Showing posts with label Pythagoras. Show all posts
Showing posts with label Pythagoras. Show all posts

Tuesday, July 1, 2025

Tuesday Special - Tetractys and Lattice Infinity

 

9 + 16 = 25

32 + 42 = 52.


a2 +b2 = c2.

Real magic. The Pythagoras Theorem. Except that it does not belong to Pythagoras. Pythagoras was a mystic, not a mathematician.

“There is not a single mathematical sentence that can be attributed with certainty to Pythagoras as an individual. The image of Pythagoras as a mathematician and scientist is a construction of later times. In contrast, the belief in the transmigration of souls and the religious character of the Pythagorean community is consistently and early attested. The historical Pythagoras appears not as a scientist, but as the founder of a way of life.”
Walter Burkert, Lore and Science in Ancient Pythagoreanism, trans. Edwin L. Minar Jr., Harvard University Press, 1972, p. 113

"Pythagoras appears as a figure of the shaman type, especially in his claim to possess a soul of a special kind and in his ability to recall its previous incarnations. He was thought to have a miraculous, semi-divine origin; he performed healings and miracles; he was able to travel great distances in a moment, to be in two places at once, and to communicate with the dead. These are traits which correspond to shamanistic ideas and practices found in Central Asia and the Near East."
— Walter Burkert, Lore and Science in Ancient Pythagoreanism, trans. Edwin L. Minar, Jr. (Harvard University Press, 1972), p. 298

Tetractys

But, it is said that the Pythagorean Brotherhood worshipped the Tetractys: 1- the Monad, 2 - Duality, 3 - the Triad (beginning of form), 4 - the Tetrad (the World).

Back to (3,4,5). Pythagorean triples ware know to Babylonians ~1800 BCE. They knew (3, 4, 5), (5, 12, 13), (7, 24, 25), and wrote it in cuneiform. They knew even larger triples, such as (119,120,169). But in the Pythagorean Brotherhood there were initiation rites and levels of access. I think that the members of its inner circle knew that beyond the popular Triad a2+b2=c2, at a deeper level, there is the well balanced Tetrad:

  a2 + b2 =c2 + d2, (a,b,c,d integers).            (1)

Of course tetrads contain triads, when one of the numbers is zero. So, those who know Tetrads, know also Triads, but not the other way. Of course we are interested in primitive solutions, that is in cases where a,b,c,d have no common divisor.  I could not find anything about tetrads in Babylonia, but I found them on math.stackexchange: Diophantine equation a2 + b2 =c2 + d2. The complete solution can be found in the textbook L.J. Mordell, "Diophantine Equations", Academic Press 1969, on p. 15.

Well, it is not explicitly complete there, it is somewhat sketchy, but here it is (I skip the proof).

Proposition 1. Every primitive solution of  (1) is of the form

a = (mp+nq)/2,
b = (np-mq)/2,
c = (mp-nq)/2,
d = (mq+np)/2,

where m,n,p,q are integers. Conversely, for any integers m,n,p,q such that a,b,c,d are integers, the formula above provides a solution of  a2 + b2 =c2 + d2.

What it has to do with the compactified Minkowski space?

Recall the quadratic form Q from The infinity ab initio:

Q(X) = (X1)2 + (X2)2 + (X3)2 -(X4)2+ (X5)2 - (X6)2,

and the equation of the null cone N:

(X1)2 + (X2)2 + (X3)2 - (X4)2 + (X5)2 - (X6)2 = 0.

Skip two dimensions X2 and X3:

(X1)2  - (X4)2+ (X5)2 - (X6)2 = 0.

Rewrite it as

(X1)2 + (X5)2  = (X4)2 + (X6)2 .            (2)

Then set X1 = a, X5 = b, X4 = c, X6 = d, and you get (1). In (2) we are interested in the projective cone PN. Each tetrad a,b,c,d satisfying (1) determines a unique point (a',b',c',d') = λ(a,b,c,d)  on PN for which a'2+b'2 = c'2+d'2 = 1. We get a point on the torus S1S1. That is the image of our compactified Minkowski space with suppressed two space-like dimensions. By assuming the X components are integers we assume that ℝ4,2 is a regular discrete lattice.

And so I did. Using Proposition 1 I generated about 1 mln of tetrads (a,b,c,d) and plotted them on a torus. Here is the result:

627169 + 627169 + 4446 points

There is some pattern there that can be seen. I do not understand where this pattern comes from, except, perhaps, of two circles around the torus. We will meet these circles soon. They represent  infinity.


Thursday, August 10, 2023

The Cosmic Context of Greek Philosophy: Part Nine

 The Cosmic Context of Greek Philosophy: Part Nine

Laura Knight Jadczyk

Delian Divers

Going in another direction now for a moment, Diogenes mentions a curious exchange in his Life of Socrates.

Unlike most philosophers, he had no need to travel, except when required to go on an expedition. The rest of his life he stayed at home and engaged all the more keenly in argument with anyone who would converse with him, his aim being not to alter his opinion but to get at the truth. They relate that Euripides gave him the treatise of Heraclitus and asked his opinion upon it, and that his reply was, “The part I understand is excellent, and so too is, I dare say, the part I do not understand; but it needs a Delian diver to get to the bottom of it.”[1]

Then, in his Life of Heraclitus, he writes:

The story told by Ariston[2] of Socrates, and his remarks when he came upon the book of Heraclitus, which Euripides brought him, I have mentioned in my Life of Socrates. However, Seleucus the grammarian[3] says that a certain Croton relates in his book called The Diver that the said work of Heraclitus was first brought into Greece by one Crates, who further said it required a Delian diver not to be drowned in it. The title given to it by some is The Muses, by others Concerning Nature; but Diodotus calls it ‘A helm unerring for the rule of life’; others ‘a guide of conduct, the keel of the whole world, for one and all alike’.[4]

What, one might ask, is a “Delian diver”? Is it as simple as assuming that Heraclitus’ work was so deep that it needed an experienced swimmer to dive to the depths to obtain the pearls therefrom? Or is there something more here? Is this a hidden allusion to something that may be important about the relationships between these individuals? Or about their ideas?

First, let’s consider one of the charges brought against Socrates; “…refusing to recognize the gods recognized by the state, and of introducing other new divinities.” At his death, Diogenes tells us that:

… according to some, he composed a paean beginning: “All hail, Apollo, Delos’ lord! Hail Artemis, ye noble pair!”

Were Apollo and Artemis ‘new divinities’?

Apollo was recognized as a god of light and the Sun, truth and prophecy, healing, plague, music, etc. He was the son of Zeus and had a twin sister, the virginal huntress, Artemis. He was known to the Etruscans as Apulu. He was the patron of Delphi – the prophetic deity of the Oracle. The lyre was one of his symbols, as it was a symbol for Orpheus. (Recall that Socrates undertook to learn to play the Lyre.) It was long assumed that, as early as the 3rd century BC, he became identified among Greeks with Helios and Artemis became identified with the Moon. However, scholar Joseph Fontenrose declared that there was no evidence of this conflation earlier than the 3rd century AD![5]

The Homeric hymns represent Apollo as a Northern intruder and his arrival must have occurred during the Dark Ages. His conflict with Earth was represented by the legend of his slaying her daughter, the serpent Python. Apollo and Artemis can bring death with their arrows. The idea that disease and death come from ‘invisible arrows’ fired by supernatural beings was common to Germanic and Norse mythology. The Vedic Rudra has similar functions to Apollo and the terrible god is called ‘The Archer’. The bow is an attribute of Shiva. Rudra could also bring diseases with his arrows. There are other dragons and serpents slithering around in all these stories, suggesting cometary connections.[6] [7]

It seems that the oracular cult goes back to Mycenaean times, and in historical times the priests of Delphi were referred to as ‘the double axe men’ which relates them to the Minoans as well. The double axe was the holy symbol of the Cretan labyrinth and is probably due to cometary plasma manifestations.



The non-Greek origins of Apollo have long been acknowledged by scholars, but it was assumed that he came from Anatolia where oracular shrines, symbols, etc. have been found and purification and exorcism texts appear on old Assyro-Babylonian tablets. A Hittite text mentions that the king invited a Babylonian priestess to come and perform a certain purification. A similar story is told by Plutarch who writes that the Cretan seer Epimenides assisted Solon (c.638 BC-558 BC) in the purification of Athens after the pollution brought by the Alcmaeonidae discussed above.[8]

Homer depicts Apollo on the side of the Trojans against the Achaeans during the Trojan War, thus he is pictured as a terrible god who is not to be trusted by the Greeks. In the late Bronze Age (1700 to 1200 BC), the Hittite and Hurrian god Aplu was a god of plague who was invoked during times of pestilence to end same. Aplu means ‘son of’ and was the title given to Nergal. (Note: Etruscan Apulu above.) Apollo’s cult was already fully established in both Delos and Delphi by about 650 BC and the frequency of ‘godly names’ given to children, such as Apollodorus or Apollonios, testify to his popularity.

