## Moakley's book, article & now correspondence with Panofsky

### Re: Moakley's book: text and discussion

#21
SteveM wrote:
mikeh wrote:
10. She says that fortune-telling was done with cards in the Renaissance, but only with the suit of Coins. I had not heard this before. Is there any basis for this? I will try to get her reference.
Can't remember the details, but if memory serves me right there was a lots type book that used the suit of coins from a pack of playing cards as the lottery device (as others used dice for example) -- it was probably this to which she refers
Francesco Marcolini
Le sorte intitolate giardino d'i pensieri
1540

### Re: Moakley's book: text and discussion

#22
Thanks Huck - cross posting as I was updating my post with a link to your site with examples of other books [Kartenlosbuch] that used all the suits of ordinary playing cards:

http://trionfi.com/0/p/41/

The Marcoloni (which was dedicated to the Duke of Ferrara, Ercole d'Este) :

http://www.tarotpedia.com/wiki/Marcolini,_Francesco

Immature poets imitate; mature poets steal; bad poets deface what they take, and good poets make it into something better, or at least something different.
T. S. Eliot

### Re: Moakley's book: text and discussion

#23
Well, yes, I knew about this one. In this book, I had thought that you use the whole trappola deck, not just coins, and ignore the suits of the cards drawn. Wikipedia says, "The tercets are divided in 50 sections, each containing 45 tercets. 45 is the number of different combinations of two cards drawn from a Trappola deck (made of four suits each with nine cards).But perhaps you do, since there are no doubles listed. But coins is not specified, if the wikipedia page is accurate. However I suspect it has left out some important things, given the lack of doubles. How is it that, if the order of the cards is a factor for the last 2 cards, that there are 45 combinations? I would have thought there were 72 (9x8) if just one suit, 9x9 = 81 otherwise. On the other hand, the last card is either a pip or a court. Maybe that makes a difference. Well, if both have to be either pips or courts, then it's 6x6 plus 3x3 = 45, using the whole deck and allowing doubles. Otherwise, I'm stumped. But nothing so far is said about coins in particular.

### Re: Moakley's book: text and discussion

#24
mikeh wrote:My comments on Moakley Chapter 3:

The numerological bit at the end is of course of interest. She has been quoted in this regard on this Forum before. The obvious unanswered question for me is, why are these mathematical facts of any explanatory value as to the number of triumphs and ordinary cards in the deck? There may be 21 throws of 2 dice and 56 combinations of 3 dice, but so what? Dice games and card games are quite different in their structure. If there were only 6 cards per suit and only 3 suits (or some multiple of 3, for successive throws), and people had to draw cards from each of 3 piles each containing shuffled members of that suit (perhaps repeatedly, using other piles of 6), I could see a similarity, but cards were never like that. The only relevance I can see is that since there were lot books at that time based on three throws of the dice, with a different fortune for each of the 56 combinations, 56 cards would make it easy to convert the dice lot-book to cards. The same would be true of a lot book with 22 combinations (the 22nd being for a misthrow), except that I don't know of any lot-books of that kind, based on two throws of the dice. In fact there is evidence that the ordinary deck was used for divination by means of lot-books at least by the 16th century, so probably earlier. There isn't any such evidence of lot-books for tarot decks.

For the tarot sequence, what seems most relevant is what she says about 21 in relation to 6:
Robert Graves, in his Nazarene Gospel Restored, refers to a triangular number as the "Philonian fulfilment" of its base; e. .g. twenty-one is the PhiIonian fulfilment of six.
That is, if 6 is a perfect number corresponding to the days of creation, then 21 is perhaps its "fulilment", and so the "New Jerusalem" at the end of time, or Adam's fulfilment in Christ. "Philonian" means "pertaining to Philo of Alexandria, according to the online dictionaries. He wrote about the Creation and the 10 commandments in Pythagorean terms.

However it seems from Andrea's quotation from Origen and from other Church Fathers, that 22 had a life of its own as a sacred number, deriving from the 22 books of the Hebrew Bible.

Graves' book is available online in snippet view only https://books.google.com/books/about/Th ... YJAQAAIAAJ). When I search for "Philonian" and "twenty-one" there are snippets for each individually, but not both together. Well, it is something I will have to get via Interlibrary Loan.

There is also what Moakley says about 7 and 11.
For seven and eleven as symbolical of sin see Hopper (Medieval) p 24, 87, and p. 52. (Dante took over eleven as the basis for the dimensions of Hell). In the Morgante of Pulci the giant Margutte boasts of having seventy-seven mortal sins.

