The Wizard’s Tower is home to a specialized numeral system centered around the numbers 18 and 108. While the relationship with the World Doors is plainly apparent, this system appears to have its basis in numerology and encryption rather than calculation and mathematics.
The Numerical System
Whoever created the Tower did so according to a hybrid octodecimal (base-18) / senary (base-6) numeral system. The concept of zero is not present, and the system appears to be highly specialized for use with basic Tower functions.1
In this numeral system, the primary numerical grouping runs from one through eighteen, similar to Earth’s decimal numeral system which runs from one through ten. These groups are repeated six times with six distinct notations for a total of 108 numbers.
Below are the 108 numbers of the fundamental numerical grouping that mirrors the doors lining the outer wall of the Tower.
A B Γ Δ Ε Z H Θ Ι Κ Λ Μ Ν Ξ O Π P Σ
ΣA ΣB ΣΓ ΣΔ ΣΕ ΣZ ΣH ΣΘ ΣΙ ΣΚ ΣΛ ΣΜ ΣΝ ΣΞ ΣO ΣΠ ΣP Τ
ΤA ΤB ΤΓ ΤΔ ΤΕ ΤZ ΤH ΤΘ ΤΙ ΤΚ ΤΛ ΤΜ ΤΝ ΤΞ ΤO ΤΠ ΤP Φ
ΦA ΦB ΦΓ ΦΔ ΦΕ ΦZ ΦH ΦΘ ΦΙ ΦΚ ΦΛ ΦΜ ΦΝ ΦΞ ΦO ΦΠ ΦP Y
YA YB YΓ YΔ YΕ YZ ΧH YΘ YΙ YΚ YΛ YΜ YΝ YΞ YO YΠ YP Ψ
ΨA ΨB ΨΓ ΨΔ ΨΕ ΨZ ΨH ΨΘ ΨΙ ΨΚ ΨΛ ΨΜ ΨΝ ΨΞ ΨO ΨΠ ΨP Ω
This system does not lack the capacity to reach higher numbers, though one might assume from its clumsiness and lack of zero that higher numbers weren’t often needed. As mentioned, this appears to have been a specialized numeral system specific to the Wizard’s Tower.
Numbers beyond 108 were notated in the following way:
Ω = 108
ΩX = 108*2
ΩV = 108*3
ΩXX = 108*4
ΩVX = 108*5
ΩVV = 108*6
ΩVXX = 108*7
ΩVVX = 108*8
ΩVVV = 108*9
ΩVVXX = 108*10
ΩVVVXX = 108*11
ΩVVVV = 108*12
Whatever the Tower truly is, it deals with concepts involving complex mathematics and numerical values both astronomically huge and miniscule. It is clear the system as outlined falls far short for such demands.
As such, it seems to be generally agreed by those who have added their observation to the Library that it is a specialized system, much like Earth computer systems use binary, senary, nonary, and other numerical systems in their designs.
But why this strange hybrid system based around the numbers eighteen and six? While the answer to that question has so far remained unanswered to me as I scour the Library, it does appear that most agree the answer lies in the arrangement of the World Doors.
The Koine Greek Question
The numbers themselves are represented as Koine Greek characters2 and appears to also have the dual purpose of representing linguistic letters3 as is typical with arithmantic and thaumatagraphic endeavors.
The Tower numerical system as it is understood by the Aurantians is derived from the engravings above each World Door showing one or two Greek letters. These engravings are repeated in engravings below each cabinet in the Key Room matching its corresponding Key.
Based on the comprehensive study of the World Door designations, Rodolfo the Clock Maker was able to reverse-engineer the the hybrid base-18/base-6 nature of the system. This unlocked much of the basic arithmantic functionality of the Tower.4
Curiously, the Tower is almost certainly vastly older than the Koine alphabet. In fact, 5 Koine itself is adapted from an earlier Phoenician alphabet. This means it evolved on Earth and Atlantis, and was not introduced to either. Yet the letters impressed into the wall atop each World Door appear to be original, dating to the creation of the Tower itself.
While Greek does exist natively in most of the Worlds of Atlantis, it seems unlikely the Tower was created by Atlantic beings. However, given the strange temporal anomalies surrounding it, such a hypothesis is possible when taking into account time travel.
Numerology and Ciphering
When you send a signal, say a television signal over a radio frequency, you aren’t actually sending out the sounds and images that make up your broadcast. You’re sending out an encoded stream of data that is interpreted by an antenna and television set to display those pictures and sounds.
In a similar way, messages meant only to be seen by one or two people are often encrypted and require a cipher to decode. Encrypted messages abound in the Tower, some perhaps hundreds of thousands of years old, the original conspiracy members long since turned to dust.
Several systems that use the Tower’s alphabetic numeral system have been identified in use within the Tower, both in “official” capacities and those adapted by presumably-alien inhabitants over the years. These can be divided into two broad categories: Arithmancy and Bibliocryption.
Thanks to its dual nature as a numeral system, the Tower’s Hellenic Alphabet is well-suited to both encryption and divination.
Isopsephy,6 Gematria,7 and other more esoteric forms were identified by Malicule the Meticulous8 and expanded upon by Rodolfo the Clock Maker9 in their research into the workings of the Tower in the 3rd and 4th centuries, 69A.
More than simple encryption, what is revealed through Arithmantic Encryption is typically a magical spell of some sort. General control and maintenance tasks hidden in engravings located throughout the Tower were the first discovered by Malicule the Meticulous and remain the most common.
For the most basic functions of the Tower, such as World Door activation and Elevator operation, symbolons are used.
It was Laddys Fermille who discovered the presence of arithmantic symbolons connected to the Tower in les Plusieurs Mondes.10 Most often these were seen in conjunction with Tower Door thaumatagrams. However, more can be found in worlds in which the original Tower Door is preserved.11
Better known in your world as a Book Cipher,12 various messages, codes, and even literature can also contain hidden messages. Bibliocryption is by far the most common type of cipher throughout les Plusieurs Mondes due its prolific usage on monoliths and other low-entropic media.
Unlike Arithmancy, which is used mainly as a container for magical spells, bibliocryption is used to pass messages, passwords, locations, and a variety of information.
The alternate Earths have been found to contain a great deal of bibliocryptic material. Fermille conjectured that this is due to the athaumatic properties of Earth universes making arithmancy difficult at best.
- Zero as a concept arose on both Earth and Atlantis. It has been present as a concept on Atlass since at least the 21st Aeon, however evidence brought to light by Laddys Fermille suggests it was imported through the Tower rather than developed natively. (Fermille, Laddys. Tower and Multiverse. 6th ed. Puce: Aurantian Concordat Press, 1322 69A.)
- The system makes use of most characters within the Greek alphabet.
- This is a similar practice to the Hebrew numeral system which uses characters to represent both letters and numerals,
- Rodolfo the Clock Maker. Rediscovering the Arithmantic Arcana of Purple-13. 1st ed. Puce: Aurantian Concordat Press, 302 69A.
- For reference: Koine Greek
- Malicule the Meticulous. Comprehensive Physical Evaluation of Purple-13. 1st ed. Vol. 19. 36 vols. Puce: Aurantian Concordat Press, 287 69A.
- Rodolfo the Clock Maker. Reverse-Engineering the Arithmantic Properties of Purple-13. 1st ed. Puce: Aurantian Concordat Press, 302 69A.
- Fermille, Laddys. Pseudo-Hemoglobular Efficacy in Ritualized Casting. 12th ed. Puce: Aurantian Concordat Press, 723 69A.
- Portals to the Tower are opened through the activation of a thaumatagrammatic inscription.
- Book Cipher