Fibonacci and the Tarot Trumps: a Conjecture (part B)

Roland Faber

… continued from Part A

The Divine Proportion

Given the historical coincidences just stated, two questions must arise: How, if at all, could Luca Pacioli’s Divine Proportion,as based on the Fibonacci Sequence, come into the Tarot?; and how can it account for its mysterious number 22, especially as conceived in the odd form of the 21+1 structure of its trumps? More generally: can this mathematics “explain” the (probable) structural subsets of the trumps and its internal microcosm? While the first more historical question will be deferred to the next section, the answer to the second, the more structural (and speculative) question, will be given now - by an experiment: the empirical application of the Fibonacci series to the 22 trumps. In other words: In order to be able to interpret the importance and consequences of the Divine Proportion for the Tarot, we must first learn by mental experiment how the Fibonacci-numbers can be related to the pattern of the Tarot trumps. By doing so, we answer the question whether there is a hidden (or in certain aspects rather obvious) Fibonacci structure in the Tarot.

To begin this experiment, consider the beginning or 'most basic' Fibonacci numbers:

1, 1, 2, 3, 5, 8, 13, 21 …

Indeed, the first element worth mentioning is the number 21. It is the eighth number of the basic Fibonacci series. Now we could—as many other theories do—just postulate this rather random match to be the missing link explaining the 21 trumps of the Tarot. But in order be an intelligible move, this naïve identification is far from being enough for justification. We must do more than just state such a connection because of the conjecture that identical numbers—in this case the number 21—might have identical intentions.

The Fibonacci number 21 (as is also true for the Tarot number 21) is not a mere opaque quantity which is without internal structure. On the contrary: since all the preceding numbers of the series are related to any higher number by being subsets of it, all the preceding numbers are moments of the substructure of any higher number. In our case of 21, we must understand it as consisting of subsets that are related to one another by the formula of the addition of any two preceding numbers:

21=13+8; 13=8+5; 8=5+3; 5=2+3; 3=2+1; 2=1+1

Altogether, the internal relation of proportions of numbers produces a highly complicated microcosm which can be depicted in a (not yet exhaustive) explication of what we shall refer to as its 'subsets':

21=13 {=8 [=5 (=3 (=2 (=1+1)+1) +2 (=1+1)) +3 (=2 (=1+1) +1))] +5 [=3 (=2 (=1+1) +1) +2 (=1+1)) +3 (=2 (=1+1) +1))]} +8 {=5 [=3 (=2 (=1+1) +1) +2 (=1+1)] +3 [=2 (=1+1) +1)]}

It is this microcosm, consisting of the subsets of preceding Fibonacci numbers that will give us one of the strongest hints regarding its probable connection with the 22 trumps, which also exhibit a microcosm of subsets as expressed by their relation, symbolism, and structural integrity.

The second basic, but very odd characteristic of the original Fibonacci series is the fact that it includes only non-recurring numbers, except for the first number 1, which is repeated in order to start the law of addition (in difference to a generalized Fibonacci series that can begin with any two numbers, as long as they follow the same additive algorithm). This might give us a hint as to its relation to the most basic, odd sub-division of the 22 trumps of the Tarot into 21 trumps, on the one hand, and the Fool, on the other, thereby generating a 21+1-structure. No other series of numbers (of my knowledge), except the Fibonacci series (in this original and most basic form), offers this essential feature of the Tarot trumps. Stated differently, the Fibonacci Sequence consists of these two sets of one recurring and indefinitely many non-recurring numbers, respectively:

{1} {2 3 5 8 13 21…}

In taking these subsets as two entities, and relating them to the trumps-numbers, they create the number 22:

{1} + {2 3 5 8 13 21…}→ 22

If we begin with the non-recurring subset: 2+3=5; 3+5=8; 8+13=21; and then add the singular recurring 1, we gain a 22 that exhibits a 21+1 structure, similar to the infamous 21 trumps and the Fool of the Tarot:

21(=13+8(=5+3(=2+1))) + 1 = 22

Of course, this is not enough to substantiate the suggestion that this “relation” between the basic Fibonacci numbers and the Tarot trumps may be more than an imaginative and associative connection. But it is already dim evidence for a possible resonance of one with the other. In my eyes, it gives us at least reason enough to further investigate deeper into the structure of the series, thereby asking whether the inner microcosm of the Fibonacci Series might correlate with the (supposed) microcosm of the Tarot trumps. For logical and historical reasons, I will concentrate on the now-classical Tarot order of the TdM. This is justified, because, on the one hand, the first completely extant Tarot we have got to compare which has numbers on its cards is the Catelin Geofroy Tarot from 1557; and its trumps precisely exhibit this structure. On the other hand, since its order appears invariantly from the late 16th century on, the TdM might, for heuristic reasons, be used as hypothetical paradigm of the trump-structure. Furthermore, since we now believe that the TdM-order may have been developing already as early as in the late 15th century, at least in Milan (as evident by the Cary Sheet), the connection between the Fibonacci numbers as revivified at the end of the 15th century and the Tarot as developing at the same time and place, their “interaction” may be more than just possible.

In order to delve deeper into the microcosm of the Fibonacci series, we will first relate the range of the natural numbers, over which it extends, to the trump-order of the Tarot. When we reduce the trumps to their position in their series of numbers, these are the positions of the Fibonacci-numbers in the continuum of the series of natural numbers as representing the trumps:

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 0

The 21 trumps are counted 1 to 21 and the Fool as 0. Since historically the position of the Fool - from a certain point in time - was given the first (0) or last (22) place in the trump-series with the Steele Sermon situating the Fool last in the described series of trumps (after the World), the Fool can be interpreted as somehow “surrounding” the numbers 1 to 21—being their ignition or their final end. Now, consider the trumps matching with Fibonacci-numbers, highlighted by this fusion (in the TdM order): Matto (0), Bagatto (1), Papess (2), Empress (3), Pope (5), Justice (8), Death (13), and World (21). What a curious, but highly intelligible series!

In the first place, Matto and Bagatto are of the utmost essence of the mystery of the symbolism of the Tarot (which cannot be explained sufficiently in this essay): They not only state the lowest incarnation of (Renaissance) society below the non-aristocratic and non-clerical hierarchies in which they, with the first five trumps (in all 15th century orders of the Tarot trumps), relate to the classical theory of the “three estates” of society. Even more appropriately, they are to be understood to express a “state” beyond all the social estates altogether: They point to figures that, in relation to any social order, were (and are) considered to represent outlaw existence, poverty, even extra-social bestiality, or more philosophically spoken: the “other” as such. To look in their eyes (psychologically) means to be confronted with the “wildness of existence” beyond social order, or more precisely: of hierarchical order determining all of one’s life (in the eye of coercive esthetic, ethical, and religious obligations of the time). In the Tarot, their presence right at the outset of the trumps seems to imply, or point us to, a statement regarding the shaky grounds on which all hierarchical society, which legitimizes itself (at least from the standpoint of their leading figures) by interpreting itself as established “from above” on Divine ground, namely as a very real structure of repression of which the Matto and the Bagatto are utterly exempt or free.

