Wednesday, July 01, 2009

Why is the Parthenon not round?

Why is the Parthenon not round?
Andre Willers
1 Jul 2009

The design started as round , but after the committees finished it ended up a bastard copy of an Egyptian temple .

Discussion :
Anybody who has ever slapped two bricks or small stones together to build something knows that the easiest way is put a stake in the center with a radius string , then stack the bricks at the end of the string . Simple and foolproof hut-construction .
This is primary human construction .
All you need is a center , and a string .
See Stonehenge , Mycenae , Norman Forts , huts , etc.
This was the traditional construction of the Western European Cyclopean Builders , culminating in the Pantheon in Rome , the oldest in-use building in the world .

Rectangular construction started as a fashion amongst the priesthood .
Large constructions necessitated larger building-blocks . Or conversely , if you only had large blocks or long timbers , rectangular or square constructions were less expensive in terms of energy .
The old circular method did not work so well for contiguous structures with large components , so the circular building method was adapted to give square buildings .

A circle was drawn , with a carefully chosen point on the circumference as the cornerstone . The whole subsequent square structure was erected with reference to this cornerstone . (Note the Biblical references) . This necessitated a center point . The Egyptian priests did not have monotheism . So multiple center-points came naturally .

A circle (like the pyramids) can have only one center . But a rectangle can be circumscribed by an infinity of possible ellipses , where the two foci are variable . This is associated with schisms .
A defining characteristic of an ellipse is that the sum of the lengths from any point on the ellipse to the two foci is constant .
This made construction a snap . Two foci (say F1 and F2) are chosen after suitable invocations , a cornerstone(Say C) is chosen after further invocations, geomancies and sacrifices . A string is spanned from F1 to C to F2 . This is kept taut and used sketch the circumscribing ellipse on the ground . From C , a line parallel to F1F2 till it intercepts the ellipse at point B describes one side , a perpendicular line from B at the this end till it intercepts the ellipse at point A describes the other side . Continue to complete the rectangle CBAD .
A very simple recipe . Any rectangular building can be constructed using two stakes and a long string .

One would expect archaeological remains at the Foci and the Cornerstone .
But this would be too simple for humans , specifically the Priesthood . While the Cornerstone could not be hidden , the Foci could .
The entire system is a trapdoor function . You can calculate this yourself using elementary elliptical analytical geometry .
Given just the rectangle , there are an infinity of possible sets of (Foci , Circumscribing Ellipses) .

Sacrifices were put into the cornerstone (still is :eg time-capsules) .
But things considered real treasures were put into the foci .
Since they probably used the foci as hiding places for Cult secrets and precious objects , it does not seem unreasonable from their viewpoint , (given their experiences with the likes of Lara Tombrobber ) to hide the foci .
Given the usual schisms and defections in Closed Conspiracies of this sort , even more draconic measures using offsets (cf Ptolemaic epicycles) were used later on .

These foci can be extraordinarily difficult to find .
It is a true trapdoor function . And the old priests never intended these reliquaries to be found . So there are no clues left for the living .(Three can keep a secret if all three are dead.) And they loved complexification .
They were put there as a part of the balance-requirement of their view of the Universe , so we know they are there .
But to find them…

Today we have powerful algorithms for finding things hidden at random , but , alas , the foci were not hidden at random .
See "Newtools : Orders of Randomness" .
Though negative randomness is not explicitly treated , it is inherent in the algorithm . Try some thinking for a change .

To get back to the Parthenon .
The temple was to be built with public funds , so every citizen had a say , and more say , and still more say and further comments , quips and sundry pieces of skullduggery the Athenians were so adept at .
They full well realized that the result will be looming over them , their children , and grandchildren for many hundreds of years .
So , everybody wanted a piece of the action .

Egypt at the time was the equivalent of Oxbridge , Harvard or Sorbonne today . The place where promising post-grads were sent to polish up their education . Rectangular temples were pioneered there , complete with esoteric and occultly significant ratio's and dimensions . (Ellipses are literally infinitely rich in these , by their very nature) .
All at a slight extra charge , of course .
They were the rage all over the Middle East for at least 1 000 years .
The bucolic , old Bronze-Age circular faction was brushed aside and the rectangular , elliptical construction got the vote at the committee stage .

