On trump 6, Decker observes that the "Hercules at the Crossroads" theme that he sees in the Tarot de Marseille trump 6 was known at the time as "the Pythagorean Y", the two diagonals of the Y being the two choices, Virtue and Pleasure. For the Cupid at the top, he shows us his drawing of a c. 1500 painting by Girolomo di Benvenuto of "Hercules at the Crossroads" topped by a the Good Genius, a robed youth holding a torch (http://commons.wikimedia.org/wiki/File: ... A09524.jpg
, given there as "first half of 16th century"). If you think the upper figure is not very close to a nude boy with a bow and arrows, Decker cites a Cristofano Robetta print on the same theme that has a winged Cupid in the same role. Looking on the Web, I find by him an "Allegory of Carnal Love", as the Chicago Art Institute calls it, c. 1530, (http://www.artinstituteimages.org/searc ... ys=robetta
). It is not clear to me that this Cupid is a "Good Genius", nor that either of the maidens qualifies as Virtue; and there is no choice, because each of the two maidens has her own male companion. The boy at the top is simply Cupid. Yet it remains true that the "Choice of Hercules" was a Pythagorean theme.
There is also a problem of how this "choice" fits into Decker's division into three groups of seven. He calls the first seven "descent of the soul" and the middle seven "probation". "Probation" suggests tests of one's mettle, whatever that might be. If anything is a test, it is this "choice of Hercules". Yet Decker has it on the "descent". How is it part of the soul's descent? It seems to me that we have already left the first group and entered the second.
What saves Decker's 7-7-7 schema here is another attribute of the 6, namely, that it is a perfect number, defined as one whose factors added together equal the number, i.e. 1+2+3 = 6. This suggests to him the perfection of reuniting with one's other half. Decker says (p. 121):
Marriage could be regarded as the restoration of the soul's perfection. The soul, when created, was perfect and was spherical (infinitely symmetrical). But events in the world's Creation divided the unisex soul into a male and a female with contrasting bodies. Thus all humans search for completion by union with a mate.
He is drawing on Plato's Symposium
, a familiar enough text in the late 15th century. However Plato there put this idea of the original "spherical" body--which might include two males or two females, not just a male and a female--in the mouth of the comedian Aristophanes and did not mean it as the soul's true yearning, which was higher. A better image, which Decker's language also suggests, is that of Adam's perfection before the creation of Eve from one of his ribs, Adam as a being made in God's androgynous image in a world of the senses that is unblemished and so not quite our own, a "terrestrial paradise" created by God on the 6th day, after which, his work perfected, he rested. But after that, we know, things got worse, and God made some adjustments. So in the 6, the soul is still descending.
God creates woman originally as a helpmate to man, so that he will not be alone. Decker points out correctly that 6 is dedicated to Venus and as such is dedicated to marriage. He offers no references; perhaps it is Martianus (736):
The number six is assigned to Venus, for it is formed of a union of the sexes; that is, of the triad, which is male because it is an odd number, and the dyad, which is female because it is even; and twice three makes six.
But Plutarch, On the E at Delphi
), says that 5 is the number of marriage. The Theologumena
says that both are numbers of marriage, one by addition and the other by multiplication (Waterfield trans. p. 75). I'll go with that.
Marriage is clearly a theme of the early Milan cards, extending into the 16th century with the Shoen Horoscope's House of Marriage, which is very close to the 1650 Vieville (http://4.bp.blogspot.com/_Lu-6PwakMv0/S ... eville.jpg
). In fact it looks to me that the figure that Decker calls "Virtue" in the Tarot de Marseille is the marrying priest with a sex change; it could even be a priestess, as Ricci suggests in his 17th century Dionysian take on the card ( http://3.bp.blogspot.com/_Lu-6PwakMv0/S ... hosson.jpg
16 relates to the 6 as being "perfection, disagreeably obtained", in comparison to the work of purification through suffering. My only quarrel is that I have never seen correlations of this type in Pythagorean documents, nor 16 as 10 + 6. Usually it is analyzed as 4 x 4, the square of the first square.