In the second place, all other trumps fused with numbers of the basic Fibonacci Sequence (with exception of the Empress) astonishingly represent—almost in painful difference to the two initial outlaws—highly religious figures and events either of the religious hierarchy on earth (Papess and Pope) or finally issuing into the eschatological layer of the Tarot (Death and New Jerusalem). The presence of the Empress in this context may well exhibit utopia, since a ruling female, especially at the highest level of the Empire, was virtually absent in the time of the development of the Tarot. Justice, on the other hand, not only sends a signal to the society of which we become aware in the Tarot (and as the most important virtue ideally controlling the aberrations of the freedom of the ruling class), but also to the realization of utopia in (Christian) eschatology. This fits with Michael Dummett’s type of trump-order, the “B-Order” of Florence and Southern Italy, where Justice was elevated to the penultimate position in the trump-order right between Judgment and World to represent the Last Judgment and its measure.

Altogether this first layout of the Fibonacci numbers presents us with a selection of trumps that seems to state the borders of human life—beyond society, be it at lowest or highest place—where Chaos and Deus lurk in; or they point to a limit that seems to be able to remind us of the finite competence of all orders in light of chaos and utopia. In terms of the TdM-iconography, this is the tension between Sophia, the female Wisdom visible on the World-card, and Death, the ultimate existential finality. Both manifest the extremes (the outside) between which we “organize” our lives, but by which we are also warned to reside in its “little happiness,” blinded for its finiteness and finality.

Another important element must be mentioned to more firmly establish a substantial relation of the trump-structure to the Fibonacci Sequence as exhibiting Divine Proportion. This second application is justified by the “otherness” that the Fibonacci series offers us to recognize as its intrinsic element when fused with the trump-series. We can materialize this second element by viewing the Fibonacci series as a Divine series, not just applied “from below,” from Chaos, but “from above,” from Deus. So, we will invert its order in relation to the trumps, thereby applying it “from above.” This is compatible to our knowledge from some of the early known orderings of the Tarot as documented in the early 16th century, e.g., some of the tarocchi appropriati, which, in fact, counted the trumps “from above” down. This habit was taken up by the early occultists, who were guided by their preoccupation with Divine matters in their interpretation of the trumps (rightly, as I think). The series, then, will also “begin” with the Fool (0) being the “last” element after the Word (21) as, e.g., in the Steele Sermon. In this inverted order “from above” the layout is this:

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 0

In viewing this second application, we encounter the strange fact that not only the weighing of the numbers changed up to the last, eschatological section of the trumps, highlighting the aim of the first application, but that again Matto (0) and Bagatto (1) are part of the group of trumps selected. Instead of Death (13), we are now confronted with Time (9) in early Tarots, or the Hermit (9) in the TdM, another existential, human condition, or a religious figure, respectively. Instead of the virtue of Justice (8), we are now pointed to the virtue of Temperance (14); and instead of any further social estates (1 to 5), on which the first application heavily relied, we now are ordered to listen to cosmological estates (17 to 21) and their even more eschatological language—Star (17), Sun (19), Judgment (20), and, again, as in the first application, the World (21).

When we now fuse the two series, the first and the second application, a very specific pattern is forming. But in order to appreciate this pattern, we must sidestep for a moment and explain an interesting feature of the TdM-order of the trumps, namely its 3x7-structure (as mentioned in the first section). When we lay out the 3x7-pattern, we realize a rhythm of 7 series of 3 trumps, thereby posing every third trump into the same series, which then produces by itself 3 series of 7 related trumps: the first series being 1, 4, 7, 10, 13, 16, 19; the second series being 2, 5, 8, 11, 14, 17, 20; and the third series being 3, 6, 9, 12, 15, 18, 21. Interestingly, the second or middle series of seven trumps obviously is based on one of the major features of the architecture of the TdM, the regular distribution of the three virtues—Justice (8), Force (11), and Temperance (14). When we extend this series in both directions, it includes all the other religious figures, present in the trump-series: Papess (2), Pope (5), Star (17), and Judgment (20). So, it may be called the “religious series.” It is precisely this “religious series” of trumps that we encounter either in the first or in the second application of the Fibonacci Sequence to the trumps: the first two (Papess and Pope) and Justice in the first application; the second two (Star and World) and Temperance in the second application. Two intimately related figures change: Time/Hermit and Death; but both either represent finitude and the end of human life on earth or, in the religious interpretation of the Hermit leading a life on the verge of death and perishing, reminding society of the transitory character of this temporal word. Only two figures add color to this picture: The Empress and the Sun, in their togetherness obviously elements of a female-male-dynamics. Generally inherent in the Tarot, this dynamic perhaps represents the utopia of a female reign without repression and, in form of the male sun-god, Apollo, the utopia of clarity—altogether stating the tension between nature and reason, creativity and intellect, soul and mind, as often symbolized in the Renaissance. Nevertheless, one figure of the “religious series” of trumps is missing: the virtue of Fortitude (11). But this, as another hint, we will see later.

Indeed, if those two applications exhibit truly a “Divine proportion” hidden in human life, we might be inclined to understand the Tarot to speak deeply to us through the Fibonacci Sequence. However, far from being satisfied about this possibility, we must investigate further, seeking an even deeper relationship. What if we fuse the two applications into one structure and then again coordinate it with the numerical location of the trumps, as we have done with them separately? Interestingly, if we do so, a new pattern arises, a symmetrical pattern, exhibiting all the trumps of the separate series as elements of pairs. These pairs again seem to be borders of force-fields. Again, only the virtue of Fortitude is missing, being no border, but right in the middle of the whole number-field (a fact of significance to which I turn in a moment). These are the pairs and borders becoming visible by the fusion of the two applications:

0 1 2 3 4 5 / 6 7 8 / 9 10 11 12 13 / 14 15 16 17 18 19 20 21 / 0
0 / 1 2 3 4 5 6 7 8 / 9 10 11 12 13 / 14 15 16 / 17 18 19 20 21 0

The first pairs forming a border we can see appear between 8/9 and 13/14. If we extend this series, we also see borders between 5/6 and 16/17; and again between 0/1 and 21/0. Does this speak to us? Now, not necessarily regarding the Fibonacci-numbers, but certainly regarding the internal order of the trumps. Let’s examine these border-pairs in relation to the structuring symbology of the trumps: While 0 is isolated between 21 and 1 and, at the same time, related to both 1 and 21, respectively, it relates 1 and 21, suggesting a circle of trumps. Indeed, this feature became a substantial part of many classical Tarot-interpretations, especially, when based on some doctrine of a “creation out of chaos” as seen to be inherent in the deeper layer of the trumps. With 5/6, the sphere of social estates ends, and it begins the sphere of human conditions. Between 8, the first virtue, and 14, the last virtue in the trump-series, the human conditions circle around the theme of change and chance in human life. With the border of the pair 16/17 the last, eschatological, section of the Tarot appears, “describing” a spiritual (or cosmic) journey (of the soul, of the world) into the heavens. Taking into account the most basic analysis of the iconographic interrelations of the trumps, this over-all structure indeed mirrors the most important division of the trumps into three sections: the estates (1 to 5), the human conditions (6 to 16 or 8 to 14), and the eschatological journey (17 to 21). Furthermore, it exhibits a strong reference to their substructure: The importance of Matto and Bagatto, the isolation of the Matto, the relations between virtues (Justice, Temperance) and the finitude of the human life (Time, Death), the difference between descent into hell (Devil) and ascent (Star to World) into heaven within the eschatological section.

