Some random things to throw into the pot:
The Saturn square is also the Lo Shu. This brings us into the I Ching being derived from the Lo Shu and the concept of the I Ching as a repesentation of a lunar calendar.
http://www.emotions.64g.ru/xron/xr5en.htm This suggests that there IS a direct way of using magic squares as an astrological forecasting device.
Similarly, Men Dun Jia is an ancient Chinese form of divination based on the I Ching and directly uses the Saturn square. ?A series of symbols is imposed on a 3 x 3 magic square, and the symbols are rotated around the magic square every two hours, in accord with the double ? hour of the traditional Chinese lunar calendar. The symbols are arranged in four levels which correspond to Heaven, Spirit, Earth, and Humanity, and rotate from square to square? tarotcanada.tripod.com/ChineseOrWesternMedicine.html
The Tibetean mewas are focussed around all nine permutations of the Saturn square. The mewas move move with each month, day and year. If you follow the track of their movement, you end up with the Saturn seal with additional lines filled in.
http://66.102.9.104/search?q=cache:I2fo ... =firefox-a
The system of Byung rTsis (Nagtsi) has no mathematical calculations or planetary observation but is based on the relationships of the five elements, twelve animal signs, nine magic square numbers and the eight parkha trigrams. Each year has its own element and animal sign, and also each month, day and hour has its own element. Elemental astrology is used to construct a birth horoscope, marriage compatibility, yearly predictions, medical calculations and death horoscopes for funeral arrangements.
This is more or less what it says at
http://www.tibetan-astrology.com/
What it doesn?t say is that the hours appear to be planetary hours, so I don?t see how we lost all calculation. Also the elemental calendar is based on a solar/lunar cycle and each year begins with a new Moon. It looks like there?s more astrology that we?d recognise here than tends to be stated.
More is at
http://www.tibetan-astrology.net/
Michelangelo?s ceiling at the Sistene Chapel:
?Another extremely important feature in the design of the ceiling is that the overall design?s pattern is in the shape of several 3 x 3 squares, Kameas of Saturn (see: Diagram #11b). These should be seen as 3 x 3 squares because the spine of the ceiling with its nine central panels is broken up into three biblical categories, Creation, Adam and Eve, and Noah. Each of these categories has three panels. When each set of three panels is viewed individually with its adjoining panels to its right and left the 3 x 3 square is depicted again and again. In looking at the mosaics in the floor of the chapel it can be seen that there is one large 3 x 3 square formed by circles in front of the altar and two smaller ones flanking the altar (see: Diagram #1).?
http://www.rosecroixjournal.org/issues/ ... meegan.pdf
The Saturn square pops up in Japan in nine stars theory:
The astrology using the 9 stars is called "kyu-sei jyutsu" (nine stars theory) and there are many variations thereof. Nine stars theory says that there are nine signs in the sky ( like zodiac signs ) and the nine stars change their places from one to another sign and the world changes accordingly. The nine signs are placed on a diagram similar to that of the magic square, one in the center, which is dominant over time and space, and 8 others surround the central sign. A star is identified for a person according to his birth year and the relations between his star and the present constellation decides his present luck.
http://www.okada.de/archive-japanasitis ... ation.html
(An odd thing I found. It's possible to create a magic square of month, day, year and day of week. So clearly, a magic square can be calendrical, using the Western calendar, which favours a direct astrological connection.
http://savantartist.com/about.html)
The Saturn square at least seems to pop up everywhere, and that in a number of systems it's the basis of a divination that's associated with astrology. The association with talismanic magic, in the West at least, seems to all hinge on Agrippa. But I can't help thinking that this is only part of their original function. I think your first premise was right. There is something lost or forgotten, it may well take us a little while to find it
Kim