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

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

#301
Andrea VITALi has published on line the Essay of Michael S HOWARD
In Appreciation of Alain Bougearel's "1+ 4 + 7 + 10 = 22"
An essay by Michael S. Howard
http://letarot.it/page.aspx?id=608

He had before translated my Essay in English
It was recently published on line by Andrea VITALI :
The arithmological tarot
The arithmological sequence of the pentagonal number 22 = 1 + 4 + 7 + 10

Translation from French by Michael S. Howard
http://letarot.it/page.aspx?id=603
http://www.sgdl-auteurs.org/alain-bouge ... Biographie

### Gosselin 1582 Le Jeu des chartes pythagoriques

#302
I'll be abroad for a little while.
I've updated considerably my article about Gosselin.

Gosselin 1582 Le Jeu des chartes pythagoriques

1582 Gosselin Jean: "La signification de l 'ancien jeu des chartes pythagoriques..."
- La plus ancienne référence française connue d' une lecture pythagoricienne du Jeu de cartes ordinaires?

I. Une lecture pythagoricienne?
II. En conformité avec la théorie platonicienne des Eléments exposée dans le Timée.

Translation in English welcomed ...

PS
If you have any comments or rectifications, please write to me on :
alainbougearel@gmail.com

Article on :

For a better editing :
http://www.sgdl-auteurs.org/alain-bouge ... Biographie

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

#303
Huck wrote,
Gosselin would have had a splendid argument for his Pythagorean suspicions, if he would have connected ...

4 points for Kings
3 points for Queens
2 points for Knights
1 point for Pages

... to the Tetraktys. What shall we conclude from the condition, that he didn't take this in his calculations?
I would conclude that he was not dealing with the game of Tarot, but with a game with only the four regular suits, in fact the one he names, Trente et Un. Also, it wouldn't be a good argument even for tarot, because the Tetratkys has to do with 1+2+3+4=10, not 11 +12+13+14, and even if it did (given that the series starts over at 11), by dropping the "1", turn into 1+2+3+4, there is no 10 in the tarot equation, which is what makes it the tetraktys.

I think it is worth trying to say exactly what is wrong with Gosselin's argument, now that we see what it was. To the extent that he wants his explanation to apply to playing cards in general, he is of course wrong because the French suit signs weren't the only ones. And if 4 suits proved more popular, in general, than 3 or 5, it wouldn't have been for Pythagorean reasons, but for what makes a good game.

But we also need to ask: does his Pythagorean reasoning explain why the French suit signs, and the names for them, are what they are? It is not enough to say that they are obviously distortions of previous signs in other countries (some say German suits, I tend to think partly German and partly Latin), because there is also the question, why those particular distortions and lack of distortions?

My inclination is to say his associations are too contrived. Clover doesn't single out water as opposed to earth or air. All are needed for the plant to grow, and there is no particular reason to single out water. There is also the color: black. When one sees a black trefoil, water does not spring to mind. It is rather the color of clover that is dead, i.e. without water. Green would be more logical. The same reasoning can be applied to hearts. While the color is right, one would not think of air when seeing that symbol. Hearts also need food, from the earth, and water, for the blood, and especially a certain body temperature, i.e. heat, inner fire. Swords are from the earth plus fire, and tempering involves water. Tiles are from earth that has been fired. And there is no particular association in the culture otherwise between those entities and the four elements however assigned. That is not to say, however, that someone couldn't invent the associations between the elements and the four suit-signs as a pedagogic device, tied to Gosselin's narrative.