Now, we can go on to refine this pattern, thereby creating an intricate substructure with even more sophisticated “border-pairs.” We do so by applying the two directions of the two applications—“from below” (Chaos) and “from above” (Deus)—in two ways, generated naturally by posing the isolated 0 into two (of its classical) formulas: The Fool can be seen as related to the 21 trumps either in the form 1+21, thereby being 0, or the form 21+1, thereby being 22.

The first application “from below”, manipulated with both of the two formulas—one beginning with the Matto as 0, the other beginning with the Bagatto as 1, now exhibits the following reassuring structure with its refined “border-pairs”:

As we can see, the internal integrity of the trump-order is not only preserved, but interpreted in a way that reaffirms the threefold iconographical division of the trumps. Besides the Matto, as isolated element (in either of the two formulas), we realize the first 5 trumps of the social estates as first part; then two sections within the second part relating to the human conditions (6 to 8 and 9 to 13); finally a long section exhibiting the eschatological part of the trumps (14 to 21).

By using the same procedure for the second application “from above,” namely beginning one series with the World (21) and the other with the “high” Fool (22), we gain the impression that the same structure that appeared in the first application is also true for this second one:

In contrast to the first application, here, the borders shift in a very sophisticated way: While the Matto still is isolated, the first section extends up to the appearance of the first virtue, Justice, relating the human estates, Love (6) and the Triumph (7) to Justice (8). The second section is identical with the core section of human change and chance of the first application. But the eschatological section now becomes a divided area of two subsections, a short one that symbolizes “descent into hell” (14 to 16) and a second one that manifests “ascent into heaven” (17 to 21).

Altogether the application of the Fibonacci numbers to the position of the trumps exhibits a symmetrical structure that not only seems “natural” to the microcosm of the trumps, but, more importantly in this context, also exhibits “naturally” the iconographic contents that builds the microcosm of the Tarot trumps. This is the final pattern when we put together the two “border-series” of the two applications “from below” and “from above”:

The final, fused series of border-pairs structures the trumps into five substantial sections—and, as any interpretation must account for, the Matto. Those five sections relate to one another by a built-in, overlapping symmetry of three main parts (congruent with the main division of the trumps). The first section (of social estates) can extend from 5 to 5+3 trumps (1 to 5 and 6 to 8). The second section (of human conditions) can begin with 3+5 cards (6 to 8 and 9 to 13), or it extends to a 3+5+3 trumps (6 to 8, 9 to 13, and 14 to 16). The third section (of cosmological or eschatological estates) may begin with 3+5 trumps (14 to 16 and 17 to 21), or contracts to just the last five trumps (17 to 21). The overall symmetry is amazing; it represents the Fibonacci-numbers and a very rigid pattern of substructures of trumps.

Together, by “mirroring” the first and the second application, the numbers (of numbers or cards, respectively, forming a section) are:

→[1] 5 3 5 8 [1]
     [1] 8 5 3 5 [1] ←

Hereby, we get a beautifully symmetrical structure consisting of Fibonacci numbers and exhibiting an amazing 'speaking' structure of trumps as intimately related to their iconographic contents and internal relations. In this comparison, the trump-series reveals itself as a microcosm that is related by Divine numbers and Divine proportions. Their fused formula, again, can be described by this overall Divine series:

→ [1] 5 3 5 3 5 [1] ←

In light of the match of numbers, structures, and contents, and given the revealing effect with regard to the trump-symbolism, we might now be inclined to suppose that this is the original structure of the trumps! The subsections of the trumps, indeed, consist of the first eight Fibonacci-numbers, breaking down 21(+1) into groups of eight, five and three elements respectively. Other than classical divisions of the trumps such as the one by Jungian interpreters into two parts, or that of occultist such as Papus and historians such as R. O’Neill into 3x7 or 7x3 parts, or other non-symmetrical structures, nevertheless exhibiting three parts as in M. Hurst, this structure of the “Divine proportion” is both more flexible and symmetrical at the same time, because it allows for shifting combinations of its Fibonacci elements into one another. We may look at the whole series as consisting either of 8+8+5 elements, or 5+8+8 elements, or even 5+13+5 elements.

To take another step in this analysis, let us more closely examine this overall structure of 5+3+5+3+5 numbers and cards. What it reveals, when we go on to further break it down into its basic Fibonacci numbers, is as symmetrically easy as it is internally sophisticated in relation to the symbology of the trump-series. Heretofore, we divide the five “visible parts” which combine 3 and 5 (or even 8) cards, respectively, into the most basic three Fibonacci numbers from which they arise, namely one, two and three. The microcosm of the five parts, then, exhibits this “Divine proportion” (presented here in two grades of primitive subdivision):

[1] (2 3) (3) (2 1 2) (3) (3 2) [1]
[1] ((1+1) (2+1)) (2+1) (2+1+2) (1+2) ((1+2) (1+1)) [1]

As we can see, at this most basic level of the “Divine proportion,” hidden and obvious relations of the trumps as known by iconographic analysis reveal their existence or gain justification. At this point of discussion, I will only highlight two important aspects: on the one hand, the borders and relations of the substructure of the trumps in the TdM-order, and on the other hand, the structural position of the hitherto missing Force (11).

Regarding the first aspect, the final substructure of the trumps, as mirrored by the Fibonacci microcosm, becomes obvious when we highlight its embedded “border-pairs.” This, then, is the refined structure, based on the three basic Fibonacci numbers:

0 /// 1 / 2 // 3 4 5 /// 6 7 8 /// 9 10 / 11 / 12 13 /// 14 15 16 /// 17 18 19 // 20 / 21 /// 0

The major five parts (divided at ///) internally divide into, and relate through, sections (//) and (their) subsections (/). Regarding the first major part (1 to 5), we can confirm with the historians that the first five trumps add to a “unity” of social estates; with the occultists, however, we can appreciate that the Magician and the High Priestess form a subsection on their own (rather than relating Papess and Pope, as historical analysis favors). Empress, Emperor and Pope, on the other hand, form their own subsection, too. After this first major part, a first intermezzo occurs (6 to 8), relating Love, Triumph and Justice; it corresponds with a second intermezzo (14 to 16), consisting of Temperance, Devil and Tower. The first intermezzo connects human estates with human conditions of change and chance; the second intermezzo connects human conditions of finality to eschatological finality. The last major part of 5 cards (17 to 21) exhibit the eschatological ascent through (neo-Platonic) spheres of the cosmos to God, or Christ, or the New Jerusalem, or the World-Soul, respectively (depending on the Tarot’s iconography we use). Within this eschatological part, however, we can sense another division between a section of the spheres (Star, Moon, and Sun), which form a “natural” unity, and the two subsections, consisting of the symbols of finality: Judgment/Resurrection and World/Christ/Soul, respectively.

