V

Evolution of a Deck Design: The Matrix

One of the first ideas put forth in the book All Things Are Numbers is how the universe appears to be binary. I can't prove that it is, and I know there are a lot of people out there who feel that any functional use of opposites is in fact an abomination against a preferred goal of transcending all notions of opposites to achieve spiritual bliss within a sanctuary of oneness. But in my highly speculative mind, working toward the task of inventing a tarot-like wisdom system that is all about functionality, the use of opposites is a simple enough pattern with which to start the creation of any wisdom system designed to describe the nature of our existence within this universe - our life, outside of unity. Yin and Yang. Absentia and Universe. Day and Night. Wax on, Wax off! Examples of binary relationships are endless. Looking even deeper than that, the idea of finding binary relationships with other binary relationships makes our universe into something fractal, with endlessly self-similar repititions of overlapping pairs. Sorting out the fractal nature of our universe can be an interesting challenge. The Numerical Tarot deck is a device designed to address this very problem of multiple sub-divisions of opposites.

In the book All Things Are Numbers, a bit of paradoxical logic is employed to describe how a beginingless beginning could come to be. From that foundation of paradox, the chaos and order of our universe is birthed. Together, the womb of paradox and the child of chaos and order become an ultimate pair of opposites. Once this ultimate pair of opposites is established our systematic analysis of what follows hinges upon our ability to sort out the resulting subdivitions of opposites into finer and finer descriptions of this one simple idea. Thus, in The Numerical Tarot deck, we see a design with an underlying structure to its form, derived from common sense thought, relative to how we live our lives in a binary universe. In this way, the The Numerical Tarot deck, actually uses this idea of sub-divisions of an "ultimate pair" to create the various "arcana" of the deck. In other words, by taking a single number line, dividing it a select number of times, we create the six different number lines of The Numerical Tarot deck. And in doing so, we observe the crossed influence of multiple divisions of binary influence within the deck’s form, creating a matrix of overlapping binary influences which, when carefully sorted out, will bring supreme clarity to each card.

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Evolution of a Matrix: A Way of Thinking

The Universe is half of an ultimate pair. Thus, to begin the evolution of The Numerical Tarot deck's underlying structure, we need to start with a plain number line that will represent the womb of paradox that births our universe. A plain number line that we will use to represent the ineffable concept of "Absentia" - the diametrical opposite to the tarot "Universe" we hope to create (see the essay Behold The Absentia! elsewhere on this site). We describe The Absentia with paradox. We describe The Universe with chaos and order. Together, they represent our ultimate pair of opposites - the one that allows our universe to be here at all! After establishing this relationship, we will need to divide this neutral number line three times, just as we have elsewhere when analyzing other models seen on this site. As an abstract entity of existence, we will allow ourselves to be influenced by the three dimensions of our physical world. Thus, our evolving design will also be divisible in three ways. Our first cut then, divides this plain line into two separate lines, each diametrically opposite to the other. This creates for us the two lines of the Major Trumps:

THE ABSENTIA and THE UNIVERSE:

Imagine... a blank number line.

NOTE: I've had to pick a color with which to draw this "blank number line" only because of the limitations of the medium of communication being employed - that of a web page. In conceptual reality, this "blank number line" would not be drawn anywhere. It's just an idea in our minds eye. Get it? But, given that it now exists in some form (however hypocritical), we can now begin the process of deck evolution.

The "blank number line" represents the concept of "Absentia", the diametrical opposite to "Universe." In this primary duality of all creation, The Absentia is characteristically not divided. While on the other hand, its diametrical opposite, The Universe, is divided - like so:

POSITIVE AND NEGATIVE:

By cutting our blank number line, we create the Positive or Ameliorate (white) and Negative or Deteriorate (black) sides of The Numerical Tarot's Major Trumps. Like day and night, they are as opposite as can be. While at the same time, leading one into the other like the amelioration and deterioration of the seasons. In this way, we see how this first cut reflects the characteristics from the disparate nature of the 1/9 sphere of our model, or the 1 and 9 on The Apart/Together model (seen elsewhere on this site). In other words, the degree of separation between these first two halves reflects the essence of polarity and irreconcilable separation found in the numbers 1 and 9 in The Apart/Together model.

