The Fool & XIII - and the Golden Mean

[smleite]

I also find relevant that the Golden Mean gives us two cycles of ten arcane each: from I to X, from XIII to XX. They could form two tetraktys, both presenting interesting groups of cards… I like in particular the group formed by arcanes number XVII, XVIII and XVIIII, The Star, The Moon and The Sun, though numbers XIII, XIV, XV and XVI are great…

 

[kwaw]

I also find relevant that the Golden Mean gives us two cycles of ten arcane each: from I to X, from XIII to XX. They could form two tetraktys,

In terms of the tetraktys:

A line 21"long: the point of the Golden Mean [rounded to nearest whole number] equals 13". The line alef, tau, the golden mean at nun.

The line alef,nun is 1, nun,tav .618. Draw an isoscles triangle, the sides = 1 (0-13, mat/mort, alef/nun), the base .618 (13-21). We have a triangle whose apex is 36 degrees. There are 10 such triangles in a circle (numeric[geometric]):

1 + [36+], 2 +[72+], 3+[108+], 4=[144=], 10 [360].

That is the apex of one golden triangle = 36 degrees, two = 72, three = 108, 4 = 144; and 1+2+3+4=10; and 36+72+108+144=360. Thus a line 21" [0"- 21", alef to tav, golden mean at 13", which matchs Nun] is related to Phi and the Tetraktys.

Kwaw

 

[jmd]

...but it DOES work!

If you were to determine the letters as each occupying a centimetre, then, as I have also indicated, the Golden mean for a line 22 centimetres long would fall at approximately 13.6, hence in the fourteenth position.

This is not, however, how the general sense for the Golden Proportion (outside of geometrical constructions) were carried out. Rather, precisely the importance of the Fibonacci series in whole numbers (and whether by that name or not), is of greater reflective significance. Hence also why Filipas points out that using the Fool in the measurement makes one 'lose' the connection.

Even if constructing relatively large structures one may gain an appreciation for the proximity to the Golden Mean and usefulness of the numbers one, thirteen and twenty-one (and hence, to their respective first, thirteenth, and twenty-first letters) by constructing squares (or even a golden spiral) within a Golden Rectangle 17cm (ie, 34/2 - or even more importantly, in terms of our considerations, (21+13)/2cm) wide and its accurately drawn height, and another within a rectangle 17cm wide by 27.5 cm (55/2) high (those measurements come out quite easily if one uses 5mm graphing paper). It will be very difficult indeed to visually perceive the difference between the geometrically determined Golden Mean of the line of 21/2, and the one which was constructed with the defined measures using the graph paper/ruler (at the thirteenth position).

The connection, however, remains, as First, as Thirteenth (not fourteenth), and as Twenty-first.

This is not diminishing the role of the Fool: rather, it requires that it be placed last... and UNNUMBERED. The card cannot be placed in first position, for it would then occupy the space between (on the ruler) 0 and 1, ie, the first numbered space, which is the province of the first numbered card - the Bateleur, or, if using the Alef-Beit, of Alef.

Part of the possible difficulties in these is precisely how one is going to determine the Golden Mean of a series.

If one uses the method applied by kwaw - a method which is also correct from a strict linear geometrical construct, then the Golden Mean of the twenty-two centimetres will be at approximately 13.6, and therefore fall in the fourteenth partition (hence the assumed Nun). This, however, contradicts the sense in which numbers and considerations of Golden Proportions are normally met. In kwaw's considerations, a card numbered zero would have to assume the space occuring before the space between 0 & 1 - ie, a negative number (between 0 & -1), and outside of the range of letters. Indeed the overall considerations lend support to the un-numbering of the Fool as final card.
_____
In terms of the Tetraktys, this is normally considered to be in the shape of an equilateral triangle.

If designed according to a Golden Triangle, then the full circle is implied by two pentagrammes - precisely for the reasons mentioned by kwaw, in which the apex of each triangular point is of 36 degrees, hence ten points are needed to complete a circle.

If one wants to place these Golden Triangles in tetraktys form, however, then another six (downward pointing ones) are created...

 

[kwaw]

Jmd wrote:If you were to determine the letters as each occupying a centimetre, then, as I have also indicated, the Golden mean for a line 22 centimetres long would fall at approximately 13.6, hence in the fourteenth position…..
…. If one uses the method applied by kwaw - a method which is also correct from a strict linear geometrical construct, then the Golden Mean of the twenty-two centimetres will be at approximately 13.6, and therefore fall in the fourteenth partition (hence the assumed Nun)[/I]

This wasn't my method, my method was based upon a line of 21cm, not 22. The Golden Mean of a 21cm line will [rounded figure] fall at 13cm [21x.618=12.978 – the centimetre space occupied by Nun/XIII], and if take Alef as zero cm, beit at 1cm etc then the letter at 13cm will be Nun, Atu XIII in the GD tradition. If we slide the rule so the line begins at 1 instead of 0, then the GM will fall at 14cm on the ruler, taking Alef as 1cm then the letter is still Nun, Atu XIV in the continental tradition.

