Re: Le Tarot arithmologique - la séquence 1+4+7+10 = 22

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I want to get back to the "arithmological tarot". Alain's essay prompts me to ask which of A, B, and C orders has the closest fit to Pythagoreanism in its symbolism. That is, if we start with the Bagat as first, how well does the symbolism of the Monad conform to the possible symbolism of the subject? Then for the second card, how well does the symbolism of the Dyad conform to the subject of that card? And so on.

The tarot is all about sequence, cards appearing in a certain order. Playing the game depends on it. The "arithmological" tarot also depends on sequence. That is why 1 + 4 + 7 + 10 fits the A, B, and C orders in different ways, because of the differences in the sequence among the three orders. Conversely, this division implies a definite way of grouping the cards. 1 + 4 implies a definite sequence of groups, in that it is not one group of 5, one group of 6 including the Fool, or two groups of 2 and 4.

Ignoring the Fool, the Bagat is always first. Putting him part of a larger group would not explain why he is always first. People remember that he is first. If so, his being remembered is distinct from being remembered as part of a larger group. The next 3 are not like that, except that the Pope is always number 5. He seems to be a dividing line between those before him and those after. But the other 3 occur in 4 out of the 6 possible combinations: (a) Empress, Emperor, Popess (Sermone de Ludis, perhaps Bologna); (b) Empress, Popess, Emperor (Susio, Metropolitan); (c) Popess, Empress, Emperor (Rosenwald, Alciati, Geoffroy, Noblet, etc.); (d) Popess, Emperor, Empress (Maison Academique). This is not counting the ones in which there are undifferentiated "papi".

TRIUMPHS 2 THROUGH 5


I have already discussed the Bagat as the Monad and the next four as a group. Now I want to go inside that group. It is the variety in in sequencing within the group, whenever it arose, that interests me.

Of these (a) is easiest to account for allegorically. The Emperor "triumphs over" the Empress, in the sense of ruling over her in the family and in the Empire. Then Pope/Popess as a pair are simply the spiritual equivalents of these secular powers; in European society there were both types of authority. The spiritual are put above the secular, so as to show that the institution of the Church is superior to that of the Empire, because the spiritual power is higher than the temporal power. Among the spiritual, the Popess is inferior to the Pope in the same way as the Empress is to the Emperor.

The Popess is an oddity because in society there was nobody so titled. But the Church was considered the wife of the Pope in canon law. Since the Pope is the head of the Church, he is superior in the cards to the Church. On another interpretation, Popess = the Faith. Again, it is the Pope who rules in matters of Faith, and the Faith rules over the temporal powers. The Church is ruled by the Pope, and rules over the temporal powers.

(b), Susio's order, shared by the Metropolitan (which is otherwise a B order), applies the same two principles but in the other order. It is the division between women and men that applies first, with the women subordinate to the men. Then within these two groups, it is the spiritual that rules over the secular.

(c), which is by far the most popular, is strange in one respect. The men are superior to the women, but only the Pope is superior to the secular powers. It is possible that this reflects the desire of the secular powers in the regions where this order held, not to be interfered with by the local spiritual authorities. They acknowledged the authority of the Pope but not those below him.

But still, it seems strange to make the Church or the Faith subordinate to the Emperor. The Church is only subordinate to the Pope, not the Emperor, much less the Empress.

One way of resolving this issue would be to say that the Popess was put so low in order to be next to the Bagat, who is an illusionist and a deceiver. She is Pope Joan or Pope Manfreda, a heretic with inflated ideas about women's proper role.

There is a way around that implication. Putting the Popess before the secular powers does not mean that they are inferior to them, but rather that the Faith is prior to the temporal powers. The temporal powers only exist in a society that is Christian. They are secular powers but also Christian. Christ is before them and provides the setting in which they rule. They rule in accord with the Faith of their upbringing. If they do not, then they will have to deal with the Pope or his representatives.

In this way of thinking, triumph cards do not necessarily triumph over, in the sense of ruling over, those preceding them; at least some of them merely are later in the story than the earlier ones. It is like in the John the Baptist Day procession in which floats passed by telling the story of the Bible; it is not that Pontius Pilate, who comes later in the parade, triumphs over the babe in the manger, but that Pilate comes later in time in the Bible.

In order (d) the female secular power is in the superior position to the male secular power. This does not occur in any known deck or other literary production; I think it is simply a mistake on the part of the publication, or the card maker whose cards the publication consulted. Conceivably they might have thought they were just conforming to the standard, thinking, well, it's about "the power behind the throne". I do not attach much significance to (d).

All of this is taking the cards at face value, that is, the value of their recognized titles, as seen in comparable images elsewhere. Pythagoreanism does something else: it looks at its number in the sequence. If so, we might ask, how could the Dyad be sometimes the Empress, sometimes the Popess? How could the Triad be sometimes the Empress, sometimes the Emperor? How could the Tetrad be sometimes the Popess and sometimes the Emperor? Is the symbolism of Pythagorean numbers that flexible? Or is it rather that one of the four historical orders of this group fits Pythagorean symbolism better than the others?

THE PYTHAGOREAN DYAD

The Theologumena Arithmeticae, translated as "Theology of Arithmetic" (or "Arithmetical Theology"), was the most comprehensive work on our subject available during the Renaissance and after. A result of Bessarion's importation of Greek works, It became available in Italy only in the late 1450s, by which time at least one of the four orders already existed and probably more. There were also, before then, three works in Latin that devoted sections to the classical interpretations of the numbers: the Introduction to Arithmetic by Nichomachus, the Commmentary on the Dream of Scipio by Macrobius (Part 1, Chapters 5 and 6), and the Marriage of Mercury and Philology by Martianus Capella.

Introduction to Arithmetic does not deal with the allegorical interpretatons of numbers. As for Macrobius, he deals with the application of the number 2 only in physical science, invoking the Dyad to explain the "errant" behavior of the planets (Stahl translation p. 105). As for Capella, the relevant pages are available on Google only in snippets. I will get the book itself next week, when college libraries open. In the snippets, I see only that it is the first actual number, female, "the mother of the elements", and the number for Juno (https://books.google.com/books?id=nZ-Z9 ... ad&f=false). If Jupiter corresponds to the Monad (Capella p. 277), which is the Pythagorean monotheistic God as Divine Creator (p. 278); then the Dyad would be the wife of God. This is not much, so I will turn to the the Theolgumena, recognizing that I am dealing with an interpretation that probably would only have been possible after the cards were already in one order or another.

According to the Theologumena, the Monad is both male and female, odd and even, and not a number but the basis for number. If I say, for example, "I have a number of cars", I will have deceived if that number is 1. "Number" implies more than one, maybe even more than two (the Theologumena insists that 2 is not a number either, Waterfield translation p. 45). The Monad is the membe of the decad associated with God, creator of the universe but not any of the things in the universe. Yet the Dyad triumphs over the Monad. It does so by breaking away from the Monad, becoming separate and creating opposition ( p. 51). If the Monad is form, the Dyad is formless matter. The Dyad is also "'anguish', 'endurance', and 'hardship'" (p. 46). To that extent it is like Juno to the Monad's Jupiter. Juno in mythology triumphed over Jupiter by wreaking vengeance on Jupiter's lovers and offspring by them, with Jupiter powerless against it.

