When looking at The Numerical Tarot, people with a traditional view of what tarot is might think that the deck of cards this study of tarot calls The Quaternary is made up of the four cards left over, after this system whittles the Major Trumps down to only 18 (see The Spine of Tarot elsewhere on this site). But in fact, from the All Things Are Numbers perspective, there is no "left over." To this study of tarot, he Quaternary is simply another expression of the fundamental parameters of existence that govern this system of numbers - another variation on a single theme.
This study of tarot uses the analogy of a planet in space to describe the stages of a theoretical model of existence. With the four stages of that planetary model (described elsewhere on this site), we establish the numbers of numerology as well as the importance of fourfold models to the nature of existence. In addition to the fourfold nature of a planetary model, there are several other fourfold models seen on this site that can also be used to help understand the characteristics of each corresponding number along a line... that is... when those fourfold models are are unfolded into a numberline form (see diagram below) (see also The Quaternary and The Court Card Matrix elsewhere on this site). One fourfold model that is very important to most tarot enthusiasts is the alchemistic elements of Fire, Water, Air and Earth. In the design of most decks, these elemental ideas are usually associated with the suits of the Minor Arcana or Pip cards. Traditionally, people define the character of each tarot suit by associating Fire with Staves, Earth with Coins, Water with Cups and Air with Swords. Unfortunately, there is often disagreement between experts as to which element really belongs with which suit, and in what sequence those element-clad suits should be arranged when the issue of understanding underlying structure becomes a subject of interest. Along these lines... the system of underlying structure being presented on this site has its own opinion regarding that matter - an opinion that leads to an outcome that many traditionalists might find objectionable. Actually... this study of tarot presents two alternatives to tradition - one that works really well, but breaks from tradition by not associating the elements to the suits at all, and another that doesn't work as well, but does associate the elements to the suits. Let's begin with the arrangement that doesn't work as well, but at least resembles the same approach used by tradition of associating the elements with the suits of the Minor Arcana.
The Planetary Model and Elements
In the All Things Are Numbers approach, elemental concepts are sorted using an allegorical model that is used elsewhere on this site to describe the various stages of our theoretical model - a planet! In examining the planetary model, we see how the element of Fire = The Fiery core of a planetary model, while the element of Earth = The Earthen surface of a planetary model. Moving outward, Water = The Watery atmosphere of a planetary model, while Air = The Enveloping Airy limits of a planetary model. In this scheme, Air contains Water, Water covers Earth, and Earth encloses Fire at its core. Thus, the enveloping Airy limits = definition of a reference frame, while the Watery atmosphere = the flow of fluid dynamics, life cycles, and things into and out of the defined reference frame. Moving inward, the Earthen surface = the tangible, visible, corporeal form of existence, while the Fiery core = the substance of the life force of existence found within. Everything in the All Things Are Numbers world, and everything in The Numerical Tarot deck is based on this extremely simple model! But a planetary metaphor is just one convenient analogy.
Like an atom, the insides of this theoretical model are positive and the outsides are negative. Of course, by positive and negative we don't mean good and bad, just charged or not charged, or coagulating vs dissolving... or incremental vs decremental, or investive vs divestive. Because this system is all about abstract concepts being labeled with numbers, this system has chosen to illustrate this positive and negative relationship using the four mathematical operations of Addition, Subtraction, Multiplication and Division as suit signs. In this system, the two suits of negativity are Subtraction and Division, while the two positive suits are Addition and Multiplication. Thus, we establish our first correspondence of models with the Fire of the Fiery core and the Earth of the Earthen surface relating to the two positive/coagulating operations of mathematics, while the Water of the Watery atmosphere and the Air of the Enveloping Airy limits relate the the two negative/dissolving operations of mathematics.