Alain's justifications by means of the four solids might have more merit. Here is Plato, not the easiest passage to understand (Timaeus 55d-56c, from http://classics.mit.edu/Plato/timaeus.html):
To earth, then, let us assign the cubical form ; for earth is the most immoveable of the four and the most plastic of all bodies, and that which has the most stable bases must of necessity be of such a nature. Now, of the triangles which we assumed at first, that which has two equal sides is by nature more firmly based than that which has unequal sides ; and of the compound figures which are formed out of either, the plane equilateral quadrangle has necessarily, a more stable basis than the equilateral triangle, both in the whole and in the parts. Wherefore, in assigning this figure to earth, we adhere to probability; and to water we assign that one of the remaining forms which is the least moveable; and the most moveable of them to fire; and to air that which is intermediate. Also we assign the smallest body to fire, and the greatest to water, and the intermediate in size to air ; and, again, the acutest body to fire, and the next in acuteness to, air, and the third to water. Of all these elements, that which has the fewest bases must necessarily be the most moveable, for it must be the acutest and most penetrating in every way, and also the lightest as being composed of the smallest number of similar particles : and the second body has similar properties in a second degree, and the third body in the third degree. Let it be agreed, then, both according to strict reason and according to probability, that the pyramid is the solid which is the original element and seed of fire ; and let us assign the element which was next in the order of generation to air, and the third to water.
Pikes, like fire and tetrahedrons for Plato, are sharp (above, "acute") and penetrating, if not light like fire. Tiles are stable and fit together well, like cubes; they are not cubes, but they are like the sides of cubes, so earth. Air's components (molecules) are indeed spaced wide apart, like octohedrons are if put together, according to Plato, and the same is true of hearts, which only exist in animals, more moveable and further apart compared to clovers. Clovers do not resemble icosohedrons or drops of water but indeed grow closer together than hearts and don't move around like animals, thus being like water in relation to air. These, too, are rather contrived reasonings, and in any case are not Gosselin's considerations. And there is no evidence that anyone associated with cards reasoned in such a way then.

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

#304
I would conclude that he was not dealing with the game of Tarot, but with a game with only the four regular suits, in fact the one he names, Trente et Un. Also, it wouldn't be a good argument even for tarot, because the Tetratkys has to do with 1+2+3+4=10, not 11 +12+13+14, and even if it did (given that the series starts over at 11), by dropping the "1", turn into 1+2+3+4, there is no 10 in the tarot equation, which is what makes it the tetraktys.
... .-) .. I would assume, that Gosselin was an old man already in 1582, and he didn't love the modern stuff ("modern stuff" = Tarot in France in 1582; I think, that Franco in his French text addressed Gosselin as personally "difficult"). And, as I said already, he wasn't a playing card historian.
Alain's justifications by means of the four solids might have more merit. Here is Plato, not the easiest passage to understand (Timaeus 55d-56c, from http://classics.mit.edu/Plato/timaeus.html):
To earth, then, let us assign the cubical form ; for earth is the most immoveable of the four and the most plastic of all bodies, and that which has the most stable bases must of necessity be of such a nature. Now, of the triangles which we assumed at first, that which has two equal sides is by nature more firmly based than that which has unequal sides ; and of the compound figures which are formed out of either, the plane equilateral quadrangle has necessarily, a more stable basis than the equilateral triangle, both in the whole and in the parts. Wherefore, in assigning this figure to earth, we adhere to probability; and to water we assign that one of the remaining forms which is the least moveable; and the most moveable of them to fire; and to air that which is intermediate. Also we assign the smallest body to fire, and the greatest to water, and the intermediate in size to air ; and, again, the acutest body to fire, and the next in acuteness to, air, and the third to water. Of all these elements, that which has the fewest bases must necessarily be the most moveable, for it must be the acutest and most penetrating in every way, and also the lightest as being composed of the smallest number of similar particles : and the second body has similar properties in a second degree, and the third body in the third degree. Let it be agreed, then, both according to strict reason and according to probability, that the pyramid is the solid which is the original element and seed of fire ; and let us assign the element which was next in the order of generation to air, and the third to water.
Pikes, like fire and tetrahedrons for Plato, are sharp (above, "acute") and penetrating, if not light like fire. Tiles are stable and fit together well, like cubes; they are not cubes, but they are like the sides of cubes, so earth. Air's components (molecules) are indeed spaced wide apart, like octohedrons are if put together, according to Plato, and the same is true of hearts, which only exist in animals, more moveable and further apart compared to clovers. Clovers do not resemble icosohedrons or drops of water but indeed grow closer together than hearts and don't move around like animals, thus being like water in relation to air. These, too, are rather contrived reasonings, and in any case are not Gosselin's considerations. And there is no evidence that anyone associated with cards reasoned in such a way then.
There are 5, not 4, platonic bodies.

https://en.wikipedia.org/wiki/Platonic_solid

The cube (6 faces, 8 corners, 12 lines) is related to the octahedron (8 faces, 6 corners, 12 lines), the dodecahedron (12 faces, 20 corners, 30 lines) to the icosahedron (20 faces, 12 corners, 30 lines) ... for logical reasons. The tetrahedron (4 faces, 4 corners, 6 lines) stands alone. All together have 50 faces and 50 corners and 90 lines and this looks not accidently so.