The Dyad is not only "reckless", and "formless matter", but the origin of vice (p. 53). It is the Pythagorean equivalent of Eve, who separates from God and creates sin. As the Popess, this characterization is perhaps suitable for the pretenders Joan and Manfreda, reckless heretics. That fits the Sermones de ludo's "quod negat Christiana fides" (that which the Christian faith denies) and Aretino's mockery in Carte Parlante: "l’astuzia di quegli che defraudano il nostro essere con le falsità che ci falsificano" (the shrewdness of those who defraud our being with falsehoods that falsify us, (http://www.associazioneletarot.it/page. ... 63&lng=ENG). But is there anything else?

I think there is, but to get to it one has to go outside classical Pythagoreanism--and so, fortunately, a source independent of the late-arriving Theologumena. In the Wisdom literature of the Bible, if Jehovah is the first principle, Sophia or Wisdom is the second. A Florentine manuscript of the time gives Wisdom precisely the attributes of a book and staff-cross, the same as in the PMB (https://2.bp.blogspot.com/-3tLOJ7FjmdM/ ... ondo-8.jpg). Of course Hochmah was also in second position in the Kabbalists' system of sefiroth; but how early that was known by Christians in the Renaissance is unknown.

This is not the Pythagorean Dyad, to be sure. But it has the right cosmic aura (I will get to this later).

Wisdom is described as the source of our knowledge of the other basic virtues:
For [Wisdom] teaches temperance and prudence, justice and fortitude, and nothing in life is more useful for men than these” (Wis. 8:7).
There is also Saint Thomas on the end of the moral virtues, i.e. human good, in reply to an objection (http://www.newadvent.org/summa/3047.htm):
The end concerns the moral virtues, not as though they appointed the end, but because they tend to the end which is appointed by natural reason. On this they are helped by prudence, which prepares the way for them, by disposing the means. Hence it follows that prudence is more excellent than the moral virtues, and moves them; yet "synderesis" moves prudence, just as the understanding of principles moves science.
The difference between wisdom and prudence for Thomas seems to be that prudence is a special kind of wisdom, that about human good: "prudence is wisdom for man". However there is also, above prudence, that which he calls "synderesis", which the New Advent explains (http://www.newadvent.org/cathen/14384a.htm) as the axiomatic truths of practical reason, e.g. the Golden Rule. These are intuitively accepted as obvious, rather like the axioms of plane geometry. Wisdom then is the understanding of the basic theorems, so to speak, that follow from these axioms, and the knowledge of how they apply in practice. These somehow also relate to the 2nd and 3rd sefiroth of the Kabbalah, wisdom as basic principles and intuitions, and intelligence as their conceptual formulation and application in practice, but I am not sure how precisely.

There is also the phrase "mother of the virtues" in a 1505 painting by Mantegna, seeming to refer to prudence. The other three cardinal virtues are in the sky, and a banner with the words "mother of the virtues" extends from what seems to be a door in which the vices have enclosed prudence (a good explanation is at http://wtfarthistory.com/post/813006713 ... -over-vice). Yet it is Athena, goddess of wisdom, that saves prudence from the vices. Wisdom is what puts prudence in its rightful place.

In the New Testament, Jesus was identified with Wisdom--and also with the number two, as the second person of the Trinity. The Popess would not seem to be Jesus. But does the number 2 only apply to the Son? In the Old Testament, Wisdom is female, with God "in the beginning of his ways" (Prov. 8:22). The Messiah is someone later, predicted in Isaiah. Perhaps it can be either.

Virgins with papal-like crowns appeared in Italian art of the time, including earlier than the tarot. An example is that of the Sienese painter Martino di Bartolomeo. c. 1400 (right below). Another, although later than the invention of the tarot probably precedes knowledge of it, is in 1446 England, in the charter for the founding of King’s College, Cambridge, for which the Virgin was one of the College’s patron saints (left below). (This last image was posted on THF by Jean-Michel David.)
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The Virgin, like Wisdom and Prudence, was often shown with a book, sometimes learning how to read from her mother, more often pointing to the Book of Isaiah at the Annunciation. For people familiar with such depictions, an association of the Popess card with the Virgin would be a natural one, and from there to Wisdom and its earthly approximations. I do not say that the Popess is the Virgin, let me make clear, just that the Virgin is another image or level of the archetype for those who knew the symbols.

An association between the Virgin and Wisdom might explain the unique way in which the Bembo workshop portrayed the Virgin’s Coronation. Marco Tanzi (Arcigotissimo Bembo 2011 p. 26) points out that all three of the Bembo “Assumption of the Virgin” invariably showed her being crowned by the Father at the same time as Christ, as opposed to the usual way, in which Christ crowns the Virgin. Tanzi concludes that this is therefore not after the Assumption, when Christ would already be crowned, but rather at the beginning of the world. If so, that would explain why she does not fall under St. Paul's dictum that all the descendants of Adam are subject to original sin: she is from before Adam. Tanzi says that Mary's immaculate conception had been part of the turbolenze at the Council of Basel, which closed in 1439. A resolution supporting the immaculate conception was part of its proceedings; if she was held to have existed before the creation of Adam, that would account for special status, alone among mortals.

Here is a composite with one of the Coronations on the top left (attributed to Ambrogio Bembo), her Ascension on the right (attributed to Bonifacio) and comparisons between the face of the Virgin and the PMB Popess.
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As you can see, there is some facial resemblance to the Popess. In the one attributed to Ambrogio Bembo, 1445-1450 (at left above), she conforms to the standard late Gothic Lombard image of the Virgin, but also has some similarity to the PMB Popess. In the "Ascension", c. 1440-1445, by his brother Bonifacio (at right above), the resemblance seems to me rather striking, but of course it could just be the way he drew women.

This way of portraying the Coronation of the Virgin on the part of the Bembo workshop was quite unique in Western art. The usual way was to have the Son crown the Virgin, or else both the Father and the Son together. It is reminiscent of a debate that went on during the Council of Florence, 1439, whether the Holy Spirit proceeded from "the Father" or "from the Father and the Son". The Western Church preferred the latter, which corresponds to the Father and the Son crowning the Virgin; the Eastern Church preferred the former. But in this case it is the Virgin rather than the Holy Spirit, and she is more the second person than the third, like the Old Testament Sophia.

I have gone outside the title I imposed upon this section, which was supposed to focus on the Dyad. So what about the number Three?

THE TRIAD, TETRAD, AND PENTAD


Another Pythagorean progression goes as follows, in the Theologumena (Waterfield pp. 56-57) and also Macrobius (Stahl pp. 96-97) and Capella (Stahl p. 277): 1 is the number of the point, pure potentiality. 2 is the number of the line, without any definite form, merely indefinite extension in space. 3 is the number of figures in a plane, where form takes shape as perfect geometrical objects perceived intellectually but corresponding to figures drawn in two dimensions seen with our eyes. 4 is the number of the solid, as it takes a minimum of 4 points in three-dimensional space to define a solid; it is the number applying to our physical world.

If God is the point, the Dyad is the line, infinitely divisible and so an infinity of points. Then, just as the one-dimensional line is superior to the dimensionless point, the two-dimensional plane is superior to the one-dimensional line. In a plane a multitude of figures can be drawn; but all lines are the same, except in length.

The Theologumena calls the Triad prudence and wisdom (p. 51):
The Triad is called "prudence' and "wisdom"--that is, when people act correctly as regards the present, look ahead to the future, and with experience from what has halready happened in the past": so wisdom surveys the three parts of time, and consequently knowledge falls under the triad.
Something very similar to the first part of this sentence is written at the bottom of Titian's famous painting, dubbed by Panofsky "Allegory of Prudence" (https://en.wikipedia.org/wiki/Allegory_of_Prudence):
X PRAETERITO/PRAESENS PRUDENTER AGIT/NE FUTURA ACTIONẼ DETURPET

(From the experience of the past, the present acts prudently, lest it spoil future actions).

