Had the Egyptians possessed both their high order of knowledge,
and a manner of expressing or encoding it similar to our
own, Schwaller de Lubicz's work would have been unnecessary
and the paradox of supposed primitives producing artistic
masterpieces would have never arisen.
Beyond a certain level, in every one of the arts and sciences of
Egypt, knowledge was secret. The rules, axioms, theorems and
formulate — the very stuff of modern science and scholarship
— were never made public, and may never have been written down.

But the question of secrecy is today thoroughly misunderstood.
It is generally agreed among scholars that most ancient
societies (and many modern primitive ones) reserved certain
types of knowledge for select initiates. At best this practice is
considered absurd and undemocratic, at worst it is considered
a form of intellectual tyranny, by which a class of priestly con men
kept the masses in a state of quiescent awe. But the ancient
mind was rather subtler than our own. There were (and are)
good reasons for keeping certain types of knowledge secret,
including the secrets of number and geometry; a Pythagorean
practice that particularly arouses the ire of modern mathematicians.
Five was the sacred number of the Pythagoreans, and members
of the brotherhood were sworn to secrecy regarding it on
pain of death. We know the secrets existed only because they leaked out.

That Egypt possessed this knowledge is incontestable in the
face of the harmonic proportions of her art and architecture as
revealed by Schwaller de Lubicz.
But perhaps unfortunately, Egypt was also much better at
keeping her secrets than the loudmouthed Greeks — so very
good that Egyptologists refuse to believe she possessed them.
Though by definition circumstantial, the evidence that she did
so is commanding, and it remains only to understand the valid
motives behind keeping this kind (or any kind) of knowledge secret.