NOTE: There is no good or bad bias at this point. Good and bad are of course subjective terms. I use my own personal, subjective sense of good and bad in this deck design only to create the kind of contrast I need to make clear the pattern of interdependence that evolves. So please understand, that Positive does not necessarily mean Good. There is Good Positive and Bad Positive. Likewise with the Negative, it too does not necessarily mean Bad. There is Good Negative and Bad Negative. This deck describes them all. The idea is that one half of The Numerical Tarot deck augments and adds, while the other reduces and subtracts. Augmenting is not always good, and reducing is not always bad. This system forces us to see all sides to every coin...or card. It is indeed A Way of Thinking.

Cutting our universe in two is a good start. But right now, these opposites are static. In order to make our universe more dynamic, we need to divide what we have again - like so:

ACTIVE AND PASSIVE:

By cutting our number line a second time into active and passive, we create a pattern of extremes and betweens. As these abstract divisions are meant to represent the number lines of a tarot deck, we can see how the two sides of the Majors (the Positive and Negative) are no longer static, they now fit together like a Yin/Yang symbol, giving the deck they represent the same kind of dynamic structure. This time, the characteristics of the 2/8 sphere influence how we view resulting sides. In this case, the difference between each side could be compared to that of dividing daytime light (the ameliorate side) into morning vs. afternoon, and night-time (the deteriorate side) into evening and night. By dividing each number line of the Majors at its midpoint, the 2/8 characteristics of entry and exit, found in the funneling action of The Funnel, Tunnel, Maze diagram, add additional detail to the basic concepts of positive and negative, creating binary subdivisions, within each of the previous Positive and Negative sides.

These are the first two cuts of three, that will be made. After only two cuts we have established the Positive and Negative aspects of the Majors as well as the equidistant qualities of each of its two number lines. Having done this much we can now stop for a moment to observe an important pattern in this formation...

In the first cut of this three cut process, the binary split was made horizontally to create two complete number lines out of one. In the second cut, we shifted our cutting action 90 degrees to create equidistant halves within each of our two lines. By shifting this binary pattern 90 degrees we created 4 distinct qualities within our Major Trumps, and in doing so created a pattern of extremes and in betweens. In the book All Things Are Numbers, a 90 degree shift is used as a two dimensional representation of the effects of a Mobius band, upon opposites. Thus the idea of Major Trumps, consisting of number lines that run one into the other in an endless process of amelioration and deterioration, is reinforced as these opposite number lines are now seen as the two sides of a one sided journey the Mobius band represents. But there's more! As we procede to the final cut, we will see how it reveals an important relationship between the Major Trumps and the Minor Suits. In describing this relationship, we will come to view the Majors as parents of the Minors, and the Minors as the children of the Majors, thus establishing a relationship of two cards in the 36 Minors for every one card in the 18 Majors - like so:

ANALYTICAL AND SYNTHETICAL:

By moving on to cut three of our deck design, we differentiate between Analytical ideas vs. Synthetical ideas - or Tangible Quantitative ideas vs. Intangible Qualitative ideas. In doing so we duplicate the binary qualities of extremes and in betweens within each half of the now divided Majors... creating four distinctly different, but still inter-dependent number lines in our deck design structure. These four number lines are now thought of as "minor" to the Majors, but obviously, cut from the same cloth! Historically, it is theorized that the 22 Trumps of tarot were added to existing decks as an additional suit of trumps. Historically, it is surmized that these two decks had no relationship to each other in their initial creation, but were in fact brought together as an afterthought, to try and make a new kind of game, or make an existing game more interesting. History is interesting, but... in inventing a new paradigm for tarot design, the Numerical Tarot chooses to invent a path of thought that clearly establishes an inexorable, and very intimate relationship between Major Trumps and Minor Suits. It is felt that this very deliberate relationship is more profound than the ad hoc relationship established by adding a suit of 22 cards to a deck with suits of only 10.

In using the theoretical model of existence, presented everywhere on this site, to determine the attributes of these four Minor number lines (or what is actually two sets of two) we look to the 3/7 sphere of existence, and the ideas of quantitative reality vs. qualitative fantasy, to observe how Analytical vs. Synthetical perceptions divide our Positive and Negative paths into finer and finer subdivisions of opposites. In following this evolutionary path of subdividing opposites, we see how each set of number lines in the Minors (either the two from the positive side, or the two from the negative side), has the same attributes for each of its two lines, rather than creating four different attributes for four different lines - as is done in so many other traditional occult tarot decks. Because each SET of Minor Suits is being cut from one half of the Majors, each set of the Minors will have a number line that represents either the Analytical or the Synthetical in perception... in either a Positive, Ameliorate vein or a Negative, Deteriorate vein.

