'First, remove the chip in your all-seeing eye.'
Jay's Analysis: In January of 2014, IMF Chief Christine Lagarde gave a speech that was lost on most of her audience and amongst the media. She stated:
“Now, I’m going to test your numerology skills by asking you to think about the magic seven, okay? Most of you will know that seven is quite a number in all sorts of themes, religions. And I’m sure that you can compress numbers as well. So if we think about 2014, all right, I’m just giving you 2014, you drop the zero, 14, two times 7. Okay, that’s just by way of example, and we’re going to carry on. So 2014 will be a milestone and hopefully a magic year in many respects. It will mark the hundredth anniversary of the First World War back in 1914. It will note the 70th anniversary, drop the zero, seven– of the Breton Woods conference that actually gave birth to the IMF.”
In his classic Secret Societies and Psychological Warfare, Hoffman wrote of coincidence, synchronicity and curious connections between 007 and 2001 that also relate to obscure subjects like numerology and gematria. The first 007 was Dr. John Dee, as will be investigated below, but the reason this is of import is the similarity between Christine Lagarde’s seemingly strange comments to her Press Club audience. Hoffman has recently commented on this, and I myself at the time of Lagarde’s comment speculated on the connections between the numbers of sevens that appeared in the downed Malaysian Plane incident(s). Numerous conspiracy sites and speculators got in on the action, but what no one (other than Hoffman) did was look at the motivations behind such a mindset. The natural approach of those in conspiratorial and alternative media circles would be to leap at the occult. While I don’t intend to deny such associations, I would like to highlight another element that almost none have considered. Yes, there are believers in dark forces in high places, but there is also another factor that should be kept in mind, as I myself had conversations with individuals about this that appeared a frightened by such calculating mumbo jumbo.
“Kerchoff’s Principle: The security of a crypto-system must not depend on keeping secret the crypto-algorithm. The security depends only on keeping secret the key. In addition to keeping the key secret, a secure cipher system must also have a wide range of potential keys.” (The Code Book, Simon Singh, pg. 12)
As researchers and analysts of the world-historical, we attempt to do just this on a much grander scale. Discovering the secrets of nature and supernature yield fulfilling mental rewards in their own right, but they also free us from the slavery to superstition. While I have attacked the Enlightenment many times over, and I think I am right in doing so for its excesses, it’s also worth considering the positive aspects of the Enlightenment, which did serve to rid the Roman dominated West of numerous bizarre superstitions and excesses that should not be excused. I doubt many of us in modernity would truly like to return to a world where we expect to almost certainly be damned, spending our days working out a complex system of penitential indulgences to try to settle debts in an absurd punishment-based system. Such is part of my reason for leaving Western Christianity years ago, but this should also not be seen as endorsement of one side of a false western dialectic of Rome versus Enlightenment. On the contrary, the truth lies somewhere in-between extremes that the cunning of history is yet to work out (as we still live under the excesses of the quantification-obsessed Enlightenment). Let us see if we can locate at least one key to cracking the code of our modern overlords and decipher the Lagardian linguistic mysteries, surveying numerology, biblical gematria and cryptography.
First, the subjects of numbers, numerology and ancient perspectives on them, are helpful. For ancient man, numbers were magical, semi-divine entities that somehow related to all things, despite being in no particular time and locale. Obviously in an article, the scope of such an analysis must be limited, so I have chosen influential representative examples. My friend James Kelley explains in his “Prajapati Purusa and Vedic Altar Construction” essay the means by which the Pythagorean Theorum was actually encoded in Vedic altar designs, much earlier than Pythagoras himself:
Simon Singh’s The Code Book.
“This blurb fails to mention the amazing insights of
Dr. Abraham Seidenberg, who found the so-called “Pythagorean theorem” at
work in the Indian texts known as the Sulvasūtras, which date from the 8th
century B.C., but which crystallize procedures and teachings that reach
back into the Neolithic mists. Though historians of mathematics before
Seidenberg noted the connection between the famous theorem and Vedic
texts, it is our contention that Dr. Seidenberg was the first to offer a
coherent presentation of the significance of this influence. The Sulvasūtras
contain explicit instructions for how to construct the altars for Vedic
worship using only ropes, stakes, and possibly rods. But what has Vedic
altar worship to do with “a² + b² = c²”?