Just the dodecahedron (which Platon seems to miss; or am I wrong ?) had a special attention in France, cause it had some favor already by the early druids (archeological findings). If one wishes to associate it to elements, then the tetrahedron should be in the middle (aither), and the other 4 should present the 4 common elements ... just for logical reasons.
As fire is paired with water (in common theories to elements), air should be paired with earth ... if cube = earth, then octahedron = air, and fire and water may consider, what they want to be in the rest program. A least this would make some logic.
Well, Timaios and Platon seem to have had another idea ... :-)

But I can live with the situation, that elements are just elements and Platonic bodies are a feature of some math, and there is no need to build connections between them.

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

#305
Related to the tetraktys theme:

Once ...
viewtopic.php?f=11&t=1051#p15877
... we had in work a text of Daniel Martin written in 1637. He translated card expressions from French to German.
Beside that he mentioned a counting method, in which the numbers 4-3-2-1 were used.
3.

This very interesting passage tells forms of translations for the expressions for French suits. It starts with the question about the 4 highest cards in the Trumpfspiel:

The highest trumps are:

hearts ace = Hertz Aß
diamonds king = Stein-König (king of Stones [= from "Eckstein" for Carreaux])
spades queen = Schauffel-Fraw (woman of "Schauffel" = engl. spades; Schaufel is another word for germ. Spaten)
clubs jack = Kleen-Bub (Klee-Jack = engl. "Clover (Trifolium), or trefoil")

or

hearts two = Hertz Saw (female pig of hearts = two of hearts; German decks mostly hadn't an ace)
diamonds king = Rauten-König (Raute - another word for Carreaux)
clubs jack = Kleber-Bub (Kleber = another word for Klee)

4.

Rules of the Trumpfspiel:
The dealer is chosen by luck, the lowest card determines the dealer.
It's not told, how many players; it's not told, how much cards and which cards.
Everybody gets 9 cards.
From the remaining cards the highest is turned and determines trump (it's not said, if the "highest cards" are also trump, but likely they are). If the turned card is an ace, the dealer can exchange this to a worthless card, if other cards follow from the trump suit, then these he may exchange also. It's not said, if the other players may exchange anything.
The game is won by the highest points.
Ace has 4 points.
King has 3 points.
Frau-Queen has 2 points.
Jack-Bub has 1 point.

(this should make 40 points totally)
If somebody gets all tricks, the win is doubled.

It may happen, that nobody wants to play ... which demands a bidding process or something like this. This is not described in the source.
Later I researched ...
viewtopic.php?f=11&t=1051#p15883
http://www.pagat.com/couillon/couillon.html

... has formed a group of games, which are similar to that which is described by Daniel Martin.
Couillon is a popular Belgian card game. Versions of it are also played in the southern Dutch province of Limburg and on the border of Luxembourg and Germany. The name "couillon" almost certainly derives from the Walloon word coyon (=testicle), which refers to the circles or balls that were traditionally used as part of the method of keeping score. However, in Flanders and Luxembourg, the name has been modified to the similar sounding Kwajongen and Kujong respectively. In the Netherlands it is known as Troeven (trumps), which makes it likely that it is related to the old game Trümpfspiel recorded in Strasbourg in 1637, which had the same card values.
* Couillon (Basic game)
* Couillon Forcé
* Couillon with the Mit' - Deal - Play - Scoring - Tournament Rules - Dame de Make - Six Players - Eight Players - Other Variants
* Kwajongen
* Kujong
* Troeven - Three Players - Two Players

There's a Durch game server, where one can play Troeven.
http://www.toepenplus.eu/CGame302/Troef.php
Dutch language.

There's a description of
http://www.jeux-de-cartes.com/jeux-de-cartes/couillon/
Historique
Le couillon est un jeu de cartes très facile. Relativement récent par rapport aux autres jeux de cartes (apparu vers la fin du XIXe siècle), le couillon est pratiqué un peu partout en Europe. Mais c’est surtout la Belgique, tant en Flandre qu’en Wallonie, qui connaît son plus grand lot d’adeptes.
Le couillon se joue à quatre. Sa convivialité et son attrait reposent sur un fait très ludique : quand le déclarant ne réussit pas son contrat et entraîne son coéquipier dans le fond ! D’où le nom évocateur du jeu : couillon !
... exists since end of 19th century.

All these games have in common, that ...