Panofsky and Saxl, who wrote the classic analysis of this painting, undisputed on the points of interest here, claim several sources for this saying; however in every case all these source say is that time (or counsel, in the case of Diogenes Laertius) is divided into three parts, past, present, and future. None is as close to what Titian wrote as the passage from the Theologumena, which probably not coincidentally had arrived in Venice only a few decades before and was quickly available for study.

Prudence is eminently suitable for the Emperor, who ideally is a model of prudence. Not only that, but he is a male, and 3 is the first male number. 3 is also the number of the Holy Spirit, and "spirito" is a masculine noun in Italian.

But there is also something to be said for the Empress. Coronations of the Virgin usually had a dove somewhere in the painting; the Bembo altarpieces do not. Tanzi says only, "l’assenza dello Spirito Santo è legata a una precisa questione dottrinale": "the absence of the Holy Spirit is linked to a precise doctrinal question" (2011 p. 27). Unfortunately he does not say what that question was. It might only be that of the immaculate conception, which arose in Basel. Another one was that at the Council's continuation in Florence 1439, on whether the Holy Spirit proceeds from the Father or from the Father and the Son. In both Greek and Roman Church art, the Holy Spirit was frequently represented by a dove; whether the form the Holy Spirit took at Mary's coronation was part of the debate I do not know. But it is not far-fetched to hypothesize that Mary, in these Bembo altarpieces, replaced the dove, so that the three figures of the Coronation are also the Trinity, in which it is no longer clear which is 2nd and which is 3rd. The Virgin is now associated with both numbers.

It could be like this. The Popess is Wisdom and Mary in the pre-lapsarian condition. Then she descends into matter, with the express purpose of giving birth to Jesus, who also existed in the pre-lapsarian heaven. Mary now is incarnate as the daughter of Anne, whereby, when she is at the right age for child-bearing, the Holy Spirit enters her and she is impregnated with Jesus, providing the matter for his divine form.

So the Popess can be number 2 as the allegorical representative of either Sophia or the Crowned Virgin, as an eternal being. Depictions of both gave the figure the characteristic Papal Crown. Then the Empress can be the Virgin incarnate, there to conceive God incarnate. It triumphs over Wisdom, in the meaning of Mary, as not just the ordering principle of the universe, but even more, the vehicle by which God enters his universe for love of humanity and salvation from sin.

The placement of the eagle-shield in the PMB is reminiscent of the Child in Madonna and Child paintings. Even where there is no such shield (e.g. the recently discovered Palermo Empress), the ruler's wife was expected to comport herself with the Madonna as her model. Then with the birth of the emperor-to-be and his crucifixion, Mary is surpassed by her child. The Popess can be number 2 as the allegorical representative of either Sophia or the Crowned Virgin, as an eternal being. Depictions of both gave the figure the characteristic Papal Crown. Then the Empress can be the Virgin incarnate, there to conceive God incarnate. It triumphs over Wisdom, in the meaning of Mary, as not just the ordering principle of the universe, but even more, the vehicle by which God enters his universe for love of humanity and salvation from sin. Until such time as Christ returns, the Holy Roman Emperor, the secular King of Kings, is his standard-bearer. In Pythagoreanism what links him to the whole, including the divine, is the Tetrakys, the sum of the first four numbers, which is ten.

Then the Pope carries Jesus's mantle as the inheritor of St. Peter, the rock to whom Jesus assigned the "keys to the kingdom". In Pythagoreanism, 5 was the first circular/spherical number, after 1, meaning a number which when raised to any power continues to end in that number (Hopper, Medieval Number Symbolism, p. 102; 6 also has that property). The circle and sphere were the geometric figures of perfection, eternity, and God. 5 is also Aristotle's "quintessence", the changeless aether of the celestials (Waterfield p. 68). In Christianity it is the 5 loaves that fed 5000, the 5 wounds of Christ, and Pentecost, the 50th day after the Resurrection (paralleling Moses' receiving of the 10 Commandments on the 50th day after the Exodus). It is that number that is beyond 4, the number of the material world. Macrobius (Commentary on the Dream of Scipio p. 100 of Stahl translation) says that since there are 5 levels from God to man (God, Nous, World-Soul, Celestial, terrestrial), the 5 is that which comprehends them all.

In this way Judeo-Christian-enriched Pythagoreanism gives sense to the progression from 1 to 5: God, then his Wisdom, from before sin entered the world; then this Wisdom come to earth and conceiving God in material form, also serving as a model for the Empress and all women; then God become man and King of Kings, in this role serving as model for the Emperor and all men, but whose representative and successor is the Pope, as the holy one of holy ones on earth.

BEYOND THE PENTAD


In this Pythagorean cosmogeny, in which the point expands to the line to the plane to the three dimensional world we live in, the Pentad transcends the universe of solid geometry by being the number that designates the next step: from the world of matter in various arrangements to the creation of life, the so-called "vegetative soul". I do not propose the Popess as the one presiding over vegetables, even if with them life and death do enter the world, of which he holds the keys. It is rather the cosmic scope of the process that is of interest. The Theologumena says (pp. 72-73):
Since in the realm of embodiment there are, according to natural scientists, three life-engendering things--vegetative, animal, and rational--and since the rational is subsumed under the hebdomad [i.e. the 7] and the animal under the hexad [i.e. the 6], then the vegetative necessarily falls under the pentad, with the result that the pentad [i.e. the 5] is the minimal extreme of life.
It is as in the illustration to Ramon Llull (his work came to be of interest in Northern Italy starting c. 1460), the great stairway of being.
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7 is also also the 7th planet, Saturn, whose deity also represented wisdom. In astronomy the sphere beyond that of Saturn is that of the fixed stars. In myth, Saturn was overcome by his wife Rhea, identified with the Octad (Waterfield p. 103). She overcame Saturn by substituting a stone for her newborn child Jupiter. In the 9th sphere, in Christianity, are the 9 choirs of angels; in the Theologumena it is the 9 curetes, the nurses and guardians of the child Jupiter on Crete (p. 107). The 10th sphere is that of God, with names like "heaven", "eternity", "sun", and "phanes" (shining one) (pp. 119-120)--but also, it seems to me, Jupiter overcoming Saturn, so that we are back to 1, Jupiter as creator-god.

There is something appealing about this Pythagorean progression from the Monad to the Dyad and so on, each number superior to the next. It gives a cosmic dimension to the succession of numbers. If the end of the tarot's series is the soul's ascent through the cosmos, as I have argued (and will repeate in another post now), the beginning should be a cosmic descent. With the Monad we are already at the top. Perhaps the descent can be seen as a succession of triumphs, in a kind of Judeo-Christianization of the Pythagorean vision.

Earlier I spoke of a temporal succession as justifying the Popess as Church or the Faith's place before the Empress and Empress in the sequence, only then followed by a a progression from inferior to superior. The same could be said on a cosmic level, in terms of a descent from above, which Wisdom/Prudence and Mary capture better than "the Faith". Moreover, this personification and person were already familiar in art with papal-style crowns. books, and cross-staff. The "Church Triumphant" had yet to grace church art wearing a papal tiara. Even "dame doctrine", described as next to the Wheel of Fortune in an anonymous English work of the late 15th century (viewtopic.php?f=11&t=937&p=13690&hilit=doctryne#p13690) and used as the basis for a papal-crowned figure in an illumination to Lydgate's Fall of Princes, is later than the tarot Popess. Thus it is possible to see these cards as a Judeo-Christian parallel to the Pythagorean cosmogeny, from the beginning of time, with the Bagat as the Monad = God, surpassing itself in His Wisdom, surpassed again in the Virgin Birth, setting the stage for the King of Kings and the Holy one among the Holy ones.