Filipas points out that using the Fool in the measurement makes one 'lose' the connection.

Yes, if you discard Tau and make Shin the extent of the line then it does work. With shin as the extent of the line then it will measure 20cm, and the GM will fall at 12cm [20x.618=12.36] if we round the figure down to the nearest whole number and this would correspond with Mem, and if we slide the ruler so the line commences at 1 then it would be 1,13,21 alef, mem, shin [although of course at 12.36 it actually occupies the centimetre space occupied by Nun, and the XIII/XXI connection no longer fits as the GM fraction of a line 20cm in length is not 13/21 but 20/12]. So yes it can be forced to fit by discarding the letter Tau and the Fool.

This is not diminishing the role of the Fool: rather, it requires that it be placed last... and UNNUMBERED. The card cannot be placed in first position, for it would then occupy the space between (on the ruler) 0 and 1, ie, the first numbered space, which is the province of the first numbered card - the Bateleur, or, if using the Alef-Beit, of Alef.

In kwaw's considerations, a card numbered zero would have to assume the space occuring before the space between 0 & 1 - ie, a negative number (between 0 & -1), and outside of the range of letters.

Not neccesarily, because alef is attributed to kether and to ain [nothing], and the fool is unnumbered; neither then have to occupy any space, positive or negative. Just as the zero [signifying the place without number] occupies no space at the beginning of the line.
However if we consider the line as circular instead of linear, alef-alef [as described in the SY], then indeed we might imagine the fool as occupying the space on the circle between tau and aleph. In this case of course, taking the space alef-beit as the first space, then tau-aleph is the 22nd space. We may note that the Steele sermon lists the Fool as 22nd but numbers it '0'. Personally I tend not to think of the fool as either beginning or end, but both beginning and end. As I have already posted in other threads, in kabbalah the letter Aleph symbolises both beginning and end. The circular line unfolded of course would measure 22cm, the GM of which is 13.596 already discussed.

 

[smleite]

Sorry everybody, I made a mistake when building the geometrical golden mean in my former posts. Please ignore them.

I cannot, however, stop thinking about it. The only way to properly draw this, in geometric terms, and according to the regular building of the Golden Mean and the use of the Fibonacci sequence, is to draw a line divided into 21 sections, and number it from 0 (zero) to 21. We cannot alter the regular and traditional method of doing it, if we want to derive real meaning from our studies; we cannot “bend” Sacred Geometry to our own will. 13 is clearly the Golden Mean. But, as I was trying to point before (and completely failed), is that it is also possible and relevant to find the Golden Mean counting backwards, from 21 to 0. We then find 8, another number that belongs to the Fibonacci sequence. Maybe someone who is more at ease with numbers will find the geometrical place of 1, 2, 3 and 5 – I certainly won’t push my luck any far.

 

[filipas]

kwaw wrote:
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.

Quite a remarkable statement to make, kwaw, considering you've presented nothing to back up your conclusion. While I encourage your effort at constructing similar lists (your preliminary lists for aleph and bet are good but I think need some refinements), they don't demonstrate your understanding that it's not the presence of one or even a handful of correlations but rather a whole body of correlations which argues that an actual connection may exist here.

And I understand the reluctance to accept the idea of such a connection. Even after several weeks of research I felt--faced with the enormous 'database' of Hebrew words--that such a connection must be far-fetched and that my continued perusal of letter-entries would not bear out the hypothesis. Nonetheless, if you haven't analyzed that 'database' yourself then you aren't in a position to know how singular the correlation may or may not be. You are refuting my findings without duplicating my research! This insults my intelligence as well as yours.

I grant that these findings have not been corroborated by any other study. And I grant that the observation of a researcher can sometimes distort his/her findings. So I don't think that either of us should be hasty in our conclusions.

Even if one sets aside the numerous iconographic elements and considers only the trump subjects--Strength, Traitor, Death, Temperance, Satan, Flash of light, etc.--the fact that twenty-two reasonable equivalents can be found in alphabetical sequence presents a substantial case indeed. I suggest that those who wish to prove, disprove, or otherwise test this theory begin by focusing on just the trump subjects themselves.

Thanks,
- Mark

 

[kwaw]

I have no interest in disproving your thesis Mark, indeed I wish you the best luck in proving it. As it stands however your work proves nothing. Your word lists in themselves are not proof, the proof depends upon a demonstration that they are statistically significant. You have stated that they are but as far as I am aware failed to provide any evidence as yet. In order to prove your thesis you need to provide a statistical evaluation and the method and data upon which you base it.

