Tiriel

The planetary magic of Mercury gathers the names, seals and number-square attached to that planet in the Western magical tradition. Its magic square, or kamea, is of order 8, a grid of 8 by 8 cells holding the numbers 1 to 64 so that every row, column and diagonal sums to 260.

Square, intelligence and spirit

From that square are derived, by gematria, the names of the planet's two governing powers: the Intelligence Tiriel, the ordering and benevolent aspect, and the Spirit Taphthartharath, 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 Ophiel, 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 Mercury table is an eight by eight square of the numbers one to sixty four, adding to two hundred and sixty in every row and column, and to two thousand and eighty in total. It is the largest of the even ordered tables and the one with the most freedom in its construction, so manuscript copies vary considerably in which number sits in which cell while the sums remain exact.

The intelligence of Mercury is Tiriel and the spirit is Taphthartharath, and this pair is the neatest illustration in the set of how Agrippa's naming works. Tiriel returns two hundred and sixty, the row sum. Taphthartharath, a much longer name with several high value letters, returns two thousand and eighty, the total of the square. The names are built to those targets, and the reduplicated syllables of the spirit name are the sound of a word being lengthened until the arithmetic comes out right.

That is worth stating plainly because it inverts how these names are usually read. They are commonly presented as ancient god names of unknown origin. They are constructions with a known method, printed in a known book, and their strangeness is a by product of gematria rather than evidence of antiquity.

The Golden Dawn revived the whole system in the late nineteenth century and Taphthartharath appears in its records as the spirit invoked in a well documented Mercury working, which is how the name reached the twentieth century occult revival.