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

#11
mikeh wrote: If that reminds us of Judas, the number 12, invariably associated with the card (except in Minchiate, which is not tarot, and the Sicilian, which is derivative from Minchiae), is also associated with Judas, the so-called 12th disciple. Judas's betrayal of Jesus is what leads to the crucifixion. So the card changes from being a "condition of life" in types B and C to a condition of salvation in A. The division 1 + 4 + 7 =10 in that case still holds. However it is a rather radical idea, that Judas is a condition of salvation, perhaps too radical for the time. In which case Alain is right that his way of dividing the sequence doesn't hold for type A.
God's "giving up" Christ the Son for sacrifice may be viewed, in a way, as a type of betrayal (giving up) of 'himself in person'.

In Calvinist terms he would perhaps more represent the condition of the reprobate than a condition of salvation, and fall into those discussions and doctrines (e.g.,: the doctrine of reprobation) that deal with concepts such as the predestination of the elect (salvation) and non-elect (reprobation).

For a Catholic viewpoint we may look perhaps to the address of Pope Benedict on Judas:

"His betrayal led to the death of Jesus who transformed this tremendous torment into a space of salvific love and in self-giving to the Father (cf. Galatians 2:20; Ephesians 5:2.25). The verb "betray" is the Greek version which means "to give up." At times its subject is also God himself in person: Out of love, he "gave up" Jesus for us all (cf. Romans 8:32). In his mysterious plan of salvation, God assumes Judas' unjustifiable gesture as the motive for the total giving up of the Son for the redemption of the world.

"... God can turn everything to a good purpose. Even Judas' betrayal became, through divine providence, the occasion for Jesus' supreme act of love, for the salvation of the world."
(VATICAN CITY, OCT. 19, 2006)
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: Le Tarot arithmologique - la séquence 1+4+7+10 = 22

#12
Hi to you 3 – Alain – mikeh & SteveM.

It's really fun to see you both trying to beat a dead horse (Alain's diagram) over the finishing line of your fantasies ...



Image




… and there is nothing wrong with having dreams – but when Alain claims that his diagram is based on the TETRAKTYS …

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

… it has to fit the bill of 10 dots arranged in that specific fashion.
Otherwise it won't be based on the TETRAKTYS …

… like I've pointed (pun intended of course) out already …

viewtopic.php?f=11&t=1102#p16920

… there CAN NOT BE a model that is based on the TETRAKTYS that has 78 dots for obvious reasons.
By addition only it can be demonstrated that 80 dots with 8 similar shaped TETRAKTYS elements MUST be the stock for such a model.

So there is a very simple explanation WHY it was so …
… notoriously difficult to put the cards of the tarot sequence into groups that actually have something in common …
… and you have obviously not thought about that because you were so busy to collaborate for your dream come true.

The explanation is that the diagram Alain made up is indeed …
… a hodgepodge …
because TESSELLATION has the following RULES …
A tessellation is a repeated series of geometric shapes that covers a surface with no gaps or overlapping of the shapes. This type of seamless texture is sometimes referred to as tiling. Tessellations are used in works of art, fabric patterns or to teach abstract mathematical concepts, such as symmetry. Although tessellations can be made from a variety of different shapes, there are basic rules that apply to all regular and semi-regular tessellation patterns.


Regular Polygons

All regular tessellations must be made of regular polygons. Polygons are geometric shapes made of straight sides connected sides. A regular polygon is a shape comprised of sides that meet to form angles that are all equal, such as a square or an equilateral triangle. However, not all regular polygons can be used to create a tessellation because their sides do not line up evenly. A pentagon is an example of a regular polygon that cannot be used to tessellate.


Gaps and Overlapping

Tessellations cannot have any gaps between shapes or overlapping shapes. Regular tessellations must have sides that match and fit together entirely, such as when you put two squares side-by-side. As mentioned previously, not all regular polygons can be used to create a tessellation because there are gaps between them when you place two side by side.


Common Vertex

All regular polygons that meet must have a common 360 degree vertex in order to be used in a tessellation. A vertex is a point where two sides come together to form an angle. For example, in an equilateral triangle, two sides come together to form a 60 degree angle. In a tessellation, a vertex refers to the point where three or more shapes come together to equal 360 degrees. For example, three hexagons, whose interior angles equal 120 degrees, come together to form a vertex of 360 degrees, while a pentagon, whose interior angles measure 108 degrees cannot equal a vertex of 360 degrees.