The various mystical factions rubbed their hands in glee and got busy .
The Parthenon has probably got more hidden esoteric significances in it's construction than any similar construction (except , maybe , some cathedrals ) . But , they seem to have overdone it a wee bit . From a distance (like 2 000 years) , the hidden meanings seem random , or worse , negatively random .

Not being dummies , they might have realized it and buried some keys at the foci .
Hint : why are there so many ramps ? Note the Greek pride-of-thought at the time was in description of slices through three-dimensional figures , mainly conics . This will give to smoothly rising or descending curves . Look for the foci as described by 3-D figures .

Think of the Acropolis-complex as a huge three-dimensional sculpture , only parts of which have been rendered in stone .
But the eye and imagination is led on to complete structures that exist only in the mind .

Hence the pride that they have that there is not a single straight line in the Acropolis . It only appears that way because of the way our minds complete the dotted lines . The curved ramps and curved ramp-floors were an integral part of this .
A magnificent tour-de-force .

Looking at the whole complex as an ellipse , we can actually identify the original foci , as well as the cornerstone for the Parthenon .

Acropolis Focus 1 (F1)
Between the Parthenon and the sanctuary of Pandion is a funny little round six pillar structure not named in my book(I am working solely from "Ancient Monuments Revealed" by Westwell and Perreira , ISBN 13 978 0 7858 2080 2) , with some unreliable (as far as measurements are concerned) cumputerised reconstructions. My only hope is that the gentle reader will savagely point out the error of my ways .

I presume this was a sop to the old-style megalithic builders . The Focus does not lie inside it , but is offset to the extreme side of the circular structure towards the center-line of the complex .

Acropolis Focus 2 (F2)
The other focus is defined by a funny little square watchtower-like building between the Parthenon and next to the Chalcothece.
Once again , the focus is offset towards the center-line .

Note that the line between the two foci intersects the corner of the Parthenon . This is the Cornerstone of the Parthenon .
(The imaginary ellipsoid hangs out over empty air. So they could not very well do the traditional thing . Indeed , they prided themselves on not doing the traditional thing (as long as it was , well , not too untraditional .))

The Critical Ovoid line between Foci :
The intersection line also follows a sloping ramp . The curvature of the floor of this ramp defines the geometrical nature of the Acropolis Virtual Sculpture . It is the heart of the whole complex , and all other significant points are related to it .

Any primary sacrifices will be stashed away at the foci of the virtual elliptical ovoid . Quite deep below F1 and F2 and the Parthenon Cornerstone . I suggest that caretakers get to it before Lara does .

The Roofs .
The roofs have a slope of 1 in 3 as far as I can tell , but the definition is bad . I would have expected a slight increase of the ratio with altitude to approach the Egyptian ratio of 1-in-1 (45 degrees) , of the buildings found inside the Pyramids .
(Ever wondered why a building inside a pyramid needs a roof ?)
This 1/3 ratio presumably indicates to the cognoscenti that there is a virtual structure covering the Acropolis .

From here on you are on your own . I have no intention of getting sucked into these occult significance games these idle minds have spent literally millennia in concocting . Most of them are in any case not worth one good textbook on analytical geometry.

Though I would not mind seeing what the ancient Greeks had in mind at the Acropolis .
A 3D model incorporating projections of all the curves in the stones should show a huge , complex structure incorporating all these ratios like The Golden Ratio (a special case ) and many others .

The data is actually already there . All the hordes of tourists with their GPS systems have accumulated enough data to make a model . Otherwise , you can trot around with your own GPS and a simple 3D modeling program . Remember , GPS's can show elevation . The curvature of the ramp-floors might need some work , though .

Mega-Acropolis .
A laser generated image over Athens (and virtual in Second Life) can easily be a new Wonder of the New World .

Sokrates drinks Coke !

Yours academically,
Andre .

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