Monday, November 30, 2009

Table of the Voice of Angels


The table of the voice of angels.

The first row: P as in Map, Ch as in Catch, K as in Lack, Ts as in Rats, T as in Art.

The second row: F as in Laugh, Sh as in Fresh, Kh as in Loch, S as in Mass, Th as in Myth.

The third row:  All are as the sound of wind, with no voice.

The fourth row: B as in Drab, Dj as in Large, G as in Morgue, D as in Had.

The fifth row: V as in Crave, Taj, Gh like Kh but vibrating, Z as in Praise, Dth as in Lathe.

The sixth row: W as in Cow, R as in Far, % carries the vowel, Rr like R but trilled, L as in Quell.

The seventh row:  M as in Lamb, Y as in Fray, Ng as in Sing, # stops the voice, and N as in Man.

Friday, November 20, 2009

Agrippa's Magic Squares - Part 2.

The Formation of the Magic Squares

In the previous part, we learned The Sequence of the Planets.

Now, we will apply that knowledge to form the Magic Squares (sometimes called Kameas) and attribute them to the Planets.

A Magic Square is an array of numbers where the sum of each of the columns, rows, and the two diagonals are all the same.  This sum is called the magic constant.

The type of squares we are dealing with are considered "Normal Magic Squares."  This means that each such square of an order N will contain integer values starting from 1 up to N-squared.

This means our Saturn square, being of the order 3, will contain integers from 1 to 9.

Magic Squares were known to Chinese mathematicians as early as 650 B.C.  There is essentially only one possibility for the normal order-3 square, although it can be reflected or rotated in various ways.  To the Chinese this was known as the Lo Shu square.

SATURN (3x3 ... Constant=15)


The Seal of Saturn (at the right, above) is made by connecting the cells with numbers 1-2-3, then 4-5-6 (the diagonal), then 7-8-9, thereby touching every cell in the Magic Square in the order it was created.  The diagonal is drawn a bit too long in the image.  The circles at the end of the line segments are most likely placed there for aesthetic purposes only, and differ between various depictions of the seal.

Agrippa's Magic Squares follow a certain pattern.  All of the squares of an "odd order" are made by placing the "1" on the middle column, one cell down from the center, then walking "southeast" and placing each subsequent number, allowing to wrap from the bottom to the top, and from the right to the left, whenever needed.  If an occupied cell is found, go "south" two squares instead of going southeast, and continue until the square is filled.  The Saturn square shown above agrees with this construction method.  (The diagonal formed by numbers 4, 5, and 6 are the easiest to see, since they neither wrap from side to side nor hit an occupied cell.)

Squares of an "double even order" (in other words, whose order is a multiple of 4) are made by counting from right-to-left, top-to-bottom starting from 1, but only filling in the diagonals (for order-4) of each 4x4 section. Then, repeating the process for the remaining squares, but counting down instead of up.  In other words, taking the black numbers from the following two squares, and combining them:

Order-4 Diagonals:


Order-4 Remaining:


The seal of Jupiter (above right) shows the method of constructing the 4x4 Square, by indicating the diagonals, and tracing a circle over the remaining cells, thereby touching every cell in the Magic Square.

Now, take the black numbers from both of the above squares, and combine them to get the following Magic Square:

JUPITER (4x4 ... Constant=34)


The following square is generated using the odd-order southeast walking method:

MARS (5x5 ... Constant=65)


I am currently uncertain what method was used to construct the following square:

THE SUN (6x6 ... Constant=111)


The following square is generated using the odd-order southeast walking method:

VENUS (7x7 ... Constant=175)


The following square is generated using the double-even-order method (I have indicated the lattice-work in bold):

MERCURY (8x8 ... Constant=260)


The following square is generated using the odd-order southeast walking method:

THE MOON (9x9 ... Constant=369)


There you have it!  All seven of our Planetary Magic Squares.

Next up...

The Names and Meanings of the Spirits and Intelligences

Agrippa's Magic Squares - Part 1.

Introduction to Magic Squares

Heinrich Cornelius Agrippa's Three Books on Occult Philosophy, Book II, gives instructions for a method of Talismanic Magic involving the Planets and Hebrew angels.  A Magic Square is given for each planet, and sigils are drawn using the square to represent the Angel (Intelligence), Demon (Spirit), and the Seal of each Planet.  These sigils and squares were copied with minor errors into Francis Barrett's Book "The Magus."

In order to decipher, check, or create the sigils on magic squares in the manner demonstrated in Agrippa's book we need to review some preliminary material.  We will be approaching the subject in the following order:

Part 1 - The Sequence of the Planets.

Part 2 - The Formation of the Magic Squares.

Part 3 - The Names and Meanings of the Spirits and Intelligences.

Part 4 - The Mispar Gadol method of Gematria.

Part 5 - Creating a Sigil.

Part 6 - Creating a Talisman.