Kwaw

 

[filipas]

kwaw wrote:
I have no interest in disproving your thesis Mark, indeed I wish you the best luck in proving it. As it stands however your work proves nothing.

I've never claimed that it does--so why resurrect that straw man?

In my opinion, the significance of the work to date is not that it proves a connection but rather that it points in a promising and cohesive direction.

Thanks,

- Mark

 

[filipas]

kwaw wrote:
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.

We do count from the beginning of the line ("0", if you wish) and find that the 'golden mean' of a 21-inch line falls at the 13-inch mark of the ruler (at 12.978 inches, to be exact).

kwaw wrote:
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.

You are characterizing point "0" of the ruler as being equivalent to a unit, which it is not.

kwaw wrote:
A line 21"long: the point of the Golden Mean [rounded to nearest whole number] equals 13". The line alef, tau, the golden mean at nun.

By placing the letter aleph at the "0" point of the ruler, you mistake that endpoint of the line to represent a unit equivalent to the other points on the ruler. It is sometimes helpful to view these proportions in terms of square units set edge-to-edge.

If we wish to find the golden mean of a 22-unit set (such as the Hebrew alphabet), then we visualize a 22-unit ruler and compute its golden mean to fall at 13.596, or at the 14-inch mark if we are rounding; this is the same as visualizing 22 blocks set edge-to-edge, with the 'golden mean' being represented by the 14th block. We can therefore say that the letter nun represents the 'golden mean' between the letters aleph and tav. But, as jmd was originally pointing out, what is striking is that this same proportion of 'phi' shows mem to be the golden mean between the letters aleph and shin. This is true no matter how we visualize it: given a line of 21 units, it is the 13th unit which designates the golden mean; given a set of 21 blocks, it is the 13th block which designates the golden mean.

kwaw:
Take a line a,b and place the letters equally spaced along it, aleph at the beginning tau at the end.

But you are attempting here to fit a 22-unit set into a 21-unit measure, a correlation which distorts the fidelity of any mathematical analogy or computation.

kwaw: Whether or not you number it 0-21 or 1-22 makes no difference as the line is the same length

But in ignoring the mathematical labels assigned to the number line, one risks obfuscating the volumetric construct which those labels represent.

Thanks,
- Mark

 

[kwaw]

- Mark wrote
Even if one sets aside the numerous iconographic elements and considers only the trump subjects--Strength, Traitor, Death, Temperance, Satan, Flash of light, etc.--

LChY vigour of youth, LAK he sent ministered, protective angel, LBSH cloak, LBB be bold, daring, give heart, encourage, LYSh strong lion, LThO he bites. [I attribute Lamed to Strength, not Teth, for the symbolism of Lamed and its relationship to Strength see my post in Hebrew Letter correlations thread].

MAL is rather an interesting word don't you think, it means 'traitor', 'lifted up' and 'upside down'. In my dictionary the word you have for 'death' MVTh is given the meaning 'cause to die, slay, sentence to death' and could equally apply to the hanged man. At least eight of the words you have under aleph are 'non-specific' to Atu I in that they could equally apply to the fool for example. In fact there are quite a few words you have listed that are non-specific in that they could equally apply to one or several other cards, especially for example those that relate to headgear and vegetation. You use several different meaning words in some cases to refer to one object, for example with animals; I think this is OK in terms that it may not be clear what the animal is and may be any one of those listed, but they should be counted as 1 'hit', not several. Some words of course are not Hebrew at all but transliterations of foreign words, which too is OK as Hebrew as any other language incorporates foreign words. However in the case of 'TMPV' time for example, which I presume is a transliteration of the latin tempus, as you note yourself on your site is not to be found in any Hebrew sources. There is also the problem that it is a conceptual abstraction, an interpretation of the card, not any actual object, it is called 'hermit' [YChD, "solitary one"], has an old [YShR old, YSHSH elderly person, aged] man in a cloak carrying staff and lamp [YQD burning, YPhO shine forth, YAYR the Lord enlightens]. Where is the depiction of time [YVM day, duration, time]? You also list TOM wisdom here, again an interpretion and not an actual object. In fact your 'hermit' listing as a whole is particularly weak. As for TRSQL three legged, [is his staff is the missing leg from the Bataleur's table? ], beyond being something of a stretch, it is again a word not specific to this card alone, we could list it under Atu I in refence to the three legged table and also the fool wlaks witha staff so can we call him three legged too? Under Star you also list another transliterated foreign word PLYDVTh Pleiades, again nothing wrong per se with foreign words, but there are two perfectly good hebrew words for Pleiades so why use a foreign one?

Kwaw

edited to remove Phi quote which has been pointed out to me might be read as a personal attack/insult, which wasn't my intention but I apologise if such was the impression given.