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Good summary, and thanks for highlighting the part about Scholem's "song of the bride" and the gnostic parallels.
I looked again at http://www.sacred-texts.com/chr/ps/ps145.htm. Different powers have different numbers of demons. One has 27, one has 32, another later on has 49. This chapter is not the end of the Pistis Sophia, it's just the end of a particular narrative. it keeps going. There are also the "36 repentances" of Sophia.

Huck wrote
I think I should learn something about gnosticism.
That is a very big topic! If you're mainly interested in their use of numbers, the Pistis Sophia is a good place to look. It's so long I don't doubt you can find any number you want there. It seems to be a treasure trove of reworked older material.

A short piece with an 8 and a 12 is the "Round Dance of the Cross", or "Hymn of Jesus".

What parallels the song of the bride is the various Gnostic writings about Sophia, and also the Wisdom literature in the Hebrew Bible.

I once wrote some introductory material on these subjects, and collected others' material, if you want to look: http://psychandgnosticessays.blogspot.c ... ntary.html. The other subjects I mentioned are in the sidebar on the right. I have more in that same blog, too, but mostly about how Gnosticism connects with other things, like Shakespare and Native American myths. No numbers there, however.

One thing to keep in mind: "Gnosticism" in most of the literature, is--or should be--a proper name, not a theoretical concept. Historically it gets its meaning from Irenaeus, pointing at certain texts, most of which we only know from him. He may or may not have understood them. So he just means those texts plus whatever else from the same period that is similar, in a way that was deemed heretical, mostly after the fact. "Similar" is rather loose, but not so much so as to include orthodox writers. Clement of Alexandria, for example, endorsed something he called "gnosis", but that is not Gnosticism.

Added later: Only one or two of the Gnostic sects reviewed by Irenaeus actually called themselves "gnostic".

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mikeh wrote:Good summary, and thanks for highlighting the part about Scholem's "song of the bride" and the gnostic parallels.
I looked again at http://www.sacred-texts.com/chr/ps/ps145.htm. Different powers have different numbers of demons. One has 27, one has 32, another later on has 49. This chapter is not the end of the Pistis Sophia, it's just the end of a particular narrative. it keeps going. There are also the "36 repentances" of Sophia.
27 = 3^3
32 = 2^5
49 = 7^2
---
108 = (2^2)*(3^3)

108/3 = 36 = 6^2

Well, there's no guarantee, that 32 only appears to indicate the binary scheme. Possibly there are other attractive math qualities in mythical texts.

*****************
Seth plots against the king.

Seth began scheming against the great king. He aligned himself with Aso, the queen of Ethiopia, and 72 other conspirators. But nothing could be done while Isis ruled the country, Her authority was unquestionable. Upon Osiris' return, an evil plot was put into motion. Seth secretly acquired the measurements of Osiris and began having a wonderfully decorated box built to fit those measurements. When the box was finished, Seth had a great feast to which he invited Osiris and the 72 conspirators Having absolutely no evil in him, Osiris suspected nothing. When the feasting was done, Seth had the box brought out. He offered it as a gift to anyone whom the box fit. One at a time they tried to fit into the box until it was Osiris' turn. He layed in the box suspecting nothing. The conspirators slammed the lid, nailed it closed, and poured molten lead in the seam to seal his fate. They threw the great chest into the Nile river. Osiris was never seen again, walking in the land of the living.
http://www.egyptartsite.com/osi.html

Other source:
Nut had four children with Geb. Osiris and his wife Isis, along with Seth and his wife Nephthys. The circumstances of their births is described in the The Story of Re. They were born on the five epagomenal days of the year (in Egyptian, "the five days over the year"). Every year these days were celebrated throughout Egypt.

Osiris, this day was considered unlucky
Horus the Elder, this day was described as either lucky or unlucky
Seth, considered an unlucky day
Isis, lucky day, called "a beautiful festival of heaven and earth."
Nephthys, unlucky day
http://www.egyptianmyths.net/nut.htm

I seems, that these pieces belong together and to the Egyptian calendar. 360 days (= 12x30) + 5 unlucky days = 365 days.

"72 conspirators" might refer to 5 days each ... 5x72 = 360, which somehow presents a state, in which the 36 dekans (10-days periods) are broken in two opposing pieces of 5 days each.