On p. 24 Hopper mentions contexts in which 7 is used in the context of Lev. 26:14, "I will punish you 7 times for your sin"; but he gives many more places where it is used positively. It seems just a way of saying "a bunch" in sacred contexts. On p. 52 there is no mention of either 7 or 11, just 3 and 4; but on p. 53 the number 7 is discussed in relation to "the established order of worlds and gods". So there are 7 planets. P. 87 talks about the number 11, and it is clear that it is a number of error and sin. So a preacher could indeed polemicize against the tarot sequence, if he wanted to, as double sinfulness, or sinfulness sevenfold if one card isn't counted.

"We have come a long way from the imaginary knights which make up the suit cards of the tarocchi, through the factual story of the family for whom the cards were made. But before we go on to the trump cards there is one more question to' consider. Why are there fifty-six suit cards, and why are there twenty-one trumps? The answer is found when we remember that cards, as a game of chance, replaced dice almost completely. In the dice games which use three dice, there are fifty-six possible throws, and with two dice twenty-one. There are other, more fanciful, considerations which make these numbers suitable. Twenty-one is a triangular number with a base of six that is, 6 + 5 + 4 + 3 + 2 + 1= 21. Fifty-six is a pyramidal number' with a base of twenty-one (a pyramid of fifty-six balls may be raised with the former triangle of twenty-one as its base). Add the "wild" Fool to get seventy-eight cards and you have another triangular number with a base of twelve. Take away the Fool and you have the product of seven and eleven, those numbers' symbolical of luck and dear to the dice player. (9)
_______________
[note originally p. 42]
9. It was Professor Maurice G. Kendall who pointed out to me that fifty-six is the number of throws with three dice. See Kendall ("Studies" p 1-14). He mentions the dice game of fifty-six throws which Bishop Wibold recommended to his clergy as a spiritual exercise in the year 970. Burckhardt (Civilization, p 409) mistakenly refers to this as a game of cards. The original source is Mon Germ SS. vii, p 433. The Chinese have special names for the twenty-one throws of two dice, just as we do. See British Museum (Catalogue .. . Lady Schreiber p 185) for a list of these names, which seem to be based on the picture made by the Chinese numerals, e. g. 2-2 which looks like this in Chinese: = =, is called "The bench." The term "triangular number" and "pyramidal number" are used in mathematical works of reference. Robert Graves, in his Nazarene Gospel Restored, refers to a triangular number as the "Philonian fulfilment" of its base; e. .g. twenty-one is the PhiIonian fulfilment of six. For seven and eleven as symbolical of sin see Hopper (Medieval) p 24, 87, and p. 52. (Dante took over eleven as the basis for the dimensions of Hell). In the Morgante of Pulci the giant Margutte boasts of having seventy-seven mortal sins. The trumps plus the Fool (twenty-two cards) faintly suggest the ancient "pi" formula, which was twenty-two divided by seven (The White Goddess, by Robert Graves, New York, Creative Age Press, 1948, p 191). This seemed too far-fetched to mention in the text."

Mikeh
Your review appears correct to me and I don't have much to add.

What I see of interest is that one of the first modern major historians of Tarot paid attention to it's numerical structure and did not dismiss it. She does not support a thesis as if the numbers in Tarot were random. On the contrary, she refers to Pythagorean arithmetic - focusing on Triangular numbers.
She considers 21 as a Triangular number of base 6 :
Gnomons : 21 = 1+2+3+4+5+6
She considers 56 as a Pyramidal number - that is stricto sensu a Tetrahedral triangular number.
Serie : 1, 4, 10, 20, 35, 56
Gnomons : 1 + 3 + 6 + 10 + 15 + 21 = 56
She finally considers 78 as the Triangular of 12 :
"Add the "wild" Fool to get seventy-eight cards and you have another triangular number with a base of twelve. "
78=1+2+3+4+5+6+7+8+9+10+11+12

"Why are there fifty-six suit cards, and why are there twenty-one trumps? The answer is found when we remember that cards, as a game of chance, replaced dice almost completely. In the dice games which use three dice, there are fifty-six possible throws, and with two dice twenty-one."

BtW, it seems to me, that she uses the reference to dices more as a possible origin of this structure than to offer an explanatory value cards read by reference to the dices throws - her take about "twenty-one is the PhiIonian fulfilment of six" is in note not in text and credited to Robert Graves.
http://www.sgdl-auteurs.org/alain-bouge ... Biographie

### Re: Moakley's book: text and discussion

#25
Alain wrote,
BtW, it seems to me, that she uses the reference to dices more as a possible origin of this structure than to offer an explanatory value cards read by reference to the dices throws
I did not understand. By "structure" do you mean triangular and pyramidal numbers of different bases? Well, yes, but how does it relate to cards. She brings these numbers up to explain something about why 56 is appropriate for cards. What is it about triangular and pyramidal numbers that makes it important that cards fit those structures? For 56, the explanation would be that it is easy to take lot books based on 3 throws of the dice and have it based on drawing one out of 56 cards instead. The only problem is that lot-books don't seem to use the number 56. If not, then 56 is not of any importance, as opposed to 52. In fact the major lot book in Italy that we know about used a deck with 36 cards.