A last mystery, namely that of the missing Force (11), now becomes an important cornerstone in this interpretation of an overall symmetrical structure exhibited by the Fibonacci order as related to the trumps: It is missing because it never appears at any border forming a division of the force-field. Instead, it only, but precisely, is situated right in the middle of the whole structure; it is its center. Guarded by this observation, a final symmetry at the most basic level of the Fibonacci-structure of the trumps rises to the surface, thereby really manifesting the “Divine proportion” of the trumps:

[1] 1+1, 2+1, 2+1, 2 ← 1 → 2, 1+2, 1+2, 1+1 [1]

In this most basic “centrifugal division” of the “field of trumps” a pattern becomes obvious that by its structurally symmetrical microcosm may really “explain” even some of the strangest idiosyncrasies of the TdM-order in an almost “natural” manner. Heretofore, we finally arrange the trumps in a way so that it exhibits this “Divine proportion” (in its centrifugal division) we found inherent in the application of the Fibonacci Sequence to the trumps:

What do we see? First, we realize symmetry of mirrored pairs of trumps: Magician and Papess mirror Angel and World; Empress and Emperor mirror Moon and Sun; Love and Triumph mirror Devil and Tower; Hermit and Fortuna mirror Hanged Man and Death. Further, we realize the exposed position of the “religious series” of trumps—from Papess and Pope, the three Virtues, to Star and Judgment—all being elements of a symmetrical division into subsections. Furthermore, we recognize the symmetrical order in relation to gender. And all of this appears as an expression of the inner symmetry of a Fibonacci-structure as related to the trump-series.

We might further ask whether some of the more exquisite extravagances of the occult interpretations might have got a basis in the peculiarity of this structure: Think, for example, of the interchange of Force and Justice: Although historically based on astrological equivalences when applied through one of its Kabbalistic systems (as in Crowley’s interpretation of Waite’s move), we may now see it as a (somehow justified) “correction” in light of the symmetry in which we may suspect a center to symbolize a “symmetrical mirror”—which is, indeed, a characteristic of the occult interpretation of Justice understood as Equilibrium. Further, we may allow for an extraordinary relation between Star and Pope (who often in occult Tarots is symbolized by his position to represent a five-pointed star); but we must deny an exchange of it with the Emperor, as Crowley has indicated (on the same astrological grounds as the exchange of position 8 and 11).

Given these new symmetrical relations, we might also be reassured of the widespread opinion (not only held by occult interpreters, but also by important historians) that the iconography and symbolism of the Tarot trumps may well allow for a deeper, philosophical interpretation, because they seem to be inherently related to Renaissance cosmology. The series of trumps may well represent levels of reality or existence with their (symbolic) correspondences to one another. Emperor and Empress, as highest social ranks, and both male and female, then, may correlate with the male and female principles of “gods” and “goddesses,” populating the higher plains, as symbolized by Moon and Sun. Or consider the strong relation of Hermit/Time and Death as well as the turnabout of the Wheel of Fortune and the turnaround of the Hanged Man. Even more paradoxically, we can establish a “mirror of plains” by the antithesis of Love and Tower, or Triumph and Devil (especially in the TdM form and the occult versions, following Levi’s famous and effective drawing of the Devil). We may begin to appreciate the justification of the occult “correspondence” of the symbology between the Magician and the World: while the TdM integrates the “four elements” into the quintessential World-card, the occult Tarot mirrors these in the Magician by his manipulation of the four elements. Thereby, the Magician becomes in persona what the quintessence is on the highest plane of existence. Finally, if the Angel reveals the truth that the Papess hides, this would be a late justification of the transfiguration of the Papess into Waite’s High Priestess.

With the application of the Fibonacci structure, the trumps begin to speak of a “Divine proportion.” If we accept this interpretation because of the intrinsic synergies that have been unearthed by the experiment we have gone through, we might now be open to at least consider the possibility of a real influence of the Fibonacci numbers on the Tarot. As has been laid out in the first section, this thesis does not include the proposition that the Fibonacci series exposes the “original structure” of the Tarot trumps, but rather declares it to be a possible element in the process by which the major elements of the final Tarot structure -imaginary, function, and numbers - came together. Therefore, as to further substantiate this claim, we are forced back to investigate the historical perspective (as was mentioned in the beginning of this section) by asking whether this transfiguration of the Tarot in light of the application of the Fibonacci Sequence could have happened in the period in which the culmination of a final constitution of the trump-series of the Tarot must historically be situated: in Renaissance Italy towards the end of the 15th century.

Historical Approximations

When Luca Pacioli revived Fibonacci’s ideas, drawing from it his conception of the Divine Proportion, we find ourselves at the right time and place: at the end of the 15th century, in Renaissance Italy at the courts of Venice, Milan, Mantua, and Ferrara—all of them being places where historical record suggests Tarot developed and flourished, finally beginning to form its now-classical gestalt. Pacioli worked on some of the same features of Fibonacci’s mathematics that are suggested to have played an important role in the formation of the Tarot. For the first part, there is the number 0, which with Fibonacci’s discussions became a pre-condition for the development of modern mathematics, and which also played a major role in the “positioning” or “outside”-placement of the Tarot’s Fool among the trumps. He was considered “zero” in the game; he was named “nulla” in the Steele Sermon from about 1470; and, later, he earned the number 0. In the second place—and most importantly—Fibonacci has given us an instrument in terms of which later mathematicians, like Luca Pacioli, and artists, like Leonardo da Vinci, began to explore the internal proportions of nature and mind. The mystery they were thinking about and experimenting with in science and art was a relation called the Divine Proportion. And, if not by this “Divine proportion,” at least the quest to understand the (physical, metaphysical and religious) world-order by its proportions and harmonies became an essential part of the construction and message of the Tarot trumps.

Since the Fibonacci-thesis does not pretend to explore the aboriginal order of the Tarot trumps, which rather may have been based on a 5x14- or 5x16-pattern, it has cleared the horizon for this question: What “catalyzer” would be able to integrate the obviously independent development of the Tarot’s three “formative elements”—the trump-image, its order, and its quantity—at a given time when they really appeared together in history, namely the time from about 1470 on? More concretely: Could the Fibonacci series, in its basic incarnation of the first eight numbers and their intrinsic structure (as analyzed in part three) historically be a possible candidate for this unification? With Pacioli at hand, his exploration of the Divine Proportion, indeed, appears at the right time—before 1500—and at the right place—Milan and other Northern Italian cities. Furthermore, the Divine Proportion, as explored right in this time by Pacioli and some of his friends, as, e.g., Leonardo da Vinci, was considered to be of basic cosmological importance so as to be of “natural” interest for subsequent developers of the Tarot. Incidentally, right at that time may have begun the formation of the later-classical TdM-order for which (as has been demonstrated) the Divine Proportion based on the Fibonacci Sequence can be shown to smoothly “explain” the togetherness of the structural elements of the trumps.