In this context the Bahir-94 passage jumps in my mind, which relates the 32 to other 32 and then to higher 8, which finally result in the number "72".

The queen of Ethiopia ... Moses was chosen to become a military commander in an Ethiopian problem (in side episodes of his myth, also reported by Flavius Josephus and Artapanus. Moses marries the Ethiopian queen, and solves the conflict.
German study ...
https://books.google.de/books?id=bIueZW ... en&f=false
... and also in the biography of Artapanus (English)
http://en.wikipedia.org/wiki/Artapanus_of_Alexandria

Moses is related by Artapanus to the invention of 36 nomes ...
According to Artapanus, Abraham taught an Egyptian pharaoh the science of astrology, while Moses bestowed many “useful benefits on mankind” by inventing boats, Egyptian weapons, and philosophy. (Eusebius, PrEv 9.27.4) He also recounts that the Greeks called Moses Musaeus and that he taught Orpheus, who was widely considered to be the father of Greek culture.[2] Similarly, Artapanus credits Moses with the division of Egypt into 36 nomes as well as the successful conquest of Ethiopia, two accomplishments traditionally attributed to the Egyptian folk hero Sesostris.[3] Throughout the narrative Artapanus insists that the public loved these Jewish figures for their impressive innovations and achievements. In fact, he remarks that the Ethiopians went so far as to circumcise themselves out of admiration for Moses.[1] While some of Artapanus’ history clearly references accounts in Genesis and Exodus, such as his description of the plagues, most of his story is completely fabricated.

One of the most striking aspects of Artapanus' works is the ease with which he syncretizes Jewish and Egyptian culture and religion. Artapanus also writes that Moses is responsible for appointing "for each of the [36] nomes the god to be worshipped, and that they should be cats and dogs and ibises."


Abraham taught the Egyptians astrology. That's somehow close to SY ideas. Artapanus "lived in Alexandria, during the later half of the 3rd or 2nd century BCE".

**************

The page ...
http://www.cais-soas.com/CAIS/Religions ... 4/pt12.htm
... based on this institution ...

The Circle of Ancient Iranian Studies (CAIS)
The First and Most Comprehensive, Informative and Scholarly Website Dedicated to Ancient Iran and Iranian Civilization.
http://www.cais-soas.com/index.htm

I'm not sure, if this is common "history" or "politic with intention". Nonetheless it offers a rather extended program about Persian history. With rather critical comments on the Jewish development occasionally.
Added later: Only one or two of the Gnostic sects reviewed by Irenaeus actually called themselves "gnostic".
Yes, of course. It's a stormy field with a lot of experiments.
Huck
http://trionfi.com

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Your Internet source for "72 conspirators" doesn't say where this number comes from. It is said by Plutarch (45-120 c.e.), in his essay on Isis and Osiris. In a nearby paragraph he notes the connection between 5 and 360, in his story of how Hermes won the 5 days from Selene gambling; he leaves out the 72, but it would be 1/72nd portion of the Moon's light that he won. How ancient this particular weaving of numerology into mythology is, I don't know. Such things are typical of Platonism but existed before that. "72" is a number used mythologically in many cultures. If you Google "72 conspirators", several books come up about this, with all sorts of interesting things; how accurate they are I don't know. The problem is that there was so much unofficial syncretizing going on (by self-appointed "historians" and their dupes) in that era, you can't tell how old anything is. That is also when Sethian Gnosticism developed, as part of the same phenomenon.

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mikeh wrote:Your Internet source for "72 conspirators" doesn't say where this number comes from. It is said by Plutarch (45-120 c.e.), in his essay on Isis and Osiris. In a nearby paragraph he notes the connection between 5 and 360, in his story of how Hermes won the 5 days from Selene gambling; he leaves out the 72, but it would be 1/72nd portion of the Moon's light that he won. How ancient this particular weaving of numerology into mythology is, I don't know. Such things are typical of Platonism but existed before that. "72" is a number used mythologically in many cultures. If you Google "72 conspirators", several books come up about this, with all sorts of interesting things; how accurate they are I don't know. The problem is that there was so much unofficial syncretizing going on (by self-appointed "historians" and their dupes) in that era, you can't tell how old anything is. That is also when Sethian Gnosticism developed, as part of the same phenomenon.
I think, it's clear, that the 12x30 + 5 calendar did run very long. How old, I can't say. Possibly since the 5th dynasty. That's c. 2500 BC.
http://de.wikipedia.org/wiki/Heriu-renpet
"Heriu-renpit" is the name for the 5 additional days.
http://de.wikipedia.org/wiki/Papyrus_Rhind
http://en.wikipedia.org/wiki/Rhind_Mathematical_Papyrus
Papyrus Rhind is given as the oldest document, which knew the 5 gods for the 5 days.
English wiki gives as date c. 1650 BC.
German wiki indicates an earlier date.