The planetary model is a metaphor. Not every entity has a Earth-like atmosphere or surface, but all entities have limits, space displaced, some kind of form and core. In this way, the analogy of Air, Water, Earth and Fiery core are reduced to the more abstract concepts of Frame, Flow, Form and Force. Thus... Fire, Earth, Water and Air are a quaternary of elements that are only roughly equivalent to the Force, Form, Flow and Frame model used elsewhere on this site to describe the fundamental parameters of a universal entity. In the same way, Addition, Multiplication, Subtraction and Division become more universal ways of describing the fourfold, positive vs. negative aspects of these same fundamental stages of existence. From there... in relating one fourfold model to the other, we can see how the positive/coagulating side includes the fiery core, which is active (burning fuel), and the surface, which by comparison would be considered passive (a line of demarcation). Likewise within the negative/dissolving side, the atmosphere is active (fluid dynamics), and the enveloping airy limits are passive (a final line of demarcation). Thus, if we were to associate active with analytical and passive with synthetical, the analytical process of ADDITION would become associated with the active fiery core or FIRE, while the synthetical process of MULTIPLICATION would become associated with the passive surface or EARTH. Moving outward, the analytical process of SUBTRACTION would equal the active flow or WATER, while the synthetical process of DIVISION would equal the enveloping limits or AIR.
Addition = Fire = Force
Multiplication = Earth = Form
Subtraction = Water = Flow
Division = Air = Frame
Those are three ways of describing the stages of our fundamental model of existence. But what happens when we try to correlate Fire/Addition, Earth/Multiplication, Water/Subtraction and Air/Division to the traditional suits of tarot - the Coin, Cup, Stave and Sword? To the minds of some people, the fourfold nature of the Minor Suits of a tarot deck are a magnet that attracts any and all fourfold models out there. Some of these correspondences work well, and... in my opinion... some don't. Some work well with the suits, but not with each other. Some work well with each other, but not with the suits. For those with a strong interest in correlating every fourfold model they find with the four suits of tarot, I can offer the following analysis. Personally, I don't think it works that well, and have come to the opinion that no arrangement of elements and suits work well. Because of that opinion I have moved from this approach to invent an alternative that I think works much better, both for the cards as well as how those cards are meant to describe the theoretical model of existence that gives the cards their meaning.
In this alternative approach, the elements are not associated with the suits at all, they are associated with the number line that represents the stages of the theoretical model of existence, while the mathematical concepts of Addition, Multiplication, Subtraction and Division describe four ascending and descending variations of that numerically/elementally described model. In this way, the elements... and the more universal concepts of Frame, Flow, Form and Force, cross against the ideas of Addition, Multiplication, Subtraction and Division as a grid of ideas that warp and woof like the fabric of a weaver on a loom. To this idea, the Earth-like idea of ascending and descending season of a year are added as a metaphorical equivalent to the more abstract ideas of Addition, Multiplication, Subtraction and Division to create a mixture of ideas that combine metaphorical elements with metaphorical seasons to give each cards a unique quality. There is more on this warp and woof approach elsewhere on this site (see the essay Seasons elsewhere on this site). For now, let's finish with the less satisfactory approach that follows the more traditional path of associating elements with suits.
Here is a peek at this warp and woof alternative. This diagram shows the entire Minor Suits, upright and reversed. By mixing one fourfold quaternary model with another as a crossed grid, conflicts concerning syncretism are reduced. This diagram shows elements describing an entity, and seasons describing the binary aspects of that entity. For more on these various subdivisions of binary influence, consult the essay Evolution of a Deck Design: The Matrix. For a more elaborate version of this diagram, consult the interpretation pages of this site.
The Numerical Tarot vs. Traditional Tarot
As just mentioned, in the essay The Seasons, I offer an alternative to the traditional practice of associating every fourfold model that comes along to the four suits of tarot. But, for those who might find that alternative less than satisfactory I will finish presenting this alternative... the best possible rationale I can muster for associating Fire/Addition, Earth/Multiplication, Water/Subtraction and Air/Division to the traditional suits of Coin, Cup, Stave and Sword or... Pentacle, Cup Wand and Sword. Bear in mind... I don't really have any rock solid rationale here, just intuitive notions that yield an interesting result.
In the approach being offered here, the four operations of mathematics are the suit signs of choice; two positive, two negative, with Addition seeming more analytical than Multiplication, and likewise with Subtraction seeming more analytical that Division. In relating these abstract concepts to the traditional suits of tarot, I would suggest we look at decks with illustrated pips - most notably, the ever-popular Rider/Waite/Smith deck. In looking at the suits of the RWS deck, I would suggest we look for suits that look like they could be seen as mostly positive or mostly negative. It won't be easy, given how inconsistent each suit is in its display of images that look variously "light" and "dark" or as designed to elicit a "Smile" vs "Frown" as I put it elsewhere on this site. But, to me, it is not hard to see at least some contrast between the suit of Swords and all the rest. The suit of Swords looks very dark and negative - lots of frowns. Likewise, in determining what the other "negative" suit might be, Staves, to me, seems to have more negativity (or frowns) to it than the others (I'm talking visually... my initial response... separate from elaborate explanations of authored intent or other people's personal interpretations... or my own reasoned response).