Symmetry

Polygons used in a tessellation must have at least one line of symmetry. Symmetry can be defined as equal parts facing each other around an axis, sometimes referred to as a mirror image. Because regular tessellations are created by repeated polygons, a tessellated figure can be divided evenly down the middle, from various angles, to create two symmetrical shapes on either side of the dividing line. Regular tessellations should have multiple lines of symmetry.

http://www.ehow.com/info_8736965_rules- ... tions.html
The site offers also tutorials for making your own TESSELLATIONs.
Maybe you should have a look BEFORE your next collaboration in this clearly defined field of GEOMETRY.

Now you are right instead here when you claim that …
… Most of it was easy to follow …
… because that's the defining streak of POPULISM (in this case not right or left winged – but TAROT colored & seemingly ignorant about the roots of problems).

Alain made up a model of 78 dots situated in an rectangular triangle and grouped those dots according to his liking to fit his TAROT idea of several defined groups. And his trick(or MISTAKE) was to IGNORE the SHAPES which must follow the TESSELLATION RULES. So making only dots and NO shapes to cover the dots of every each group and joining these grouped dots with a line created the ILLUSION that there is TESSELLATION when in reality there is NONE


By definition the RULES for TETRAKTYS & TESSELLATION are not met.
So the diagram as a model based on these principles is REFUTED in totality.


He could instead leave OUT these terms TETRAKTYS & TESSELLATION – and all would be totally OK!
But NOBODY would CARE about such a diagram – am I right?
YES I AM.

And now you can IGNORE this again – like you did before – and hide this TRUTH behind some other WALL of meaningless details (and NAMES!) that can NOT be applied to this already DEAD horse.

This is putting a nice and precious bridle on the dead horse after it came back from the taxidermist and presenting it to the press as the winner.

In real life this would be FRAUD.
What is such called in your TAROT world?

Adrian

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

#13
Hi

First of all, thanks Mikeh for translating in English my essay.

With your permission, I will propose it to A. VITALI.

Reading all the posts of this thread, I now see that maybe there is some kind of interest for another publication later one.

I will try to do so.

PS
For the critics about the layout I gave the priviledge, see the discussion with Jean Michel DAVID on Aeclectic History Forum :
http://www.tarotforum.net/showthread.php?t=29707&page=3


Now, this said, what is the actual situation about the neo-pythagorean hypothesis?

The research is yet un - achieved.
But some major parts are or on the point to be.

78 cards
78 is a triangular+ number
1+2+3+4+5+6+7+8+9+10+11 +12

40 numerical cards : 4x10
10 is a triangular number : 1+2+3+4

4 is a square number : 4x4 = 16

22 is a pentagonal number :
1+4+7+10

I offered my proposition for the disposition of the 22 Trumps in the Pentagonal Number 22 as :
1+4+7+10

Rule : 1 is one dot, two must come in second dot... 22 in twentysecond dot.

The 4 decades should also follow the same "exigence" :

The As is first dot, two in second dot ...10 in tenth dot.

1
2+3
4+5+6
7+8+9+10

NB . Further research is needed to decide in which precise decade is the emblem ...

The 16 Honors would be disposed in 4 squares of 4.

NB ; further research is needed to determine the hierarchy between the honors and also the right succession of the emblems ( same lacking information as for the 4 decades).

That's all folks for the moment...


PS /
My reference is Nicomaque de Gerase.
Web page : http://letarot.it/page.aspx?id=23&lng=eng

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

#14
I do not write in English because it is too difficult for me to
debate in this langage.

I'll nevertheless make a try to summarize my article but I do hope
that my phrases won't be twisted in a wrong manner.

For the historical academic consensus there is no need to search for
a numerical coherence ipse facto.

Cards pre-date Tarot Trumps.

Trumps are not listed as 21+1=22 before some time : variations in
number of the Atouts.

If we accept the Petrarch 's hypothesis of the origin of Trionfi,
then their number pass progressively from 6 (Petrach's poem)to
21+1=22 (Atouts)....

So the mathematical inner coherence of the number of the Tarot cards
(78) is a non-sense from an academic historical point of view.

But, and I love these "but", mathematically, I insist on "
the indeed fascinating (neo-Pythagorean) relation of three
geometrical figures—triangle, square, and pentagon—on the base of
the number 4 (as expression of the four elements). They then produce
a coherent relation between the odd composition of the Tarot-deck of
4x10 (=40) pips, 4x4 (=16) royals, and 22 trumps, because 16 is a
square number of base 4, 10 is a triangular number of base 4, and,
likewise, 22 is a pentagonal number of base 4." (Laurent Faber)

Moakley noted " the astonishing fact that there is, indeed,
something related to both the 4x14 suit cards and the 21 trumps,
namely the much older game of dice, from which they might have
stemmed. If we take the total number of choices possible when
throwing three or two dice, it adds up to either 56 (= 4x14) or 21,
respectively. " (Laurent Faber)

Now, if we consider as 22nd or 'nulla' an invalid throw of dices,
then there are 22 throws.

