## Saturday, February 16, 2008

### Coffins

Coffins .
Andre Willers
16 Feb 2008

Why is the coffin shape recognizable and in use for at least 10 000 years ?
(See wikipedia images) .

Why is it central to the Third degree initiation (the highest) of Freemasons ?
(Reminiscent of Chod in the Tibetan Book of the Dead .)

The reason is the deep esoteric and number significances .
Remember we are dealing with myths .

The coffin is essentially a kite truncated at the top and bottom according to the Golden Ratio .

I took the standard coffin ( 17.3” at top by 28” at widest , 14” at bottom , with about 21” from the top to middle and about 53.5 inches from middle to the bottom . Extend the lines at the top and bottom to get the kite shape for further analysis .

To design a perfect coffin
Measure the corpse’s shoulder width (typically 28 inches) of say W inches .
Draw a horizontal line of width W and mark the middle as M .
Draw a vertical line of length L = W * 7 * 1.618 through M so that the top length is a third of L . Denote the top of the kite by A and the bottom by B .
Connect the top of L (ie A) , the two shoulders of W and the bottom of L (ie B) . This gives a kite shape .

Truncate the top portion of the kite at the point P so that AM / AP =1.618
Truncate the bottom of the kite at half of MB . (ie MB/2)

Now you have the standard coffin , thousands of years old .

This gives a Coffin with deep esoteric significance .
Note that the top of the kite has an angle of 30 degrees and the bottom half of that , namely 15 degrees . The various lengths are ratios of the Golden Ratio .
There are all sorts of delicious numerical titbits
Like Tan(15) + tan (7.5) = 0.4 = 1/25 .

Note L = W * 7 * 1.618 . This is deliberate . Seven is Sacred Number .
It derives from the mind-blowing
Tan(90 – 15) + Tan(90 – 7.5) = 7* 1.618… nearly exactly .
A really elegant formulation .

I doubt whether they had Seven Zombies against Tombs in mind ,
This is why the ancients loved it and why it is still a symbol .
It hints at mysteries .
You might as well be buried in a container that contains our underlying concept of restful beauty .

The Golden Ratio .
This is a very important constant (also called phi) .
It plays a fundamental role in describing growth processes where the increments cannot be decreased to infinitesimal . If they can , we use Euler’s constant e .

It is derived from the Fibonacci series
1,1,2,3,5,8,13,21,… where every term is the sum the previous two terms . The ratio of succeeding terms approaches a limit , which is called phi . Also the Golden Ratio .

Iteratively :
Any term A(n) can be expressed as :
A(n+1) = A(n-1) + A(n)
Divide by A(n) . This gives
[A(n+1)] / [A(n)] = [A(n-1)] / [A(n)] +1

We know that the ratio of successive terms quickly approaches a limit
phi = [A(n+1)] / [A(n)]

Thus ,
Phi = 1/phi +1
Phi^2 – phi –1 =0
Solving this quadratic equation (school maths) gives
Phi = 0.5( 1+-Sqrt(1+4))
Phi= 1.618033… (the Golden Ratio) or 0.618033…)
This number pair has the extremely significant property that 1/1.618… = 0.618… .
Also , since the square root of 5 is involved , phi can be measured with a string (Pythagorean triangle 1,2,Sqrt(5) ) Thus ,phi can be measured by strings or strings and a square . This is important from a Freemason viewpoint . (For string read compass)

The meaning of phi .
It crops everywhere where non-infinitesimal growth processes are described mathematically .

Each element is dependant on two preceding elements . In essence , a two-dimensional coupled array .

Visually , the retina and brain operate mostly in a two-dimensional mode . Depth modalities are usually a function of nervous-system processing . Forward jittering is extensively used . The most predictable images are the lowest resource-intensive , and usually the most pleasing (restful , least-energy) .
In other words , a horizontal rectangle of phi ratio takes the least time and energy to process .

Phi can be seen directly where cells grow from a single point , where there has already been previous growth . Obviously , the new cell cannot take up the space of previous cells . Hence the spiral effects in sunflowers , shells , etc .

Why go to all this trouble ?
A coffin is more expensive than a casket (ie a box) . The extra labour involving all the carpentry must easily double the costs .

I draw your attention to the Golden Ratios in the volume where the head lies . Many people believed (and still believe) that this gives the corpse , well , a head start in the afterworld .
(Remember , I have only cursorily touched upon all the interesting numerical things flowing from the 30 degree top and 15 degree bottom relationships of the kite-shape . )

The Pyramids .
There is reason to believe that the truncation of the kite-shape was a degenerate form of interment . The first pyramids (Saqqara) were originally designed to have a top apex of 30 degrees . These were supposed to have been vertical coffins (maybe even the original design) . Unfortunately , the stone they used collapsed under the weight and we ended up with the Bent pyramid and later pyramids with a top apex of 23.5 degrees .

But what is interesting , is that at depths of 0.618 , 1 and 2 times the height of the pyramid , there should be chambers filled with goodies .

Why should these still be filled ?

The gods of light of Egypt were recycling gods . This is how they kept their tiny little eco-system going for 5 000 years . But the nether gods (Seth , etc) represented the inevitable entropy loss . So buried wealth above ground was deliberately lightly guarded to encourage recycling (note their really good recycling of copper) .

But the bribes for the nether gods were simply rendered unreachable to their technology . Underground passages deliberately left with mud-forming aggregates and flooded after depositing the treasures spring to mind . These would be under the Nile-water table (ie below the pyramids) . Even with our technology , it is doubtful whether these items could be recovered economically for the value of the gold alone . Archeological value is another matter .

Value Sink .
In the Old Kingdom , the value of this unrecyclable wealth must have been calculated to a nicety . Too much silver and gold , and they would have serious inflation problems . Note what happened to Spain after 1492 . So they buried all the surplus gold from Africa (Niger , Congo , Zimbabwe , etc) in sludge and ooze under the pyramids .

It worked too .

After the collapse of the old kingdom , they turned their backs on the rest of Africa . In retrospect this does not seem to have been the wisest decision . One wonders whether it was an individual that made the decision (ie is an alternate history possible where an Egyptian and Phoenician led African civilization conquered Europe and the Middle East . It nearly happened with Carthage under Hannibal . )

The crux decision seems to have been a failure of altruism . Egypt did not help parent Abyssinia to recover after the big Drought . They could have done it . But they refused and in shame buried their heads . The whole continent paid a dreadful price .

Think Europe without the Marshall-plan . The US would now be fighting WW4 or WW5 , with Russians , Germans and English as enemies instead of the present bunch of piss-willies who have to buy their weapons from their enemies .

Egypt ended up fighting the Greeks and Romans without any significant help from Abyssinia or the rest of Africa . Even gold from trade would have enabled them to do their old trick of hiring mercenaries . But they did not have the money .

The lesson seems clear : When moving into a negative climate change , be selfish . When moving into a positive , recovery phase , be altruistic .

If there is no recovery phase , tough .

Andre