I have so far been considering this sequence in the order Popess, Empress, Emperor. It seems to me that Empress, Popess, Emperor comes to much the same thing. The Empress of Heaven becomes the Popess as Mary giving birth to the King of Kings. The only disadvantage is that the eagle-shield loses its significance. It belongs on the third card. It is even worse when the Popess is fourth? We have an Empress and Emperor in heaven, of which their earthly counterparts are exemplars, and then a Mary on earth, without any explicit recognition of her child on the card, and then the Pope as the representative of Christ's mission on earth. Putting the Empress before the Popess, on this level of cosmic allegory, is not as appropriate as the other way around, when there is the shield on the Empress card. Then, too, the Empress can be made younger than the Popess, befitting her child-bearing role. This is precisely what happens, as early as the Cary Sheet and Rosenwald Popesses and continuing in the "Marseille" versions in France.

APPLICATION TO OTHER CARDS

I will deal with the Pythagorean Hexad through Decad in another post. But there is more to be said about the 2-5. If such a quasi-Pythagorean account justifies the sequence of four triumphs, it might apply elsewhere that these numbers 2, 3, 4, and 5 appear in the sequence. It is not required, since Pythagoreanism's application to the cards would most likely would have been an afterthought, but it would add a dimension to these cards' interpretation and perhaps account for what appear to be changes in the sequence in different places, such as France. Ronald Decker has worked out some of the interpretations, at least for the C order, in The Esoteric Tarot, pp. 125-8 (https://books.google.com/books?id=qW11T ... ad&f=false); they seem to me worth repeating and amplifying upon. (Alejandro Jodorowsky, The Way of Tarot, 2004, has also done so, with similar understandings, but does not try to justify their historicity. For those, see my post at http://neopythagoreanisminthetrot.blogs ... blank.html.)

After 10, Pythagoreans usually simply started over, so that 11 = 1, etc. (as Decker and Jodorowsky correctly understand). So the Dyad would be considered again for the 12th card, and so on. The 12th and 13th cards are the same in the B and C orders but different in the A. The 14th and 15th cards are the same in A and B but different in C. These differences need to be taken into account.

Here I am going to refer to the lists given in Depaulis, Le Tarot Revele, as representative of all of them, a simplification which for these cards does not leave out much.
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The Hanged Man, the 12th triumph of the B and C orders, is there for and in an act of separation from his fellows, reviled as a traitor for his reckless daring in joining the enemy camp. That points to Judas, but also Jesus himself, a heretic to Judaism. These ranks included, let us not forget, Muzio Attendola, Francesco Sforza's father, in the eyes of anti-pope John XXIII. That could explain, in the PMB, the green (for fertility) leggings and the hole in the ground under his head (to plant him as a seed, for rebirth in spirit as well as the genesis of Francesco Sforza). Later the side-poles got 11 notches, pointing to Judas as the 12th, with a notch on the top pole; but at some point the notches on the side were changed to 12
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Jesus could be meant as the one in the middle. Decker comments on the symbolism of the red ends to the lopped branches (= blood).

Then in 13, Death is the opposite of birth, its antitype in the 3. But for Christians, "in dying we are born to eternal life", as the hymn falsely attributed to St. Francis proclaims. Those being swept under by the scythe of Death--cardinals and popes in both the CY and CVI--are the ones whose devotion earns them such life (unless it didn't, of course).

Corresponding to the 4 there is 14, which in order B is the Devil, in C Temperance. These are both concerned with the material world of temptations, whether to yield (the antitype) or exercise self-control.

For the 5 there is 15, which in B is Lightning, in C the Devil. Like the Pope, the lightning destroying man's towers is the mouthpiece of God in the material world. The Devil and his legions are a spiritual power pitted against the Pope and the Church in that world, a kind of antitype.

In the A order, it is the Old Man who is the 12th triumph. It is a stretch, interpreting an old man with an hourglass as a figure of Wisdom or Prudence, as opposed to the passage of time. That would be reason enough to change the hourglass to a lantern, but I do not find where the A order ever did that. Dropping one of cards 2-5, as in Minchiate, or simply starting the numbers at 5 for Love, as in Bologna, would make the A numbers correspond to B and C for trumps 12 and 13. That numbering, unfortunately, changes the whole sequence. And it seems like a device after the fact, precisely to attain that result. I will stick to ordinal numbers and the 78 card version.

In A the Traitor is 13th. If we see him as the agent of rebirth, in that Judas paves the way for the crucifixion, that fits well enough. In that case Death is 14th, with the number (4) for the 3 dimensional world of our senses. There is no rebirth implied. 15 is again the Devil, the Pope's antagonist.

Applying the Pythagorean allegories again in the higher numbers thus seems to work, more or less, and best in C. With B there is the problem of the Popess, an allegory that fits the best on the non-Pythagorean level but not as the Pythagorean Tetrad; with A the problem of the Old Man as the Dyad, and the lack of the Christian message about Death in the Tetrad. If we assume that Pythagorean considerations were an afterthought as far as organizing the sequence, that would suggest, so far, that the C order is later than the others. But there are more cards to consider, and anyway, it is all pure hypothesis.

From both a Pythagorean a non-Pythagorean perspective, the A order as it stands would seem not to be the original order. This is because Judas was traditionally the 12th disciple, for whom another 12th disciple had to be chosen after the crucifixion. So he would appropriately be the 12th card in the sequence. An example of this tradition is in the hanged-man poster that anti-pope John XXIII put up against Muzio Attendola on all the bridges of Rome: (http://www.associazioneletarot.it/page.aspx?id=108, citing the Diario Romano of Antonio di Pietro, Anno Domini 1412, in Ludovico Antonio Muratori Rerum Italicarum Scriptores, Tomo XXIV, Milano, Ex Tip. Societatis Palatinae, 1738, col. 1031-1032):
Io sono Sforza vilano de la Cotignola, traditore, che XII tradimenti ho facti alla Chiesa contro lo mio honore, promissioni, capitoli, pacti aio rocti.

(I am Sforza peasant of Cotignola, traitor, who twelve times have betrayed the Church against my honor: promises, compacts, agreements have I broken.)

In the A order, however, he is 13th. It even may be that the device, in Bologna, of leaving the Bagat unnumbered--or of removing one of the papi, as in minchiate--was invented so as to make him number 12 in accord with the tradition. (It also makes Death number 13, but there is no evidence that before the invention of the tarot death ever was associated with the number 13.) This is not to say that the tarot did not originate in the A region. It is only to say that if it did, there is reason for thinking that either the Hanged Man or some card before it, such as the Bagat, was not part of the sequence at that point.

There is also the issue of the number cards in the deck, which conveniently are numbered 1 to 10. These of course were not created with Pythagoreanism in mind; it applies only to their interpretation, in contemplation or divination. In this regard there is no problem of variations in the order, obviously, but there is the problem that no manual existed for their interpretation until Etteilla in 1770. However there is the Sola-Busca, which has distinct scenes on its number cards as opposed to merely flowers and vines. This is something I have explored in another thread ("Deciphering the Sola-Busca pips"), but not as well as I might. Rather than repeat what I said there, with revisions, I will simply, at some point, revise there what I wrote.