With the negative suits determined, the next step would be to determine which of the two positive suits should oppose which of the suits that we have determined to be mostly negative. Personally, in a traditional deck like the Rider/Waite/Smith deck, I see more interesting oppositions between Cups and Swords than anything else; the joy vs. sorrow the the 3s, the parallel harmony vs. crossed tension of the 2s, the friendship vs. alienation of the 6s, the dreaming vs. scheming of the 7s etc. So... I would associate Cups and Swords as opposites, leaving Coins and Staves to be opposites. With this in mind, the next step would be to see if we can determine any analytical vs. synthetical difference between the two suits that we have determined to be mostly positive and the two suits that look mostly negative. Personally, I see more synthetical ideas in the Cups and Sword opposition than in the Coin and Stave opposition. So... I would consider Coins and Staves to be more analytical and Cups and Swords to be more synthetical.
By using our theoretical model of existence, with its Fiery core, Earthen surface, Watery atmosphere and Airy limits, we can see how the action of traversing an area is perhaps slightly more analytical, while being a neutral line of demarcation is perhaps a bit more synthetical... being that one involves moving bias and the other stationary symmetry. In our model of existence, the core and surface correlate to the positive insides, and the atmosphere and circumsphere correlate to the negative outsides. In addition to that... the mass and atmosphere are considered areas to be traversed, while the skin of Earth and the limits of Air are considered lines of demarcation that divide one area from another. The skin of Earth divides the inner mass from the outer atmosphere. And the Circumsphere divides the totality of the model from everything outside the model, as it marks the limit to the "sphere of influence" for any manifest entity.
From these various associations of positive/negative, analytical/synthetical, suits, and math, the following associations result:
Positive - Analytical = Addition = Coins
Positive - Synthetical = Multiplication = Cups
Negative - Analytical = Subtraction = Staves
Negative - Synthetical = Division = Swords
When combined with previous conclusions about Fire/Addition, Earth/Multiplication, Water/Subtraction and Air/Division, the transitive properties of logic would dictate that we make the following associations:
Positive - Analytical - Addition - Coins with the Mass = Fire
Positive - Synthetical - Multiplication - Cups with the Skin = Earth
Negative - Analytical - Subtraction - Staves with the Atmosphere = Water
Negative - Synthetical - Division - Swords with the Circumsphere = Air
So... for those who want to employ every fourfold model they find in describing the suits of tarot, this system of analysis would dictate that, Coins = Fire, Cups = Earth, Staves = Water and Swords = Air. Pretty wacky huh? That, in my opinion is what single-minded syncretism yields - imperfect, less than satisfactory results. Actually... to me, these results are really no better or worse than the many variations I've encountered from others concerning the association of elements to traditional suits. However, I'm sure many will disagree and view the differences put forth here as unworkable heresy! For example: changing Cups to not be associated with Water will undoubtedly repulse a great majority of people devoted to traditional views. But... if they take the time to look at the qualities that are associated to the suit of Cups by way of other quaternary associations made elsewhere on this site, they will see a great many similarities to the essential meaning attributed to Cup cards, and their traditional association to Water. Likewise, moving Water to the suit of Staves may seem ridiculous, as it douses the flames of Fire that are traditionally associated with that suit. But again, if the madness of the method is studied, rather than rejected out of hand for being so "wrong" a new kind of sense will be found... even in this less than satisfactory result.