Ace = 4
King = 3
Queen = 2
Jack = 1

... as in the game of Strassburg 1637.
The region seem to be mostly Luxembourg, Belgium, Netherlands, also Western border of Germany, often connected to Alsace in playing card matters, possibly cause of older Burgundian connections.

The special rule of Strassburg 1637, that ...

ace of hearts, king of diamonds, queen of spades, jack of clubs have some special function

... isn't in these games, beside something special about the queen of spades.

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

#306
Huck wrote
There are 5, not 4, platonic bodies.
Plato describes the dodecahedron a little earlier than the passage I cited, at 54c. (The part I quoted, beginning, "To earth, then..." starts at 54d.) The transcription of the Jowett translation of Plato I used earlier omits the end of the sentence, so I will give it from another site (http://www.faculty.umb.edu/gary_zabel/C ... oSolid.htm):
There was yet a fifth combination which God used in the delineation of the universe with figures of animals.
The dodecahedron is the Platonic solid that most closely resembles the sphere, which is for Plato the shape of the universe as a whole. So the dodecahedron is assigned to the whole and the other four to the constituents. Another thing is that it has 12 faces. Each of them can be assigned a different zodiacal sign, which is what he means by "figures of animals." It is like a soccer ball made out of 12 pieces of animal skin sewn together.

Some scientists, 2003, have theorized that the universe is in fact a "dodecahedral space" as described by Poincare in the 19th century. This theory is linked to at the above site. It is from another crazy Frenchman, probably influenced by Druids.

Huck wrote,
If one wishes to associate it to elements, then the tetrahedron should be in the middle (aither), and the other 4 should present the 4 common elements ... just for logical reasons.

Aristotle assigned the dodecahedron to the "quintessence", perhaps the substance he imagined filling the space between stars, the "aether". Disagreeing with the Pythagoreans, whom he thought illogical, Aristotle thought that "nature abhores a vacuum" and the space between stars had to be filled with something, for logical reasons (Physics IV, 6-9; see note 1 at https://en.wikipedia.org/wiki/Horror_va ... physics%29). That is a story we need not get into.

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

#307
Yes, there are 5 and Gosselin knows only 4 suits for his playing card meditation. As far playing cards are concerned, he stays very much on the humble surface, he actually loves to tell about his favored topic and that is Pythagoreanism.

The I-Ching, a topic, about which I myself love to talk about, actually is also a Tetraktys model. 2 (yin+yang) and 3 (3 lines of the trigrams ... one line for heaven, one line for man, one line for earth) and 4 (for the 4 numbers 6-7-8-9 as representatives of the 4 seasons) arrive after a complex combination of the values 2^(3*4) = 2^12 finally 4096 possible results of a divination process, as a math operation much more interesting than this boring and primitive 1+2+3+4 = 10, which Western esoteric tradition tries to sell as a big mystery.

Well, it seems to be just a disguise, the Pythagoreans had to keep the mouth shut about the more complex knowledge, as it is said, probably cause their also complex political intentions.

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

#308
An obvious point probably expressed many times is that if the 4 ordinary suits correspond to the four elements of our world, and hence four of the five Platonic solids, then the 5th suit, the tarot sequence, corresponds to the fifth element, Aristotle's "quintessence", the substance of the spheres above fire, the fifth Platonic solid, and in Plato's terms the cosmos as a whole in all its spheres.

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

#310

The 5 platonic bodies have indeed a further quality, which I myself didn't observe before:

3 bodies are formed by triangles (tetrahedron, octahedron, icosahedron), one body out of squares (the cube) and onebody (dodecahedron) out of pentagons.

Now there is curious relationship between this observed structure ... 3 of one kind (triangle = 3) , 2 are special (cube = 4, dodecahedron = 5) ... and the 5 chinese elements, as they appear at the so-called Ho-Tu plan (a diagram, which is given in the Richard Wilhelm translation of the I-Ching). I wrote about this diagram once in our intensive Sepher Yetzirah discussion (MikeH and Steve participated), so I copy-paste the text here:

viewtopic.php?f=11&p=15948#p15958
In the later Kabbala at least one likely has to interpret:

"five opposed pairs, first (= 1 Kether) and last (10 Malkuth), good (= 2 Chochmah) and bad (= 3 Binah), high and low, north and south, and east and west (= the six directions, Sephiroth 4-9).

