my corner
cir...@access.ch
DejaNews changed its interface. I take this as an opportunity for
opening a new thread under the name 'my corner'. If you believe
in the evolution of civilization, and if you are willing to credit
Africa, Egypt, Mesopotamia, Anatolia, India, Asia, ... and women
with their manyfold contributions to the evolution of civilization
you are welcome in my corner.
However, it may be that I get no response. In that case I shall
publish for a future reader who may find my articles via DejaNews
and Power Search.
In my next post I shall propose a project for a young open-minded
Egyptologist.
Today I make it short, just trying to install my corner in here.
Regards Franz Gnaedinger Zurich cir...@access.ch
-----------== Posted via Deja News, The Discussion Network ==----------
http://www.dejanews.com/ Search, Read, Discuss, or Start Your Own
cir...@access.ch
cir...@access.ch wrote:
> In my next post I shall propose a project for a young open-minded
> Egyptologist.
Sorry, I need more time for presenting that project. Thank you for
your patience.
I got several e-mails from readers who asked me about the Rhind
Papyrus. Well, I am sure pleased that there are people around who
are interested in this great scroll.
In my opinion, many problems of the Rhind Mathematical Papyrus can
be read on three levels of understanding:
Level A learning how to calculate with unit fractions
Level B geometric problems
Level C demanding geometric problems, theoretical approach
Let me explain. In no. 32 of the Rhind Papyrus, Ahmes divides
2 by 1 1/3 1/4 or simply 1 '3 '4 and obtains 1 '6 '12 '114 '228.
On level A, one learns how to carry out a division. On level B,
one may formulate a geometric problem. Please imagine a right
parallelepiped of these measurements:
height 2 units
length 1 '3 '4 units
width 1 '6 '12 '114 '228 units
How long are the diagonals of the volume? Simply
1 '3 '4 units plus 1 '6 '12 '114 '228 units
or
1 1 plus '3 '6 plus '4 '12 plus '114 '228 units
or
2 '2 '3 '76 units
On level C may follow a lecture on magic parallelepipeds (as I call
them). Please carry out the following division:
2 / a = b
Now use the numbers as the measurements of a right parallelepiped:
height 2 units
length or width a or b units
width or length b or a units
base / top area ab square units
volume 2ab cubic units
diagonal volume a + b units
If you like to carry out a calculation by yourself: imagine that
a granary has a volume of 500 cubic cubits (while a royal cubit
equals 7 palms or 28 fingers). Find reasonable numbers for a granary
whose shape is a magic parallelepiped. All these volumes have the
same height - how high are they? Then look out for reasonable numbers
a and b. A special case: what if a = b or almost b?
My interpretations of the RMP follow this pattern: I study the
numbers of level A and try to get on level B and then on level C.
You will find my interpretations via http://www.dejanews.com and
Power Search. Please type my e-mail address into the search line
and look out for my threads
Professor Ahmes (1) till Professor Ahmes (5)
cir...@access.ch
my new thread 'my corner' got associated with another one
- 'my corner of the world'. Now I rename my thread into
'my c-o-r-n-e-r' and hope to find a free place in the
DejaNews archive. Here again my post from this morning:
Level B geometric problems
If all goes well with my renamed thread, I will present tomorrow
Derk Ohlenrath's interpretation of linear A (disk of Phaistos)
and next week my project for a young open-minded Egyptologist.
cir...@access.ch
cir...@access.ch wrote: ...
Dear reader,
if you understand German and ancient Greek and if you are interested
in linear A and the Phaistos Disc you must read the following book:
Derk Ohlenroth, Das Abaton des Lykaeischen Zeus und der Hain
der Elaia, Zum Diskos von Phaistos und zur fruehen griechischen
Schriftkultur, Max Niemeyer Verlag, Tuebingen 1996 (481 pages,
16 years of work)
Derk Ohlenroth reads the 45 different pictograms of linear A as an
encoded version of a very ancient Greek dialect: as magic formulas
understandable for insiders only.
Phaistos Disc, side A (my simplifying transscription):
SEYR.KI.PHAAINOS.SEYR.AI.YLKIOS.OI.KYOYSANS.GONOS.ISOS.
KA.SLRYNS.ISOSLA.PHAAINOS.ISOS.KA.SLRYNS.EII.SLGOS.EON.
KAI.YNOS.AII.KOY.SAOS.PAN.O.EN.NAOI.OS.AEII.ENIOO.ASKIOS.
Greek version (my simplifying transscription):
Zeus kai phaennos, Zeus ai Ylkaios, ho kyousais gonos isos'
kan Siryns isosia, phaennos isos kan Siryns eiae(n?). sigos
eon kai ynos aii kou saos pan ho en nao hos aeie, anioi askios.
Derk Ohlenroth:
Zeus ist auch der 'Strahlende', wenn Zeus 'der Lykaeische' ist,
(er,) dessen Geliebten ein Spross erwaechst wesensgleich: und
wenn Tiryns 'die Gottgleiche' ist, ein (goettlich) 'Strahlender'
gleichen Wesens duerfte (dann) auch (ich,) (der Eponymos) Tiryns
(,) sein. ('Vom Gott') gezeichnet und vereinsamt immerdar und
heillos ganz soll der im Heiligtum, der es zu betreten suchte,
umkehren schattenlos.
My own private babblefish:
Zeus the radiant, Zeus Lykaion, whose loved ones give birth
to an offspring his like: and if Tiryns, the famous town in
the Argolis, is a divine twon, I, a hero named Tiryns, may be
of a divine nature too. And everyone who tries to enter the
inner sanctuary of the Zeus temple at Tiryns shall be branded
by the god and grow lonely and return whithout a shadow
Phaistos Disc, side B (my simplifying transscription):
EN.YLAEI.ELAIAS.ESITHI.PERIXASLEEN.EAISE.YLAEN.PERIX.ENIIPI.
PERI.KNISAI.GAIA.KAI.SOAE.AIPSA.AI.KSYNORIS.AIO.AE.Y(AY)AX.
SKIERA.IKI.OSLAE.OPSAA.NYX.SLAS.AIEN.NEOXOS.
Greek version (my simplifying transscription):
E(i)n hylae Elaias esithi' perixestaen anaise hylaen' perix
eniipe peri knisa gaian kai syae aipsa ai xynoris' 'aio ae,
hyauax' skiera hike oslae opsia Nyx, Sias aien neossos.'
Derk Ohlenroth:
In den Hain der Elaia tritt ein: Entzuende rings geglaettetes
Holz: im Kreis um den Opferrauch schlag ein auf die Erde,
und wiehere jaehlings wie ein Pfrede-Paar: 'Aio ae! hyauax!
Schattige, komm, o edle spaete 'Nacht', von der Goetting immer
neu geboren!'
My own private babblefish:
Enter Elaia's grove: kindle polished wood round about: beat
the ground in a circle around the smoke of the offering and
neigh suddenly like a pair of horses: Aio ae! hyauax! Come,
shadowy, noble, late night, always reborn by the goddess!
A Demeter cult. Poseidon and Demeter loved each other in the shape
of horses, thus making the cult grotto of Elaion Oros famous. Beating
the ground was a means of getting in contact with the dead and the
gods and goddesses of the underworld.
Regards Franz Gnaedinger Zurich cir...@access.ch
-----------== Posted via Deja News, The Discussion Network ==----------
cir...@access.ch
cir...@access.ch wrote:
an article on Derk Ohlenroth's interpretation of linear A and his
translation of the magic formulas on the Phaistos Disc.
A reader asked me for informations on the Egyptian goddess Seshat.
Well, here are a few quotes.
Christian Jacq, La Tradition Primordiale de l'Egypte Ancienne
selon les Textes des Pyramides, Bernard Grasset, Paris 1998
page 120/121:
Pyramid Text 616 a-c:
Nephtys a assemble pour toi tous tes membres en ce sien nom
de Sechat, maitresse des batisseurs. Elle rend le pharaon
en bonne sante.
Christian Jacq's comment:
Nephtys, dont le nom signifie "la maitresse du temple" est
le milieu sacre ou s'epanouit le pharaon; Sechat, patronne de
l'ecriture et des traces geometriques (y compris le maquillage),
participe a la creation du temple. Elle est egalement la
souverain de la Maison de Vie ou le pharaon est initie au
mystere supreme, celui de la vie en eternite.
My translation of PT 616 a-c:
Nephtys assembled all your limbs for you (Osiris, Wenefer NN)
in her name of Seshat, mistress of the architects. She (Nephtys)
renders Pharaoh in good health.
My tranlation of Jacq's comment: Nephtys, whose name signifies
"mistress of the temple" is the sacred milieu wherein Pharaoh
develops; Seshat, patroness of writing and geometrical drawings
(including make-up) participates in the creation of the temple.
She is also the sovereign of the House of Life wherein Pharao
is initiated into the supreme mystery, the one of eternal life.
Peter H Schulze, Frauen im alten Aegypten, Selbstaendigkeit
und Gleichberechtigung im haeuslichen und oeffentlichen Leben,
Gustav Luebbe Verlag Bergisch Gladbach 1987
page 106:
An der Spitze der Schreibkunst steht als Patronin die Goettin
Seschat und das bereits in den aeltesten Schriftdenkmaelern,
noch bevor der Gott Thot auftaucht (Hans Bonnet, Reallexikon
der aegyptischen Religionsgeschichte, 2. Auflage Berlin 1971,
Seiten 806 f.) (...) Seschat erscheint (...) von Anfang an als
Herrin der koeniglichen Archive, beim Ausmessen und Abstecken
von Tempelbauplaetzen und beim Festlegen der Regierungsjahre
und Sed-Feste der Koenige. Noch in der Spaetzeit ist sie
"die zuerst geschrieben hat" (Bonnet, op.cit., S. 669)
My translation: Seshat was the patroness of writing, and this
already on the oldest memorials, long before god Thoth appeared
(Hans Bonnet, Reallexikon der aegyptischen Religionsgeschichte,
2. Auflage Berlin 1971, pages 806 f.) (...) Seshat appears right
from begin as mistress of the royal archives, measuring out and
marking out the building site of a temple, and fixing the reigning
time of the kings. Still in the late period, Seshat was called
"the one who wrote (has written) first" (Bonnet, op.cit., p. 669).
Doris Wolf, author of the book
Was war vor den Pharaonen? Kreuz Verlag Zurich 1994
points out that the scribe on the Narmer Palette is a woman.
She says that the numinous sign of Seshat was already registered
in Dynasty I. Furthermore, she mentions the ostracon DW from the
time of Ramesses VI that gives the members of a scribe team as
16 (sixteen) men and 46 (fourtysix) women. Doris Wolf believes that
2/3 of the artists working in the Theban necropole have been women.
Now for the enigmatic hieroglyph of Seshat. Originally, it was a
pair of horns turned upside down, ornated with a pair of feathers.
The horns remind of the heavenly cow. Seshat was an alter ego of
Nephtys, while Nut and her daughters Isis and Nephtys have been
goddesses of the heavens. We may see the round form of Seshat's
hieroglyph as a symbol of the sky. The former pair of feathers may
have symbolized the eyes of the Horus falcon - sun and moon -, and,
earlier on, the eyes of the Primeval Goddess who was a woman with
the head of a bird (while the lower part of her body sometimes had
the shape of a carrot, meaning the fertile soil or earth in general).
If the round form symbolizes the sky or heaven, the small round or
rectangular form on top (place of the former pair of feathers) may
symbolize the house of the sun and the moon while the leaf with
5, 6 or 7 fingers may represent the orbiting sun, moon and stars
and the observation of the celestial bodies, hence astronomy and
the calendar. (These are my own interpretations.)
A wonderful relief of Seshat is found at Luxor. See page 11 of:
Werner Forman and Stephen Quirke, Hieroglyphs and the Afterlife
in Ancient Egypt, British Museum Press London 1996
cir...@access.ch
cir...@access.ch wrote:
an article on Seshat, on request of a reader who asked me now if
there are connections between Seshat and Neith. Well, here is what
I can say.
A general remark:
The kinship of the more than 2,000 Egyptian gods and goddesses
is highly complicated - and yet very simple when we assume that
all the many deities are the offspring of the Primeval Goddess
(female figurines from El-Mamarija) and the Primeval God (Horus
the Elder). The Primeval Goddess and the Primeval God live on in
their children and children's children: as their own reincarnations,
displaying their many properties and abilities in various deities,
thus being mother, wife or daughter / father, man or son to each
other (an example: Nut can be the mother of the sunchild Ra or Re,
his wife, or his daughter, depending on the context) while similar
deities can be drawn together again (for example Atum, Re and Horus
into Atum-Re and Re-Horakhty; or all the female deities into Isis).
Now for Neith:
Neith originally was a goddess from Lower Egypt, but worshipped
in whole Egypt already in Dynasty I. Queen Merithneith carried
her name (Merith-Neith).
Neith was a goddess of creation, according to Peter H. Schulze
probably a forerunner of Nut. - Or may there have been two equally
important predynastic goddesses from Lower and Upper Egypt, one living
on in Neith, one in Hathor, and both in Nut?
Neith was credited with the invention of weapons and of weaving.
Her hieroglyph shows a pair of crossed arrows.
The annual flood of the River Nile was released by the following
goddesses:
NEITH
ANUKIS - goddess of the cataracts, a friend and possibly an alter
ego of Nephtys; Seshat was another alter ego of Nephtys
SATIS
SOTHIS - an alter ego of Satis; Sirius, whose heliacal return
announced the annual flood, was known as Sothis star
ISIS - sister of Nephtys, alter ego of Sothis, probably present
in Sirius (her heavenly throne)
If the Primeval Goddess of Egypt lived on in Hathor, Neith and Nut,
we get the following genealogical connection of Neith and Seshat:
PRIMEVAL GODDESS
Hathor - Nut - Neith
I
Sothis - Isis Nephtys - Seshat
Christian Jacq (La Tradition Primordiale de l'Egypte Ancienne selon
des Textes des Pyramides, Bernard Grasset Paris 1998):
Neit (creatrice du monde par le verbe et le tissage)
Neith, creator of the world by means of the word and of weaving.
Creator of the world by means of the word: this links Neith with
Seshat, goddess of writing.
Jacq Christian again:
Selon 606b, l'energie primordiale protege quatre deesses, Isis,
Nephtys, Neit et Serket qui, dans ce context, semblent organiser
l'espace de creation
According to Pyramid Text 606b, the primordial energy protects
four goddesses, namely Isis, Nephtys, Neith and Serket, who,
in this context, seem to organize the space of creation.
Isis, Nephtys, Neith and Serket protect the guilded canope shrine
of Tut'ankhamun. Hence they may organize the space of a new creation
= a new world to come in a million years (my interpretation).
The world emerged as the Primeval Mound or Hill, rising above the
Primeval Water Nu(n). The Primeval Water Nu(n) was symbolized by
three vessels, a zigzag line and further signs. The hieroglyph of
Nut was a vessel again. I therefore assume that the three vessels
of the Nu(n) stay for Nut, Isis and Nephtys, a triad which is also
mentioned in the Pyramid Texts and might have been represented by
the life symbol Ankh, which, in my opinion, may be seen as a female
figurine (Nut), a Sacred Knot (Nephtys/Seshat) and a vessel turned
upside down with a jet of water falling out (Isis).
Now the floor of Tut-ANKH-Amun's sarcophagus chamber was laied out
with rudders, turning the floor into the subterranean Nile whereon
the sunboat is traveling during the night, and into a representation
of the Primeval Water Nu(n) as well, out of which the Primeval Hill
rose, releasing the sun and the sky ...
I hope you get an idea of the fine way of ancient Egyptian reasoning
for which I have no better formula than: simple yet complex.
cir...@access.ch
cir...@access.ch wrote:
on Seshat and Neith, by request of a reader who now asked me for
a word on Horus the elder and Horus the younger. A little patience
please. I just read an article that made me angry, and so I have
to say a word on :-( Manfred Korfmann :-(( first.
You may remember that I wrote several posts on Eberhard Zangger's
thesis that Plato's Atlantis was Troy, that Eberhard Zangger's
geoarchaeological reconstruction of the Troas (plain of Troy)
will be tested in March 1999, and that I promised to inform you
when I hear something new. Well, this morning I read an article
in the weekly FACTS (issue of April 1 - a hoax? I believe not).
Here follows a commented compilation:
Last monday, a team of experts of the German Bundesanstalt fuer
Geowissenschaften und Rohstoffe (BGR) Hannover wished to go on
a probing mission to the Turkey. The flight was booked, the dates
have been fixed, but the Turks split up the mission on short-terms.
Reason: missing papers.
Eberhard Zangger says that Manfred Korfmann, chief excavator of
Troy, moves heaven and hell to stop the project. What is illogical
according to Eberhard Zangger: Korfmann must feel that Zangger is
on the richt track, or else Korfmann would be glad about the BGR
mission: if Zangger's geoarchaeological reconstruction of the Troas
is wrong, it will show, and the trouble (Spuk) is over. But Korfmann
obviously fears that Zangger is right and that he, Korfmann, may
lose his position as Troy-pope. FACTS calls him thus, and he really
seems to behave in a pope-like manner: everyone who wishes to take
a photograph of Troy has to pay a lot of money; furthermore, Korfmann
is on good terms with Demirel, and together they wish to build an
archaeological national park in Troy ...
A dubious idea in my opinion (if it ain't an April hoax): imagine
an archaeological Disney World in the Troas and a vast infrastructure
(streets, parking lots, hotel complexes, and so on) hampering further
archaeological projects in that region.
More about Eberhard Zangger's expedition that shall take place in
fall according to FACTS: Eberhard Zangger is especially interested
in the Kesik channel that corresponds with a channel mentioned by
Plato (a drag way for ships? like the one of Korinth?) and a flat
piece of land (a former harbour basin?). Klaus-Peter Sengpiel, chief
of the BGR flying division: that research project is a technological
challenge. A helicopter shall scan a field of 182 square kilometers
along a grid of 50 meters (? im 50-Meter Raster). At a string will
hang a torpedo-like instrument capsule (a so-called bird) that will
be able to examine the ground to a depth of 100 meters. A detector
will measure the magnetism of the underground, another one gamma
rays. Thus, the layers of the ground can be discerned, for example
deposited ooze from a former harbour sole. Even better results are
expected from a third sensor measuring the electrical conductivity
of the ground: as it examines the first 10 meters especially well
it might even find remains of buildings. According to Huerriyet,
Korfmann and Turkish colleagues wish to stop the project. However,
Sengpiel is optimistic: the Turkish ambassady of Bonn showed great
interest and promised support for this highly fascinating project
of which all involved scientists may profit in the end.
cir...@access.ch
cir...@access.ch wrote: ...
----------------------------------------------------------
War in Europe:
S S S S S S S S S S S
S S
S S S S
S S S S
S S S S
S S S S
S S S S
S S S S
S S
S S S S S S S S S S S S S S S S S S S
S S
S S S S
S S S S
S S S S
S S S S
S S S S
S S S S
S S
S S S S S S S S S S S
Stop Milosevic, Arkan and the orthodox church !!!
No archaeology today, for the house of Europe is burning,
set on fire by a Nazi regime of the Balkan.
cir...@access.ch
cir...@access.ch wrote: ...
--------------------------------------------------------------------
On early navigation, a quote from the February 1999 issue of the
Scientific American, pages 19-21:
Profile - Bones to Pick - Refusing to take "no" for an answer,
The Smithsonian Institution's Dennis Standford has carved out
a niche as a leader of American archaeology / by Steve Mirsky
(...)
Stanford's main research interest, which he shares with wife and
Smithsonian colleague Margaret Jodry, focuses on when the first
people came to North America and who they were. In the early 1970s
the consensus was that the first Americans were northeastern Asians
who crossed the Bering Strait into Alaska around 11,000 years ago.
They would have been the so-called Clovis people, named for the
site in New Mexico where archaeologists discovered a treasure trove
of bone and stone tools. According to the standard theory, these
newcomers populated the continent, spreading all the way to the
east coast and from Canada to central Mexico in only one century.
This belief was based on other finds of similarly crafted tools
and on radiocarbon data.
Stanford and other upstarts began to question the common wisdom.
The lack of any ancestral form of Clovis artifacts troubled him.
"The (Clovis) technology was just so radically different from any-
thing I was aware of in Siberia or even Alaska," Stanford explains.
Ultimately, research led by the University of Kentucky's Tom D.
Dillehay revealed a Western Hemisphere presence of humans at least
a millenium before Clovis.. This literally and figuratively ground-
breaking work took place at a site near Monte Verde in Chile,
about which Dillehay has recently published a second large volume.
Stanford had a role, which he describes as small, in reviewing
this data. Monte Verde has nailed down the pre-Clovis peopling of
the Americas, which is now thought to be a much more complex issue
that entailed multiple migrations originating in Asia.
At this moment, Stanford and Bruce A. Bradley, one of the world's
foremost lithic technologists, are analyzing upper Paleolithic
artifacts from Spain that raise additional provocative questions.
Clovis points tend to be bifacial - that is, worked to a fine edge
from two faces. Most European artifacts have been worked on only
one surface. Some points from France and the Iberian peninsula,
however, are more similar to Clovis than the other tools found
in their own neighborhoods. Stanford thinks it may be possible
that some Paleoamericans actually originated in what is now Europe
and found their way around to Maine by island hopping in boats.
It's a belief that "people are throwing rocks at me for," he
admits.
Geologists are piecing together what conditions were like 20
millenia ago, and the weather and currents may have made such
migrations far easier than they would appear to us today. "People
were getting into Australia 50,000 years ago," Stanford says,
"which requires crossing some pretty good chunks of the Pacific
Ocean." Perhaps chunks of the Atlantic were likewise traversed
long before Erikson or Clumbus. The willingness to think outside
the artifact box does not mean, however, that Stanford accepts any
old, or more likely new, theory that comes along. "He's very prag-
matic," says fellow Smithsonian researcher Anna K. Behrenmeyer,
one of the world leaders in taphonomy, the study of how organisms
fossilize. "He's just looking for all the bits of evidence."
(...)
How nice to have open-minded people around.
cir...@access.ch
cir...@access.ch
quoted from an article in the February 1999 issue of the Scientific
American (on early navigation).
Here follows an article on Horus the elder and Horus the younger,
by request of a reader.
I told my vision of early Egypt in the form of a fairy tale.
If you wish to read it, please go to DejaNews (link below)
and Power Search, type my e-mail address into the search line
and look out for my threads 'A Fairy Tale' and 'Continuation
of my Fairy Tale'. Here is a short version of those parts
that concern Horus, in one way or another:
5500-3400 As the Sahara got more and more arid, various tribes
from various regions populated the Nile Valley and brought into
cultivation a formerly hostile environement. They made simple yet
clever inventions like for example the shaduf and the nilometer.
They worshipped a Cosmic Mother Goddess, a woman with the head of
a bird. Two feathers from her eyebrows became the Moon bird and
the Sun bird. She was also worshipped as the bearer of the Heavenly
Gourd filled with the Holy Water of Life. She once filled her gourd
at the Arabian waterhole and made it for the Libyan desert; it was
evening, the sun was down, the moon didn't yet appear, so it was
dark and the goddess stumbled over the cliffs of Deir el-Bahari;
her gourd fell down, the water rushed through the valleys of the
Western Mountain and over the cliffs of Deir el-Bahari, filling
the plain of Thebes (where the world was created according to an
old legend) with the Primeval Lake and a formerly dry valley with
a mighty river; and out of the holes in the ground, which had been
filled with water, animals and the first human beings grew in the
warm sunshine of the next morning ... This happy misadventure
(stumbling goddess, falling gourd, creating the Nile and mankind)
can still be seen in a magnificient constellation: ORION shows the
goddess, Heka her beak, Aldebaran and the Plejades (on one side),
Alhena and Castor and Pollux (on the other side) show her raised
arms, and Sirius shows her falling gourd: the heliakal return of
this bright and sparkling star announced the annual rise of the
River Nile. And/Or the goddess was seen in Orion while her helpful,
charming and wise daughters have been seen in Sirius and Aldebaran.
3400-3100 BC A warrior tribe from Asia Minor entered Upper Egypt
throught the Wadi Hammamat, built a forteress at Hierakonpolis
and a royal court at Abydos. They and their successors conquered
the Nile Valley during a long war. They called themselves Followers
of Horus. They adopted the religion of the Nile Valley and changed
it according to their needs. Now the KING was the ruler of the Nile
Valley. He replaced the goddess, and instead of a round gourd he
wore a crown that reminds of a long, conical shaped gourd. One side
of the famed Narmer Palette shows king Narmer in the pose of Orion
(that was to become the classical pose of the Egyptian deities and
royals):
Horus
Narmer Aldebaran
Servant Orion
Sirius
OLD KINGDOM The legend of Isis and Osiris combines the dramatic
events of the unification of Egypt with a farsighted description
of the very special geographical and climatic conditions of the
Nile Valley. Horus was split into Horus the elder, representing
the predynastic kingdom, and Horus the younger, representing the
dynastic kingdom.
So far my interpretation.
Now let me recommend a new book:
Rolf Krauss, Astronomische Konzepte und Jenseitsvorstellungen
in den Pyramidentexten, Aegyptologische Abhandlungen Band 59,
Harrassowitz Verlag Wiesbaden 1997
Rolf Krauss identified the mysterious h-channel with the stripe
of the ecliptic (its visible parts above the horizon); Osiris with
Orion; Sothis-Isis with Sirius; Seth with Mercury; Horus with Venus
- Horus the younger with the morning star and Horus the elder with
the evening star.
cir...@access.ch
cir...@access.ch wrote:
on Horus the elder and Horus the younger.
In another thread (Great Pyramid Question) someone wrote
that Ra and Osiris played no role in Khufu's pyramid.
Here is my reply:
Ra or Re, Amun, Osiris and Isis have already been worshipped
as local deities in Dynasty I while they appear as all Egyptian
deities in the Pyramid Texts of Dynasty V. We may assume that
the walls of Khufu's valley temple, causeway, pyramid temple,
temenos wall and the casing blocks of his cult pyramid have been
inscribed with similar texts, however, almost all these blocks
are lost. Khafre called himself Son of Re. This may mean that
Khafre, a son (?) of Khufu, was the son of his deified father
(literally or symbolically) who might have been worshipped as Re.
We should also consider that a god was known under many names.
Re was called by 75 names in the tomb of Sethos I. Osiris was known
as Wenefer (the deified king becoming Osiris), or Sh (Sah, Sahu,
Osiris as Orion). They also changed their names: for example Neith,
a symbol of heavens, of the Primeval Water and Mound, became Sothis
(Sirius), Nut (an alter ego of Hathor), Isis (an alter ego of Sothis)
and probably, my assumption, also Nephtys and her alter ego Seshat,
and maybe others.
My speculation: from Dynasty III on, the priests of Heliopolis
developed a new theological system, combining the old legends of
the predynastic and early dynastic eras and the dramatic events
of the so-called unification of Egypt with an amazingly farsighted
description of the very special geographical and climatic conditions
of the Nile Valley, using those local gods and goddesses who served
best the purpose of a coherent story. The new theological system
might have been developed in the time of Imhotep and Djoser, Huni,
Sneferu and fully established in the reigning time of Khufu. The
Pyramid Texts may combine archaic formulas with new names. We know
that Khufu let close all sanctuaries and may interprete this as
an attempt to introduce a new religion or at least a new theolo-
gical system. A further indication of an old and a new religion or
theology may be the presence of Horus the elder and Horus the younger.
---------------------------------------------------------------------
A beautiful description of the Egyptian pyramids and the Nile Valley
is found in Mark Twain's 'The Innocents Abroad'. He tells the visit
at Giza in chapter 58, near the end of the book. Let away the jokes
and you get pure poetry. Mark Twain has an intuitive understanding
of ancient Egypt. In my opinion, the seemingly simple form of a
pyramid contains various other forms, virtual forms evoked by the
numbers and measurements; and the real achievement of ancient Egypt
was bringing into cultivation the Nile Valley, turning a formerly
hostile environement (Rushdi Said, The River Nile, Pergamon Press
1993) into a flowering garden. Mark Twain says much the same by
a few lines:
(Distant View of the Pyramids)
At the distance of a few miles the pyramids rising above the
palms looked very clean-cut, very grand and imposing, and very
soft and filmy as well. They swam in a rich haze that took from
them all suggestions of unfeeling stone and made them seem only
the airy nothings of a dream - structures which might blossom
into tiers of vague arches or ornate colonnades maybe, and change
and change again into all graceful forms of architecture, while
we looked, and then melt deliciously away and blend with the
tremulous athmosphere.
(Superb View from the Top of the (Great) Pyramid)
On the one hand, a mighty sea of yellow sand streched away toward
the ends of the earth, solemn, silent, shorn of vegetation, its
solitude uncheered by any forms of creature life; on the other,
the Eden of Egypt was spread below us - a broad green floor, cloven
by the sinuous river, dotted with villages, its vast distances
measured and marked by the diminishing stature of receding clusters
of palms. It lay asleep in an enchanted athmosphere. There was
no sound, no motion. Above the date palms in the middle distance
swelled a domed and pinnacled mass, glimmering through a tinted,
exquisite mist: away toward the horizon a dozen shapely pyramids
watched over ruined Memphis; and at our feet the bland impassible
sphinx looked out upon the picture from her throne in the sands
as placidely and pensively as she had looked upon its like full
fifty lagging centuries ago.
cir...@access.ch
cir...@access.ch wrote:
on Re, Osiris, Horus the elder, Horus the younger and the
Great Pyramid again. Now for something completely different:
An Archaeological Aspect of Pablo Picasso's Guernica
You certainly know this famous painting, so I don't have to give
you a description or explain the historical background. Let me go
directly to an interpretation of the main symbols. In my opinion,
the large painting can be 'read' on several levels:
Political level:
Horse - Franco, Mussolini, Hitler, fascism in general; if you've
got visual phantasy you can make out a distorted swastika between
the hind legs of the horse (the center being marked by two points)
Bull - Republicans
Woman with lamp - world ("anteilnehmende Weltoeffentlichkeit"),
public, media
Human level:
Horse - civilization
wounded, therefore becoming angry and evil - unemployement for
example (to mention just one form of suppression and humiliation)
drove many people, even proletarians and social democrats, into
the fascist parties
Bull with human eyes - human nature
protecting woman and child - symbol of a family; use your visual
phantasy again and the necklines of the woman and the bull form
an egg, symbol of life
Table - culture, material world ruled by the human measure
Bird - art, poetry, music, painting
broken wings; grey, black and white - the Guernica painting
itself shows broken forms and hardly any colors
Level of gender:
The figures below are a man and a woman. The man could also be
a fallen and broken warrior statue. In his right hand he holds
a broken sword - contrasted by a flower, sign of hope, symbol of
peace. The lines of his left hand show a star: if staying he would
reach the sky. While the statue of the man is broken, the suffering
woman, obviously a farmer with a heavy (earthbound) knee, is bended
and distorted but still a whole figure, and the flower belongs to
her field of light and hope. Man and woman occupy the whole length
of the painting and may symbolize mankind: ready for exploring
space, leading a war instead
Level of time:
We are supposed to be in a village, inside and outside of the
houses, so to speak in the house of mankind - however, a house
set on fire by the fascist parties of then Europe. As the large
animals, bull and horse, move from left to right, we may assume
the arrow of time going in this direction. On the left we see
an opening, therein the hind body of the bull. Use your visual
phantasy again and you see a volcano. Hence the left edge may
symbolize the very early times on Earth and the begin of life.
Another opening is seen at the right edge: a door - an open door?
a closing door? what will hapen with mankind? will human life
come to an end? or will it go on? Actually, the door only seems
to be almost closed, it stays wide open
And where is the archaeological aspect?
We can be sure that Picasseo was most impressed by the cave art
discovered in his lifetime, especially by the horses, bulls and
the hands which may remind of stars, and by the excavations on
Crete and the discovery of the Minoan culture as well.
cir...@access.ch
cir...@access.ch wrote:
an interpretation of Pablo Picasso's Guernica.
You may remember my posts on the A t l a n t i s = T r o y
thesis by Eberhard Zangger. Here follows an appendix on the warm
and cold spring of Atlantis, and on The Odyssey being a modern book.
Plato, Critias, 112 D and 113 D (Loeb Classical Library):
And near the place of the present Acropolis there was one spring
- which was choked up by the earthquakes so that but small trick-
lings of it are now left round about; but to the men of that time
it afforded a plentiful stream for them all, being well tempered
both for winter and summer.
And Poseidon himself set in order with ease, as a god would,
the central island, bringing up from beneath the earth two springs
of waters, the one flowing warm from its source, the other cold,
and producing out of the earth all kinds of food in plenty.
Homer, The Iliad, book XXII (Penguin Classics):
... Hector fled before him (Achilles) under the walls of Troy,
fast as his feet would go. Passing the lookout and the windswept
fig-tree and keeping some way from the wall, they sped along the
cart-track, and so came to the two lovely springs that are the
sources of Scamander's eddying stream. In one of these the water
comes up hot; steam rises from it and hangs about like smoke above
a blazing fire. But the other, even in summer, gushes up as cold
as hail or freezing snow or water that has turned to ice. Close
beside them, wide and beautiful, stand the troughs of stone where
the wives and lovely daughters of the Trojans used to wash their
glossy clothes in the peaceful days before the Achaeans came.
According to Eberhard Zangger's first book The Flood From Heaven
(Sidgwick & Jackson 1992), Odysseus' visit at the mysterious place
called Scherie (= commerical center) was a *time travel* to that
very Troy 'in the peaceful days before the Achaeans came' while
Nausicaa was one of those 'lovely daughters of the Trojans' ...
Atlantis = Troy = Scherie. The blind singer Demodocus (= teacher
of people) recites the well-known ballad on the Trojan War and the
deeds of Odysseus. No on is impressed or moved but Odysseus himself
who is weeping. May it be that the blind singer, unable of seeing
what happens around him, can see into the future? And therefore
no one knows what his ballad means? except Odysseus who now realizes
what a beautiful place Troy was in a former time? When the ballad
is over, Odysseus tells his adventures. In my opinion, his colorful
stories may be a dreamlike report of what happened to the Achaeans
during the twenty years of the Trojan War. For example Circe may
be one of those 'wives and lovely daughters of the Trojans': we
may well assume that many a Greek hero found a lovely girl in the
region around Troy and forgot about the war, at least for some time.
Circe transformed men into mountain wolves, lions and pigs: possibly
meaning that many soldiers behaved like beasts when meeting women.
The frightening Cyclops may mean Troy again: his one eye being the
castle with the gilded w3alls, gleaming in the sun, and the sheeps
may be symbols of boats and small ships while the episode in the
grotto of Cyclops may mean a slip into Troy and an audacious flight
in Trojan boats - only detected because a leader meant to be save
and made fun of the Trojans whereupon a group of soldiers might
have shot at them down from a cliff. The passage beteween Scylla
and Charybdis may be the Hellespont: very difficult to navigate.