Elsewhere on this site, an analogy of a piano octave is used to illustrate the idea of Analytical vs. Synthetical, where Analytical is compared to scales, and Synthetical is compared to chords. In relating the number lines of the Minor Suits to the piano octave analogy, we can see how each SET of the Minors represents both physical features or conscious thought, as well as non-physical features or unconscious thought - with the same range of numbers. And because this third division has been faithfully cut from the previous two it also carries on their attributes within its form. Therefore, in conclusion, we see how each set of the Minor Suits (either the two positive lines or the two negative lines) will represent the Analytical or Synthetical (3/7), in either a Positive or Negative vein (1/9), with equidistant, Active or Passive similarities in each line (2/8)! By viewing the Minor Suits as children of the Majors, the Minor Suits repeat important ideas with greater specificity (two cards instead of just one).

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The Four Suits of The Numerical Tarot:

With only three cuts, we have gone from a blank number line to an elaborate system of coordinates that will tell us something significant about how each card relates to the binary universe is hopes to describe. We have also established an intimate relationship between Major Trumps and Minor Suits that is not really seen in any other deck design out there today. In the last step of this deck design, I choose to label the four suits of the Minors with the four operations of mathematics, and then associate those operations of mathematics with the four suit signs of traditional tarot decks.

Analytical + Active + / Positive +	Analytical + Passive - / Positive +			Coins (The Tangible)
Synthetical - Active + / Positive +	Synthetical - Passive - / Positive +			Cups (The Intangible)
Analytical + Active + / Negative -	Analytical + Passive - / Negative -			Staves (The Tangible)
Synthetical - Active + / Negative -	Synthetical - Passive - / Negative -			Swords (The Intangible)

In creating suits signs for The Numerical Tarot, I decided that the four operations of mathematics described the subdivisions of the deck more clearly than representations found in traditional decks. In this arrangement, Addition is considered a more Analytical process of augmentation, while Multiplication requires more Synthetical, conceptual leaps of thought. Both belong on the Positive or Ameliorate side of our established matrix of inter-dependent binary influences. Likewise, Subtraction is also the more Analytical, being the diametrical opposite of Addition, while Division again requires conceptual leaps.

But how, one might ask, do the existing suits of traditional tarot come to be associated with each of these mathematical concepts? Well, one possible answer would be to associate the suit of Swords with Division because swords divide! One might then choose to associate the suit of Staves with Subtraction because the subtraction symbol looks like a stave, or wand. From there, one might continue on to associate the suit of Cups with Multiplication because a chalice viewed sideways on looks like a multiplication symbol. It is fun to imagine how these visual-based associations relate, but, unfortunately, there is no historical evidence with which to prove any such intent by the creators of tarot. Thus... these ideas are simply put forth here as a way of correlating one deck design to another. In fact, along those lines, one might also think about correlating the suits of traditional playing cards, with these mathematical suit signs and traditional tarot suit signs. In a regular playing card deck we would probably want to associate the two RED suits to the suits of Coins (Diamonds) and Cups (Hearts) and view them both as Positive, and Staves (Clubs) and Swords (Spades), both BLACK, to be Negative. But that would be silly. Or is it? What would happen if these kinds of associations were actually made? How would that alter our perception of traditional tarot decks?

Personally, I think viewing tarot in this balanced, symmetrical, contrasting and consistent way would improve our perceptions greatly! In fact, after making these somewhat arbitrary associations and superimposing my knowledge of the numbers over other decks, numerous correlations appeared that lead me to conclude a "fortunate" arrangement of suits. This so-called "fortunate" arrangement of suit signs is interesting to use, when viewing existing decks, but it is not important to the creation of the Binary Matrix just described. The Binary Matrix does not care if we relate the suit of Addition to the suit of Swords or Cups or whatever. In the designing of the Numerical Tarot deck, the subdividing of numerology into a system of inter-related ideas is what's important. If, however, we do choose to relate the suit of Addition to the suit of Swords, we will probably not see very many correlations between this system and existing tarot decks. However, if we accept the arrangement given above, we will!!

For more on how this type of common sense subdividing of an abstract conceptual entity can be used to construct a tarot deck with improved functionality, consult the essays The Binary Influence Calculator and Dream Analysis Calculator, or The Numbers in Space, or the Shake the Trees game. For more on how these abstract subdivisions of opposites can be associated with the suits of traditional tarot, consult the essay The Quaternary and the Elements of Tarot.