In his seminal article “Ritual Origin of Geometry,”
Seidenberg demonstrates exactly how the “Pythagorean theorem” was used
in creating the falcon-shaped altar used in the Vedic fire ritual, the
agnicayana. The altar was built based upon an aerial measure called a
“Purusa”! The falcon altar, we are told in the sutra, must be a square
with an area of 7 ½ square Purusas (about 56 ¼ square feet). A śulba,
or cord, is used to measure out a “Purusa” (about 7 ½ feet, and marked
on a section of the cord from an end), and this section is stretched
taut between two pegs, one end of the pegged-down cord extending out
past a peg, the other end being a meeting point of peg and cord-end.
Next, the loose cord is stretched back and wrapped around the apposite
peg. This peg-to-peg cord stretch is repeated until the desired length
is reached (to achieve the “half Purusa,” the initial Purusa-length has
been measured by joining both ends of the section and pulling the loop
taut by hand and marking the new end with chalk or ink).
The square is created next, in a manner that we would
find odd, by stretching a second cord from the midpoint of the initial 7
½ Purusa cord, the end result being a “T” shape. Then the altar
boundary parallel to the initial side is stretched, making an “H,” the
final step being a simple stretching of two boundaries parallel to the
central connecting cord. It is not important to trace the subsequent
“unnecessary” (from our “practical” perspective) steps in creating a
square that is 7 ½ Purusa by 7 ½ Purusa (we moderns would simply stretch
the loose cord, once measured, to make a 7 ½ Purusa “L,” then repeat
the process twice more to get a square). Instead, our attention must be
focused upon what the Vedic priests did next: They believed that it
was necessary to increase the area of the altar by 1 Purusa, without
changing the altar’s shape!”
In this fascinating and illustrative section we have
an important insight that is lost on many: the primal and archetypal
rites of ancient man, in what might be considered a serious contender
for the origin of the “perennial tradition” (India), we see that the
rites of the gods here encode mathematical forumlae.
Specifically in this case, the message is a geometrical formula, and in
fact the most famous one. While one is left to speculate on his own as
to the divine status of such “gods,” what can be divined from this
section is the fact that the ritual encodes a mathematical form and
functions as a veil for a more axiomatic principle. This seems to
suggest a conscious desire to cloak abstract principles from the profane
by the priestclass, keeping the secrets from the populace through
religious fear.
Continuing with this survey of ancient thought,
Egyptologist Wim van den Dungen analyzes the Pythagorean and Western
conceptions of basic number principles and numerology. Dungen’s linked
chart also demonstrates the similarity in the various religious
traditions through the numerological principles. We see again the theme
of hiding numerological doctrines under the divine:
“The first standard is immanent. Using the first ten cardinal numbers of N, the set of all natural numbers, the decadic set N’
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is isolated (cf. Pythagorism based on
Ancient Egyptian thought and later replicated by the Qabalah). By means
of N’, all subsequent natural numbers can be derived. Each cardinal number of N’ is then coupled with a symbol one-to-one. These combinations give form to the famous neo-Platonic formula : exitus a Deo, reditus in Deum (outgoing
from and return to God). This “numerology” is backed by a process in
which the “exit” is an involution (a materialization of spirit) and the
“return” an evolution (a spiritualization of matter). Immanence and the
realms of process (becoming) prevail.The second standard is transcendent. Transcendence is approached with negatives (radical apophatism). Three kinds emerge : unknowing itself, virtuality (the possible, or {Ø}) and nothingness (the void, or “0”). The first is a nothingness with potential, the second the non-existent (cf. Nature abhors a void). The set of all relevant criteria of measurable differences is given 10 ordinal positions defining 10 dimensions. The logic of creation (transcendence into immanence and vice versa) links with this.” (Van Den Dungen, “Tabularm Esotericum”)
In another influential example, the first century collection of documents known as the Corpus Hermeticum relates these numbers to the original creation act, echoing the same Indian, Hellenic and Egyptian principles:
“I saw in the darkness of the deep, chaotic water without form permeated with a subtle intelligent breath of divine power, Atum’s Word fell on fertile waters making them pregnant with all forms. Ordered by the harmony of the Word, the four elements came into being, combining to create the brood of living creatures the fiery element was articulated [aether] as the constellations of the stars, and the gods of the seven heavenly bodies, revolving forever in celestial circles. The Word leapt up from the elements of Nature and reunited with the mind of the Maker, leaving mere matter devoid of intelligence….