I do think that her reference to Graves and the connection between 6 and 21 might be important, even if it is only in a note. (Some of her best things are in the notes, I think.) I will try to get the book.

### Re: Moakley's book: text and discussion

#26
mikeh wrote:.... For 56, the explanation would be that it is easy to take lot books based on 3 throws of the dice and have it based on drawing one out of 56 cards instead. The only problem is that lot-books don't seem to use the number 56. If not, then 56 is not of any importance, as opposed to 52. In fact the major lot book in Italy that we know about used a deck with 36 cards.
56 is occasionally used in lot books ... Wibold for instance
http://www.maa.org/press/periodicals/co ... -his-world

### Re: Moakley's book: text and discussion

#27
mikeh wrote:Alain wrote,
BtW, it seems to me, that she uses the reference to dices more as a possible origin of this structure than to offer an explanatory value cards read by reference to the dices throws
I did not understand. By "structure" do you mean triangular and pyramidal numbers of different bases? Well, yes, but how does it relate to cards. She brings these numbers up to explain something about why 56 is appropriate for cards. What is it about triangular and pyramidal numbers that makes it important that cards fit those structures? For 56, the explanation would be that it is easy to take lot books based on 3 throws of the dice and have it based on drawing one out of 56 cards instead. The only problem is that lot-books don't seem to use the number 56. If not, then 56 is not of any importance, as opposed to 52. In fact the major lot book in Italy that we know about used a deck with 36 cards.

I do think that her reference to Graves and the connection between 6 and 21 might be important, even if it is only in a note. (Some of her best things are in the notes, I think.) I will try to get the book.

Maybe am I wrong. English = "me bad"!
But as I read Moakley, she :
- does not consider 78, 56 and 21 as random.
She sees there specific Triangular Pythagorean Numbers related to Tarot.
In the same time, she notes that 56 and 21 would come from dices throws with two or three dices.
In the same paragraph, she postulates that dices game were at origin of cards game.

Nota
Yes, her take about 6 even in Note is interesting for sure...
http://www.sgdl-auteurs.org/alain-bouge ... Biographie

### Re: Moakley's book: text and discussion

#28
No, the tarotpedia page too says suit is irrelevant - OTOH, only the suit of coins is used for the illustrations, so perhaps this was a cause of confusion --

re: doubles, they are used, as far as I can tell from the illustrations*:

Consulting Marcolini with a pack of cards, the top of the pack of cards shows a court card of swords or batons, so all the suits could be used to come up with the two numbers, but only the coins are illustrated as they are irrelevant to the answer, only the nine cards king, knight, knave, ten, nine, eight, seven, two and ace of each suit are used:

quote from Metropolitan Museum:
'The evocative woodcut that adorns the frontispiece of this fortune-telling book is prominently signed by the artist Giuseppe Porta (ca. 1520–ca. 1575) from the Garfagnana region of northern Tuscany, who later took the name Salviati in honor of his teacher, the well-known Mannerist painter Francesco Salviati. However, the composition is not original to Porta but closely copies an engraving by Marco Dente, a student of Marcantonio Raimondi who died in the Sack of Rome of 1527. By changing the book opening to show two pages from Marcolini's Le Sorti instead of an image of stars and planets, and by adding a pack of playing cards, the image has shifted from a gathering of scientists to a group of fortune-telling enthusiasts. The three women are probably intended as the three Parcae or Fates, who in ancient mythology spun, measured, and cut the thread of human life. Shown carrying out these actions in an allegorical image on page 21 of the book, the Fates are especially appropriate to the cover of a publication entitled Le Sorti, or The Fates. In this frontispiece, where they are engaged in the pleasurable pursuit of fortune-telling, they seem more relaxed than in the engraving by Dente—the one in the foreground even seems to smile as she shows Marcolini's book to the pensive man beside her."

SteveM

*Don't know whether it applies with the Marcoloni, but in some lot books illustrations and readings are given for combinations that are impossible in some cases from the given instructions: that this was done intentionally rather than ignorance of the results of combinations, is suggested by the content of such -- which often are amusing, or berating of those ignorant enough of those who consult lots and believe in fortunes --
Immature poets imitate; mature poets steal; bad poets deface what they take, and good poets make it into something better, or at least something different.
T. S. Eliot

### Re: Moakley's book: text and discussion

#29
Huck wrote:
mikeh wrote:.... For 56, the explanation would be that it is easy to take lot books based on 3 throws of the dice and have it based on drawing one out of 56 cards instead. The only problem is that lot-books don't seem to use the number 56. If not, then 56 is not of any importance, as opposed to 52. In fact the major lot book in Italy that we know about used a deck with 36 cards.
56 is occasionally used in lot books ... Wibold for instance
http://www.maa.org/press/periodicals/co ... -his-world
Note about the 56 throws of 3 dices with 6 faces :
The 56 distinguishable occurences were associated with practise of Virtues for monacal reasons by Wibold of Cambrai circa 1000 AD.
He enumerated 56 virtues - one corresponding to each of the ways 3 dices could be thrown irrespective of order
The use of dices for the purpose of choosing among a number of possibilities is much older than Wibold.