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The Matrix, Math, Suit Sign Mandala

Here is a mandala you can use to meditate on some of the concepts put forth so far. To the left and right of the central grid of tiny squares, we see how a single line is divided into Majors (two bars) and Minors (four bars). When the four bars are divided again, to represent the moderate versus extreme variations of each card, we arrive at the tiny squares of the central grid. To the top and bottom of the central grid of tiny squares, we see a single line being divided left and right several different ways; in half, in thirds, insides versus outsides, etc. The grid in the center is the result of these combined influences: nine numbers, divided into four suits, with upright and reversed interpretations. Around the outside is a series of waxing and waning moon-like spheres bordered by the associated symbols of mathematics.

In the center is a number line! It's divided once, twice, thrice etc. to create a matrix of possibilities for any one card in the deck. Waxing and waning spheres coincide with the ascending and descending operations of mathematics which become the four suits of the deck.

Addition waxes; it adds. Subtraction wanes; it subtracts. One operation leads to the other. One destroys or restores the other. Like a waxing and waning moon, two suits lead into light, two suits lead into dark. Like the notion of a point and sphere being essentially the same (discussed elsewhere on this site), each side achieves its nine numbers by sharing its first and last sphere with the next side, making each sphere the point of the next nine step progression. At each corner of the inner square are solid and open line combinations that indicate the ovelapping influence of Yang and Yin upon the matrix of the deck... described above with the words Positive - Active (solid/solid), Positive - Passive (solid/broken), Negative - Active (broken/solid), Negative - Passive (broken/broken) which leads to the idea of certain cards in the deck being dominantly influenced by Action or Thought or Feeling or Emotion.

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IN and OUT:

Three simple cuts created the Major Trumps and Minor Suits of our tarot deck. With these three overlapping subdivisions of binary influence we can now determine at least three attributes for any one card, before we even look at the numerological symbolism it contains. And, because we have been associating each cut of a number line to a sphere of the theoretical model of existence being put forth everywhere on this site, the attributes of The Five Ways of Being and fundamental directions of orientation, have also played an important part in the shape of this system. As it stands now, only two more of these five ways of being remain. The matrix of overlapping binary influences that we have so far can tell us a lot about a card before we ever us it in a reading. The one thing it can’t tell us though is whether the message of the card in question is describing behavior that is sent out from the quarent or behavior that is being felt inward by the quarent. It also can’t tell us if this behavior is being pushed out or pulled out, or if it is being pushed or pulled in.

Typically we will find that the "in" and "out" characteristics of a card are all decisions that cannot be made until a card is actually used in a reading. In other words, while the overlapping of linear opposites can determine one card to be more Positive, Negative, Analytical or Synthetical or Active or Passive than another, all cards are affected by the characteristics of "in" and "out." Therefore an introspective or extrospective state is not a precondition that can be logically determined. But it is one to be considered.

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GOOD and BAD:

The terms "Good" and "Bad" are of course infinitely subjective. What is bad for me might be good for you. What is bad today might lead to something good down the road. But as infinitely subjective as good and bad might be, they remain an inescapable component of life and living. Good and bad tell us what is right and wrong in this world. That's where we, as individual societies, get laws that help to protect and preserve life. An optimist will find something good in everything bad. A pessimist will find something bad in everything good. But individual bias does not make good and bad go away.

Elsewhere on this site, the number 5 - being the midpoint of our number line - is compared to a infinitessimal moment in time. Time draws in a future and exhausts a past. The "event" we perceive as time is focused on the center of any entity. The number 5 is that center. Thus moments in time are seen as an infinitely indeterminable mixture of future and past. In the same way, the number 5 alternates between the two sides of our number line, perpetually favoring one side, then the other. The number 5 represents good and bad fused together, thus explaining how events in time, or events in our lives, can be seen as either good or bad, at the same time.

Even an optimist has to acknowledge that what they think is good might still be perceived as bad by someone else. And vice versa for the pessimist. Thus all events are both good and bad, at the same time. Elsewhere on this site, the ability of one thing to be two opposite things at the same time is compared to a Mobius strip, where a two sided piece of paper is allowed to have only one side, or a one sided Mobius strip is seen as having two sides and one side at the same time. Thus good and bad become the last things to consider when adding up all these binary influences.

But this compounding of binary influence doesn't fully explain how our matrix of overlapping opposites see good and bad. For a complete analysis of how Good and Bad enter into the design of The Numerical Tarot, consult the essay entitled A Spectrum of Possibilities. For more on the subject of good and bad, and whether such concepts exists at all... or not, consult the essay entitled Good and Bad, Right and Wrong, Smile and Frown.

This is how our matrix of tarot is constructed, but how it it used?