In the beginning there is unity. Unity separates into two fundamental forces, which like negative and positive poles of a battery, generate everything. Hermes describes them as Life and Light, which become Mind and Soul. We experience them as thoughts and feelings.” (The Hermetica, By; Timothy Freke and Peter Gandy, pgs. 13, 14, 35)
This tradition would continue in the Jewish and biblical tradition, as van den Dungen expounded, with Kabbalah and gematria. In Kabbalah, the first ten numbers, like in Pythagoreanism, correspond to the divine energies or attributes that shine forth from the One (or God). With this belief, ancient Jewish belief considered the very letters of the Torah to be divinely inspired and their particular forms and lexical constructs could encode secret meanings. Jewish scholar and Kabbalah expert Gershom Scholem defines gematria as follows:
“Gematria (from Gr. geometria), is one of the aggadic hermeneutical rules for interpreting the Torah (in the Baraita of 32 Rules, No. 29). It consists of explaining a word of group of words according to the numerical value of the letters, or of substituting other letters of the alphabet for them in accordance with a set system. Whereas a word is normally employed in this sense of manipulating according to a numerical value, it is sometimes found with the meaning of “calculations” (Avot 3:18)….The use of letters to signify numbers was known to the Babylonians and the Greeks. The first use of gematria occurs in an inscription of Sargon II (727-707 B.C.E.) which states that the king built the wall of Khorsabad 16,283 cubits long to correspond with the numerical value of his name. The use of gematria was widespread in the literature of the magi and among interpreters of dreams in the Hellenistic world.” (Gershom Scholem, Kabbalah, pg. 337)
What is relevant to our analysis of Lagarde’s comments is that we begin to see that the learned and priest classes would naturally see the pragmatic usage of gemtaria and numerology for conveying messages in a covert fashion. Espionage and statecraft have always gone hand in hand, and the desire of rulers to send encrypted messages is an ancient art. Thus, religious traditions and languages (such as Hebrew and Greek) where letters also functioned as numbers would naturally serve as a medium for secret communications.
Given Lagarde’s comments involve a peculiar focus on sevens, it might be worthwhile to look, not just at the hermeneutical principle of gematria, but at the symbology in Scripture of the number seven. Seven serves to convey the idea of completion, finality and perfection, as the Oxford Bible Companion relates:
“Number Symbolism. In common with most people in the ancient world, the Israelites attached symbolic significance to numbers. So whenever the biblical writers mention a number, it is likely that they had a symbolic meaning in mind; in many cases the numbers must not be taken in their literal sense at all….