As a matter of fact, historically we find very intricate connections between persons, their professions, their social and intellectual intercourse, and the places at which they were working, to relate this “cultural force-field” to that of the creation of Tarot. In their combination, these “coincidences” point to a possible intersection of their circles: the circles in which the rediscovery of the Divine Proportion by Pacioli can be assumed to have been discussed and applied, and the circles in which the Tarot might have been developed especially around and after 1470. Such an interconnection of circles is far from being out of hand when we acknowledge that the intellectuals of the Renaissance, as, e.g., Pacioli and da Vinci, were part of the same new, fluent, urban class of merchants, artists, craftsman, and free entrepreneurs who, between the aristocratic courts and the countryside population, were also the social and cultural “sphere” for the development of the Tarot. In the late 15th century, this new “urban class” (as a whole) gained considerable wealth, being able to send their children to universities as well as being financially potent enough to commission art of every kind and at any level. This new “urban network” also had the resources to prepare for that kind of “creative space” which not only allowed for free time and interest in the game of Tarot, at the time widely played, but also could further an understanding of the Tarot as a sophisticated instrument by which one could “read” the Divine nature of the cosmos. As did the Tarot, so did mathematics proliferate in this new “urban space” between market place and court, free economy and university, intellectual studies of the universe and games. This was the “sociosphere” of Luca Pacioli. His life, his mathematics, and his rediscovery of Fibonacci, will be the subject of a first examination of possible historical connections between the Fibonacci series and the trump-series:

In reviewing Pacioli’s lifetime, we immediately recognize many of the persons, locations, and incidences, which were involved not only in his life, but also exhibit probable connections to the emergence of the Tarot. In a second examination, therefore, we will find reasons to believe that the Fibonacci-code as rediscovered by Pacioli and the Tarot do, indeed, exhibit a common creative space that is more than accidental.

The Vitruvian Man

In light of the historical approximations to a common social force-field for the developments in mathematics as well as the enjoyment of the Tarot, and in light of the appearance of the mysterious number 22 in the Tarot in this context, we may now — in a more speculative manner — gather further arguments for interconnections between the Fibonacci Sequence on the one hand, and the evolution of the Tarot as related to the urban setting of the late 15th century in Northern Italy on the other.

(1) If we understand the trumps as a manifestation of a kind of neo-Platonic universe of hierarchical spheres that reveal the alleged structure of the universe — as many interpreters have suggested, and increasingly so on historical reasons rather than iconographic deductions — the Divine Proportion does seem to be a veritable choice for the affirmation for the presence of the already lingering cosmological horizon visible in the Tarot. It springs from the neo-Platonic contention that the universe can be understood as a harmony of numbers, relations, and proportions. Like the neo-Platonic world-view with its basically magical background of all-interconnectedness, mathematics does not only explain proportions, but it describes similarities. Through proportion everything in the universe is connected in essential similarity so that the universe of levels and spheres of existence mirrors lower and higher levels into one another.

When we apply this “world of harmonious similarities” to the trump-order, we see the same principles at work in the ascent from the Fool to the World. If the Fibonacci-numbers were part of the “harmonies,” we may expect that its cosmological value is both intimately connected with the numbers it exhibits for itself and to the numerical structure of the trumps as representing this “harmonious cosmos.” Then, more than incidentally, they form a unity. If the Fibonacci-numbers reveal a Divine proportion of all things related in the universe, they really speak of God and the World, the fundamental order of creation we encounter in God’s “structural” presence, or even more delicate, the Mind of God as presented by the natural order of numbers, proportions, and analogies.

In fact, the Tarot, in the second half of the 15th century, was understood as being concerned with matters of Divinity. Besides the iconographic evidence, my best historical witness for this contention is the 1449-letter of Jacopo Marcello that accompanied several packs of trionfi for Queen of Isabella of Lorraine in France. If, for a moment, we do not look at the “new kind” of Tarot he was offering the Queen by sending her the newly recovered Michelino-deck (which really has no similarities in contents with standard Tarot-imaginary), but instead listen to what he has to say about another “ordinary” deck of Tarots he also included in his package, the connection becomes clear. He writes:

By some chance the conversation turned to this game, which is called “Triumph”, certain cards that had been offered to me and which I give as they were given. When Scipio had seen them, being a thoughtful and diligent man, he said your Majesty would be very much pleased by them: and he urged exceedingly and immediately that they should be sent to you at the first opportunity. Thus indeed he affirmed that with them you might give considerations to divine things, as such great things are the business of royalty.

In their conversation, so recalls the writer, Scipio and Marcello thought that this game of “Triumph” might be fitting the Queen, because through it she might give consideration to Divine things. Indeed, that is what the Divine Proportion is about: it gives consideration to Divine things.

(2) When Pacioli published his Divina proportione, he also wrote a small book on the ancient Roman architect Vitruvius in whom he was interested because of his conceptualization of sacred buildings in relation to the proportion of the human body. As with the other book, the Summa, Leonardo da Vinci drew sketches to the text of Pacioli, one of which depicts the universal proportions of the human body suggested by Vitruvius. This drawing is the Universal Man or, now more famously called, the Vitruvian Man. Although we do not know whether the Vitruvian Man exhibits the Divine Proportion by accident or whether it was built in deliberately, as a common work of Pacioli and da Vinci it reveals the proportions of the human body in relation to some Divine proportion that, regarding Vitruvius, governs the universe, architecture, and the human body.

Given the suggestive iconography of the Tarot trumps, we may now also consider them to have been readily interpreted as manifestation of the Universal Man. This may be evidenced by the inherent process of approximation of the human soul to the Soul of the World as exhibited by the series of the trumps with its three progressive parts of social, existential, and cosmological (or eschatological) layers. We might be inclined to see this similarities of content to happen because of the same related circles of neo-Platonic humanists, who were interested in the re-creation of old symbol-systems in light of their humanism. It should not be a surprise to us that they could see the trump-order to be the instantiation of a universal analogy as it manifests in the analogical proportions of microcosm (man) and macrocosm (universe). There is indeed a direct hint for this contention, i.e., that the interpreter of the trumps in the late 15th century, indeed, saw this analogy. What other sense would it make to read in the Steele Sermon (as quoted in the first part) that the Chariot is to be considered a mundus parvus — a microcosm, which it is only in analogy to the mundus itself, the World as macrocosm. (Here, we may even consider the position of the Chariot and of the World in the trump-series to mirror the presence of the holy numbers 3 and 7, because the mundus parvus as 7 could easily be seen to be numerologically related to the mundus as 21, itself being 3x7).