In the end, though, all this rigmarole is just to seek out coincidences in form between my approach and a traditional deck like RWS. I only do that to help people who might want to make a transition, and to demonstrate to those who don't want to make a transition the possible benefits of a more consistent design, where the concepts, and presumably the subsequent illustrations, of each suit are more obviously balanced and contrasting in orientation (and also relate as parent and child to the Majors). I, personally, think that things like balance, symmetry, contrast and consistency are beneficial (see the essay Balance or Bias elsewhere on this site). They reduce ambiguity and project a clearer statement of intent. But alas, as so many people tend to ignore intent and make up meanings of their own from whatever illustrations cross their path, such organization seems - at times - to be of little value to most tarotists. Unwavering devotion to tradition, history and mystery also seems to win out over alternatives, causing inconsistent designs to be faithfully adopted no matter what. In fact, learning ones way around the inconsistencies of a deck's design seems to be accepted by many people as part and parcel to the mystery that so many find so enchanting. Personally, I found all those inconsistencies, ambiguities, mysteries and malicious blinds to be disenchanting.
As I said, I have no concrete rationale for the arrangement of ideas just given, so my associations to tradition are more or less arbitrary personal choices of mine. In this system, the four suits of choice are Addition, Multiplication, Subtraction and Division. So, in this system, Addition = Core = Fire, and Subtraction = Atmosphere = Water. In the end, this system does not care if someone equates the suit of Addition with the suit of Coins, Swords, Cups or whatever. The subdividing of numerology into a system of inter-related ideas is what's important here. If, however, that person chooses to equate the suit of Addition to suit of Swords for example, they will probably not see very many correlations between this system and existing tarot decks. However, if they accept the arrangement given here, they will. And the arrangement given here associates:
I leave it up to each individual to decide if the suit of Coins (found in traditional decks) equates with this system's suit of Addition and its proposed associations to a Fiery Core. Take a look at the concepts put forth in the suit of Addition (and the Majors that equal those cards, and the Quaternary that equals those Majors). If they seem to resemble the concepts found in any particular suit of Coins, then Coins = Core = Fire. Likewise with the others. To witness just such an examination, go to the BOOK section and check out the Waite vs. Palm analysis.
A Mental Adjustment
Of course, for those who actually want to accept the arrangement of suits to elements being offered here, doing so might still require some mental adjustments in order to see those elemental concepts attached to suits in a way other than that seen in tradition. One of the many obstacles to accomplishing a willing acceptance of the arrangement of elements to suits is the mental adjustment required to see those elements as describing the stages of our theoretical model of existence, rather that seeing them as tools of Alchemy. As mentioned above, this system does not use Alchemy or Astrology to explain concepts. In fact... I don't really want Alchemy or Astrology to be associated to this system at all. The arrangement of elements here, is based on a planetary model alone, and nothing more.
In most of the Alchemistic arrangements of elements Earth is considered Dry and Cool, while Air is considered Moist and Warm. But... if the concept of Hot is attributed to the Fiery inner core of our own Earth, and Wet is attributed to the Watery atmosphere, then it seems appropriate to consider the Earth between to be Moist and Warm. If we associate Earth with Moist and Warm, what better colors could we hope to have appear at that stage than five shades of Green? Of course, our actual Earth exists at all kinds of temperatures and degrees of moisture, but then... so does the air. That's why this diagram also includes the more traditional arrangement of Air being Warm and Moist and Earth being Cool and Dry... which interestingly enough... doesn't alter the qualities of Fire or Water at all.
So, with this arrangement, one can take their pick as to whether they want an Earth that is Cool and Dry or Moist and Warm... without changing the sequence of Fire, Earth, Water and Air as representing stages of our theoretical model of existence as seen in the stages of our own home planet.
For more on the colors being used in this diagram, consult the essay Enjoy the Pretty Colors elsewhere on this site. And... for a fun little print-out, fold-down 3D model of colors that involes this arrangement applied to the sides of a tetrahedron, consult the essay Three Sacred Solids - A Trinity of Triangles. Below is a vertical arrangement, of the Warm Moist Earth version.