Seven. The sum of three plus four, of heaven and of earth, signifies completeness and perfection. There were seven chief heavenly bodies (sun, moon and the five planets known to ancients), seven days of the week, seven archangels. The great festivals lasted seven days, and there were seven weeks between the Passover and the Festival of Weeks (Pentecost). Every seventh year was a Sabbath year, when the land would lie fallow, and Hebrew slaves were allowed to go free; and every fiftieth year was a jubilee, when alienated property had to be returned. The seventh day represented God’s completed work (Gen. 2:2-3), and in the Book of Revelation, the seventh seal, trumpet, bowl, etc., represent the completion of God’s plan. The seven spirits of God (Rev. 1-4) represent either the seven archangels, or “all spirits,” of the Holy Spirit. Seven churches represent the universal church (Rev. 1:20). It is necessary to forgive, not just seven times, but seventy times seven (Matt. 18:21-22, Gen. 4:24), that is to say, always.” (Oxford Guide to the Bible, pg. 562-3)
The most famous example of gematria most are familiar with is the reference in the Apocalypse to “666,” the number of the beast. Biblical scholars have long considered it a usage of gematria, where John encoded the name of Nero Caesar or another contemporary Roman Emperor. Biblical scholar Dr. Kenneth Gentry elucidates of “666”: “‘This method, called gematria, or geometrical, that is, mathematical, was used by the Jews in exegesis of the Old Testament.’ The point is clear: cryptograms were common among the ancients, even among Christians. Hence, the gematria in Revelation is not something created de novo by John; rather, the idea involved a familiar concept to the ancients.” (Before Jerusalem Fell: Dating of the Book of Revelation, pg. 196)
Another relevant association with “666” is the number squares that can be generated with that give rise to various speculations, but for the purposes of our discussion relate to the topic of magic squares. Biblical scholar E.W. Bullinger gives an example on page 286 of his Number in Scripture:
Bullinger’s number square of “666,” which gives 111 in all directions.
The number square is alleged to derive from the geometrical structure of the pattern found on the shell of a tortoise in ancient China (See “The Malekulan Journey of the Dead” by John Layard in Spiritual Disciplines: Papers From the Eranos Yearbooks). Ancient mathematicians associated the number or magic square with various planets and planetary deities and their representative angelic sigils. However, rather than fixating on the religious, it is my thesis that the number square also has a relation to cryptography and the rise of the computer. Since the square gives an ordered regularity, it was reasonable to suppose that a machine might be constructed to calculate and encode. I have written elsewhere of Leibniz’s speculations regarding a machine that would mirror the human mind, storing information and mirroring it back. The medieval mythology of the golem also factored into this equation, linking once again gematria and Kabbalah, where the matrix of external reality itself could be imaged in a 2D virtual realm, which I will touch on later. Before that, consider biblical scholar David Chilton’s arrangement of “666” in triangulation in his Days of Vengeance, page 349.
The triangulation of “666” produces a pyramid that recalls the tetraktys of Pythagoras, as well as other esoteric notions.
When wrapped around the right size staff, the scytale revealed a hidden message.
“As the danger of discovery was great, there was only one way in which he could contrive to get the message through: this was by scraping the wax off a pair of wooden folding tablets, writing on the wood underneath what Xerxes intended to do, and then covering the message over with wax again. In this way the tablets, being apparently blank, would cause no trouble with the guards along the road. When the message reached its destination, no one was able to guess the secret, until, as I understand, Cleomenes’ daughter Gorgo, who was the wife of Leonides, divined and told the others that if they scraped the wax off, they would find something written on the wood underneath. This was done; the message was revealed and read, and afterwards passed on to the other Greeks.” (The Histories, Bk. V)
Likewise, in the case of Julius Caesar, we have examples of what would become known as the “Caesar Cipher,” in messages to Cicero. Suetonius recounts of this transposition process:
Caesar Salad Alphabet Soup Cipher.
“There are also letters of his to Cicero, as well as to his intimates
on private affairs, and in the latter, if he had anything confidential
to say, he wrote it in cipher, that is, by so changing the order of the
letters of the alphabet, that not a word could be made out. If anyone
wishes to decipher these, and get at their meaning, he must substitute
the fourth letter of the alphabet, namely D, for A, and so with the
others.” (Suetonius, The Lives of the Caesars, “Caesar,” No. 56)The substitution cipher is the oldest form of encryption, but was not immune to being cracked, and this honor fell to the Arabs in the Middle Ages, who in fact invented the practice of cryptanalysis. Singh comments: “This simplicity and strength meant that the substitution cipher dominated the art of secret writing throughout the first millennium A.D. Codemakers had evolved a system for guaranteeing secure communication, so there was no need for further development – without necessity, there was no need for further invention…..The breakthrough occurred in the East and required a brilliant combination of linguistics, statistics and religious devotion.
