The Four Elements
The four elements of fire, earth, air and water are ubiquitous and have been known since antiquity. In my opinion the original four elements are best understood as metaphors for metaphysical things that were too sophisticated to be expressed directly and specifically by the ancient cultures.
|Element||AMOQ Quadrant||Tarot Suite||Card Suite|
It is usual to perceive Tarot as occultism, divination or even magic. I do not think so. Some people, with significant intuitive abilities, are just able to shuffle the cards so that they reveal their own expectations to them. This motor association to future events is similar to the one I developed at a time I used dictionaries a lot. I became able to frequently open a 1000-page dictionary at the right page, plus minus two page turns, and this did not require any effort on my part. That was not magic. In a similar way, Tarot cards are not magic but the user merely shuffles them so that he reveals his own expectations to himself, should he choose to do so. But he is not aware of doing so.
Tarot cards are not supposed to be used for magic. They are pictograms, each of which refers to an analytically definable abstract concept. Frequent use of Tarot cards has the effect of familiarizing the user with these concepts. But nobody knew what these concepts are - how they shoud be defined. My research seems to have produced a definition of the metaphysical domain described by the Tarot pictograms.
The Major Arcana
The number cards of Minor Arcana
The number cards of the Minor Arcana form a coordinate system so that staves stand for mystical quality, swords for normative quality, cups for subjective quality and pentacles for objective quality. The Fool arguably stands for the origin as some authors report it not to belong exclusively to the Major Arcana even though it is associated with it. Within each quadrant, the ace is closest to the origin or pole. Cards 2, 4 and 6 are laid out horizontally away from the origin or pole in ascending order. They stand for decent quality. Cards 3, 5 and 7 are laid out vertically away from the origin or pole in ascending order and stand for badness. Cards 8, 9 and 10 stand for excellence and are laid out diagonally away from the origin or the pole.
It is unclear whether the coordinate system is Cartesian or polar. In a polar system the aces would stand out. In a Cartesian system they wouldn't but apparently at least some of the other cards would not represent square areas of the Cartesian plane. This means that even though the Minor Arcana can be projected on the Cartesian coordinate system, the inaccuracy of the projection adds a complication in the interpretation of mathematical operations such as, and particularly, vector summation.
Relevant differences and similarities between the AMOQ grid and the number cards of the Minor Arcana include:
- The number cards of the Minor Arcana have a smaller resolution because each quadrant is split into ten segments instead of sixteen.
- The number cards of the Minor Arcana do not include AMOQ slots whose X and/or Y coordinate is zero. Therefore their scope is smaller.
- The scope of the number cards is equal to the scope of those AMOQ slots whose X and Y coordinates are not zero.
The court cards of Minor Arcana
These cards could be used to patch up the nonrelativizable slots. But if placed in their current arrangement they need to be rotated and they can be rotated either clockwise or counterclockwise. The counterclockwise rotation is:
- Pentacles stand for the positive X axis
- Cups stand for the negative Y axis
- Swords stand for the positive Y axis
- Staves stand for the negative X axis
A clockwise rotation would be:
- Pentacles stand for the negative Y axis
- Cups stand for the negative X axis
- Swords stand for the positive X axis
- Staves stand for the positive Y axis
Problematically, these rotations seem approximately as bad. I would lay out the Rider-Waite Minor Arcana so that Pentacles stand for Rationality (and objectivity), Swords for Tangibility (and normativity), Cups for Gnosis (and subjectivity) and Staves for Abstract (and mysticality). The cards are arranged thus (in hexadecimal so that The Fool is O, each Ace is 0 and P, N, Q and K stand for Page, Knight, Queen and King):
9..6K6..9 .8.4Q4.8. ..72N27.. 5310P0135 KQNPOPNQK 5310P0135 ..72N27.. .8.4Q4.8. 9..6K6..9
A Minor Arcana specific for the AMOQ
We wish to follow the spirit and perceived intentions of the developers of Tarot, whoever they might be. On the other hand we do not wish to restrict the use of Tarot due to mere traditional prejudice. I have taken the liberty to increase the size of the Minor Arcana to sixteen cards per suite so that the Minor Arcana cards could be laid out as a Cartesian coordinate system with The Fool as the origin. There are only number cards in a suite. The "nonrelativized cards" or court cards probably need a new name and are situated on the axes. There would be a temptation to call them "land cards" Magic the Gathering-style if that did not seem slightly vulgar. However, in my opinion it would be more vulgar to introduce a Minor Arcana with X and Y coordinates as card identifiers. A numeric playing/divination card identifier should be a number, not an ordered pair. If it's an ordered pair it will be too complicated to speak about the cards.
The revised Minor Arcana has 64 number cards, 16 land cards as the axes and The Fool as the origin. Numbers are in hexadecimal again.
F6ACKCA6F BE48Q84EB 97D2N2D79 5310P0135 KQNPOPNQK 5310P0135 97D2N2D79 BE48Q84EB F6ACKCA6F
The placement of number cards 13 and 16 is especially implicative that this Minor Arcana could be an improvement to the earlier standards. Also 15 and 14 comply to a remarkable degree. I would name the epistemological land cards like "Queen of Rationality" or "King/Champion of Gnosis", "Lady of Gnosis", "Master of Gnosis" and "Plain Gnosis" (with a little girl pointing a finger at the viewer, as illustration?). The ontological or existential "land cards" would be more aptly named as "Extreme King" or "Vulgar Page" and so on.
This is mostly a negative result. Because Yijing has 8 × 8 = 64 hexagrams and I had already found an unexpected simulacrum between my work and Tarot, I thought it's possible that I have duplicated some metaphysical research that was already published in the Book of Changes. However, this seems not to be the case. The corners of the Primal Heaven Arrangement in the Eight House Matrix appear strikingly similar with the corners of the AMOQ coordinate system. However, interpreting them as such contradicts the Tarot interpretations presented by Bradford Hatcher in his translation of the Book of Changes. And besides them I have found no correlation between AMOQ concepts and hexagrams, trigrams or other Yijing concepts. Furthermore, mathematical considerations involving vector summation have made me adopt a 9 × 9 coordinate system which has further distanced my work from Yijing. A more thorough investigation would probably reveal more associative potential (ie. the potential for associating two concepts in a way that facilitates stream-of-consciousness thinking whose output can be rationally justified) but this can only be done at the risk of disregarding some of the finer nuances of Yijing or the AMOQ.