Geomancy, a system of divination documented by Cornelius Agrippa, was highly popular in the Middle Ages. Geomancy is based on the principle that Earth's energies could be contacted, honed and intuitively understood by a geomancer in order to answer questions about the future. Though many methods of probability and chance were used to "draw the earth energies", the most common was for the geomancer to cut a series of lines or dots in soil or sand. These dots were then formed into "characters", using a set system of interpretation (based on binary numbers), with a total of sixteen character possibilities.
Caput Draconis and Fortuna Major are two of these geomantic characters. "Caput Draconis" (Head of the Dragon) is the first password into Gryffindor tower that Harry learns in Book 1 {Ch 7}, whereas, in Book 3, "Fortuna Major" (Greater Fortune) is the Gryffindor password.
Albus and Rubeus are two other geomantic characters with a special relationship. Albus (white) represents peace, wisdom and purity, while Rubeus (red) indicates passion, power and violence. The sixteen geomantic characters are divided into eight pairs of opposites. Albus and Rubeus are one set of opposing figures.
By JKR's accurate use of the geomantic passwords, it's clear to me that she must be aware of geomancy and, thus, of the implications behind the choice of names for Dumbledore and Hagrid. Their role in the septology probably carries geomantic hints as well.
This discussion will analyse how Dumbledore and Hagrid reflect their geomantic characteristics, how they relate to each other, and their interaction with Harry. I will also focus briefly on a few related symbols from alchemy that refer back not only to Dumbledore and Hagrid, but bring in Sirius Black and Severus Snape as well. Finally, I'll provide an overview on how these geomantic and alchemic clues could play out in the final book.