“Had Arabs been merely familiar with the use of monoalphabetic substitution cipher, they would not warrant a significant mention in any history of cryptography. However, in addition to employing ciphers, the Arab scholars were also capable of destroying ciphers. They in fact invented cryptanalysis, the science of unscrambling a message without knowledge of the key. While the cryptographer develops new methods of secret writing, it is the cryptanalyst who struggles to find a weakness in these methods in order to break into secret messages. Arabian cryptanalysts succeeded in finding a method for breaking the monoalphabetic substitution cipher, a cipher that had remained vulnerable for several centuries.” (Ibid., 15)
In fact, it was not merely Arabs who were interested in cracking cryptological codes, but medieval monastics and the Vatican, too, who were also skilled in the same arts. Singh explains of the medieval monks who encountered another example of Jewish encoding in the text of Jeremiah:
“Medieval monks were intrigued by the fact that the Old Testament contained deliberate and obvious examples of cryptography. For example, the Old Testament includes pieces of text encrypted with atbash, a traditional form of Hebrew substitution cipher. Atbash involves taking each letter, noting the number of places it is from the beginning of the alphabet, and replacing it with a letter that is an equal number of places from the end of the alphabet. In English this would mean that a, at the beginning of the alphabet, is replaced by Z, at the end of the alphabet, b is replaced by Y, and so on. The term atbash itself hints at the substitution it describes, because it consists of the first letter of the Hebrew alphabet, aleph, followed by the last letter taw, and then there is the second letter, beth, followed by the second to last letter shin. An example of atbash appears in Jeremiah 25: 26 and 51: 41, where “Babel” is replaced by the word “Sheshach”; the first letter of Babel is beth, the second letter of the Hebrew alphabet, and this is replaced by shin, the second-to-last letter; the second letter of Babel is also beth, and so it too is replaced by shin; and the last letter of Babel is lamed, the twelfth letter of the Hebrew alphabet, and this is replaced by kaph, the twelfth-to-last letter.” (Singh, The Code Book, pg. 26)
Renaissance Europe was awash in intrigues and subterfuges that often called forth the use of encryption. It is at this point we should shift back to the esoteric and consider Cornelius Agrippa, considered the father of western hermeticism. Agrippa was accused of being a conjurer, but was also learned in the arts described above. The Renaissance brought classical learning back into fashion and, as a result, the desire to crack hidden codes by the means of linguistics and numerology and gematria was again en vogue. In the below section Agrippa is an excellent example of the associations and connections of numerology, theology, alchemy and techne. Agrippa writes:
“God himself though he be only one in Essence, yet hath diverse names, which expound not his diverse Essences or Deities, but certain properties flowing from him, by which names he doth pour down, as it were by certain Conduits on us and all his creatures many benefits and diverse gifts; ten of these Names we have above described, which also Hierom reckoneth up to Marcella. Dionysius reckoneth up forty five names of God and Christ. The Mecubales of the Hebrews from a certain text of Exodus, derive seventy-two names, both of the Angels and of God, which they call the name of seventy two letters, and Schemhamphores, that is, the expository; but others proceeding further, out of all places of the Scripture do infer so many names of God as the number of those names is: but what they signifie is altogether unknown to us: From these therefore, besides those which we have reckoned up before, is the name of the Divine Essence, Eheia äéäà, which Plato translates wn, from hence they call God TO ON , others O UNthat is the being. Hu àåä is another name revealed to Esay, signifying the Abysse of the Godhead, which the Greeks translate TAUTON , the Latins, himself the same….
Vitruvian Man in Agrippa, recalling Kelley’s essay.
a b r a c a d a b r a
a b r a c a d a b r
a b r a c a d a b
a b r a c a d a
a b r a c a d
a b r a c a
a b r a c
a b r a
a b r
a b
a
Cornelius Agrippa, Three Books of Occult Philosophy, Bk. III, XI
The pyramidal structure of abracadabra is reminiscent of the triangulation of “666” or the tetraktys. It is not merely an encoded hermetic message, but also a geometric form – a triangle. As an undergrad I read a large portion of volume 1 of Charles Heckethorn’s The Secret Societies of All Ages, and one aspect that came to the fore was the pigpen cipher. Not only is the pigpen cipher an ancient method of secret communication, the nine squared box can also enclose all the letters of the English alphabet as well as the first 9 numerals (which make up all numbers). It is easy to see how the magic square, the emergence of linguistics, number forms, the pigpen cipher and various esoteric ideas would all intertwine. Yet aside from the religious and esoteric views, there is also the ever-present usage of these ideas by the state for secret communications.