And so on. Like in a dream, many symbols and localities may blend.
You will remember that no one believed Cassandra while Teiresias
was another blind singer who really had the gift of prophecy.
Odysseus was known for his ruses. He built the Trojan Horse and
succeeded entering Troy therein. And now, in his dreamlike time
travel, he enters Troy again, secretly again ... not in a wooden
horse this time (which might have been a big, well made, beautiful
Greek ship with a bow in the shape of a horse) but riding on a piece
of wood over a troubled sea churned up by the wrath of Poseidon,
patron of Troy, creator of the horse, god of the sea.
cir...@access.ch
cir...@access.ch wrote:
an interpretation of some episodes of The Odyssey; ideas from 1992,
based on a key idea by Eberhard Zangger.
Here follows a new interpretation of book 9.
Odysseus raches the land of the cyclopes (Penguin Classics):
Then I climbed into my ship and told my men to follow me and loose
the hawsers. They came on board at once, took their places at the
oars and all together struck the whole surf with the blades. It
was no great distance to the mainland. As we approached its nearest
point, we made out a cave close to the sea, with a high entrance
overhung by laurels. Here large flocks of sheeps and goats were
penned at night, and round the mouth a yard had been built with
a great wall of quarried stones and tall pines and high-branched
oaks. It was the den of a giant, who pastured his flock alone,
a long way away from anyone else, and had no truck with others
of his kind but lived aloof in his own lawless way. And what a
formidable monster he was! He was quite unlike any man who eats
bread, more like some wooded peak in the high hills, standing
out alone apart from the others.
The land of the cyclopes may be Anatolia and the giant who lives
a long way away from everyone else may be the acropolis of Troy.
His den may be the harbours of the Troas (plane of Troy), his flock
may be the ships and their crews that have to pay off when using
the harbours and waiting for a favorable wind allowing to navigate
the perilous waters of the Hellespont. The giant is called lawless,
and later on he kills and devoures two men: this may mean that the
Trojans asked for high pay offs and forced their claims through.
"Strangers!" he (Cyclops) cried. "And who are you? Where do
you come from over the watery ways? Is yours a trading venture;
or are you cruising the main on chance, like roving pirates,
who risk their lives to ruin other peoples?"
'Our hearts sank. The booming voice and the very sight of the
monster filled us with panic. Still, I managed to find words to
answer him. "we are Achaeans," I said, "on our way back from Troy
- driven astray by contrary winds across a vast expanse of sea
- we're making our way home but took the wrong way - the wrong
route - as Zeus, I suppose, intended that we should. We are proud
to say that we belong to the forces of Agamemnon, Atreus' son,
who by sacking the great city of Ilium and destroying all its
armies has made himself the most famous man in the world today.
Odysseus left Ilium, hoping to find home soon. But he was driven
astray by contrary winds. He took the wrong way and the wrong route.
May we assume that he returned to Ilium / Troy, traveling 20 years
back in time so that he has to enlive the war again, and if only
in his haunting dreams and memories? The wrong way: back to Ilium.
And the wrong route: backwards in time ...
My name is Nobody.
Odysseus fools Cyclops by saying that he is a nobody. In a similar
way he fooled the Trojans by hiding in the Trojan Horse, making
himself invisible, thus being kind of a nobody too. Then Odysseus
blinded the one-eyed cyclops with a glowing pole. If the giant means
the acropolis of Troy, his eye would have been the palace with the
round and gilded walls on top of the hill, gleaming in the sunlight.
Blinding the cyclops would then mean ramming the door of the palace
and setting it on fire.
If my assumption is right, all the stories reported by Odysseus
at the court of Alcinous tell the Trojan War: over and over again,
always from a different point of view.
And Homer as an author was no less cunning than his hero.
cir...@access.ch
cir...@access.ch wrote:
a new interpretation of the cyclops episode in Homer's Odyssey.
In my opinion, all the stories told by Odysseus in the palace
of Alcinous (book 9 till book 12) are reports of the Trojan War.
Odysseus leaves Troy, goes astray and comes to unknown places:
Ismarus, land of the cicones (9, 39-61), land of the Lotus-eaters
(9, 83-104), land of the cyclopes (9, 105-566), island of Aeolia
(10, 1-79), Telepylos in the land of the Laestrygonians (10, 76-132),
island of Aeaea, the home of the beautiful Circe (10, 134-574), Hades
(book 11), island of the sirenes, Scilla and Charybdis, land of Helios
Hyperion, and finally Scherie (book 12). Scherie was identified with
Atlantis by several earlier scholars. Eberhard Zangger identified it
both with Atlantis and an early Troy before the war. I went a step
further and assumed that all the above places may be Troy: Odysseus,
while sailing home, is haunted by his memories and carried back by
his dreams over and over again. Only that Ilium or Troy has a new
name every time. Yet most of the above places are easiliy recog-
nized as Troy. An example:
Cyclops or Polyphem, 'quite unlike any man who eats bread,
more like some wooded peak in the high hills, standing out
alone apart from the others' - acropolis of Troy
his one eye - the palace of Troy, its round and gilded walls
gleaming in the sunlight
his cave or den - the harbour of Troy
his flock - the ships
Blinding Cyclops would mean destroying the palace of Troy. This would
go along with the sacking of a town in Ismarus, land of the Cicones,
while the Telepylos episode strongly resembles the one in the land
of the cyclopes, only that the giant is now
a woman of mountainous proportions
the sight of her apalling Odysseus' men. Let me quote the description
of the harbour of Telepylos (book 10, verses 87-94, Artemis and
Penguin Classics):
Hochberuehmt war der Hafen, in den wir da kamen: ein schroffer
Felsen umgibt ihn links und rechts ohne Luecke; die Ufer
springen vor, einander entgegen und werden am Zugang
Hoeher; wie eine Rinne so schmal ist also die Einfahrt.
Dorthin steuerten wir die Schiffe, die doppelt geschweiften,
Nah aneinander band man sie an im geraeumigen Hafen;
Niemals naemlich erhob sich darin eine Welle zur Woge,
Klein oder gross; es herrschte dort blendende Meeresstille.
Here we found an excellent harbour, closed in on all sides by an
unbroken ring of precipitous cliffs, with two jutting headlands
facing each other at the mouth so as to leave only a narrow channel
in between. The captains of my squadron all steered into the harbour
and tied up in the sheltered waters within. They remained close
together, for it was obvious that there was never any swell there,
slight or strong, but always a flat calm.
This description of the harbour of Telepylos goes together perfectly
well with Eberhard Zangger's geoarchaeological reconstruction of
the Troas (plain of Troy). My proposition: when professor Korfmann
and other envious minds hamper his fine geoarchaeological expedition,
he may read again the Odyssey instead (for the time being) and look
out for more informations there.
cir...@access.ch
cir...@access.ch wrote:
an interpretation of the books 9-12 of Homer's Odyssey.
Sorry for having forgotten Ogygia, the island of Calypso.
Book 12, verses 447-453 (Penguin Classics):
Nine days of drifting followed; but in the night of the tenth
the gods washed me up on the island of Ogygia, the home of Calypso
of the braided tresses, that formidable goddess with a woman's
voice; and she received me kindly and looked after me. But why go
again through all this? Only yesterday I told you and your noble
wife the whole story here in your home, and it is tedious for me
to repeat a tale already plainly told.
According to my view, Odysseus told the Trojan War over and over
again. So when he finally says that repeating a tale already plainly
told is tedious for him, Homer is joking.
Now let us have a closer look at Calypso; book 1, verses 48-51,
Athena speaking:
It is for Odysseus that my heart is wrung, the wise and unlucky
Odysseus, who has been parted so long from all his friends and
is pining on a lonely island far away in the middle of the seas.
The island is well-wooded and a goddess lives there, the child
of the malevolent Atlas, who knows the depths of all the seas
and supports the great columns that hold earth and sky apart.
Calypso was a daughter of Atlas. In the Greek original (1, 52):
Atlantos thygataer
Troy was a foundation of Atlas and his daughert Atlantis and was
therefore called ATLANTIS by English historians like Jacob Bryant
and William Gell. According to the Roman grammarian Servius, one
passed the columns of Heracles also wehen sailing to the Black Sea.
The island Ogygia of Calypso lies in the middle of the seas while
Troy lies between the Aegaeis and the Black Sea ... Hence Ogygia
would be Troy again.
Odysseus returning from Troy has a false start (book 3, 159-164):
... eager to be home, we sacrified to the gods. But Zeus had no
intention of letting us reach home so soon, and he mercilessly
stirred dissension among us once more. As a result, one squadron
swung the curved prows of their vessels round and turned back
towards Troy. These were the followers of Odysseus, that wise
and subtle king ...
He was 20 years away and now he needs 20 years for reaching home.
These must be imaginary years, out of the following reasons: he joined
the expedition to Troy when his son Telemachos was born, and he told
his wife Penelope to marry again when Telemachos is grown up. When
Odysseus reaches home, his faithful wife is just about to marry again,
as her husband told her to do. Hence their son is grown up and may
be 20 years of age. This means that Odysseus was 20 years away:
20 years in Troy and possibly a week for sailing home while his 20
years of going astray must be imaginary journeys: he is haunted by
his memories and carried back to Troy by his dreams. And accordingly
he tells his dreamlike adventures in the night, in a very long night
in the shadowy hall of king Alcinous, as this one points out very
clearly (Gesang 11, 373, Artemis):
Lang ist die heutige Nacht, unsagbar wie lange
And we, reading the epos, accompanying Odysseus in our mind, are
hold up by the same adventures and have to go through more than 12
books until we finally reach Ithaca ...
The opening verses of the Odyssey:
Tell me, Muse, the story of that resourceful man who was driven
to wander far and wide after he had sacked the holy citadel of
Troy. He saw the cities of many people and he learned their ways.
He suffered great anguish on the high sea in his struggles to
preserve his life and bring his comrades home. But he failed
to save those comrades, in spite of all his efforts ...
Wandering far and wide: haunted by his dreams. Suffering great
anguish on the high sea, struggling to preserve his life and bring
his comrades home: a symbol of the Trojan War, gone through again
while sailing home, having Poseidon against him now ... I assume
that the Greeks and the Trojans worshipped a similar god of the sea,
and while we encounter the Greek Poseidon in the Iliad, Odysseus,
returning home and being haunted by his dreams, encounters the Trojan
Poseidon. Our cunning hero, dauntless and all-daring, an arch-schemer,
a nimble-witted man, haunted by as 'cunning' dreams ...
cir...@access.ch
cir...@access.ch wrote:
on Homer's Odyssey again.
Follows a tentative reconstruction of the Trojan War:
'Lovely Troy' in north-east Anatolia was a beautiful place,
a most important commercial center of the Bronze Age, owing its
wealth to all kinds of natural resources; to a large harbour where
the passing ships coming from and sailing to the Black Sea waited
for favorable winds; and to the skills of the Trojan pilots who
navigated the foreign ships through the perilous waters of the
Dardanelles. However, the ships arriving at and leaving Troy had
often been captured by the sea-people: pirates living on the Aegean
islands and on some parts of the coast of the Peleponnes. Thus, the
Trojans had been forced to fortify their harbour. The ships had to
pass a channel when coming from the Hellespont and a drag-channel
when coming from the Aegean. The Trojans could blockate the channels
and shoot at the pirates from above when they passed a channel, or
throw stones or even rocks down on the ships. Troy was taken over
by a new king (Priam) who used the fortified harbour to extort much
higher pay offs and who treated all the ships coming from west as
potential pirates. There have been many coincidences between the
Trojans and the Greeks. Finally, a son of the Trojan king (Paris)
captured a Greek ship with a lovely princess on board (Helen) whom
he made his wife, whereupon the Greeks sent an army to the shores
of Troy. It stayed there for years, watching over the Greek ships
passing the Dardanelles. The Trojan king (Priam) neglected all the
warning voices (Cassandra). There have been several battles. The
war escalated, and the Greek alliance won. Returning home, Odysseus
found his country (his house and bed built around an olive tree)
besieged by the sea-people (suitors of Penelope). So the returning
warriors had to lead another war, this time against the sea-people,
until they finally made peace.
All these events have been remembered in poems which then have been
compiled by several bards, among them Homer (1 and 2).
Homer (1), in his Iliad, tells the 50 days of the Trojan War:
Athena was the patroness of Troy, however, she stays deliberately
on the side of the Greeks. Poseidon built the walls of Troy together
with Apollo, and he helps saving Aeneas in order that he may follow
Priam as king of Troy. Athena and Poseidon change their side and help
the Achaeans against Priam and his people (although Poseidon tells
Athena not to be so aggressive and later on, in the Odyssey, punishes
the 'sacker of the holy citadel of Troy'). Their help means that the
war against Priam is righteous. On the other hand, the opening lines
of the Iliad criticize the Achaeans too (Penguin Classics):
The Wrath of Achilles is my theme, that fatal wrath which,
in fulfillement of the will of Zeus, brought the Achaeans
so much suffering and sent the gallant souls of many noblemen
to Hades ...
Homer (2), in his Odyssey, tells the return of a Greek chief-captain
and his war against the sea-people:
Odysseus and his men leave Troy, get in a heavy storm, turn their
ships and spend a long night on the shores of Troy. In this night,
Odysseus, haunted by dreams, goes through the Trojan War again. In
his dreams, everything looks different. Troy is now called Telepylos
(literally a far away doorway, as Troy was kind of a doorway leading
to the Black Sea), and the Acropolis of Troy is a woman resembling
a mountain, only the harbour remains the same. In a later dream,
the Acropolis of Troy is a giant resembling a hill (Polyphem), his
one eye the palace, the harbour his den, and the ships are his flock.
Odysseus blinds Polyphem (sacks the 'holy citadel of Troy') and thus
makes Poseidon (builder of the Trojan walls) his enemy. Finally, in
his last dream, his ship is destroyed by angry Poseidon. Odysseus
reaches the peninsula of Scherie (a former Troy) where he tells his
fate in the shadowy hall of king Alcinous and realizes what a lovely
place Troy was in a former time and what he and his men destroyed.
Now he falls into a deep sleep. On the next morning the sea is calm.
Odysseus returns to Ithaka, where he has to fight the sea-people,
and then, finally, the Greek tribes on the mainland and on the
Aegean islands make peace.
cir...@access.ch
cir...@access.ch wrote:
a reconstruction of the Trojan War, based on Homer's Odyssey.
In a former post I made a mess of the numbers of years Odysseus spent
in Troy and on his journeys. Here is the correct version: according
to Homer, Odysseus was 10 years in Troy and again 10 years on his
journeys, making a total of 20 years.
Let me try again.
Around 1240 BC, a Greek expedition looking out for copper succeeded
in passing the Dardanelles and the Bosporus yet was considered as
pirates by King Laodemon of Troy. The Greeks led a first war against
Troy. One Telamon, by losening a single stone, brought to fall a wall
of Troy. Laomedon and his sons were killed. Only his youngest son
Podacres survived. He changed his name into Priam and let build much
stronger walls. Around 1210 BC, an army of Greek allies installed
itself in the Troas and stormed the palace of Troy around 1200 BC,
killing Priam and his people. Aeneas became king of Troy. The Greeks
stayed another ten years in the Troas, escorting Greek ships going
to and coming from the Black Sea - as remembered in book 12 of the
Odyssey: the island of the Sirens might be the Dardanelles (I could
imagine a specially shaped rock 'singing' in the wind), Scylla and
Charybdis may be the Bosporus, and the island of the Sun-god Hyperion
might be the Krim. Odysseus tells his men to keep their hands off
Hyperion's cattle and sheep 'or else we shall come to grief.' The
men follow his advice in the beginning but neglect it later on. This
may mean a Greek attack on foreign ships (animals like sheep, goats,
cattle and horses may all be understood as ships). A capital mistake,
for now the Greeks had new enemies in that region and had to pay a
very high price for the pure copper traded there: a long way to sail,
a dangerous passage, and an expensive enforcement of the Greek army
in the Troas. The hypothetical battle near the Krim must have been
an important event, for it is mentioned in the opening lines of the
Odyssey; book 1, verses 6-9 (Penguin Classics):
But he failed to save those comrades, in spite of all his efforts.
It was their own transgression that brought them to their doom,
for in their folly they devoured the oxen of Hyperion the Sun-god
and he saw to it that they would never return.
Finally, Odysseus leaves Troy. A storm forces him to return. He sleeps
on the shores of Troy. Dreaming, he goes through the war again. In his
last dream he reaches Scherie, peninsula of the Phaiacians, a former
Troy, a lovely place. Now he realizes what he and his men destroyed,
and he weeps. Still in his dream, the Phaeacians navigate him home
(13, 70-93):
When they had come down to the ship and the sea, the young nobles
who were to escort him took charge of his baggage, including all
the food and drink, and stowed it in the polished ship. For Odysseus
himself they spread a rug and a sheet on the ship's deck, well aft,
so that he might enjoy an unbroken sleep. Then he too climbed on
board and quietly lay down, while the crew took their seats at the
oars in order, and untied the cable from the pierced stone that
held it. No sooner had they swung back and churned the water with
their blades than sweet oblivion sealed Odysseus' eyes in sleep,
delicious and profound, the very counterfeit of death. / And now,
like a team of four stallions on the plain who start as one at
the touch of the whip, leaping forward to make short work of the
course, so the stern of the ship leaped forward, and a great dark
wave of the surrounding sea surged in her wake. With unfaltering
speed she forged ahead, and not even the wheeling falcon, the
fastest creature that flies, could have kept her company. Thus
she sped lightly on, cutting her way through the waves and carrying
a man wise as the gods are wise, who in long years of war on land
and wandering across the cruel seas had suffered many agonies of
spirit but was now lapped in peaceful sleep, forgetting all he
had endured.
Continuation follows.
cir...@access.ch
cir...@access.ch wrote:
a modified reconstruction of the Trojan War, based on Homer's Odyssey
and some remarks by Eberhard Zangger. Here follows the continuation:
Odysseus goes on board in the evening and falls in a deep sleep.
In the morning the ship arrives at Ithaca. However, Odysseus doesn't
recognize his home whereas we don't really know where he came from.
Where does Scherie lie? Many assume that it was Corcyra (Corfu). A
shiplike rock in the bay of Corcyra is called 'the ship of Odysseus'
by the locals and seen as proof that Phaeacia was Corcyra (compare
book 13, 153-183). Eberhard Zangger identified Scherie with Troy.
In his first book The Flood from Heaven (Sidgwick and Jackson 1992)
he published a drawing by Henry W. Acland from 1849 showing shiplike
rocks in front of the Trojan shore. Now a Corcyran may say that one
could reach Ithaca overnight when starting from Corcyra but certainly
not when coming from Troy. Whereupon Zangger might reply that Homer
doesn't say how long the Phaeacians needed: leaving Scherie in the
evening they reached Ithaca in the early morning, but not necessarily
on the next morning. Odysseus is sleeping deeply, an 'unbroken sleep'
resembling death. It may well be that he slept through several nights
and days and had only the impression to arrive on the next morning.
In that case Scherie could be Troy again.
Who is right? Well, I believe that the ambiguity of the place was
intended by Homer, and Scherie was both an earlier Troy AND Corcyra.
Let me explain.
According to Eberhard Zangger, the Swedish scientist Olof von Rudbeck
(1630-1702) and many following authors believed that Homer's Scherie
was Plato's Atlantis while English historians like Jacob Bryant and
Wiliam Gell identified Troy, a foundation by Atlas and his daughter
Atlantis, with Atlantis again. Eberhard Zangger goes a step further
by stating:
early Troy = Scherie = Atlantis
Now let me compare Troy and Corcyra and summarize the Odyssey out
of Athene's perspective:
Troy, west of the Black Sea and the shores of Eurasia
Corcyra, west of Greece and the Aegean
Athena, patroness of Troy, worshipped at a shrine in Ilium, was
deeply disappointed by the unworthy kings Laomedon and Priam. She
changed her side, joined the Greeks and helped Odysseus destroy Ilium.
Then she introduced him to Scherie, a former Troy. Odysseus realized
what a beautiful place Troy was in an earlier time, and he weeps.
Arriving home, he doesn't know where he is. Back home? or possibly
still in Scherie? He is save home, and his home is much as lovely
and beautiful as Scherie was. However, there are the 'shameless
Suitors' (pirates living on Aegean islands and partly on the shores
of the Peleponnes) besieging his faithful wife Penelope and her house
and bed built around an olive-tree (Greece). Their power has to be
broken before Greece can unite and become a new empire, so to speak
a New Troy in the Greek archipelago. Athene is once more a driving
force. She tells Odysseus that he has to come to grips with the
'presumptuous Suitors' and inflames him in the 'Battle in the Hall'
(civil war). Finally, Zeus has to stop her fury, whereupon Athene
... still using Mentor's form and voice for her disguise
established peace between the two sides. (End of Homer's epos)
And now her resourceful, wise, unlucky, admirable, patient, great,
godlike, good, noble, dauntless, indomitable, lion-hearted, valiant,
stalward good, ingenious, nimble-witted, much-enduring, subtle,
shrewd, cunning, long-suffering, inventive, great-hearted, steadfast
good, quick-witted, brave, ready-witted, handsome hero may fulfill
her vision of a new Troy in the Greek archipelago while she, Athene,
shall be his mentor.
Unoutspoken end of the Iliad: fall of Trojan Empire ...
Unoutspoken end of the Odyssey: rise of the Greek Empire ...
cir...@access.ch
cir...@access.ch wrote:
on the Odyssey again.
You may remember my astrologer from some former posts of mine.
Well, she had another long look into her fine magic crystal ball
and then she told me the following on the author of the Odyssey:
'Homer 2' was born around 725 BC in PHOCAIA (Foca near Izmir),
on a peninsula at the mouth of the River HERMOS, a fishing and
commercial harbour where a singing wind blowing around the rocks
detoured many a poor fisherman. Phocaia belonged to the Greek part
of Anatolia. Homer's father was a Greek from the mainland while his
mother was from Anatolia. The father, a merchant, traveled widely,
to the Black Sea, Greece, Corcyra, Rhodos and Naukratis, an Ionian
colony on the Nile Delta. He was fond of his boy and often took him
with him on a journey. The boy was eagerly learning all kinds of
songs, and he astonished his parents by reading a clay tablet in
the soft age of 5 years. From then on, the boy collected all kinds
of clay tablets and soon had a collection of legends concerning Troy,
and he learned by heart the Iliad by Homer, always reciting some lines
on a suiting occasion. His mother loved him dearly, as he was a pretty
boy, and she told him all about lovely Anatolia. She was a beautiful
woman, however, the daughter of a poor farmer and swineherd, having
herded pigs and sheep and goats herself when she was a girl. The
boy wanted to know all, he had a most vivid phantasy, he loved to
play with words and to hide away and disguise himself. His parents
called him 'our boy of the nimble wits', and he liked his nick-name
very much. A journey to Naukratis was to become most important for
him. On board was an Egyptian priest who told him about the legend
of Isis and Osiris, and explained what the symbols mean: Osiris
= Nile, Isis = green land, and so on. The young man was deeply
impressed, and he had an idea: how about unifying the various songs
and poems on Troy to a new epos and make it symbolical much in the
way of the Egyptian legend? There will be a loving couple, she may
symbolize the land (Greece) and he may symbolize the sea (Ionian
and Aegean), and instead of Seth their enemy is Troy, the town of
Leomedon and Priam. However, Troy ain't a bad place, on the very
contrary: it belongs to the western shore of Anatolia, his blessed
home. And so Odysseus, his hero, shall return in a dream to an early
Troy and recognize how lovely it was, then he shall return to Greece
and punish the pirates who made unsure the whole Ionian and Aegean,
and then he shall found a new Troy in Greece. And the lovely place
of early Troy shall be called Scherie (commercial center), but also
PHAEACIA, a wordplay on his home PHOCAIA, while his own alter
ego in the epos shall be HERMES, a pun on the River HERMOS which
flows to Phocaia ...
So far my astrologer. Now who was Hermes? my Webster calls him
Hermes: the ancient Greek herald and messenger of the gods
and the god of roads, commerce, invention, cunning, and theft
Cunning like Odysseus ... Being a god of theft, Hermes might well
be a patron of Homer who was stealing songs and poems and arranging
them into an epos of his own ... Hermes is called the Giant-killer,
for he overcame the monster Argus whose hundred eyes have then been
transferred to the feathers of the peacock - while Homer transforms
a war into a pleasant epos ... Hermes owns a pair of golden sandals
that bring him everywhere swiftly as the wind - while Homer's mind
can be on the Olympos and a few lines later in Scherie ... Book 5
(Penguin Classics):
... he bound on his feet the lovely sandals of untarnishable gold
that carried him with the speed of the wind over the water or the
boundless earth; and he picked up a wand which he can use at will
to cast a spell upon men's eyes or waken them from sleep ...
Well, we know that from our author ;-) Book 15:
Hermes the Messenger, who gives grace and dignity to every kind
of common labour
Homer the Poet, who makes a swineherd one of his most amiable figures.
(Hermaes - Hermos - Homaeros -- another wordplay?)
cir...@access.ch
cir...@access.ch wrote:
a speculation on the author of the Odyssey.
Now who wrote the Iliad? My astrologer had another look into her
crystal ball and told me the following:
'Homer 1' was born around 790 BC in Mantineia on the Peleponnes.
As a young man he made it for Argos where he worked in the royal
archives. He was a diligent and most careful scribe, and he loved
to go through the oldest clay tablets kept in a secret room of the
royal palace. People made fun of him: how many hour did you spend
therein again? you risk to get blind when you bury yourself in the
dark. Have a break, leave your cellar, join us here in the warm sun
of early spring and tell us what you found down there in that beloved
dungeon of yours ... Well, he joined his friends and told them about
the lists he found in the archive: lists of the troups that fought
in Troy! And he recited names and places, names and places, names
and places again until his friends sighed and said: long gone times;
what are all these names good for? let them sleep in the Hades of
your archive. Whereupon he told his friends: you shall see me bring
them to life again! His words made the round in Argos. Other scribes,
who were envious of his privileges, made fun of him and called him
a crazy fool. He didn't care and buried himself in the archives again
and a week later he came up with a poem made from a list of names,
and verily did they come to life again. The king was pleased to hear
his verses, freed him from all common work and sent him to Pylos,
the palace of Nestor, to go through those archives, and as he feared
for the eyelight of the young man he looked out for a young woman
to join him. The king found a woman, and she did her job very well:
reading the clay tablets, doing much of the scribe work, keeping
the names of people and places in her memory, and she came up with
reasonable and sensible comments so that the half-blind poet called
her his Muse. They found several peoms on the Trojan War in Nestor's
archive, and the young man began compiling them, or, moreover, he
wrote them anew, assembling them to an epos, filling the gaps between
the scenes by means of his lively phantasy. On one level he tells
50 days of the Trojan War, on another level he asks a philosophical
question: what is done by us humans? and what is done by the gods?
His answer: Priam loses the Trojan War for he stood in the way of
history, hampering the Greeks and the rise of a new and most promising
civilization. As soon as Hector fell and Achilles dragged him around
the walls of Troy in order to break their magic protection (Eberhard
Zangger in his new book) and thus making the downfall of Troy final,
the arch-enemy of the Achaeans, King Priam, turns out to be a noble,
admirable man. His only fault was to stay in the way of history,
represented by some main deities like Athene.
'Homer 2', born around 725 BC in Phocaia, a Ionian colony in
western Anatolia, learned the Iliad by heart and got its message
well. His Odyssey is a much different work, full of dreamlike tales
and yet providing a similar message: the war against Laomedon and
Priam was justified, but sadly destroying a lovely place and killing
wonderful people. Somewhere he says that not all our ways and deeds
are determined by fate, giving us hope that we may do better. By
listening to our poets and blind prophets and wise people we may
foresee the future and thus, perhaps, avoid some further wars. While
'Homer 2' used Hermes as his alter ego in the Odyssey, he made Mentor
- a close friend of Odysseus, a good, even godlike man whose 'form
and voice' are used as disguise by Athene - an alter ego of 'Homer 1'
(Mantineia, Nestor, Mantor, Mentor), and, loving jokes, he introduced
him as a wise man who gives the shameless and preposterous Suitors
of Penelope a very good advice whereupon they call him a 'crazy fool',
thus reminding of a then famous anecdote in the life of the young
poet (see above) and also repeating a central message: listen to
the wise people and you may avoid or overcome a bad fate. Many could
have survived if only they had listen to godlike Mentor, symbol of
the poet through whom sometimes Athene herself was speaking.
cir...@access.ch
cir...@access.ch wrote:
a speculation on the author of the Iliad.
Follows a glossary, speculative again:
CRONOS - time (both creating and destroying)
ZEUS, son of Cronos - father of mankind; patron of Troy and Achaea
as well
ATHENE, daughter of Zeus - history; once on the side of holy Ilium,
lovely Troy, now on the side of the upcoming Greek civilization
ILIAD - written between 770 and 735 BC in Argos and Pylos, based
on tablets in the royal archives, telling 50 days of the Trojan War;
Athene on the side of the rising Greek civilization, helping Achaeans
win the war; a fragmentary epos, finished and partly worked over by
the author of the Odyssey
AUTHOR OF THE ILIAD - born around 790 BC in Mantineia in Arkadia
on the Peleponnes, going to Argos and Pylos, working as a scribe
in the royal archives; myopic (?), in later years almost blind,
working with the help of a woman (Muse); name of poet unknown,
MENTOR his alter ego in the Odyssey; died around 735 BC
ODYSSEY - written between 705 and 660 BC; a compilation of old songs
and poems hold together by an ingenious frame: Odysseus leaving Ilium
has a false start, sleeps on the shores of Troy, dreams of the war,
the Acropolis of Troy appears as a woman of mountainous proportions,
as a one-eyed giant resembling a hill, and so on, finally Zeus sends
him to Scherie (= commercial center according to Eberhard Zangger),
peninsula of the Phaeacians, an early Troy, now Odysseus recognizes
how lovely a place Troy was in a former time and what he and his men
destroyed, and he weeps (according to Eberhard Zangger again); finally
coming home to Ithaca, he has to lead a war against the sea-people
(pirates living on Ionian and Aegean islands and partly on the shores
of the Peleponnes), he wins the war whereupon Greece was united (unout-
spoken end of the Odyssey); on another level of time, the 'Battle in
the Hall' means the first Messenian War (740-720 BC)
AUTHOR OF THE ODYSSEY - born around 725 BC in Phocaia (Foca), an
Ionian colony in western Anatolia, near the River Hermos and Smyrna
(Izmir); son of a Greek merchant and an Anatolian mother, a beautiful
woman, daughter of a poor farmer; as a boy he traveled with his father
as far as Troy and the Black Sea, Argos, Ithaca and Corcyra, Rhodos
and Naucratis, an Ionian colony on the Nile Delta; premature, reading
already as a boy, collecting poems and fables on Troy; learning by
heart the fragmentary Iliad, which he partly worked over and finished;
HERMES argeiphontes his alter ego in the Odyssey, a pun on the River
Hermos (ancient mouth near Smyrna), argeiphontes meaning watchful
and a dragonkiller like Argos (later misinterpreted, also by me in
a former post); Homer, author of the Odyssey, editor of the Iliad,
died around 660 BC, on the eve of the second Messenian War and during
the attacks of Gyges (680-654 BC), who conquered Colophonia
NAUSICAA and the peninsula of the Phaeacians - Troy around 1700 BC,
resembling Phocaia of Homer's time, also reminding of Corcyra (Corfu)
CALYPSO, her cave and garden - Anatolia around 1200 BC
PENELOPE, her house and bed - Greece around 1200 BC
TELEMACHUS, son of Penelope and Odysseus - Greece around 700 BC;
speaking name meaning a) first Messenian War b) war against Gyges;
Homer concerned about Greek empire (strength and unity of mainland,
security of his home in western Anatolia): will Telemachus equal
his father? Homer not really sure but optimistic, Odyssey book 2,
lines 270-280, Athene speaking through Mentor (Penguin Classics):
Telemachus, you will be neither a coward nor a fool in the future,
if your father's manly vigour has descended on you - and what a man
HE was in word and deed!
It is only if you were not the true son of Odysseus and Penelope
that I would think your plans might come to nothing
... if you are by no means lacking in Odysseu's resourcefulness,
and since you will be no fool or coward in the future, you can
hope to succeed (...)
cir...@access.ch
cir...@access.ch wrote: ...
Dear reader,
DejaNews changed a lot: its name and design and sadly also the
format of the messages in the newsgroups, giving up the WYSIWYG
principle (what you see is what you get / my carefully layed-out
articles appearing in the same way online), a principle I need
for publishing my work. If Deja (formerly DejaNews) won't return
to it, I have to leave the usenet.
Does anyone know a good archaeological forum on the web?
An open-minded group, an alien/Atlantian free forum?
A scientific forum where new ideas and approaches are welcome?
An archaeological forum where people are truly interested in the
ancient ones who achieved great things by means of simple tools
and clever ways?
If you know such a forum (that works according to the WYSIWYG
principle and has a reliable archive) please inform me via e-mail.
Thank you very much.
Goodbye (for a while or maybe forever)
Franz Gnaedinger Zurich cir...@access.ch
--== Sent via Deja.com http://www.deja.com/ ==--
---Share what you know. Learn what you don't.---
cir...@access.ch
cir...@access.ch wrote: ...
No archaeology today, for Deja (formerly DejaNews) made a mess of my
articles by changing the format. Instead a secret message for the aliens
among you (a majority I guess ;-)
pweruit34'gf8 vfäsdpbvj3 äpojt23g kgvfämbüzihtk wäehktrwtr'0$b^ds
b9n
edgh54 zk54z938'4h0gnb fgüohi56'z0969^0ht gnbcďnfhgtrl65ö4
khzf'0gnbndf56h r0tü'n9ogf0nifrtp5ü6 z4äü56klz^'foghnd
"fghlklt
ghi'0gnbgkölhörtz,'0ongf^0oghkölrtö4zk45üp6kzu^h9odfg^'dfg0dfghlärötlhrt
'^9oh^fghjölrhzu6,546ofüghnfg'0hrt^'zul6äörlzärölnb^f'gn0fg^hjrtrlözurlö
tähzrtüohf^g'hofrtlhärtölz4'6574^5to"üepohtgfhbg0h6rezlä$ö334r
45z^0h45^21$ö1 ,ttglr"weübv
eze45^345z^hzuthrth
gnbcv.,nb-cfg$"üre"ü4555557z46zu0hjurtzlöhäögfn,fälkgnf'0h95z6u'05964'95
4ükpothüw
Captain H'mon Planet Bil-el Alpha Eridani
Sail Fi
>
>
>In article <7h91mr$om2$1...@nnrp1.deja.com>,
> cir...@access.ch wrote: ...