The Chinese had a similar arrangement (5 pairs), but with another basic idea.

http://www.landandspirit.net/html/fuxi-bagua.html

1 + 6 Water
2 + 7 Fire
3 + 8 Wood
4 + 9 Metal
5 + 10 Earth

They used it for their 60 calender cycle with 12 zodiac-animals (rat, bull, tiger etc.) and 10 stems of heaven, so that 60 years had (for instance) 5 horse years: Fire-horse, Water-horse etc.
This arrangement likely was related to the shortened abacus with 4 or 5 lower pearls and 1 or 2 upper pearls used for normal number calculations (addition, subtraction, division, multiplication).

http://en.wikipedia.org/wiki/Abacus

So there's some confusion. The actual "5 elements" or better "5 principles", which the I-Ching really uses, are ...

The Yang state
The Yin state
The first line = defined as "earth"
The second line = defined as "man"
The third line = defined as "heaven"

This group of 5 shows two different groups, states and lines. If you proceed with the principles, then you get the 8 trigrams. These 8 trigrams got associative names by tradition.

111 heaven ... no line is focussed ... associated to metal by tradition
000 earth ... no line is focussed ... earth
100 thunder ... 1st line is focussed ... should by name belong to "fire"
010 water ... 2nd line focussed ... should by name belong to "water"
001 mountain ... 3rd line is focussed ... should by name belong to "???"
011 wind ... 1st line is focussed ... should by name belong to "air"
101 fire ... 2nd line focussed ... should by name belong to "fire"
110 lake ... 3rd line is focussed ... should by name belong to "water"

The names, as they are, associate "elements", as we know them (fire, water, air (or wood), earth, metal).

There's the problem, that "mountain" can't be identified by the name. But we have, that air appears only once and fire and water appear twice. Creating a balance can only be solved by the definition, that mountain belongs to air (which is logical, as a mountain ends at its top in the air). The mathematical opposite of mountain is lake. A lake gathers at the deepest point, the mountain is naturally high. So we have there the top-bottom-dimension, also used in the SY.

Following the identification, then we get for the ...

1st line = WATER
---------
100 thunder = fire
011 wind = air

2nd line = AIR
---------
010 water = water
101 fire = fire

3rd line = FIRE
---------
001 mountain = air
110 lake = water

The 3rd line is high (in I-Ching) and FIRE goes the top (in nature)
The 2nd line is in the middle and AIR is the balance between fire (top) and water (bottom)
The 1st line is low (in I-Ching) and WATER goes to the bottom (in nature)

Going back the start of this consideration we get as the 5 basic principles:
The Yang state ... presenting heaven = element METAL
The Yin state ... presenting earth = element EARTH
The first line = defined as "earth" = element FIRE
The second line = defined as "man" = element AIR (or WOOD)
The third line = defined as "heaven" = element WATER

I hope you got it. The surprising action is, that you have clearly the trigrams fire and water as representative of the second line, and you can only solve the conflict by declaring the second line to AIR. And so you have to do it with the others.

Generally the Chinese or German or English sources, that I've seen at the time, when I studied this, didn't spoke about details, but just repeated some stuff, which they had found somewhere. Similar confusions appeared in Western esoteric interpretations and traditions.
This - my concept about the Chinese I-Ching trigrams - has the same structure as observed at the 5 platonic bodies: 3 of a kind (as the 3 children-trigram-pairs) and 2 specials (parent trigrams father-mother or heaven-earth or metal-earth).
Curiously now the Chinese mother-earth-element is connected to the number 5 (and 10; see Ho-Tu plan) and the father- heaven-metal element is connected to the number 4 (and number 9; see Ho-Tu plan).
And the platonic body cube is rather elementary connected to squares and with that to the number 4 and the platonic body dodecahedron is connected to pentagons and with that to the number 5.

Well, Timaios/Platon had cube (4) for earth (if I understood this correctly) and the Chinese heaven-metal is somehow opposite to the idea of "earth" (but also connected to 4 in China). And the dodecahedron with the pentagons (5) is associated to Aither (if I understood MikeH correctly) in Timaios/Platon and father/heaven/metal would fill the position perfectly, but is connected to 4 and instead mother/earth has the 5.

Checking the probability of a "lucky accident" seems to be accurately 10% by 12 chances against 120 possibilities, that's relative high and not totally alarming. But, anyway, it gives a suspicion of a context.

I've no idea, if the old Chinese knew about the platonic bodies.

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