The classic pigpen cipher. When the “X” is laid over the #, the entire English alphabet and the first 9 numerals are present.
Fast forward now to Renaissance England, and think of Dr. John Dee,
the first “007,” and court astrologer for Queen Elizabeth. Dee was
involved in many intrigues, one of which was cryptology. However, as NSA
scholar Leslie Rutledge explains, not a very good one. In fact,
despite the many legends of Dee as a conjurer talking to the dead with
his crystal ball, the evidence seems to weigh in on Dee as a con man,
calling to mind Agrippa. Regardless, Dee is another example of the
intersect of the esoteric and cryptography. Rutledge writes in his “John Dee: Consultant to Queen Elizabeth”:“Mathematics lifts the heart above the heavens by invisible lines, and by its immortal beams melteth the reflection of light incomprehensible, and so procureth joy and perfection unspeakable.” -Dr. John Dee citing Plato
“The book was notorious, I just now pointed out. Trithemius, the Abbot of Spaheim, began to write it in the year 1500, and he sent a partial copy of it to a clerical friend in another religious establishment. But unknown to Trithemius, his friend had died. His friend’s abbot opened the correspondence, and he was appalled. “Secret writings,” he read, “will reveal secrets not found by ordinary means.” And there was more. In order to send a secret message, you make an image of a planetary angel, speak the message over it at a moment determined by complicated astrological calculations, wrap the image up with an image of the addressee, and bury the images. This network of planetary angels could always be used for messages-and even for thought transference.
Cryptography, even of this heavenly sort, was not just a means of disguising messages; it was the medium through which intelligence from the spirit world might be transmitted. The secrets of the universe-the philosopher’s stone “The elixir of life-might be received in a heavenly cipher, like the obscure oracles of Delphi.” The abbot denounced Trithemius as a conjuror, trafficking with spirits, and he lost his clearance. Although he stopped all work on the Steganographia, the manuscript of it appears to have circulated as an underground classic for nearly a century until Dee copied it in 1563. was finally published in Frankfurt, near the end of Dee’s life, in 1606.
It was, you see, the supernatural context of the Steganography which attracted attention. Heads of state-or adventurers of all sorts could be persuaded that secrets of the future, hidden in the stars, and the marvelous formulae for prolonging life and for converting base metals into gold were knowable-and might be revealed by the supernal powers in cipher. It is hard perhaps to realize, but rational and wholly illusory notions like this could and did exist in the 16th Century scientific mind. Even Copernicus did not disbelieve in astrology. There were two gates to the other world. There was a gate of horn, through which came the rational finding which would lead to our times, and an extraordinary perception of the nature of man and his world. But there was also agate of ivory, through which dreams and illusions came.”