>
>
>No archaeology today, for Deja (formerly DejaNews) made a mess of my
>articles by changing the format. Instead a secret message for the aliens
>among you (a majority I guess ;-)
>
>pweruit34'gf8 vfäsdpbvj3 äpojt23g kgvfämbüzihtk wäehktrwtr'0$b^ds
>b9n
>edgh54 zk54z938'4h0gnb fgüohi56'z0969^0ht gnbcïnfhgtrl65ö4
>khzf'0gnbndf56h r0tü'n9ogf0nifrtp5ü6 z4äü56klz^'foghnd
>"fghlklt
>ghi'0gnbgkölhörtz,'0ongf^0oghkölrtö4zk45üp6kzu^h9odfg^'dfg0dfghlärötlhrt
>'^9oh^fghjölrhzu6,546ofüghnfg'0hrt^'zul6äörlzärölnb^f'gn0fg^hjrtrlözurlö
>tähzrtüohf^g'hofrtlhärtölz4'6574^5to"üepohtgfhbg0h6rezlä$ö334r
>45z^0h45^21$ö1 ,ttglr"weübv
>eze45^345z^hzuthrth
>gnbcv.,nb-cfg$"üre"ü4555557z46zu0hjurtzlöhäögfn,fälkgnf'0h95z6u'05964'95
>4ükpothüw
>
>Captain H'mon Planet Bil-el Alpha Eridani
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
And, on THAT note............beam me up Scotty............
cir...@access.ch
sai...@aol.com (Sail Fi) wrote:
> And, on THAT note............beam me up Scotty............
Beam me up DEJA ...
When I write on archaeology, I get few replies, but when I write
nonsense I always get one. Funny, ain't it? So here you are with
some more nonsense, a quote from the epos MONDIM, famous on planet
Bil-el:
Erqwz"gikrtaäbnlfjmüqzü35rqejhm
"'rwgkopwrkg,wä$erk,g$wüerkbgwa
$eügreüpigrjroü$mvmfv lös$kjg$035$gik$
wer^qgitf$q"weifgtüp$"wrekgp"üwkre
4q230^tiüp$rejgadsöfljerotüä3uqwit^0
frwoe'"wrüeof"$wle$gflw"$üerlgtf
ü"prktg$qürmüae$fpj bvüe$qzt$ükq4$ügäkw
fr3"'ktgqreäwkgärewkgäAEKRkgew
'3"qito"qprgik$"pewroigh"w
r4ögt"rog"frwktz$eqwrkzgü$reiztg$ü
gfrpoigtp"ürogp"üero"gtore"$otö"qreot
türe3witgü$reikgü$erpü$ti3o"ür$5otz
rtgi$re"üphgiü"$erpkgi$üëpgki"ü$peroi
rüwigü$perigkp$ürkbüp$e"rhgi"üehgi
rweitg$"üerztig$"püeroi"gpreo"gpio
gfrüpigü$perhig$ü"perktg5rz5r3"goi
gerü"pogiüëprgik"ü$pe"$pgto"reotg"üer
fgrpigükreükgjüerkt3älw4rmtgäflbkvg
wei"wreigkpürkgürwëpitkü"34pkt"polrg
tfewiptg$üprkgüperzitü"rizgtpürekgh
grepkbhprekg"püewr$tzi"35pohöhrtiët
rgweögërohg"p$erlzöä5,z"w5'oih"teoh
gre"pohgkpëälrkht5ä4özot'"hpholteäphlk
rtg"3wotgpürelghk$älhrt$ütelh$üeth
r gteo"geüphl$tölkh$öshgdl
z54'ozh"4htr"phpötrläh$äölrth"rt
Gerwpzipü45ikzälittü0ehi9w45^0zi54
zt530z95^ü$izp4äkh40ô4^0ü5uikhtrg0'ü46
t54^0tziü54pkhärts'izüpo65uzjöl4th
zt50ziühkrgl'40üiuhjtoörhkütrpiuk"64pou
5z3z0iüthktl45w^0üzitpährkähkstrüäphk
r5tüizpäetkhätrhkrtähkät6ölku4üui4
z5ü0izhteäpkhtälkh64ku60üuhijütrphir
z530üzipw5täkhlk064üuik4äk65jhtl-
4tü3itzpkälörkhglewkz0ü54wktlheöjkher
t4öziäp5re3kzöethkltàEélzh45w'"pzo
43üizpt35kzäältkzwle5kz7uäl
The aliens among you can read this quote by means of a MFD (Multi-
Facetal-Decoder), something like a crystal: depending on which facet
you are using you can read the lines in English, Japanese, Chinese,
Suaheli, and so on, however, not in German, for this language heates
up the decoder, might be dangerous) - or you can see a 3-D picture
of the most famous pyramids on planet Bil-el (alpha Eridani) ...
PS.
I wrote a lot on archaeology in here, and I would love to go on doing
so. However, Deja changed the format of the messages and made a mess
of the lay-out of all my articles. This makes me feel unhappy.
Just now I work over my 'fairy tale' (a vision of early Egypt)
and my interpretation of the Iliad and Odyssey (bringing all into
a chronological order, omitting some ideas in favour of new ones),
with the help of Kathy, a professional American translator. I planned
to publish the corrected and improved versions here in sci.archaeology.
But now I don't feel like doing so anymore. Why should I publish my
work in here and hand over the copyright to a company that makes a
mess of my articles? And anyway, all I ever wrote in here was neg-
lected or immediately forgotten, for example my proposition of ramps
for the Great Pyramid (volume of the ramps 1/7 of the pyramid's volume,
blocks of Tura limestone, reused for the many minor buildings of the
pyramid complex).
Marcio, thank you for the kind e-mail. I replied, but my answer
was returned to me by a Mailer Demon.
A reader asked me about astronomy and constellations in ancient Egypt.
Well, I wrote several articles on these topics in here. You can find
them via http://deja.com and Power Search. However, in a messed-up
lay-out.
Sail Fi
>
>
>> And, on THAT note............beam me up Scotty............
>
>
>Beam me up DEJA ...
>
>When I write on archaeology, I get few replies, but when I write
>nonsense I always get one. Funny, ain't it? So here you are with
>some more nonsense, a quote from the epos MONDIM, famous on planet
>Bil-el:
~~~~~~~~~~~~~~~~~~
Alas and alack....I'm new to this group....and, as is always the case with my
natural impetuous self, sent a response which had sprung to the screen, via the
keyboard......without my realising it. ::sigh:: You are not alone in your
dismay, my horde would commiserate with you.......Back to lurking for
me....::hanging head in shamed contrition::
cir...@access.ch
sai...@aol.com (Sail Fi) wrote:
> Alas and alack....I'm new to this group....and, as is always the case
with my
> natural impetuous self, sent a response which had sprung to the
screen, via the
> keyboard......without my realising it. ::sigh:: You are not alone in
your
> dismay, my horde would commiserate with you.......Back to lurking for
> me....::hanging head in shamed contrition::
Welcom in sci.archaeology, the forum of aliens and Atlantians.
Please do not despair if you couldn't understand my messages
to the aliens in here. Perhaps you are an Atlantian instead?
Find out. Have a look at tzhe following lines. Common people
will see the letter a repating while the true Atlantians among
you will recognize the encoded message:
aaaaaaaaaaaaa a aaaaaaaaaaaaaaaaa a a aaaaaaaaaaaaaaa
aaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa aaaaaaaaa
aaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaa
aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaa aaaaaaaaaaaaaa
aaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaa aaaaaaaaaaaaa aaaaaaaaaaaaa
aaaaaaaaaa aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa
aaaaa aaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaa aa aaaaa
aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa aaaaaaa aaaaaaaaaaaaaa
aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa aaaaaa a aaaaaaaaaaaaaaaaaaaa
aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa aaaaaa
aaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa aaaaaaaaaaa
aaaaaaaaa aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa a
aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa
aaaaaaaaaaaa aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa
aaaaaaaa aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaa
aaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaa aaaaaaaaaaa
aaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa aaaaaaaaaaaaaa
aaaaaaaaaaaaa aaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa
aaaaaaaa aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaa aaaaaaaaaaaaaa aaaaaaaaaaaaa
aaaaaaaaa aaaaaaaaaaaaaa aaaaaaaaaaaaaa aaaaaaaaaaaa aaaaaaaaaaaaaa
aaaaaaaaaaaaaa aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa aaaaaaaaaa aaaaaaaaaaaa
aaaaaaa aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaa aaaaaaaaaaaa aaaaaaaaa
aa aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa aaaaaaaaa
aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaa aaaaaaaaaaaaaa aaaaaaaaaaaaaaaa
aaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaa
End of the message for the Atlantians in here.
(Sorry, folks. As long as Deja goes on making a mess of the layout
of my articles I gon on writing nonsense like that)
Sail Fi
>
>Welcom in sci.archaeology, the forum of aliens and Atlantians.
>Please do not despair if you couldn't understand my messages
>to the aliens in here. Perhaps you are an Atlantian instead?
>Find out. Have a look at tzhe following lines. Common people
>will see the letter a repating while the true Atlantians among
>you will recognize the encoded message:
>
>aaaaaaaaaaaaa a aaaaaaaaaaaaaaaaa a
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
AARRGHHHHHH!!! Now what am I??? Not Alien......not
Atlantian.........::identity crisis looming::
Do I even exist..????? (Thanks for the welcome, by the way!)
marci...@my-dejanews.com
cir...@access.ch wrote:
> PS.
>
> I wrote a lot on archaeology in here, and I would love to go on doing
> so. However, Deja changed the format of the messages and made a mess
> of the lay-out of all my articles. This makes me feel unhappy.
>
> Just now I work over my 'fairy tale' (a vision of early Egypt)
> and my interpretation of the Iliad and Odyssey (bringing all into
> a chronological order, omitting some ideas in favour of new ones),
> with the help of Kathy, a professional American translator. I planned
> to publish the corrected and improved versions here in sci.archaeology.
> But now I don't feel like doing so anymore. Why should I publish my
> work in here and hand over the copyright to a company that makes a
> mess of my articles? And anyway, all I ever wrote in here was neg-
> lected or immediately forgotten, for example my proposition of ramps
> for the Great Pyramid (volume of the ramps 1/7 of the pyramid's volume,
> blocks of Tura limestone, reused for the many minor buildings of the
> pyramid complex).
>
> Marcio, thank you for the kind e-mail. I replied, but my answer
> was returned to me by a Mailer Demon.
>
> A reader asked me about astronomy and constellations in ancient Egypt.
> Well, I wrote several articles on these topics in here. You can find
> them via http://deja.com and Power Search. However, in a messed-up
> lay-out.
Hi Franz
I received your e-mail and was very proud of your answer to my comments on
your decision about Deja.com. And I repeat here that your contribution to
archaeology is outstanding and ask, as many others in this forum, your
permanence among those really interested in the truth. Regards, Marcio
cir...@access.ch
sai...@aol.com (Sail Fi) wrote:
> AARRGHHHHHH!!! Now what am I??? Not Alien......not
> Atlantian.........::identity crisis looming::
> Do I even exist..????? (Thanks for the welcome, by the way!)
Neither an alien nor an Atlantian? You must be joking. What in
the world are you looking for in sci.archaeology? Archaeology?
Only fools abuse this forum for archaeological purposes ;-)
I was a fool too. But last week I saw a TV documentary on the
prophets of the last days who pop up everywhere, and although
I tried my very best to withstand their hypnotic eyes I finally
succumbed. When so many people believe in the Gospel according
to Graham Hancock, how can I make fun of him? So I finally came
to reason, and in the following night I had a VISION ...
Let me explain.
Some of you may remember my interpretation of Homer's Odyssey.
Well, this was boring stuff. I was foolishly missing the simple
and obvious truth that Odysseus was --- an ATLANTIAN!
He came from far away --- from Atlantis ...
A man of nimble wits --- in possession of a higher technology ...
His home was the island Ithaca in the Ionian sea. Ionian - Ion
(ian) - Ion ... this means that the technology of Atlantis worked
with ions (anions and cations, ion generators, ion propulsion ...)
Please consult a map of the Peleponnes and have a look at the island
Ithaca: doesn't it strongly resemble the two Americas?
The palace of Odysseus and Penelope stood at Neiriton (Stavros).
When we compare Ithaca with America, the bay of Neiriton corresponds
to the Queen Charlotte Sound in British Columbia. This proves that
ATLANTIS was AMERICA while the capital of Atlantis was a now sunken
island in the Queen Charlotte Sound ...
PROOF: the distance of the Queen Charlotte Sound from Giza and
the Great Pyramid measures 1/3 of the circumference of our planet!
Now all was becoming very clear for me: Atlantis, former capital
of America, built on an island in the Queen Charlotte sound, sank
11,500 years ago. Most of the surviving Atlantians returned home
to Sirius and alpha Eridani. A few ones remained on our planet,
living in a submarine commando central in the Queen Charlotte
Sound. From time to time an Atlantian was sent on a mission among
the ordinary humans: Menes, Imhotep, Khufu, Gilgamesh and Odysseus
who built a palace on Ithaca, for the shape of this island resembles
the one of America, which is the only true Atlantis.
Graham Hancock speaks of a mysterious device in the Great Pyramid.
It will release a flood at the end of 1999 (or eventually in 2013
or 2030), and the flood shall drown almost everyone. A rasonable
man, this Graham Hancock, and a worthy patron of sci.archaeology.
However, he doesn't really explain how it will happen. So let me
do it for him: the Atlantians in the submarine commando central
in the Queen Charlotte Sound will generate an Ion-empowered High
Energy Maser Pulse Wave, transform it into a geophysical wave and
tune this wave to a very specific frequency pattern so that the
wave, running around the mantle of our planet, will reach the
maximal efficiency in the region of Giza and activate a hidden
device in the Gantenbrink Chamber in the Great Pyramid whereupon
the FLOOD will be released and six billion people drowned and our
planet purgated while Atlantis, the sunken island in the Queen
Charlotte Sound, shall rise again ...
Only a few ordinary humans will survive the FLOOD.
You wish to be among the chosen ones? Well, send me 1000 bucks
and I'll give you a hint where to hide on December 31, 1999.
For a million dollars you may become Minister of New Atlantis,
Queen Charlotte Sound, British Columbia ... Send me the money
and you will get a certificate.
PS. This was NONSENSE of course, meant to show people how easily
such a 'theory' can be fabricated and 'proven'
PPS. Dear Deja, please return to the former format, allowing us
to edit our replies, messages and articles. Then I shall write
and publish reasonable articles again
Sail Fi
>
>You wish to be among the chosen ones? Well, send me 1000 bucks
>and I'll give you a hint where to hide on December 31, 1999.
>
>For a million dollars you may become Minister of New Atlantis,
>Queen Charlotte Sound, British Columbia ... Send me the money
>and you will get a certificate.
>
>
>PS. This was NONSENSE of course, meant to show people how easily
>such a 'theory' can be fabricated and 'proven'
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
NONSENSE???? And there I was........cheque book in one hand.......pen in the
other....
Ah well .....another bubble burst........(I just hope the ensuing 'flood' of
tears doesn't drown anyone...........!!!)
cir...@access.ch
marci...@my-dejanews.com wrote:
> I received your e-mail and was very proud of your answer to my
> comments on your decision about Deja.com. And I repeat here that
> your contribution to archaeology is outstanding and ask, as many
> others in this forum, your permanence among those really interested
> in the truth. Regards, Marcio
Hi Marcio, thank you for your kind support. However, I don't believe
that more than a few people read my posts. Well, this monday I got
a book I had awaited for a long time:
Guenter Dreyer, UMM EL-QAAB I, Das praedynastische Koenigsgrab U-j
und seine fruehen Schriftzeugnisse; 195 pages, 109 illustrations,
47 tables, folio; Archaeologische Veroeffentlichungen 86, Verlag
Philipp von Zabern, Mainz 1998 (176 Swiss francs)
Predynastic kings and their signs according to Guenter Dreyer
(new first director of the German Archaeological Institute Cairo):
Standard of ORYX (?)
FINGERSNAIL (Fingerschnecke, pteroceras, a mollusque)
FISH (perhaps later)
ELEPHANT
BULL (standard of oxhead?)
STORK (not quite certain) (((king Osiris of my fairy tale?)))
CANIDE
Standard of OXHEAD (perhaps earlier: identical with bull?)
SCORPION I, tomb U-j at Abydos, around 3320 BC; nine chambers
of the tomb are seen as a model of the royal palace, the former
palace might have measured 24 x 30 royal cubits
FALCON I, first conqueror of the Nile Delta
Standard of MIN plus a part of a plant
?
? (FALCON II ?)
LION
DOUBLE FALCON
IRJ-HOR
'KA'
SCORPION II
NARMER
In the tomb of King Scorpion I at Abydos (cemetery U, tomb j)
have been stored more than 2,000 vessels, many coming from Palestine.
The signs on the ivory tablets and two stone tablets show semograms
(depictions and symbols) and phonograms plus phonetic complements
and determinatives. For example an elephant above a mountain is read
as a phonogram: b dw = Abydos (simplified transscription). Guenter
Dreyer assumes that the origins of writing in Egypt go back to Naqada
IIc while the writings found in tomb U-j are from Naqada IIIa2:
numbers and about 50 signs. There might have been more signs. Primary
use in economy and administration, further developed for trading
reasons. Signs on three potsherds of Naqada IIc might be protoelamic.
Presence of artisans from Elam possible. An Egyptian group of fish
read as jnw = duty, tax (Abgabe) appear on several early Mesopotamian
seals - according to Guenter Dreyer a hint for a possible transfer
of ideas from Egypt to Mesopotamia too.
The book is fairly expensive but highly interesting.
Regards Franz Gnaedinger Zurich cir...@access.ch
CHRIS C
Youre problems with Deja did you no good... ;-)
Remember that problems are there just to solve them.
About sci. archeology
you wrote:
When I write on archaeology, I get few replies,
but when I write nonsense I always get one.
I know the feeling.
I think I know why this is.
A big part of our US friends on this newsgroups, and God knows how whe love
them, are raised and educated in the shadow of the two american pillars:
Hollywood and the Bible.
TV (Hollywood) brainwashed lots of promessing young people to believe in
Captain Marvel, Rambo and Star Wars!
The Bible did the rest.
You should really treat these people with more care and understanding, their
minds are not always prepared for plain science.
Be patient. Archaeology newsgroups are young and they will grow to a real
scientific forum.
Don't expect to much of those who are "inspired" by the Bible.
The dammage is too hard to repair.... ;-)
For those who wanted to reply and feel the need to call me an
anti-american...
I LOVE peanut butter, The Mothers of Invention, MacDonalds, Carly Simon,
Cesar's Salad, Bruce Willis, CNN, Fred Astaire, Playboy, Humphrey Bogard,
Jane Mansfield, The Simpsons, The Byrds, Otis Redding, Arnold Scharzenegger,
Lou Reed, Loretta Lynn, Cameron Diaz, NYPD, Cornell Wilde, John Candy, The
Commodores, The Mississippi, Harrison Ford, George Lukas, Lt Uhura, Percy
Sledge, The Adams Family, Kaptain Kirk, John Denver, Manhattan, Ford
Mustang, Johnny Cash, Malcolm X, Kim Basinger, L.A. Lakers, Randy Newman,
the lyrics of Louie, Louie, Friends, Louis Armstrong, Danny Kaye, Mannix,
The Cosby Show, blue jeans, Simon and Garfunkel, Step by Step, Twenty fours
from Tulsa, Will Smith, The Beach Boys, Independance Day, Woodstock, James
Dean, Apollo IX, King Kong, Rabbit Ridge Wine, Elvis Presley, Geronimo,
Apple Computers, J.R., Sidney Poitier, Neil Young, New Orleans, William
Boney, Kim Basinger, Frank Sinatra, Bonanza, Woopi Goldberg, Apache
helicopters, Bourbon, Demi Moore, X-files, Patti Labelle, The Lone Ranger,
Winslow-Arizona, Martin Luther King, Eddy Cochran, The Chicago Tribune, John
Wayne, Apocalypse Now, Lindenberg, 42nd street, the B52's, Joe Louis, The
Fonz, Patton, Michael Jackson, Frank Black, Budweiser, Woody Allen,
Internet, Soul Coughing, Little Big Horn, Eddy Murphy, Don Corleone, Happy
Days, Bob Dylan, Charles Bukowski, Jerry Springer, Walt Disney,
Indianapolis, Lauren Bacal, Marihuanna, Esther Williams, Chubby Checker, The
Harlem Globetrotters (1958), USAF, Marylin Monroe, Monument Valley, Jimmy
Durante, John Sebastian, The Rocky Horror Show, Chief Crazy Horse, Walter
Matthau, Germaine Greer, John and Robert Kennedy, DEA, China Town, Junior
Walker and the Allstars, Coca Cola, T-bone steaks, The Twist, The Hully
Gully, The Watusi, The Mashed Potatoes, The Swim, The Madison and Rock 'n
Roll...!
chris C
cir...@access.ch
"CHRIS C" <chris.c...@village.uunet.be> wrote:
> Dear Franz,
> Youre problems with Deja did you no good... ;-)
> Remember that problems are there just to solve them.
Dear Chris,
thank you for the reply. Let me explain my problems with our forum
and the new format of Deja by means of a digression into the field
of brain surgery, hoping that my English will be good enough for
that purpose.
In the July 1998 issue of the Scientific American was an interesting
article: The Split Brain Revisited / Groundbreaking work that began
more than a quarter of a century ago has led to ongoing insights
about brain organization and consciousness, by Michael S. Gazzaniga.
When a heavy epilepsy can't be cured in any other way, the corpus
callosum, so to speak the bridge between the two hemispheres of the
brain, is severed and the patient is getting relief.
Now Gazzaniga, working with so-called split brain patients, made
an experiment. He chose composite words like for example SKYSCRAPER
and flashed a card with the word SKY to one eye and a card with the
word SCRAPER to the other eye of a patient. Asked to draw these words,
everyone with an intact corpus callosum draws a TALL BUILDING whereas
Gazzaniga's patient drew a SKY in form of a sun and clouds atop of
a comblike SCRAPER, obviously unable to combine the words ...
Well, this reminded me somehow of our forum sci.archaeology:
Mention the Great Pyramid and hardly anyone will honour the
achievements of ancient Egypt. One party will say that building
a pyramid was nothing more than piling up some blocks, requiring
neither real mathematics nor astronomy nor even an interest in
numbers and stars and philosophy, for the Great Pyramid is a big
but fairly simple and meaningless building, a former tomb of a
Pharaoh, and nothing else than a tomb. Hereupon the opposite party
will say the very contrary: building the Great Pyramid was a most
demanding task, by far exceeding the abilities of the Egyptians,
therefore it must have been built by aliens or Atlantians while it
embodies the knowledge of all times, past and future as well ...
Can you see the analogy?
A skyscraper split up into a small and simple device (scraper) and
heaven (sky) - the Great Pyramid downsized by one party, so to speak
the rational hemisphere of sci.archaeology, people who have a good
background in science, whereas the same monument is blown up by the
other party, so to speak the intuitive hemisphere of our forum, people
who have a rather poor idea of science but sometimes a fine sensory.
If ratio and intuition would go along, we could do real archaeology,
but alas, the bridge between them is damaged. Ratio ruling one bank
and intuition living on the other side can't join, whereupon ratio
is getting rigid and dogmatic while intuition goes astray ...
My attempt is to reconcile them: for example by showing that the
pyramids are meaningful buildings and embody a wide range of know-
ledge including numbers like pi and phi, however, these numbers have
been approximated by means of very simple methods, mainly by drawing
up number patterns. Now for publishing my patterns I need a reliable
format like the usenet format or the e-mail format, or else all my
patterns will be a mess and no one can follow my reasoning.
How can I possibly build a bridge when my blocks are shaken up
and tumbling down?
By the way, new computer-tomograhical examinations show that there
are two ways of understanding mathematics: a numerical understanding
located in the left temporal lobe of the brain (exact calculations)
and a more intuitive understanding in the visual center located in
the hind part of the brain (comparing smaller and greater numbers).
Einstein for one is believed to have worked mainly with the second
areal. - Give intuition more room and you may win more children for
mathematics and more people for good science; mathematics and good
science INCLUDING numerical calculations and careful reasoning, for
when people have the joy most of them are willing to do the work too.
Hope I made myself halfways understandable.
CHRIS C
Hi Franz,
You wrote:
>Hope I made myself halfways understandable.
Yes did... and I was thinking..
You must be family of that other great, but Austrian, psychology
doctor....;-)
Time will tell Franz, the bridge between the two could be sooner build than
one knows.
Remember Schliemann?
I am sure that as we speak. Young scientist in every fields are building at
that bridge.
Meanwhile there is the gap between as they say in french universitys:
les Serviettes et les Torchons.
Being from a bi(tri?)lingual country you will understand.
I have no problem with being a "Torchon"
They clean up the dirt left by the Serviettes but find the lost golden
watch!
By the way, any news about "Gunther Dreyer's pre-dynastiche Könige"
publication whe talked about?
Was good to hear you again,
seeya
chris C
cir...@access.ch
"CHRIS C" <chris.c...@village.uunet.be> wrote:
> By the way, any news about "Gunther Dreyer's pre-dynastiche Könige"
> publication whe talked about?
Did you miss my post from May 19 on Guenter Dreyer's book?
If so, you may find it via Deja (http://www.deja.com)
Good news from Eberhard Zangger. He wrote me a kind letter,
telling me that his project is on a good way. Follows my reply:
Zürich, 20. Mai 1999
Sehr geehrter Herr Dr. Zangger,
vielen Dank für Ihre netten Zeilen, die mich natürlich sehr freuen.
Es ist ein grosser Aufsteller zu erfahren, dass Ihre Expedition
in die Troas auf gutem Weg ist.
Was die Odyssee angeht, so haben wir damals in der Klosterschule
Einsiedeln (meine 6 Jahre Jugendknast) Teile des Epos im Original
gelesen, und obschon mir die Sprache sehr gut gefiel habe ich nie
verstanden, worum es eigentlich ging. Das Nausikaa-Kapitel war
meine Liebelings-Episode. Aber was soll das Ganze? und vor allem
das kriegerische Ende? Ich fragte zwanzig Jahre lang vergeblich
nach dem Sinn des Buches. Eine Griechin sagte mir zum Beispiel,
die Odyssee wäre eine Reise zum inneren Selbst. Dann erschien
Ihr erstes Buch mit einer plausiblen Idee, die mir zum erstenmal
dem Genie Homers würdig schien. Ich ging dann ein paar Schritte
weiter indem ich annahm, dass auch das "Seemaqnnsgarn" traumartige
(verschlüsselte, verschobene und verdichtete) Erinnerungen an den
Trojanischen Krieg wären. Inzwischen überarbeite ich eine Serie
von Artikeln zur Ilias und Odyssee mithilfe einer amerikanischen
Uebersetzerin und werde Ihnen das Papier zustellen, wenn es fertig
ist. Hier ein Glossar zu meiner höchst spekulativen Interpretation:
Trojanischer Krieg: Argonauten auf der Suche nach reinem Kupfer
passieren Dardanellen und Bosporus, werden von Laomedon als Piraten
angesehen und behandelt, erster Krieg, nur jüngster Prinz überlebt,
nennt sich Priamus, verstärkt Mauern, Griechen richten sich in
der Troas ein, Zwischenfälle, Priamus überhört warnende Stimmen,
Eroberung Trojas. Griechen bleiben vorerst, begleiten Schiffe.
Griechischer Ueberfall auf eine fremde Flotte in einem Krim-Hafen,
schwerwiegende Folgen, neue Feinde, Griechen müssen nocheinmal
zehn Jahre bleiben und zahlen alles in allem erinen sehr hohen
Preis für das reine Kupfer: lange Anreise, gefährliche Passage,
und für jeden guten Mann der nach Troja kommt fehlt einer zuhause.
Als die Griechen endlich heimkehren, müssen sie einen Bürgerkrief
gegen die Piraten führen, die auf ägäischen und ionischen Inseln
sowie zum Teil an den Küsten des Pennelopes leben. Bis dann endlich
Friede einkehrt und Griechenland (Archipelag) geeint werden kann.
Autor der Ilias: geboren um 790 BC in Mantineia, arbeitet in den
Archiven von Argolis und Pylos, stirbt um 735 BC, zu Beginn des
ersten Messenischen Krieges.
Aussage der Ilias: sobald das Schicksal von Troja besiegelt ist,
erweist sich Priamus als ein gottgleicher, bewundernswerter Mann;
sein einziger Fehler war, dass er sich dem Lauf der Geschichte,
verkörpert von Athene, entgegenstellte.
Autor der Odyssee: geboren um 725 BC in Smyrna, Sohn eines
griechischen Händlers und einer anatolischen Bauerstochter,
frühreifes Kind, erfährt von seiner Mutter alles über seine Heimat
und das einfache Volk, begleitet seinen Vater auf mancher Reise:
Schwarzes Meer, Ithaka und Korfu, Rhodos und Naucratis im Nildelta.
Lernt Ilias auswendig und vollendet sie, überarbeitet auch einige
Passage. Schreibt Odyssee auf Reisen und zuhause. Stirbt um 660 BC.
Odyssee: Odysseus will endlich heimkehren, gerät in einen Sturm,
kehrt zurück, schläft am Ufer (im Hafen?) von Troja und wird in
seinen Träumen von Erinnerungen an den Krieg verfolgt: er kehrt
immer wieder nach Troja zurück, das sich mehr und mehr verfremdet,
bald als einäugiger Riese von Gestalt eines Berges und einer Frau
von bergähnlichen Proportionen erscheint ... Am nächsten Tag kehren
die Griechen heim. Zuhause angekommen hat Odysseus wieder einen
Traum, diesmal einen sehr langen: er kehrt nocheinmal nach Troja
zurück, diesmal ein Troja von früher, es heisst Scherie (Hommage
an Smyrna), Halbinsel der Phaiaken (Hommage an Halbinsel Phokia).
Ein blinder Sänger trägt eine wohlbekannte Ballade vom Trojanischen
Krieg vor (die Ballade ist bekannt, nicht aber der Krieg selber),
einzig Odysseus versteht sie, erkennt was er und seine Männer
zerstörten, und er weint (geniale Idee eines gewissen Eberhard
Zangger) und erzählt den Krieg in seiner subjektiven Art. Immer
noch in seinem Traum trinkt er Wein, geht schlafen und besteigt
am nächsten Abend ein Schiff der Phaiaken (wieder wach in seinem
Traum) und schläft ein (schläft im Schlaf), ein tiefer Dauerschlaf,
todähnlich. Am Morgen (es wird nicht gesagt: am nächsten Morgen,
also kann die Fahrt mehrere Nächte und Tage gedauert haben) langt
er zuhause an, wo er es dann mit den Freiern seiner treuen Penelope
aufnehmen muss, angefeuert von Athene, bis endlich Friede einkehrt.
Kronos - Zeit (erschaffend und zerstörend)
Zeus - Welt; für alle Völker da, auf Seiten von Troja wie auch
der Griechen
Athene - Geschichte: einst auf der Seite Trojas, nun entschieden
auf der Seite der Achäer, der aufsteigenden neuen Zivilisation
Nausikaa - Anatolien um 1700 BC
Calypso, ihre Höhle und ihr bezaubernder Garten - Anatolien um
1200 BC
Penelope, ihr Haus und Bett (Olivenbaum) - Griechenland um 1200 BC
Telemachus - Griechenland um 700 BC (sprechender Name meint ferner
Krieg, möglicherweise Messenische Kriege, Homer offenbar in Sorge
um das Schicksal und die Einheit der griechischen Reiches)
Blinde Sänger - Propheten
Mentor - alter ego für den Dichter der Ilias
Hermes - alter ego für den Dichter der Odyssee; Argeiphontes meint
ursprünglich einen wachsamen Schlangentöter wie Argus, politisch
zu verstehen; Hermes kann sich in Windeseile vom Olymp zur Insel
der Calypso begeben, so wie der Dichter in seinem Geist; Hermes
kann die Menschen beliebig schlafen machen und wecken, wie das
Homer höchst witzig mit seinem Helden macht; und schliesslich
kann Hermes die einfachste Arbeit veredeln, wie denn Homer einen
Schweinehirten über die wohlgeborenen Prinzen stellt. Hermes/Homer
besorgt um das Schicksal von Telemachus/Griechenland, aber auch
optimistisch: wenn Telemachus wirklich der Sohn von Odysseus und
Penelope ist und ebenso tapfer und schlau wie sein Vaster darf
man hoffen.
Homer - nom de plume, ein Wortspiel auf den Götterboten Hermes
und den Fluss Hermos, der damals nahe bei Smyrna mündete:
HERMAES - HERMOS - HOMAEROS ...
Tiere wie Schafe, Ziegen, Rinder und Pferde - Boote, Schiffe
Mein Tip: schauen Sie, ob die phantastischen Orte und Begebenheiten
in der Odyssee brauchbare Informationen für die geschichtliche
Rekonstruktion des Trojanischen Krieges und die geoarchäologische
Rekonstruktion der Troas hergeben ...
(...)
Mit freundlichen Grüssen (...)
Franz Gnaedinger
An English translation may follow.
cir...@access.ch
cir...@access.ch wrote:
on Guenter Dreyaer's book on early writing in Egypt.
Follows a test.
Originally, I called this thread
my corner
When it got associated with another thread whose title contained
the word 'corner', I had to change the title into
my c-o-r-n-e-r
what looks pretty silly. Now that Deja changed the interface
again, I try to rename my thread into
my corner
A layout test.
My hypothetical key-figure for the Egyptian way of calculating
the circumference and area of the circle:
. . . . . d . . . . .
. . e . . . . . c . .
. f . . . . . . . b .
. . . . . . . . . . .
. . . . . . . . . . .
g . . . . + . . . . a
. . . . . . . . . . .
. . . . . . . . . . .
. h . . . . . . . l .
. . i . . . . . k . .
. . . . . j . . . . .
The grid contains 10 x 10 squares measuring
1 royal cubit x 1 royal cubit = 7 palms x 7 palms
= 28 fingers x 28 fingers
each.
The whole square measures
10 royal cubits x 10 royal cubits = 70 palms x 70 palms
= 280 fingers x 280 fingers
while the diagonal measures 99 palms = 356 fingers (with only
a tiny mistake).
If you draw a circle of the radius 5 royal cubits or 35 palms
or 140 fingers into the grid, the circumference will pass 12
points of the grid, namely the points a, b, c, d, e, f, g, h,
i, j, k.
The short arcs bc, ef, hi, kl measure 40 fingers, the long arcs
ab, cd, de, fg, gh, ij, jk, la measure 90 fingers; with only tiny
mistakes again.
The whole circumference measures
90 + 40 + 90 + 90 + 40 + 90 + 90 + 40 + 90 + 90 + 40 + 90
= 880 fingers = 220 palms
while the diameter measures 280 fingers or 70 palms.