In conclusion, we can say that, no, Apollo and Artemis were not ‘new divinities’ being introduced by Socrates, so the claim must apply to something else. Perhaps he came to these views after reading the works of Heraclitus and Pythagoras? We recall regarding Heraclitus’ work:

… his treatise ON NATURE was divided into three discourses, one on the universe, another on politics, and a third on theology. He deposited the book in the temple of Artemis and, “according to some, made it the more obscure in order that none but adepts should approach it.”

The claim that only an adept can penetrate the work of Heraclitus immediately brings to mind the Delian diver as a descriptive name of such an adept.

Referring back to the apparent northern origin of Apollo leads me to this point: Pythagoras was associated with ‘Hyperborean Apollo’ also, and one of the links between Socrates and Pythagoras is that they both practiced a form of divination. In reference to Socrates, Diogenes writes:

He used to say that his supernatural sign warned him beforehand of the future…

Considering the several connections between Apollo and pestilence/plague, one is reminded of the special point that Diogenes made of mentioning that Socrates was unaffected by the plague that struck Athens during the Peloponnesian wars.


Another curious thing is the remark by Diogenes that “Unlike most philosophers, he had no need to travel, except when required to go on an expedition”, followed later by:

Ion of Chios relates that in his youth he visited Samos in the company of Archelaus; and Aristotle [said also] that he went to Delphi…

So, he never traveled unless required, but two trips are mentioned. Was a visit to Samos, the hometown of Pythagoras, ‘required’ as an expedition of some sort? What about the expedition to Delphi? Was this also ‘required’ for some reason? Additionally, a fragment by Heraclitus states the following:

The Sibyl with raving mouth utters things mirthless and unadorned and unperfumed, [in short, no BS!] and her voice carries through a thousand years because of the god who speaks through her.[9] The lord whose oracle is in Delphi neither declares nor conceals, but gives a sign. [Emphasis, mine][10]

This reminds us that Pythagoras was said to have been taught by the Delphic priestess, Themistoclea. And despite the fact that Heraclitus put Pythagoras on his short list of people who weren’t able to figure everything out, he acknowledged that he was, indeed, possessed of a great deal of knowledge.



So, just what is this “Delian diver” business about? Who is Croton and what is his book The Diver about? Who is Crates, said to have brought Heraclitus’ book to Greece and to have given the same opinion of it, using the same term, as Socrates himself? (Note that it is said that it was Euripedes who gave the book to Socrates.)

The only Crates we know of is the Stoic philosopher, Crates of Thebes, who lived between 365 and 285 BC, much too late to have brought the book to Greece during the time of Socrates. There is no other Crates to be found. There is no ‘Crates’ or ‘Croton’ mentioned as persons in the Suda. In fact, the Suda fuses both of Diogenes Laërtius’ versions of this Delian diver story into one, giving the impression that the author of the remark is only Socrates; that they assumed Crates and So-crates (shades of Bill and Ted!) were one and the same person.

The only thing respecting Croton that occurs to me is that it was the city that Pythagoras moved to in 530 BC, where he and his followers were apparently welcomed and became active in the local politics until they were destroyed.[11]

What about the Delian diver? Why a diver from Delos and not just any other place? During classical times, divers from this island were not considered to have any special abilities nor to perform any special tasks that might distinguish them from divers living on any other island. So the term underscores the difficulty of penetrating what Heraclitus wrote and, as I noted above, can be compared to being an adept, which might suggest some sort of secret society or Mystery cult.

At this point, I want to refer back to something I wrote in my first volume, Secret History, which marvelously brings several of these elements together, including bringing in Hecataeus, one of the others on Heraclitus’ short list of wise people who were close but didn’t quite go the distance. Diodorus Siculus tells a very strange story about the Hyperboreans that is an extract from the work of Hecataeus:

Of those who have written about the ancient myths, Hecateus and certain others say that in the regions beyond the land of the Celts (Gaul) there lies in the ocean an island no smaller than Sicily. This island, the account continues, is situated in the north, and is inhabited by the Hyperboreans, who are called by that name because their home is beyond the point whence the north wind blows; and the land is both fertile and productive of every crop, and since it has an unusually temperate climate it produces two harvests each year.

The Hyperboreans also have a language, we are informed, which is peculiar to them, and are most friendly disposed towards the Greeks, and especially towards the Athenians and the Delians, who have inherited this goodwill from most ancient times. The myth also relates that certain Greeks visited the Hyperboreans and left behind them costly votive offerings bearing inscriptions in Greek letters. And in the same way Abaris, a Hyperborean, came to Greece in ancient times and renewed the goodwill and kinship of his people to the Delians. [Emphases, mine][12]

Diodorus’ remark about the relations between the Hyperboreans and the Athenians and Delians is extraordinary in the specific terms that it was “inherited from most ancient times.” What gets my antennae quivering is the statement that something costly and inscribed was taken to the Hyperboreans and left with them. That this story was common enough is demonstrated by the fact that Herodotus also writes about the relationship of the Hyperboreans to the Delians:

Certain sacred offerings wrapped up in wheat straw come from the Hyperboreans into Scythia, whence they are taken over by the neighbouring peoples in succession until they get as far west as the Adriatic: from there they are sent south, and the first Greeks to receive them are the Dodonaeans. Then, continuing southward, they reach the Malian gulf, cross to Euboea, and are passed on from town to town as far as Carystus. Then they skip Andros, the Carystians take them to Tenos, and the Tenians to Delos. That is how these things are said to reach Delos at the present time. [13]

Why is Scythia depicted as being east of the Adriatic? I suspect there are clues here, but I don’t have time to stop and go in ten different directions on that. We have to follow this particular thread to the end. The legendary connection between the Hyperboreans and the Delians leads us to another interesting remark of Herodotus, who tells us that Leto, the mother of Apollo, was born on the island of the Hyperboreans

Leto with the infants Apollo and Artemis, by Francesco Pozzi (1824)

That there was regular contact between the Greeks and the Hyperboreans over many centuries is the claim here, but for modern historians, it is highly questionable. Here, we don’t know if we are talking about real people who have been assimilated to comet myths or not. But my thought is that it suggests an origin for the peoples who came down into Greece and Anatolia at some point in the distant past, at the time of a great cometary bombardment, and those people could be the later Mycenaeans and the Hittites, and even the Roman, but formerly the Trojans who were the people of Apollo who was Hyperborean! That, of course, leads to the idea, long theorized by a number of scholars, that Troy was not in the Mediterranean. [14] Herodotus has another interesting thing to say about the Hyperboreans and their sending of sacred offerings to Delos:

On the first occasion they were sent in charge of two girls, whose names the Delians say were Hyperoche and Laodice. To protect the girls on the journey, the Hyperboreans sent five men to accompany them … the two Hyperborean girls died in Delos, and the boys and girls of the island still cut their hair as a sign of mourning for them… There is also a Delphic story that before the time of Hyperoche and Laodice, two other Hyperborean girls, Arge and Opis, came to Delos by the same route. …Arge and Opis came to the island at the same time as Apollo and Artemis[15]

It does sound like something of a migration took place and there are some mysterious elements that offer shadowy allusions to objects of power and an exodus. Herodotus mentions at another point, when discussing the lands of the ‘barbarians’, “All these except the Hyperboreans, were continually encroaching upon one another’s territory.” Without putting words in Herodotus’ mouth, it seems to suggest that the Hyperboreans were not greedy, power-hungry and warlike.

A further clue about the religion of the Hyperboreans comes from the myths of Orpheus. It is said that when Dionysus invaded Thrace (coming from the South to the North), Orpheus did not see fit to honor him but instead preached the evils of sacrificial murder to the men of Thrace. He taught “other sacred mysteries” having to do with Apollo, whom he believed to be the greatest of all gods. Dionysus became so enraged that he set the Maenads[16] on Orpheus at Apollo’s temple where Orpheus was a priest. They burst in, murdered their husbands who were assembled to hear Orpheus speak, tore Orpheus limb from limb, and threw his head into the river Hebrus where it floated downstream still singing. It was carried on the sea to the island of Lesbos. Another version of the story is that Zeus killed Orpheus with a thunderbolt (comet imagery) for divulging divine secrets. He was responsible for instituting the Mysteries of Apollo in Thrace, Hecate in Aegina, and Subterrenean Demeter at Sparta. And this brings us to a further revelation of Diodorus regarding the Hyperboreans:

And there is also on the island both a magnificent sacred precinct of Apollo and a notable temple, which is adorned with many votive offerings and is spherical in shape. Furthermore, a city is there which is sacred to this god, and the majority of its inhabitants are players on the cithara; and these continually play on this instrument in the temple and sing hymns of praise to the god, glorifying his deeds… They say also that the moon, as viewed from this island, appears to be but a little distance from the earth and to have upon it prominences, like those of the earth, which are visible to the eye. The account is also given that the god visits the island every nineteen years, the period in which the return of the stars to the same place in the heavens is accomplished, and for this reason the Greeks call the nineteen-year period the “year of Meton”. At the time of this appearance of the god he both plays on the cithara and dances continuously the night through from the vernal equinox until the rising of the Pleiades, expressing in this manner his delight in his successes. And the kings of this city and the supervisors of the sacred precinct are called Boreades, since they are descendants of Boreas, and the succession to these positions is always kept in their family.