7 is the number of Minerva, the goddess of wisdom, also a warrior-goddess, a "manish goddess", because it is not generated by multiplication of other numbers within the decad and does not by multiplication generate any other number in the decad. Similarly, Minerva is born of no parents (except the One, he should have said, i.e. Jupiter: "it is called Pallas because it is born only from the multiplication of the Monad", says Macrobius at VI.11); nor does she have any children. She is the patroness of strategic warfare, he says. Appropriately the charioteer in the Tarot de Marseille wears armor. I would add that in the CY and PMB it is even a female charioteer.
Also, Decker says, 7 is 3 plus 4, for the three parts of the soul plus the four elements of the body which is what we see n the Chariot. This is a correlation that the Pythagorean texts do not make as far as I can see. However this doctrine appears many times in medieval Christian writings. Albertus Magnus (quoted in Hopper, Medieval Number Philosophy
, p. 112):
For the human body is composed of 4 humours, and varies through the 4 seasons of the year, and it is composed of 4 elements. On the part of the soul, on the other hand, are 3 powers or forces by which the spiritual life of man is ruled. [Hopper's footnote: Commentary on Psalm 6, ed. by Borgnet, XIV, 72.]
There is also Honorius of Autun, explaining why the 10 commandments divide into one group of 3 and another of 7 (Hopper p. 114):
The other, of 7, concerns the love of neighbor. It is 7-fold, to signify the 3-fold soul added to the 4-fold body. [Hopper's footnote: Ecclesia, P. O. 172, 873.]
Decker's point is that the Chariot marks the end of the descent of the soul. It is now on the level of material reality, with the chariot as an allegory of the body (hence the four elements, and the 2 lower parts of the soul). It is the space in which Macrobius says that there are seven directions of motion: right, left, up, down, forward, back, and rotational. It is also that world in which development happens, i.e. growth. "Macrobius relates Seven to stages of human gestation, maturation, and time cycles in general" (Deckerp. 117). So in the tarot there are three cycles of seven.
17 is the number of the Star card, with its seven small stars on it. It is that by which the soul "ascends to its repose in heaven". It seems to me that such a statement is a bit premature, since there are four more cards. I would say rather that it is the first triumph of the disembodied soul over that which would pull it down from its ascent.
8 is Macrobius's number of Justice (I found it at V.17); and Nichomachus' number of "the law" (reference unknown). Although there are other numbers of Justice in Pythagoreanism (2, 4, and 5 in the Theologumena
), 8 is the one that the tarot designer apparently chose, according to Decker. I notice that 8 is identified with Judgment by Albertus Magnus (quoted in Hopper, p. 112):
From this it follows that the day of Judgment will be 8. Or better, it is called 8, because it is the consequence of this life which runs the circuit of 7 days. [Hopper's footnote: Commentary on Psalm 6, ed. by Borgnet, XIV, 72.]
18 then draws on Eight as the number of "untimely birth", as it was believed that seven month and nine month foetuses would survive outside the mother's womb, but not eight months. Decker compares the crayfish in is lake with a fetus in the womb.
9 is near the end of the sequence from 1 to 10; so it is fitting that an Old Man be there. For 19, the Sun is the close of the soul's celestial life, Decker says. My only quarrel is that Decker has not related the Sun with the end of the soul's celestial life in any Pythagorean-inspired document. I think it can be argued in terms of Plutarch's On the Face that Appears in the Orb of the Moon
, as I have explained above.
10 is the end of a cycle, appropriately pictured by a Wheel. It is the number of "mundane changes", whereas 20 is the number of "miraculous changes". My only quarrel is that if it is the end of a cycle, then the sequence should be seen as 1-10-10-1, not 7-7-7.
With 21, we are back to the One, this time envisioned as female and as goal instead of beginning; it is "reunion with the world-soul".
THE BROADER PICTURE
Decker maintains not only that Pythagoreanism of the first ten numbers fits the tarot in the C order, but that its designers had Pythagorean number theory in their minds when they created it. Unlike the actual look of the cards, the order of the cards in Milan is not contra-indicated by known facts. Nobody knows the order of the first Milanese decks. There were no numbers on the cards, or even titles, and no lists in consecutive order until Alciato in 1544. So by default, the facts do not suggest anything different for Milan decks.