According to Rutledge, Dee was not successful at this magical, astrological means of cryptography. However, the essay does relate the story of Dee mentioning the ability to project images through screens, which I have noted elsewhere appears to relate to the seminal idea of the computer, and it is to Leibniz that we once again return. Leibniz’s idea of a characteristica universalis would be instrumental in the development of calculation machines, arising from the project of a universal logic for all phenomena. Milkov explains:
“The first variant of Leibniz‘s project for a new language was set out in a letter from Marin Mersenne to Descartes. In fact, Mersenne‘s idea was that of pasigraphy, a general language that helps one to understand all languages. In his reply to Mersenne of 11 November 1629, Descartes found this project rather interesting; however, he suggested a much wider variant of it: a project for ideography that mirrors human thoughts. This ideography would be connected with a mathesis universalis that could conceive of anything thinkable as a calculation. ―The greatest advantage of such a language would be the assistance it would give to men‘s judgment, representing matters so clearly that it would be almost impossible to go wrong.” (Nikolay Milkov, “Leibniz Project for a Characteristica Universalis in Relation to the Early Analytical Philosophy,” pg. 2)
Amazingly, Leibniz wrote of a possible “imagined” machine:
“17. It must be confessed, moreover, that perception and that which depends on it, are inexplicable by mechanical causes, that is by figures and motions. And, supposing that there were a machine so constructed as to think, feel and have perception, we could conceive of as enlarged and yet preserving the same proportions, so that we might enter into it as into a mill. And this granted, we should only find on visiting it, pieces which push one against another, but never anything by which to explain a perception. This must be sought for, therefore, in the simple substance and not in the composite or in the machine. Furthermore, nothing but this (namely perception and their changes) can be found in the simple substance. It is also in this alone that all the internal activities of simple substances can consist. 18. The name of entelechies might be given to all simple substances or created monads, for they have within themselves a certain perfection; there is a certain sufficiency which makes them sources of internal activities, and so to speak, incorporeal automata.” (pg. 536)
Grandfather Patriarch to all Computers.
Physicist Paul Davies relates an interesting story about the advancement of computers by Los Alamos Laboratory scientists that also recalls Leibniz’s walk-in computer, based on the same principle of universal logic and a characteristica universalis. This time, however, the purpose is to mimic life. Davies explains:
“The fact that universal computers can simulate each other has some important implications. On the practical level it means that, properly programmed and with enough memory space bolted on, a modest IBM PC can perfectly imitate, say, a powerful Cray computer as far as output (not speed) is concerned. In fact, a universal computer need be nowhere as sophisticated as an IBM PC. It might consist of nothing more than a checkerboard and a supply of checkers! Such a system was first studied by the mathematicians Stanislaw Ulam and John von Neumann in the 1950s as an example of what is called “game theory.” Ulam and von Neumann were working at the Los Alamos National Laboratory, where the Manhattan atomic bomb project was conducted….He [von Neumann] was fascinated to know whether a machine could in principle be built that is capable of reproducing itself, and if so, what its structure might be. If such a von Neumann machine is possible, then we would be able to understand the principles that enable biological organisms to reproduce themselves. The basis of von Neumann’s analysis was the construction of a “universal constructor” analogous to a “universal computer.” This would be a machine programmed to produce anything, much as a Turing machine can be programmed to execute any computable mathematical operation.” (Paul Davies, The Mind of God: The Scientific Basis for a Rational World, pgs. 111-2)
In Leibniz, the principle of gnomonicity is applied to the monads, and with computers, supercomputers and personal computers, the same gnomonic principle applies. This is reminiscent of Chilton’s trangulation of “666,” where removing one layer leaves a smaller, yet same shape. The point here is that the gnomonic principle is based on the mirroring principle, that what is true in thought, logic and nature is also true from the macro-scale to the micro-scale. It is in this way that the secrets of nature encode the rites of the gods. What we see at the subatomic level mirrors what we see in galaxies and the solar system. Wisdom 11:20 states, “But you have disposed all things by measure and number and weight.” However, that scientists will create a “sentient” computer is impossible, given the objective truth of Godel’s Theorums and the impossibility of accounting for all infinite potentialities. AI scientist and semiotician Douglas Hofstadter comments:
