The Werewolf of the North: The Mystery of Ancient Mathematics


The Second Consciousness

The art of counting finite things precedes civilization itself. It is simply inconceivable that primitive hunter-gathers had no sense of number. Even the higher animals, the warm-blooded predators, arguably have some kind of rudimentary sense of number.

The mortal mind cannot conceive of numbers as purely abstract units, but only as particular numerals, words, or things counted. Therefore numbers do not exist in the mind. But the mind’s discriminatory faculty is the only thing that makes one number different from any other number in its place. Therefore numbers do not exist outside the mind, either. But if numbers do not exist in the mind, nor outside the mind, from whence do they come into being? Numbers exist only insofar as they are feared. They are material things, at least as understood from this planet, and all matter is fear.

Motion, attraction, repulsion, gravity, friction, expansion, contraction, and all other abstract terms related to matter are just that, and only useful to the extent of their practical applicability. They are by no means concrete terms or representative of undying systems of law, no matter how advanced or primitive the way in which they are applied. There are really only three simple rules of matter: Everything for fear, nothing above fear, and nothing outside of fear.

But what happens when fear is conquered? Surely that conquest reveals a second consciousness, one that stands above the ordinary, fear-driven existence. Where else would the idealistic concept of the number, the number as an idea, come from, if not from the conquest of fear?

 

Zalmoxis and Pythagoras

Numerical systems, in the complete sense, are as old as the ancient Sumerians. What is known as “Babylonian mathematics” predates the empire of Babylon, and also outlasted it. Egypt also developed its own mathematics around this time, different but related. The “Babylonian” system placed a high emphasis on the number sixty, which still survives in our systems of counting time.

The Greeks, once thought to have been the sole inventors of mathematics, have been considerably knocked down a peg in this regard, ever since it was proven that this was in no way the case. This has gotten tiresome, and even if the Greeks were not as all-important to mathematics as once thought, they still contributed far too much to the art of number to justify the current practice of dragging their names through the mud as mathematicians. This is particularly true of Pythagoras.

Many modern scholars, the type with the habit of distrusting ancient sources simply because they’re ancient, question whether Pythagoras discovered any original mathematical theorem at all. It is unlikely, however, that a mathematically inclined cult could have been founded by anyone other than somebody with a high understanding of mathematical ideas. Some ancient sources say Pythagoras traveled to Egypt, borrowing influences from the older civilizations of the south. But Pythagoreanism was equally influenced by the Indo-European north, by Phrygia and especially Thrace.

North of the Danube was northern Thrace, much of which was later termed Dacia, cradle of the cult of Zalmoxis. According to Herodotus—correcting the contemporary Greek slander of the Thracian beliefs—Zalmoxis, thought by the Greeks to have been Pythagoras’ slave and learned the latter’s famous theorem, actually lived long before Pythagoras. Zeno charged Pythagoras and his followers with having plagiarized the Orphics, the Greek Dionysian cult whose beliefs and practices scholar Walter Wili showed to have been of northerly, Indo-European—mainly Thracian—origin.[1]

Heraclitus deplored Pythagoreanism for its alien Thracian origins, associating it with the cult of Dionysus – a cult that, in its original Orphic form, also came from Thrace. This influential pre-Socratic Greek philosopher was dismayed by what he considered “drunken Greeks initiated into the Thracian ecstasies of Dionysus,”[2] and many of Heraclitus’ fellow Greeks shared that attitude. Heraclitus heavily influenced later Greek philosophers, but so did the Thracian-influenced Pythagorean mathematicians.

 

 The Northerly Wolf

In the second chapter of The Decline of the West, Oswald Spengler demonstrates that modern infinitesimal mathematical systems did not develop as a direct continuation of the mathematics of the Greek philosophers. Rather, they were a negative reaction to Greek mathematics by what he calls the “Faustian” (medieval-to-modern Western) civilization. In a similar way, the entire tradition of Greek philosophy, starting with pre-Socratic philosophers like Heraclitus and Zeno, was a negative reaction to the un-Greek Thracian influences in Pythagoreanism.

Spengler viewed technics (die Teknik), which is closely related to science, as an expression of man’s predator instincts. His concept of “man as a beast of prey” is similar to the primeval belief in werewolves, which was likely of Indo-European origin, perhaps originating from whichever component of the Indo-European steppe came from the forests even further north. Originally, lyncanthropy was viewed in positive terms.