The only facts to suggest otherwise pertain to other regions: The first known list was in the Ferrara area is somewhat different: the Popess is at 4, Temperance is early, and Justice is at the end. Other lists, and numbers written on cards, were similar, except that they the Popess sometimes was number 2. Justice was always last or next to last.
Decker, however, insists that the Milan order was the original one. What chance is there that such a claim is true?
The Milan order certainly fits Pythagorean philosophy the best, at least for the first 10. After that, Pythagorean teachings are less clear. I find no doctrine of anti-types or complementary types in the Pythagorean writings; if numbers over 10 are discussed, it is in relation to the first 10. If 12 is of interest, it is as the product of 4 and 3, and almost never as 10 + 2. If 27, it is as the cube of 3, and so on. But it is easy enough to make the numbers 11-21 repetitions of the cycle of the first ten.
But there are many variations in Pythagoreanism. The number of justice is variously 2, 4, 6, and 8. Even the 1 pertains to justice, according to Macrobius, in that it is God. Thus 21 is also a possibility, the number of Justice in the A and B orders. The number of marriage is 5 or 6. 5 is the number of the Lover card in some decks. The number of wisdom, which Decker assigns to 2, is in the Theologumena
3. But neither of these is that of the Popess in the B order, where she is 4. But at least both the Popess and the Empress, 4 and 2, have feminine numbers, since even numbers are feminine.
It thus remains a realistic possibility that Pythagoreanism as such figured into the ordering of the tarot, or at least in people's interpretations of this ordering, if only because arithmology was applied to almost everything, not only by pagan writers but even more by Christian ones (as amply documented in Hopper, Medieval Number Philosophy
). All the same, for Decker's interpretations it seems to me that we should look at when, where, and with whom in 15th century Italy Pythagoreanism as such was popular, and what was said. Here Decker is not much help. He does not concern himself with the historical setting of Pythagoreanism in Italy, beyond verifying that at least the ones in Latin (which he by no means restricts himself to) were extant by the 1430s.
So I did a little reading on the subject, not nearly as much as there is, even in English, but at least something. In Pythagoras and Renaissance Europe: Finding Heaven
, Christiane l. Joost-Gaugier discusses who the champions of Pythagoreanism were in 15th century Italy. They include most of the same people who would have had copies of Horapollo at that time: Filelfo, Cyriaco da Ancona, Gemistos Plethon, Pogio, Alberti. There were also others, starting in Florence with Salutati, the admirer of Petrarch and great Chancellor Florence in the early 15th century. His successor Leonardo Bruni, was so as well; after him came Pogio, whom I've already mentioned. In Padua in Salutati's time there was Vergerio, editor of Petrarch; there was much interaction between Salutati and Vergerio. It would perhaps not be correct to say that these people were Pythagoreans; but they at least thought that Pythagoras had things to say worth studying.
Salutati is surprisingly specific in his account of Pythagoreanism, discussing not merely the scientific and moral qualities of Pythagoras but the numbers themselves, which is what we want to see. Although he does not name Pythagoras, when anyone talks of 1 as the number of the point, 2 of the line, etc., the reference is to Pythagoras. In a letter couched in such terms, we see a detailed discussion of 1, 3 and 6 (see Humanism and tyranny: Studies in the Italian trecento
, by Emerton, pp. 363-365, at http://babel.hathitrust.org/cgi/pt?id=m ... up;seq=379
). 3 stands out in particular because it expresses the Trinity. This doctrine was stated by many theologians. Roger Bacon, for instance (Hopper p. 107):
For unity multiplied into itself cubically, that is, thrice, as once one taken once, does not multiply essence, but remains the same although it is produced equally in 3 directions. And so by a familiar example theologians designate the blessed Trinity. [Hopper's footnote: Opus majus,, Burke, I, 245.]