(3) One of the more interesting features of the Fibonacci Sequence, able to demonstrate the analogy of microcosm and macrocosm, is the fact that the limit of the ratio of all of its consequent members of the series converges to the Golden Ratio (as has been demonstrated in part two). This ratio, however, is intimately related to the number 5 — since 5 = (2Φ — 1)2. It is also the only of the first 8 Fibonacci-numbers (other than 1), generating the 21 trumps, that is identical with itself, because 5 is the fifth Fibonacci-number. Mathematically, the number 5 was understood to be of universal relevance as, e.g., symbolized by the pentagram in which to every length can be found another segment in the proportion of the Golden Ratio. Metaphysically, the number 5 in the form of the pentagram was the most important symbol of the Pythagoreans, standing for the Universal Man in relation to the Universe. And it was the pentagram of which the Pythagoreans realized that (some of) its proportions could not be stated as an integer or, for that matter, as a ratio of integers. Indeed, the Golden Ratio is an irrational number. (This insight was held under arcane discipline until one of them revealed this shocking fact to the public for which he had to die.) Anthropologically, it became a symbol for the human body as mundus parvus in its relation to the Universe. And theologically (in the Order of Sin and Salvation), it was considered to represent the Five Wounds of Christ. (It is here that we find the relation to the Franciscans who with St. Francis had the first holy man documented to have had stigmata. After 1470, Pacioli became one of them.)

With the 5 essentially inscribed into the Fibonacci Sequence as expression of the Golden Ratio, it is now possible to understand that it was possible for artists with Renaissance-education to install a connection of it not just to the Universal Man, who in ancient and medieval numerology generally was symbolized by the number 5, but, furthermore, with the quintessence of the Universe, the Divine element that holds together the 4 basic elements water, fire, air, and earth. In the Vitruvian Man this is not only suggested by the defining characteristic of the human body with its 4 extremities and the head (being 5), but, on a higher level, we find it to be demonstrated by the presence of the mystical mathematics of the Pythagoreans: When da Vinci circumscribed the Universal Man with both a square and a circle, he signified the microcosm of the human body to symbolize the four elements and the Divine principle or the quintessence — both in their most harmonious proportions. While the universe is symbolized by the rectangle and the 4 extremities, its quintessence is symbolized by the perfection of the circle and the human head as expression of the World-Soul. In their combination, they express the hidden “form” of the “cosmos” — which for the ancients (and from there on) signifies the structural beauty of the universe.

It is almost of indispensable suggestiveness to suppose the same structure to be realized in the emergent Tarot: In recalling the application of Fibonacci-numbers to the trump-series (as has been analyzed in part three), we will immediately realize the importance the number 5 plays in the rhythm of trumps either consisting of 5 parts (5-3-5-3-5) of either 3 or 5 numbers/elements/cards (the numerological significance of which will be discussed soon). The most basic visibility of the 5 in the Tarot, however, is its presence in the Tarot-structure as such. Indeed, it makes its inevitable structural presence in the essential fact that the series of trumps is one of 5 suits, or the fifth suit itself, respectively.

Although we do not possess a real hint as to the identification of the 4 suits with the four elements until the book La Signification de l’ancien jeu des chartes pythagorique by Gosselin from about 1580 (there exemplified on a 52-card French-suited deck), we may assume that the development for allegorical identifications began rather early — at least in relation to the game played with the trumps. In the first place, allegory is implanted into the trumps, be it existential like the Death, religious like the Angel, or moral like the three virtues Force, Justice and Temperance. For the early years of the 16th century, we know of an intense interest in the allegorical density of card games as evidenced by the educational interpretations of the Franciscan monk Thomas Murner (1502) or the games mentioned in the Rosselli Inventory, a catalogue of Francesco Rosselli that lists games like “The game of the triumph of Petrarch”; “the game of Apostles with our Lord”; “the game of seven virtues”; or “the game of planets with their borders.” We also know of social interpretations of the “trumps” of Karnöffel—a game intimately related to the Tarot—by Bishop Johann Geiler of Kaiserberg, Germany, in 1515. And we know of the emerging Florentine Minchiate, which adds the 4 elements and the zodiac, as well as of Innocentio Ringhieri’s allegories of the 4 suits, which he in his book Cento Giuochi liberali dt d’ingegno (Bolognia, 1551) takes to represent the 4 virtues (Cups for Temperance, Columns for Strength, Swords for Justice, and Mirrors for Prudence).

The most intricate hint, however, is given by the emerging TdM-iconography, which can be traced back to a 1499 TdM-style Two of Coins, recovered from Sforza Castle, and the Cary Sheet from about 1500. Especially with this highest card of the trump-series, we see the drive of the series of trumps aiming at the World. It differs significantly from the earlier Visconti-Sforza Tarots by directly representing the allegory of the Universal Man in form of either the World-Soul (or Wisdom) with the 4 elements in form of the fixed signs of the zodiac (Man, Lion, Eagle, Bull) in its corners, or, put religiously, of Christ with the 4 Evangelists. Since it arose at the same time, around 1500, and at the same place, Milan, where Fibonacci’s “mathematical miracle” was revived by Luca Pacioli, and presumably within the same circles, we may think of a deliberate introduction of the TdM-symbology as caused by a new cosmological interpretation of the Tarot in the wake of which also the number 22 was introduced as expressive of the Divine Proportion in the order of nature (in its Renaissance-interpretation as analogy between microcosm and macrocosm).

(4) The specific relation of the Fibonacci Sequence in relation to the Divine Proportion underlines the probability of the deliberate integration of the Divine Proportion to the Tarot—namely its form as a series of numbers. Indeed, when we ask how a process as that of the transformation of the soul (the moral or spiritual aspect) — which often is interpreted as the “Fool’s journey” to wisdom — could, if at all, be represented by a static “proportion” or “ratio,” the only way immediately fitting the representation of a process as a series of events (physically symbolized by cards) may be a series of numbers. In not being an accidental assemblage, but a complex microcosm structured by the Divine Proportion, the most natural way of “saying” that this series of cards is the process of the transformative becoming the Universal Man (in approximation to the quintessence) is to symbolize the quintessence of the process as a serial structure.

While we can assume that at the beginning of the 16th century (if not much earlier) the 4 suits where identified with the 4 elements, the trumps most naturally would have to be regarded to represent the quintessential element in the cosmos, or the World-Soul as depicted in the TdM. Since the Fibonacci Sequence precisely is this incarnation of the Divine Proportion as a series, the trump-series as “fifth suit” becomes this “quintessential series.” Furthermore, if the Fibonacci Sequence plays this role in this formative process, it is also most natural to assume that at the end of the 15th century the cosmic number 22, or, for that matter, 21 (and a “zero”), came into this cosmological reinterpretation of the Tarot. Symbolized by a “fifth suit” of serial Divine proportions, it becomes a mirror between microcosm and macrocosm.

