The Fool & XIII - and the Golden Mean

punchinella

Thank you Jmd, in a general way I think I understand the principle in question now. I'm still not entirely clear on how it relates to tarot though--I'm assuming that this magic point occurs at or around the number thirteen, given the numerical sequence provided . . . but gather that this occurence is contingent on placement of Le Mat (??) --My question is, where? --Over the top of XIII, so that the only numbers involved are 1-21, not 1-22?

Sorry to be so dense, but I really do want to understand this.
 

jmd

The Golden Mean of the 22 cards, with the Fool at the end, occurs at approx. between 13 & 14 (depending on how one 'measures').

It thus provides a point which could be used, if one wanted to, as the third significant point. By placing the Fool over it, the sequence is only re-affirmed in some reflective ways.

Numbers one, thirteen and twenty-one are also Fibonacci numbers. Having a twenty-second card again only shows that the numbers go on... there is more than simply twenty-one.

Similar reflections to this can also of course be made with the Fool placed initially prior to the Bateleur. Though this works from a purely Golden Mean perspective, there are other considerations which, to my mind make of this later ordering one not as 'natural'. One of the reasons for this is that the three 'ends' end up, with the letter allocations I also suggest, allowing for the three mother letters to become immediately apparent - a good pedagogical technique.

The idea is therefore to begin with the twenty-two in order (Fool as twenty-second, but un-numbered and therefore of no fixed abode/place), then to work out the Golden Mean (at thirteen - coinciding with Mem), and placing the image with apparent complimentary iconography over it - ie, Fou over XIII.

The three 'ends' or mother-letters (Alef, Mem and Shin) now stand out, and death remains hidden and un-named.
 

kwaw

jmd said:
There is an earlier version of what has come to be called the Fibonacci series which begins with just 1, the ensuing numbers being the same (as there is nothing before one, the next number is 1, each succeeding number from then on being the sum of the previous two).


The same series as Fibonacci is testisfied previously and begining with one? I didn't know that, have you got a reference to a pre-1200 fibonacci series begininng with one instead of zero? If you have does this prove anything? Which in terms of historical proximity and testament was most well known in 15th century N. Italy? [Fibonacci series, which begins with zero, or your as yet unreferenced series that begins with one?].

Kwaw rightly brings a criticism to what I mentioned by asking about the assumed correlation between Tau and Saturn. Even were I to provide someone's relevant writing, this was not the point. There were certainly various planetary attributions made between the double letters and the planets, some which seem more sensible than others.


The question is, is this attribution made in the relevant time period, prior to 1650? And not from what our modern perspective considers 'more sensible', but sensible or not what was considered at the time. In none of the redactions of the SY is Tau connected directly with Saturn, though in some later redactions there may be an indirect connection through its attribution with Saturday [though even in those it is not attributed to Saturn. The late redactionists who attribute it to Saturday attribute it directly to the planets Jupiter [Gra], Moon [Raavad], Moon [Donash], Moon [Ramak]]. Tau-Moon is the oldest attribution in keeping with the Chaldean order Saturn-Moon, Beth-Tau.

On a different point raised, I would suggest that there are other reasons - more important than statistical ones from my personal perspective - why for myself allocating an alphabetic sequence from Alef to Tau to cards from the Bateleur to the Fou make sense, but I suppose that is the subject of another thread...

No doubt, but the points you raised were 'The Golden Mean', 'Saturn-Tau' and the work of Mark Filipas [which he has claimed to be statistically significant]. While you may have good reason to think the fool goes at the end, none of these three necessarily support it. As you yourself mention the same golden mean argument can be made placing the fool at the beginning, Saturn-tau is arguable and in the oldest and most redactions is attributed to Beit, Filipas work is statisticallly insignificant and proves nothing - anyone with a decent hebrew-english dictionary can come up with their own list of words starting with their own prefered letter attributions. As to them belonging to another thread, surely their discussion belongs in any thread in which someone seeks to bring them up as an 'authority' to their own position?

Kwaw
 

filipas

jmd wrote:
In yet another thread in the Kabalah section, I also mention that the mother letters are, within the sequence, arranged according to Golden Proportion: as first, as thirteenth, and as twenty-first.
This is fascinating, JMD! I never noticed before that if you take 21 and multiply by .618, the result is 12.978 (13). This shows that the three Hebrew mother letters indeed reflect the 'phi' proportion -- the letter mem marking the 'golden mean' between aleph and shin! Its amazing to find 'phi' so fundamentally embedded within one of the most sacred and magical of alphabets.

