The Numbers

"Every number is infinite; there is no difference." -- Liber AL vel Legis, I:4

In the history of mysticism, numbers have long been held as sacred. There is a sense that they exist "a priori" in a Kantian sense, i.e., that they exist whether or not there are any humans or other sentient creatures around to count them. Some have suggested that they might be the only "true" universal alphabet. It is hard to imagine that they might be explicitly human developments -- a concept which lends itself readily to the notion that they are divine.

Pythagoras believed that numbers were literally the "stuff" out of which the things of universe were made. By this of course he meant integers, or ratios of two integers -- rational numbers. What, after all, cannot be described with numbers? To describe is to name, and to name is to have power over something; this lesson is codified prominently in the Biblical book of Genesis, and is a powerful formula in magick. Therefore numbers "ruled" the universe. How vexing it was, then, for Pythagoras when he discovered that there were irrational numbers that could not be described with other numbers. Numbers important to geometry, which could not just be cast aside, turned out to be irrational -- pi, the square roots of 2, 3, and 5, and so on.

Pythagoras developed notions about numbers that exist to this day. In his theory of numbers, 1 was considered the ancestor of the other numbers, and, in a sense, not properly a number as the others were. Even numbers were "female" while odd numbers were "male." He also developed the concept of the prime number, a number that cannot be evenly divided by any other number. Another concept introduced by Pythagoras was that of the perfect number: this is a number such that its multiplicative factors (except itself) also add up to give the number. The first perfect number is 6: 1, 2, 3, and 6 are the factors of 6 (since 6 = 1x6 = 2x3), and 1+2+3 = 6. Relationships between two numbers were important to Pythagoras; for example, he defined friendly numbers which had a relationship such as this, between 220 and 284:

284 = 1x284 = 2x142 = 4x71

220 = 1x220 = 2x110 = 4x55 = 5x44 = 10x22 = 11x20

Adding the factors as though they are perfect numbers (all but the number itself), we find that

1+2+4+71+142 = 220

1+2+4+5+10+11+20+22+44+55+110 = 284

He also defined functions for the various plane figures: triangles, squares, etc.:

number	triangle	square
1	1	1
2	3	4
3	6	9
4	10	16
5	15	25
6	21	36
7	28	49
8	36	64
9	45	81
10	55	100

The square numbers, as you can see, are still used today.

Qabalistic meanings of the numbers

Number	Sphere / Path	Hebrew Letter	Name	Gematric Value	Tarot	Attribution
1	Kether		Crown		Aces
2	Chokmah		Wisdom		Twos, Kings	Zodiac
3	Binah		Understanding		Threes, Queens	Saturn
4	Chesed		Mercy		Fours	Jupiter
5	Geburah		Strength		Fives	Mars
6	Tiphareth		Beauty		Sixes, Princes	Sun
7	Netzakh		Victory		Sevens	Venus
8	Hod		Splendor		Eights	Mercury
9	Yesod		Foundation		Nines	Moon
10	Malkuth		Kingdom		Tens, Princesses	Earth
11	0	Aleph	Ox	1	Fool	Air
12	1	Beth	House	2	Magician	Mercury
13	2	Gimel	Camel	3	Priestess	Moon
14	3	Daleth	Door	4	Empress	Venus
15	4	Heh	Window	5	Emperor	Aries
16	5	Vau	Nail	6	Hierophant	Taurus
17	6	Zain	Sword	7	Lovers	Gemini
18	7	Cheth	Fence	8	Chariot	Cancer
19	8	Teth	Snake	9	Strength	Leo
20	9	Yod	Hand	10	Hermit	Virgo
21	10	Kaph	Fist	20, 500	Wheel	Jupiter
22	11	Lamed	Ox Goad	30	Justice	Libra
23	12	Mem	Water	40, 600	Hanged Man	Water
24	13	Nun	Fish	50, 700	Death	Scorpio
25	14	Samekh	Prop	60	Temperance	Sagittarius
26	15	Ayin	Eye	70	Devil	Capricorn
27	16	Peh	Mouth	80, 800	Tower	Mars
28	17	Tzaddi	Fish Hook	90, 900	Star	Aquarius
29	18	Qoph	Ear	100	Moon	Pisces
30	19	Resh	Head	200	Sun	Sun
31	20	Shin	Tooth	300	Judgment	Fire
32	21	Tau	Cross	400	Universe	Saturn

Another way to look at the numbers qabalistically is to list what they count:

3, Mother letters
4, Elements, Directions, Worlds
7, Planets (traditionally); Double letters
10, Sephiroth
12, Signs of the Zodiac; Simple letters
22, Paths
28, Mansions of the Moon; Kings+Seniors (Enochian)
30, Aethyrs (Enochian)
36, Decans of the Zodiac
72, Quinances of the Zodiac; Shemhamphoresh Angels
78, Cards in the Tarot
91, Parts of the Earth (Enochian)
216, Letters in the Shemhamphoresh
231, Gates to Understanding

Many sets of symbols in magick are based on these numbers. For example, each decan of the Zodiac has an angel, and each has a demon. In many ways these numbers are magickal "codes" or "keys" of use in raveling, and unraveling, the symbolism used in ritual. (Another key, of course, is gematria, which is discussed elsewhere.)

Here is a link to a numerical spreadsheet listing the various number theory properties of the numbers 1-1000.

Bibiography and Works Cited.

Terry, Leon. The Mathmen. New York, NY: McGraw-Hill, 1964.

Wang, Robert. The Qabalistic Tarot. York Beach, ME: Samuel Weiser, 1983.