That is one of Salutati's points, that the three dimensions of the cube show how one thing can also be three. He also uses the sides of the triangle to the same effect.
There was also the good Dominican Thomas Aquinas, repeating the Pythagorean litany:
...by his rising on the third day, the perfection of the number 3 is commended, which is the number of everything, as having beginning, middle, and end.
In addition, we can see Pythagorean ideas reflected in the art and architecture of the time. Art became intensely mathematical starting in the 1420s, with Brunelleschi's rediscovery of the techniques of perspective around 1415 and the resulting need for geometry in laying out a painting. One of the first to put Bruneleschi's ideas in practice was Masaccio. After that, Alberti simplified the procedure in his On Painting
, developing what is now called one-point perspective. He then wrote on architecture, following Pythagorean ratios that were founded in musical theory (for details see the links at http://go.owu.edu/~jwbiehl/architects.htm
). Filarete in Milan and Palladio in Padua in their writings followed in Alberti's footsteps.
In relation to the tarot, there is also Sigismundo Malatesta, the recipient of the thus far first recorded tarot deck, made for him in 1440 Florence. In around 1450, judging from a medal of the design made in that year, he commissioned Alberti to remodel an existing Gothic church. Rudolf Wittkower (Architectural principles in the age of Humanism
, 1952) discusses the innovations that Alberti applied to the exterior of that Church, which remained unfinished at Malatesta's death in 1466, concluding (p. 41):
No later architect has come nearer to the spirit of Roman architecture, as found, say, in the inner arcades of the Colisseum. [footnote: Alberti may have been influenced by arcades of Theodoric's Tomb at Ravenna wwhich he calls a 'mobile delubrum' (Bk I, ch. 8). Nor had any earlier architect so thoughtfully welded together an entire bulding by the flawless application of Pythagorean proportions. [Footnote: The Pythagorean theme was convincingly demonstrated by Gerda Soerge, Untersuchungen ueber den theoretischen Architekturentwurf von 1450-1550 in Italien, Munich, 1958 (Dissertation), p. 11, and, abbreviated in Kunschronix, XIII, 1960, p. 349f.]
I might add that the 1450 medal was done by de Pasti, who also supervised the work in Rimini. De Pasti is known to tarot researchers for his 1440 letter to Piero de' Medici about his work on cassoni paintings of Petrarch's Triofi
Although Wittkower's book is on architecture, he doesn't confine his remarks to that field. He begins his discussion on "Religious Symbolism of Centrally Planned Churches" as follows (p. 27):
Renaissance artists firmly adhered to the Pythagorean concept 'All is Number' and, guided by Plato and the neo-Platonists and supported by a long chain of theologians from Augustine onwards, they were convinced of the mathematical and harmonic structure of the universe and all creation.
Later in the book he discusses this point in relation to Brunelleschi (p. 117), Leonardo (p. 118), Michelangelo (p. 119), Agostino Carracci (p. 119), Raphael (p. 125), and a host of architects and architects' consultants. Earlier he had discussed Giovanni Bernini's drawings (p. 15). He could have included Mantegna, Piero della Francesco, and many others.
MASACCIO AND PYTHAGORAS
I want to expand on the above with particular reference to Masaccio, in part because he was so early--he died in 1428--but also because of connections to the tarot. First, his fresco of the expulsion from Eden seems to be the model for the Minchiate "Tower" card, with its woman fleeing in fear. Why that is so is a mystery. It might simply be that the image was admired and thus copied by others for a different purpose. Another connection is that his younger brother, known as "Lo Scheggio", is a known painter of playing cards, probably including tarot, in the early 1450s or 1460s.
The most mathematical of his works, and the most influential as well, is his Holy Trinity
of c. 1425-1427, the first known work to employ Brunelleschi's perspective techniques, combined with the use of shading--chiaroscuro--to create naturalistic depth. I could find no satisfactory online reproductions, as they all lose either the color or the bottom of the painting; the best is probably at http://upload.wikimedia.org/wikipedia/c ... %C3%A0.jpg
), although the colors are too dark; Mary's robe should be blue, for example.