Agrippa's Magic Squares - Part 1

The Sequence of the Planets

First, lets examine the relationships between the Planets and the days of the Weeks.  I will also list the names of the Sumerian, Babylonian, Greek, Roman, and Norse deities that were ascribed to these.

1. Sunday, Planet=Sun
Sumerian=Utu, Babylonian=Shamash  (Justice and Law)
Greek=Helios, Roman=Sol/Janus

2. Monday, Planet=Moon
Sumerian=Nanna, Babylonian=Sin (Wisdom)
Greek=Selene, Roman=Luna

3. Tuesday, Planet=Mars
Sumerian=Gugalanna (Great Bull of Heaven), Babylonian=Nergal (War, Lion)
Greek=Heracles/Ares, Roman=Mars, Norse=Tiw

4. Wednesday, Planet=Mercury
Sumerian=Enki, Akkadian=Ea, Babylonian=Nabu (Wisdom & Writing, Crafts, Water)
Greek=Apollo/Hermes, Roman=Mercury, Norse=Woden

5. Thursday, Planet=Jupiter
Sumerian=Enlil (Lord of the Wind), Babylonian=Marduk (Water, Solar Calf)
Greek=Zeus, Roman=Iuppiter, Norse=Thor

6. Friday, Planet=Venus
Sumerian=Inanna, Babylonian=Ishtar (Goddess of Love, Fertility)
Greek=Aphrodite, Roman=Venus, Norse=Freya

7. Saturday, Planet=Saturn
Sumerian=Ninurta, Babylonian=Ninurta (Lord of the Earth)
Greek=Kronos, Roman=Saturnus

This basic order should be familiar enough to all of us.  The ancient year was divided using a lunar calendar, but the astrologers used the stars to divide the year instead.  The ancient Babylonians split the year into 12 astrological signs of the zodiac or "houses."

They ascribed the following attributes to the twelve houses:

1. Life
2. Poverty/Riches
3. Brothers
4. Parents
5. Children
6. Illness/Health
7. Wife/Husband
8. Death
9. Religion
10. Dignities
11. Friendship
12. Enmity.

If we divide the year or the ecliptic into twelve equal sections of 30 degrees, we find that each sign lasts for 30 days plus a little change.

You will see that at the beginning of every sign (or zodiac-month), the starting day shifts by two.  For example, if the following sign begins with Sunday, it ends with Monday, and the next sign will start on Tuesday:


So if we follow the months for a whole year, we come up with a repeating sequence like this:

Sunday, Tuesday, Thursday, Saturday, Monday, Wednesday, Friday.

To translate these back into planets, we get:

Sun, Mars, Jupiter, Saturn, Moon, Mercury, Venus.

If we start that sequence with the Moon, because it is closest to us -- we come up with:

Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn.

This is the classical order of the Planets.  Now, I've actually had you work this problem in reverse.  This is the true starting point of the problem, and the order and layout in the weeks (or the assignment of the celestial bodies to the deities) was derived from this, but I wanted you to see how it connects to time and the zodiac.

You will note that this is not the order of the Planets from the Sun outward, instead it is the Z-Order (like the painters algorithm) of the planets in the depth that we perceive them from our vantage point here on earth.

We know the Moon is the closest, because none of the others ever pass in front of it.

We perceive Mercury and Venus as being between us and the Sun because when they pass in front of the Sun they transit it (like an eclipse.)  A transit can be observed by the naked eye but this is dangerous and will damage your eyes.  A safer way is by passing the light of the Sun through a telescope or pinhole, and projecting it onto a screen.

(Illustration:  The first observation of the transit of Venus.)

The relative distance of the other planets is derived from the speed of their orbit.  The longer the orbit, the farther out it must be.

Now, reverse the sequence, so that the list is in order from far to near:

Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon.

You will see that these correlate to the ruling planets on a traditional chart of the astrological houses:

1st House, ruled by Saturn, has joy in Mercury.
2nd House, ruled by Jupiter.
3rd House, ruled by Mars, has joy in the Moon.
4th House, ruled by the Sun.
5th House, ruled by Venus, has joy in Venus.
6th House, ruled by Mercury, has joy in Mars.
7th House, ruled by the Moon.
8th House, ruled by Saturn.
9th House, ruled by Jupiter, has joy in the Sun.
10th House, ruled by Mars.
11th House, ruled by the Sun, has joy in Jupiter.
12th House, ruled by Venus, has joy in Saturn.

This is the sequence in which the planets are ascribed to the Magic Squares.  But first, one problem has to be resolved.  There are not suitable magic squares for every number, specifically:  The 1x1 Magic Square doesn't make a lot of sense since the only possible sigil would be a single point, and it is impossible to form a 2x2 Magic Square, so the numbering of the Planets for our purposes will begin with 3:

3 = Saturn
4 = Jupiter
5 = Mars
6 = The Sun
7 = Venus
8 = Mercury
9 = The Moon

See Also: Wikipedia, Planets in Astrology and Wikipedia, Babylonian Astrology.

Next up...

The Formation of the Magic Squares.