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# Numerology in Tarot Cards

To most people, mathematics is a branch of knowledge in the service of science and accounting, or something tedious but necessary for the mundane calculations of everyday life. But in ancient times mathematics and numbers were interrelated with religion and mysticism. Our ancestors were a superstitious bunch who found deeper meaning in numbers and geometric shapes. For instance, only in modern times have astronomy and astrology been decoupled into distinct branches of knowledge on opposing ends of the logic-vs-magic spectrum, while the occult history of mathematics and numerology has been completely eradicated from school curricula to make room for the modern practical uses of math.

Numerology is an older method of divination than tarot cards, and tarot decks incorporate many aspects of numerology, which makes them a much richer divination or meditative tool than may be obvious at first glance. Here are some of the many ways in which tarot cards embody mathematical mysticism.

## Brief History of Tarot Cards

The exact origins of tarot cards are unknown, but historians have a general idea of how they evolved over the centuries. Arab traders brought four-suit 13-rank playing card decks to Europe in the 1300s where they spread throughout the region. Several decks evolved from this proto-deck. In France it became a deck with suits of hearts, clubs, diamonds, and spades that we still use today for most card games. In Spain the suits remained closer to Arab originals: clubs, swords, cups, and coins.

But in Italy the number of ranks was expanded from 13 to 14, and 21 more "trump" cards and one wild card were added to the deck, increasing the total number of cards from 52 to 78. People who got their hands on these decks began using them for divination games, which evolved into what we now recognize as tarot card reading. The word "tarot" derives from the French "taraux," which is derived from the Italian "tarocco," the name of a trick-taking card game people played with the 78-card deck. The origin of the word "tarocco" is unknown.

These days, tarot decks are almost exclusively associated with metaphysical pursuits, fortune-telling, and other New Age practices. Very few people outside of Italy use them for card games.

## Numerology of 78, 56, and 22

In a standard tarot deck there are 78 cards, 22 of them are called the major arcana and the remaining 56 are called the minor arcana. The 56 minor arcana cards are much like today's decks of four-suited playing cards with number cards and court cards (aka royals or face cards). The numbers 78, 56, and 22 have many curious mathematical properties.

**Seventy-Eight:**

- 78 is the 12th triangular number, aka the sum of the first 12 positive integers. Twelve is an interesting number in its own right.
- The prime factorization of 78 is 2 x 3 x 13 = 78. The sum of the prime factors is 18, an auspicious number in gematria, the Jewish religion's version of numerology.
- The sum of all the factors of 78 is 1 + 2 + 3 + 6 + 13 + 26 + 39 + 78 = 168. There are 168 hours in a week.
- Seventy-eight is the atomic number of platinum, one of the rarest elements in the crust of Earth and thus a symbol of prestige. Platinum is the most expensive precious metal used in jewelry.
- Nitrogen is 78% of the Earth's atmosphere.
- If a regular deck of cards had six suits instead of four, the total number of cards would be 78.

**Fifty-Six:**

- The sum of the first six triangular numbers is 1 + 3 + 6 + 10 + 15 + 21 = 56. This means 56 is the sixth tetrahedral number.
- The prime factorization of 56 is 2 x 2 x 2 x 7 = 56. The sum of the prime factors is 13, which is either a lucky or unlucky number depending on your view.
- The sum of all the factors if 56 is 1 + 2 + 4 + 7 + 8 + 14 + 28 + 56 = 120.
- In 1920, archaeologists discovered 56 depressions in the ground surrounding Stonehenge, evenly spaced in the form of a circle. They determined these holes once contained large wooden beams. The conclusion is that the number 56 was meaningful to the ancient Europeans who built Stonehenge.
- There are 56 ways to partition the number 11.
- The tetranacci sequence with the minimal initial values of {0, 0, 0, 1} is 0, 0, 0, 1, 1, 2, 4, 8, 15, 29, 56, 108, 208, 401, 773... Each term in the sequence (starting with the fifth term) is the sum of the previous four terms. 56 is the 11th term in this sequence.
- Yet another connection between the numbers 56 and 11: the sum of the digits of 56 is 5 + 6 = 11.

**Twenty-Two:**

- The pentagonal number sequence is 1, 5, 12, 22, 35, 51, 70, 92,... Twenty-two is the fourth number in this sequence.
- The number 22 has exactly four factors: 1, 2, 11, and 22.
- Another connection between the numbers 22 and four: the sum of the digits of 22 is four.
- Like 56, 22 is also a partition number. There are 22 ways to partition the number eight.
- If you draw six chords across a circle, the maximum number of regions you can divide the circle into is 22. This is shown in the diagram below.
- The prime factorization of 22 is 2 x 11 = 22. Like 56, the sum of the prime factors of 22 is 13.
- The sum of all the factors of 22 is 1 + 2 + 11 + 22 = 36. Thirty-six is a number rich in mathematical properties.
- The numbers 22 and 78 sum to 100, another very significant number.
- The atomic number of titanium is 22. Titanium has the highest strength-to-density ratio of any pure elemental metal.

## Math Facts About the Tarot Deck

The 22 major arcana cards are numbered from 0 to 21. The 56 minor arcana cards are divided into four suits of 14 cards each; each suit consists of 10 cards numbered ace through 10 and four court cards (page, knight, queen, and king). In games, it is conventional that an ace is worth one, a page worth 11, a knight worth 12, a queen worth 13, and a king worth 14. If you add up the values of all 78 cards in a traditional tarot deck, you get

(0 + 1 + ... + 21) + (4)(1 + 2 + 3 + ... + 12 + 13 + 14) = 651

The number 651 is the 21st term in the pentagonal number sequence. The sum of all the factors of 651 (including 651 itself) is 1024, which is the 10th power of two.

There are 4,675,765,217,094,107,136,000 possible Celtic cross spreads if you include reversals, but only 4,566,176,969,818,464,000 possible spreads if you don't count reversals. These numbers differ by a factor of 1024.

There are 73,920 possible three-card tarot spreads using only the major arcana, where both the order of the cards and their orientation (right side up or reversed) matter.

There are 3,651,648 possible three-card tarot spreads using all 78 cards, where both the order of the cards and their orientation matter.

## References

Pegs and Rope: Geometry at Stonehenge (Nature Precedings)

Partition Numbers (Wolfram Research)

Tetranacci Sequence (Online Encyclopedia of Integer Sequences)

A Cultural History of Tarot: From Entertainment to Esoterism (Journal of Folklore Research)