“Clearly there is much more going on in typefaces than meets the eye–literally. The shape of letterform is a surface manifestation of deep mental abstractions. It is determined by conceptual considerations and balances that no finite set of merely geometric knobs could capture. Underneath or behind each instance of “A” there lurks a concept, a Platonic entity, a spirit, This Platonic entity is not an elegant shape such as the Univers A, not a template with a finite number of knobs, not a topological or grouping-theoretical invariant in some mathematical heaven, but a mental abstraction–a different sort of beast. Each instance of the “A” spirit reveals something new about the spirit without ever exhausting it. The mathematization of such a such a spirit would be a machine with a specific set of knobs on it, defining all its “loci of variability” for once and for all. I have tried to show that to expect this is simply not reasonable.” (Douglas Hofstadter, Metamagical Themas: Questing for the Essence of Mind and Pattern, pg. 279)
In other words, there is clearly something beyond the letter on paper, the letter spoken, and the letter in mind. Something invariant and not bound by time must link all these particular instantiations, and thus by the wayside falls reductionist materialism (though they are almost incapable of grasping this). The danger is not from sentient supercomputers like some ridiculous Hollywood blockbuster, but from the actual supercomputer spy grid that was erected under the auspices of the Cold War. in his 1982 book on the NSA, James Bamford mentions a curiously titled cryptographic program:
“The timing could not have been better for IBM, which submitted for consideration its Lucifer cipher. Labeled by David Kahn “the tiniest known ‘cipher machine’ ever produced,” Lucifer actually consisted of a thumbnail-sized silicon “chip” containing an extremely complex integrated circuit. The “key” to the cipher was a long string of bits – 0s and 1s – the combination of which would vary from user to user…From the very beginning, the NSA had taken an enormous interest in Project Lucifer.” (James Bamford, Puzzle Palace, pg. 435)
First, remove the chip in your all-seeing eye.“The German version of this [cipher] machine was called the Enigma, on of which was obtained by the British. The Enigma, in conjunction with cryptanalysis techniques allowed the British to decipher many German messages, which significantly altered World War II’s outcome….Companies and governments worldwide are not adopting the public-key cipher system. RSA Data Security, Inc. has grown to be the leading cryptographic marketing company in the nation….
With the phenomenal growth in the use of public-key encryption methods, such as the RSA system, we might be led to believe that public key codes will soon become the national, or even world standard. However, the U.S. Government has been fighting to avoid such a situation. The National Security Agency of the U.S. Government is responsible for breaking the codes of foreign governments- they are our secret spy agency. But the NSA knows it cannot break the public key-codes….No wonder the NSA is upset about the RSA success story.
The government has not been idle, and is now working on a competing system to public-key encryption. In 1987, Congress authorized NIST to develop an acceptable encryption system that would satisfy the needs of user privacy, yet allow law enforcement agencies and the NSA to decipher transmitted messages. This effort became the Capstone Project. Under Capstone, a computer chip, called a Clipper Chip, would be manufactured and installed in computers that interface with the U.S. Government.” (Mathematical Mysteries, pgs. 186, 199-200)
Lucifer and Capstone: Names undoubtedly imbued with esoteric significance. Even in my semi demythologizing project in this essay, I am unable to avoid esoteric notions as we move into the 20th century. It seems that cyrptography, which developed from ancient message writing and gematria, and eventually produced the Enigma machine of World War II and the computer itself, is still deeply related to occult ideas. Does that mean we can decode Lagarde’s cipher? We may not have all the keys for her message, but what we do have is a grounding in the understanding that Lagarde is primarily using her message as a message of statecraft, as old as the art of language itself. Whether one regards the “magic” as real or not, one thing we can be certain of is statecraft and cryptography.
What of gods, then? Must we conclude that it is all statecraft and sciencia and techne,
man in search of secret ways of communicating and being, apart from
anything religious? No, not at all. Man is more religious than ever,
only his gods have changed. Instead, just as we plumb the depths of
nature and science, like Hofstadter’s comments on the Platonic nature of
signs and symbols, each new revelation conceals as much as it reveals.
We are not left with a dry, barren Enlightenment rationalism, nor are
we returning to an ancient superstition. We are involved in the
ever-progressing revelation of reality that spirals for all eternity, as
St. Gregory of Nyssa wrote, up, eternally into the divine. It’s not
dialectics, it’s a principle of unification, and synthesis, and not in a
Hegelian sense (Hegel’s view was based on dialectical tension). This
eternal learning constantly removes superstition as it simultaneously
invites us deeper into theological mystery. It is the acceptance of
paradox, which is very different from a contradiction in philosophy,
that is the appropriate (and Eastern) attitude.Source
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