To me its geometry suggests Pythagorean influence, especially as stated in Salutati's explanation of the "inexpressable Trinity" in terms of the triangle and cube (see the whole long paragraph at p. 365 of http://babel.hathitrust.org/cgi/pt?id=m ... up;seq=381
). This is a point made in passing by Joost-Gaugier (p. 172), expanded on by Bruskewietch, http://archive.org/detail/TheSearchForM ... ithin)--to
an extreme I am not prepared to follow.
First, there is the circle formed by the hemispherical vault, with the forehead of God the Father as its center--the mind of God. This serves to fix one of the apexes of the triangles formed starting at that point. The circle does not correspond to any of the numbers as far as I can tell, except that if "God is a circle whose center is everywhere and circumference is nowhere," as Cusa unoriginally said (Wittkower, p. 28), it is related to God. In Ptolemaic astronomy, for another example, the planets were held to follow circular orbits due to the perfection of that figure. Wittkower adds that
The geometrical definition of God through the symbol or sphere has a pedigree reaching back to the Orphic poets.
He then cites Plato, Plotinus, and pseudo-Dionysus. So the circle became the dominant organizing principle of sacred architecture, a striking contrast to the middle ages, with its organization around the shape of a Latin cross and an emphasis on the vertical, away from this world. The circle, in contrast, puts God everywhere, including the human soul, as Wittkower points out; it exemplifies the correspondence of microcosm to macrocosm.
Salutati, it will be recalled (again, here is the link: p. 365 at http://babel.hathitrust.org/cgi/pt?id=m ... up;seq=381
), uses the triangle to illustrate the three in one principle of the Trinity. In the painting, one triangle is formed if you go from the forehead of God the Father down to the heads of the Virgin and the Evangelist. You can also go up in a straight line from the heads of the lower figures to the apex of a triangle at the level of the heart of Christ.In Pythagorean terms--although this is not necessary to appreciate the theme of the Trinity--the Virgin represents his beginning, the Evangelist his middle--i.e. his period of teaching--and the crucifixion his earthly end. Another triangle is made by the nails in Christ's hands and feet.These two triangles overlap to form a 6-pointed star; this is one of the 6s in the painting. Another 6 comes if you add the two donors and the skeleton to the pair of the Virgin and the Evangelist plus Christ; it forms a large triangle similar to that showing 6 as a triangular number in the arithmetic textbooks, i.e.
or two triangles, formed by the two donors and the skeleton beneath, along with its mirror image, the upper triangle of Christ with the Virgin and the Evangelist, the lower a kind of mundane reflection of the upper:
There is also the 3 of the Trinity, of course: the Son, the Father, and the white dove of the Holy Spirit (between the Father's beard and the Son's head), each on its own plane as a single One. And at the bottom, the tomb on which the skeleton sits has three vertical bars.
With the dove, there would be 7 living figures in the painting, a sacred number in both pagan Pythagoreanism ("they give it reverence" says the Theologumena
) and Christianity (i.e. seven days of creation, seven sacraments, etc.) The addition of the skeleton makes 8.
In the vault, there are 7 rows. 8 deep, of coffers on the vault (the dark rectangles), each of which is a square when seen as the surface of a solid rather than on the plane of a photograph. Besides that, there are 9 lines in the vault forming the boundaries of the coffers. 9, besides being the square of 3, is the number before 10, i.e. the number that ends the cycle begun at 1. It is also the number of choirs of angels in pseudo-Dionysus, etc.
These numbers are not so clear in photographs of the painting, due to damage, including cutting off the top border of the fresco. I invite people to consult the reconstruction of the original paintings as proposed by Ursula Schlegel (and reproduced enthusiastically by Janson):
Joost-Gaugier (p. 172) suggests that the 8 coffers represent Justice, as 8 is the number of Justice in Macrobius. But what does the scene have to do with Justice? The 8 could be merely a consequence of being between the 9 lines that serve to create the illusion of depth. 9 is significant as 3 squared. On the other hand, 8 as Albertus Magnus's number of Judgment might possibly work.