First of all, it appears obvious that this spherical temple may be Stonehenge. Well, Stonehenge is actually circular now, but who knows what it looked like in ancient times? Perhaps it was made to appear spherical with its finishings? The second thing is the music which was so important to the Orphics and Pythagoreans. We also note that after reading Heraclitus’ book, Socrates apparently took up playing the lyre! The third thing is the reference to the prominences on the Moon which reminds us that Anaxagoras declared that there were hills and valleys and dwellings on the Moon. Was he researching in these areas and – perhaps – mixing things up just a bit, but most dangerous of all, talking about it publicly, leading – ultimately – to his death? Finally, the dancing of the god brings us to consider something rather important. Diodorus is suggesting that the 19-year lunar calendar is a product of the Hyperboreans and that it relates to a period in which the ‘return of the stars’ is accomplished. This is easily understood as the Metonic cycle[17], but there is more to this than just that: there is the god dancing through the night from the vernal equinox until the rising of the Pleiades!  One can imagine plasma phenomena dancing in the sky, looking like the humanoid figure of a god.

A "Dancing God"? 

Could this knowledge of cycles of destruction and certain perspectives on the impersonal nature of the universe, and the attempt to share it widely, be the key to the executions of both Anaxagoras and Socrates? Could this knowledge of comet cycles have been the same knowledge possessed by Heraclitus and Pythagoras? Could it be that Anaxagoras did, actually, predict a period of cometary bombardment as suggested, which then actually occurred during the Peloponnesian wars? Was there a Tunguska-like event at the time of the final defeat of the Athenians? Such knowledge would be terrifying to the wealthy elite and their need to control and dominate populations of people which would explain why individuals who knew such things went underground and gave out the clues in a sort of code about ‘Delian divers’. Tatian, (c. 120-180 AD) the early Assyrian Christian, writes along this line:

I cannot approve of Heraclitus, who, being self-taught and arrogant said, ‘I have explored myself.’ Nor can I praise him for hiding his poem in the temple of Artemis, in order that it might be published afterwards as a mystery; and those who take an interest in such things say that Euripides the tragic poet came there and read it, and, gradually learning it by heart, carefully handed down to posterity this darkness.[18]

Well, certainly, as a Christian, he would think that the physics of Heraclitus was demonic, but it seems that he was offended by more than just that. The Christians had a very good reason to conceal the possibilities of cyclical cosmic destruction that was not under the control of their god!

Now, what about Delos, itself? We find the answer with Pherecydes and his Pentemychos Recall the lines from the Odyssey:

There is an island called Syrie – perhaps you have heard of it – above Ortygie, where are the turnings of the sun.

Compare it to Diogenes’ report about Pherecydes:

There is preserved of the man of Syros [Pherecydes] the book ... and there is preserved also a solstice-marker in the island of Syros.

Obviously, if this marker was known to Homer, it was there long before Pherecydes! Also, as it happens, the former name of Delos was Ortygie. The name, Delos, alludes to the concept of brilliance, clarity and transparency. The myth tells us that Apollo, in gratitude, changed the name of the island on which he was born, formerly called Ortygia, to Delos, ‘visible’, ‘manifest’, ‘clear’.[19] Further, according to Diogenes Laërtius, Pythagoras included in his list of former incarnations a Delian fisherman named Pyrrhus. No, it’s not a ‘Delian diver’, but one who fishes from the surface, and afterward he was reincarnated as Pythagoras, a Delian Diver?  Additionally, the name Pyrrhus was also given to the son of the warrior Achilles who died in the Trojan war. I’ve already mentioned that I suspect that the Trojan war itself was a cometary event or was related in some way to same.

So, the question is: was there some sort of knowledge passed on to such as Socrates, from Heraclitus and Pythagoras, and others, Delian divers all? And did that knowledge include ideas relating to periodic cometary bombardments and destruction of society? Were those ideas predicated in terms of the behaviors of society – particularly the wealthy elite rulers - attracting or repelling destruction? Is that the sort of thing that would have gotten both Anaxagoras and Socrates executed because it was seen as disruptive to the public order because it challenged the very existence of a wealthy elite?

Finally, in respect of the term Diver, let me remind you of what I wrote above:

A selection of the stories of the Northern Eurasians – mainly those living between the Black Sea and the Caspian Sea[20] – have been collected together, along with some of the geological and archaeological evidence, by Heinrich Koch in a book entitled The Diluvian Impact.[21] It is highly recommended, with a small caveat: he seems to have conflated a number of events. Nevertheless, I found there the origin of certain stories that are said by Yuri Stoyanov[22] to be the oldest forms of dualism:

The Palaeo-Siberians have created remarkable rock drawings, so-called petroglyphs, which not only represent a peculiar early artistic style, but also reveal incredibly precious traditions from hoary antiquity. One motif, which is repeatedly outlined, is the Mudur, the divine sky-dragon… The Mudur is connected to coiled and crooked-line ornaments, the Amur-spiral, and the Amur-network, symbolizing the divine serpent, another figure that represents the comet. …

It is the primeval myth of the three suns which is permanently repeated among almost all Palaeo-Siberian peoples, and it says this: In former times, three evil suns were standing in the sky which brought death and devastation over Earth in a violent fire-storm and an everything-destroying forest fire. The heat, as it is reported, even softened stones, so that birds left marks of their claws on them when stepped upon. The legendary hero Boa-Enduri destroyed two of the suns by arrowshots, however, he missed the third one. The splinters and fragments of the evil suns got spread as stars over the whole firmament. Earth and water boiled in the ardour. Finally, the whole globe was covered with water. Thereafter, the sky or water-dragon disappeared from the firmament, and since that time it lives hidden in the swamp or under water. Also the diver’s motif re-appears here: Three swans fetch earth from the bottom of the water which covered the whole country for seven days. After this, the ground solidified again….Recent newborns died from the ardour, later on from the cold… On Earth, the corpses piled up, however, it was impossible to bury them… (p. 51)

 

Now, I've asked a lot more questions than I have answered; that seems to be the way of history when so much has been destroyed.  In the case of the archaeological leavings, we can imagine now why they have been largely destroyed; but as for the records of the reasons for the destructions, it seems that human hands have often covered up more than has been revealed.  Keep in mind that both Socrates and Pythagoras were ‘handled’ by Plato after their deaths, possibly for reasons having to do with self-preservation. Their ideas and teachings were modified and ‘Platonized’ and, in the end, whether it was conscious and deliberate to keep on the right side of the authorities, or simply ego, it still amounts to a systematic cover-up of the truth. 







[1] Diogenes Laertius, II 21-23.

[2] Father of Plato.

[3] Seleucus of Alexandria, a Roman-era Grammarian. He was nicknamed ‘Homeric’. He commented on most of the ancient poets, wrote a number of exegetical and miscellaneous works, the titles of which are given by Suidas but there’s not much else to go on.

[4] Diogenes Laertius, IX 11-13.

[5] Bowden (2005) Classical Athens and the Delphic Oracle: Divination and Democracy.

[6] Nilsson (1992) Die Geschicthe der Griechischen religion, Vol. I p.543.

[7] Hall (2005) ‘Getting Shot of Elves: Healing, Witchcraft and Fairies in the Scottish Witchcraft Trials’.

[8] Nilsson, op. cit., pp. 563-564.

[9] DK 22 B 92.

[10] DK 22 B 93.

[11] Also, while it cannot possibly have any relationship, I am reminded of Virginia Dare and the lost colony of Roanoke. The only clue to the colonists' fate was the word 'Croatoan' carved into a post of the fort, and the letters 'Cro' carved into a nearby tree.

[12] Diodorus of Sicily, trans. C. H. Oldfather, Volumes II (1935) and III (1939). All quotes from Diodorus are from the same translation.

[13] Herodotus, The Histories, Book IV, trans. Aubrey De Selincourt, p. 226.

[14] See Iman Wilkens’ book Where Troy Once Stood for details, but keep in mind that he is working without taking cometary bombardment into account and is assuming that the Trojan War was actually a human-fought conflict.

[15] Herodotus, The Histories, pp. 226-227.