Morever, such an invalid throw could be seen as outside of of the
geometrical perimeter of a game of tables such as described by the
King Alphonse X (He makes a difference between game of spirit such
as chess, games of chance such as dices - the games of tables being
midway ) or more simply if the dices do not fall correctly...




As for the discussion about the relation between the Trumps , it is
a 1+4+7+10=22 relation that the Arithmology points to.

This cuts the game at Pope and Death.

This not contradictory with the orders B and C.

Discussion is about the alpha (Bagat) and omega (Math) : I list in
the article some orders of the XVIth century adequate with such an
ordinal relation.

Last but not least : usually it is considerated that the Math cannot make a trick so it isn't a
Trump.

Not entirely true, because tte most ancient rules in French consider
that there are 22 Trumps (in which 3 Highs -Bagat, Monde et Math).

Moreever, the Math can also make the last trick in a great schlem...
Web page : http://letarot.it/page.aspx?id=23&lng=eng

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

#15
Alain wrote,
16 is asquare number of base 4, 10 is a triangular number of base 4, and,
likewise, 22 is a pentagonal number of base 4." (Laurent Faber)
And also:
[PS /My reference is Nicomaque de Gerase.]
I.e. Nichomachus of Gerasa

I knew about triangular and square numbers, but not about pentagonal numbers, which indeed seem to derive from Nichomachus and would have been familiar to educated people of the 15th century, as these teachings were part of the trivium. The image below is from the Loeb Classics edition of Iamblicus on Nichomachus Introduction to Arithmetic. I get it from https://www.loebclassics.com/view/pytha ... 335.99.xml


The principles on which pentagonal numbers are generated can be found at https://en.wikipedia.org/wiki/Pentagonal_number.

If you look at the pentagonal sequence above, it is not only the number 22 that is of interest but also the ones before it. The first pentagonal number, 1, characterizes Alain's first group; the number 5 characterizes the first two groups; the number 12 characterizes the first three groups; and the number 22 characterizes all four groups.

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

#16
SteveM wrote
For a Catholic viewpoint we may look perhaps to the address of Pope Benedict on Judas:

"His betrayal led to the death of Jesus who transformed this tremendous torment into a space of salvific love and in self-giving to the Father (cf. Galatians 2:20; Ephesians 5:2.25). The verb "betray" is the Greek version which means "to give up." At times its subject is also God himself in person: Out of love, he "gave up" Jesus for us all (cf. Romans 8:32). In his mysterious plan of salvation, God assumes Judas' unjustifiable gesture as the motive for the total giving up of the Son for the redemption of the world.

"... God can turn everything to a good purpose. Even Judas' betrayal became, through divine providence, the occasion for Jesus' supreme act of love, for the salvation of the world."
You will have noticed that Benedict reverts to the traditional translation of the Greek word when speaking of Judas, as opposed to saying "Even Judas' giving up [of Jesus to the Romans]...

Benedict has perhaps been studying his concordance. In Greek, the word is "paradōsei", uniformly translated as "will betray":
http://biblehub.com/interlinear/matthew/26-21.htm

However if you look at the concordance for this word (by clicking on it), on the right side on that page you see a list of occurrences of the verb various forms in other contexts:
http://biblehub.com/greek/parado_sei_3860.htm

In Mark 15:10 it means "delivered" or "handed over" (of Jesus to Pilate).
http://biblehub.com/greek/paradedo_keisan_3860.htm

In Acs 15:26 it means "risked" or perhaps "given up" (their lives)
http://biblehub.com/greek/paradedo_kosi_3860.htm

In Acts 14:26: it means "commended" (to his grace).
http://biblehub.com/greek/paradedomenoi_3860.htm

In II Corinthians 4:11 it means "delivered over" (to death).
http://biblehub.com/greek/paradido__3860.htm

And so on.

But when referring to Judas--and only then, as far as I can tell--it is translated as "betray". It is not inconceivable to me that at that time in Florence, when people were seriously studying Greek en masse for the first time in a thousand years, and as a result finding what they thought were mistakes in the Vulgate, at least one even exposing a certain traditional document as a fraud (i.e. the "donation of Constantine") they may have noticed this oddity as well, and wondered about it, since it occurs right after Jesus had handed Judas the "sop" and declared that the person to whom he had handed it would "paradosei" him, yet when Judas immediately leaves the disciples have no suspicion of what he is going to do.