In a world of hydrogen bombs, bacteriological warfare and
other progressive horrors, it is self evident that knowledge is
dangerous. It is also self evident that the ancients possessed no
technology capable of unleashing such brutal power. However,
if we look more closely at the manner in which we are
emotionally and psychologically influenced — which in turn
makes predictable the manner in which we will react to given
situations — we will see that dangerous knowledge lies behind
this curious Pythagorean number symbolism.
A work of art, bad or good, is a complex vibratory system.
All our five senses are constructed to pick up this data in the
form of visual, aural, tactile and probably olfactory and rapid
wavelengths. The data is interpreted by the brain and provokes
a response that — given wide variations among individuals —
is more or less universal: no one thinks the last movement of
Beethoven's Ninth Symphony is a lullaby.
Accomplished artists know instinctively that their creations
conform to law: consider Beethoven's famous statement, made
while working on the late quartets, that 'music is a higher revelation
than philosophy'. But they do not understand the precise
nature of these laws. They arrive at mastery only through
intense discipline, innate sensitivity and a long period of trial
and error. There is little they can pass on to pupils or disciples.
Only technique can be passed on, never 'genius'. But in ancient
civilizations, a class of initiates had precise knowledge
of harmonic laws. They knew how to manipulate them to
create the precise effect they wanted. And they wrote this
knowledge into architecture, art, music, paintings, rituals and
incenses, producing Gothic cathedrals, vast Hind u temples,
all the marvels of Egypt and many other sacred ancient works
that even today, in ruins, produce a powerful effect upon us.
This effect is produced because these men knew exactly what
they were doing and why they were doing it: it was done
entirely through a complex of sensory manipulation.
Now, if we look at our twentieth century, we find no masterpieces
of sacred art, but we do see countless examples of scientifically
proven harmful effects resulting from a misuse of sensory data.
Torture is a misuse of sensory data. Men have known about
torture for a very long time. But never before has it been studied
scientifically. When it is analyzed, it becomes clear that torture
takes two forms: sensory deprivation (solitary confinement) and sensory
over stimulation (tying someone to the clapper of a bell, the rack, etc.).
It is also well known today — and continuing work reveals
ever more subtle and insidious effects — that the stresses and
strains of modern life take a real, even a calculable, toll of our
emotional and psychological faculties. People go haywire living
to o near an airport or working in the incessant noise of a
factory. Office buildings that recirculate air and make extensive
use of synthetic materials create an atmosphere depleted of
negative ions. Though undetectable by the senses directly, this
is ultimately a vibratory phenomenon on the molecular level,
and it has powerful, measurably harmful effects: people
become depressed and irritable, tire easily and lose resistance
to infection. The subsonic and ultrasonic frequencies produced
by a wide variety of machinery also exert a powerful and
dangerous influence. Designers today have some knowledge of
the effects of colors and color combination; they know those
effects can be beneficial or harmful, though they do not know why.
In effect, then, the daily life of city dwellers today is technically
a form of mild but persistent torture, in which victims
and victimizes are equally affected. And all call it 'progress'.
The result is similar to that wrought by deliberate torture. The
spiritually strong recognize the challenge, meet it and surmount
it. The rest succumb, become brutalized, apathetic, easily
swayed ; anything or anyone promising relief from an
intolerable situation is followed slavishly , and men are easily
moved to violence or to condoning violence in what they
imagine to be their interests. All of this is brought about by
men professing high ideals, but ignorant of the forces they manipulate.
It is incontestable that all of these phenomena work their
effects either through the senses directly or (as with unionized
air and subsonic and ultrasonic sound) through subtler physiological
receptors. It is, therefore , clear that they may be reduced
to mathematical terms, at least in principle.
The ancients could not have built an H bomb had they
wanted to. At the same time, while the military mind may consider
killing people an aim in itself, the ultimate aim of war is
not so much genocide as the psychological conquest of the
enemy. Brute force alone invariably provokes violent reaction;
tyrannies seldom last long when based solely upon military
power. But when the enemy is psychologically helpless, the
ruler is secure.
We look at our own society and see human beings reduced to
slavery by sensory and supra sensory phenomena imposed by
men who do not know what they are doing. We can easily postulate
a situation in which wiser but equally egotistical men
produce a similar effect deliberately, through the knowledge able
manipulation of the senses.
In the cathedrals and sacred art and architecture of the past,
we see the knowledge of harmony and proportion employed
rightly, provoking in all men who have not had their emotions
permanently crippled or destroyed by modern education a
sense of the sacred. It therefore takes no great leap in imagination
to conceive of the same knowledge put to an opposite use
by the unscrupulous. In principle, buildings, dances, chants
and music could be devised that would reduce the mass of any
given population to helplessness. It would not be difficult for
men who knew the secrets, since men who deny that the secrets
exist produce the effect consistently in the twentieth century.
And there is a tradition repeated throughout history (though
no concrete evidence I know) that Egypt waned and ultimately
fell through the widespread misuse of magic, which is
ultimately the manipulation of harmonic phenomena.
This is but one valid reason for keeping certain types of
mathematical knowledge secret. There are many others pertaining
to the course of development and initiation of the individual:
th e ma n foun d incapabl e o f keepin g a simpl e secre t
cannot b e entruste d wit h a mor e complex , mor e dangerou s
secret. Finally , w e mus t conside r th e possibilit y tha t ou r
undeniably develope d Wester n intellect s ar e purchase d a t the
price o f intuitiona l an d emotiona l sensitivity ; i n time s past ,
the misus e o f mathematical knowledg e migh t have been more
dangerous tha n i t woul d b e today .
In every fiel d of Egyptian knowledge, th e underlying principles
were kept secret, bu t made manifest in works. If this knowledge
wa s eve r writte n i n book s — an d ther e i s mentio n o f
sacred librarie s whose contents hav e never been foun d — then
these book s wer e intende d onl y fo r thos e wh o had earned the
right t o consul t them . Thus , i n writing , w e hav e bu t a few
mathematical papyr i intende d fo r students and apparently of a
purely practica l an d mundan e nature : the y involv e problems
of distributing bread and beer among X number of people, and
so on . Later , I shal l briefl y sho w ho w Schwalle r d e Lubic z
proves tha t these school exercises are necessarily derived from a
high an d exac t theoretica l mathematica l knowledge .
In astronomy , ther e ar e no texts , bu t a marvellousl y precise
calendrical syste m indicate s beyon d an y possibilit y o f doubt
that th e Egyptian s possesse d an advanced astronomy. I n geography
and geodesy there are no texts , bu t th e work of a number
of scholar s ha s show n tha t th e sitin g an d dimension s o f the
Great Pyramid , an d o f tomb s an d monument s datin g back to
the First Dynasty, as well as the whole complex system of Egyptian
weights and measures, coul d not have been achieved without
precis e knowledg e o f th e circumference of the earth, of the
flattening o f th e poles , an d o f man y othe r geographica l
details.
In medicine , agai n ther e i s th e proble m o f a shortag e o f
texts, an d th e problem i s compounded by technica l difficulties
in translation . Bu t th e availabl e text s allud e t o a bod y o f
unwritten knowledge , whil e tha t committed t o writing , when
studied closely , divulge s a profoun d knowledg e o f anatomy,
pathology an d diagnosis .
Finally, an d most convincingly, ther e are no texts relating to
architectural techniques . Egyptia n mural s ar e rif e with depictions
o f ostensibl y everyday occupations. (Actually , the y have
a deeper meaning as well, but more of this later.) We see carpenters,
potters , stickmakers
, fishermen , boatwrights , brewmas ters
— al l th e trade s commonl y associate d wit h a developed
artisan culture . Bu t nowhere in Egypt is there a scene showing
an architec t a t work . Nothin g indicate s th e manne r in which
the prodigiou s monument s o f Egyp t wer e planned , designed
or executed . A fe w fragmentar y plan s lai d ou t carefull y on papyri se t out in grids prove that plans existed — which comes
as n o surprise . Bu t no t a wor d o f th e knowledg e underlying
those plans . Tha t architectura l knowledg e existed . Ther e i s
the architectur e t o prov e it . Th e technica l skil l o f th e Egyp tians
ha s alway s bee n selfevident
. I t i s no w equall y eviden t
that thi s wa s matche d b y a profoun d knowledg e o f harmony,
proportion, geometry and design. And it is clear that all of this
knowledge, technica l an d theoretical , wa s secre t an d sacred ,
and tha t thes e secret s wer e kept .
They wer e manifeste d i n Egypt' s works , wher e the y migh t
produce thei r effects . Schwalle r d e Lubicz' s wor k consist s in
abstracting from th e ar t and architectur e th e profound mathematical
an d harmoni c understandin g responsibl e fo r th e
design o f thes e works, and in delving beneath the confused and
complex appearanc e o f th e hieroglyphs , mytholog y and sym bolism
t o th e simpl e metaphysica l realit y from whic h al l thi s
apparently arbitrary bu t actually consisten t and coherent complexity
devolved .