And, looking to the trumps, the 'golden mean' between Trump I and Trump XXI happens to be the one trump which traditionally bore no title!

jmd wrote:
Namadev mentions the three 'ends' of the Tarot being I the Bateleur, XXI le Monde, and the un-numbered Fool. This harkens back to a long tradition in game-playing, also reminiscent of the same in the modern ongoing version of the card-game of Tarot.
But this has nothing to do with 'phi'. In Tarot, the 'phi' proportion is reflected by Trumps I, XIII, and XXI; The Fool is not part of the 'phi' equation.

Thanks!
- Mark
 

Namadev

Golden Ratio and the number 22

Hi,
The number 22 and it's relation to PI as 22:7 has also to do with the Golden Ratio - if not with the Alephbeith when linking the four "arbres de vie" in the four worlds.

22Phi = [(56xracine dePhi]
while :
56:2 = 22xracine de Phi.

Further on :
A)4 four decades of the suits : 40 represent 220.
1 +2+3+4+5+6+7+8+9+10= 55
10+9+8+7+6+5+4+3+2+1 = 55
1 +2+3+4+5+6+7+8+9+10= 55
10+9+8+7+6+5+4+3+2+1 = 55

_____________________________

22+22+22+22+22+22+22+22+22+22= 220

B)The 16 Honours represent :
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16=136


Numerical cards of the suits divided by honours :
220 : 136 = Phi

It happens that the 56 cards of the suits represent then :
220+136=356


356 :220 = Phi


Alain


BtW these goden proportions rae those of Kheops :
356 = hauteur suivant le plan d'une face

"le nombre d'or permet de partager asymétriquement une donnée numérique quelconque de façon parfaite.
La Hauteur suivant le plan de Khéops longue de 356 coudées royales se partage en moyenne et extrême raison en :
220 et 136 coudées égyptiennes.
La propriété spécifique la pluys connue du partage en moyenne et extrême raison propre au nombre d'or est que la somme de deux nombres (356 =220+136) divisée par le plus grand des nombres (220) composant la somme est égale au rapport du plus grand de ves deux nombres (220) au plus petit (136).
356:220=Phi=220:136"

Origines te histoire du Tarot


The architeque of Kheops had "intuitively" understood the Golden Mean long before it's theorisation by the Greek Mathematicians...
 

jmd

I'm not sure as to how respond in this thread... there are so many interesting directions.

As a first point of note, let me first bring to mind a thread started by smleite: Tarot, number four, and some random thoughts on the Kabala. What is fascinating there is also that this base number four highlights many aspects of the Tarot.

I don't recall if I mentioned it there or elsewhere (I didn't check when I got the url for the thread), but, as also something which smleite mentions, the number four seems to unperpin many aspects.

For example, there are 'obviously' four 'colours' or suits (though the Atouts may be considered a fifth).

Each of the suits has 10 pips, ten being a triangular number of base 4.

There are 16 courts, 16 being a square number of base 4.

...and there are 22 Atouts, 22 being a pentagonal number of base 4.

Additionally, if the pips are placed as tetractys (triangle), and the four triangles are joined, they form a tetrahedron (with twenty 'points', each face a tetractys).
_____

Returning to considerations of the Golden Mean, I will have to dig out some of my older references for the earlier rendition of the Fibonacci sequence which does not make use of '0'. Irrespective, it is implied if not named, as a sequence beginning with '1', but needing two numbers to be added, adds nothing in the first instance - and hence adds zero.

Both kwaw and I are probably using the same key reference when discussing the planetary associations to the double letters: A. Kaplan's Sefer Yetzirah. As mentioned, the association to Tau is through the association of Saturday to Saturn, not the direct attributions made.

With regards to the allocation of Tau to that day of the week, various versions do indeed make that allocation. There is no need to maintain all aspects of earlier allocations, especially if there were apparent contradictions. If there was indeed a letter-to-card-to-planetary consideration at the time of Tarot's development, then the possibility of reflecting on the pre-12th century connections of Tau with Saturday, and of Saturday with Saturn, already existed.
_____

With regards to whether the Fool is 'part of the equation' - to refer to Filipas's reply - part of what swung me over to Mark's preferred order (out of the three main ones: Filipas, Levi, and GD), was precisely the positioning of the Fool in such a way that its Kabalistic possible historical connections remained.

What I mean by this is that if there was a Hebrew letter association which played in the development of the Atouts, then, to cast oneself back to earlier times, though there may be numerous 'hidden' (until an unveiling key is found) aspects, there needs to also have been some quite 'obvious' ones.

The most obvious of these is the beginning numerical sequence and value of 1 with 1, 2 with 2, &c. Of course, after a time this breaks down if one assumes the value of Kaph to be 20 (there may have been another system which continued number value according to ordinal value - as there was in late antiquity Alexandria for the Greek alphabet). Even if we assume that the cardinal value as correlated with its ordinal value stops at ten, the sequence makes more sense.