The earliest approch to the counting of the numebrs of ways in which 3 dices can fall appears to occur in a latin poem "De vetula"; this remarquable work was regarded as Ovide's for some time, and is included in some of the medieval editions of his poems. It is however suppositious and several candadates have been proposed for authorship. The relevant passage may be briefly and freely construed as follows :
If all three numbers are alike, there are 6 possibilities.
if two are alike and the other different, there are 30 cases because the pair can be choosen in 6 ways
and if all three are different, there are 20 ways because 30 x 4 = 120, but each possibilities arises in 6 ways [120 : 6 = 20]

Nota bene
The number 56 in classical antiquity relaated to "divination" :
Two kinds of dice were used in classical antiquity: dice proper (kuboi, tessarae), which are virtually identical to six-sided modern dice, and knucklebones (astragali, tali), which have four sides (Halliday 205-15, esp. 213-15; David 1-7; Ore 193). For divination, five astragali were rolled, and the resulting combination was looked up on a four-sided pillar, many examples of which survive in more or less fragmentary form (e.g., Sterrett "Epig.", "Wolfe"; Kaibel). It so happens that the number of possible five-astragali throws is 56, exactly the number of Minor Arcana, and that the throws were listed on the tablets in four "suits" (two of 15 throws, two of 13; see Halliday 213n3).
(http://wisdomofhypatia.com/OM/BA/PT/Mintro.html)
http://www.sgdl-auteurs.org/alain-bouge ... Biographie

### Re: Moakley's book: text and discussion

#30
BOUGEAREL Alain wrote: Nota bene
The number 56 in classical antiquity relaated to "divination" :
Two kinds of dice were used in classical antiquity: dice proper (kuboi, tessarae), which are virtually identical to six-sided modern dice, and knucklebones (astragali, tali), which have four sides (Halliday 205-15, esp. 213-15; David 1-7; Ore 193). For divination, five astragali were rolled, and the resulting combination was looked up on a four-sided pillar, many examples of which survive in more or less fragmentary form (e.g., Sterrett "Epig.", "Wolfe"; Kaibel). It so happens that the number of possible five-astragali throws is 56, exactly the number of Minor Arcana, and that the throws were listed on the tablets in four "suits" (two of 15 throws, two of 13; see Halliday 213n3).
(http://wisdomofhypatia.com/OM/BA/PT/Mintro.html)
I presume the Halliday reference is to -- W R Halliday : Greek Divination*

https://archive.org/details/cu31924058563259

I found the full reference in this essay by Charles Picard:

Les antécédents des « Astragalizontes » polyclétéens, et la consultation par les dés
http://www.persee.fr/doc/reg_0035-2039_ ... 2_195_6944

SteveM

*quote p213

From Asia
Minor we have inscriptions which contain a
list of the possible throws and their interpreta-
tion. The system in the different inscriptions
is identical, all are written in bad metre and
indifferent Greek, the names of the throws are
constant in the various fragments, and the
variants in the text itself are surprisingly few.
There is a fragment of a system of astragalo-
mancy with seven astragali from Termessos,^
but the normal code is constructed for five
astragali. Of this code we have fragments
from Kosagatch, Tefeny, Yarishli, Sagalassos,
Termessos, Ordekji, Indjik, and Adalia.^ The
astragalos has only four numbered sides with
the values i, 3, 4, and 6. The totals, therefore,
range from 1 + 1 + 1 + 1 + 1 = 5 ^o 6 + 6 + 6 + 6
+ 6 = 30. Some of the intervening numbers,
e.g. 6 or 29, cannot be made out of combina-
tions of I, 3, 4, and 6, but on the other hand
many of the possible totals can be made by
various combinations..., In all 56 throws
are possible, and of these all except the 12th,
though some of them only in fragments, can be
obtained from the various stones.^ The inscrip-
tions seem to have been cut in columns, on the
sides of a four-sided pillar. They give in the
case of each throw the combination of figures
and the total, followed by the name of the
power to whom the throw belongs. The second
line in some of the inscriptions consists of an
attempt to force the numbers of the throw into
metre. The meaning of the whole is given in
three hexameters of very inferior quality. The
second throw, for example, is : —

see book for the greek text
Immature poets imitate; mature poets steal; bad poets deface what they take, and good poets make it into something better, or at least something different.
T. S. Eliot

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