A researcher "Alexander Scharff believed that the Old Kingdom period observed a year with 320 days". But that would be very early.
At least Plutarch heard just a story from Egypt. I've read, that the Greek found it, when they conquered Egypt, and imitated it.
Huck
http://trionfi.com

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mikeh wrote: The big advantage of the cube model is that it allows for a natural transition from 3d to the 2d "tree" model ...
Have you ever read The Tree of Life Projected in the Third Dimension by Andrew Catero and Darcy Küntz? It shows the (GD/Kircher/Cordovero pattern) tree as a tetrahedron and octohedron -- however it is sort of opposite to the way I see the SY 3d tree, with Octohedron at the top and Tetrahedron at the bottom, instead of tet at top and oct at bottom.

http://hermetic.com/caduceus/articles/2 ... nsion.html

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No, I hadn't read that piece, Steve, thanks. That will work, but it seems a bit complicated and contrived. The cube is much more natural.

I notice that they ask,
How is the Tree of Life formed in three dimensional space? In other words what is the minimum shape used to separate the inside of itself from the outside.
Their answer is 1 octohedron and 1 tetrahedron[/i]. My answer is: 1 cube with 2 lines drawn inside it, one for time and the other for value.

However, that's too minimalistic if you think of sefirot as spheres. For that, I need an octohedron as well as the two lines. Then to get the tree it is projected onto a sphere, and a cube inside that, projected onto a flat piece of paper twice and then rearranged. It ends up being more complex than theirs, but I think more natural, because it corresponds to the actual cosmos as seen at night, with small spheres behind it and inside it, with God at the center and the circumference. .

Against that, what do the tetrahedron and the octohedron get you, except a tetrahedron and an octohedron?

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Checking further, I am not sure that in the SY the sefirot were thought of as spheres. The word means "enumeration" or "counting", according to Wikipedia at
he "Sefirot" (סְפִירוֹת), singular "Sefirah" (סְפִירָה), literally means "counting"/"enumeration", but early Kabbalists presented a number of other etymological possibilities from the same Hebrew root including: sefer (text), sippur (recounting a story), sappir (sapphire, brilliance, luminary), separ (boundary), and safra (scribe). The term sefirah thus has complex connotations within Kabbalah.[1] (Note 1: Scholem, Kabbalah, p. 100, cited on Kabbalah page, note 14.
Here the closest is "luminary", but "sefira" is not "sappir". Pico, for example, translated the word as "enumeration". To be sure, once they had the two-dimensional "tree", they were points on the tree, and so assimilable to spheres as seen from far away. But the SY's picture is three-dimensional, at least. So they could just as well be surfaces, either on a cube or a sphere (the Ptolemaic 9th sphere, I am thinking). And so no need for an octohedron, although it might well have occurred to them.

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In commenting on Alemanno - viewtopic.php?f=11&t=1049&start=40#p15958 – Huck wrote:
This is simply the Sephiroth-tree with 11 elements (not with 10). The missing Sephira Daath.
Does use of the “proto-sephirah” Da’at—viz. on the middle pillar above Tiphereth—predate 16th Century Lurianic Kabbalah? I ask as I had assumed—perhaps, incorrectly—that Christian adaptation of Kabbalah prior to Luria located “Knowledge” at Tiphereth (= Sun), and with “Knowledge,” in turn, being identified with the Spiritual Gift of Prophecy in accordance with Pauline epistles.