According to Mircea Eliade, “the Dacians called themselves ‘wolves’ or ‘those who are like wolves’, who resemble wolves. Still according to Strabo (7. 3. 12; 11. 508, 511, 512), certain nomadic Scythians to the east of the Caspian sea were also called daoi. The Latin authors called them Dahae, and some Greek historians daai. In all probability their ethnic name derived from Iranian (Saka) dahae, ‘wolf’. But similar names were not unusual among the Indo-Europeans.” [3]

As late as 1850, Sabine Baring-Gould, reflecting on Ovid’s legend of the lycanthropic king of Arcadia, reports that “Half the world believes in, or believed in, were-wolves, and they were supposed to haunt the Norwegian forests by those who had never been remotely connected with Arcadia: and the superstition had probably struck deep its roots into the Scandinavian and Teutonic minds, ages before Lycaon existed; and we have only to glance at Oriental literature, to see it as firmly engrafted in the imagination of the Easterns.” [4]

 

The Pain of the Steppe

Nicolae Iorga was partly correct and partly wrong when he described the Scythians thus:

 

“The soldiers were mainly Turanians, of dark skin and squat frame, like the Turcomans of central Asia and the Tartars of a later date, who, having consumed the fruits of their ruthless incursions and the tribute rendered by tribes subjected to their authority, lived on the produce of their flocks.” [5]

 

Iorga is more or less right about the Scythian lifestyle and political economy, but like many historians of his era, he errs about the Scythian racial and ethnic characteristics. The Scythians, like the Thracians and the Sarmatians, were linguistically Indo-European and racially Europid.[6] However, like the original Indo-European horsemen they closely resembled and descended from, the Scythians were indeed semi-nomadic herdsmen.

All law originally derives from some type of collective land-appropriation. Thrace represents the first time in history that a new form of law was born out of the Indo-European land-appropriation of Old Europe. The Pontic Steppe’s conquest of the south began at Thrace.

From 4200 to 3900 B.C., long before the Indo-Europeans reached Greece or India, over “six hundred” Old European settlements “were burned in the lower Danube valley and eastern Bulgaria.” These Old European cultures tried to escape to a settlement in Jilava, but “Jilava was burned, apparently suddenly, leaving behind whole pots and many other artifacts. People scattered and became much more mobile, depending for their food on herds of sheep and cattle rather than fixed fields of grain. The forest did not regenerate; in fact, pollen cores show that the countryside became even more open and deforested.”[7]

According to Eliade, “it appears that the Indo-Europeans shared a common system of beliefs and rituals pertaining to young warriors.” [8] However, it would be a mistake to confuse these young Indo-European warrior societies with what one historian of mathematics describes as the intellectually influential “military-industrial complex” seen in the pre-Indo-European civilizations.[9] The original founders of the Dacian culture, for example, were “either immigrants from other regions, or young men at odds with the law.” [10]

The original Indo-European lycanthropic initiatory societies were related to pastoral paramilitaries, not settled city-state militaries. The sky-worshipping Indo-European conquerers brought to earth-worshipping Old Europe, starting with Thrace, not only a new idea of military tactics, but also a new idea of law. A revolution in tactics is inconceivable without a revolution in jurisprudence.

The Indo-Europeans were in no way work-shy. Their steppe culture was no convention of gay cowboys, and had no room for luxury. This is evident in the fact that the horses they were the first to domesticate were in fact ponies, a tradition which survived in Wallachia into the 19th Century. The “extremely sure-footed,” if joyless, Wallachian pony described by Field Marshal Count Moltke in his memoirs was actually the original Indo-European war chariot horse. [11]

We can say then, that their groundbreaking technology revolutionized the way the Indo-Europeans perceived work, and more deeply, the way they perceived pain. They possessed the early-Roman spirit of Cato the Elder, who described an ideal master who works at least as hard as his slaves. It was the spirit of the warrior-worker, the Arbeiter-aristocracy.

Some Indo-European steppe warriors were female, although the extent to which this was common, and the extent to which they served in frontline combat, are both disputed. It seems likely that, in addition to bearing and raising children, the Indo-European women served a role similar to the German Landsknecht women of the 16th century German mercenary outfits — that is, an important role in the back lines of war. [12]

Whatever the lost details, from the revolutions in technology and in the perceptions of work and pain clearly proceeded revolutions in sexual division of labor. This revolution had the destiny of an army of mechanized insects, and left very little room for something as decadent and unproductive as homosexuality. Whereas Old Europe had emphasized plurality, the Indo-European steppe prioritized polarity.

 

Zalmoxis and Anubis: Blood and Ink

            Ant-like revolutions in technology and sexual division of labor are related to what Ernst Jünger called a “second consciousness” that stands above and beyond pain. Only under these circumstances, the great German soldier and thinker argued, does man come to objectify his own body as an “outpost.”[13] This revolutionary second consciousness of the Indo-Europeans was reflected in the Thracian sacrifices to Zalmoxis, in which an unfortunate victim was thrown onto a set of spears – surely an ordered set of spears, in light of such a sacred ritual.