The ratio gives
880/280 = 220/70 = 22/7 = 3 1/7 or 3 '7
a very good first value for pi, suggested by the measurements
of the Great Pyramid:
former base 440 royal cubits = 11 x 40 royal cubits
former height 280 royal cubits = 7 x 40 royal cubits
double base / height = 22 / 7
In my opinion, the Egyptians have well been able to find this
value long before Archimedes, without being aliens or Atlantians.
The above figure and lines look perfect in the Usenet-format
and e-mail format. How will they look in the new Deja-format?
Regards Franz Gnaedinger Zurich cir...@access.ch
Sent via Deja.com http://www.deja.com/
cir...@access.ch
cir...@access.ch wrote:
> The above figure and lines look perfect in the Usenet-format
> and e-mail format. How will they look in the new Deja-format?
Messy.
So I have to say at the begin of every post of mine:
If you read the following article via Deja, the layout
may be a mess. If so, please scroll down to the end
and use the function 'view original usenet format',
or go to Power Search and Deja Classics and try to find
my article there. (I sure hope that Deja will make things
more easily for those people in here who publish scientific
articles.)
My key-figure again:
. . . . . d . . . . .
. . e . . . . . c . .
. f . . . . . . . b .
. . . . . . . . . . .
. . . . . . . . . . .
g . . . . + . . . . a
. . . . . . . . . . .
. . . . . . . . . . .
. h . . . . . . . l .
. . j . . . . . k . .
. . . . . j . . . . .
If the side of the whole square measures 10 royal cubits
= 70 palms = 280 fingers, the diagonal measures 99 palms
or 396 fingers, the short arcs cb, ef, hj, kl measures
40 fingers, the longer arcs ab, cd, de, fg, gh, ij, jk,
la measure 90 fingers, the circumference of the circle
abcdefghijkla measures 880 fingers or 220 paalms, the
diameter ag measures 280 fingers or 70 palms, and the
ratio circumference/diameter gives the value 22/7.
Now let us join the points a, b, c ... with straight
lines. Thus, we get a polygon of 4 short and 8 longer
sides. The short ones equal the square root of 2 while
the longer ones equal the square root of 10
= square root of 2 x square root of 5
If we choose the simple ratios 10/7 for the square root
of 2 and 9/4 for the square root of 5 we get the following
numbers:
periphery = 4 x 10/7 + 8 x 10/7 x 9/4 royal cubits
= 40/7 rc + 720/28 rc = 160/28 rc + 720/28 rc
= 880/28 rc = 220/7 royal cubits
The periphery of the polygon measures 220/7 royal cubits.
Now the values 10/7 and 9/4 are slightly greater than
the square roots of 2 and 5 while the circumference of
the circle abc...a is slightly larger than the periphery
of the polygon abc...a. Therefore we may assume that
the measurement 220/7 royal cubits corresponds to the
circumference of the circle, and if we divide this number
by the diameter 10 royal cubits, we obtain 22/7 again.
In my next post I will show you how to derive a systematic
method for the calculation of the circle from the above
key-figure. (I described my method several times in here,
but as everyone knows, this group has a short memory.)
James H. E. Maugham
> My hypothetical key-figure for the Egyptian way of calculating
> the circumference and area of the circle:
>
> . . . . . d . . . . .
> . . e . . . . . c . .
> . f . . . . . . . b .
> . . . . . . . . . . .
> . . . . . . . . . . .
> g . . . . + . . . . a
> . . . . . . . . . . .
> . . . . . . . . . . .
> . h . . . . . . . l .
> . . i . . . . . k . .
> . . . . . j . . . . .
>
Thanks for that excellent depiction and explanation Franz.
> In my opinion, the Egyptians have well been able to find this
> value long before Archimedes, without being aliens or Atlantians.
My "Pet Peeve" with the von Daniken followers is that they can't grasp
the fact that WE are no smarter than the AEs were. Yes, we have better
tools, communications, educational opportunities, etc.,etc., but that
doesn't make us inherently more intelligent.
Given the proper impetus it _is_ truly amazing what 'man' has created,
whether by the AEs or today, but that doesn't mean we needed the
guidance of any outside influence from space travelers or advanced
civilizations to identify the need or point us in the proper direction.
Were an average AE somehow transported to our time period and raised in
our culture, they would score just as highly on an aptitude test as an
average modern individual.
Short of the development of a means to travel backwards in time, we will
NEVER know all that has been invented throughout the millenia and lost
through war, religious schism, fear of 'witchcraft', or simply the
inability to identify an application.
I have friends who are back to nature types and frequently bring 'new
inventions' to my attention. Recently they waxed eloquently and at
length about a water hammer pump that will pump water when immersed in a
flowing stream. They were somewhat deflated when I pointed out to them
that the exact same type of pump was used hundreds of years ago to
hydraulically power the organs in European cathedrals and were only
supplanted by the finding that the same flowing water could be made to
DIRECTLY compress air by a simple modification of the same pump.
Regards,
James
cir...@access.ch
Hi James,
thank you very much for your reply. I couldn't agree more.
Sorry for rearranging your lines, Deja made a mess of them.
I have to say it again: the new format is hard to work with,
at least for those among us who publish scientific articles
and care about the layout of their messages.
I wished to publish my systematic method for the calculation
of the circle today, but now, with that layout mess. I don't
feel like doing so. Perhaps next week.
marci...@my-deja.com
cir...@access.ch wrote:
>
> I have to say it again: the new format is hard to work with,
> at least for those among us who publish scientific articles
> and care about the layout of their messages.
>
> I wished to publish my systematic method for the calculation
> of the circle today, but now, with that layout mess. I don't
> feel like doing so. Perhaps next week.
>
>
I followed your two last post in Deja.com new format and the old Usenet
format. To us that look at your post as scientific one it is better to read
them in the old format until the people involved can correct the distortion
that result when converting the old to the new. You noted that your
circumference becomes an ellipse and this could suggest what correction
should be used when considering the demonstration of the area of the ellipse
resulting of the interception of a cylinder by a plane inclined of a
determined angle. Anyway we await your demonstration of how did the old
Egyptians calculate the area of the circle. Regards, Marcio
cir...@access.ch
marci...@my-deja.com wrote:
(...)
> Anyway we await your demonstration of how did the old
> Egyptians calculate the area of the circle. Regards, Marcio
Thank you, Marcio. Here it comes.
(If you read my article via Deja, the layout may be a mess.
If so, please scroll down to then end and use the function
View original Usenet format. Thank you.)
. . . . . B . . . . .
. . 3 . . . . . 2 . .
. 4 . . . . . . . 1 .
. . . . . . . . . . .
. . . . . . . . . . .
C . . . . + . . . . A
. . . . . . . . . . .
. . . . . . . . . . .
. 5 . . . . . . . 8 .
. . 6 . . . . . 7 . .
. . . . . D . . . . .
Please imagine a grid of 10 x 10, 50 x 50, 250 x 250,
1250 x 1250 ... units (which might become smaller and
smaller). Inscribe a circle. The radius will measure
5, 25, 125, 625 ... (ever smaller) units while the
circumference will pass through the four ends of the
axes (A, B, C, D) plus 8, 16, 24, 32 ... inner points
of the grid.
The distances of the latter points from the axes and
the center of the grid are defined by the following
triples:
3-4-5 or 15-20-25 or 75-100-125 or 375-500-625 ...
7-24-25 or 35-120-125 or 175-600-625 ...
44-117-125 or 220-585-625 ...
336-527-625 ...
If you know a triple a-b-c and wish to find the following
one please use the formulas
3a plus/minus 4b 4a plus/minus 3b 5c
Choose the positive values ending on 1, 2, 3, 4, 6, 7,
8, 9 (neither 5 nor zero).
The 4 ends of the axes and the 8, 16, 24, 32 ... inner
points of the grid give us 12, 20, 28, 36 ... points of
the circle. If we join them with straight lines, we get
a sequence of polygons of 12, 20, 28, 36 ... sides.
Now these polygons have a remarkable property: the sides
are whole number multiples of the square roots of 2 or 5
or 10 = 2x5. Hence if there is a clever way to approximate
the square roots of 2 and 5 we have a complete method for
the calculation of the circle.
Well, the square root of 2 can be approximated by means
of the following number column (you will easily find out
the basic algorithm):
1 1 2
2 3 4
5 7 10
12 17 24
29 41 58
70 99 140 and so on
The mirror values 10/7 and 7/5 are simple approximations
for the square root of 2 while the mirror values 140/99
and 99/70 are already very fine approximations.
Now for the square root of 5:
1 1 5
2 6 10
1 3 5
4 8 20
2 4 10
1 2 5
3 7 15
10 22 50
5 11 25
16 36 80
8 18 40
4 9 20 and so on
Or, as a column:
1° 1' 5
2 6 10
1° 3' 5
4 8 20
2° 4' 10
1 2 5
3° 7' 15
10 22 50
5° 11' 25
16 36 80
8° 18' 40
4 9 20
13° 29' 65
42 94 210
21° 47' 105
68 152 340
34° 76' 170
17 38 85
55° 123' 275
178 398 890
89° 199' 445
288 644 1440
144° 322' 720
72 161 360 and so on
The values 20/9 aqnd 9/4 are first useable approximations
while the values 360/161 and 161/72 are already very fine
approximations. By the way, the marked numbers represent
two golden sequences, the so-called Fibonacci sequence
(below) and Lucas sequence (above):
1 3 4 7 11 18 29 47 76 123 199 322 ...
1 1 2 3 5 8 13 21 34 55 89 144 ...
Our polygons have 12, 20, 28, 36 ... corners and as many
sides. The respective arcs are slightly longer than the
sides. We may hope to counterbalance this by chosing values
for the square roots of 2 and 5 that are slightly greater
than the exact values. If we calculate the first polygon
by means of the values 10/7 for the square root of 2 and
the value 9/4 for the square root of 5, we obtain the
circumference 220/7, and if we divide it by the diameter
10 we obtain 22/7 or 3 1/7 for pi. If we calculate the
second polygon by means of the value 17/12 for sr2 and
again 9/4 for sr5 we obtain the circumference 157, and
if we divide it by the diameter 50, we obtain the value
157/50 = 3.14 for pi.
All the elements and some numbers of my method are found
in the Egyptian pyramids, as I shall demonstrate in my
next posts.
Regards Franz Gnaedinger Zurich cir...@access.ch
Sent via Deja.com http://www.deja.com/
cir...@access.ch
cir...@access.ch presented:
a simpler method for the calculation of the circle than the
one of Archimedes. Now in this and the following posts I will
show you that the pyramid builders of ancient Egypt could well
have known this method. (If you read my article via Deja, please
scroll down to the end and use the function View original Usenet
format).
The caves of the Ile de France (Paris and region around it)
abound of paleolithical rock incisions showing lines, parallels,
crosses, grids, round forms and their various combinations.
Grids are also well knwon from ancient Egypt.
Playing with grids, combining them with squares and measuring or
counting the areas of the squares easily leads to the so-called
formula of Pythagoras.
The following dots represent a grid while the point a, b, c, d
define a square:
. . . . . . . . .
. . a . . . b . .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. . c . . . d . .
. . . . . . . . .
The square is 4 houses high and 4 houses long while the area
measures 4 x 4 = 16 houses.
Now let us draw an oblique square:
. . . . . . . . .
. . . . a . . . .
. . . . . . . . .
. . . . . . . . .
. d . . x . . b .
. . . . . . . . .
. . . . . . . . .
. . . . c . . . .
. . . . . . . . .
The square abcd consits of 4 triangles: xab, xbc, xcd, xda.
Two triangles can be arranged to form a smaller square measuring
3 x 3 = 9 houses while the four triangles and hence the above
suare have an area of 18 houses.
Every oblique square drawn in a grid has an area that measures
a WHOLE NUMBER of houses:
. . . . .
. . a . .
. d x b . area of square abcd = 2 houses
. . c . .
. . . . .
. . . . . . . .
. . . . . a . .
. d 3 . . 4 . .
. . . . . . . .
. . . . . . . . atea of square abcd = 17 houses
. . 2 . . 1 b .
. . c . . . . .
. . . . . . . .
Square 1234 = 9 houses. Triangle 1ab plus triangle 3cd = 4
houses. Triangle 2bc plus triangle 4da = 4 houses. Whole area
of square abcd = 9 + 4 + 4 = 17 houses.
. . . . . . . . . .
. . . . a . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . 1 2 . . b . area of square abcd = 25 houses
. d . . 4 3 . . . .
. . . . . . . . . . square 1234 = 1 house
. . . . . . . . . . triangles 1ab + 3cd = 12 houses
. . . . . c . . . . triangles 2bc + 4da = 12 houses
. . . . . . . . . . sum = 25 houses
25 houses are 5 x 5 houses. Hence the sides of the above square
measure 5 houses each. Every side is found by going 3 houses
in one direction and 4 houses in the other direction. And thus
we found the so-called Sacred Triangle 3-4-5 which is the base
of my keys figure for the calculation of the circle:
. . . . . o . . . . .
. . o . . . . . o . .
. o . . . . . . . o .
. . . . . . . . . . .
. . . . . . . . . . .
o . . . . + . . . . o
. . . . . . . . . . .
. . . . . . . . . . .
. o . . . . . . . o .
. . o . . . . . o . .
. . . . . o . . . . .
Regards Franz Gnaedinger Zurich cir...@access.ch
PS. I know very well that new ideas and approaches are
warmly welcomed in the natural sciences but not welcome
at all in archaeology. And yet I go on publishing some
of my ideas: for the open-minded readers in this group,
and for a future reader who may find my articles via
Deja and Power Search.
cir...@access.ch
cir...@access.ch showed:
how the ancient Egyptians might have found the so-called formula
of Pythagoras. Here follows Wolf Meyer-Christian's analysis of
the Djoser sarcophagus. (If you read my article via Deja, please
scroll down to the end and use the function View original Usenet
Professor Wolf Meyer-Christian (who teaches at the Technische
Hochschule, Kaiserstrasse 12, 7500 Karlsruhe) wrote a highly
interesting althoug widely neglected article:
Der 'Pythgaroras' in Aegypten am Beginn des Alten Reiches
In: Mitteilungen des Deutschen Archaeologischen Institutes,
Abteilung Kairo, Band 43, 1987, Verlag Philipp von Zabern,
Mainz am Rhein (pages 195-203)
According to professor Wolf Meyer-Christian, the subterranean
granite beam sarcophagus in the southern tomb of the Djoser
Complex at Saqqara has the following measurements in fingers
(1 finger = 1.87 cm, 28 fingers = 52.36 cm = 1 royal cubit):
80 f 84 f 66 f
South A--------B---------C-------D North
: : : :
: : : : 55 fingers
: : : :
E--------F---------G-------H
: : : :
: : : : 80 fingers
: : : :
: : : :
I--------J---------K-------L
: : 41 fingers
: :
M--------N---------O-------P
This cross-section contains the following so-called Pythagorean
triangles:
MA-AD-DM 176-210-274 fingers or 2 x 88-105-137 fingers
IJ-JF-FI 60-80-100 fingers or 20 x 3-4-5 fingers
GK-KJ-JG 80-84-115 fingers or 4 x 20-21-29 fingers
HL-LJ-JH 80-150-170 fingers or 10 x 8-15-17 fingers
48 f 84 f 48 f
West a-----b---------c-----d East
: :
: : 55 fingers
: :
e-----f---------g-----h
: : : :
: : : : 80 fingers
: : : :
: : : :
i-----j---------k-----l
: : 41 fingers
: :
m-----n---------o-----p
This cross-section contains the following so-called Pythagorean
triangles:
mo-oc-cm 132-176-220 fingers or 44 x 3-4-5 fingers
np-pd-dn 132-176-220 fingers or 44 x 3-4-5 fingers
ea-ac-ca 55-132-143 fingers or 11 x 5-12-13 fingers
cd-dh-hc 48-55-73 fingers
jk-kc-cj 84-135-159 fingers or 3 x 28-45-53 fingers
ld-da-al 81-108-135 fingers or 27 x 3-4-5 fingers
np-pd-dn 132-176-220 fingers or 44 x 3-4-5 fingers
The last two triangles overlap. Their common area forms again
a Sacred Triangle measuring 81-108-135 fingers or 27 x 3-4-5
fingers.
All these triangles combine the vertical direction with the
horizontal one: symbolically joining heaven and earth. By the
way, the chamber avbove the stone beam sarcophagus was decorated
with stars.
If you think that the above so-called Pythagorean triangles
are coincidences, please check the horizontal cross-section
measuring 60+84+66 fingers x 48+84+48 fingers -- this grid
doesn't contain a single Pythagorean triangle.
Wolf Meyer-Christian based his analysis of the southern tomb
of the Djoser Complex on the plans by Jean-Philippe Lauer.
Unfortunately, the drawings and measurements of the sarcophagus
strongly vary from publication to publication, so it's hard
if not impossible for me to check Meyer-Christian's results.
However, judging from his dissertation, he is a very exact
worker.
Regards Franz Gnaedinger Zurich cir...@access.ch
cir...@access.ch
cir...@access.ch wrote:
on Wolf Meyer-Christian's analysis of the stone beam sarcophagus
in the southern tomb of the Djoser Complex at Saqqara. Here
follows my analysis of the Bent Pyramid. (If you read my article
via Deja, please scroll down to the end and use the function
View original Usenet format.)
Sneferu let build 3 pyramids:
Maidum Djed Sneferu
Dahshur South Sneferu's Southern Epiphany, Bent Pyramid
Dahshur North Sneferu's Northern Epiphany, Red Pyramid
Robert Bauval (who fell into the arms of Graham Hancock and
is now lost for Egyptology) identified the Bent Pyramid with
epsilon Tauri in the Hyades and the Red Pyramid with Aldebaran
while Rolf Krauss (a serious Egyptologist, neither a Hancock
nor a von Daeniken) identified the mysterious h-channel with
the stripe of the ecliptic wherein the sun, the moon and the
planets are moving. Now let me go a step further and propose
the following pattern:
PLEJADES
Maidum Pyramid
ooooooo h-channel or stripe of ecliptic ooooooooooooooooo
EPSILON TAURI IN THE HYADES
Bent Pyramid
ALDEBARAN
Red Pyramid
The Hyades and Plejades had been called GOLDEN DOOR by the
astronomers of Mesopotamia. Now let me assume that Sneferu's
pyramids represented this Golden Door, or better: the harbour
of the h-channel where the deified king hoped to start his
heavenly journey in a sun boat (which might have been stored
in a high chamber of the Bent Pyramid).
Any evidence for my opinion? Yes, the measurements of the Bent
Pyramid: they clearly show that the peculiar shape of Sneferu's
Southern Epiphany, which resembles the Hyades, was intended.
(Furthermore, the building rubbish of the Maidum Pyramid was
removed and there was no sign of a catastrophe at all so that
the argument that the steep angle of Sneferu's Southern Epiphany
was lowered in order to avoid a second catastrophe doesn't hold
any longer.)
o Epsilon Tauri o
o o o
o o Hyades o
------------------- o
Bent Pyramid Aldebaran o
Square of temenos 570 royal cubits x 570 royal cubits
square of pyramid base 360 royal cubits x 360 royal cubits
square of bending lines 228 royal cubits x 228 royal cubits
Height of lower part 93 royal cubits
lower slope practically 114 royal cubits
height of upper part 108 royal cubits
upper slope practically 157 royal cubits
The grid of the three squares (temenos, pyramid base and bending
lines)
105+66+228+66+105 rc x 105+66+228+66+105 rc
contains the following so-called Pythagorean triples:
171-228-(285) or 57 x 3-4-5 *
105-360-(375) or 15 x 7-24-25 *
66-360-(366) or 6 x 11-60-66
* The triples 3-4-5 and 7-24-25 are part of the hypothetical
Egyptian method for the calculation of the circle while the
key number 57 (multiples 114, 171, 228, 285, 342, 399, 456,
513, 570) can be used for an astronomical purpose:
0 7 fingers
0
ooooooooooooooooooooooooooooooooooooooooo
57 fingers 0
0 7 fingers
A simple device like this allows to measure small angles from
1 degree till 7 or 14 degrees (while 10 degrees are a decan).
Regards Franz Gnaedinger Zurich cir...@access.ch
PS. Last year a moderator of sci.archaeology moderated told
me that mathematics has nothing to do with archaeology, and
all other moderators agreed with him. And I, foolish as I am,
still hope that archaeology might evolve into a truly scientific
discipline that welcomes new ideas and approaches and a simple,
cheap, powerful and non-invasive method like mathematical
examinations ...
cir...@access.ch
cir...@access.ch wrote:
a mathematical examination of the Bent Pyramid. Now for
the Great Pyramid at Giza. (If you read my article via Deja,
please scroll down to the end and use the function View
original Usenet format.)
The former base of the Great Pyramid measured 440 royal cubits
and the former height 280 royal cubits (1 royal cubit measuring
52.36 cm according to Rainer Stadelmann and Rudolf Gantenbrink).
Over hundred years ago, one John Taylor found the following
relations:
Use the former height as the radius of an imaginary circle
and the circumference equals the periphery of the base
Divide the double of the base length through the height
and you get pi, the number of the circle
Use the height as the diameter of another imaginary circle
and its area equals the cross-section area of the pyramid
Base length = 440 royal cubits, double base = 880 royal cubits,
height = 280 royal cubits, 880/220 = 22/7 = 3 1/7 - a fine value
for pi. The same value is found by means of my key figure:
. . . . . d . . . . .
. . e . . . . . c . .
. f . . . . . . . b .
. . . . . . . . . . .
. . . . . . . . . . .
g . . . . + . . . . a
. . . . . . . . . . .
. . . . . . . . . . .
. h . . . . . . . l .
. . i . . . . . k . .
. . . . . j . . . . .
The side of the above square measures 10 royal cubits = 70 palms
= 280 fingers. The diagonal measures practically 99 palms = 396
fingers. The short arcs bc, ef, hi, kl measure 40 fingers each
while the longer arcs ab, cd, de, fg, gh, ij, jk, la measure 90
fingers each (with only tiny mistakes). The whole circumference
measures 880 fingers while the diameter ag measures 280 fingers
whereby 880/280 equals 22/7 or 3 1/7.
By joining the same points with straight lines we get a polygon
whose sides are given by the square root of 2 and by the square
root of 2 x the square root of 5. By using the ratios 10/7 and
9/4 for the square roots of 2 and 5 we find that the short sides
bc, de, gh, kl measure 10/7 royal cubits each while the longer
sides ab, cd, ef, fg, hi, ij, jk, la measure 10/7 x 9/4 = 90/28
= 45/14 royal cubits each. The whole periphery measures 220/7
royal cubits = 220 palms = 880 fingers. If we divide it by the
diameter ag = 10 royal cubits = 70 palms = 280 fingers we get
880/220 = 220/70 = 22/7 = 3 1/7 again.
Georges Goyon defined the shape of the Great Pyramid as follows:
height / half base = 14 / 11
height / half diagonal of base = 9 / 11
By combining these very close definitions we find the following
numbers:
height 126 a (280 royal cubits)
base 198 a (440 royal cubits)
diagonal of base 280 a
half diagonal 140 a
diagonal of base / base = 280 / 198 = 140 / 99
base / half diagonal of base = 198 / 140 = 99 / 70
The fine values 140/99 and 99/70 are found in my number pattern
for the approximation of the square root of 2.
The downleading gangway has the following measurements:
vertical distance of ceiling and floor 72 fingers
horizontal distance ceiling - floor 144 fingers
corresponding slope 161 fingers
These numbers are found in my number column for the approximation
of the square root of 5.
Jean-Philippe Lauer, who spent seventy years of his long life
restauring the Djoser Complex at Saqqara, found a Sacred Triangle
in the measurements of the King's Chamber in the Great Pyramid.
The room is 10 royal cubits wide, 20 royal cubits long and 11.18
royal cubits high. This leads to the following numbers:
diagonal of small wall 15 or 5 x 3 royal cubits
length of chamber 20 or 5 x 4 royal cubits
diagonal of volume 25 or 5 x 5 royal cubits
Hence all the necessary elements and some important numbers
of my method for the calculation of the circle are present
in the Great Pyramid at Giza.
Regards Franz Gnaedinger Zurich cir...@access.ch
PS for Sue:
I can understand your feelings about our silly forum, chatroom
of aliens and Atlantians, however, complaining alone won't help,
the only way to bring our group any further is by publishing
reliable archaeological informations, posts, messages, articles
or whatever.
cir...@access.ch
cir...@access.ch wrote:
> Hence all the necessary elements and some important numbers
> of my method for the calculation of the circle are present
> in the Great Pyramid at Giza.
I just read the book THE ELEGANT UNIVERSE by Brian Greene on
string theory and M-theory (W.W. Norton & Company New York London
1999). Compared with high-spirited modern physics, archaeology
resembles Sleeping Beauty. Dream on, little darling. Sooner or
later a prince will come and kiss you so that you finally wake
up ...
Let me return to the Great Pyramid. Allow me some more numbers.
Then I will show you that the numbers make sense. (If you read
my article via Deja, please scroll down to the end and use the
function View original Usenet format).
According to Georges Goyon, the base of the Great Pyramid
measured 440 royal cubits while the height measured 280 royal
cubits. Heighten the Goyon Pyramid by 5.9 centimeters only and
you obtain the Taylor Pyramid ruled by the number of the circle.
Lower the Goyon Pyramid by 8.15 cm only and you obtain the Golden
Pyramid ruled by the golden number.
If we use the value 3 1/7 for pi, the Taylor Pyramid goes over
into the simple Goyon Pyramid while the Golden Pyramid may be
approximated by the so-called Fibonacci numbers
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
13 + 21 = 34
21 + 34 = 55
34 + 55 = 89 (and so on)
which are also found in my number column for the approximation
of the square root of 5. Half the base measures 4 x 55 royal
cubits while the slope measures practically 4 x 89 royal cubits.
The simple Goyon Pyramid may well combine the highly demanding
Taylor Pyramid and Golden Pyramid whose shapes can be associated
with imaginary by-forms, namely the Taylor circle (whose vertical
diameter is given by the pyramid's height and measures about 280
royal cubits) and a hemisphere in the frame of the Golden Pyramid
(the radius of the imaginary hemisphere equals the golden major
of the pyramid's height and measures practically 173 royal cubits
according to the golden sequence 9, 16, 25, 41, 66, 107, 173,
280 ...)
Now for the meaning of these numbers and forms.
As far as I know, all serious Egyptologysts agree that the
Egyptian pyramids
a) have been built and used as tombs
b) have been seen as symbols of the Primeval Hill
In the beginning, the Primeval Mound or Hill rose above the
Primeval Water Nu(n). In a similar way the pyramids of the Old
Kingdom rise above the River Nile.
Out of the Primeval Mound or Hill rose the sun god Ra or Re,
a golden disk in the bow of the horns of the heavnely cow Hathor
whose alter ego was Nut, goddess of the heavens, mother of the
sunchild.
Nut bending over the eart might well be symbolized by the
imaginary hemisphere in the frame of the Golden PYramid while
Re might be present in the Taylor circle - an imaginary circle
that may symbolize the soul of the deified king reborn by Nut
and leave the pyramid as the new sun god ...
When WE look at the pyramids, we see mere ruins and bare stone
whereas the ancient Egyptians might well have seen their holy
monuments in a gloriole of powerful gods and goddesses.
By the way, the hieroglyph of Re was a small circle. According
to the Egyptian way of reasoning, every property of a person,
even his or her name, body color and shadow, was considered
as a genuine part of his or her very being. Hence the circle
was more than just a symbol of Ra or Re: it belonged to the
very being of the supreme sun god. Calculating the circle and
finding a systematic method for approximating the secret number
living in this perfect form may thus have been a way of sharing
the secrets and powers of Re and enabling the king to become
this god.
Regards Franz Gnaedinger Zurich cir...@access.ch
cir...@access.ch
cir...@access.ch wrote:
on the Great Pyramid again (how the numbers and imaginary by-
forms make sense). Now for a problem of the Rhind Mathematical
Papyrus that mentions the number 3 1/7 - possibly a value of pi?
(If you read my article via Deja, please scroll down to the end
In problem no. 38 of the Rhind Mathematical Papyrus (RMP),
Ahmes comes up with a funny formula:
1 hekat x 3 1/7 x 7/22 = 1 hekat
What is a hekat? A measure of the volume. Another problem of
the RMP makes it clear that 30 hekats equal one cubic cubit.
Hence 1 hekat equals 1/30 of a cubic cubit and may be defined
as a right parallelepiped of the following measurements:
1/2 royal cubits x 1/3 royal cubits x 1/5 royal cubits
A royal cubit is subdivided as follows:
1 royal cubit = 7 palms = 28 fingers
or 56 Re marks
or 84 Maat marks
or 112 Shu marks
or 140 Geb marks
or 168 Nut marks
or 196 Osiris marks
or 224 Isis marks
or 252 Seth marks
or 280 Nephtys marks
or 308 Horus marks
or 336 Mesta marks
or 364 Hapi marks
or 392 Tuamutf marks
or 420 Qhebsenuf marks
or 448 Thoth marks
or ...
Now we may redefine a hekat like this:
28 Re marks x 28 Maat marks x 28 Geb marks
or like this:
210 Qhebsenuf marks x 140 Qhebsenuf marks x 84 Qhebsenuf marks
while the diagonal of the right parallepiped measures exactly
266 Qhebsenuf marks, according to the quadruple
84-140-210-266 or 14 x 6-10-15-19
General formula for this kind of quadruples:
ab --- ab + aa --- ab + bb --- ab + aa + bb
If a = 2 and b = 3 we obtain the quadruple 6-10-15-19.
The royal cubit of the Old Kingdom measured 52.36 centimeters,
the one of the Middle and New Kingdom 52.5 centimeters. A hekat
measures 26.25 cm x 17.5 cm x 10.5 cm while the diagonal measures
33.25 centimeters.
Now let me insert the above numbers in Ahmes' equation:
210 Qm x 140 Qm x 84 Qm x 3 1/7 x 7/22 = 1 hekat
The number 3 1/7 reminds me of pi. This made me ask if there might
be a cylindrical hekat of reasonable numbers?
The following formulas define a hekat in the shape of a cylinder:
area of circle times height = volume of cylinder
1/4 x diameter x diameter x pi times height = volume
1/4 x d x d x 3 1/7 times height = 1 hekat
Now you may transform the above equations accordingly and look
out for a simple solution. I found the following one:
1/4 x 105 Qm x 105 Qm x 3 1/7 x 285 1 /11 Qm = 1 hekat
15 Qhebsenuf marks equal 1 finger. Hence I obtain
1/4 x 7 f x 7 f x 3 1/7 x 19 1/165 f = 1 hekat
The diameter of my cylindrical hekat measures 7 fingers while
the height measures 19 1/165 fingers. I let go the small fraction
1/165 and keep the number 19. Now my hekat measures:
diameter 7 fingers (13.125 cm)
circumference 22 fingers (41.25 cm)
height 19 fingers (35.625 cm)
while a quadruple-hekat measures:
diameter 14 fingers (26.25 cm)
circumference 44 fingers (82.5 cm)
height 19 fingers (35.625 cm)
The numbers are very simple and the mistakes very small.
If you are interested in my interpretations of several dozen
problems of the Rhind Mathematical Papyrus (in my opinion one
of the greatest and wittiest mathematical writings of all times)
please go the Deja (link below) and Power Search and look out for
my threads
Professor Ahmes (1) till Professor Ahmes (5)
Steve Whittet
>
Hi Franz,
>In article <7k7hrb$cju$1...@nnrp1.deja.com>,
> cir...@access.ch wrote:
>on the Great Pyramid again (how the numbers and imaginary by-
>forms make sense). Now for a problem of the Rhind Mathematical
>Papyrus that mentions the number 3 1/7 - possibly a value of pi?
>(If you read my article via Deja, please scroll down to the end
>and use the function View original Usenet format.)
I like where you are going with this. Its pretty evident
that to someone used to working with unit fractions it
would be possible to make a set of measures such that
the volumes of containers with whole number dimensions
would add up to be taken as equal to the volume of
larger containers.
This would be useful in terms of selling or distributing
bulk goods or liquids.
Such a set of measures might persist through a very
long period of time and we might find some of them
still hanging around in our own ststem of measures.
Take for example your hekat of height 19, circ. 22, dia 7,
it has a volume of 232.75 cu in and is a cube of just over 6"
38 go into a cubic cubit and its close to 1 US liguid gallon.
Suppose you make it so 32 go into a cubic cubit. You get
a cube with a side of 6.5" and a British Imperial Gallon.
What do you think?
regards,
steve
cir...@access.ch
whi...@shore.net (Steve Whittet) wrote:
> Suppose you make it so 32 go into a cubic cubit. You get
> a cube with a side of 6.5" and a British Imperial Gallon.
Hi Steve,
nice to have you back, and thank you for the reply.
For the definition of the Egyptian volume measure hekat:
problem no. 41 (?) of the Rhind Mathematical Papyrus
makes it very clear that 1 cubic cubit equals 30 hekats.
I never found any other number. If you have evidence
for another ratio cc/h please tell me, I would like
to consider that case too. By the way, there are many
interesting measures depicted in the tomb of Hesy.
There is a publication of Quibell dating from 1917 (?)
which I was not able to find. Would be fascinating to
have a new and fresh look at those systems of measures.
Now for the (hypothetical) values of pi in the Rhind
Mathematical Papyrus. (If you read my article via Deja,
please scroll down to the end and use the function
View original Usenet format.)
By carefully measuring the circumference of a circle, eventually
by means of a stone wheel, the Egyptians might well have found
that the ratio circumference / diameter is a constant value:
greater than 3 and smaller than 4, also a little greater than
25/8 or 3 1/8 or 3 '8 while smaller than 19/6 or 3 1/6 or 3 '6
and even a little smaller than 22/7 or 3 1/7 or 3 '7.
My method for the approximation of pi provides 22/7 or 3 '7
and 157/50 or 3 '10 '25 as first values.
These numbers allow us to obtain many more useful approximate
values. Let me write 4 above 1 and add continually 3 above 1:
4 (plus 3) 7 10 13 16 19 22 25 28
1 (plus 1) 2 3 4 5 6 7 8 9
Now let me write 3 above 1 and 6 above 2 and 9 above 3 and add
continually 19 above 6:
3 (+ 19) 22 6 (+ 19) 25 44 9 (+ 19) 28 47 66
1 (+ 6) 7 2 (+ 6) 8 14 3 (+ 6 9 15 21
85 104 123 142 161 180 199 218 237 256
27 33 39 45 51 57 63 69 75 81
If the side of a square measures 8 units and the diameter
of a circle 9 units, the two shapes have about the same area.
This well known formula from the Rhind Mathematical Papyrus
leads to the approximate value 256/81 for pi.