Re: Le Tarot arithmologique - la séquence 1+4+7+10 = 22

464
Mikeh

What a beautiful reflection...
Eager to read more

NB
In French ...

Réflexions en vrac...

+ Votre idée de procéder à une lecture pythagoricienne à la lumière du judéo-christiannisme me semble pertinente.
+ L'analyse que vous faites des différentes séquences possibles à l'intérieur de la progression pentagonale : 1+4+7+10 me semble aussi tout à fait à propos.
- La proposition de Decker de s'arrêter à la Décade et donc de reparir à 1 pour 11 n'est pas dénuée d'intérêt.
Added today
Elle est justifiée en arithmétique : la décade se succédant à ell-même indéfiniment de
1 à 100 etc.
Toutefois, cette analyse pourtant pythagoricienne ne rend pas compte de l'expansion arihmologique c"est à dire figurée géométriquement du Nombre pentagone 22.
Pour reprendre la correspondance que vous évoquez avec Hockmah dans votre étude, ce serait un peu comme réduire les 22 sentiers lumineux de l' Arbre de Vie de la Qabbale aux 10 réceptables ... Ce serait passer à côté d'une grande richesse symbolique et de part trop simpliste.
A titre personnel, je retiens de l'idée de Decker le fait de ne pas dépasser la décade mais en gardant à l'esprit la progression arithmologique 1+4+7+10. Aucune des Quatre enceintes successives ne dépassent alors la Décade...


La disposition arithmo-géométrique du Nombre Pentagone est
1, 5, 12, 22
Image

1=1
5 =1+4
12= 5=7
22=12+10

Ce qui met en relief les Quatre Nombres Pythagoriciens
1+4+7+10 = 22
Image


Une arithmologie simple, accessible à l'époque, de Quatre Nombres:
1 Unité
4 Carré
7 Septénaire
10 Décade

Added now : Pour ce qui est des 40 numérales, oui, c clair que nous avons affaire à 4 Tetractys de 10 successives.(Et probablement pour les 16 Honneurs, à 4 Tétrades à 1+2+3+4 : "a Tetractys game")
Par ailleurs, le décompte des Emblèmes dans chacune des 4 Décades donne le nombre 55 cher aux Pythagoriciens car somme des 10 premiers nombres.
Multiplié par le Quaternaire, cela donne 55x4=220.
La clef, si clef il y a, serait-elle une lecture à 22 x 10 OU 22x10 = 220?
http://www.sgdl-auteurs.org/alain-bouge ... Biographie

Re: Le Tarot arithmologique - la séquence 1+4+7+10 = 22

465
Nota
See : Global survey
http://www.academia.edu/24629466/_Le_li ... enaissance

Out of topic maybe, but I believe that Pythagorism was during the Renaissance very present in arts or architecture.
Artistic Harmony was pythagorean.
Pythagorism gives of Numbers a Géometrical figuration =arithmological
So the Pythagorean doctrin of Numbers is scientific (arithmetical) and symbolical (arithmological).

A specificity of the Number 22 in it's arithmo-géométrical disposition is the presence of visual perspective from 1 4 7 10.

Image


This intuition of perspective could be of interest.
In the last quarter of the XVth century, for example ...

Leon Battista Alberti will theorise the notion of perspective.
https://fr.wikipedia.org/wiki/Leon_Battista_Alberti



Painters :
Melozo de Fornil
https://fr.wikipedia.org/wiki/Melozzo_de_Forl%C3%AC
Piero della Francesca
https://fr.wikipedia.org/wiki/Piero_della_Francesca
Marco Palmezzano
https://fr.wikipedia.org/wiki/Melozzo_de_Forl%C3%AC


Note : Fra Luca de Paoli and the Divine Proportion : https://fr.wikipedia.org/wiki/Luca_Pacioli
There is, indeed, something linked to the Divine Proportion or Golden ratio in the Numbers fo the classical Tarot.
For example :
1. J avais noté dans le temps que la Racine carrée de PHI régissait les rapports entre le nombre 22 et le nombre 56
22 x racine carrée de Phi = 56/2 = circa 28
Modern value : Racine carrée de phi / (1+[5^(1/2)])/2]^(1/2) = (approx.) 1.272 ...
(Here I'd say a very good approximation : circa 27.90 )

2. JMDAVID avait aussi suggéré une possible équivalence entre les 220 emblèmes des 40 numérales et l'Angle d'Or :
360°/ PHI = 220°
Modern value : PHI = (1+[5^(1/2)])/2 = (approx.) 1.618 ...
(Here, I'd say an empirical approximation : circa 222.49)

Added today : La proportion des 22 Triomphes aux 56 cartes emblématiques est donc sans contestation possible une proportion "dorée" régie par la racine carrée du Nombre d'Or.
22Phi = (56 x racine carrée de Phi) / 2

"Le nombre d'or, un nombre réel considéré depuis l'Antiquité comme esthétique, soit un segment divisé en deux parties d'inégale longueur ; si le rapport des longueurs de la plus grande et de la plus petite partie est égal au rapport des longueurs du segment entier et de la plus grande partie, on dit que le segment est divisé en « section dorée ». Le rapport commun s'appelle le nombre d'or et est noté PHI. Il est approximativement égal à 1,618..."
Well these kind of problematics were present at time ...
http://www.sgdl-auteurs.org/alain-bouge ... Biographie

Re: Le Tarot arithmologique - la séquence 1+4+7+10 = 22

466
Jean-Michel was my first exposure to pre-19th century Tarot History. I took his online course on the Noblet. He has a real respect for the ancient and medieval esoteric tradition, which eventually became Science and, for some, forgot its origins. After him came Aeclectic, Huck, and THF. Plus ça change, plus c'est la même chose. Or something like that.

So here is the rest of what I was going to say. Except that I will have more to say after that, but in a different vein. I wish I could write more clearly.

For the numbers 6 through 11 (which reduces to 1), there are six cards most of which exist in every version of the sequence; the only exceptions are Justice and Temperance, which sometimes occur in the next group. Then come the Hanged Man and Death, which, whatever their numbers divide this group from the next. That much is simple. The problem is that they come in a multitude of different orders; so each of the numbers gets assigned to a wide variety of cards identified by subject. How can Pythagorean symbolism account for them all? All I can do is examine to what extent the Pythagorean account of these numbers fits the various cards assigned to that number, among the A, B, and C, orders. It is bound to be quite impressionistic.

Here are the various fairly confirmed sequences found (Dummett for A and B, plus the "Order of Trumps" thread; Marco for C): http://4.bp.blogspot.com/-YlU6F53x-_E/U ... .35+PM.png, B: http://1.bp.blogspot.com/-1EdTAS9Qo6E/U ... .56+PM.png; C: http://2.bp.blogspot.com/-rEbZ-DxvUhs/U ... rders2.jpg

A order (6 cards). I put the confirmed ones in bold, for the decks with just a few cards:
Bologna: Love, Chariot, Temperance, Fortitude, Justice, Wheel, Old Man
Charles VI, Rosenwald (for which last 2 unclear): Love, Temperance, Fortitude, Justice, Chariot, Wheel, Old Man
Orfeo, Catania: Love, Temperance, Fortitude, Justice, Wheel, Chariot, Old Man
Colonna: 6 Love, [Temperance, Fortitude, Justice, Old Man, ?] 10Chariot, 11Wheel

B order (5 cards):
Sermones: Temperance, Love, Chariot, Fortitude, Wheel, Old Man
Garzoni/Bertoni, Met., Pomeran, Rouen, Anonymous (appropriati), Imperiali, Citolini: Temperance, Chariot, Love, Fortitude, Wheel, Old Man.