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Kate wrote:In commenting on Alemanno - viewtopic.php?f=11&t=1049&start=40#p15958 – Huck wrote:
This is simply the Sephiroth-tree with 11 elements (not with 10). The missing Sephira Daath.
Does use of the “proto-sephirah” Da’at—viz. on the middle pillar above Tiphereth—predate 16th Century Lurianic Kabbalah? I ask as I had assumed—perhaps, incorrectly—that Christian adaptation of Kabbalah prior to Luria located “Knowledge” at Tiphereth (= Sun), and with “Knowledge,” in turn, being identified with the Spiritual Gift of Prophecy in accordance with Pauline epistles.
hi Kate,

I personally made my statement on the base of my assumption, that the object of SY is the same as that what was used in the Chinese I-Ching (just the same or at least a rather similar mathematical concept). In the I-Ching you've three lines, which define the universe: Earth-Man-Heaven. If you import to this Yin and Yang (two different states for each of the 3 lines), then you get "8 trigrams". 3 + 8 is trivially 11.

In the SY context the "10" was very important, perhaps cause of earlier Pythagorean preferences. So they interpreted the same or similar consideration (3+8=11) as 3 + 7 = 10, which is easily reached, if one takes the trigram Kien = heaven as a creative God, which as a trigram is inside the 8 trigrams, but as the dominating God also in all the other 3 elements (the lines in the Chinese context).

Well, SY and Kabbala mystified the case, the more pragmatic Chinese mind preferred no complications.

From Da'ath I've read somewhere (long ago), that it appeared as a word together with Binah and Chochmah in biblical contexts (it's long ago and I don't remember, where I've read this). From Kether I've the opinion, that it is an artificial word to present the number "620" ... K = 20, T = 400, R = 200 (20+400+200 = 620). Some Kabbala texts are eager to explain this as the reason, why there are "620 columns of light" in Kether.

Well, this is nonsense in my humble opinion. There's a rather complicated mathematical reason for the number 620 inside the math scheme (of I-Ching, and also in that of SY). Kether is just an artificial word to express the number.

Kether was then used to explain 613 laws or commandments, which are grouped in 248 parts of human body and 365 for the days of the year. 248 + 365 = 613. 7 laws for the priests were added to get the number 620 (at least in one of the rare comments, which are given to the "620 columns of light").

If one adds 365 + 7 = 372, one gets, that 372:248 have the ratio 3:2, or in other words, 248*1.5 = 372. And 372 + 248 are still naturally = 620.
I've no idea, why this 3:2 relation had been important to them.

I also don't know enough about later Kabbala, generally it's my impression, that the original math had been more or less lost in preference to new ideas. Kabbala ideas knew a lot of differences. So I can't help you with your detailed question. ... :-) ... when I read modern Kabbala books, I'm astonished, what they all claim to know.

I got, that Daath, Binah and Chochmah were an older triad.
Huck
http://trionfi.com

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Kate asked
Does use of the “proto-sephirah” Da’at—viz. on the middle pillar above Tiphereth—predate 16th Century Lurianic Kabbalah? I ask as I had assumed—perhaps, incorrectly—that Christian adaptation of Kabbalah prior to Luria located “Knowledge” at Tiphereth (= Sun), and with “Knowledge,” in turn, being identified with the Spiritual Gift of Prophecy in accordance with Pauline epistles.
In Gikatilla's "Gates of Light", Da'at, i.e. Knowledge, is the entire Middle Pillar (p. 228), all the way to Kether. As such, it is the reconciler of the left and the right at all levels where those pillars (or "lines", in his terms) exist. If you take an isolated passage, as on p. 226 of the English translation, it appears to be just between Binah and Chochmah, but if you read further, you'll see that it is the whole line. P. 227, which is the middle part of this discussion, is not in Google Books, but it is not really necessary to verify the point.

See https://books.google.com/books?id=u6fXj ... at&f=false

"Gates of Light", c. 1290s Spain, was known to the Christian Kabbalists, 15th century on, both in Hebrew and in a Latin translation by Paolo Ricci. Ricci's translation wasn't published until 1515 or so, but he is one of the converts that translated for Pico, so it was probably available in manuscript for Pico, i.e. before 1487. It is a condensation as well as a translation, so I don't know if the part on Da'at/Dat was included in the translation.

What you say about Da'at in relation to the "spiritual gift of prophecy" is interesting. I'd like to hear more. Sorry to be so late reading this. I have been otherwise engaged.