Numerology

Numerology is the study of numerical values in the letters of words, names and ideas, and the belief in mystical relationships between numbers and coinciding events.

In Toaru Majutsu no Index, certain numerological aspects are connected to various forms of Magic.

Principles
In various traditions across the world, certain numbers have been given certain meanings. These meanings, representation and symbolism, can be utilized in and affect magic in certain ways.

There are various numerological techniques for calculating the values associated with a particular subject. Two such methods are and.

Gematria
Gematria (ゲマトリア) is a code system used in Kabbalah and other fields, which assigns numerical values to Hebrew characters and words made from them, with various meanings derived from these values.

The twenty-two letters of the Hebrew alphabet (which are also associated with the paths of the Sephiroth) are each assigned an initial numerical value. For a word made up of these characters, the respective numbers of its components are used to calculate the word's number. For characters and combinations with a multiple-digit value, the digits are added together to produce a single-digit number (e.g. for 300, 3+0+0=3). For example, a combination of Mem and Shin (40 + 300), with each digit split out separately and summed together, the result comes out as a 7. If the result of the sum is a multiple-digit value, the process is repeated with the digits of this value until a single-digit number is left (e.g. for 390=300+90, 3+9+0=3+9=12, then for 12, 1+2=3).

Two words with the same number are considered to have the same meaning. However, a result can have more than one meaning - they can be read simply as they are, or they can be read as a sum (e.g. Shin's numerical value is 300, which becomes 3 - this can be 3 (Gimel) or 1+2 (Aleph and Bet)). Depending on how it is broken down, the possibilities are endless, which has been noted as why a powerful grimoire can be a hotbed of misreadings.

The numerical values typically assigned to Hebrew characters in Gematria are:

Angel Fall Arc
Misha Kreutzev chants an incantation and forms several serpentine columns water taken from a nearby source to strike Kamijou Touma like a sword. The incantation uses Hebrew numerals, a number corresponds to a letter of the Hebrew alphabet.

Academy City Invasion Arc
Aspects of numerology were incorporated into the -derived Wooden Stake Magic which the Roman Catholic Church intended to use to skewer the residents of Academy City who had been rendered unconscious by Vento of the Front's Divine Punishment.

British Royal Family Arc
When Elizard explained to Kamijou Touma about the Curtana, it was mentioned that made use of the four nations of England, Scotland, Wales and Ireland as part of one large nation in the spell he was constructing, in order to use the 'land' aspect symbolized by the number four.

World War III Arc
When Fiamma of the Right uses the Star of Bethlehem to reset the distorted four elements as part of Project Bethlehem, he was referred to as monopolizing the numbers three and four, associated with the heavens and the earth, which were important numbers in Christian culture.

Aleister Crowley Arc
During the events in Windowless Building on December 11th, it was mentioned that the number associated with both Aiwass and Thelema is 93.

Processor Suit Arc
During the events in the evening of December 11th and the morning of December 12th, Aiwass's numerical value of 93 is mentioned again, together with Coronzon's numerical value of 333.

Coronzon Arc
The final barrier of the England-Londinium Fortress was said to have been intentionally randomized, such that enemies cannot make fixed correspondence tables using and other similar methods to untangle it. Being composed of triple barriers of four different types, a combination of 3 and 4 just like the UK's combination of three factions and four regions, it was noted by Index to give physical repulsive force to the rules permeating the land and space, using aspects of national or regional character which work to distance outsiders.

During the events surrounding the Ceremony of Mo Athair, the Honours of Scotland (three regalia, together with the Stone of Scone) were noted to be another pair of 3 and 4, like the system behind the Curtana. The ten sides of the Queen Britannia's heliport temple were also noted to represent the ten Sephirah. Later, during the attack on the Queen Britannia, Qliphah Puzzle 545 realized her essence as a guide to the Abyss inherited from her creator, declaring her number to be the true 11, meaning 'the stepping stone of wickedness that supports good deeds'.

Christmas Day Arc
During the battle with Kamijou Touma and St. Germain on Christmas Day, Anna Sprengel made use of Gematria, in conjunction with the rose symbol with twenty-two petals corresponding to Hebrew characters, in order to determine the type of power that was formed within her right hand using Aiwass's power. The jewel store which the fight ended up in, one affected by R&C Occultics, was offering a December Gematria Special, converting customers' names to numbers free of charge to find gems for them.

Uses of Numerology within the story

 * Gematria: An alphanumeric code for assigning numerical values to Hebrew or English word based on its letters, and a system of numerology.
 * Misha Kreutzev used an incantation, which included both Hebrew characters and their respective numerical values, to form several serpentine columns water taken from a nearby source to strike a target like a a sword.
 * Index refers to Gematria while discussing the intentional randomization of the England-Londinium Fortress's final barrier, which prevents people from untangling it via correspondence tables using Gematria and other similar methods.
 * Anna Sprengel has made use of Gematria in the control mechanism for determining and switching between different powers formed within her right hand using Aiwass's power.