Now I write 3 above 1 and add continually 22 above 7:
3 (+ 22) 25 47 69 91 113 135 157 179 201 223 245
1 (+ 7) 8 15 22 29 36 43 50 57 64 71 78
267 289 311 333 355 377 399
85 92 99 106 113 120 127
When the side of a square measures 10 royal cubits or 70 palms,
the diagonal measures 99 palms and the circumference of the
circumscribed circle 311 palms.
311 / 99 = 3 1/9 1/33 or simply 3 '9 '33
377 / 120 = 3 '8 '60 or 3 '10 '24
Now I multiply 333 above 106 by 4 and obtain 2331 above 742,
whereupon I add continually 22 above 7 again:
2331 (+ 22) 2353 2375 2397 2419 2441 2463 2485 2501
742 (+ 7) 749 756 763 770 777 784 791 798
2529 2551 2573 2595 2617 2639
805 812 819 826 833 840
If the radius of a circle measures 1 royal cubit or 28 fingers,
the square of the radius measures 784 square fingers and the
area of the circle measures 2463 square fingers.
Now I write 6 above 2 and add continually 22 above 7:
6 (+ 22) 28 50 72 94 ... 600 ... 424 ...
2 (+ 7) 9 16 29 30 ... 191 ... 135 ...
When the circumference of a tower measures 600 palms,
the diameter measures 191 palms.
191 / 600 = '4 '30 '40 '100 or '4 '24 '60 '100
424 / 135 = 3 '9 '45 '135
According to my interpretation of several dozen problems of
the Rhind Mathematical Papyrus, the Egyptian mathematicians
used many of the above values for pi and chose the one that
was most convenient for a given calculation.
Steve Whittet
>
>In article <Z1va3.415$7X1.1...@news.shore.net>,
> whi...@shore.net (Steve Whittet) wrote:
>
>> Suppose you make it so 32 go into a cubic cubit. You get
>> a cube with a side of 6.5" and a British Imperial Gallon.
>
>
>Hi Steve,
>
>nice to have you back, and thank you for the reply.
its always a pleasure to see your well documented ideas.
>For the definition of the Egyptian volume measure hekat:
>problem no. 41 (?) of the Rhind Mathematical Papyrus
>makes it very clear that 1 cubic cubit equals 30 hekats.
>I never found any other number. If you have evidence
>for another ratio cc/h please tell me, I would like
>to consider that case too.
Gillings follows Chace who gives 1 Hekat = 292.24 cu"
30 hekats to a cubit
Vogel gives 1 hekat = 1/8 bushel which would be 1/2 peck
4 quarts, 8 pints and 1 gallon
32 hekats to a cubit.
Gunn uses gallon and Peet Bushel
My consideration was the horus eye fractions used to
calculate quantiies of bread and beer
'2,'4,'8,'16,'32, 64', ro, 2 ro, 3ro, 4 ro
It semed like that scale ought to continue up as well as down
so that there would be 16 rather than 15 double hekats to a
cubic cubit and 8 rather than 7.5 quadruple hekats to a cubic cubit
the hekat measures would then double the cube and be cubes with
sides aproximately 5/4 the size of each preceeding measure.
If that were the case the hekat measure and English measure
would be virtually identical.
the double hekat would be the 1/4 bushel or peck and the
quadruple hekat would be the bushel of 8 gallons
Now all these values calculate using the royal cubit as "cubit"
but the royal cubit was used only for public works. The ordinary
cubit would be the common unit of measure.
There were other lengths which could be cubed as volumes which
ought to fit into the same scheme namely the finger, palm,
hand, fist, span, foot, remen and ordinary cubit.
A cubic royal cubit has 21952 cubic fingers 32 gallons
1/2 cubic royal cubit is 10976 cubic fingers 16 gallons
1/4 cubic royal cubit is 5488 cubic fingers 8 gallons
1/8 cubic royal cubit is 2744 cubic fingers 4 gallons
1/16 cubic royal cubit is 1372 cubic fingers 2 gallons
1/32 cubic royal cubit is 686 cubic fingers 1 gallon
1/64 cubic royal cubit is 343 cubic fingers '2 gallon
1 cubic ordinary cubit is 20 gallons
1 cubic remen is 12 gallons
1 cubic roman pes (foot) is 6 gallons
1 cubic span is '2 gallon
taking a cubic remen measure from an ordinary cubic cubit measure
would leave 1/4 cubic royal cubit or bushel.
> By the way, there are many
>interesting measures depicted in the tomb of Hesy.
>There is a publication of Quibell dating from 1917 (?)
>which I was not able to find. Would be fascinating to
>have a new and fresh look at those systems of measures.
yes, it would.
yes, nicely done.
Some of their problems seem to suggest they were aware
that when the area of a circle and a square have the same
circumference their areas have the constant ratio 4/Pi
Yes, it seems clear they used more than one value,
even 3, '8, '64 related to their horus eye scale
is better than 256/81
>
>Regards Franz Gnaedinger Zurich cir...@access.ch
regards,
steve
cir...@access.ch
whi...@shore.net (Steve Whittet) wrote:
> A cubic royal cubit has 21952 cubic fingers 32 gallons
> 1/2 cubic royal cubit is 10976 cubic fingers 16 gallons
> 1/4 cubic royal cubit is 5488 cubic fingers 8 gallons
> 1/8 cubic royal cubit is 2744 cubic fingers 4 gallons
> 1/16 cubic royal cubit is 1372 cubic fingers 2 gallons
> 1/32 cubic royal cubit is 686 cubic fingers 1 gallon
> 1/64 cubic royal cubit is 343 cubic fingers '2 gallon
Hi Steve,
we might well subdivide the cubic cubit according to the
famous series of the Horus Eye (if you read my article via
Deja, please scroll down to the end and use the function
View original Usenet format):
1 = '1
1 = '2 '2 meaning 1 = 1/2 + 1/2
1 = '2 '4 '4
1 = '2 '4 '8 '8
1 = '2 '4 '8 '16 '16
1 = '2 '4 '8 '16 '32 '32
1 = '2 '4 '8 '16 '32 '64 (...)
1 cubic cubit --- a cube measuring
28 fingers x 28 fingers x 28 fingers
1/2 cubic cubit --- right parallelepiped measuring
28 fingers x 28 fingers x 14 fingers
diagonal exactly 42 fingers
1/4 cubic cubit --- a right parallelepiped measuring
28 fingers x 14 fingers x 14 fingers
1/8 cubic cubit --- a cube measuring
14 fingers x 14 fingers x 14 fingers
1/16 cubic cubit --- a right parallelepiped measuring
14 fingers x 14 fingers x 7 fingers
diagonal exactly 21 fingers
1/32 cubic cubit --- a right parallelepiped measuring
14 fingers x 7 fingers x 7 fingers
1/64 cubic cubit --- a cube measuring
7 fingers x 7 fingers x 7 fingers
This set of volume measures would certainly make sense.
However, according to the Rhind Mathematical Papyrus
- an ancient source of the highest quality - one hekat
equals 1/30 cubic cubits and n o t 1/32 cubic cubits.
Hence the subdivisions of the cubic cubit according
to the series of the Horus Eye and the subdivision
in hekats and ro's would have been two different or
complementary sets of measures.
1 cubic cubit equals 30 hekats
This definition allows me to assume and propose a hekat
in two shapes, a right parallelepiped and a cylinder,
both of remarkable properties:
RIGHT PARALLELEPIPED:
1/2 royal cubit x 1/3 royal cubit x 1/5 royal cubit
28 Re marks x 28 Maat marks x 28 Geb marks
210 Qhebsenuf marks x 140 Qhebsenuf marks x 84 Qhebsenuf marks
diagonal exactly 266 Qhebsenuf marks
(26.25 cm x 17.5 cm x 10.5 cm, diagonal 33.25 centimeters)
volume exactly 1 hekat
CYLINDER:
diameter 7 fingers (13.125 cm)
circumference 22 fingers (41.25 cm)
height 19 fingers (35.625 cm)
volume 1 hekat with only a tiny mistake
diameter 14 fingers (26.25 cm)
circumference 44 fingers (82.5 cm)
height 19 fingers (35.625 cm)
volume 1 quadruple-hekat with only a tiny mistake
Now let me compare some Egyptian and British measures:
royal cubit Old Kingdom 52.36 cm (Stadelmann, Gantenbrink)
7 royal cubits Old Kingdom 366.52 centimeters
4 yards = 12 feet = 144 inches 365.76 centimeters
rc Middle/New Kingdom 52.5 centimeters (various authors)
1 hekat Middle/New Kingdom 4.82343 litres
1/32 cubic cubit Middle/New Kingdom 4.52197 litres
4 quarts = 1 British imperial gallon 4.54596 litres
1/4 cubic cubit M/N Kingdom 36.17578 litres
8 gallons = 1 bushel 36.3677 litres
2 cubic cubits M/N Kingdom 289.40625 litres
8 bushels = 1 quarter 290.9416 litres
While the Egyptian measures are intercorrelated, I wasn't able
to find a clear numerical correlation between the British linear
measures (inch, foot, yard, rod) and the liquid measures and
measures of capacity (fluid ounce, gill, pint, quarter, imperial
gallon, bushel, quarter).
If you reply again, please choose a single point for further
discussion instead of commenting my whole article - Deja asks
for relatively short messages (no more than about 4.3 kilobytes)
that can be archived in one single part. Thank you.
Regards Franz Gnaedinger Zurich cir...@access.ch
Sent via Deja.com http://www.deja.com/
Steve Whittet
>
>In article <2sNa3.590$7X1.1...@news.shore.net>,
> whi...@shore.net (Steve Whittet) wrote:
....
>While the Egyptian measures are intercorrelated, I wasn't able
>to find a clear numerical correlation between the British linear
>measures (inch, foot, yard, rod) and the liquid measures and
>measures of capacity (fluid ounce, gill, pint, quarter, imperial
>gallon, bushel, quarter).
Giving their cubes in cubic inches and ounces (oz) it looks like
we have a doubling system based on the cubit with the foot, remen
and yard marking the even decimal thousands of ounces.
7,762,392 cu in = 1 cubic rod = 4476065 oz (4,500,000 oz)
1,728,000 cu in = rod = 996420 oz 1000 cu ft
177544 cu in = last = 102378 oz
172,800 cu in = register ton = 99642 oz 100 cu ft
155,351 cu in = puncheon = 89581 oz
88,791 cu in = wey = 51200 oz = 10 cubic royal cubits
71,017.6 cu in chaldron or corn ton = 40960 oz
46, 656 cu in = 1 cubic yard = 26903.47 oz (27,000 oz)
34954.9 cu in = butt = 20156.21 oz
17,754.4 cu in = quarter or seam = 10240 oz
9987.01704 cu in = barrel = 5760 oz
8,877.2 cu in = comb = 5120 oz = cubic royal cubit
6657.9 cu in = bag or sock = 3840 oz = 3 bushels
5548 cu in = cubic cubit = 3200 oz = 10 pecks
4438.6 cu in = strike = 2560 oz
3468.4 cu in = remen = 2000 oz
2219.3 cu in = bushel = 1280 oz
1728 cu in = 1 cubic ft = 996.42 oz (1000 oz)
1109.7 cu in = tuffet or bucket = 640 oz
554.8 cu in = peck, pail = 320 oz
277.42 cu in = gallon = 160 oz
138.71 cu in = pottle = 80 oz
69.35 cu in = quart = 40 oz
34.675 cu in jug or pint = 20 oz
17.342 cu in gill,jill 1/2 pint = 10 oz
8.669 cu in jack, noggin, 1/4 pint = 5 oz
jock, 1/8 pint = 2 1/2 oz
joey 1/16 pint = 1 1/4 oz
cir...@access.ch
whi...@shore.net (Steve Whittet) wrote:
> 277.42 cu in = gallon
Hi Steve,
David Eugene Smith gave a more precise number:
The imperial (British) gallon contains 277.274 cu.in.
See volume II, page 644, footnote 8 of
David Eugene Smith, History of Mathematics, the evolution
of arithmetic, geometry, trigonometry, calculating devices,
algebra, the calculus ... with a wealth of problems, recre-
ations, constructions, applications explained and illustrated,
Dover Publications 1925/1953 -- What about a reprint of this
rich source of valuable informations?
When I use the above definition
277.274 cubic inches = 1 gallon
and combine it with your assumption
1 gallon = 1/32 cubic royal cubit = 686 cubic fingers
I obtain the following ratio
inch / finger = 70 / cube root of 138,637 = 1.35250326...
If the British measures would have been derived from the Egyptian
ones I would expect a clear and simple ratio.
For the hekat again. Four hekats are one quadruple-hekat.
This measure is mentioned in the problems 41-47 of the Rhind
Mathematical Papyrus. Sylvia Couchoud's translation of no. 41:
Exemple de calcul d'un granier rond d'un diametre de 9,
et d'une hauteur de 10. Tu dois soustraire un 1/9 de 9.
Il reste 8. Multiple 8 fois 8. Il advient 64. Tu dois
multipler 64 par 10. Il advient 640. Ajoute lui sa moitie.
Il advient 960. Ceci est la quantite mesuree en khar. Tu
dois prendre 1/20 de 960 qui est 48. Le montant en ble
mesure en 100-quadruple hekat est 48.
See the book
Silvya Couchoud, Mathematiques Egyptiennes, Recherches
sur les connaissances mathematiques de l'Egypte pharaonique,
Editions Le Leopard d'Or Paris 1993 -- This very fine book
contains hieroglyphic and phnoetic transscriptions and a French
translation of about 64 problems of the RMP and other papyri
and is still available (now, in June 1999)
You propose a system of liquid measures or measures of capacity
based on the royal cubit and the series of the Horus Eye:
1 1/2 1/4 1/8 1/16 1/32 1/64 cubic cubit
Judging by the numbers, I find this/your set of measures
highly convincing:
1 cc cube 28 fingers x 28 fingers x 28 fingers
1/2 cc right parallelepiped 28f x 28f x 28f diagonal 42f
1/4 cc right parallelepiped 28f x 14f x 14f
1/8 cc cube 14 fingers x 14 fingers x 14 fingers
1/16 cc right parallelepiped 14f x 14f x 7f diagonal 21f
1/32 cc right parallelepiped 14f x 7f x 7f
1/64 cc cube 7 fingers x 7 fingers x 7 fingers
These volume measures might well have been used as an alternative
set of liquid measures and measures of capacity.
Regards Franz Gnaedinger Zurich cir...@access.ch
PS. Now for something completely different. If you are
interested in the Nasca lines you have to order a splendid
BBC video: FLIGHTPATHS TO THE GODS. Finally, the riddle of
Nasca has been solved. (On request I'll write a recension
of the video and a Nasca exhibition in the Rietberg Museum
Zurich.)
cir...@access.ch
cir...@access.ch reccommended a book and a video:
> Silvya Couchoud, Mathematiques Egyptiennes, Recherches
> sur les connaissances mathematiques de l'Egypte pharaonique,
> Editions Le Leopard d'Or Paris 1993 -- This very fine book
> contains hieroglyphic and phnoetic transscriptions and a French
> translation of about 64 problems of the RMP and other papyri
> and is still available (now, in June 1999)
> PS. Now for something completely different. If you are
> interested in the Nasca lines you have to order a splendid
> BBC video: FLIGHTPATHS TO THE GODS. Finally, the riddle of
> Nasca has been solved. (On request I'll write a recension
> of the video and a Nasca exhibition in the Rietberg Museum
> Zurich.)
As no one asked for a recension or summary of that video and
exhibition I return to problem no. 41 of the Rhind Mathematical
Papyrus. (If you read my article via Deja please scroll down
to the end and use the function View original Usenet format.)
In my opinion, the problems of the Rhind Mathematical Papyrus
can be read on several levels:
On level one a pupil learns how to handle numbers and simple
geometrical formulas
On the second level a pupil solves more demanding geometrical
problems - which we may reinvent by playing with the numbers
provided by Ahmes
On the third level of studying the advanced pupils may learn
how to deduce general formulas
RMP 41 ON LEVEL 1
A granary in the form of a cylinder has an inner diameter of 9
royal cubits and an inner height of 10 royal cubits. Now please
consider a simple formula:
If the diameter of a circle measures 9 units
and if a square measures 8 units x 8 units
the circle and the square have about the same area
By using this very simple formula we find that the area of the
floor measures 64 square cubits. When we multiply this area
by the height 10 royal cubits we get the volume 640 cubic cubits
or 960 khar or 4,800 quadruple hekats or 19,200 hekats.
RMP 41 ON LEVEL TWO (my reinvention)
Let us carry out a more exact calculation of the granary:
diameter 9 royal cubits or 63 palms or 252 fingers
height 10 royal cubits or 70 palms or 280 fingers
By using the value 3 1/7 for pi we obtain:
diameter 63 palms or 252 fingers
circumference 198 palms or 1386 fingers
area of wall 13,860 square palms
area of floor 49,896 square fingers
volume 13,970,880 cubic fingers or about 636 cubic cubits
A better result than the first one.
Now we may change the numbers and assume a granary of these
measurements:
diameter 10 royal cubits or 70 palms or 280 fingers
height 9 royal cubits or 63 palms or 252 fingers
circumference 220 palms or 880 fingers
area of wall 13,860 square palms
area of floor 3,850 square palms or 61,600 square fingers
volume 15,523,200 cubic fingers or about 707 cubic cubits
The walls of the two cylinders have the same area while the
volumes stay in the ratio 9 : 10.
The diameter and height of another cylinder measure 15 cubits
and 6 cubits. The area of the wall is the same again while
the volume increases to 23,284,800 cubic fingers or about 1061
cubic cubits.
Still another cylinder may have a diameter of 90 cubits and a
height of 1 cubit. The area of the wall would be the same again
while the volume would increase to about 6364 cubic cubits.
RMP 41 ON LEVEL THREE (my reinvention)
Now the pupils may study the following sequence of cylinders:
diameter 1 2 3 5 6 9 10 15 18 30 45 90
height 90 45 30 18 15 10 9 6 5 3 2 1
The walls have the same area while the volume increases in
a peculiar way: divide the height of the wall by any number A
and the volume will increase by the same factor A - the lower
the cylinder the bigger the volume ...
Then the pupils may examine more cases and finnaly come up
with a general formula:
If the product of diameter and height equals 90 square cubits
(or any other constant number of square units) the walls of
the cylinders have the same area while the volume increases
in reciprocal proportion to the height: the lower the wall
the bigger the volume - and if the wall has no height at all
the volume is infinite!
A pretty paradox to be discussed in the seminary of professor
Ahmes.
My invitation: play with the numbers of the Rhind Mathematical
Papyrus, dive into the ancient ways of reasoning.
Regards Franz Gnaedinger Zurich cir...@access.ch
cir...@access.ch
cir...@access.ch wrote:
> My invitation: play with the numbers of the Rhind Mathematical
> Papyrus, dive into the ancient ways of reasoning.
Follows problem no. 43 of the RMP (- if you read my article
via Deja, please scroll down to the end and use the function
View original Usenet format).
In problem no. 43, Ahmes calculates the volume or capacity
of a cylindrical granary whose inner diameter measures 6 royal
cubits while the inner height measures 9 royal cubits. However,
his result is wrong, because in the middle of his calculation
he jumps from one formula to another one. Possibly an intended
mistake in order to challenge his pupils?
Here I don't care about the mistake or eventual intention,
my interest goes for the numbers of the cylinder.
If a circle of diameter 9 and a square of side length 8
have the same area, the volume of the above cylinder measures
256 cubic cubits.
Now let me compare two cylinders:
diameter 6 or 9 royal cubits
height 9 or 6 royal cubits
If you remember my interpretation of problem no. 41 you can
easily calculate the second cylinder: its round wall has the
same area while the volume equals
9/6 x 256 cubic cubits = 384 cubic cubits
Now I ask you a question: imagine a granary in the shape of
an ellipse, hence a hemi-ellipsoid in the frame of the second
cylinder -- what would its volume be?
The circle of the second cylinder has a diameter of 9 royal
cubits. Let us first imagine a sphere of the same diameter 9
royal cubits and calculate its volume by means of the formula
1/6 diameter x diameter x diameter x re
're' being the number of the circle. By using the value 256/81
or 1/81 x 256 again we obtain:
1/6 x 9 x 9 x 9 x 1/81 x 265 ccc = 384 cubic cubits
What a nice result:
A cylinder of diameter 9 and height 6 and a sphere
of diameter 9 have the same volume
Now for the ellipsoid. This geometrical body is nothing else
than a sphere lengthend in one dimension. The diameter of the
above sphere measures 9 cubits in every dimension while the
vertical diameter of the ellipsoid measures 6 + 6 = 12 cubits.
We obtain the volume of the ellipsoid by multiplying the one
of the sphere by a factor of 12/9 = 4/3:
sphere diameter 9 x 9 x 9 volume 384 ccc
ellipsoid diameter 9 x 9 x 12 volume 512 ccc
Now the volume of the hemi-ellipsoid equals 1/2 x 512 ccc
= 256 cubic cubits - exactly the volume of the first granary.
A granary in the shape of a cylinder have a diameter
of 2 or 6 units and a height of 2 or 9 units
another granary in the shape of a hemi-ellipsoid have
a diameter of 3 or 9 units and a height of 2 or 6 units
their volumes are exactly the same
Regards Franz Gnaedinger Zurich cir...@access.ch
Sent via Deja.com http://www.deja.com/
cir...@access.ch
cir...@access.ch wrote:
an interpretation of RMP 43. Follows my interpretation of
RMP 44. (If you read my article via Deja, please scroll down
to the end and use the function View original Usenet format.)
In problem no. 44 of the Rhind Mathematical Papyrus Ahmes
calculates the volume and capacity of a granary in the shape
of a cube that measures 10 royal cubits x 10 royal cubits x
10 royal cubits.
If you wish to build such a granary you have to know the lengths
of the diagonals of the floor, of the sides and of the volume.
The diagonals of the floor and the sides are found by means
of a simple number pattern:
1 1 2
2 3 4
5 7 10
12 17 24
29 41 58
70 99 ...
If the side of a cube measures 10 royal cubits or 70 palms,
the diagonal of a side measures practically 99 palms.
Now let me draw up a similar pattern for the diagonal of
the cube's volume:
1 1 3
2 4 6
1 2 3
3 5 9
8 14 24
4 7 12
11 19 33
30 52 90
15 26 45
41 71 123
112 194 ...
56 97 ...
If the edge of a cube measures 10 royal cubits or 70 palms
or 280 fingers = 5 x 56 fingers, the diagonal of the volume
measures practically 5 x 97 = 485 fingers.
Now we may go a step further and imagine a cone, a sphere,
a hemi-ellipsoid and a cylinder in the frame of the cube.
By using the value 157/50 or 3 1/10 1/25 or 3 '10 '25
for re or pi we obtain the following numbers:
CONE
diameter of base 10 royal cubits
area of base 78 1/2 square cubits
height 10 royal cubits
volume 261 2/3 cubic cubits
SPHERE
diameter 10 royal cubits
volume 523 1/3 cubic cubits
HEMI-ELLIPSOID
diameter of base 10 royal cubits
area of base 78 1/2 square cubits
height 10 royal cubits
volume 523 1/3 cubic cubits = volume of sphere
CYLINDER
diameter 10 royal cubits
area of base 78 1/2 square cubits
height 10 royal cubits
volume 785 cubic cubits
Volumes CONE : HEMI-ELLIPSOID : CYLINDER = 1 : 2 : 3
The granary in the shape of the cube has a volume of 1,000 cubic
cubits while a granary in the shape of a hemi-ellipsoid in the
frame of the cube has a volume of about 523 cubic cubits.
When we transform the cube into a right parallelepiped the reatio
of its volume and the one of the inscribed hemi-ellipsoid remains
the same: 1000/523 or about 2/1. This leads to a simple formula:
If you see a granary in the shape of a hemi-ellipsoid and wish
to estimate its volume carry out the following calculation
1/2 x diameter of base x diameter of base x height
and you obtain the approximate volume of the granary.
Regards Franz Gnaedinger Zurich cir...@access.ch
Steve Whittet
In article <7l7712$9a1$1...@nnrp1.deja.com>, cir...@access.ch says...
This is really good, clean simple and easy to put to good
practical use. thanks
steve
>
>In article <7kvfcp$v1q$1...@nnrp1.deja.com>,
> cir...@access.ch wrote:
>an interpretation of RMP 43. Follows my interpretation of
>RMP 44. (If you read my article via Deja, please scroll down
>to the end and use the function View original Usenet format.)
>
>Regards Franz Gnaedinger Zurich cir...@access.ch
>
>
cir...@access.ch
whi...@shore.net (Steve Whittet) wrote:
> This is really good, clean simple and easy to put to good
> practical use.
Thank you, Steve, for your kind comment on my interpretation
of problem no. 44 of the Rhind Mathematical Papyrus. By the
way, the moderators of sci.archaeology.moderated go on telling
me that mathematics has nothing to do with archaeology. Rigid
as can be. No wonder that their forum is such a dry meadow.
Here follows an idea for alternative 'Bucky Domes' (if you
read my article via Deja, please scroll down to the end and
use the function View original Usenet format).
The MUSEUM FUER GESTALTUNG ZUERICH shows a delightful
Buckminster Fuller exhibition. I am fascinated by the many
variations of the geophysical domes and like to propose still
another variant which is based on my Egyptian method for the
calculation of the circle and would perhaps resemble a cutted
diamond.
You may remember my key figure:
. . . . . d . . . . .
. . e . . . . . c . .
. f . . . . . . . b .
. . . . . . . . . . .
. . . . . . . . . . .
g . . . . + . . . . a
. . . . . . . . . . .
. . . . . . . . . . .
. h . . . . . . . l .
. . i . . . . . k . .
. . . . . j . . . . .
By joining the points a-b-c-d-e-f-g-h-i-j-k-l-a with straight
lines we obtain a polygon of 4 short sides (square root of 2)
and 8 longer sides (square root of 2 x square root of 5).
Now we can build similar polyhedrons.
In the simplest case the radius measures 3 units. The following
grid represents a plane of 6 x 6 units with a hemi-polyhedron
or a dome. The numbers give the heights of the corners above
the ground level which is marked by points:
. . . 0 . . .
. 1 2 . 2 1 .
. 2 . . . 2 .
0 . . 3 . . 0
. 2 . . . 2 .
. 1 2 . 2 1 .
. . . 0 . . .
Now for the hemi-polyhedron of radius 9:
. . . . . . . . . 0 . . . . . . . . .
. . . . . 1 . . 4 . 4 . . 1 . . . . .
. . . . . 4 . . . . . . . 4 . . . . .
. . . 3 . . 6 . . . . . 6 . . 3 . . .
. . . . . . . . . . . . . . . . . . .
. 1 4 . . 7 . . 8 . 8 . . 7 . . 4 1 .
. . . 6 . . . . . . . . . . . 6 . . .
. . . . . . . . . . . . . . . . . . .
. 4 . . . 8 . . . . . . . 8 . . . 4 .
0 . . . . . . . . 9 . . . . . . . . 0
. 4 . . . 8 . . . . . . . 8 . . . 4 .
. . . . . . . . . . . . . . . . . . .
. . . 6 . . . . . . . . . . . 6 . . .
. 1 4 . . 7 . . 8 . 8 . . 7 . . 4 1 .
. . . . . . . . . . . . . . . . . . .
. . . 3 . . 6 . . . . . 6 . . 3 . . .
. . . . . 4 . . . . . . . 4 . . . . .
. . . . . 1 . . 4 . 4 . . 1 . . . . .
. . . . . . . . . 0 . . . . . . . . .
Radius 3, quadruple 1-2-2-3
radius 9, quadruples 3-6-6-9, 1-4-8-9, 4-4-7-9
radius 27, quadruples 2-7-26-27, 2-10-25-27, 2-14-23-27,
3-12-24-27, 7-14-22-27, 9-18-18-27, 10-10-23-27, 12-12-21-27
radius 7, quadruple 2-3-6-7
radius 11, quadruples 2-6-9-11, 6-6-7-11
radius 15, quadruples 0-9-12-15, 2-5-14-15, 2-10-11-15,
5-10-10-15
and so on
Regards Franz Gnaedinger Zurich cir...@access.ch
cir...@access.ch
cir...@access.ch wrote:
> By the way, the moderators of sci.archaeology.moderated go on
> telling me that mathematics has nothing to do with archaeology.
And two years ago a professor told me that Egyptian mathematics
doesn't really belong to the history of mathematics ...
Well, I go on with my interpretation of the Rhind Mathematical
Papyrus, still considering my work as a serious contribution to
a better understanding of the ancient world.
(If you read my article via Deja, please scroll down to the end
and use the function View original Usenet format.)
Problems no. 44 and 45 of the Rhind Mathematical Papyrus mention
a granary in the shape of a cube measuring 10 royal cubits x 10
royal cubits x 10 royal cubits.
The granaries in the following problems, RMP 46 and 47, measure
10 x 10 x 3 1/3 and 10 x 10 x 5 royal cubits.
Now let us transform these right parallelepipeds into prismas
whose bases are given by the regular octagon that can be
inscribed into the square of 10 x 10 royal cubits:
A a b B
h c
g d
D f e C
Square ABCD
A-B = B-C = C-D = D-A = 10 royal cubits
inscribed octagon abcdefgh
a-b = b-c = c-d = d-e = e-f = f-g = g-h = h-a = ???
Let me draw up my first number pattern again:
1 1 2
2 3 4
5 7 10
12 17 24
29 41 58
70 99 140
169 ... ...
These numbers can be used for approximating the square root
of 2. They also help calculate a regular octagon:
side of octagon and side of circumscribed square
7 5 + 7 + 5 = 12
10 7 + 10 + 7 = 24
17 12 + 17 + 12 = 41
24 17 + 24 + 17 = 58
41 29 + 41 + 29 = 99
58 41 + 58 + 41 = 140
By doubling the last numbers we find:
side of octagon 116 side of square 82 + 116 + 82 = 280
T%he side of our square measures 10 royal cubits or 70 palms
or 280 fingers. Hence the side of the inscribed octagon measures
116 fingers or 4 royal cubits 1 palm.
The area of the octagon is smaller than the one of the square.
Accordingly the new granaries of the same volume are higher.
The ratios are again provided by the above pattern:
height of granary based on square 10 24 58 140 ...
height of granary based on octagon 12 29 70 169 ...
The heights of the parallelepipeds measure 3 1/3 and 5 cubits.
By using the numbers 10 and 12 or the ratio 12/10 we find the
new heights
3 1/3 royal cubit x 12/10 = 4 royal cubits
5 royal cubits x 12/10 = 6 royal cubits
Very simple numbers.
If you wish to get a more precise result, use the better ratio
169/140:
3 1/3 cubits = 280 Maat marks
280 Maat marks x 169/140 = 4 cubits 2 Maat marks
5 cubits = 150 fingers
140 fingers x 169/140 = 6 cubits 1 finger
Now for the area of the walls:
base 10 royal cubits x 10 royal cubits
periphery 4 x 10 c = 40 royal cubits
height 5 royal cubits
area of wall 40 c x 5 c = 200 square cubits
side of octagon 116 fingers or 4 1/7 cubits
periphery 8 x 116 fingers = 928 fingers or 33 1/7 cubit
height 169 fingers or 6 1/28 cubits
area of wall 33 1/7 c x 6 1/28 c = 200 1/28 1/196 cc
The two granaries have the same volume or capacity and their
walls have practically the same area. Even better: the walls
have exactly the same area! The small mistake 1/28 1/196 is
due to the small mistakes in the ratios 58/41 and 169/140
used for the calculation of the regular octagon.
Theorem:
Imagine a pair of ideal granaries with vertical walls,
one based on a square, the other one based on the regular
octagon inscribed into the square. Now if the granaries
have the same capacity their walls have the same area.
Regards Franz Gnaedinger Zurich cir...@access.ch
Sent via Deja.com http://www.deja.com/
Steve Whittet
In article <7li5f8$8ml$1...@nnrp1.deja.com>, cir...@access.ch says...
>
>In article <7l9rtb$8db$1...@nnrp1.deja.com>,
> cir...@access.ch wrote:
>
>> By the way, the moderators of sci.archaeology.moderated go on
>> telling me that mathematics has nothing to do with archaeology.
>
>And two years ago a professor told me that Egyptian mathematics
>doesn't really belong to the history of mathematics ...
>
>Well, I go on with my interpretation of the Rhind Mathematical
>Papyrus, still considering my work as a serious contribution to
>a better understanding of the ancient world.
>
>(If you read my article via Deja, please scroll down to the end
>and use the function View original Usenet format.)
I need to ask if you think its possible that ancient measures could
have used the same standards but varied their divisions according
to whether their base was sexigesimal, septigesimal, decimal
octal or duodecimal so that the following relations would hold.
A Mesopotamian royal cubit of 600 mm divided sexigesimally
would have 30 fingers of 20 mm and be divided into 6 hands of 5 fingers.
Its ordinary cubit would be its "3 and its foot its '2.
An Egyptian royal cubit of 525 mm (523.748) divided septagesimally
would have 28 fingers of 18.7 mm and be divided into 7 palms of 4 fingers
Its ordinary cubit would be 6 palms and its foot would be 4 palms
A Greek royal cubit of 616.8 mm divided decimally and sexigesimally
would have 30 fingers of 20.56 mm and be divided into 6 hands of 5 fingers
or 10 nails of 3 fingers. Its ordinary cubit would be its "3 and its foot its
'2
A Roman royal cubit of 592 mm divided octally would have 32 fingers
and be divided into 8 palms of 4 fingers
Its ordinary cubit would be its "'4 and its foot its '2
An English royal cubit would be a yard of 36 inches
and would be divided into 12 palms of 3 inches
Its ordinary cubit would be its "3 and its foot its '2
I put a few sample values in so you can see where I'm
going with this, Essentially I figure an Egyptian rod
of 10 royal cubits divided in 16 parts by the Romans
would have a side of 13" and form the cube which
contains the bushel.
value in mm
Unit Fing In palm hand feet Mes Egypt Grk Roman Eng
finger 1 18.75 18.5
inch 1 20 10.56 25.4
nail 3
palm 4 3 75 74
hand 5 1 100
span 7
link
quarter 9
foot 16 300 308.4 296 304.8
foot 15 300
remen 15 371
cubit 18 450 444
royal cubit 28 21 525
royal cubit 30 6 600
royal cubit 32 592
royal cubit 36 36
yard 36 12 3 914.4
pace 60 5 1480
orgia 72 6 1850.4
fathom 72 6 1828.8
rod 5250
chain
furlong 600
stadion 600
stadium 625
mile 4800
mile 5000
mile 5280
degree 365240
Would you agree an Egyptian [h3yt] or rod of 10 royal cubits
could have been divided into 16 parts by the Romans to become
a bushel?