This sacrifice ritual has been dismissed as barbaric, and that it was. But it was a productive barbarism, like the even crueler rituals of the Amerindian Mayans. Like Mayan mathematics, the art of Pythagorean geometry invokes nothing if not more intense stab wounds than those of the older mathematics of the pre-Indo-European civilizations.

Like the Mayans, the Thracians invented a mathematics of blood. Unlike the hapless Mayans, the Thracians were surrounded by older civilizations with older mathematical achievements. The Thracians influenced the omnivorous Greeks, who synthesized this mathematics of blood with the Egyptian mathematics of ink. The dynamic Thracian torture-cult of Zalmoxis was the blood, the morbid old embalmment-cult of Anubis the ink, of Greek mathematics. That is why there is so much life and energy in the stab wounds of Pythagorean and Mayan mathematics, compared to the dull embalmment scars of pre-Indo-European mathematics. Plato synthesized life-giving blood-mathematics with decayed ink-mathematics, thus completing the Indo-European mission to reunite the primordial polarity of life and death.

The pain-affirming idea of the body as an outpost was alien to the pleasure-seeking cultures of Old Europe, but the idealistic, contemplative aspects of Greek mathematics would have been inconceivable without it. The concept of the body as a prison of the soul was a Thracian import, rejected by Greek critics of Pythagoreanism and Orphism, but it is reflected in Plato’s view of numbers. The empirical and militaristic aspect of Plato’s mathematics is of southern, pre-Indo-European origin and probably came from Egypt, but the abstract idea of numbers existing in themselves was the Greek response to ideas inspired by the Thracian cult of Zalmoxis.

Out of this synthesis of empiricism and idealism proceeded the Greek contributions to mathematics, especially geometry. These innovations would later influence the medieval Arabs and Persians, who synthesized it with the ideas of ancient India. The infinitesimal systems of the European Age of Discovery could not escape the fact of being heirs to the Classical systems, even if they were backlashes against their ancient predecessors.

In many ways, the Arab and “Faustian” systems continued the purely contemplative aspects of Greek mathematics, heightening these abstractions to their maximum potential. These were the elements of Greek mathematics that originated in Thrace, the very first space in the world where the pain-affirming Indo-Europeans conquered pleasure-seeking Old Europe. Thus, for the first time in the history of mathematics, was man’s fear of matter conquered by man’s second consciousness.

           Notes

[1] [Wili in Eranos Yearbooks: The Mysteries]

[2] [from Heraclitus, Fragments, Penguin edition introduction, p. xxv]

[3] [Eliade, Zalmoxis: The Vanishing God, p. 2]

[4] [Baring-Gould, Cosimo Classics edition, p.8]

[5] [Iorga, Nicolae, A History of Roumania, pp. 13-14]

[6] [Hildinger, Erik, Warriors of the Steppe: A Military History of Central Asia 500 B.C. to 1700 A.D., p. 33; Сергей Иванович Руденко, Frozen Tombs of Siberia: The Pazyryk Burials of Iron age Horsemen, Ch. 3 (p.45).]

[7] [Anthony, David W., The Horse, The Wheel, and Language: How Bronze-Age Riders from the Eurasian Steppes Shaped the Modern World, p.227]

[8] [Eliade, Zalmoxis: The Vanishing God, p. 6]

[9] [Hodgkin, Luke, A History of Mathematics: From Mesopotamia to Modernity p.262]

[10] [Eliade, Zalmoxis, p.3]

[11] [Hildinger, p. 16; Florescu, Radu R. and McNally, Raymond T. Dracula, Prince of Many Faces: His Life and His Times, p.141; Brzezeinski, Richard, Polish Armies 1569-1696, p.23 Helmuth Graf von Moltke, Moltke: His Life and Character, p.130]

[12] [For differing interpretations of the role of Sarmatian women, for example, see Beckwith, p.70, and Hildinger, p. 47. As for the role of women on the primeval Indo-European steppe, this question has provoked a scholarly study called Are All Warriors Male? Gender Roles on the Ancient Eurasian Steppe, edited by Katheryn M. Linduff and Karen S. Rubinson. For the role of women in early modern German Landsknecht units, see “Kampfrau Dress Germany/Switzerland 1500,” Lady Alesone Gray (Wendy Marques)]

[13] [Jünger, On Pain, 2008, Telos Press]



By: A. E. Stern



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