Re: Strange Maths (was Re: Why not 13 months?)

Whittet (
23 Jul 1995 23:20:19 GMT

In article <>, says...
>In article <3urtmj$> (Whittet) writes:
>>I want you to think of this in terms of what an Egyptian of the 4th Dynasty
>>has to work with. The wheel hasn't been introduced to Egypt, what you are
>>looking at is an artifact of a people to whom accuracy in measurement was
>>sacred. It was what was right and proper and expected.
>You challenged someone to explain 51d51'. Doing so is my only personal
>interest in the thread at the moment. Now you say my explanation can't
>work, because the wheel hasn't been introduced to Egypt. This is
>just wrong. It is true that they do not have the chariot nor the
>wheeled cart as used for transportation. However, predynastic pottery was
>made on a potter's wheel. Children's toys of the era have wheels. Temples
>have columns constructed from cylindrical blocks, which surely were rolled
>into place, and could all by themselves have been used as a rolling
>measurement device. They had the wheel, alright.

cites Doug?

1.) prehistoric pottery made on a potters wheel: In the first three Dynasties
most bowls, vases, plates, cubs and jars seem to be laboriously carved by hand
out of stone. I have seen an example of a potters wheel from Lachisi, Israel
dated 2,200 BC and there is amodel of a woman working a pot on a disk from
Egypt dated to the New Kingdom.

"It is not always possible to determine where theseinnovations were first used.
In Mesopotamia, Egypt, China and the Indus Valley the pivoted tournette appeared
relatively early around the end of the fourth millenium BC. The tournette was a
small wheel which improved pottery making but did not rotate with sufficient
speed to make full use of the centrifugal forces which were harnessed by the
later fast wheel."

The Times Atlas of Archaeology, Hammond, Maplewood NJ, 1988 p.101
"Development of the potters wheel"

At any rate, prior to the 4th Dynasty, I will give you the wheel in the form
of the tournette, but not the axle to make it turn,

2.) childrens toys or models with wheels:
Model of a chariot; copper, Tel Agrin; 2,700BC - Model of a cart 2,500BC Harrapa
Ugarit 1,400 BC
Nothing in Egypt prior to the fourth Dynasty to my knowledge

3.) cylindrical columns

I don't know of many examples of columns that early, let alone round ones. The
Mastabah construction which preceeded the pyramids was all pilasters. In Dzosers
complex there are rows of ribbed engaged columns in the processional hall but
they are all tied back into the wall; In Cheprens valley temple there are square
piers, you lose on this one.
>So your rebuttal is wrong, and the 51d51' angle is perfectly understandable.

Doug, even if the wheel had been in use, it would not have been used for
making measurements for buildings. For one thing, the Pi relationship in the
pyramid is between the perimeter of the pyramid and twice its height.
The relationship is indirect. Secondly, as I have tried to point out, the
blocks were measured and cut off site. Third, the coursing is at a ratio
of about 14:11 to the height, so there is no linear or systematic relation
between the height of the courses which is about 30", but varies to more than
3 feet, and the slope. The relationship is not quite so simple as it looks.

>As for your comments about Maat and its implications as to their
>worship of measurement, I think that this is merely misleading,
>for one thing because it incorrectly emphasizes the role of
>measurement in Maat, which is a far wider and deeper concept than
>that in their culture, and for another because it causes you to digress
>away from perfectly ordinary construction techniques.

Maat is absolutely integral to the Egyptians approach to accuracy in measures,
and yes it is far wider and deeper:

E.A. Wallis Budge. "The Gods of the Egyptians", studies in Egyptian Mythology,
in two volumes, Dover Publications, Inc., New York; the Dover version,
(available in paperback from any of the bookstores in Harvard Square),
is a 1969 reprint of the origional, first published in the US by the
Open Court Publishing Co., in 1904- there are other source but most seem
to refer back to here.

direct citations to Maa't are i: 20, 80, 153, 323, 338, 339, 346, 352, 370,
416-420, 432, 433, 501, 502; ii:5, 10, 11, 13, 19, 26, 75, 145, 184, 256, 33

also mentioned:Maa't - boat of, feather of, goddesses of, lords of,
assessors of, pedestal of

vol1, page 416-420 is the place to start

"Closely associated with Thoth"... (Thoth, the scribe, is associated with reading,
writing and 'rithmatic; wisdom in general; philosophy and mathematics in particular)...