>
>Problems no. 44 and 45 of the Rhind Mathematical Papyrus mention
>a granary in the shape of a cube measuring 10 royal cubits x 10
>royal cubits x 10 royal cubits.
...snipping a really beautiful set of calculations
>The two granaries have the same volume or capacity and their
>walls have practically the same area. Even better: the walls
>have exactly the same area! The small mistake 1/28 1/196 is
>due to the small mistakes in the ratios 58/41 and 169/140
>used for the calculation of the regular octagon.
>
>Theorem:
>
> Imagine a pair of ideal granaries with vertical walls,
> one based on a square, the other one based on the regular
> octagon inscribed into the square. Now if the granaries
> have the same capacity their walls have the same area.
I wonder what happens if the grain goes from Mesopotamia
to Egypt or from Egypt to Greece?
>
>Regards Franz Gnaedinger
regards,
steve
cir...@access.ch
whi...@shore.net (Steve Whittet) wrote:
> I need to ask if you think its possible that ancient measures could
> have used the same standards but varied their divisions according
> to whether their base was sexigesimal, septigesimal, decimal
> octal or duodecimal so that the following relations would hold.
>
> A Mesopotamian royal cubit of 600 mm divided sexigesimally
> would have 30 fingers of 20 mm and be divided into 6 hands of 5
> fingers. Its ordinary cubit would be its "3 and its foot its '2.
(...)
> A Greek royal cubit of 616.8 mm divided decimally and sexigesimally
> would have 30 fingers of 20.56 mm and be divided into 6 hands of 5
> fingers or 10 nails of 3 fingers. Its ordinary cubit would be its
> "3 and its foot its '2.
(...)
Hi Steve,
thank you for the reply. As I know very little or almost nothing
of other measures than the Egyptian ones (and the metric system
we use in Switzerland) I can't really answer your question. But
I can give you an advice: choose one single system of measures,
for example the one of ancient Mesopotamia, and play with the
numbers, try to solve practical problems of their daily life
and look out if the chosen system offers any implicit solutions
like the ones in the Egyptian system of measures which contains
many such solutions, for example
diameter of a circle 1 royal cubit
circumference 3 cubits 1 palm
side of a square 10 royal cubits = 70 palms
diagonal 14 cubits 1 palm
There are also very simple solutions for the equilateral
triangle and the hexagon, and many others. Just dive into
a system of your choice and play with the numbers.
Follows my interpretation of problem no. 48 of the Rhind
Mathematical Papyrus. (If you read my article via Deja
please scroll down to the end and use the function View
original Usenet format.)
Problem no. 48 of the Rhind Mathematical Papyrus contains
a famous drawing of a square with an inscribed octagon:
A a b B
h c
g d
D f e C
Square ABCD octagon bcdefgha
A-B = B-C = C-D = D-A = 9 royal cubits
A-a = a-b = b-B = B-c = ... = g-h = h-A = 3 royal cubits
The octagon has four shorter and four longer sides. The area
of the square measures 81 square cubits while the area of the
octagon measures 63 square cubits.
Now let us imagine a circle in the square. Its area would be
about the same as the area of the octagon. Hence the area
of the square and the one of the inscribed circle stay about
in the ratio 81/63 or 9/7. This leads to the value 28/9 or
3 1/9 for re or pi.
63 square cubits are about 8 cubits x 8 cubits. From this we
get a well known formula: if the diameter of a circle measures
9 units and if the side of a square measures 8 units the circle
and the square have about the same area.
This formula leads to the value 256/81 for re or pi.
256/81 or 3 1/9 1/27 1/81 is about 19/6 or 3 1/9, according
to a simple multiplication:
256 19 256 x 6 = 1536
81 6 81 x 19 = 1539
We found the value 3 1/9 and now a second value 3 1/6.
The equally simple values in between are 3 1/8 and 3 1/7.
Advanced pupils may look out for other octagons that offer
new solutions and values for re or pi. Here is one:
If the square measures 58 fingers x 58 fingers the side of
the inscribed regular octagon measures 24 fingers, according
to the partition 17 + 24 + 17 = 58 (see my previous post).
Now let us carry out another partition and draw the octagon:
19 + 20 + 19 = 58. The area of this octagon comes very close
to the area of the circle of radius 29 fingers or diameter
58 fingers and measures
58f x 58f - 2x19fx19f = 2642 square fingers
2642 divided by 29f x 29f = 2642/841
This value for re or pi is practically 333/106 according
to the following crosswise multiplication:
2642 333 2642 x 106 = 280,052
841 106 841 x 333 = 280,053
A general remark:
Trying to understand Egyptian mathematics in terms of Greek
geometry and modern algebra is much like walking in water:
tiresome, you hardly get any further, and you have to stay
near the bank or shore where the water is shallow. But swim,
and you will move easily and freely, you have fun, and you
will soon gain open water ...
Regards Franz Gnaedinger Zurich cir...@access.ch
cir...@access.ch
cir...@access.ch wrote:
> Trying to understand Egyptian mathematics in terms of Greek
> geometry and modern algebra is much like walking in water:
> tiresome, you hardly get any further, and you have to stay
> near the bank or shore where the water is shallow. But swim,
> and you will move easily and freely, you have fun, and you
> will soon gain open water ...
Follows my interpretation of problem no. 49 of the Rhind
Mathematical Papyrus. (If you read my article via Deja, please
scroll down to the end and use the function View original Usenet
format.)
In problem no. 49 of the Rhind Mathematical Papyrus, Ahmes
mentions a rectangle that measures 2 khet x 10 khet = 200 royal
cubits x 1000 royal cubits while the area measures 200,000 square
cubits.
Let me invent a story to this problem.
A farmer saves the life of a Vizier. This one, very grateful,
asks if the farmer has a wish? The farmer says: Well, my field
measures about 2 x 10 khet. I have to walk a long way from one
end to the other one, and even a much longer way around it. So
if I could give away my field for a rounder one that has the
same area but shorter ways? This would be a relief for me ...
Replies the Vizier: My dear man, I am happy to fulfill your
modest wish. Go to Ahmes and let him carry out the calculation.
Then bring me his numbers and I shall give you a new field ...
So the farmer goes to Ahmes who proposes a field in the shape
of an octagon and asks one of his pupils to carry out the
calculations. This one begins by writing down some numbers:
the field measures about 2 x 10 khet or 200 x 1000 cubits
way to walk from one end to the other one 1000 royal cubits
way to walk around the field 200+1000+200+1000 = 2400 cubits
area of the field about 200,000 square cubits
Now he draws up a well known number pattern:
1 1 2
2 3 4
5 7 10
12 17 24
29 41 58
70 99 140
169 239 ...
By playing with these numbers he finds a pair of fine
solutions:
New field in the shape of a regular octagon:
periphery 204+204+204+204+204+204+204+204 = 1632 cubits
circumscribed square 492 royal cubits x 492 royal cubits
partition of the side 12 times 12+17+12 royal cubits
grid 144+204+144 royal cubits x 144+204+144 royal cubits
area 200,592 square cubits
way to walk from one side to the opposite one 492 cubits
way to walk around the field 1632 royal cubits
Alternative solution:
periphery 169+239+169+239+169+239+169+239 = 1632 cubits
circumscribed square 507 royal cubits x 507 royal cubits
(area of inscribed circle 201,886 square cubits)
(way to walk around the circle 1593 royal cubits)
grid 169+169+169 royal cubits x 169+169+169 royal cubits
area 199,927 square cubits
way to walk from one side to the opposite one 507 cubits
way to walk around the field 1632 royal cubits
Then he carries out fine drawings and calls the farmer ...
Regards Franz Gnaedinger Zurich cir...@access.ch
PS.
Thank you for your e-mail, Marcio, and for your attachement
on archaeology in Brazil. I would like very much to read
your lines, however, being a computer moron, I am not able
to read wallpaper mails. How about sending a summary of that
article to our forum sci.archaeology? We are always in need
of good archaeological informations. Thank you very much
in advance.
cir...@access.ch
cir...@access.ch wrote:
an interpretation of problem no. 49 of the Rhind Mathematical
Papyrus. Follows my interpretation of problem no. 50. (If you
read my article via Deja, please scroll down tot he end and
In problem no. 50 of the Rhind Mathematical Papyrus Ahmes
calculates the area of a circle whose diameter measures 9 khet
= 900 royal cubits. By using his well known formula he obtains
8 khet x 8 khet = 64 square khet = 64 aroures = 640,000 square
cubits.
Now the advanced learners may try to solve a more demanding task:
transforming the circle into a regular octagon of the same area.
Let me draw up an enlarged version of my first nunmber pattern:
1 1 2 2
2 3 4 6
5 7 10 14
12 17 24 34
29 41 58 82
70 99 140 198
169 239 338 478
... ... ... ....
The squared side of a regular octagon and the area of the same
octagon stay in a relation that can be aproximated by means
of the above numbers:
side x side 12 17 29 41 70 99 ... square cubits
area octagon 58 82 140 198 338 478 ... square cubits
The number of the circle may be chosen from the following
sequence:
3 (plus 22) 25 47 69 91 113 135 157 179 201 223
1 (plus 7) 8 15 22 29 36 43 50 57 64 71
245 267 289 311 333 355 377 399
78 85 92 99 106 113 120 127
Two values contain the number 99:
478 / 99 or 1/99 x 478
311 / 99 or 1/99 x 311
Now the area of a regular octagon and the one of a circle may
be defined as follows:
side x side x 1/99 x 478
radius x radius x 1/99 x 311
The octagon and the circle have the same area, therefore:
side x side x 1/99 x 478 = radius x radius x 1/99 x 311
side x side x 478 = radius x radius x 311
side x side = radius x radius x 311 x 1/478
The diameter measures 9 khet or 900 royal cubits, hence
the radius measures 450 royal cubits:
side x side = 450 cubits x 450 cubits x 311 x 1/478
side x side = practically 131,752 square cubits
By consulting a table of square numbers you will find:
.....................
360 x 360 = 129,600
361 x 361 = 130,321
362 x 362 = 131,044 --- 708 less than 131,752
363 x 363 = 131,769 --- only 17 more than 131,752
364 x 364 = 132,496 --- 744 more than 131,752
.....................
The number 363 is a fine solution to our problem. Hence a circle
of the diameter 9 khet and a regular octagon of the side length
363 royal cubits have practically the same area.
Circumscribed square:
2629 x 1/3 cubit times 2629 x 1/3 cubit
Grid:
770+1089+770 1/3 cubits x 770+1089+770 1/3 cubits
Unfortunately I have no translation of problem no. 51, therefore
I finish this series of interpretations (at least for the moment
being).
Let me close with a quote by Theophile Obenga:
Si jamais Thales etait l'auteur du titre du Papyrus Rhind,
l'Occident l'aurait sans doute place le plus pres possible
du Demiurge divin lui meme.
(Theophile Obenga, La Geometrie Egyptienne, Contribution
de l'Afrique antique a la Mathematique mondiale, Editions
L'Harmattan Paris 1995, page 291)
Regards Franz Gnaedinger Zurich cir...@access.ch
cir...@access.ch
cir...@access.ch wrote:
> Unfortunately I have no translation of problem no. 51, therefore
> I finish this series of interpretations (at least for the moment
> being).
>
> Let me close with a quote by Theophile Obenga:
>
> Si jamais Thales etait l'auteur du titre du Papyrus Rhind,
> l'Occident l'aurait sans doute place le plus pres possible
> du Demiurge divin lui meme.
>
> (Theophile Obenga, La Geometrie Egyptienne, Contribution
> de l'Afrique antique a la Mathematique mondiale, Editions
> L'Harmattan Paris 1995, page 291)
Sorry for a silly mistake: I miss a translation of RMP 51
in the book by Sylvia Couchoud but there is one in the above
book by Theophile Obenga. Well, here follow my interpretations
of the problems no. 51 and 52 of the Rhind Mathematical Papyrus.
(If you read my article via Deja, please scroll down to the end
and use the function View original Usenet format.)
Problem no. 51 of the Rhind Mathematical Papyrus is somewhat
tricky. Ahmes calculates the area of a triangle whose base
measures 4 khet while the height measures 10 khet, giving
an area of 20 aroures or 200,000 square cubits. We found
this area already in RMP 49. The transformation into an
octagon lead me to a pair of solutions:
Octagon A
periphery 204+204+204+204+204+204+204+204 = 1632 cubits
grid 144+204+144 cubits x 144+204+144 cubits
Octagon B
periphery 239+169+239+169+239+169+239+169+239+169 cubits
grid 169+169+169 cubits x 169+169+169 cubits
Now comes the tricky part: the drawing of RMP 51 shows a triangle
of the same base 4 khet while the height is given as 13 (!) khet.
In that case the area measures 260,000 square cubits while the
regular octagon of about the same area has the following numbers:
periphery 8 x 232 cubits
grid 164+232+164 cubits x 164+232+164 cubits
area 259,808 square cubits
Problem no. 52 concerns a trapezoid whose base measures 6 khet
while the upper side measures 4 khet and the height measures
20 khet. Area 100 aroures or 1,000,000 square cubits. Numbers
of the regular octagon of approximately the same area:
periphery 8 x 455 cubits
grid 7 x 46-65-46 cubits x 7 x 46-65-46 cubits
area 1,000,433 square cubits
The numbers 46 and 65 are found in the following pattern:
2 1 4
3 5 6
8 11 16
19 27 38
46 65 92
111 157 222
268 379 536 and so on
You can begin such a pattern with any pair of numbers,
for example 1 and 3, or 2 and 5:
1 3 2
4 5 8
9 13 18
22 31 44
53 75 106
128 106 256
309 437 618 and so on
2 5 4
7 9 14
16 23 32
39 55 78
94 133 188
227 321 454
548 755 1096 and so on
These patterns provide many more approximate values for the
square root of 2 and many more numbers for calculating octagons.
In my next article - an interpretation of problem no. 53 of the
Rhind Mathematical Papyrus - I will show you another way to ease
difficult calculations. (The base of a trapezoid is given by the
number 6, the upper line by the number 2 1/4, and the height by
the number 3 1/4. The oblique sides measure practically 3 1/2 1/4
units each while the side of the regular octagon of the same area
measures practically 1 2/3 units. How are these numbers found?)
Regards Franz Gnaedinger Zurich cir...@access.ch
marci...@my-deja.com
article <7lkl4u$3gc$1...@nnrp1.deja.com>, > cir...@access.ch wrote: > > >
Trying to understand Egyptian mathematics in terms of Greek > > geometry and
modern algebra is much like walking in water: > > tiresome, you hardly get
any further, and you have to stay > > near the bank or shore where the water
is shallow. But swim, > > and you will move easily and freely, you have fun,
your e-mail, Marcio, and for your attachement > on archaeology in Brazil. I
would like very much to read > your lines, however, being a computer moron,
I am not able > to read wallpaper mails. How about sending a summary of
that > article to our forum sci.archaeology? We are always in need > of good
Thnk you the kind PS. Well I resend to you through this forum my e-mail only
to inform taht there are some studies on the old inscriptions in Rio's
mountains. And I took from the newspapers one very good photo of what is
called the Ibis. We have: Hi Franz. I am following with great pleasure and
attention your recents posts in "my corner" and wise discussion with Steve.
But I had promissed to you to return to the old discussion in 'My Fairy
Tales" when you asked about archaeology in Brazil and I said we had in Rio
some interesting spots and a very knew symbol of the city, the sugar-loaf,
has some indication of old phenicians travels. Here is one photo taken in
recent Summit or Cimeira held by some authorities of Latin America and
Europe. Enjoy that Ibis and I will appreciate your coments. ... In the e-mail
it was possible to attach the photo. Here I should go to one http and I do
not have one. May be I can send via e-mail to someone interested and he
could post in his home page. Thank you. Your advise in the beginning is a
valid one, but we should have a mean to translate the mathematical reasoning
of the old Egyptian into our Greek way of thinking because we are human
beings with the same biological brain. Your work on Rhind papyrus show that
to us. Regards, Marcio.
cir...@access.ch
cir...@access.ch wrote:
an interpretation of RMP 51 and 52. Follows my interpretation
of the drawing in RMP 53 (if you read my article via Deja,
please scroll down to the end and use the function View
The drawing in no. 53 of the Rhind Mathematical Papyrus
shows an isoscele triangle with two additional lines
parallel to the base. Here are the numbers (P = peak,
AL = additional line, B = base):
7 (P) 7 '2 '4 '8 2 '4 (AL) 3 '4 6 (AL) 5 6 (B)
I read the numbers as a combination of several problems
of a similar kind.
The additional lines mark a trapezoid of these measurements
(in upright position):
top 2 1/4 khet (225 royal cubits)
height 3 1/4 khet (325 royal cubits)
base 6 khet (600 royal cubits)
Now the advanced learners may answer the following questions:
a) how long are the oblique sides? b) how long are the sides
of the regular octagon of the same area?
Many problems can be simplified when we multiply the numbers
by a factor and divide the results by the same number again.
Let us multiply the above numbers by a factor of 8:
top 18 18
height 26
base 48 15+18+15
The trapezoid is composed of the rectangle 18 x 16 units and
a pair of two rectangular triangles measuring 15 units (base)
and 26 units (height). By removing the rectangle and joining
the pair of triangles we obtain an equilateral triangle of the
side length 30 units and the height 26 units, according to one
of my number patterns:
1 1 3
2 4 6
1 2 3
3 5 9
8 14 24
4 7 12
11 19 33
30 52 90
15 26 45
41 71 123
112 194 336
56 97 168 and so on
These numbers approximate the equilateral triangle:
half side 4 7 15 26 56 97 ...
height 7 12 26 45 97 168 ...
side 8 14 30 52 112 194 ...
Now the trapezoid can be defined as follows:
top 18
slope 30
height 26
base 48
(angles 60 and 120 degrees)
We answered the first question. Now for the second question.
I multiply the numbers by a factor of 3 and obtain:
top 54
height 78
slope 90
base 144
The area of the trapezoid is found as follows:
(base + upper side) x height x 1/2
(144 + 54) x 78 x 1/2 = 198 x 39
The octagon can be approximated by means of these numbers:
1 1 2 2
2 3 4 6
5 7 10 14
12 17 24 34
29 41 58 82
70 99 140 198 and so on
side x side 12 17 29 41 ...
area octagon 58 82 140 198 ...
The area of the trapezoid is given by the product 39 x 198
while the area of the octagon may be defined like this:
side x side x 198 x 1/41
The octagon and the trapezoid have the same area, therefore:
side x side x 198 x 1/41 = 198 x 39
side x side x 1/41 = 39
side x side = 39 x 41
side of octagon = practically 40
Now let me divide all numbers by 3 x 8 = 24 in order to obtain
measurements in khet:
top trapezoid 2 1/4
height trapezoid 3 1/4
slope trapezoid 3 1/2 1/4
base trapezoid 6
side octagon 1 2/3
The other numbers of the drawing may represent isoscele triangles
of these measurements:
height 5 7 '2 '4 '8 7 7 (khet)
base 6 2 '4 7 '2 '4 '8 6 (khet)
I transform the triangles into octagons of about the same area.
Solutions in short:
base height factor side of octagon
6 5 21 37 or 1 '2 '4 '84
6 7 12 25 or 2 '12
2 '4 7 '2 '4 '8 12 23 or 1 '2 '3 '12
7 '2 '4 '8 7 72 172 or 2 '3 '18
Regards Franz Gnaedinger Zurich cir...@access.ch
cir...@access.ch
cir...@access.ch wrote:
part 1 of an interpretation of RMP 53. Follows part 2.
(If you read my article via Deja, please scroll down to
the end and use the function View original Usenet format.)
In my opinion, problem no. 53 of the Rhind Mathematical Papyrus
is an assemblage of 8 or more similar problems that we may hope
to reconstruct in the context of the previous calculations.
The drawing of RMP 53 lead me to a trapezoid and four triangles
whose areas are quite easily transformed into regular octagons.
However, I overlooked one possibility. The numbers
7 7 '2 '4 '8 2 '4
define a triangle of the base 2 '4 khet and the height 7
khet while the area measures 7 '2 '4 '8 square khet or setat
(or aroure, the Greek name for setat). This area is found in
the last part of the written calculation:
2 '4 x 7 setat x 1/2 = 7 '2 '4 '8 setat
Now let me transform this area, 7.875 setat or 78,750 square
cubits, into a regular octagon:
1 1 2
2 3 4
5 7 10
12 17 24
29 41 58
70 99 140
side x side 12 17 24 99 ...
area octagon 58 82 116 140 ...
78,750 x 29 x '140 = 16,312 '2
127 x 127 = 16,129
128 x 128 = 16,328
No simple numbers. Let me begin anew and try it with palms:
700 x 7 x 225 x 7 x '2 = 3,858,750 (square palms)
3,858,750 x 29 x '140 = 799,312 '2
893 x 893 = 797,449 --- 1863 '2 less
894 x 894 = 799,236 --- 76 '2 less
895 x 895 = 801,025 --- 1712 '2 more
A triangle of the base 255 royal cubits and the height
700 royal cubits aqnd a regular octaqgon whose side measures
894 palms have about the same area.
Now let me look out for a suiting grid. The number 894 doesn't
appear in the above pattern, but we may proceed like this:
6 x 140 plus 41 plus 10 plus 3 = 894
6 x 99 plus 29 plus 7 plus 2 = 632
9 x 99 plus 3 = 894
9 x 70 plus 2 = 632
Hence the grid of the octagon measures
632+984+632 palms x 632+984+632 palms
while the octagon's area measures 3,858,116 square palms or
practically 78,737 square cubits, only 13 square cubits less
than 78,750 square cubits.
From this calculation the pupils may learn that there are many
ways to calculate an octagon - you don't have to fear difficult
numbers, there is always a way to get around the problems,
and the mistakes even out fairly well in the long run.
To be continued (I am not really sure if my interpretation
of RMP 53 is valid; have to do some more homework).
Regards Franz Gnaedinger Zurich cir...@access.ch
PS for Marcio. Thenk yaou for the reply to a former post.
Personally I believe that the ancient ones have been much
better sailors, astronomers and so on than they are allowed
to have been by our dear but sometimes rather narrow-minded
professors of archaeology. I am prone to believe that several
groups of people reached the Americas on the seaway a long
time before the Vikings, the Norse and Columbus. However,
an archaeological thesis must be based on clear and unambiguous
material evidence. Phantasy resembles the yeast while material
evidence resembles the flour. If you bake a bread without yeast
or sour dough or leaven you get a stone, and if you have yeast
but no flour there will be no bread at all. If you know what
I mean. Regarding Brazil I am more interested in old irrigation
techniques and would much appreciate any informations on this
topic.
Steve Whittet
In article <7m48mk$47j$1...@nnrp1.deja.com>, cir...@access.ch says...
>
>In article <7m1im2$3ct$1...@nnrp1.deja.com>,
> cir...@access.ch wrote:
>part 1 of an interpretation of RMP 53. Follows part 2.
...
>In my opinion, problem no. 53 of the Rhind Mathematical Papyrus
>is an assemblage of 8 or more similar problems that we may hope
>to reconstruct in the context of the previous calculations.
>
>The drawing of RMP 53 lead me to a trapezoid and four triangles
>whose areas are quite easily transformed into regular octagons.
>However, I overlooked one possibility. The numbers
>
> 7 7 '2 '4 '8 2 '4
>
>define a triangle of the base 2 '4 khet and the height 7
>khet while the area measures 7 '2 '4 '8 square khet or setat
>(or aroure, the Greek name for setat).
The problems in the Egyptian Mathematical papyri often are
worked out in terms of measured units and its presumed as above
that there is just one cubit, the royal cubit.
This is the traditional interpertation,
that the khet is a linear measure of royal cubits
the setat is its square and the aroura is a Greek name for setat.
We know the royal cubit can be divided up into fingers, palms, and spans
then recombined to make hands, feet, remen, and ordinary cubits.
I would like to raise it as a point to be considered that most fields
were actually measured in ordinary cubits, the royal cubit being
reserved for public lands, areas upon which public buildings
would be constructed, roads and canals.
It seems likely to me that square fields should be constructed on
sides of 100 cubits of both units giving 1/2 acre khet and 2/3 acre setat.
I think the Aroura would be based on the khet and not the setat
and be an Egyptian rather than a Greek unit.
4900 Egyptian [bs] of 300 mm would be 1470000 mm
Assuming that foot was 4 palms, the cubit 6 palms
and the royal cubit 7 palms, the ordinary cubit
is 450 mm and the royal cubit is 525 mm
in round numbers
Using a Greek mile as equal to a Roman mile
as equal to a 8 stadion x 600 =4800 Greek pous of 308.4 mm
or a 8 stadiums x 625 = 5000 Roman pes of 296 mm
or 1480000 mm
lets begin with the unit of the foot, pied, pes and pous
We have the ratio 144 Greek <pous> = 147 Egyptian [bs]
= 150 Roman <pes> = 150 French <pied> = 146 English feet
The Greeks divided their measures like the Egyptian horus eye
fractions into multiples or fractions of a Greek foot called <pous>
stadion = 600 pous
arkana = 10 '4 pous = 3160 mm
orgyia = 6 pous
xylon = 4 '2 pous
bema = 3 pous = 925.2 mm
spitame = 1 '3 pous = 411.2 mm
long p = 1 '32 pous = 318 mm (Milatus)
= 1 '40 pous = 316 mm (Athens)
pous = 308.4 mm
Dichas = '2 pous
Palaste = '4 pous
Gondylos = '8 pous
Daktylos = '16 pous
Pecha = '32 pous
If Greek measures divided the acre into unit fractions
based on squares whose sides were 100 units
acre/x square ft side in ft side/100 in mm fingers of 19.875mm
1 43560 208.7 636.15 32f
3/4 32670 180.75 550.9 27.72f
2/3 29040 170.4 519.4 26.13f
1/2 21780 147.6 449.8 22.63f
1/3 14520 120.5 367.3 18.48f
1/4 10890 104.4 318 16f Miletus Foot
1/8 5445 73.8 224.46mm 11.29f
If Egyptian measures divided the acre into unit fractions
based on squares whose sides were 100 units
acre/x square ft side in ft side/100 in mm fingers of 18.7mm
1 43560 208.7 636.15 34f
3/4 32670 180.75 550.9 29.5f
2/3 29040 170.4 519.4 27.78f
1/2 21780 147.6 449.8 24f Egyptian cubit
1/3 14520 120.5 367.3 19.64f
1/4 10890 104.4 318 17f
1/8 5445 73.8 224.46mm 12f
An ordinary cubit of which 100 formed the side of 1/2 acre
would be 449.8 mm
We take a royal cubit as 20.62" or 523.75 mm but its actual
range as measured by Wilkenson from rulers and Nilometers
varied more than +/- 1mm
An Egyptian setat, Greek aroura or Roman jugerum defined as
the square formed on sides of 100 Royal cubits would measure
29527 sq ft. This is not exactly 2/3 acre or 29040 sq ft
but might be taken as close given some variation over time.
The 1/2 acre square or khet formed on the side of 100
ordinary cubits seems like a closer match. IMHO The even
divisions are all arrived at by doubling or halving and
the ordinary cubit rather than the royal cubit would be
the original Egyptian base and would itself be derived
from the definition of the Mesopotamian <iku> as
squares of 100 and 120 cubits to a side.
This area is found in
>the last part of the written calculation:
>
> 2 '4 x 7 setat x 1/2 = 7 '2 '4 '8 setat
>
>Now let me transform this area, 7.875 setat or 78,750 square
>cubits, into a regular octagon:
Or into a square whose side is 28 [h3yt] where 10 [h3yt]
is the side of the khet and 10 royal [h3yt]
is the side of the setat.
...
>
>To be continued (I am not really sure if my interpretation
>of RMP 53 is valid; have to do some more homework).
>
>Regards Franz Gnaedinger
regards,
steve
cir...@access.ch
whi...@shore.net (Steve Whittet) wrote:
> The problems in the Egyptian Mathematical papyri often are
> worked out in terms of measured units and its presumed as above
> that there is just one cubit, the royal cubit.
>
> This is the traditional interpertation,
> that the khet is a linear measure of royal cubits
> the setat is its square and the aroura is a Greek name for setat.
>
> We know the royal cubit can be divided up into fingers, palms,
> and spans then recombined to make hands, feet, remen, and ordinary
> cubits.
>
> I would like to raise it as a point to be considered that most fields
> were actually measured in ordinary cubits, the royal cubit being
> reserved for public lands, areas upon which public buildings
> would be constructed, roads and canals.
Hi Steve,
you are quite right with all you say above, however, the cubit
in the Rhind Mathematical Papyrus is always the royal cubit,
as Sylvia Couchoud states quite clearly.
Let me go on with my interpretation of RMP 53 and discuss
the Greek system of measures on another day. (If you read
my article via Deja, please scroll down to the end and use
the function View original Usenet format.)
One of the written calculations of RMP 53 seems to concern
a triangle of these measurements:
base 2 1/4 khet or 2 '4 khet = 225 royal cubits
height 4 1/2 khet or 4 '2 khet = 450 royal cubits
area '2 x 225 cubits x 450 cubits = 50,625 setat
(1 setat being 1 square khet or 10,000 square cubits)
Now let me transform this area into a regular octagon:
1 1 2
2 3 4
5 7 10
12 17 24
29 41 58
70 99 140
side x side 5 12 29 ...
area octagon 12 58 140 ...
50,265 x 29 x '140 = 10,487 (rounded up)
101 x 101 = 10,201 --- 286 less
102 x 102 = 10,404 --- 83 less
103 x 103 = 10,609 --- 122 more
104 x 104 = 10,816 --- 329 more
The side length of the octagon lies between 102 and 103 royal
cubits. A little nearer to the number 102. Probably 102 '5 '5
(102.4)? Let me try it again with '5 cubits or a factor of 5:
'2 x 255 x 5 x 450 x 5 = 1,265,625
1,265,625 x 29 x '140 = 262,165 (rounded)
511 x 511 = 261,121 --- 1044 less
512 x 512 = 262,144 --- 21 less
513 x 513 = 263,169 --- 1004 more
We found a good value: the side of the octagon measures
practically 512 x '5 royal cubits. Now for the grid:
3 x 140 plus 58 plus 17 plus 17 = 512
3 x 99 plus 41 plus 12 plus 12 = 362
5 x 99 plus 17 = 512
5 x 70 plus 12 = 362
Hence the grid measures
362+512+362 fifth cubits x 362+512+362 fifth cubits
while the area of the octagon in the grid is found as follows:
362+512+362 = 1236 fifth cubits
1236 x 1236 - 2 x 362 x 362 = 1,265,608
1,265,608 x '5 x '5 = 50,624 '5 '10 '50 square cubits
area octagon 50,624 '5 '10 '50 square cubits
area triangle 50,625 square cubits
mistake only '2 '6 '75 square cubits
We had a lot of luck: we found a result with a tiny mistake
of less than 1 square cubit on an area of over 50,000 square
cubits! Or the other way round: the numbers of the triangle
had been chosen in such a way as to yield a fine result ...
Regards Franz Gnaedinger Zurich cir...@access.ch
cir...@access.ch
cir...@access.ch wrote:
part 3 of an interpretation of RMP 53. Follows part 4.
(If you read my articla via Deja, please scroll down to
the end and use the function View original Usenet format.)
Now for the remaining calculation of problem no. 53 of the
Rhind Mathematical Papyrus (translation by Thomas Eric Peet,
measurement transformed by me):
1/10 of an area measures 14,750 square cubits
1/10 of the area subtracted, then this is the area
There are obviously two areas, one of them 1/10 or '10 smaller
than the other one. - Perhaps an octagon in a circle?
Let us consider an octagon in a simple grid:
side 10
square 24 x 24
partition 7 + 10 + 7
grid 7 + 10 + 7 x 7 + 10 + 7
diameter of the inscribed circle 24
diameter of the circumscribed circle 26
according to the triple 2 x 5-12-13
diameter (26) / side (10) = 13 to 5
The area of the octagon measures
24x24 - 2x7x7 = 478 square units
The area of the circle is given by the following formula:
radius x radius x re
The radius measures 13 units:
13 x 13 x re
Is there a suitable value for re?
3 (plus 22) 27 47 69 91 113 135 157 179 201 223
1 (plus 7) 8 15 22 29 36 43 50 57 64 71
245 267 289 311 333 355 377 399 421 433 465 487
78 85 92 99 106 113 120 127 134 141 148 155
509 531 553 575 597 619 641 663 685 707 ... 22
162 169 176 183 190 197 204 211 218 225 ... 7
Yes, the value 531 above 169, for 169 equals 13 x 13:
13 x 13 x 531 x '13 x '13 = 531
Area of the circle 531 square units
area of the inscribed octagon 478 square units
The ratio is practically 10 to 9, according to a crosswise
multiplication:
531 10 531 x 9 = 4779
478 9 478 1 10 = 4780
Hence the two areas mentioned in RMP 53 might well be a circle
and an octagon!
Now let me invent a problem to the area of 14,750 square
cubits of RMP 53:
The radius of a circle measures 2 '6 khet or '3 x 650 royal
cubits - how long is the side of the inscribed octagon?
I calculate the area of the circle by means of the formula
radius x radius x '169 x 531
'3 x 650 x '3 x 650 x '169 x 531 = 147,500 square cubits
area of the circle 147,500 square cubits
minus '10 (RMP 53) 14,750 square cubits
= area of the inscribed octagon 132,750 square cubits
Diameter / side = 13 to 5
diameter = 2 x 2 '6 khet = 4 '3 khet = '3 x 13 khet
side = '3 x 13 x 5 x '13 khet = '3 x 5 or 1 '6 khet
If the radius of a circle measures 2 '6 khet the side of
the inscribed regular octagon measures about 1 '6 khet.
A more precise result is found by means of another octagon:
draw the square 24 x 24 - the diagonals measure practically
34 units
prolong the axes by 5 units on every side - the prolonged
axes measure 34 units
join the ends of the axes and the corners of the square,
thus you obtain an octagon - its side measures 13 units,
according to the triple 5-12-13
Diameter / side = 34 to 13
The diameter of my circle measures 4 '3 khet or '3 x 1300
royal cubits while the side of the inscribed octagon measures
'3 x 1300 x 13 x '34 = 165 '2 '6 '51 royal cubits
(mistake only one palm on 165 royal cubits)
So far my interpretation of problem no. 53 of the Rhind
Mathematical Papyrus. The seemingly incorrect calculations
and messy numbers turned out to be an assemblage of similar
problems: subject matter for a whole semester in the seminary
of professor Ahmes ... Tomorrow will follow my interpretation
of RMP 54&55. A pair of simple divisions yield the areas 7,000
and 6,000 square cubits. We shall transform these areas into
octagons and refine their grids as follows:
27+38+27 x 27+38+27 --- 539+762+539 x 539+762+539
25+35+25 x 25+35+25 --- 489+704+498 x 498+704+498
An amazing property of the octagons shall lead us then to a
theorem on regular polygons: the circumscribed and inscribed
circle form a ring - define the area of such a ring ...