Also, there are twenty-two letters, with the three mothers at those key Fibonacci locations. That, whether or not we wish to argue about Tarot, is unmistakable. If there is a Tarot-Hebrew letter association, however, then how does one differentiate also the Golden-Meaned position card? a lack of name certainly aids.

By not numbering the last card, a number of other significant attributes also emerge. For one, there occurs in an obvious way that important number made mention of in the Sefer Yetzirah: 231. This being, as mentioned earlier, and in addition to the possible combinations of 22 letters taken two at a time, also the sum of the numbered cards (1 + 2 + 3 + ... + 21).

As well as this, and as mentioned elsewhere here and in other places, the different letters used to form the tetragrammaton (YHV) add to twenty-one. But its fulness requires another letter (another 'H'). Similarly, the full sequence of the Atouts requires an additional card to the twenty-one numbered ones. Interestingly, assuming it is allocated to Tau, there is also a striking similarity (in Hebrew) of form between these two which need to complete the respective terms ('H' & 'T').

Tarot bears, however, also an unmistakable Christian flavour (of what peculiar kind is questionable). How one may relate the World to Shin appears 'obvious' if the sequence is accepted (though I also mentioned this elsewhere, I'll re-encapsulate it here): within the tetragrammaton (the four elements/ YHVH / the four living creatures) appears Christ. This, even in reflections and exegesis of those early times, meant inserting a Shin within the four-lettered name: YHVH became YHShVH - 'Jesus'.

It may be, by the way, that those considerations may even have been made by Christian Jews of the 12th century. As at its beginning, and as also now, there are some who consider Christ to have been the Messiah within a quite otherwise orthodox Judaic framework.
_____

To my way of thinking, there need not be a statistically significant correlation between the Hebrew alef-beit and the Atouts, but rather a likely and meaningful one. If I were to design a deck which reflects the Roman alphabet, I would not go about trying to find words which have, as a series, statistical significance - though it may end up having such. Rather, I would choose from amongst possibly existing and significant imagery a sequence which also reflects what I was attempting to illustrate.

This to me is the brilliance of Filipas's work.

It provides a framework which makes sense of not only a pattern which has ordinal value, but also even explains their order - an order which otherwise may best be altered to have, for example, representatives of the (depicted) cardinal virtues placed together.

As another interesting aside, and continuing from the wonderful post by Namadev, that addition of the total number of depicted pips (ie, if one adds the one cup to the two cups to the three cups, &c, for all four suits), the number 220 has also been used (mathematically incorrectly) in considerations of Hebrew letter permutations... again I refer to A. Kaplan here, though I do not have his books with me at the moment...
 

kwaw

jmd said:

As another interesting aside, and continuing from the wonderful post by Namadev, that addition of the total number of depicted pips (ie, if one adds the one cup to the two cups to the three cups, &c, for all four suits), the number 220 has also been used (mathematically incorrectly) in considerations of Hebrew letter permutations... again I refer to A. Kaplan here, though I do not have his books with me at the moment...

The 220 gates are not necessarily incorrect, they belong to a different school that worked them out sleighly differently to that given in the SY. How the 220 gates are linked to the letters and 10 circles of the sefiroth I explained in the SY thread so won't repeat again here. Interesting to note that many, including the first, of the emblematic books have 220 emblems.

Continuing with Phi I am not sure I am following correctly, maths is not a strong point with me. The Golden Ration is .618:1, so what I think your saying is that .618 of 13 is 8.034, which we round down to 8 and add to 13 to give us 21. You make Atu I alef then the three mother letters AMSh fall on 1, 13 and 21, the unnumbered card going at the end. What doesn't make sense to me is let us say draw a line, mark the line at 13 inches, then at 21. Let us mark of each inch and number them 1-21, what you seem to then say is that we don't count from the beginning of the line, at point zero, but from point 1. This now means that your line is no longer 13 inches but 12, so the golden ratio is lost. To keep a correlation the fool needs to go at the beginning as zero, then the points rest on the fool, death and the world. We lose the wonderful AMSh correlation though:(

No doubt I am missing something fairly basic, and would appreciate if you could explain in simple terms where I am going wrong.

Kwaw
 

jmd

I cannot reply here on the assumption that you are 'going wrong', for reflections and insights which may be different only add to the overall picture...

Rather than beginning with the number 13 and adding to it its approximate golden proportion, let us take the whole letters and see where this leads.

For the purposes of this part of the post, note that I am avoiding discussion of the cards, for whatever allocation is preferred, the Golden Mean remains within the Hebrew letter mothers - if considered in 'simple' ways... what do I mean by that.

If one takes a line 22 cm/inches long, than its Golden Mean is at approximately 13.6 cm/inches (ie, 22*Phi' ; 21*Phi' is just under 13 cm/inches, but so close as to be visually equal). But that is perhaps not even the best place to begin.