[16] This word reminds me of Alcmaeonidae.

[17] A period of very close to 19 years, which is nearly a common multiple of the solar year and the synodic (lunar) month. The Greek astronomer Meton of Athens (5th century BC) observed that a period of 19 years is almost exactly equal to 235 synodic months, and rounded to full days counts 6,940 days. The difference between the two periods (of 19 years and 235 synodic months) is only a few hours.

[18] Tatian, Oratio ad Graecos and Fragments, III.

[19] “Delos, celebrated for its temple of Apollo… According to the story, Delos for a long time floated adrift … Aristotle has recorded that it owes its name to its having suddenly appeared emerging from the water…” Pliny, Natural History, 4.66.

[20] Today’s Azerbajian, Armenia and Georgia.

[21] Koch (2000).

[22] Stoyanov (2000) The Other God.


P.S.1. (A.J) Updated Photon states on loops.


P.S.2. (A.J)

P.S.3.(A.J)

"If you want to find the secrets of the universe, think in terms of energy, frequency and vibration." - Nikola Tesla

Friday, July 28, 2023

The Cosmic Context of Greek Philosophy. Part Five

by Laura Knight-Jadczyk

The Agenda of the Milesian School

In 1997, William Mullen, Professor of Classical Studies at Bard College, gave a conference talk entitled: Natural Catastrophes during Bronze Age Civilisation in which he outlined what he saw as the Agenda of the Milesian School.

Topics held in common by the first three pre-Socratic philosophers from Miletos in the Sixth Century B.C.E., Thales, Anaximander, and Anaximenes, and by Xenophanes[1] from neighbouring Colophon, taken together may be viewed as constituting the agenda of a "Milesian School".

The agenda included a survey of the known kosmos (the orderly arrangement of the inhabited world surrounded by regularly moving heavenly bodies); redefinitions of divinity; and theories of the natural processes, constantly in operation, by which both kosmos and divinity are to be understood. It also included explanations of phenomena most men deemed terrifying: thunder, lightning, earthquakes, eclipses, and periodic destruction of the kosmos itself. It set about to explain these phenomena in terms of the same elemental processes (transformations of water, rarefaction and condensation of air, separating out of fire, air, water and earth, periodic reabsorption of these elements into a state of dynamic equilibrium) as it invoked to explain the orderly arrangement of the earth and the heavenly bodies. In so doing, it implied the baselessness of the traditional Olympian religion which attributed lightning and earthquakes to whims of Zeus and Poseidon and world-destructions to battles of the sky-gods. 

The ultimate Milesian agenda may therefore have been to liberate people from paralysing fear of the immediate recurrence of celestial disturbances in the recent past. By insisting that world-destructions occurred only in vast cycles of time (such as a "great year" whose winter solstice was Deluge and summer solstice Conflagration) the Milesian School was schematically distorting memories of recent disturbances, and its activity may be seen as part of a general pattern of oblivion and psychological distancing common to all cultures after the end of the Bronze Age catastrophes. But by insisting that these world-destructions occurred only as the result of unalterable elemental processes, it was also erecting a proto-scientific bulwark against apocalyptic thinking and behavior.[2]

So, indeed, it may have been a conscious program to quell the disorder that inevitably arose when comets appeared, which suggests that comets were, indeed, appearing with some regularity, though they were no longer as threatening as they had been in the previous era of mass destruction. Nevertheless, the philosophers of the Milesian school lived in very interesting times. The period of time during which they philosophized dated (roughly) from 630-475 BC. Recall our catalogue of historical comet sightings[3] from above which I’ll repeat here:

633 BC, China: A broom star comet appeared in Auriga with its tail pointing toward Shhu State. (Ho, 4)

613 BC, Autumn, China: A broom star comet entered the constellation of the Great Bear. (Ho, 5)

532 BC, Spring, China: A new star was seen in Aquarius. (Ho, 6)

525 BC, Winter, China: A bushy star comet appeared in the winter near Antares. (Ho, 7)

516 BC, China: A broom star comet appeared. (Ho, 8)

500 BC, China: A broom star comet was seen. (Ho, 9)

482 BC, Winter, China: A bushy star comet appeared in the east. (Ho, 10)

481 BC, Winter, China: A bushy star comet was seen. (Ho, 11)

480 BC, Greece: At the time of the Greek battle of Salamis, Pliny noted that a comet, shaped like a horn (ceratias type), was seen. (Barrett, 1)

So keep that in mind as you consider the details of these philosophers’ lives.

Thales 624 – 548 BC

The earliest blossoming of Greek science following the Dark Age that prevailed after the collapse of the Bronze Age is associated with the Ionian or Milesian school located at Miletus, on the Western coast of Anatolia, in what is modern day Turkey. During the 6th century BC, it was considered to be the greatest and wealthiest Greek city even though it was not in Greece proper. This city, formerly occupied by speakers of an Indo-European language, Luwian (closely related to Hittite), who disappeared in the collapse of the Bronze Age, was said to have been resettled by Ionian Greeks around 1000 BC. Please notice that Ionia really isn’t Greece. So it looks like ‘Greek Civilization’ as we know it actually belongs to Anatolia, and only later did they colonize Greece, proper. That, of course, doesn’t mean that there weren’t connections between the Mycenaean Greeks and the Ionians; perhaps some of them fled Greece to Anatolia during the disruptions. It might even be thought that the Thracians were the remnant of the Mycenaean Greeks. We do know that there was intellectual discourse taking place in Greece, proper, i.e. Homer, Hesiod, Alcman and Pherecydes, and that it was somewhat different from what was going on in Anatolia.

In any event, Thales founded a school at Miletus (Diogenes tells us that his parents were Phoenician, so even he was not Greek) around 600 BCE, that was destined to be the root of ‘Greek art and philosophy’. Thales taught that the Earth was a flat disc or short cylinder floating on a vast primordial ocean of sorts. His main agenda seemed to be to explain natural phenomena without involving mythology. As we will see, almost all of the pre-Socratic philosophers followed this trend.

Thales is hailed as the first true mathematician because he used geometry to calculate such things as the height of pyramids and the distance of ships from the shore. According to Herodotus, Thales predicted a solar eclipse which has been determined to have occurred on May 28th, 595 BCE. (The same time Epimenides was heading to Athens to save them from a plague.) He supposedly wrote works concerning the solstices and equinoxes, but nothing has survived. Diogenes apparently had some texts to hand because he quotes letters of Thales to Pherecydes and Solon. In these letters, he states that the Milesians were actually Athenians, which suggests that they were refugees from Greece.

Thales was apparently into making weather predictions based on his studies and utilizing his accuracy in this respect to make the point that philosophy wasn’t a waste of time. He also engaged in political life. It was in the context of the military defense of the region against the Persians that he made his solar eclipse prediction. Apparently, it was so impressive that the two peoples laid down their arms and made peace sworn with a blood oath!

Thales was counted among the ‘Seven Sages of Greece’, a list made up (obviously) sometime after all of them were dead. According to Demetrius Phalereus, the list of honorees was made up about 582/1 BC. Dicaearchus of Messina[4] (350-285 BC) commented that none of them were either sages or philosophers, but merely shrewd men with a turn for legislation. That suggests even more strongly that their ideas were driven by a need for political stability and to change the way the public perceived the relationship between the leaders and the cosmos. A parallel (and complementary) perspective is that Thales and his colleagues represented a new kind of community: one that inquires into the nature of things without recourse to the ‘old ways and explanations’. They were possessed by the ideal of Truth, so to say.


Thales profoundly influenced later philosophy, and we are told that his student was Anaximander, who was alleged to be one of the teachers of Pythagoras. As we will see, not all of these philosophers thought the same things. This age is often referred to as the ‘Axial Age’ and it is notable for the fact that revolutionary thinking arose in widely separated places at the same time: China, India, Iran, the Near East, and so on. One really gets the idea that something about the environment had changed dramatically since the cosmic and environmental cataclysms at the end of the Bronze Age.



Anaximander 610 – 545 BC

Thales was followed by Anaximander, who is thought to have introduced the sundial to the Greeks, which he got from the Babylonians. He also drew a map of the inhabited world. He claimed that nature, like human societies, is ruled by laws and anything that breaks natural laws suffers repercussions. Right there we have a hint of his interest in power politics and social control.

Anaximander thought that everything was derived from some undifferentiated living mass (as opposed to the primordial ocean). Things just grew out of this ‘cosmic egg’, the first four things being fire, air, water and earth. This cosmology partly resembles modern cosmological theories such as the Big Bang.

Anaximander proposed that air or denser vapors would have burst out of fiery surrounding membranes, and then enveloped the remaining flames, producing wheels of fire enclosed in mist. These enveloped wheels of fire then encircled the Earth. Planets and stars were circular wheels of fire which became visible due to holes in the enclosing hoops (globes?) that permitted the fire to ‘leak out’. That is, Anaximander’s cosmic bodies were rather like lighted jets of gas shooting through a punctured sheet of metal.