Regards Franz Gnaedinger Zurich cir...@access.ch
cir...@access.ch
cir...@access.ch wrote:
> So far my interpretation of problem no. 53 of the Rhind
> Mathematical Papyrus. The seemingly incorrect calculations
> and messy numbers turned out to be an assemblage of similar
> problems: subject matter for a whole semester in the seminary
> of professor Ahmes ... Tomorrow will follow my interpretation
> of RMP 54&55.
Here we go. Please imagine that you are an advanced learner
in the seminary of professor Ahmes - or, if you like, a time
traveler on a step visit in ancient Egypt ... (And if you
read my article via Deja, please scroll down to the end
and use the function View original Usenet format.)
RMP 54 & 55
7 setat of land are divided into 10 fields, each one measuring
7,000 square cubits.
3 setat of land are divided into 5 fields, each one measuring
6,000 square cubits.
You may say that these are very simple calculations compared
with the many and most complex problems of RMP 53. Whereupon
Ahmes will smile and propose that you transform the above
areas into regular octagons. You will do so and find the
following solutions:
OCTAGON A
side 38 royal cubits
square 92 royal cubits x 92 royal cubits
partition 27 + 38 + 27 = 92 royal cubits
grid 27+38+27 cubits x 27+38+27 cubits
area octagon 7006 square cubits
OCTAGON B
side 35 royal cubits
square 85 royal cubits x 85 royal cubits
grid 25+35+25 cubits x 25+35+25 cubits
area octagon 5975 square cubits
Ahmes will be pleased. Then he may propose that you multiply
the numbers by a factor of 20 and refine the grids and look
out for more accurate octagons. With all you learned before
you will find quite easily the following solutions:
OCTAGON A
side 762
square 1840 x 1840 (92 fingers x 92 fingers)
grid 539+762+539 x 539+762+539
diameter of the inscribed circle 1840 (92 fingers)
OCTAGON B
side 704
square 1700 x 1700 (85 fingers x 85 fingers)
grid 498+704+498 x 498+704+498
diameter of the circumscribed circle 1840 (92 fingers)
according to the pseudo-triple 4 x 176-425-460
Now Ahmes will tell you a formula:
Draw a sequence of regular octagons in such a way that the
inscribed circle of one octagon serves as the circumscribed
circle of the next smaller octagon. The linear measurements
of two subsequent octagons will stay in the ratio 92 to 85
while the areas will stay about in the ratio 7 to 6.
And if you get curious and wish to know more and even quote
the opening words of the Rhind Mathematical Papyrus
CORRECT METHOD OF RECKONING, FOR GRASPING THE MEANING
OF THINGS AND KNOWING EVERYTHING THAT IS, OBSCURITIES
... AND ALL SECRETS (Gay Robins & Charles Shute)
Ahmes will smile again, mumble some words about the impatient
youth of today :-) and then come up with a very fine theorem:
Draw a regular polygon of 3, 4, 5, 6, 7, 8 ... equal sides.
Draw a circle into the polygon, and another one around it.
The two circles form a ring. Now the ring has exactly the
same area as a circle around a side ...
You may check this in the cases of octagon (a) and (b):
Side of Octagon (a) 10
grid 7 + 10 + 7 x 7 + 10 + 7
diameter of inscribed circle 7 + 10 + 7 = 24
diameter of circumscribed circle 26 (10-24-25)
area of ring = area of a circle of diameter 10
Side of octagon (b) 352
grid 249 + 352 + 249 x 249 + 352 + 249
diameter of inscribed circle 249 + 352 + 249 = 850
diameter of circumscribed circle 920 (352-850-920)
area of ring = area of a circle of diameter 352
Ahmes will look over your shoulder and say that his problems
are like dry leaves of tea: you have to pour water over them
and wait for a while ... if you know what I mean ...
Regards Franz Gnaedinger Zurich cir...@access.ch
Sent via Deja.com http://www.deja.com/
cir...@access.ch
cir...@access.ch wrote:
in a hurry and omitted a whole passage. Follows the complete
version.
Here we go. Please imagine that you are an advanced learner
in the seminary of professor Ahmes - or, if you like, a time
traveler on a step visit in ancient Egypt ... (And if you
read my article via Deja, please scroll down to the end
and use the function View original Usenet format.)
RMP 54 & 55
OCTAGON A
side 38 royal cubits
OCTAGON B
side 35 royal cubits
OCTAGON A (20 units = 1 royal cubit)
side 762
square 1840 x 1840 (92 royal cubits x 92 royal cubits)
partition 539 + 762 + 539 = 1840 (92 royal cubits)
grid 539+762+539 x 539+762+539
OCTAGON B
side 704
square 1700 x 1700 (85 royal cubits x 85 royal cubits)
partition 498 + 704 + 498 1700 (85 royal cubits)
grid 498+704+498 x 498+704+498
Hereupon Ahmes will ask you to draw the grids and octagons,
using Maantef marks instead of royal cubits:
OCTAGON A and B
partitions 539+762+539 and 498+704+498 Maantef marks
(20 Maantef marks = 10 Nut marks = 1 finger = 1,875 cm)
Then Ahmes will ask you to draw a circle around the smaller
octagon and another one into the larger octagon. By doing so
you will be surprised: the circles have the same diameter!
Here are the numbers:
OCTAGON A
side 762
grid 539+762+539 x 539+762+539
OCTAGON B
side 704
grid 498+704+498 x 498+704+498
Regards Franz Gnaedinger Zurich cir...@access.ch
(I hope this time all is fine. Sorry for the mess I made
in the first version. I really admire Ahmes for having made
so few mistakes on his long scroll)
cir...@access.ch
marci...@my-deja.com wrote: ...
Marcio, I already wrote a reply in another post of mine
(hope you saw it).
In order to avoid an eventual archaival problem I change to this
file. Follows problem no. 56 of the Rhind Mathematical Papyrus.
(If you read my article via Deja, please scroll down to the end
and use the function View original Usenet format.)
The base of a pyramid measures 360 royal cubits while the height
measures 250 royal cubits.
Beginners calculate the sekad: how much does the slope recede
on 1 royal cubit or 7 palms of height?
half base / height = 180 : 250 = '2 '5 '50
sekad = 7 palms x '2 '5 '50 = 5 '25 palms
Advanced learners may solve more demanding problems:
a) imagine a circle in the square of the base and calculate
the circumference
b) transform the base into a regular octagon of about
the same area; imagine a circle in the octagon
and calculate the circumference
c) transform the volume of the pyramid into a cube
and calculate the cube's edge
If the diameter of a circle measures 1 royal cubit or 7 palms,
the circumference measures more than 3 royal cubits and a little
less than 22 palms. When we have a pair of such values we can
draw up a number sequence that provides more and better values:
3 (plus 22) 25 47 69 91 113 135 157 179 201
1 (plus 7) 8 15 22 29 36 43 50 57 64
201 223 245 267 289 311 333 355 377 ...
64 71 78 85 92 99 106 113 120 ...
The diameter of our circle measures 360 = 3 x 120 royal cubits
and the circumference practically 3 x 377 = 1131 royal cubits.
Now for the octagon. The area of the base measures
360 x 360 = 129,600 square cubits
By applying the method you learned from the previous problems
you will quite easily find the following octagon:
side 164 royal cubits
grid 116+164+116 cubits x 116+164+116 cubits
area 396x396 - 2x116x116 = 129,904 square cubits
side length of grid 116 + 164 + 116 = 396 royal cubits
diagonal 560 royal cubits
diameter of inscribed circle 4 x 99 = 396 royal cubits
circumference 4 x 311 = 1244 royal cubits
By the way, 311/99 and 377/120 are fine values for the number
of the circle and can be given as handy unit fraction series:
'99 x 311 = 3 '9 '33
'120 x 377 = 3 '10 '24
Finally for the cube. The volume of the pyramid measures
'3 x 360 x 360 x 250 = 60 x 60 x 60 x 50 cubic cubits
while the edge of the cube of the same volume measures
60 royal cubits x cube root of 50
How do we approximate the cube root of 50?
By using the following equation
A x A x A = 50 x B x B x B plus mins C
and looking out for such numbers A and B that keep C small:
4 x 4 x 4 = 50 x 1 x 1 x 1 plus 16
11 x 11 x 11 = 50 x 3 x 3 x 3 minus 19
70 x 70 x 70 = 50 x 19 x 19 x 19 plus 50
The value 4 is too great:
4 x 4 x 4 = 64
The value '3 x 11 is a little too small:
'3 x 11 x '3 x 11 x '3 x 11 = '27 x 1331 = 49 ...
The value '19 x 70 is again a little too great:
'19 x 70 x 19 x 70 x 19 x 70 = 50 ...
Such values allow us to draw up number sequences of the following
kind, providing more and better values:
4 (plus 11) 15 26 37 48 59 70 81
1 (plus 3) 4 7 10 13 16 19 22
11 (plus 70) 81 151 221 291 361 431 501 571
3 (plus 19) 22 41 60 79 98 117 136 155
641 711 781 851 921 991 1061 1131 1201
174 193 212 231 250 269 288 307 326
The value '307 x 1131 is the best approximation for the cube
root of 50 (funny, we had the number 1131 already) while the
numbers 221 and 60 yield a simple solution to our problem:
60 x cube root of 50 = about 60 x 221 x '60 = 221
A pyramid of the base 360 royal cubits and the height 250
royal cubits and a cube of the edge 221 royal cubits have
praqctically the same volume.
Regards Franz Gnaedinger Zurich cir...@access.ch
cir...@access.ch
cir...@access.ch wrote:
an interpretation of problem no. 56 of the Rhind Mathematical
Papyrus. Follows RMP 57. (If you read my article via Deja,
please scroll down to the end and use the function View
original Usenet format.)
The base length of a pyramid measures 140 royal cubits
while the sekad measures 5 palms 1 finger.
Beginners calculate the height and obtain 93 '3 royal cubits.
Advanced learners may solve the following problems:
a) imagine a circle in the square of the base and another
one around the base - how long are the circumferences?
how long are the average diameter and circumference?
b) transform the area of the base into a circle
c) how long are the four edges of the pyramid?
The diameter of the circle in the square of the base measures
140 royal cubits while the diagonal measures 198 royal cubits:
140 royal cubits x '7 x 22 = 440 royal cubits
198 royal cubits x '99 x 311 = 622 royal cubits
---------------------------------------------------
169 royal cubits x '169 x 531 = 531 royal cubits
A circle has the same area as the base of the pyramid. How long
is the radius? We might calculate the area of the base and divide
it by re or pi, the number of the circle. Or we may look out for
a good value for the square root of re and divide the base by
that value:
'7 x 22 = 'A x B x 'A x B
22 x A x A = 7 x B x B
22 x 4 x 4 = 7 x 7 x 7 plus 9
22 x 22 x 22 = 7 x 39 x 39 plus 1
'4 x 7 is a good first value while '22 x 39 is already a very
fine value for the square root of re or pi.
The base length measures 140 royal cubits. When we divide it
by '4 x 7 or '22 x 39 or when we multiply it by 4 x '7 or
22 x '39 we obtain the radius of the circle of the same area:
140 royal cubits x 4 x '7 = 80 royal cubits
140 royal cubits x 22 x '39 = practically 79 cubits
exact number 78.986...
How long are the four edges of the pyramid?
edge x edge = 70x70 X 70x70 plus '3 x 280 x '3 x 280 cc
edge x edge = '3 x '3 x 70 x 70 x 2 square cubits
edge = '3 x 70 x square root of 17 x square root of 2
The roots can be approximated by means of the following numbers:
8 - 33 - 136 70 - 99 - 140
square root of 34 '8 x 33 or '33 x 136
square root of 2 '70 x 99 or '99 x 140
edge '3 x 70 x '33 x 136 x '70 x 99 = 136 cubits
'3 x 70 x '8 x 33 x '99 x 140 = 136 '9 cubits
--------------------------------------------------------
average 136 '18 cubits
136 '18 = 136.055555...
exact number 136.055544...
Regards Franz Gnaedinger Zurich cir...@access.ch
Sent via Deja.com http://www.deja.com/
cir...@access.ch
cir...@access.ch wrote:
an interpretation of problem no. 57 of the Rhind Mathematical
Papyrus. Follows RMP 58. (If you read my article via Deja,
please scroll down to the end and use the function View
original Usenet format.)
Base and height of a pyramid measure 140 and 93 '3 royal cubits.
Beginners calculate the sekad and obtain 5 palms 1 finger.
Advanced learners may solve the following problems:
a) imagine a hemi-sphere in the frame of the pyramid
- how long is the radius?
b) imagine a sphere in the frame of the pyramid
- how long is the diameter?
Let us multiply the numbers by a factor of 3:
height 280
base 420
Height and base stay in the ratio 2 to 3:
height 280 = 2 x 140
base 420 = 3 x 140
The shape of this pyramid is based on a Sacred Triangle:
half base 210 = 3 x 70
height 280 = 4 x 70
slope 350 = 5 x 70
Now let us multiply the original numbers by a factor of 12:
height 1120
slope 1400
half base 840
base 1680
You may draw a small scale version of the cross-section and
inscribe a semicircle as representation of the hemisphere in
the frame of the pyramid. The radius measures 672 units while
the touching point of the hemisphere and the slope (or the
semicircle and the oblique side of the Sacred Triangle)
partitions the slope as follows:
partition slope (from top) 896 + 504 = 1400
The radius of the touching point divides the Sacred Triangle
840-1120-1440 into a pair of smaller Sacred Triangles:
lower part of slope 504 = 3 x 168
radius 672 = 4 x 168
half base 840 = 5 x 168
radius 672 = 3 x 224
upper part of slope 896 = 4 x 224
height 1120 = 5 x 224
The radius of the hemisphe in the frame of the pyramid measures
672 divided by 12 = 56 royal cubits
Simple numbers:
height 20
slope 25
base 30
radius of inscribed hemisphere 12
Now for the sphere. The radius measures 420 small units:
height 1120
slope 1400
half base 840
base 1680
radius of inscribed sphere 420
partition height (from top) 700 + 420 = 1120
partition slope (from top) 560 + 840 = 1400
half base = lower part of slope = 840
radius 420 = 3 x 140
upper part of slope 560 = 4 x 140
upper part of height 700 = 5 x 140
Radius and diameter of the sphere measure:
420 divided by 12 = 35 royal cubits
840 divided by 12 = 70 royal cubits
Simple numbers:
height 4
slope 5
base 6
diameter of inscribed sphere 3
(All these numbers are exact, no approximations.)
Now let us imagine a circle around the cross-section:
radius 525
partition height (from top) 875 + 245 = 1120
partition height (from top) 700 + 700 = 1400
Triangles:
radius 525 = 3 x 175
upper part of slope 700 = 4 x 175
upper part of height 875 = 5 x 175
radius 525 = 3 x 175
lower part of slope 700 = 4 x 175
center sphere - corner 875 = 5 x 175
lower part of height 245 = 7 x 35
half base 840 = 24 x 35
center sphere - corner 875 = 25 x 35
Simple numbers:
height 32
slope 40
base 48
diameter of sphere around cross-section 50
The triples 3-4-5 and 7-24-25 are the first triples required
for my method for the calulation of the circle - a method
which I ascribe to the school of Imhotep.
Regards Franz Gnaedinger Zurich cir...@access.ch
cir...@access.ch
cir...@access.ch wrote:
an interpretation of problem no. 58 of the Rhind Mathematical
Papyrus. Follows RMP 59. (If you read my article via Deja,
please scroll down to the end and use the function View
original Usenet format.)
Base, height and sekad of a pyramid measure 12 royal cubits,
8 royal cubits and 5 palms 1 finger.
Please imagine a wooden model of this pyramid:
height 8 fingers
base 12 fingers
Height and base stay in the ratio 2 to 3:
height 8 fingers = 2 x 4 fingers
base 12 fingers = 3 x 4 fingers
The shape is given by a Secret Triangle:
half base 6 fingers = 3 x 2 fingers
height 8 fingers = 4 x 2 fingers
slope 10 fingers = 5 x 2 fingers
Let me call such a pyramid a Sacred Pyramid.
Now for the surface of the model:
area base 12 fingers x 12 fingers = 144 square fingers
area of one face '2 x 12 f x 10 f = 60 square fingers
area of all four faces 4 x 60 sf = 240 square fingers
whole surface 144 sf + 240 sf = 384 square fingers
And the volume?
'3 x base x base x height
'3 x 12 fingers x 12 fingers x 8 fingers = 384 cubic fingers
The same number 384!
How long is the radius of the inscribed sphere?
exactly 3 fingers
How long is the distance of the center of the sphere and a corner
of the base?
exactly 9 fingers according to the quadruple 3-6-6-9
Now let us imagine a sphere whose diameter measures 9 fingers.
Tell me the volume ...
'6 x diameter x diameter x diameter x re
Use the value '81 x 256 for re:
'6 x 9f x 9f x 9f x '81 x 256 = 384 cubic fingers
Again the same number 384, and a new formula that resembles
another well known formula of the Rhind Mathematical Papyrus:
If the side of a square measures 8 units and if the diameter
of a circle measures 9 units, the square and the circle have
about the same area
If the height of a Sacred Pyramid (a pyramid whose shape
is defined by a Sacred Triangle) measures 8 units and if
the diameter of a sphere measures 9 units, the pyramid
and the sphere have about the same volume
cir...@access.ch
cir...@access.ch wrote:
an interpretation of problem no. 59 of the Rhind Mathematical
Papyrus. Follows RMP 60; end of recto. (If you read my article
via Deja, please scroll down to the end and use the function
View original Usenet format.)
The base of a cone has a diameter of 15 royal cubits while
the height measures 30 royal cubits.
The area of the base may be calculated by means of the following
formula:
'4 x diameter x diameter x re
Use the simple value '15 x 47 for re:
'4 x 15 cubits x 15 cubits x '15 x 47 = 176 '4 square cubits
Now calculate the volume of the cone:
'3 x area of base x height = volume
'3 x 176 '4 cc x 30 c = 1762 '2 cubic cubits
Let us imagine a sphere of the same diameter as the base and
calculate its volume:
'6 x diameter x diameter x diameter x re
'6 x 15 c x 15 c x 15 c x '15 x 47 = 1762 '2 cubic cubits
The sphere and the cone have the same volume!
We may imagine wooden models:
cone diameter base 15 fingers height 30 fingers
sphere diameter 15 fingers
Cone and sphere have the same weight. What means that they
have the same volume.
Theorem:
A sphere of a given diameter and a cone whose base has
the same diameter while the height measures double as much
have the same volume
cir...@access.ch
cir...@access.ch
finished a series of interpretations (problems no. 44-60) of
the Rhind Mathematical Papyrus. Follows a quote from an article
by Walther Hinz on Linear A. (If you read my message via Deja,
please scroll down to the end and use the function View original
Usenet format.)
Professor Walther Hinz teaches Orientalistic at the University
of Goettingen, he is a regular member of the German Archaeolo-
gical Institute Berlin, he deciphered Elamitic and the Sinai
writings, and he published an article on Linear A in MUSEION
2000, ABZ Verlag Zuerich, 6/1991:
Michael Ventris deciphered Linear B in the year 1952, enabling
us to read also Linear A (Linear A & B have 60 signs in common).
But Linear A is hard to understand. Then Cyrus H. Gordon from
the Brookline University Massachusetts noticed that many lists
on the tablets of Hagia Triada, a Minoan palace near Phaistos
on Crete, end with the word ku-ro and the sum of the addition.
As the letters r and l had been given by the same sign, ku-ro
can be read as ku-lo what resembles the Arabian kullo = all
in the meaning of sum. And if Linear A is a semitic language?
Gordon found several signs on vessels that turned out to be
semitic, as they are known in Ugaritic and Hebrew. However,
only few scholars followed Gordon: Jan Best, Robert Stieglitz
and Walther Hinz who finally succeeded in translating tablet
no. 95 from Hagia Triada. According to Gordon and Hinz, Linear
A is of a northwest semitic origin, kin to Ugaritic, Eblaitic,
Phoenician and Canaanitic. It was invented around 1800 - 1700
BC and later developed into Linear B by the Dorians on Crete.
Both Linear A and B are sloppy writings: r = l; b and f are
written as p; q is written as k; soft h, sharp s and sh have
simply been omitted; t was also outspoken as in the English
word 'think'; pe-ma = sperma (seeds); pa-te = pantes (all)
or pater (father); da-pu-ri-to = labyrinthos ... A rough
ealry Greek in sloppy notations. Now a quote in German,
followed by a summary in English:
EUROPAS ERSTE SCHRIFT STAMMT AUS KRETA von Walther Hinz
(...) In 25 Jahren haben nur zwei Fachgelehrte Gordons These
zugestimmt: Jan Best und Robert Stieglitz. Allein, auf Grund
eigener Studien stelle ich fest: Cyrus H. Gordon hat recht.
Das Minoische war eine nordwestsemitische Sprache, und die
Texte in Linear A sind in dieser Sprache geschrieben, die
mit dem Ugaritischen, Eblaitischen, Phoenikischen und
Kanaanaeischen verwandt ist.
Taefelchen HT 95 - der Beweis
(...) Aufnahmen und Zeichnungen entnahm ich dem meisterhaften
Werk Receuil des inscriptions en lineaire A von Louis Godart
und Jean-Pierre Olivier, Band 1 (Paris 1970), Seite 154f.
Wir fangen mit der Vorderseite (...) an. In Zeile 1 begegnen
uns, von links her zu lesen, vier Zeichen: da-du-ma-ta. Der
Punkt dahinter zeigt an, dass das Wort damit beendet ist.
Dann folgt, gegen den Rand hin, ein Zeichen, das keine Silbe
wiedergibt, sondern ein Wort, das wir nicht kennen, das aber
eine Aehre wiedergibt. Wir haben es hier mit einem Ideogramm
zu tun, das besagt: was nun folgt, sind Zerealien, das heisst
verschiedene Getreidesorten. Das Wort da-du-ma-ta bezeichnet
offenbar den Empfaenger dieser Zerealien, ist also ein Name.
Auf ihn kommen wir zurueck.
In Zeile 2 steht zunaechst ein Wort mit zwei Silbenzeichen.
Das erste kennen wir schon aus Zeile 1, es ist da. Das zweite
Zeichen ist me; das Wort lautet also dame. Es folgt ein kurzer
waagrechter Strich; er bedeutet die Zahl 10 und meint 10 Mass;
denn Getreide wurde und wird im Orient mit Hohlmassen bemessen.
Wie gross das Minoische Hohlmass war, wissen wir nicht. Da
es auch halbe und viertel Masse gab, duerfte die Masseinheit
mehrere Liter betragen haben. Vielleicht acht oder zehn.
Summary: the first word reads da-du-ma-ta and is followed
by an ideogram of a cereal, meaning that someone by the name
dadumata (the wife of Baal, as we shall see later on) obtains
the cereals mentioned in the following lines. The second line
reads dame and is followed by a short stroke (almost a point)
meaning 10 measures of cereals. The capacity of the Minoan
measure might have been some 8 or even 10 liters. What does
the word dame mean? Oat, as we shall see in the next part.
cir...@access.ch
cir...@access.ch
quoted from an article by Walther Hinz on Linear A. Follows
the second part, again with an English summary at the end.
(If you read my article via Deja, please scroll down to
the end and use the function View original Usenet format.)
(Europas erste Schrift stammt aus Kreta, von Walther Hinz)
(...)
Doch welches Getreide ist mit dame gemeint? Jan Best dachte
an Brot und wollte das dame als laheme lesen, zu hebraeisch
lehem, Brot, das wir alle aus dem Ortsnamen Bethlehem kennen,
der 'Haus des Brotes' bedeutet. Die Einschaltung eines h ist
unbedenklich, weil dieser Laut in Linear A nie geschrieben
wurde, obschon es in der gesprochenen Sprache sowohl ein
weiches als auch ein scharf gehauchtes h gab. Jan Best's
Lesung des ersten Zeichens da als la halte ich jedoch fuer
bedenklich, obwohl in Linear B, wie wir sahen, die erste
Silbe des griechischen Wortes 'Labyrinthos' minoisch da
geschrieben wurde. Mir scheint das ein Sonderfall zu sein.
Zudem: In orientalischen Hofspeichern wurden zwar verschiedene
Getreidearten aufbewahrt und ausgegeben, aber Brot wurde dort
nicht gebacken. Ich schlage darum vor, das Wort dame als
dachnme zu lesen in der Bedeutung 'Hirse', indem ich es zu
hebraeisch dachan (Ezechiel 4, 9) und zu arabisch duchn stelle,
was beides Hirse bedeutet.
Die drei letzten Silbenzeichen in Zeile 3 lauten mi-nu-te.
Gordon hat darin den Namen einer Gegend erkannt, die fuer
ihren Weizen beruehmt war und in Syrien gelegen haben duerfte;
denn der Ortname kommt in Ebola (heute Tell Mardich, 40 km
suedlich von Aleppo) als mi-nu-ti-um schon im Jahr 2200 v.Chr.
vot. Im Ugaritischen, dessen Keilalphabet nur Konsonanten
enthaelt, erscheint dieselbe Gegend als mnt; bei Ezechiel
(27, 12) heisst in der hebraeischen Fassung die Gegend Minuit.
Wir haben es beim minoischen Wort also mit 'Weizen aus Minuit'
zu tun. Die angegebene Menge betrug wiederum 10 Mass.
In Zeile 3 lauten die ersten beiden Zeichen sa-ru. Dies
ist als scha'ru zu lesen (anstelle des Apostrophes waere ein
kleines, hochgestelltes c zu denken; FG), was Gerste bedeutet
wie im Ugaritischen, Hebraeischen, Arabischen usw. Die an-
schliessenden zwei waagrechten Striche bezeichnen als Ausgabe
20 Mass. Gerste war also minderbewerted. (...)
Summary: Hinz reads dame as a sloppy version of dachnme what
means millet, in analogy to the Hebrew dachan (Ezechiel 4, 9)
and the Arabic duchn that both mean millet. Gordon recognized
the meaning of mi-nu-te in line 2: a region that was famous
for its wheat, probably in Syria. The name already appeared
in around 2200 BC in Ebla (today Tell Marduch, 40 kilometers
south of Aleppo) as mi-nu-ti-um. In Ugaritic, a cuneiform
writing that gave only consonants, this region was mentioned
as mnt while Ezechiel (27, 17) calls it Minuit in the Hebrew
version. Hence the word mi-nu-te on tablet no. 95 from Hagia
Triada means wheat from Minuit. Again 10 measures (or about
80 - 100 liters). The word sa'ru in line 3 may be read as
sha(c)ru and mean barley, as in Ugaritic, Hebrew, Arabic and
so on. This time 20 measures (about 160 - 200 liters) what
would mean that barley was less valued than millet and wheat
- and emmer, oat and roasted corn as we shall see next time.
cir...@access.ch
cir...@access.ch
quoted again from an article by Walther Hinz on Linear A.
Sorry for two mistakes:
wrong: Minuit right: Minnit (Ezechiel) Minut (HT 95)
Here follows part 3, with an English summary and a complete
translation of tablet no. 95 from Hagia Triada. (If you read
my article via Deja, please scroll down to the end and use
the function View original Usenet format.)
(Europas erste Schrift stammt aus Kreta, von Walther Hinz)
(...)
Es folgen in Zeile 3 die Silbenzeichen ku-ni-su, was kunischu
zu lesen ist und Emmer bedeutet, auch Spelt und Dinkel genannt,
eine zweikoernige Weizenart. Die dazugehoerige Mengenangabe
findet sich zu Beginn von Zeile 4 und betraegt wieder 10 Mass.
Die anschliessenden drei Zeichen lauten di-De-ru. Das
mittlere Zeichen habe ich mit Grossbuchstaben wiedergegeben,
weil es zwar in Linear B den Lautwert de hat, nicht aber in
Linear A, wo sein Wert noch unbekannt ist. Jan Best liest
das Zeichen zu Recht als scha, so dass wir di-scha-ru erhalten.
Dies ist dasselbe wie babylonisch discharru und bedeutet Hafer.
Wieder betraegt die Menge 10 Mass.
In Zeile 4 ist das letzte Zeichen qe und gehoert zu den
beiden Silbenzeichen von Zeile 5. Dies ergibt das Wort qe-la-u,
gehoert zu babylonisch qalu und bedeutet Roestkorn. Es folgen
sieben senkrechte Striche: ein solcher Strich bezeichnet eine
Eins. Die Mengenangabe belaeuft sich also bei der Delikatesse
Roestkorn auf nur 7 Mass.
Nun kommen wir zu Rueckseite des Taefelches HT 95. Neu
ist darauf nur das erste Zeichen in Zeile 1, naemlich a. In
Zeile 2 begegnet in der Zeichnung ein Punkt zwischen eckigen
Klammern. Dieses Zeichen ist auf dem Taefelchen fast unleserlich;
wir setzen aber getrost das Zeichen Aehre ein, das auf der
Vorderseite in Zeile 1 das letzte Zeichen ist und Zerealien
bedeutet. Alles uebrige koennen aufmerksame Leser selbst
entziffern. Das erste Wort lautet a-du und ist wie da-du-ma-ta
auf der Vorderseite der Name des Empfaengers der Getreide-
zuteilungen. Zum leichteren Verstaendnis bringe ich hier aber
die Uebersetzung der Rueckseite von HT 95:
1. Adu (bekommt)
Gerste 10 (Mass);
2. Hirse 10 (Mass);
(Weizen aus) Mi-
3. nut 10 (Mass); Emmer
4. 10 (Mass); Hafer 10 (Mass);
Roest-
5. korn 10 (Mass)
Summary: ku-ni-su = ku-ni-shu = emmer. Jan Best read di-de(?)-ru
as di-sha-ru, what means oat like the Babylonian disharru; 10
measures again (one measure of grain being about 8 - 10 liters).
The syllables qe-la-u in line 4 and 5 belong to the Babylonian
qalu meaning roasted corn, a delicatessen; this time only 7
measures, indicated by seven vertical strokes. On the verso
is found only one new sign, namely an a in line 1.
Now a complete translation of tablet no. 95 from Hagia Triada:
Recto:
Dadumata (wife of Baal) (obtains) millet 10 (measures),
(wheat from) Minut 10 (measures), barley 20 (measures),
emmer 10 (measures), oat 10 (measures), roasted corn 7
(measures)
Verso:
Adu (Baal) (obtains) barley 10 (measures), millet 10
(measures), (wheat from) Minut 10 (measures, Emmer 10
(measures), oat 10 (measures), roasted corn 10 (measures)
Explanations of the name Adu (Baal) and Dadumata (loved
by Baal) follow in the next part.
cir...@access.ch
cir...@access.ch wrote:
> Now a complete translation of tablet no. 95 from Hagia Triada:
>
> Recto:
>
> Dadumata (wife of Baal) (obtains) millet 10 (measures),
> (wheat from) Minut 10 (measures), barley 20 (measures),
> emmer 10 (measures), oat 10 (measures), roasted corn 7
> (measures)
>
> Verso:
>
> Adu (Baal) (obtains) barley 10 (measures), millet 10
> (measures), (wheat from) Minut 10 (measures, Emmer 10
> (measures), oat 10 (measures), roasted corn 10 (measures)
>
> Explanations of the name Adu (Baal) and Dadumata (loved
> by Baal) follow in the next part.
Here we go. (If you read my article via Deja, please scroll
down to the end and use the function View original Usenet format.)
(Europas erste Schrift stammt aus Kreta, von Walther Hinz)
(...)
Abrechnung von Opfergaben fuer die Unterwelt
Doch wer waren diese beiden Empfaenger von Zerealien?
Bei genauerem Zusehen begegnen uns in ihnen - und das
macht das Taefelchen HT 95 zu einem einzig dastehenden
minoischen Quellenzeugnis fuer uns - zwei alte Bekannte,
naemlich die beiden fuehrenden Wesenheiten der Unterwelt!
Denn der Name a-du (...) ist Haddu zu lesen. Er begegnet
uns auch im Ugaritischen. In Mesopotamien und Elam hiess
dieser Unwetter- und Sturmgott Hadad. Er ist kein anderer
als der Baal der Kanaanaeer. Das ist in der orientalischen
Fachwelt unbestritten.
Nun zu Baals weiblichem Gegenstueck. Sie heisst auf
unserem Taefelchen Dadumata. Im Vorderglied dadu erkannte
Gordon ugaritisch dd, 'geliebt'. Das Hinterglied -mata war
bisher raetselhaft geblieben. Immerhin: im Ugaritischen
tauchte die Goettin Dadumata in Konsonantenschrift als
d-d-m-sch auf. Yigael Yadin fand 1960 auf einem hebraeischen
Siegel aus Tell Djemmeh den Namen der Goettin als d-d-y-m-sch.
Wir beobachten, dass der letzte Laut des Namens, auf unserem
Taefelchen -ta, in den beiden anderen Belegen offenbar -scha
war. Daraus ist zu folgern: das -ta in Hagia Triada ist in
Wirklichkeit ein -tha, auszusprechen wie in englisch 'thank'.
Wir erhalten so das Wort matha, und das kennen wir jetzt,
mehrfach belegt, aus den althebraeischen Inschriften auf
Steinen und an Felswaenden der suedwestlichen Sinai-Halbinsel
(...) Diese Inschriften habe ich inzwischen veroeffentlicht
in der Zeitschrift der Deutschen Morgenlaendischen Gesellschaft,
Band 141, Stuttgart 1991, Seiten 16-32. So wissen wir jetzt,
dass das semitische Wort matha 'Chef, Herr, Meister' bedeutet.
Damit verstehen wir auch den Namen Dadumatha. Er bedeutet
'geliebt vom Herrn und Meister', mit anderen Worten: von Baal.
Dadumatha ist also nur einer von vielen Namen jener weiblichen
Unterweltsgestalt, die in Kanaan als Anat erscheint (...)
Summary: The name a-du on tablet no. 95 from Hagia Triada
must be read as Haddu. We find this name also in Ugaritic.
In Mesopotamia and Elam this god of storm was called Hadad.
No one else than Baal of the Canaanites. Now for the name
Dadumata on the other side of HT 95. In dadu Cyrus H. Gordon
recognized Ugaritic dd = loved. The second part of the name,
mata, remained a riddle. Nevertheless, in Ugaritic the goddess
Dadumata appeared as d-d-m-sh. In 1960, Yigael Yadin found
the name of the goddess as d-d-y-m-sh on a Hebrew seal from
Tell Djemmeh. The last syllable -ta on HT 95 is given as -sh
in the cases d-d-m-sh and d-d-y-m-sh and must be read as -sha.