The number 5 (of the 5 loaves for 5000 people) is also present, in the number of cornices on the two outside columns; this may be mere coincidence, as I don't see 5 elsewhere. The same may be true for the instances of 7 and 8 that I have identified.
The floor and sides of the painting are dominated by the number 4. This point has been emphasized by Jenson in his essay "Ground Plan and Elevation in Masaccio's Trinity
" (in Essays Presented to Rudolf Wittkower
). With its architectural structure clearly influenced by Brunelleschi, the painting is an early example of how the square was of central importance in Renaissance architecture. Janson notes (footnote 6, p. 84):
On the pervading importance of the square as a perfect figure in Renaissance religious architecture, see Rudolf Wittkower, Architectural Principles in the Age of Humanism, London 1952, passim.
The fresco is a series of rectangles and squares: the tomb, the three floors on which the various figures hang, stand, kneel, or lie. There is also the vault, with a square floor, with 4 columns that perhaps form a cube. The coffers on the vault are also squares (rectangular only if not imagined in a space defined by the laws of perspective).
This goes to confirm 4 as the number of material reality, I think. As Schlegel says (Art Bulletin 45:1, March 1963, p. 27):
Although God's throne is in heaven, the scene depicted by Masaccio has nothing to do with the heavenly realm, but rather as a sacred space on earth.
Yet the three-dimensionality also reflects the Trinity.
The members of the Trinity are above, each alone its own plane, as opposed to the 2 male-female pairs below them, while counterbalancing the one skeleton beneath them.
What could be the purpose--or better, purposes--of the numerical relationships pervading the Trinity? They bring to mind, of course, the Pythagorean tradition of harmonious numbers, whose significance for Renaissance architecture has been pointed out by Rudolf Wittkower [footnote 15: op. cit.
Janson gives two other reasons: to correlate ground plan and elevation, and surface and depth; and also to transfer the design easily and quickly from small preparatory drawings to the large fresco. These are not negligible; but the first is omnipresent and appears much more abundantly in the painting than is needed for the practical purposes Janson mentions.
There may be other things in the painting. Not only did Masaccio die mysteriously in Rome at the age of 26 or so, but the painting itself was completely covered over by an altar that Vasari installed in 1570--after first praising it to the skies in his book! Why was a painting generally considered to be the pioneering work in the new Renaissance style suddenly hidden from view? The only explanation I have seen is "modernization". I read that as a shift in values marked by the Council of Trent. As a sign of the times, Wittkower (p. 31f) cites Cardinal Carlo Borromeo's c. 1572 application of the Council's edicts to church building; he recommended a return to the "formam crucis" of the Latin cross and called the circular form "pagan". That might indicate that the principle of "the macrocosm in the microcosm" was now out of favor. Either that or, as Bruskewietch proposes, too many 6s were interpreted by someone as an unfortunate number.
One other consideration: Mary has an unusual facial expression in the painting, rather unique, not only imperious but with her eyes on the viewer rather than her son (http://upload.wikimedia.org/wikipedia/c ... lio_01.jpg). Rona Goffen (Masaccio's Trinity, p. 18) interprets Mary here as a symbol of the Church, in effect repeating her words at Cana (John 2:3), "Do whatever he tells you", directed now at the viewer. So another reason for covering up the painting might be that the Church now, in the fight against Protestantism, preferred a gentler image for itself. I will discuss this image of Mary further on the Popess thread.
I conclude that although the precise Pythagorean correspondences needed for the tarot are not present in the art and art theory of the Renaissance, the omnipresence of Pythagorean arithmology suggests that such application would likely have taken place. Decker's correspondences by and large do reflect writings available and in use at the time. I see nothing so far to indicate that the C order was the original one. But the research is still at a primitive level.
My own prior contribution to these issues, from 2010, is at viewtopic.php?f=12&t=530&p=8518#p8518. It is not bad, but Decker has certainly moved things forward.
I also have a more extended application of Pythagoreanism to all 78 of the cards, at http://neopythagoreanisminthetrot.blogspot.com/.