"About the meaning of the word maa't {hieroglyphic} there is fortunately no
difficulty, for from many passages in texts of all periods we learn that it
indicated primarily 'that which is straight', and it was probably the name
which was given to the insument by which the work of the handicraftsman of
every kind was kept straight; as far as we can see the same ideas which were
attached to the Greek word {kav'wv} which first of all seems to have meant any
straight rod used to keep things straight, then a rule used by masons, and
finally, metaphorically, a rule, or law, or canon, by which the lives of men
and their actions were kept straight or governed, belong to the Egyptian word
Maa't. The Egyptians used the word in a physical and a moral sense, an thus it
came to mean 'right, true, truth, real, genuine, upright, righteous, steadfast,
unalterable,' etc;

"The goddess Maa't was, then the personification of physical and moral law,
and order and truth"

"As a moral power, Maa't was the greatest of the godesses"...

her feather symbolises truth
the base she stands on symbolises accuracy in measurement
truth is therefore measured, weighed and judged

you may see some correlation here to the Dialogs, keep in mind the
associations to Egypt with the progression Solon, Thales, Pythagoras,
(various other pre-socratics) Socretes, Plato...

The goddess Diatoma, I don't know if you could carry it far enough to
see each dialog as examiningthe aspects of Maa't one by one, and using them
to build a set of standards with which you can measure, weigh and judge,
but it is a definite theme.

Let me know if you have any thoughts on this

>>I don't want glib thoughtless solutions that spin wheels. If you think all
>>the answers are in some book, or a TV program you can watch for 15 minutes
>>and understand the marvelous sophistication this building incorporates in
>>its proportions, you must be tuned to a channel I don't get yet.
>I do not think that the construction of the pyramids was in any
>sense trivial, and that is why my interest in this debate is focussed;
>if I addressed every issue you raised, we could be at this for years.
>I think it suffices for me to pick one of your points and illustrate
>that you are under-informed and wrong, and that's what I've done.

It would perhaps help if you gave some cites for your opinions Doug,
now, I an not an archaeologist, just an architect, but I do have a
long standing interest in this particular area. If you can't address
all of the issues I raise it may be because, like many young people,
you like to skim the surface of an idea and then float on by...
>Besides, I'm addressing this from sci.physics, and the 51d51' angle
>is the only aspect of this thread that remotely justifies a crossposting

Ok, what is being discussed is the architecture; to include the structural
engineering, and general level of scientific knowledge within which the
structure was designed and built. You might wish to consider things like
allowing for the coeficient of expansion on a stone structure that size,
and how the placement of the expansion joints affects a continuous
>I don't even want to know what your underlying agenda is. It's clear
>that you believe in some oddball theory, like that the pyramids are
>actually 10000 years old, or that they were built by Atlantians or
>space aliens or something. I don't know and don't care what your
>theory is; I just see that as part of that, you are intent on rebutting
>nominal archaeological theory, and I think it's equally clear that
>you have insufficient grounds for doing so.

Actually I am an architect , interested in their architecture and how and
why they were built. I know when they were built, by who, and have a pretty
good idea what the builders were capable of doing and what they weren't.

I will stipulate that I by no means Know everything I would like to know
about them.
>>Although I have been studying the architecture and archaeology of this
>>monument for a quarter of a century
>Fine, good thing to do. Keep it up.
> Doug
>Doug Merritt

Now if you want to seriously discuss the topic without developing an attitude,
you might begin with the way the corners of Sekhemkhets pyramid is laid at Saqqara,
the development of corbeling, and the use of relieving vaults above the chambers
in the Great Pyramid.

To be a bit more precise for your calculations Smyth obtained an angle of 51d49',
Sir John Herschel got 51d52'15.5" from the dimensions as reported by Howard Vyse,
and Smyth chose to take the mean of these available measures as 51d51'14.3"