Hence the syllable -ta on HT 95 was outspoken as -tha like in
the English word 'thank'. Thus we obtain -matha, and this name
is well known from the inscriptions on stones and rocks in the
south-west part of the Sinai peninsula. Walther Hinz published
those inscriptions in the journal "Zeitschrift der Deutschen
Morgenlaendischen Gesellschaft", volume 141, Stuttgart 1991,
pages 16-32. Now the whole name reads Dadumatha and means
Loved by the Lord and Master, or simply Loved by Baal. Hence
Dadumatha was only one of many names of the goddess of the
underworld known as Anat in Canaa (...)
cir...@access.ch
cir...@access.ch
finished a series of quotes from an article by Walther Hinz
on Linear A, containing a complete translation of tablet
no. 95 from Hagia Triada:
Recto:
Dadumata (wife of Baal) (obtains) millet 10 (measures),
(wheat from) Minut 10 (measures), barley 20 (measures),
emmer 10 (measures), oat 10 (measures), roasted corn 7
(measures)
Verso:
Adu (Baal) (obtains) barley 10 (measures), millet 10
(measures), (wheat from) Minut 10 (measures, Emmer 10
(measures), oat 10 (measures), roasted corn 10 (measures)
Those who are interested in the Phaistos Disk may look up
message 4 of this thread where I speak of Derk Ohlenroth's
fine work.
While the name of a certain charlatan is mentioned over and
over again in our forum, other people like for example Eberhard
Zangger, Michael A. Ventris, Cyrus H. Gordon, Jan Best, Walther
Hinz, Derk Ohlenroth, Rainer Stadelmann, Guenter Dreyer, Jan R.
Hodder and many more who brought and bring modern archaeology
further by miles and even lightyears are hardly ever mentioned
in here - if at all.
Those who wonder where all that alienated stuff in sci.archaeology
comes from should read this very good online publication by
Franz Wegener:
http://www.intro-online.de/atlantis.html
E-mail him and ask him to publish an English translation too.
At the begin of my thread I promised to present a project
for open-minded people with a serious interest in Egyptology.
Finally, here it comes, and I make it very short. I miss this
book:
W A T E R S Y M B O L S I N A N C I E N T E G Y P T
by (your name)
with (at least) 763 illustrations
Published by the Getty Foundation (or someone else)
Thanks very much for writing it :-)
Regards Franz Gnaedinger Zurich cir...@access.ch
PS. Eberhard Zangger's geoarchaeological mission to the Troas
will officially start in September. I expect great discoveries.
Eberhard Zangger already discovered the Mycenaean harbor of
Pylos, a most ingenious system of basins and channels. Now he
hopes to find a similar harbour system in the plain of Troy.
Good luck!
cir...@access.ch
cir...@access.ch wrote:
Just keeping my thread alive ...
Next week I shall say more on water symbols in ancient Egypt,
beginning with an interpretation of the life symbol ankh.
cir...@access.ch
cir...@access.ch wrote:
> Next week I shall say more on water symbols in ancient Egypt,
> beginning with an interpretation of the life symbol ankh.
Erik Hornung on the nature of symbols (in: Idea Into Meaning,
New York 1992), quoted by Richard H. Wilkinson (in: Symbol
and Magic in Egyptian Art, Thames and Hudson, London 1994):
... a symbol is essentially polysemic (having or being
capable of several meanings) and complex: it stands for
concepts and insights that individual words in a language
can intimate but never fully capture.
(Follow some of my ideas)
The life symbol ankh may be seen as a combination of 3 signs:
- a female figure, the heavenly mother goddess (Nut)
- a vessel turned upside down, with a jet of water falling
out (Isis)
- a ribbon with the sacred knot, worn around the head,
neck or waist (Nephtys)
Nut, Isis and Nephtys may be understood as one single woman:
Nut - body, organic life, giving birth, unconscious life,
its resources and healing powers
Isis and Nephtys - limbs (arms and hands, wings, legs and
feet), doing, healing by means of medecines, feeling and
magic (Isis), reasoning and judging (Nephtys, Seshat, Maat)
Nut and her daughters Isis and Nephtys are mentioned on a stone
sarcophages: Nut in the middle, Isis and Nephtys on her sides.
In a papyrus of the New Kingdom, the swollen sail of a ship
was called Nut while the ropes were called Isis and Nephtys.
When Isis and Nephtys appear as a symmetrical couple, her
mother may be present invisibly between them, giving birth to
Re-Osiris ... (have a look at the beautiful painting of Isis,
Nephtys and Re-Osiris in the shape of a standing mummy with
the head of a ram and the solar disk on his horns in the tomb
of Nefertari, Valley of the Queens, Thebes). In another papyrus
of the New Kingdom, the pylon towers of a temple are called
Isis and Nephtys - hence the high and narrow entrance between
the towers may symbolize Nut. According to Erik Hornung the
Egyptian temple was a representation of the cosmos. Now if
the entrance was a symbol of Nut, passing it would have been
a symbolical birth ... The last days of the year have been
called Isis and Nephtys. If we see them as a pylon of time,
Nut may be present again, giving birth to a new year ...
(When Isis and Nephtys are shown from the front and near by
each other their body lines may even evoke the negative form
of a third women in between.)
Every goddess was an emanation of the primeval goddess.
A goddess could turn into any other one and be her alter ego,
her friend, sister, mother, and so on. According to Pyramid
Text 616a-c, Seshat was an alter ego of Nephtys. Furthermore,
there are several parallels between Seshat and Maat (both
women stood in a relation with Thoth, and both played a most
important role in temple building) while Maat was often shown
as a couple of women resembling the one of Isis and Nephtys
(dual Maat: one in the world, one in the beyond; according
to Erik Hornung).
Now for the water symbols:
Nut was carrying a vessel on her head (her hieroglyph) while
Isis was represented by a vessel carried ahead of the annual
procession in honor of her husband Osiris (Plutarch, Moralia,
De Iside et Osiride).
Isis released the annual flood of the river Nile, together
with Anukis (goddess of the cataracts and a friend of Nephtys),
Satis, Sothis (who replaced Satis and was herself replaced by
Isis), and Neith.
Ankh means life. Water means life too, especially in a dry land
like Egypt.
The word ankh also means mirror - the first mirror certainly
was a quiet pond or well.
The water poured over a person was often depicted as lined up
ankh signs what might be read as follows: May the honored and
blessed person be born again (many times), and may he or she
have many children and children's children ...
As Erik Hornung said so well:
a symbol is essentially polysemic and complex
Regards Franz Gnaedinger Zurich cir...@access.ch
cir...@access.ch
cir...@access.ch wrote:
on the life symbol ankh. Follows my interpretation of a bird
goddess in the Egyptian Museum of Turin.
The brid goddess was omnipresent in the neolithic times,
in Europe (see: Marija Gimbutas, The Language of the Goddess,
HarperCollins, San Francisco 1989) and in ancient Egypt as well,
see for example the most elegant figurines that have been found
at El-Mamariya by Henri de Morgan in 1906-7 (Brooklyn Museum;
a photograph of a still undamaged figure is shown in: Christiane
Desroches Noblecourt, La femme aux temps des Pharaons, Stock/
Laurence Pernoud, Paris 1986). A fine collection of predynastic
objects is kept at the Egyptian Museum of Turin; see:
Egyptian Museum of Turin; Egyptian Civilization,
Egyptian Beliefs; Electa Spa, Milan 1988
On page 32 is shown a clay figurine from the end of Naqada I
Period or the beginning of Naqada II Period: a stylized sitting
woman with the head of a bird. The material, unbaked clay or
simply earth, may mean that her body represents the Earth while
her bird head on a long neck may represent heavens. Her eyes
are black: this may mean that she symbolizes night and death;
yet the black eyes are surrounded by malachite, a green mineral
that was a symbol for rebirth (color of the growing plant;
the round forms of that mineral might also remind of a pregant
woman and paleolithic figurines like the one from Lespugue).
All over the woman's womb are painted small ars - tombs?
a cemetary? A black form on the left side below the arcs may
symbolize a lake or a part of the river Nile and the amniotic
fluid as well while there are fish painted on her breasts. On
her back are painted leaves (below) and antelops (shoulders);
this would mean again that her body is a symbol of the earth
while her bird head would be a symbol of the air - all in all
an early 'Gaia' ...
May I recommend a book of biology?
Lynn Margulis and Dorion Sagan (son of Lynn Margulis
and Carl Sagan), What is life? Preface by Niles Eldrege;
Simon and Schuster, New York 1995
You wonder why I recommend such a book when I speak of
a predynastic Egyptian figurine? You will find out ...
cir...@access.ch
cir...@access.ch wrote:
on a predynastic Egyptian 'Gaia'
Five years ago I had the luck to see a pair of Kykladic violin
idols of shining white marble with perfectly round heads, and
I was kindly allowed to make contour drawings of them.
Violin idols are stylized figurines and may symbolize
the cosmic mother goddess:
round body --- fertile inner of the Earth
round shoulders, meaning arms and breasts --- surface
of the Earth, whereupon we live and work (arms) and find
our food (nourishing breasts)
round head of shining white marble --- moon, sun, heaven
(straight head --- air, light, height, heaven)
This would go along with the bird goddess of predynastic Egypt:
lower part of the body, often in the shape of a carrot
--- fertile inner of the Earth
upper part of the body, streched out arms or raised arms,
breasts --- Nile Valley, where people lived and worked
(arms) and found their food (nourishing breasts); eastern
mountain and western mountain (raised arms); stars, rising
above the eastern horizon and sinking down on the western
horizon and rising again above the eastern horizon, thus
being a symbol of life, death and rebirth (hands; compare
the five fingers with the five rays of an Egyptian star)
head of a bird --- air, heaven; one eye the moon,
one eye the sun
cir...@access.ch
cir...@access.ch wrote:
on a pair of Kykladic violin idols, and again on the predynastic
Egyptian bird goddess
In the Brooklyn Museum are kept two elegant female figurines
from El-Mamariya (Naqada IIa period, around 3600 BM, before
Mary; excavations of Henri de Morgan, 1906-7; terra-cotta,
height over 30 centimeters; one figurine with broken arms,
the other one with broken fingers; a photograph of the still
undamaged second figurine is found in: Christiane Desroches
Noblecourt, La femme aux temps des Pharaons, Stock / Laurence
Pernoud, Paris 1986).
The white lower part of the body in a carrot-like shape may
once have stuck in the ground and been a symbol of the fertile
inner of the Earth, while the red upper part of the body may
have been a symbol of the Nile Valley where people lived (red,
color of blood, symbol of life, compare with the Isis Blood)
and worked (arms) and found their food (nourishing breasts).
The raised arms may symbolize the eastern mountain and the
western mountain while the hands may symbolize the stars that
rise above the eastern horizon, set on the western horizon
and appear again on the eastern horizon, thus being a symbol
of birth, death and rebirth (five fingers, five rays of an
Egyptian star). The bird head on a long neck in the circle
of the raised arms may symbolize heavens, the (invisible)
eyes could mean moon and sun ...
The figurine might have shown a telling phase of a hypothetical
rite of evocation - a speech of the mother goddess to a child
that shall soon be born (or born again):
Hands on the womb --- My dear child ...
hands on the breasts --- may the plants grow that shall
nourish you, may there be fish aplenty (see the Egyptian
'Gaia'), may there be food for you in all your life ...
hands on the head, fingertips touching the parting ---
my thoughts are with you ...
arms raised, forming a closed circle --- you are still
in my womb; you are still in the womb of the woman who shall
give birth to you ...
opening the circle of the arms and spreading the fingers
--- soon you shall be born (born again); for you I shall
open the World Egg again, divide the Primeval Mountain again,
as I did a long time ago - shove apart the eastern mountain
and the western mountain and thus create the Nile Valley and
adorn it with a blue sky, a warming sun, a lovely moon and
a myriad of twinkling stars ... for you I shall create again
the numbers 2, 3, 4 and 5, and the numbers 6, 7, 8, 9 and
10 as well, hence the multitude of things, for nothing shall
lack in your life and world ...
Pietro Mario Puddu-Collu
regards,
Piermario
cir...@access.ch
cir...@access.ch wrote:
on the figurines from El-Mamariya
Do you remember the hypothetical rite of evocation?
All its phases are found in figurines from predynastic Egypt
and other regions of the Mediterranean, especially in figurines
from Anatolia and Crete. I asked a pretty woman to perform that
rite of evocation, of calling into life. She did it very well,
really beautifully, with fluent gestures that came naturally.
It was a great pleasure to see her performance.
Hereupon I asked another woman, a professinal ceramist,
to make a terra-cotta copy of a figurine from El-Mamariya.
Her second trial succeeded. She made a pretty (even humorous)
figurine that is now standing on my window-sill where I look
at her from time to time, and I can tell you that her gesture
really is of an evocative type (not mourning, as one can often
read).
How do the El-Mamariya figurines look when stuck into the ground?
I made drawings, both on paper and on a PC (with the help of
a friend, as I am a computer moron). They look great, monumental.
So I could imagine that the figurines from El-Mamariya are small
size copies of a some five meters high statue: a temporary statue
of the upper part of her body (while the lower part of her body,
symbol of the fertile inner of the Earth, was supposed to stuck
in the ground) - built for a special feast say in early March,
perhaps on an isle in Upper Egypt, for example El-Gebelein.
One would have made a wooden construction, filled it with hay,
wrapped it with linen, covered the linen with clay and painted
the hardened clay with a mixture of water, red ochre, milk and
blood. However, it would have been a temporary statue only.
(Clay figures of a god or a goddess are still made in India
for a certain feast, carried around in processions, and put
into the Ganges when the holy days are over.)
A green shist palette, 15.5 centimeters high, from around
3000 BM, found at El-Gerse / Faiyum, kept in the Egyptian
Museum Cairo, shows the head of a cow that resembles the
figurines from El-Mamariya when stuck into the ground:
head of the cow --- upper part of the female body
star on the cow's head --- bird-head of the figurine
star decorated eyes --- breasts
horns --- raised arms
ending in stars (five rays) --- hands (five fingers)
For the symbolical meaning of the bucranium see:
Marija Gimbutas, The Language of the Goddess,
HarperCollins, San Francisco 1989
Regards Franz Gnaedinger Zurich cir...@access.ch
Sent via Deja.com http://www.deja.com/
Before you buy.
marci...@my-deja.com
> cir...@access.ch wrote:
> on a pair of Kykladic violin idols, and again on the predynastic
> Egyptian bird goddess
>
> In the Brooklyn Museum are kept two elegant female figurines
> from El-Mamariya (Naqada IIa period, around 3600 BM, before
> Mary; excavations of Henri de Morgan, 1906-7; terra-cotta,
> height over 30 centimeters; one figurine with broken arms,
> the other one with broken fingers; a photograph of the still
> undamaged second figurine is found in: Christiane Desroches
> Noblecourt, La femme aux temps des Pharaons, Stock / Laurence
> Pernoud, Paris 1986).
>
As usual I follow your lessons in "My Corner" and learn a lot.
This is the second time I see you date chronology that way. The first one was
in your 'my fairy tale' and there you used "before Myriam". I hope I am sure
in this citation and apologize previously any error. In an Internet world and
politically correct world scholars are using BCE as Before Current Era, a
substitute to the classical Before Christ.
I ask you to inform what do you intend doing that. It presumes you follow one
line of thinking, that is mine, that the line of generation until Jesus comes
through Myriam that should be of David's house to marry a man of that house.
Well, this is not sci.archaeology( here I am advancing the remark that Lloyd
Bogart will do ) but it is something that matter to me and some people like
me that search truth. And in that search your opinion is a valuable one.
Regards, Marcio
cir...@access.ch
marci...@my-deja.com wrote:
> As usual I follow your lessons in "My Corner" and learn a lot.
>
> This is the second time I see you date chronology that way.
> The first one was in your 'my fairy tale' and there you used
> "before Myriam". I hope I am sure in this citation and apologize
> previously any error. In an Internet world and politically correct
> world scholars are using BCE as Before Current Era, a substitute
> to the classical Before Christ.
>
> I ask you to inform what do you intend doing that. It presumes
> you follow one line of thinking, that is mine, that the line
> of generation until Jesus comes through Myriam that should be
> of David's house to marry a man of that house. Well, this is
> not sci.archaeology( here I am advancing the remark that Lloyd
> Bogart will do ) but it is something that matter to me and some
> people like me that search truth. And in that search your opinion
> is a valuable one.
>
> Regards, Marcio
Hi Marcio,
thank you for the reply. BM means before Mary, instead of BC,
before Christ. I use the version BM when speaking of predynastic
Egyptian figurines, and of women's manyfold contributions to the
rise of civilization in general. You know, the dogma of classical
archaeology says that civilization including real science, real
mathematics, real philosophy, real historiography and so on was
founded by a handful of male Greeks --- outer-European peoples
didn't contribute anything really noteworthy, let alone women ...
I call this dogma the Greek phantasma. It ain't any better than
the alien / Atlantian phantasma of kooky archaeology.
Something is irritating me. Deja is changing the interface again.
The search field on the homepage is getting smaller and shorter,
and now they introduce the messy format also in Deja Classics.
Do they read the messages? Don't they see how messy the lay-out
is? Some lines are short, others half a meter long!
In my opinion, they should place a field on top that says:
a) I wish to publish my message and read the other messages
in the ASCII format
b) I don't care about the format
and then you can choose.
What do you think about that? Any hint or tip?
Many thanks in advance.
Regards Franz Gnaedinger Zurich cir...@access.ch
cir...@access.ch
cir...@access.ch wrote: ...
(If you read my post via Deja, please scroll down to the end
and use the function View original Usenet format or Text
only)
The heavenly mother goddess Nut carried a jar on her head.
She might well have been the successor of the predynastic
mother goddess. Many predynastic vessels show anthropomorphic
forms (female breasts, female body), and there are several
predynastic female figurines carrying a jar on the head ...
Osiris was the symbol of the River Nile. However, the annual
rise of the Nile was released by women: Anukis, Satis, Sothis,
Isis, Neith. Ahead of the annual procession in honor of Osiris
was carried a vessel filled with water - a symbol of Isis.
The popular Nile god Hapi was a man with female breasts while
Isis made a wooden phallus for her husband Osiris ...
Osiris was also present in the magnificient constellation
of Orion. Yet in a line of the Book of the Dead Pharaoh says
(German translation by Erik Hornung):
Ich bin der grosse weibliche Orion
I am the great female Orion
The predynastic goddess might well have carried a round gourd
on her head (water of life, symbol of her womb, symbol of the
Nile as well) while the crowns of the first Pharaohs (e.g. the
one of Narmer on his famous palette) are perfectly symmetrical
and remind of a gourd in the shape of a cone (a phallic form
this time, making Pharaoh the new Lord of the Nile).
May a popular book on ancient Egypt gives the impression that
the splendour of Pharaonic Egypt rose virtually out of nothing.
I believe that much of it was prefigurated in predynastic times.
Bringing into cultivation the Nile Valley was a demanding task,
and much of the work must have been done by women. I could well
imagine that the first Nilometer, a simple pole in the water,
and the first shaduf have been invented by the priestesses
of the cosmic mother goddess and their helpers: an invention
that was remembered in the episode of Isis making a wooden
phallus for her husband Osiris, symbol of the River Nile ...
To explain just one of the strangest episodes in the legend
of Isis and Osiris.
If you are interested in my view of early Egypt you may look
up my threads
A Fairy Tale (6 parts)
Continuation of my Fairy Tale (11+ parts)
to be found via Deja (link below). My fairy tale begins with
a hypothetical myth of creation based on several figurines and
is followed by a both geographical and historical interpretation
of the legend of Isis and Osiris. Presenting a historical thesis
in the form of a story or even a fairy tale has many advantages:
- the form of a fairy tale is so to speak an overall
conjunctive, allowing you to let go dry formulations
such as: let us assume that, it might well be that,
and so on
- telling a story or a fairy tale is the easiest way
to formulate and present a historical thesis: you can
easily see where something is missing, you can sketch
a most complex situation with a few words, you can say
more with less lines, and you can easily smooth out your
thesis while the gaps become obvious and invite your
phantasy to fill them with a new idea that may already
be waiting somewhere in your mind
- the human brain likes following the arrow of time
(my own experience, and recently proved by means
of a physiological experiment)
- telling a story or a fairy tale is fun
- it enables you to read and understand (better) an ancient
myth or legend and reveal it's rational and historical core
marci...@my-deja.com
> What do you think about that? Any hint or tip?
>
> Many thanks in advance.
>
Hi Franz.
I agree with your proposal. At Deja.com they have the power to do the
things the better possible to attend the participants. This is a very
important place to collect the information people have on different
fields of knowledge and it is a site that is reference to many serious
scholars.
May be the owners of Deja.com do not know the value of the ng they
manage.
I hope they will care of that important place in Internet.
Regards, Marcio
cir...@access.ch
marci...@my-deja.com wrote:
> I agree with your proposal. At Deja.com they have the power
> to do the things the better possible to attend the participants.
> This is a very important place to collect the information people
> have on different fields of knowledge and it is a site that is >
> reference to many serious scholars.
>
> May be the owners of Deja.com do not know the value of the ng
> they manage.
>
> I hope they will care of that important place in Internet.
>
> Regards, Marcio
Some projects for young, open-minded Egyptologists:
A book I would love to read:
WATER SYMBOLS IN ANCIENT EGYPT
by ............ (your name?)
729 pages, richly illustrated
Getty Publications, Malibu 2006
Geoarchaeology in the Nile Valley:
Eberhard Zangger should be back from Troy by now, hopefully
with a positive result (I will tell you more as soon as I get
some informations). His geoarchaeological expedition costs him
several hundred thousand Swiss francs. A lot of money for him
- nothing for the Getty Foundation that is obliged to spend
400 million dollars every year. If Eberhard Zangger's mission
turns out to be successful, the Gettys might finance a similar
expedition to the Nile Valley. Here is what they might look for:
plain of Abydos - covered remains of a parallel Nile
digged between 3300 and 3100 BDE? (see my fairy tale)
western desert, from Al-Lisht towards Qasr as-Sagha,
corresponding to the h-channel (ecliptic) in the Orion
scheme - remains of a building, a village, a road?
Nile Valley on the height of Abusir, corresponding to
Betelgeuze in the Orion scheme - remains of a building,
perhaps a harbour?
Nile Valley on the height of Abu Rawash, corresponding
to Saiph in the Orion scheme - remains of a building,
perhaps a harbour?
Giza:
If there is a hidden chamber in the Great Pyramid at Giza
it may lie in the vertical axis on a height of 173 royal
cubits or about 90.6 meters above the base. Measurements
of the hypothetical chamber:
ideal length 20 Horus cubits or 666.4 centimeters
ideal width 16 Horus cubits or 533.12 centimeters
lateral height 12 Horus cubits or 399.84 centimeters
central height 15 Horus cubits or 499.8 centimeters
It would be the SUN CHAMBER wherein the soul of the deified
king is raised as the sun child. A statue showing the young
Pharaoh might be 7 Horus cubits or 233.24 centimeters tall.
In my opinion the Gantenbrink chamber ain't a room but some
kind of a limestone sarcophagus containing a statue of Khufu
as Wenefer-Osiris facing the rise of Sirius and Orion. The
hypothetical statue may have the same ideal length of 7 Horus
cubits or 233.24 centimeters.
1 royal cubit = 7 palms = 28 fingers or 52.36 cm
1 Horus cubit = 7/11 royal cubits or 33.32 cm
(By combining the royal cubit with the hypothetical Horus cubit
one can solve a few demanding geometrical problems in a fairly
simple and amazingly exact way, for example the calculations
of the circle, sphere and square.)
Preview:
In my next post I shall speak of a rock painting in the Sahara,
namely of the Dame Blanche at In Aouanrhat on the Tassili n'Ajjer
(above the oasis Djanet in south-east Algier).
Then will follow a series of posts on a missing link between
Egyptian, Greek and Roman antiquity and the Italian Renaissance
(Leonardo Bigollo Pisano, Giacomo da Lentini, Francesco Petrarca,
Dante Alighieri).
Regards Franz Gnaedinger Zurich cir...@access.ch
cir...@access.ch
cir...@access.ch wrote:
> In my next post I shall speak of a rock painting in the Sahara,
> namely of the Dame Blanche at In Aouanrhat on the Tassili n'Ajjer
> (above the oasis Djanet in south-east Algier).
I imagine:
Around 1700 BM (before Mary) a princess from Upper Egypt,
her lover and her followers left the Nile Valley and wandered
from oasis to oasis until they finally arrived at the oasis
Djanet in the central Sahara, a well known oasis in a valley
between the Tassili n'Ajjer and the Al Hoggar. They have been
warmly welcomed, for they were jolly people who loved dancing,
blowing the flute, and brought with them seeds from the Nile
Valley that grew very well in the Saharian oases. They lived
happily, had many children, teached the locals, have been
teached by them in turn, and combined the Saharian rain goddess
with the Egyptian goddesses Hathor and Nut. Sometimes life was
hard: when the rain-clouds failed to appear. On such times
a young man climbed up to the plateau of the Tassili n'Ajjer,
took place on a long stone in the shape of a fish on the rim
of the plateau, high above the valley, and blew a melody on
a long flute, or on a round horn, thus calling the rain goddess
whose wide horns of the heavenly cow were filled with rain drops:
rain drops that will fall into the plain, become grains, sprout,
sway in the wind, bear new grains, be earned and nourish everyone
in the valley below ... And when the melody was nice and pleasing
the heavenly goddess came running by, on swift feet, with long
and easy steps, more flying than running, swinging her arms,
then bend forwards, emptying her delicious freight, waning as
the rain fell down, turn around, becoming smaller and smaller,
an almost empty cloud by now, leaving the place with a rainbow
above her round head. - This happy event was performed as a
rain-dance down in the valley, and again the same lovely scene
was painted in an 'abris' on the Tassili n'Ajjer, namely at
In Aouanrhat (I-n-Aouanghat) near Jabbarene ...
Archaeology is not an exact science but a speculative one
- a science of imagination Gael de Cuichen
You can find a complete drawing after the 'Dame Blanche' for
example in this fine book:
Umberto Sansoni, LE PIU ANTICHE PITTURE DEL SAHARA,
L'arte nelle teste rotonde; Jaca Book, Milano 1994
Most books show only the main figure. - Be careful, do not
believe the very high ages given in many books (also by Sansoni).
The paintings on the Tassili n'Ajjer are much younger. The phase
of the round heads begun roughly at 4000 BC instead of around
8000 BC (numbers from my memory, might be wrong). The painting
in question belongs to the final phase of the round heads, was
created under an Egyptian influence and may date from around
1600 BC (no guarantee for any number; there are still many open
questions, but I hope to raise a little interest for an amiable
rock painting in the central Sahara.)
cir...@access.ch
cir...@access.ch wrote:
on a rock painting in the Sahara. Now for:
A missing link between antiquity and Renaissance? (part 1)
I found geometry in Renaissance art (Piero della Francesca,
Leonardo da Vinci, Raphael ...), in ancient Greece (kouros from
Tenea, Getty kouros, Kroisos from Anavyssos, Poseidon from Cape
Artemision ...) and in ancient Egypt (pyramids, Rhind Mathematical
Papyrus; see my publications in sci.archaeology) - but I missed
a link between antiquity and Renaissance.
Then, early in the summer of this year, I got a kind letter
from professor Wilhelm Poetters (University of Wuerzburg,
Germany) and a couple of his publications:
Wilhelm Poetters, LA NATURA E L'ORIGINE DEL SONETTO,
UNA NUOVA TEORIA, Firenze, Leo S. Olschki Editore, 1983
Wilhelm Poetters, WER WAR LAURA? Versuch einer Identifi-
zierung der namentlich bekannten Unbekannten in Petrarcas
Liebesdichtung; MISCELLANEA MEDIAEVALIA, Veroeffentlichungen
des Thomas-Instituts der Universitaet zu Koeln, Herausgegeben
von ALbert Zimmermann; Band 16/2, Mensura, Mass, Zahl, Zahlen-
symbolik im Mittelalter; Walter de Gruyter, Berlin New York
1984
Wilhelm Poetters, "Un cinquecento dieci e cinque" (Dante,
Purgatorio 33, 43), Der Name des Boten Gottes als Problem
der Wortbildung und der poetischen Kosmologie; LATINITAS
ET ROMANITAS, Festschrift fuer Hans Dieter Bock zum 65.
Geburtstag, herausgegeben von Annegret Bollee und Johannes
Kramer, Romanistischer Verlag Bonn 1997
Wilhelm Poetters, NASCITA DEL SONETTO, Metrica a matematica
al tempo di Federico II; Presentazione di Furio Brugnolo,
Longo Editore Ravenna 1998
Wilhelm Poetters proposes a highly interesting thesis,
namely that the medieval
DEUS ES SPHAERA (God is a sphere)
inspired Giacomo da Lentini's invention of the sonnet, Francesco
Petrarca's Canzoniere, and Dante Alighieri's Divina Commedia.
Please imagine a circle of the radius 7 units and the diameter
14 units. Let us calculate the area of this circle by means of
the approximate value 22/7 for pi and then transform the area
into a rectangle:
7 x 7 x 22/7 = 154 = 14 x 11
A circle whose diameter measures 14 units and a rectangle
that measures 14 units x 11 units have practically the same
area. Now Wilhelm Poetters proposes that this calculation was
the very origin of the sonnet which counts 14 'endecasillabi'
- 14 lines of 11 syllables each (spoken syllables, not written
ones). An example. The sonnet MOLTI AMADORI LA LOR MALATIA by
Giacomo da Lentini (who most probably invented this lyric form):
Molti amadori la lor malatia
portano in core, che'n vista non pare;
ed io non posso si celar la mia
ch'ella non paia per lo mio penare:
pero che son sotto altrui segnoria,
ne di meve nonn-o neiente a.ffare,
se non quanto madonna mia voria,
ch'ella mi pote morte e vita dara.
Su'e lo core e suo son tutto quanto,
e chi non a consiglio da suo core
non vive infra la gente come deve;
cad io non sono mio ne piu ne tanto
se non quanto madonna e de mi fore
ed uno poco di spirito e 'n meve.
1 2 3 4 5 6 7 8 9 10 11
Mol- ti a- ma- do- ri la lor ma- la- ti- a
por- ta- no in co- re che'n vi- sta non pa- re
e- d io non pos- so si ce- lar la mi- a
ch'el-la non pa- ia per lo mio pe- na- re
pe- ro che son sot- to al-trui se- gno- ri- a
ne di me- ve non- n-o ne- ien- te a.f-fa- re
se non quan- to ma- don- na mia vo- ri- a
ch'el-la mi po- te mor- te e vi- ta da- re
Su' e lo co- re e suo son tut- to quan- to
e chi non a con- si- glio da suo co- re
non vi- ve in-fra la gen- te co- me de- ve
ca d io non so- no mio ne piu ne tan- to
se non quan- to ma- don- na e de mi fo- re
ed u- no po- co di spi- ri to e'n me- ve
(To be continued)
Steve Whittet
>
>In article <7t4g1j$d5p$1...@nnrp1.deja.com>,
> cir...@access.ch wrote:
>on a rock painting in the Sahara. Now for:
>
>
>...Wilhelm Poetters proposes a highly interesting thesis,
>namely that the medieval
>
> DEUS ES SPHAERA (God is a sphere)
>
>inspired Giacomo da Lentini's invention of the sonnet, Francesco
>Petrarca's Canzoniere, and Dante Alighieri's Divina Commedia.
>
>Please imagine a circle of the radius 7 units and the diameter
>14 units. Let us calculate the area of this circle by means of
>the approximate value 22/7 for pi and then transform the area
>into a rectangle:
>
> 7 x 7 x 22/7 = 154 = 14 x 11
>
>A circle whose diameter measures 14 units and a rectangle
>that measures 14 units x 11 units have practically the same
>
>(To be continued)
The 14:11 proportion is indeed interesting from the perspective
of practical reckoning and pleasing proportions. Call it alpha.
If you inscribe a circle in a square the ratio of their
relative circumferences can be taken as alpha
Given a circle whose circumference is equal to the perimeter of a square
the circles diameter can be taken as alpha x the side of the square
If you use this alpha ratio for the sides of 2 cubes the volume of the larger
can be taken as double that of the smaller.
It seems to be connected to the fibonicci series and Phi.
in that 2/alpha can be taken as a rough aproximation to phi
There are probably many more such relations and an
easy explanation.
>
>Regards Franz Gnaedinger Zurich cir...@access.ch
regards,
steve
cir...@access.ch
whi...@shore.net (Steve Whittet) wrote:
(on the numerical scheme of the sonnet:)
> There are probably many more such relations and an
> easy explanation.
Professor Gerhard Goebel (Institute of Romance Languages and
Literature, Goethe University, Frankfurt am Main) says much
the same. In a recension of Wilhelm Poetters' book NASCITA
DEL SONETTO Goebel wrote that the scheme of the sonnet is
over-determined (ueberdeterminiert) what may be the reason
of its longevity.
(If you read my post via Deja, please scroll down to the end
and use the function View original Usenet format / text only)
A missing link between antiquity and Renaissance? (part 2)
In the first part I gave a short summary of Wilhelm Poetters'
thesis on the nature and origin of the sonnet. Now for Francesco
Petrarca's Canziere. Who is Laura? Who is that unreachable woman?
By examining both Laura's attributes and the numerical structure
of the Canziere, Wilhelm Poetters came to this conclusion:
LAURA - laverta - Donna Veritas - an unreachable woman
- the unreachable truth - symbolized by the number pi
Wilhelm Poetters found similar and even more complex ideas
in Dante Alighieri's Divina Commedia and these (and a few
more) key numbers:
3 and 9 (symbols of totality)
10 (Plato's perfect number)
100, 1000, 10000, 100000 (powers of 10)
7 or 14 and 11 (numbers of the sonnet)
'un cinquecento diece e cinque' = 515 (divine messenger)
61 (a complementary number to 515; according to Gerhard
Goebel the number of the 60 virgins plus Beatrice)
1510010500000 (un cinque cento diece cinque x 100,000)
Wilhelm Poetters multiplies the number 515 (divine messenger)
by the number 61 (60 virgins plus Beatrice) and obtains
515 x 61 = 31415
Hereupon he divides the product by a power of 10 and obtains
a very fine approximate value of pi:
515 x 61 / 100 x 100 = 31415 / 10000 = 3.1415
Now for the number 1510010500000, which, according to Wilhelm
Poetters, would represent the volume of a sphere whose diameter
measures about 14334.005 units while the Divina Commedia counts
14233 lines. If Dante's work is the symbol for the human world
the number 14233 may stay for the universe in which we live,
whereas the number 14234.005 may symbolize the divine sphere
around the universe: the first layer of the 'Empirio' where
the divine messenger will come from ...
In a second letter professor Wilhelm Poetters invited me
to help him with a mathematical problem regarding Dante's
Divina Commedia. So I had a closer look at his key numbers.