What would have emerged to those who reflected and used such sequences as the Fibonacci is that 21 is part of that series, and that 13 forms its Golden Mean as part also of that series. Reflecting on the three Mother letters in terms of their ordinal value, it becomes apparent that here too they are so placed.

The beginning (1), (golden) middle (13) and last (21) are thus each of special significance, yet it is also the case that the last Mother letter is not the last letter, for there is yet another (the 22nd).

To return to the Tarot, this is lost if one places the Fool first, for we would then not be talking of the first, thirteenth and twenty-first as numbered, and also then have yet another.

Thus, although the Fool is not part of the mathematical equation - as Mark puts it - he is well placed to maintain the onward march of the cards as also numbers... perhaps even chased out by the animal of the otherwise clean system.

In terms of the over-lay of the Fool & XIII, it is also interesting, as a side-note, that one of the most important stars of the northern hemisphere, alpha Canis Majoris (ie, Sirius), as well as obviously being linked to the Dog, is there linked to being an omen of Death: the Dog brings both pestilence and rabies... and generally other harbinger of death, such as drought and disease.
 

kwaw

Sorry, but it doesn't work.

jmd said:

If one takes a line 22 cm/inches long, than its Golden Mean is at approximately 13.6 cm/inches (ie, 22*Phi' ; 21*Phi' is just under 13 cm/inches, but so close as to be visually equal). But that is perhaps not even the best place to begin.

What would have emerged to those who reflected and used such sequences as the Fibonacci is that 21 is part of that series, and that 13 forms its Golden Mean as part also of that series. Reflecting on the three Mother letters in terms of their ordinal value, it becomes apparent that here too they are so placed.

The beginning (1), (golden) middle (13) and last (21) are thus each of special significance, yet it is also the case that the last Mother letter is not the last letter, for there is yet another (the 22nd).

To return to the Tarot, this is lost if one places the Fool first, for we would then not be talking of the first, thirteenth and twenty-first as numbered, and also then have yet another.

Thus, although the Fool is not part of the mathematical equation - as Mark puts it - he is well placed to maintain the onward march of the cards as also numbers... perhaps even chased out by the animal of the otherwise clean system.

You seem to be disregarding the fact that a ruler starts at zero, not 1. If you count your measure from 1 on the ruler then the length of the line is reduced by 1 inch, and it will not be at the point of the Golden Mean. The Fool is actually essential to the equation.

Take a line a,b and place the letters equally spaced along it, aleph at the beginning tau at the end. Whether or not you number it 0-21 or 1-22 makes no difference as the line is the same length and the Golden Mean is still going to fall in the same place at Nun. The Phi ratio is Alef, Nun, Tau, not Alef, Mem, Shin. Placing the fool at the end then gives us Atu I, XIV and XXII [0]. Placing the fool at the beginning gives us 0 [at the beginning of the line/ruler], XIII [at 13" on the ruler] and XXI [at 21 on the ruler]. Neither relates to the mother letters, but if you place the fool last then you lose the XIII/XXI relationship.

Kwaw
 

smleite

Originally posted by punchinella

(…) Diana has suggested to me that Le Mat actually represents death in TdM, which--if true--explains a great deal. --The dog eating the flesh, the flesh falling off, "check-mate" as a possible translation of the word Mat (…).


I have no idea of what Diana said about this, but in chess the word “mate” comes from the Persian “mat”, meaning death (“mort”, in French). You probably knew this already, but I thought that I was important to state it clearly. In French, the intonation of the words Mat and Mort also allow a possible word game.

About the Golden Mean, I must say I do not work very well with figures and arithmetic… but I enjoy a lot to study numbers in geometric dispositions. If you draw a line and divide it from 1 to 22, you will obviously find number 13 as the Golden Mean, as stated above. But try to do it reversely, that is, from 22 to 1: the Golden Mean is then set on number ten. I did some studies about this in architecture, and I can guarantee this: it is a process often used to trace cathedrals. In Portugal, where I have really studied it, to take the full length of certain churches (I worked on a very coherent group of churches, from the early years of the sixteenth century) and find BOTH golden means, from the front door to the altar and back, gives us the location of some very important structural elements. Mainly, it gives us the EXACT location of several side doors – which, in Portugal, are often treated, in artistic and symbolic terms, as if they were the true main doors.

I’ve always seen arcanes number X and number XIII to be the two main “gates of Tarot”, dividing the major arcana in two sets of 10 + 12 cards. In geometric terms, the “entrance” would be between both; they are, in this sense, two “pillars” defining an entrance. Could it be that cards in-between, that is, cards number XI and XII, can be understood as a sort of “middle chamber”, before the higher spiritual path displayed by cards XIII – XXI (or XXII)?