In associating the elements to each other, I prefer to think about them in a linear fashion, as they help to visualize the idea of concentric spheres of containment that define a manifest entity that is coagulating or dissolving. But I know that many like to view them in a circular format as well. In both cases, I have invented a unique rearrangment of the concepts of Hot, Cold, Wet and Dry in a way that also violates tradition, but makes more sense to me when applied to the linear model of planetary stages of concentric containment. In the diagram above, I also add some additional vocabulary in order to suggest a certain kind of flow from one element to another i.e. warm flowing to hot and moist flowing to wet etc. - something that could surely be used during readings to suggest a certain kind of flow between cards representing these various elements, and the cards they are attached to in the Quintagram Quilt shown above. In this unique arrangement Air, adjacent to empty space, is dry and cool. Further in, Air contains the Water of an atmosphere. In the upper atmosphere, Water is cold and wet. As that water rains down on the Earth, it fills the oceans and moistens the continents of Earth, so that things can grow, it makes the Earth moist. Beneath the surface of the Earth, a geothermal furnace makes the Earth warm. Fire removes moisture and is hot and arid. The circle is complete... if one wants to view it as a circle. And while this alternative arrangement might seem odd, one look at the diagram above shows that adherence to the traditional arrangement of Air being warm and moist and Earth being cool and dry would not require any change to the sequence of elements, nor the flow of one element to the other, as seen in the diagram above where the cool of Earth flows into the cold of Water, and the warm of Air flows into the hot of fire etc.
The elements can be viewed as a circle, or, as concepts that are linearly successive from one to the next, in a way that replicates the four concentric stages of our theoretical model of existence. They could also be placed onto the four sides of a tetrahedron, as shown in the diagram above! For another, more triangular example of this, consult the essay Three Sacred Solids - A Trinity of Triangles seen elsewhere on this site. Or... download these CMYK versions of the RGB example shown above, and fold it down! Here is the Warm Moist Earth version, and here is the Cool Dry Earth version. After studying these triangular elements, take a look at how the same idea of alternating traiangles along a line manifests in the essay The Accordionistic Dovetail Joint.
In conclusion, it may have been noticed, that the only traditional association that remains intact with this arrangement is the association of Swords and Air. The other three are all shifted over one step. But, if we take the time to acquaint ourselves with the symbolic meaning of each stage of our theoretical model of existence, not only does each elemental association make sense, but associations to tradition might be seen as similar enough to make the mental adjustment with little effort.
In this arrangement, the suit of Cups does not equal water, but within this system, the 3/7 sphere of our model equals a sensorial soul and the idea of feelings and emotions... concepts similar to that of tradition. The surface of the Earth is where things grow. It's where we find life itself, nature and the sensitive souls who are infinitely connected to life. The suit of Staves equals water instead of fire, but whereas tradition associates the depth of water, and the unseen mysteries of the deep, to the concept of intuition and the unconscious, here, the idea of water suggests flow, and the action, motion, and vision of a Perceptual Spirit navigating a path through life. The suit of Coins does not equal Earth, but I think a Visceral, fiery personality fits the idea of money and material matters even better. When examining the personality types that result from elemental associations, this idea of 4/6 Visceral types and materialism makes lots of sense.
There are in fact some traditional systems that switch the Earth association with Coins and the Fire association of Staves, making this system's Fire with Coin association not entirely out of the realm of tradition. If such an association were to be accepted, based on tradition, then, in fact, only two of this systems associations would need mental adjustment... the hardest of which will no doubt be the swapping of Fire for Water with the suit of Staves. For those who can manage this one mental adjustment, I think they might see the tarot a whole new way. I would urge everyone to give it a try, and examine how mathematical suits, traditional suits and elements are used throughout the rest of this system before making any final judgments. Traditionally, I believe the four elements to be utilized to an excessive degree. There are so many other quaternary concepts that one can employ to understand the nature of numbers along a line and suits in a deck. I would encourage everyone to seek out those many sources elsewhere on this site.
This was my best effort to rationalize an association of alchemistically significant elements to the suits of traditional Tarot. If associations to tradition seem strained it is probably because of the radically different view of elements being compared. My approach attempts to be universal by examining how elements can describe things like the Earth itself, whereas alchemistic associations are geared more towards a description of life on the surface of planet Earth. Thus, among other things, the concept of FIRE is made somewhat incompatible, as I put fire inside at the core of an entity, while alchemy puts it outside where it can be experienced in mundane ways by an observer. In putting fire outside the alchemistic uses of elements to describe the suits in ways that focus on how those elements interact in the presence of a human observer, while my universal design is meant to describe the body of that observer in spacetime and its fiery passions of the heart, the sensitive skin of its surface, the space displaced by its aura or atmosphere, and the airy limits of its sphere of influence.
If this analysis of these incompatible views of elements, and their relationship to traditional suits, remains unsatisfactory, I would suggest reading an alternative idea - The Seasons -that doesn't even associate the elements to suits at all! It might make more sense to some.