Anaximander taught that the world was transitory and would eventually dissolve back into infinite space (the ‘Big Crunch’). He also said that there were many worlds, which he identified with the gods who were also transitory and renewable. He associated this dissolution and renewal with definite cycles and this strongly suggests influence from Iranian/Persian cosmology and, possibly, study of comets.

An important point about Anaximander’s cosmology was his insistence that the hoops-with-holes, that were supposed to be ‘stars’, all lay beneath the Sun and Moon. This idea has puzzled many commentators, but it might be understood if Anaximander was actually talking about comets or even fireballs in the Earth’s atmosphere. Intense meteor showers associated with a bright comet would easily give the impression that the stars lay below the Sun and Moon.

We can, of course, ask the question: was the Greek word for ‘star’ used to describe a single class of objects? The fact that some stars were described as disappearing due to their increasing distance from the viewer on Earth suggests that some of these ‘stars’ were actually comets.

Important to our study is the fact that the 3rd century Roman rhetorician Aelian claims that Anaximander was the leader of the Milesian colony to Apollonia on the Black Sea coast. Aelian’s Various History[5] tells us that philosophers often dealt with political matters. Most scholars suppose that leaders of Miletus sent him there as a legislator to create a constitution or simply to maintain the colony’s allegiance. But we are reminded of the comment of Dicaearchus cited above: that these really weren’t philosophers, but shrewd men with political agendas and I will make note (as I have already) of those who appear to have had political connections.

If they were, truly, philosophers and, by some miracle, the powers of the time saw wise men as useful in government, one is still compelled by the idea that there was a political agenda to giving philosophers of this orientation such roles so as to establish and maintain certain ideas in respect of the cosmos for political reasons, as Ballie, Clube and Napier suggest. Is it even possible that leaders of those times could sit down and consciously decide that ‘this business about comets being gods needs to be dealt with since it threatens the control of the rulers’? It would probably have been clear that it did, in fact, threaten them because the ‘old way’ had been to sacrifice the leaders if it was perceived that the gods were angry or hungry.



Pythagoras – The Italian School

Pythagoras of Samos (570-495 BC) was the founder of the religious movement called Pythagoreanism. Let me first tell you the briefest outline of the story about him before we get to the actual facts, as far as we can find them out.

Pythagoras was born on the Greek island Samos and traveled widely seeking knowledge. He had himself initiated into all of the mystery schools in Greece and foreign countries. He learned the Egyptian language and journeyed to the lands of the Chaldeans and Magi. Then, in Crete, he went into the cave of Ida with Epimenides where the baby Zeus was said to have been hidden from his father, Chronos. After all that, he returned to Samos and found his country under the rule of a tyrant, Polycrates, so he sailed to Croton[6] (about 530 BCE) and there, became a leader who created a constitution for the Italian Greeks. He and his 300 followers thereby instituted a ‘true aristocracy’ or government by the best qualified (as Diogenes puts it). According to other sources, when Polycrates effected his coup at Samos, members of the old aristocracy were either sent into exile or voluntarily left. Otherwise, Polycrates was said to have been a very popular ruler who worked hard to improve the quality of life of the people of Samos. He was an ally of the Egyptian king Amasis who paid the Samians well to maintain naval defense in the region.

Diogenes quotes Heraclitus in refutation of the idea that Pythagoras left no writings:

Pythagoras, son of Mnesarchus, practiced inquiry beyond all other men, and in this selection of his writings made himself a wisdom of his own, showing much learning but poor workmanship.[7]

He then goes on to say that Pythagoras wrote three books: On Education, On Statesmanship, and On Nature. Then he mentions that Aristoxenus said that Pythagoras derived his moral doctrines from the Delphic priestess, Themistoclea. In short, at least one of his teachers was a woman. Diogenes then enumerates the teachings of Pythagoras from the three books as follows:

He forbids us to pray for ourselves, because we do not know what will help us. Drinking he calls, in a word, a snare, and he discountenances all excess, saying that no one should go beyond due proportion either in drinking or in eating. Of sexual indulgence, too, he says, “Keep to the winter for sexual pleasures, in summer abstain; they are less harmful in autumn and spring, but they are always harmful and not conducive to health.” Asked once when a man should consort with a woman, he replied, “when you want to lose what strength you have ...”


The following are excerpts from Diogenes’ Life of Pythagoras.

According to Timaeus[8], he was first to say “Friends have all things in common”… indeed, his disciples did put all their possessions into one common stock …

Indeed, and his disciples held the opinion about him that he was Apollo come down from the far north …

This is interesting considering other clues that Pythagoras’ (and Pherecydes) ideas had a more northern origin.

We are told by Apollodorus the calculator that he offered a sacrifice of oxen on finding that in a right-angled triangle the square on the hypotenuse is equal to the squares on the sides containing the right angle. …

Apollodorus, surnamed Logisticus (the Calculator), may have been Apollodorus of Seleucis, a Stoic philosopher and pupil of Diogenes of Babylon. He wrote on ethics and physics and is otherwise frequently cited by Diogenes Laërtius. Cicero comments on this statement, saying that he does not question the discovery, but doubts the story of the sacrifice of the ox.

He is also said to have been the first to diet athletes on meat, trying first with Eurymenes – so we learn from Favorinus[9] in the third book of his Memorabilia – whereas in former times they had trained on dried figs, on butter (cheese), and even on wheat-meal… some say it was a certain trainer named Pythagoras who instituted this diet, and not our Pythagoras, who forbade even the killing, let alone the eating, of animals… as we are told by Aristotle…

Here we have a little difference of opinion on the dietary matter. I would suggest that, if it is true that Pythagoras was strongly influenced by northern teachings, he most certainly advocated the eating of meat strongly and it was only later mythmakers who created the vegetarian fraud. In fact, it is most likely that the life and doings of Empedocles, a philosopher cum religious prophet born in Sicily about 490 BCE, was conflated with Pythagoras.

Like Epimenides, Empedocles was reputed to have miraculous powers such as the ability to cure disease, avert epidemics, control storms, etc. He wrote in verse and one of his poems is entitled Purifications and seems to have promised miraculous powers, rejuvenation, destruction of evil, etc. He was associated with various Pythagoreans, and his abstinence from meat was widely known. He also claimed to be a god incarnate. His doctrine of the four elements remained fundamental for the theory of matter for more than twenty centuries. In this we see that the dual role of a religious prophet and a mathematical philosopher that the tradition assigns to Pythagoras is certainly possible – even a common topos of the time – but not necessarily historical.

Down to the time of Philolaus it was not possible to acquire knowledge of any Pythagorean doctrine and Philolaus alone brought out those three celebrated books which Plato sent a hundred minas to purchase. Not less than six hundred persons went to his evening lectures; and those who were privileged to see him wrote to their friends congratulating themselves on a great piece of good fortune …

Here we discover something crucially interesting: that the alleged books of Pythagoras were placed into the hands of none other than Plato! And, we can’t be certain that Philolaus didn’t write them himself!

The rest of the Pythagoreans used to say that not all his doctrines were for all men to hear, our authority for this being Aristoxenus in the tenth book of his Rules of Pedagogy

This next excerpt is particularly interesting in light of the diet issue:

Above all, he forbade as food red mullet and blacktail, and he enjoined abstinence from the hearts of animals and from beans and sometimes, according to Aristotle, even from paunch and gurnard (two types of fish) …

Obviously, if his students are warned not to eat the hearts of animals, that is an explicit acknowledgement that they were eating the rest of the animal as is confirmed by the following:

He used to practice divination by sounds or voices and by auguries, never by burnt-offerings, beyond frankincense … some say that he would offer cocks, sucking goats and porkers… but lambs, never. However, Aristoxenus has it that he consented to the eating of all other animals, and only abstained from ploughing oxen and rams …

Diogenes cites Aristotle:

Aristotle says, in his work On the Pythagoreans, that Pythagoras enjoined abstention from beans either because they are like the privy parts, or because they are like the gates of Hades (for this is the only plant that has no joints), or because they are destructive, or because they are like the nature of the universe, or because they are oligarchical (being used in the choice of rulers by lot). Things that fall from the table they were told not to pick up – to accustom them to eating with moderation, or because such things marked the death of someone. And Aristophanes, too, says that the things that fall belong to the heroes, when in his Heroes he urges: ‘Do not taste what falls inside the table.’ They must not touch a white cock, because this animal is sacred to the Month and is a suppliant, and supplication is a good thing. The cock was sacred to the Month because it announces the hours; also, white is of the nature of the good, black of the nature of the bad. They were not to touch any fish that was sacred, since it was not right that the same dishes should be served to gods and to men, any more than they should to freemen and to slaves. They must not break the loaf (because in old times friends met over a single loaf, as barbarians do to this day), nor must they divide the loaf which brings them together. Others explain the rule by reference to the judgment in Hades; others say that dividing the loaf would produce cowardice in war; others explain that it is from the loaf that the universe starts.[10]

The first thing to point out is that none of these rules enjoin vegetarianism. There is, in fact, no 5th century evidence whatsoever that the Pythagoreans renounced animal sacrifice and the subsequent eating of the sacrifice. In fact, since the focal point of the Greek polis, in which Pythagoras and his followers played such a leading role for several generations, was the regular public sacrifice and feasting, is a powerful implication that they were not, at all, in any way, vegetarians. The evidence for Pythagoras being a meat eater are more numerous, and older, than the evidence for vegetarianism which seems to be both a conflation with Empedocles and a consequence of the later Platonic myths.