C order (5 cards):
Susio, Piscina, Vieville, Giovio: Love, Justice, Chariot, Fortitude, Wheel, Old Man
Alciati: Justice, Fortitude, Love, Chariot, Wheel, Old Man
Geoffroy, Noblet, etc.: Love, Chariot, Justice, Hermit, Wheel, Fortitude

6 is given to Love in A and C but in B to Temperance. In Pythagoreanism, 6 is the "female marriage number", in that it is the product of 2 and 3, even (female) times odd (male) equaling even (female). Capella (p. 280) gives it to Venus, a female, which is not Cupid but at least is his mother. The "male marriage number" is 5, which is 2 (even) plus 3 (odd) equaling 5 (odd). I cannot see the any application of the idea of "male marriage number" to the Pope card, except perhaps that a priest is needed to carry out a proper marriage. In Florence, at least, it was only at the betrothal that a priest was involved, in a church; marriages were conducted by a notary and performed in the bride's home (I get that from Watson's Ph.D. dissertation). If so, then we might have the betrothal in card 5 and the marriage in card 6.

The Bologna and Minchiate practice giving the number 5 to Love fits the Pythagorean "masculine marriage number" idea.

Between the two, 6 is the more auspicious, because it is a "perfect number", meaning the sum of its divisors equals the number (3+2+1=6). Another thing to recommend 6 over 5 is that multiplication is a "blend" of 2 and 3 rather than their "juxtaposition": blending produces the proper harmony. The Theologumena observes also that 6 cubed is 216, which is the time a fetus must be in the womb, which is 7 months plus 6 days for the egg to fully fertilize. 7 months is the earliest a fetus can survive outside the mother's body, according to Pythagorean medicine. Macrobius agrees on the relation between the number 6 and the 7 months pregnancy, but with a different calculation (p. 102). Finally, 216 years is the time between incarnations according to the Theolugumena's calculations based on Pythagoras's memory of his past lives. So in general, 6 is the best number for generation of the soul in a new body.

The B order's Temperance (= self-control over instinctive urges), appropriate for a card devoted to marriage.

7 is sometimes Temperance, sometimes Love, sometimes Justice, sometimes Chariot. Temperance and Chariot with a woman charioteer (as Chastity) fit the number 7 best, because it is the number of the virgin warrior goddess Athena, born from her father's head with no mother, just as 7 is the product of no other number except 1 (1 corresponding to Jupiter). Also, it is with the aid of wisdom that the soul wins its victories. As the number representing the time of crisis--7 months in pregnancy, 7 hours for the umbilical cord to fall off, 7 days for something else, then 7 weeks, etc. leading to the 7 ages of man--it the time at which an old way of being must be replaced by something new, the victory of a new self over an old one, and to let it pass is to be plunged into difficulties. 7 guides the soul in the ability to choose the right time, the "kairos" in Greek.

In Florence the three moral virtues come before the Chariot. It is by means of them that the soul triumphs in its preparation for the ascent back to God. In Bologna they come after, as the force regulating the moral virtues, which for St. Thomas was Prudence, the "charioteer of the virtues", auriga virtutum.

7 is in some orders assigned to Love. Athena, the goddess associated with 7, has nothing to do with love, except perhaps the love of wisdom. As for "critical time", crisis point, the B order card shows two people besides Cupid, a man kneeling before a woman, whom Cupid has just stabbed with an arrow. It is indeed a critical moment.

The Pythagorean texts do not associate 7 with Justice. The Theologumena associates Justice with 5, but its argument--that the number has one monad as the fulcrum and two on each side, for a balance--would work equally well for 7. However it is not done.

Numerous subjects take the 8th position: Temperance, Fortitude, Chariot, Love, and Justice.

Macrobius says in so many words that the Pythagoreans consider 8 the number of Justice (Stahl p. 98), because it can be divided into two equal parts twice. The Theolgumena does not confirm Macrobius, but Macrobius was widely known. I cannot fit the Theologumena's account of the Octad, which is rather abstract, to any of the Triumphs.

9 is near the end of the cycle. Fortitude is a popular choice, and also Justice.There is nothing relating to either virtue in the Pythagorean accounts of 9 that I can find. But fortitude = endurance, which is what it takes to withstand the whole cycle. Also, fortitude is a good virtue to have before what usually comes next, namely, the Wheel.

The most logical fit between the Pythagorean 9 and a card is with the French order's Hermit, one who is near the end of his life, just as 9 is near the end of the decad.

10 is the end of a cycle, after which everything repeats on a higher level. That quite naturally applies to the most popular choice for this number, Wheel of Fortune, an eternal round of ascent and descent through life and beyond. Sometimes 10 is the Chariot. at puts the Wheel at 11 is that the A order has all 3 virtues before the Wheel, as opposed to only two in B and C. The A order makes sense internally, but not as far as Pythagorean correspondences.

11 is 1 repeated. If the Wheel is 1, it could represent the beginning of a new cycle. Otherwise, the Old Man is the universal choice.. This seems a little late, although at least it is before Death. I think that Fortitude, in the French order, yields the best allegory. The picture is of a lady with her hands in the mouth of a Lion. If we think of the lion as a solar animal, with the sun as God, or as the king (of beasts), or as the Lion of Judah, another name for God, then her fortitude is born of a trust in God. It is the courage of belief, even if it means one's mortal death.

It would seem to me that for 6 to 10 so far, the French modification of the C order fits Pythagoreanism best, as in the case of the numbers from 2 to 5.

Now for the cards after 15. Again I am going to use Depaulis's list:
Image

The striking thing is that from Devil through Sun the three orders are absolutely the same, not only in the examples that Depaulis gives but in every document and deck known, except the Sicilian, which seems to have been controlled by one or two specific individuals in the 17th century and which I therefore do not count; it is too recent and marginal to be of interest in this regard.

The fact that they are everywhere the same suggests that they became standard at a time when there was maximal communication among regions, i.e. after 1450, and with a common narrative to remember it by. We may never know the exact details. I expect that someone decided that there should be a series of cosmic powers after the Death cards, instead of Hope, Faith, and Charity, and perhaps the Sun. Hope suggests the Star of Bethlehem. Faith, as what lights one's way in a dark time, is comparable to the Moon. And Charity, the free giving of life-giving energy, is aptly represented by the Sun. They are arranged in "ascending order of light" for easy recognition by the players. Later cards draw from the "children of the planets" series. But these cannot be the source of their order, because the order of the planets is not followed.

Then someone decided to put in representatives of the spheres between the celestial region and the earth, perhaps stimulated by Macrobius's account in Commentary on the Dream of Scipio, where the soul ascends through the spheres. These spheres are linked to the cards in Piscina's c. 1565 Discorso (http://www.tarotpedia.com/wiki/Piscina_Discorso_5). First are the demons that fly about grabbing souls in the air. Then there is the sphere of fire (where lightning comes from). And then the celestials, in order of brightness, he says. If you look at the fresco of Dante and his imaginative world in the Florence Duomo, elements of all five cards are there in order: Satan with devils (although not in the air, where Piscina puts them), a tower with fire on top as the Mount of Purgatory, and then the celestial bodies, in their standard order.

