seventh
hand added. One can find examples
of septenary units also outside Egypt."

"For the sake of geographical calculations the royal cubit was given as multiple the atur of
15,000 royal cubits so as to make
Egypt equal to the perfect figure of 100 atur. The term atur litteraly means 'river', it could
be translated as river measure. It was
understood that an atur corresponds to an hour of travel along the Nile."

"The edge of a cube containing an artaba is a foot."

"From the artaba there was derived a unit of 3 artabas which is the cube of the Roman cubit."

"The cube of the foot was called talent in Greek or by equivalent terms in other languages."

"The multiple of the geographic foot is the stadia of 600 feet.)"

"In the ancient world the degree of latitude was usually reckoned as 360,000 feet (600 stadia)"
The calculations of the degree of latitude as 360,000 geographical feet (240,000 geographical
cubits) proves to be of Egyptian

"We shall see that the Pharoah Ankhenaten attacked the authority of the Temple of Amon at Thebes
by questioning the
exactitude of the second geodetic system of Egypt, and of the calculations by royal cubits."

If you find this sort of thing interesting the next six sections of the appendix begin to get
into the specifics.

Let me know what you think.

>Doug Weller