Hieronymus … says that, when he [Pythagoras] had descended into Hades, he saw the soul of Hesiod bound fast to a brazen pillar and gibbering, and the soul of Homer hung on a tree with serpents writhing about it, this being their punishment for what they had said about the gods; he also saw under torture those who would not remain faithful to their wives.

According to Diogenes, this is what Aristotle said about Pythagoras at one point:

But Pythagoras’ great dignity not even Timon[11] overlooked, who, although he digs at him in his Silloi, speaks of: Pythagoras, inclined to witching works and ways, Man-snarer, fond of noble periphrase. …

Further, we are told that he was the first to call the heaven the universe and the earth spherical (according to Favorinus), though Theophrastus says it was Parmenides, and Zeno that it was Hesiod.[12]

The spherical Earth was actually first asserted in the work of Parmenides and Empedocles while the Ionian school continued with their flat-earth theories for a rather long time.

Allegedly, Pythagoras followers practiced rites developed by him based on what he had learned and developed via his travels and studies. What is more, the Pythagoreans took an active role in the politics of Croton and this is what led to their downfall, apparently. The Pythagorean meeting places were burned and Pythagoras and his followers were forced to flee and he is said to have ended his days in Metapontum, not far from Tarentum, which will figure in our tale shortly.

As we see from this very quick review of a few of the things Diogenes collected together, Pythagoras is presented in a vast body of literature as the genius of marvels, the inventor of mathematics, music theory, heliocentric astronomy, and metaphysical philosophy. The 20th century philosopher, Alfred North Whitehead sang paeans of praise about Pythagoras. But the sources closest in time to the man (who certainly existed) are satirical, mildly insulting, or completely ambiguous. So why did the figure of Pythagoras accumulate so much baggage so that, even down to the time of the Renaissance, there were people claiming to be 'followers of Pythagoras'?

The Pythagoreans are said to have taught that a release from the wheel of reincarnation was possible but only via a process of purification of the soul including a vegetarian diet (which was probably not true). Aristoxenus said that they also used music to purify the soul just like medicine was used to purge the body, a likely Orphic connection. Pythagoras was said to have proclaimed that the highest purification of a life is in pure contemplation. It is the philosopher who contemplates about science and mathematics who is released from the ‘cycle of birth’. The pure mathematician’s life is, according to the tradition created for Pythagoras, the life at the highest plane of existence.[13] [14] Thus the root of mathematics and scientific pursuits in Pythagoreanism is also based on a spiritual desire to free oneself from the cycle of birth and death.

It’s a great story, isn’t it? I didn’t even include all the miracle parts, including the one telling how Pythagoras had a golden thigh, could bi-locate, and so forth. So what is true? Well, let’s look at the evidence, starting with a rather surprising remark made by Heraclitus and preserved by Diogenes:

The learning of many things does not teach understanding; if it did, it would have taught Hesiod and Pythagoras, and again Xenophanes and Hecataeus.[15]

Empedocles wrote, preserved in Porphyry’s Life of Pythagoras, as follows:

And there was among them a man of surpassing knowledge, master especially of all kinds of wise works, who had acquired the utmost wealth of understanding: for whenever he reached out with all his understanding, easily he saw each of all the things that are, in ten and even twenty generations of men.[16]

The impression that Empedocles gives is that Pythagoras’ methods were most definitely not mathematical or scientific! But that he was widely perceived as a seeker and having a great range of knowledge and extraordinary influence over people appears to be a secure fact.

Diogenes Laërtius reports that Xenophanes had this to say about Pythagoras:

Now I will turn to another tale and show the way… Once they say that he [Pythagoras] was passing by when a puppy was being whipped, and he took pity and said: “Stop, do not beat it; for it is the soul of a friend that I recognized when I heard it giving tongue.”[17]

Obviously, this is a joke made by Xenophanes with Pythagoras as the butt of it. In any event, that the teaching of reincarnation by Pythagoras was widely enough known to be the topic of ordinary conversation – and even jokes – makes that something that we can securely attach to him.

Additional evidence provides a weak connection between Pythagoras and the Orphic Mysteries. Orphism appears to have been mainly a system of purification that was practiced privately at that time, while the Pythagoreans definitely formed a very secretive sect. The Orphics taught that the body was a prison, a tomb, in which the soul is buried until it finds or earns its way out. Their methods were designed to purify and release men and cities from their errors. They neither ate nor sacrificed animals and taught complete avoidance of bloodshed. The later Orphic poems seem to imply that certain behaviors could forestall, avoid, or end cosmic punishment. (I suspect that Orphism had very little to do with anyone named Orpheus.) But were Orphic practices and concepts part of the original Pythagorean ideas, or were they simply connected thanks to Plato?

Next we have a quote from Porphyry, the 3rd century CE Neoplatonic philosopher of Phoenician extraction:

What he said to his associates, nobody can say for certain, for silence with them was of no ordinary kind. Nonetheless the following became universally known: first, that he maintains that the soul is immortal; next, that it changes into other kinds of living things; also that events recur in certain cycles, and that nothing is ever absolutely new; and finally, that all living things should be regarded as akin. Pythagoras seems to have been the first to bring these beliefs into Greece.[18]

It could be said that a lot of historically worthless literature about him began, mainly, with Plato. It seems that he, and his followers, radically altered not only accounts of the life of Pythagoras, but actually invented doctrines and assigned them to him. One expert suggests that “all the discoveries attributed to Pythagoras himself, or to his disciples by later writers were really the achievement of certain South Italian mathematicians of Plato’s time.”[19] What is more, it wasn’t until after Plato spent time with Archytas at Tarentum that his formerly rather cool view of Pythagoras warmed up, and this can be definitely noted in his dialogues, as analyzed by Charles Kahn in Pythagoras and the Pythagoreans.[20] There are surviving fragments from the work of Archytas that strongly suggest that it was he, not Pythagoras, who formulated many of the scientific and mathematical ideas attributed to Pythagoras by Plato. Perhaps Plato was jealous of Archytas, stole his ideas, and attributed them to Pythagoras with the idea that, of course, everyone would know that it was all him, only he was so modest! Or he sought to attach his ideas to someone who everyone else held in awe which was rather common in ancient times.


The main players in the Phaedo are represented by Plato as a sort of link between the Pythagoreans and Socrates.[21] The implication is that Plato set a fashion of presenting his newest theories as age-old wisdom. While he may have done it more or less playfully, as some suggest, assuming that everyone would naturally understand that he was being modest, but that in reality he, of course, thought all this stuff up, it appears that his students and followers took him literally. Two of his students in particular, Speusippus and Xenocrates, took him very seriously and treated the cosmology of the Timaeus as the teaching of Pythagoras, which may have been partly true.[22] Walter Burkert, in a massive monograph on the subject published in 1962 (translated into English in 1972), says that the evidence shows only that Pythagoras was a shamanistic figure, a charismatic spiritual leader rather like Moses, who was very influential in the politics of his day but contributed nothing whatsoever to mathematics or philosophy.[23] All that we know of ‘Pythagoreanism’ was created later by Plato and others.

Thus it was right there, in Plato’s Academy, that the twisting and distortion of the work of Pythagoras was formulated. Aristotle, Plato’s student, vigorously resisted this development and spent some time carefully studying Philolaus and the pre-Plato Pythagorean system. Aristotle became the last author to draw a distinction between the two schools.


At the beginning of the 4th century there was another refugee from the conflict in Southern Italy who came to Thebes: Lysis of Tarentum. He became the teacher of the general Epaminondas. So there were respectable Pythagorean communities from which Plato could both extract ideas as well as influence with his possession of the inside scoop on what Pythagoras actually said, since he allegedly had possession of the three books.