(5) Because of the universal cosmological relevance of the Fibonacci Sequence, we should also be able to find the numbers and proportions otherwise recognized basic for the structuring of the trumps to be expressed by the “serial Divine proportions.” Besides the relevance of the number 5 for the overall structure of the Tarot, the trumps being the quintessential suit, his must especially be true for such numerological “entities” as the 3x7- or 7x3-structure, which is of utmost importance in the classical interpretation of the trump-series. In their combination they represent the two ancient holy numbers known to the Renaissance mind. Although (as we have already seen) the number 7 does not play any significant role in the Fibonacci Sequence, namely as a Fibonacci-number, nevertheless is the sum of the first 4 Fibonacci-numbers 1+1+2+3. Interestingly, the other holy number 3 is the fourth Fibonacci-number. Both holy numbers obviously are connected to the number 4, so to say, which again, in the Fibonacci-sequence, is the sum of the first 3 numbers. But even if we consider these “coincidences” as irrelevant for the structuring-effect of the two holy numbers, we can demonstrate that the basic 5-3-5-3-5-pattern of the Fibonacci-ordering of the trumps allows for a reconstruction of the 3x7-rhythm, since it appears to be a “reformulation” of the basic 1+1, 2+1, 2+1, 2 ← 1 → 2, 1+2, 1+2, 1+1-symmetry of the Fibonacci series when applied to the trumps. All 3 series of 7 cards, emerging from the 7x3-rythm of their ordering, are to be found in the Fibonacci-symmetry, when we consider the second, the “religious” series (as was referred to in part three), to be its axis around the ideal middle term Fortitude (11). Then, the Fibonacci-sequence really can reconstruct the 7x3-rhythm:

1+1(2), 2+1(5), 2+1(8), 2 ← 1(11) → 2, 1(14)+2, 1(17)+2, 1(20)+1

Furthermore, the number 3, together with the number 5, is a basic building element of the trump-structure, when laid out in a Fibonacci-pattern. It is evident that both cling together in the symbology of the time by representing the allegory of the Divine (3) and the universal human (5), or the Trinity and the World-Soul. This cosmological scheme is virtually all-present in articulations of the neo-Platonic lay-out of the cosmos in a Christian context; and so we may suppose that this has not been overlooked in the numerological application of the Fibonacci series as expression of the Divine Proportion in the Tarot.

As to the higher numbers 8, 13, and 21 of the Fibonacci Sequence when applied to the Tarot, we realize their immediate relevance by referring to the cards they represent. 8 is the number of Justice, but also the number of Christ, of the Resurrection on the “eighth day,” indicating the New Creation, which than most conclusively can be found on the Star, either as eight-pointed star (as in many Tarots of the TdM-type) or as 8 stars (as in the Nicolas Conver Tarot). Through the Star, there is also an intimate relation between 8 and 5 because sometimes the stars are five-pointed or we only find 5 eight-pointed stars, as in the Cary Sheet.) If we count 5 down from the top of the series, we reach this Star. If we, however, count 8 down, however, we reach 13, the invariable number and position of Death — a counter-part of the 8 of the Star, or Christ, with the 5 of the Universal Man. 21 of course, the combination of 8+13, is either Death defeated by Christ or Eternity incarnated in finitude, the World-Soul, or Christ, as the resurrected Universal Man. All Fibonacci-numbers fit harmoniously when expressing Renaissance cosmology.

(6) When seen in relation to Fibonacci’s original problem, the structuring element of the Fibonacci Sequence that initiates its sequential growth becomes obvious in its relevance to the trumps. What gave birth to the series in the first place was the problem of the mating of two rabbits (1+1). In other words, the genetic force of the series is of sexual nature; the production of the series is the sexual interaction of a female and a male creating a “family-tree” of generations that (approximately) express the Divine Proportion. Indeed, in Alchemical (and Kabbalistic) circles the aim of the World-Soul was understood as (female) Wisdom “mating” with God so that the Universal Man expresses either an androgynous or a sexually uniting process that is equated with ecstatic bliss. At least in the final TdM-iconography, the interplay of female and male elements as well as their interfusion is a central message of the pictures.

So, we find the explicit presence of a female/male-symmetry in the archetypical pairs Empress/Emperor and Moon/Sun, or the highly paradoxical symmetry of Papess/Pope (since, in reality, there is no Papess). The female Virtues Justice, Force, and Temperance are counterbalanced by the “male vices” of the Traitor, Death, and Devil. Love and Victory imply the antagonism of Venus and Mars, as do the possibly heretical accounts of the duality of Bagatto and Papess (especially in the form of the occult antagonism of Magician and High Priestess as the archetypical female/male-pair). We find sexual interfusion in the Temperance, which not without good reasons was reinterpreted later as Alchemy, and, of course, the androgynous figure in the World, sometimes changing gender, sometimes hiding it. In any case, the generating energy of the first two Fibonacci-numbers 1+1 is an exceptional feature allowing us to see the application of the Fibonacci Sequence in accordance with the symbology and iconography of the trumps — at least from the time of the formation of the TdM on.

(7) Another feature substantiating the claim of the inclusion of the Fibonacci Sequence in the Tarot, especially in the TdM-versions of it, is the fact that we can find basic Fibonacci-numbers that, while representing geometrical and proportional properties in the arts, are also present in some geometrical structures of the iconography of the trumps. Some of these basic geometrical figures can be found right away, some are more hidden; but once we begin to recognize them, they appear to be ubiquitous and pervasive.

Let’s begin by looking at the numbers (in its Renaissance awareness) as representing a symbolic account of the universe: 1 is Oneness; 2 is fundamental Duality, or the Initiation of a Process, or Contrast, or Generation; 3 is Fertility (think of the original problem Fibonacci wanted to solve), or Divine Perfection, or Mind; 5 is the Quintessence, or the Universal Man, or the Crucified Christ, or the Word-Soul under Material Conditions (Suffering); 8 is Divine Justice, Last Judgment, the Justified and Saved Humanity, or Christ Resurrected; 13 is Death, Finitude, Finality, Impartial Equality of Perishing, or the Condition of Sin; and 21 is the World as Cosmos, or the World-Soul as Freed from Finite Conditions, or Christ Triumphant, or the Vision of the New World.

As Fred Gettings in his The Book of Tarot (1973) has demonstrated consistently, we do find these basic numbers inscribed in the pictures of the trumps. So we may look and find Oneness as a circle; Duality as a line, or as two intersecting circles, or as an opposition of other geometrical figures; (the Divine) Mind as a triangle; Quintessence in figures like rectangles inscribed in circles, or circles with centers, or surrounded with 4 figures, or in relation to a cross (which actually is not just a 4, but through the intersection of two Dualities, and united by the Quintessence, a hidden 5!); Justice or Equilibrium by two rectangles or crosses or their combination; 13 by the combination of 8 and 5 like in stars; and 21, highly abstractly, though, as a combination of the holy numbers in the 3x7-structure.

The fact that the number 4 is not a basic, but a derivative Fibonacci-number, as is 7, does not mean that it is second rated. Remember that 4 is reconstructed by the first 3 numbers 1+1+2, which means, that it is reconstructed as a combination of the two generating principles (sexual duality) in terms of opposition. In this sense, the 4 fits the ancient meaning to represent matter. Since the pre-Socratic philosophers, matter is seen as the generation of difference and plurality by means of antagonism (Heraclites) or as a hierarchy of 4 elements of whom some were considered more basic than the others—Fire and Water being the basic opposites that, in their intercourse, generate the principles of Air and Earth. The same is true for 7—being reconstructed as combining 3, Mind, and 4, Matter. So in terms of the application of the Fibonacci series, 7 is present as the first 4 numbers 1+1+2+3, as 4 is present as the first 3 numbers.