Another source could be the last ten pages of Plutarch's On the Apparent Face in the Orb of the Moon (its relevance was noticed first by John Shephard, 1980), which describes the soul's course through the upper air, which Plutarch calls Hades, through lightning and then a pleasant place, called "the Meads", for those who get that far, then the Moon and finally the Sun. In Christianity, Heaven would be above that. For the Cary lady with the two jugs in the Star card (in the "Meads"), there is Dante's depiction of Mathilda and the two streams of Lethe (forgetting) and Enoue (from nous, Greek for mind, Dante's version of Mnemosyne, remembering) in the Terrestrial Paradise of Purgatorio, which Dante must drink from in order to enter the world of the Paradiso. There are also the two gates in the Cave of the Nymphs, but I think they fit the Moon card better.

In this program there is not much room for additional considerations such as Pythagoreanism. However we can still look for correspondences.

The 16th card is Lightning in A and C. The arrow shot by Cupid from his sunburst in card 6 is similar to the "Saetta" of lightning shot by God at the tower of card 16. They are both acts of Love, the one to initiate the "ladder of love" and the other to burn away impurities from the lower levels and put the soul on course.

Among the three orders, the B order is one number behind A and C. The 16th B-order card is the Star. Capella assigned 6 to Venus, which fits especially the "Leber" B-order Star card (http://www.letarot.it/cgi-bin/pages/sag ... lle/10.jpg); it shows Venus as guide of sailors. In other B order cards it is the Star in the East followed by the three kings, another form of Love, God's love for humanity.

17 applies to the Star in A and C. The A card has again the three kings and the Star of Bethlehem. It is the spiritual triumphator, and the bearer of Athena's wisdom come at just the right time. He will come again at the end of time as the "bright and morning star". In the C card of the Cary Sheet and the later French cards, it is an offering of the waters of purification (although in the Cary Sheet, curiously, there is a star on the lady's shoulder, suggesting a planetary god, surely Venus).

In the B order, 17 is the Moon card. The d'Este Moon card has an astronomers tracing circles apparently using the Moon as his model. It is difficult to see as an allegory. Perhaps it has to do with learning from the heavens, as a principle for finding wisdom.

The Metropolitan card has a different image, a sad-looking lady holding the moon in her hands above her head, but looking down (https://tarotmeditations.wordpress.com/ ... ropolitan/). It is reminiscent of the PMB Moon card. All I can think of is dissatisfaction with Diana's brand of chastity, as in one of the Boccaccian romances of the triumph of love. In this deck the Chariot card is 7, with a child, perhaps Cupid, seeming to lead and a man and woman as passengers (see previous link).

In A and C, the Moon is 18, and so 8. The Florentine card has two astronomers tracing circles, no easier for me to figrelate 8 than one astronomer. The number 8 in Pythagoreanism relates to the Moon in two ways. First,it is associated with changeableness (the Theologumena does not say why), and the moon is constantly changing its phase. Second, it is associated with untimely birth. For some reason they believed that a 7 month baby would survive, and also a 9 month, but not an 8 month. For the Moon there is also, Neoplatonic if not Pythagorean, Plutarch's Apparent Face in the Moon: the soul spends a long time on the Moon, in suffering and learning. Then it either descends into generation (through the gate of Cancer, according to Macrobius and Porphyry) or advances higher (the gate of Capricorn), depending on what is appropriate and just. So there is a connection between 18 and 8, Macrobius's number of Justice. The Cary Sheet and subsequent "Marseille" style decks appropriately have a crayfish (Cancero) at the bottom of the card and the Moon, the next step, on top. According to Plutarch, there is a region called "the gates" (i.e. the towers on the card) for the step after that.

In the B order18 is the Sun. I cannot see anything about the Pythagorean 8 that relates to the B order Sun card. It does not show anything about Justice. However since God = Sun, there might be a conneciton to God's Justice.

In A and C the number 19 is associated with the Sun. The Sun in Plutarch Moon is the soul's final destination. In another essay, there is one more. In Christianity the Sun is a symbol for God, but the individuals on the card aren't there yet. (I am thinking of the "Marseille version" mainly, but also the Cary Sheet and the d'este, with its Diogenes wanting to enjoy the sun, even the Charles VI, with its Fate Clotho about to cut the thread of an individual life.) Their situation is more like the Pythagorean 9, almost to the end.

20, in A and C, is the end of the second cycle, where one is judged. 21 is 1 again, in Glory with God. 22 would be the 2 again, God's companion, now including all the "Fools for God".

In the B order 19 is the Angel. That fits the concept of "almost there" well enough.

In A, 20=10 and is the World, while 21 = 1, the Angel. In C, 20 is the Angel and 21 is the World. 20 is the end of one cycle and 21 is the beginning of the next. A Pythagorean interpretation would be that in A the World is what is being left behind, whereas in C it is what is being entered.

In B, 20=10 is Justice. 10 is not about Justice that I can find. 21 in B is the world, which would be what is entered after Justice has been rendered.

So that's tarot by the numbers, lots of them. To conclude: the order that is most Pythagorean in the French C order, with the other C and the A probably in second place. The B numerical assignments of the Sermones do not work as well, a perhaps surprising result given that it is that order that most naturally divides into 1+4+7+10. But perhaps the order was already fixed by the time Pythagoras was in the air, and the only thing left to do was to put the Fool, who isn't fixed anywhere, at the end.

Re: Le Tarot arithmologique - la séquence 1+4+7+10 = 22

468
For the moment, the focus has been about the similarity between the 22 Triomphes and the Pentagonal Number 22 in it's arithmological expansion as 1+4+7+10 - not forgetting the "Tetractys game of the 56" with 4 Numerical Tetractys (4x10)and Four Honours Tetrades (1+2+3+4).

Could there be something else - something unearthed that could be of interest ... beyond the game of 78 cards itself?
HARMONIA? "The whole universe is Harmonia and Number " (Aristotle Met.926a2-3)

I'm amazed by some remarquable pythagorean relations of the numbers of the classical Tarot and I don't believe that they are only random.
For example : Fra Luca de Paoli and the Divine Proportion : https://fr.wikipedia.org/wiki/Luca_Pacioli

In history of the approximations of the value of PHI, it was estimated at it's :
Limit inferior as 8/5 =1.6
Limit superior as 5/3 =1.666
http://villemin.gerard.free.fr/Wwwgvmm/ ... bOrVal.htm

Real value is circa 1.618

1. 56 and 22 : square root of PHI
[Here the value of PHI is absolutely correct until 3 decimals after the coma.
The fourth decimals after the comma of PHI seems to be between the real value of PHI = 1.618 and formula Number 16 and PI : 16 / PI au carré = 1.6211] that is for the value of the square root of PHI :

Real value with PHI as 1.61818 = square root as1.2720
Value of square root given by : 56 : 2 / 22 = 1.2727
Approximate value with formula 16/PI x PI = 1,2732

La proportion des 22 Triomphes aux 56 cartes emblématiques relève d'une proportion "dorée" régie par la racine carrée du Nombre d'Or.
22 x racine carrée de Phi = 56/2 = 28

"Le nombre d'or, un nombre réel considéré depuis l'Antiquité comme esthétique, soit un segment divisé en deux parties d'inégale longueur ; si le rapport des longueurs de la plus grande et de la plus petite partie est égal au rapport des longueurs du segment entier et de la plus grande partie, on dit que le segment est divisé en « section dorée ». Le rapport commun s'appelle le nombre d'or et est noté PHI. Il est approximativement égal à 1,618..."

2. 22 and 40 : 4 times the Tetractys
Le décompte des Emblèmes dans chacune des 4 Décades donne le nombre 55 cher aux Pythagoriciens car somme des 10 premiers nombres.
1+2+3+4+5+6+7+8+9+10 = 55
(Theleogoumena, On the Decad From Anatolius [86], pp.114-115 and Note 25)
Multiplié par le Quaternaire, cela donne 55x4=220.