There is another type of Pythagorean represented by Diodorus of Aspendus in Asia Minor, a 4th century BCE ascetic vegetarian who was described as having long hair, long beard, worn cloak, a beggar’s wallet and staff.[24] Also, in Athens at the same time, there were barefoot vegetarians who were mocked in comedy skits as ‘Pythagorists’. In other words, the barefoot vegetarian Pythagorean is a post-Plato appearance of half-crazed mendicant philosophers that were little more than comic figures of the time and were used to attack Pythagoras. This lifestyle was actually taken over later by the Cynics, and after their appearance there are no further references to Pythagoreans in this light; the Cynics are the comic relief! It appears to be a fairly typical response of social and political power structures to ridicule and defame their critics. Thus, we should pay attention to whether a particular philosopher was on the side of the power elite, or a critic thereof. Such an observation won’t necessarily say anything about their philosophies or cosmologies, but it could, especially when we notice whose work has been ‘lost’ and whose has been preserved.

As mentioned, after Plato got hold of a few ideas, and stole many others from wherever he could get them, the two central ideas of Pythagoreanism become 1) the destiny of the immortal soul as expounded by Plato; and 2) mathematics as the key to unlock the secrets of the universe. This last was, I believe, his own spin and a red herring put out there to keep generations of seekers spinning in circles trying to work out the right formula. It was in Plato’s imagination that mathematics enabled a soul to become free and only in his mind do these ideas reach their culmination.


Of this massive mess, only three sources seem to have anything to offer us: Diogenes Laërtius, Porphyry and Iamblichus, in that order, with each one giving an account that is more fantastic than the previous one. Eduard Zeller, in his 19th century history of Greek philosophy, noted that the further a document is from Pythagoras’ own time, the fuller the account becomes![25] These histories amount mainly to cut and paste compilations from the Christianizing era which followed Plato, and contain a lot of nonsense, but they also include summaries of fairly early traditions about Pythagoras to which they still had access.

The invented tradition of Plato tells us that the school of Pythagoras split at some point and one group followed the more mathematical line, extending the scientific work of Pythagoras. The other group focused on the more religious aspects, declaring that the ‘scientific’ breakaway group was not really following Pythagoras, but rather the renegade Hippasus,[26] about whom very little is known. Iamblichus says about Hippasus:

It is related to Hippasus that he was a Pythagorean, and that, owing to his being the first to publish and describe the sphere from the twelve pentagons, he perished at sea for his impiety, but he received credit for the discovery, though really it all belonged to HIM (for in this way they refer to Pythagoras, and they do not call him by his name).[27]


The more scientific ideas appear to be those of Philolaus, who developed the work of Anaximander of the Milesian school who – along with Pherecydes – was also said to be one of the teachers of Pythagoras. Why are we not surprised?  Philolaus argued that at the foundation of everything is the part played by the limiting and limitless, which combine in a harmony. He said that the Earth was not the center of the universe, and thus he is credited with the earliest known discussion of heliocentrism. Philolaus described a Central Fire as the center of the universe and that spheres (including the Sun) revolved around it.  According to Plato's Phaedo, he was the instructor of Simmias and Cebes at Thebes, around the time the Phaedo takes place, in 399 BC. That would make him a contemporary of Socrates, and would agree with the statement that Philolaus and Democritus were contemporaries.[28]

The idea most central to Pythagorean mystical teachings was the transmigration of souls which was an idea that was actually native to India and to the Celts and related Germanic tribes (all three of which had their origins in the steppes of central Asia). Much of the Pythagorean mysticism concerning the soul seems similar to the Orphic tradition. The Orphics included various purification rites and practices as well as incubatory rites of descent into the underworld, which bring to mind Central Asian Shamanism. Orphism was said to have originated in Thrace which brings us to the following story from Herodotus:

As I have heard from the Greeks who live on the Hellespont and the Black Sea, this Salmoxis was a man, who was a slave in Samos, the slave in fact of Pythagoras son of Mnesarchus… The Thracians lived a miserable life and were not very intelligent, whereas this Salmoxis knew the Ionian way of life and minds deeper than the Thracians’, since he had associated with Greeks and among Greeks with Pythagoras, not the weakest of their wise men. So he [Salmoxis] built a hall in which he received and entertained the leading citizens, and taught them that neither he nor his guests nor any of their descendants would die, but that they would go to a place where they would survive forever and possess every good thing.[29]

This story of Herodotus’ is quite intriguing since Salmoxis, or Zalmoxis, is a divinity of the Getae[30] mentioned by Jordanes.[31] He is saying that he heard from Greeks in Western Anatolia that a certain Salmoxis, who was a former slave of Pythagoras, was hoodwinking the poor, ignorant Thracians.  I’m wondering if this is a hint of the source of Pythagoras’ ideas about reincarnation: that he gathered them from Gothic/Alanic tribes to the north or even along the Black Sea coast?

The archaism of the Salmoxis doctrine (which I omit here) points to an Indo-European heritage.[32] Diogenes reports in an epitome of Aristotle’s Magicus that Aristotle compared Zalmoxis with the Phoenician Okhon and the Libyan Atlas. Anthropologist Andrei Anamenski suggests that Zalmoxis was another name of Sabazius, the Thracian Dionysus, or Zeus. Sabazius appears in Jordanes as Gebelezis. Without the suffixes -zius/-zis, the root Saba- is equivalent to Gebele-, suggesting a relationship to the name of the goddess Cybele, as in ‘Cybele’s Zeus’. Mnaseas of Patrae identified him with Chronos. Plato mentions Zalmoxis as skilled in the arts of incantation. Zalmoxis also gave his name to a particular type of singing and dancing, i.e. ‘Hesych’, which is a word meaning ‘to be still or quiet’ and is used to describe a mystical sect of the Greek Orthodox Church of the 14th century. (One naturally wonders how a person can sing and dance being still and quiet?!) A curious connection indeed. Salmoxis’ realm as a god is not very clear, as some considered him to be a sky-god, a god of the dead or a god of the Mysteries.[33] All of this merely suggests a northern version of the same old cosmic catastrophe stories and myths but possibly with a cleaner transmission.

Lactantius (240-320 CE), referring to the beliefs of the Getae, quoted the emperor Julian the Apostate, who was quoting the emperor Trajan (in other words, three removes in the chain of evidence):

We have conquered even these Getai (Dacians), the most warlike of all people that have ever existed, not only because of the strength in their bodies, but, also due to the teachings of Zalmoxis who is among their most hailed. He has told them that in their hearts they do not die, but change their location and, due to this, they go to their deaths happier than on any other journey.

Another related item from Herodotus:

Moreover, the Egyptians are the first to have maintained the doctrine that the soul of man is immortal, and that, when the body perishes, it enters into another animal that is being born at the time, and when it has been the complete round of the creatures of the dry land and of the sea and of the air it enters again into the body of a man at birth; and its cycle is completed in 3,000 years. There are some Greeks who have adopted this doctrine, some in former times, and some in later, as if it were their own invention; their names I know but refrain from writing down.[34]

Herodotus erroneously gives the Egyptians credit for the idea of reincarnation. Nothing of the kind is attested in anything Egyptian. In fact, they believed that the body had to be preserved in order for the dead person to have any afterlife at all; when the body was destroyed, so was the afterlife ‘life’, which could only be experienced through a well-preserved physical body. Curiously, Herodotus often ascribes Greek ideas and practices to Egyptian origins. One wonders if he was even talking about the Egypt we know as Egypt? (It wasn’t named ‘Egypt’ until after Alexander the Great.)

Ion of Chios, who we met earlier in the account of Pherecydes, seems to have expressed doubt about Pythagoras’ ideas of reincarnation, though he didn’t seem to doubt that he was a learned man. He was writing in the middle of the 5th century, as was Herodotus, who presented the former slave of Pythagoras as a rogue selling salvation. These stories strike me as pejorative but interesting nonetheless for what they convey in an offhand way.

Nevertheless, Pythagoras was said to have had full recall of all his past lives, the list being given in Diogenes Laërtius as follows: First Aethalides, the presumed son of Hermes, who awarded him the gift of remembering his lives after death. Then he incarnated as Euphorbus, and after that Hermotimis, who visited the Branchidae, and in whose temple he recognized the shield that Menelaus had dedicated to Apollo. After Hermotimus he was Pyrrhus, a fisherman of Delos, and after that he was finally reincarnated as Pythagoras.

Pythagoras advocating vegeterianism?