In any case, there is a close association of Judas with Jesus's crucifixion, with Judas initiating the process. An identification with Judas continues in the Tarot de Marseille, I think, where in Noblet there are six notches on one pole, five on the other, and one in the mdidle, where the rope hangs down, from the twelfth notch. In Conver this is changed to six on one side and six on the other, perhaps suggesting Jesus himself.

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

#17
mikeh wrote: The order of the Triumphs in the documents of the 16th century (p. 120)

The proposed provision is found to comply with the earliest orders. dated circa 1500 "Sermones de ludo" and the 1521 "Pasquinata"

Anonymous, Sermones de ludo, circa 1500

1 El bagatella
2 Imperatrix
3 Imperator
4 La papessa
5 El papa
6 La temperantia
7 L’amore
8 Lo caro trimphale
9 La fortezza
10 La rota
11 El gobbo
12 Lo impichato
13 La morte
14 El diavolo
15 La sagitta
16 La stella
17 La luna
18 El sole
19 Lo angelo
20 La justicia
21 El mondo
22 El Matto
The math, Matto/Nulla, is not listed as the last of the Triumphs in the Ludo Sermon, nor is it numbered 22. It is listed after the 21 Triumphs, as being separate from them, and is numbered zero in the text. The sermon is very clear that there are 21 Triumphs (as there are steps leading into the depths of hell) - not 22 trumps but 21 trumps and the Matto, 1 - 21 + 0. As well as the numeration 0, it is given the epiteth Nulla.
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: Le Tarot arithmologique - la séquence 1+4+7+10 = 22

#19
In the notes of the essay, I noted that the Bagat was listed in first position and the Math unumbered on a twenty second line after the last numbered Trump (21 first).


Notes:

- The position of the Pope in Vth position is also reflected in the order of the 1565 F. Piscina "Discorso".

- The position of the 'Math' in the XXIInd position is also reflected in the orders of 1534 "Triomphi" of Troilo Pomeran, an anonymous "Motti" ca. 1525-1540, another anonymous ca. 1530-1560 "Trionfi di Tarocchi" likewise in the order of 1585, T. Garzoni "Piazza Univerzale".

- The position of "La Mort" XIII is confirmed in the "Sermones de Ludo" (circa 1500), Pasquinata (1521) and the Catelin Goefroy (1557).

- The position of the Bagat I, which is found on the "Sermones de Ludo" (circa 1500) and "Pasquinata" 1521 is confirmed at the alpha of the Trumps sequence in the Tarot of Catelin Goefroy 1557. This will be the order of the Tarot de Marseille starting with the Tarot de Marseille of Jean Noblet 1650.

- In addition, the Maison académique (1654-1659) assigns the number 1 spot to the Little One and the Excuse to the twenty-second line, after 21. In this connection, it will be remembered that the oldest Rule, 1637, states that there are 22 triumphs, and cites as the 3 High, the World, the Math and the Bagat. Knowing that the Bagat is the first and World the twenty-first, we deduce that Math is the twenty-second. Not so surprising, if one conceives that the object of the game is to win all the tricks. Now, what happens in the case if a Slam? The Petit is played in the penultimate round, and the Excuse is played last.
Web page : http://letarot.it/page.aspx?id=23&lng=eng

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

#20
In my sense, the important is which is first, that is which of the Bagat or the Math begins the allegorical sequence of 22
As the Bagat is FIRST, the Math cannot be first as in a mathematical count starting with 0 (for example the Mayan count starts with ZERO).
The Listing would have been
O or "null" , 1, 2, 3 .... 21 st

This is not the case.
The count starts with the First Bagat
1,2,3 ...21st and the 22nd nammed "nulla"
The math is after the 21st on a twentysecond line.

I personnaly sse it not as a ZERO of numeration.
Maybe at the best, as I suggested in my comment of Moakley such as an ANNULATION ou invalid throw of dices ...

"Moakley noted " the astonishing fact that there is, indeed,
something related to both the 4x14 suit cards and the 21 trumps,
namely the much older game of dice, from which they might have
stemmed. If we take the total number of choices possible when
throwing three or two dice, it adds up to either 56 (= 4x14) or 21,
respectively. " (Laurent Faber)

Now, if we consider as 22nd or 'nulla' an invalid throw of dices,
then there are 22 throws.

Morever, such an invalid throw could be seen as outside of of the
geometrical perimeter of a game of tables such as described by the
King Alphonse X (He makes a difference between game of spirit such
as chess, games of chance such as dices - the games of tables being
midway ) or more simply if the dices do not fall correctly..."
Web page : http://letarot.it/page.aspx?id=23&lng=eng

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