Also of interest but less accurate ...
3. 360° and 220° : Golden Angle [Here the value of Phi appears to be : 1.636]
The approximation of PHI is must less accurate than in the squares roots of Phi - yet acceptable because within it's inferior and superior limits ...
JMDAVID avait aussi suggéré une possible équivalence entre les 220 emblèmes des 40 numérales et l'Angle d'Or :
360°/ PHI = 220°


4. 22 and 14
Note about the suggestion of JMD
A mon sens, la référence à l'Angle d'Or est aussi intéressante pour établir la relation entre les Nombres
22 et 14 = 36
22 = circa 36/PHI

Nora : Also an elegant way of setting in an OUROUBOROS of 360° the 22 - each one of the 22 is equal to circa PHI
http://www.sgdl-auteurs.org/alain-bouge ... Biographie

Re: Le Tarot arithmologique - la séquence 1+4+7+10 = 22

469
Aparte

There has been a focus on Numbers 6, 8 and 16 in another thread.

In the proto-Tarot, there are 16 Gods.

Also San Lorenzo in Florence
Zodiac with 12 signs and 4 directions?
The Sacristie of San Lorenzo build under Cosme de Medicis has an Astronomical Heaven in the ceiling.
"L'ancienne sacristie, la Sagrestia Vecchia (1422-1428) au fond gauche du transept : Fresque du ciel astronomique du 4 juillet 1442 peint sur la voûte de la chapelle de l'abside par Giuliano Pesello."
Image


https://fr.wikipedia.org/wiki/Giuliano_Pesello
Image


In ancient times, Number 16 is present in the 16 columns (8 and 4+4) of the Pronaos of the Roman Pantheon whose structure is clearly Pythagorean :
Image

"Le portique de façade comporte 16 colonnes corinthiennes monolithes de granite, à chapiteaux de marbre, disposées sur trois rangs : huit colonnes en façade suivies de deux rangs de quatre colonnes. Les colonnes extérieures sont en granite gris clair, les quatre colonnes intérieures sont en granite rose plus sombre."
https://fr.wikipedia.org/wiki/Panth%C3%A9on_(Rome).
The same Number 16 is also in favor under Cosme de Medicis for example San Lorenzo in Firenze :
"16 arches portées par 16 colonnes ; or 16 est le carré de 4 et 4 est la Tétrade"
http://www.academia.edu/24629466/_Le_li ... enaissance

Nota : True also that in San Lorenzo Numbers 6 and 3 are also present ...6x3 = 16?
"6 quadrilatères de la nef croisent les 3 du transept "
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Re: Le Tarot arithmologique - la séquence 1+4+7+10 = 22

470
I've read Mikeh's excellent and valuable study of the Trumps sequence from a Pythagorean vision.


I agree with two main points of the methodology but I have another position on the third point.
This difference is not an opposition but a necessary emphasis...

Point 1 : agreement for a Pythagorean lecture linked to judeo-christianism
Point 2 : agreement on the analyses of the permutations of the Trumps numbers - within the different sequences of the orders A B C
Point 3 : agreement on the Pythagorean orthodoxy of the method of Decker reducing 11 to 1 and so on - the series of numbers being seen as a succession of decades ad infinitum...
But necessary, from my point of view, to emphase on the Pythagorean arithmological expansion of Pentagone Number 22 as 1+4+7+10 that could be not taken in account on the basis of a simple arithmetic decimal succession of decades..
Nota
The correlation between 22 and 10 is also already present in the simple fact that the Four Decades of the Suits sum up to 220 emblems
The sum of the first ten numbers of the Decade is Number 55 :
1+2+3+4+5+6+7+8+9+10 = 55
(Cf Theleogoumena, On the Decad From Anatolius [86], pp.114-115 and Note 25)
55x4 = 220
That is :
22 times 10 or 10 times 22



Better in French ...
+ Votre idée de procéder à une lecture pythagoricienne à la lumière du judéo-christiannisme me semble pertinente.
+ L'analyse que vous faites des différentes séquences possibles à l'intérieur de la progression pentagonale : 1+4+7+10 me semble aussi tout à fait à propos.
- La proposition de Decker de s'arrêter à la Décade et donc de reparir à 1 pour 11 n'est pas dénuée d'intérêt.
Added today
Elle est justifiée en arithmétique : la décade se succédant à ell-même indéfiniment de
1 à 100 etc.
Toutefois, cette analyse pourtant pythagoricienne ne rend pas compte de l'expansion arihmologique c"est à dire figurée géométriquement du Nombre pentagone 22.
Pour reprendre la correspondance, toutes proportions gardees (See Note), que vous évoquez avec Hockmah dans votre étude, ce serait un peu comme réduire les 22 sentiers lumineux de l' Arbre de Vie de la Qabbale aux 10 réceptables ... Ce serait passer à côté d'une grande richesse symbolique et de part trop simpliste.
A titre personnel, je retiens de l'idée de Decker le fait de ne pas dépasser la décade mais en gardant à l'esprit la progression arithmologique 1+4+7+10. Aucune des Quatre enceintes successives ne dépassent alors la Décade..

METHODOLOGIE PRECONISEE
In English : as I wrote before, Pythagorism gives of Numbers (Arithmetic) a Géometrical figuration (Arithmology)
So the Pythagorean doctrin of Numbers is scientific (arithmetical) and symbolical (arithmological).
In French : La voie de la recherche me semble t il est de donner les propriétés arithmologiques (arithmétiques et géométrqiues) des nombres successifs de 1 à 22, triangulaires carrés polygones , leurs composants, les propriétés symboliques recencées par les gloses pythagoriciennes etc. Et de là, découleront, de part leurs figurations arithmologiques, dans les quatre enceintes du Nombre polygone 22, leurs potentialités symboliques - à confronter avec les différentes Triomphes positionnés à cette dite place selon les ordres A B ou C.
Un énorme travail mais que nous pourrions mener - en réunissant nos compétences...


Note :
Je ne suis en rien opposé à une présence de la pensée de la Kabbale christiannisée lors de la fixation de la structure du Tarot classique.
(Pour ma part, j'ai étudié et sais monter impeccablement les 32 Voies de la Sagesse (22 en 10) selon l'Eclar Etincelant de la Qabbale provencale d'Aboulafia de même que méditer pour les interpréter sur les racines linguistiques composées de la rencontre de 2 Lettres Nombres ou Tserouf de l'alphabet mosaïque telles qu'elles se présentent dans l'hébreu moderne...)
La figure d'un Pic de la Mirandole au bon moment et au bon endroit militerait dans ce sens.
Néanmoins, pour l'heure, la référence à la Qabbale juive même christiannisée - Kabbale - relève encore de la contingence et non de la nécessité.
La disposition arithmologique des 78 est Pythagoricienne- même si, par ricochet, s'en trouvent confortées, indirectement, certaines analogies avec l'Arbre de Vie de la Qabbale .
Pour l heure, seule la référence aux 22 Chapitres de la Bible selon Origène, confirmée par d'autres Pères de l'Eglise, est à prendre en considération.
La recherche exhaustive et documentée d' une présence juive donc possiblement au fait de la Qabbale en contact avec des Pythagoriciens constituerait un pas en avant pour les tenants de cette thèse.
Seul Pic de la Mirandole possède cette spécificité.
Je ne dis pas que c'est impossible.
Je dis que c'est non démontré.

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