The Branchidae were expelled by Darius’ Persians, who burned the temple in 493 BCE, but Alexander the Great undertook to restore the temple and the oracle. Apparently, this project was never completed. Pausanias visited Didyma in the later 2nd century AD.[35] Pliny reported[36] the worship of Apollo Didymiae – Apollo of Didymus – in Central Asia, transported to Sogdiana by a general of Seleucus and Antiochus whose inscribed altars there were still to be seen by Pliny’s correspondents. Corroborating inscriptions on amphoras were found by I.R. Pichikyan at Dilbergin.[37] [38]

Back to Pythagoras: I’ve read some rather silly explanations here and there saying that the ancient Pythagorean pentagram, with two legs up, represented the Pentemychos or ‘five sanctuaries’, derived from the cosmogony of Pherecydes, who is said to have been Pythagoras’ teacher and friend. However, that is rather doubtful. Wikipedia tells us that the Pentemychos was ‘the island or cave’ where the first pre-cosmic offspring had to be put in order for the cosmos to appear… the divine products of Chronos’ seed, when disposed in the five recesses, were called Pentemuxos. The source citations the Wikipedia author gives for this silly claim are Kirk, Raven and Schofield. Believe me, they say nothing that could be construed in that way. Go back to Pherecydes and read about Ortygie. If you see anything there that suggests such a thing (and I quoted the reference pretty much in full, whereas it was selectively edited on Wikipedia!), I must be blind or nuts.  Using Wikipedia is sometimes an iffy proposition.

Nevertheless, I’ve already suggested that the five hidden recesses might represent an early attempt to map the sky, and what we now know as constellations were designated by Pherecydes as ‘recesses’ or ‘caves’ that went below the horizon, and that they were related to the appearance, and disappearance, of comets from below the horizon or off in space. If that is the case, then it deprives the Pentemychos of any occult significance, whether it came from Pherecydes or not, so I’m sure the folks who are into magick and all that nonsense will not be happy about that.

I’ve skipped over the material from the sources that talk about Pythagoras’ political activities in Croton. As already mentioned, he and members of his society attained positions of political power throughout southern Italy. Polybius reports that, in the middle of the 5th century, when the Pythagorean meeting places were torched, “the leading men from each city lost their lives.” [39] That means that pretty much everybody who was anybody around there was involved with Pythagoras. Considering the overall history of the time, it appears to me that Pythagoras’ organization may have been one designed to dominate the political scene but we don’t know if that was to achieve power for the good of all, not for personal gain. It really sounds as though the common people were the ones who burned out the Pythagoreans.  It also raises questions about what, exactly, the Pythagoreans were really doing.  They probably were NOT sitting around, listening to music and contemplating mathematics!

In any event, Pythagoras himself is said to have died a refugee after a ‘popular revolt’ against him and his companions.  This could have been masterminded by the wealthy seeking power and increase of their wealth, utilizing propaganda and rabble-rousing techniques that were highly developed at that time; we just don’t know. After this disaster, we find Pythagoreans in Greece, including Philolaus in Thebes. And then, the stories began to spread.

It is also entirely possible that Plato’s famous tale of Atlantis in Timaeus and Critias was one of the main things stolen from the alleged books of Pythagoras. I’ll expound on this when we come to our discussion of Plato.

All of this is much more interesting than the fanciful tales told about the man. One even wonders if the stories were made up to distract attention away from the truth. And, when that is the case, it is usually a decent person or a group with high ideals that have been overthrown by ravening seekers of power for its own sake, and following such acts, they erect a smoke-screen such as the one created by Plato.

We are oft to blame in this, tis too much proved - that with devotion's visage and pious action, we do sugar o'er the devil himself.[40]

 



[1] (c.570-c.475 BC), Greek philosopher, theologian, poet, and social and religious critic. He satirized traditional religious views of his time as human projections. Xenophanes wrote about two extremes predominating the world: wet and dry (water and earth). These two extreme states would alternate between one another and with the alteration human life would become extinct, then regenerate. He was one of the first philosophers to distinguish between true belief and knowledge.

[2] From a talk given by William Mullen, Professor of Classical Studies at Bard College, SIS Conference: Natural Catastrophes during Bronze Age Civilisations, 11th – 13th July, 1997.

[3] Most comet references from Yeomans (1991) Comets: A Chronological History of Observation, Science, Myth, and Folklore.

[4] Greek philosopher, cartographer, geographer, mathematician and author. Also Aristotle’s student. Very little of his work remains extant. He wrote on the history and geography of Greece, of which his most important work was his Life of Greece. He was among the first to use geographical coordinates in cartography.

[5] Aelian: Varia Historia (III, 17).

[6] Crotone is a city and comune in Calabria, Italy. Founded c. 710 BCE as the Achaean colony of Croton. Pythagoras founded his school, the Pythagoreans, at Croton c. 530 BCE. Among his pupils were the early medical theorist Alcmaeon of Croton and the philosopher, mathematician, and astronomer Philolaus. The Pythagoreans acquired considerable influence with the supreme council of one thousand by which the city was ruled.  See Wikipedia for a fuller discussion of the interesting history of the city.

[7] Diogenes Laertius, VIII, 4-6.

[8] Greek historian (345 -250 BC), born at Tauromenium in Sicily. He was a student of Isocrates and wrote some 40 books of history.

[9] A Gaulish Roman sophist and philosopher (80-160 AD) during the reign of Hadrian. He was described as a congenital hermaphrodite (Philostratus) or “a eunuch born without testicles” (Polemon of Laodicea). He was beardless and had a high pitched voice. He was once silenced in an argument with the emperor when he could easily have won, but later explained that it was foolish to criticize the logic of the master of 30 legions. See: Holford-Strevens (1997) Favorinos: the Man of Paradoxes, in J. Barnes et M. Griffin (eds.), Philosophia togata, vol. II.

[10] Diogenes Laertius VIII, 34-5, trans. W. D. Ross, cited by Kirk, op. cit.

[11] Timon of Phlius (c. 320 BC – c. 235 BC) was an Ancient Greek philosopher from the Hellenistic period, who was the student of Pyrrho. Timon wrote satirical philosophical poetry called Silloi. The subject was a sarcastic account of the tenets of all philosophers, living and dead; an unbounded field for scepticism and satire.

[12] Diogenes Laertius, VIII, excerpts in order.

[13] Burnet (1892) Early Greek Philosophy.

[14] Russell (1967) History of Western Philosophy.

[15] Diogenes Laertius, IX, 1.

[16] Porphyrius: Life of Pythagoras, 30.

[17] Diogenes Laertius, VIII, 36.

[18] Porphyrius: Life of Pythagoras p.19.

[19] Frank (1923) Plato und die sogenannten Pythagoreer, vi.

[20] Kahn (2001).

[21] Phaedo, 61 d.

[22] Kahn (2001) ibid.

[23] Burkert (1972) Lore and Science in Ancient Pythagoreanism.

[24] Kahn, op. cit. p. 49.

[25] Zeller (1892) Die Philosophie der Greichen in ihrer geschichtlichen Entwicklung.

[26] Hippasus of Metapontum was a Greek philosopher and follower of Pythagoras, though about a century after the latter.  He is sometimes credited with the discovery of irrational numbers. Iamblichus says that Hippasus was the founder of a sect of the Pythagoreans called the Mathematici in opposition to the Acusmatici but elsewhere he makes him the founder of the Acusmatici in opposition to the Mathematici.

[27] Iamblichus, Vita Pythagorica, 18 (81)

[28] Plato, Phaedo, 61DE

[29] Herodotus IV, 95.

[30] A Thracian-related tribe that once inhabited the regions on either side of the Lower Danube, in what is today northern Bulgaria and southern Romania. The area had a few Greek colonies on the Black Sea coast, bringing the Getae into contact with the ancient Greeks from an early date.  Strabo wrote that the Dacians and Getae spoke the same language, after stating the same about Getae and Thracians. Strabo, VII 3,14.

[31]  6th-century CE Eastern Roman bureaucrat widely believed to be of Gothic descent. Late in life he wrote two works, one on Roman history (Romana) and the other on the Goths (Getica). Jordanes was asked by a friend to write Getica as a summary of a multi-volume history of the Goths by Cassiodorus that existed then but has since been lost. Jordanes himself states that his paternal grandfather was secretary to a leader of the Alans which modern historians have connected with Central Asian Yancai of Chinese sources and with the Aorsi of Roman sources.

[32] Paliga (1997) ‘La divinité suprême des Thraco-Daces’.

[33] Znamenski (2007) The Beauty of the Primitive: Shamanism and Western Imagination.

[34] Herodotus II, 123.

[35] Pausanias, Description of Greece, 7.2.6.

[36] Pliny's Natural History, 6.18.

[37] Parke (1986) ‘The Temple of Apollo at Didyma: The Building and Its Function’.

[38] Haselberger (1983), ‘Die Bauzeichnungen des Apollontempels von Didyma’; (1985) ‘Antike Planzeichnungen am Apollontempel von Didyma’; (1991)‘Aspekte der Bauzeichnungen von Didyma’.

[39] Polybius II, 39. 1-2.

[40] Shakespeare, Hamlet, Polonius to Opheila, Act III, Scene 1.

To Part 6








Biolocation

  On Tuesday, December 23, Vlad Zhigalov (see e.g. here ) had a talk at the " Temporology " seminar hosted at Omsk.  He spoke abo...