From this starting-point, combinations are infinite. Just to name a few possibilities: If, e.g., human beings, counting as 5 (the pentagram of the human body), appear in groups of 3—as in Love, Devil, or Wheel—this is a hint of the relation of Divine Mind (3) to the Material Conditions (5). In a more subtle form, this same symbolism appears in the combination of Triangle (3) and Cross (5) as in the Emperor, the Hanged Man, and the World (in the TdM-iconography). Further differencing symbolism refines this interpretation: the scepter (Duality) and the orb (circle with cross) of the Emperor; the rectangle surrounding the Hanged Man as a sign of opposition; the circle around the dancing World-Soul as a sign of Oneness. Other than humans (representing 5), angles—as in Love, the Angel, and in the (Visconti-Sforza) World, would count as 7 (=5+2), because in addition to their five extremities they incorporate the sign of holy beings, the two wings. The 8 of mirroring micro- and macrocosm appears in the Chariot, consisting of two rectangles (4+4), a heavenly, and an earthly one, but also as judging 8 more subtle appears in the combination of 3 humans beings, signifying the 5, in the Love-card, symbolizing Decision under a Holy Being. This, again, is also true for the Angel, depicting a Divine Judgment—which, in both cases, incidentally, adds up to 22 (as [3x5]+7)—but this may already be to far-fetched a speculation.

(8) Of the projected Fibonacci-structure of the trump-series, one feature has so far been omitted for explanation, namely the “missing” number 11. Regarding our analysis of the basic symmetry of the Fibonacci-code (1+1, 2+1, 2+1, 2ß1à2, 1+2, 1+2, 1+1), it should count as a central feature of the trump-structure since it is the center of the Fibonacci-symmetry. Its ancient appeal is that of a dangerous number: Isn’t it the number of Apostles minus Judas? Isn’t it in the Kabbalistic Tree of Life the “non-sephira” Da’at, the abyss between the supernal 3 sephirot and the other creational 7, and also a door to the dark side, the k’lipoth? Isn’t it the one law too much, beyond the Ten Commandments; the origination of sin? Nevertheless, after the analysis of the two reconstructed numbers 4 and 7, we gain another picture of the number 11 when we realize that it is the composition of both numbers: 4+7=11. So, as is true for 4 and 7, the number 11 is only reconstructed. This corresponds with the fact that, although it is the center of the symmetry of the Fibonacci-structure, it is in fact virtually invisible, that is, it makes only sense as hidden center, as an utmost integrating element. And indeed, it never appears at any “border” of Fibonacci-substructures, generating a subsection. Rather it signifies the only number that never appears as any border of a subsection. While, in the first place, it becomes visible as the center of the central five trumps; in the second place, it “disappears” in the center of the whole symmetry, thereby signifying its invisible wholeness. Hence, the number 11 does not appear as the dividing center of the mysterious number 22, but as uniting center of 21, the trump-series, as 10+1+10!

While, as later in the Waite-like Tarots, the exchange of Fortitude and Justice may appear justified on the superficial condition that 11 suggests to be a “deciding center,” a Judgment, an Equilibrium (of symmetry), in deeper consideration Fortitude fits much better in being a symbol of unity and wholeness. While Justice is dividing, Fortitude, in its ancient meaning of being a Virtue of integrated diverging power, or in its medieval depiction as “fighting the low instincts,” is a complex integration of opposites (Mind and Body) and, hence, an (Alchemical) symbol of Oneness amidst Oppositions. Therefore, instead of dividing the trump-series at the Wheel, namely into a group of 10 and another group of 11 trumps (both without counting the Fool), it is precisely the 11 that integrates the trumps into a perfect symmetry. This is underlined by the symmetry of the TdM-order as structured by the “religious series” of 7 trumps of which the three Virtues are the backbone — with Fortitude in their center.

If, indeed, 11 generates a perfect symmetry of 10+1+10, we may now refine the whole conception of the “mysterious number” when seen in interaction with the Fibonacci series. It primary value would not be 22, but 21! As we have seen, all elements of the Divine Proportion in form of the Fibonacci Sequence, point to the eighth Fibonacci-number 21. It is the sum of trumps, except for the Fool, which is no trump. Since the first Fibonacci-number when related to the Fool counts as 0 (as has been shown in part three), the true mathematical statement of the mysterious number “22” is not 1+21=22, but really is 0+21=21! As true Divine proportion it is able to include and reinterpret the rhythm of the two holy numbers 3+7=10 and 3x7=21. It thereby mirrors the perfect symmetry found when 11 is the invisible center of the Fibonacci-code, namely 21=10+1(11)+10, which seems to present us with a mirror of microcosm and macrocosm exhibiting the Pythagorean tetractys (as a triangle on the base 4) as well as the Kabbalistic 10 sephirot on both plains, respectively. Indeed, Fortitude at position 11 would unite the truth of the “turnabout” of the whole process in the Wheel (10) and the spiritual “turnaround” of the Hanged Man (12) and from their on, until all “turns (around again and together)” into the unity of the World (21)—mirroring the external and internal journey to spiritual and cosmic consciousness.

Conclusion

As the great Alberti has demonstrated: Mathematics and games have not been understood to be mutually exclusive in the late 15th century. So it gains some probability to see “avant-garde” mathematics, as in Pacioli’s account of Fibonacci, to be included in a game that, by its symbolic disposition, seems per se to imply a cosmological out-look. This becomes all the more true, when we remember that this “new” mathematical element restates an ancient feature of Divine order, the Divine Proportion that was already discussed by Euclid, on who’s Elements Pacioli has written in the same context as on Fibonacci.

The mysterious number 22 may than be understood as the combination of the two important insights into cosmic structure Fibonacci became famous for: first, the generation of a series of proportions which exhibit the Golden Ratio from the generating interaction of two basic elements (1+1); and second, the infamous “0” being a number. So, with this Fibonacci-code of the trumps, we can restate the uniting symmetry of the Divine Proportion of the mysterious number 22 as really being 0+21—the structure of the Tarot trumps.

If we take into account that all important events that may explain the appearance of the “modern” Tarot, as instantiated in the TdM, cumulate in the last decades of the 15th century, it might be, indeed, possible that the Tarot, in its transition of the game of trionfi of the earlier decades to the 15th century to the game of tarocchi of the early 16th century, was restructured by a Fibonacci-code. At least, in light of the evidence presented, it might be considered to have its development happen in this way, and that it was only forgotten (as the meaning of the very notion of the “Tarot” was forgotten) by the middle of the 16th century, rather than such not to have taken place.

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ATS Publications

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Tarotpedia

Tarotpedia - the Association for Tarot Studies's Online Encyclopedia of Tarot

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