Nakhiel

The planetary magic of Sun gathers the names, seals and number-square attached to that planet in the Western magical tradition. Its magic square, or kamea, is of order 6, a grid of 6 by 6 cells holding the numbers 1 to 36 so that every row, column and diagonal sums to 111.

Square, intelligence and spirit

From that square are derived, by gematria, the names of the planet's two governing powers: the Intelligence Nakhiel, the ordering and benevolent aspect, and the Spirit Sorath, the raw and unmediated force. This apparatus was set out by Heinrich Cornelius Agrippa in the Three Books of Occult Philosophy (1533), drawing on earlier Hebrew and Arabic number-magic. To the same planet is also joined an Olympic Spirit, here Och, one of the seven planetary governors named in the Arbatel of Magic (1575).

These names, squares and hierarchies are described here as an element of the documented tradition of Renaissance ceremonial magic, studied historically; the spirits are not reified.

The solar table is a six by six square of the numbers one to thirty six, adding to one hundred and eleven in every row and column, and to six hundred and sixty six in total. That total is the reason this square is the best known of the seven outside the tradition, because six hundred and sixty six is the number of the beast in Revelation, and the coincidence has been remarked on continuously since the tables were printed.

It is a coincidence of construction rather than a hidden message. The sum of the first n squared integers is fixed once the order is chosen, so a six by six magic square cannot total anything else. Any planet assigned a six by six table would have produced the same figure. The Renaissance writers knew this and were not much troubled by it; later commentators, arriving from the Revelation end, generally have not.

The names follow the usual derivation. The intelligence Nakhiel returns one hundred and eleven, the row sum, and the spirit Sorath returns six hundred and sixty six, the square's total, so the pair encodes the two characteristic numbers of the table between them. This is the clearest single demonstration of how Agrippa's naming scheme works, and it is worth reading alongside any of the other six.

Six is also an even order, which means the square admits very many valid arrangements and manuscript copies disagree about which cells hold which numbers. The sums do not vary, and it is the sums the system is built on.