How to create a custom gematria system for a world? [closed]

Question

I just recently asked What are the origins of the various forms of Gematria? and What are the rules for constructing a gematria system? Now I am wondering how to create a custom gematria system for a world building project.

What are the rules for creating a gematria system? By this I mean associating letters of some writing system / conscript to numbers. How did the ancient people go about mapping numbers to the letters? I get the obvious ones like 1-26 A-Z (well, even then, its obvious now because there is an order, but how did they decide to order them is another question!), but as the other post demonstrate, some are not so obvious. Do they need to reflect reality in some way, or does it even matter what numbers you select to go with each letter/symbol in your conscript?

Answer 1

Two Ingredients

Ordering

The first ingredient is the ordering of the letters. Greek, Roman, Cyrillic, and Hebrew go something like ABC. . . I imagine this was a conscious decision. For example Ancient Roman teachers were aware of the Greek language and alphabet. Arabic seems to be its own thing. Farsi seems to be related. I imagine other languages in the same group use the same order. Futhark is different again.

If you make up your own alphabet you get to decide the order. It is up to your imagination.

Reduction

On the first step we assign each letter to a number and then add up the numbers. If that number is too big we reduce it again. The most common rule reduces $$1349 \to 1+3+4+9 = 17 \to 1+7=8$$

and we stop when we get a single digit.

This reduction rule depends entirely on how we write the number. It only makes sense to people who write things in base 10. If we wrote in binary or octal or hexadecimal we'd get a different reduction rule, and a different range of final values rather than just 0,1,2,3,4,5,6,7,8,9.

To understand this the decimal reduction can be described as

Lower the number by 1000 and add a bean to a pile. Keep lowering the number by 1000, and adding another bean, until the number is less than 1000. Then repeat the process with 100, 10 and 1. Each time the number decreases add an extra bean. When the number is reduced to zero, count the beans. This is the reduction.

In a different system the numbers 1000,100,10,1 might be different. For example the Ancient Mayans used 360,20,5,1.

The dots are 1s and the bars are 5s. One example of a reduction works like this.

$$37 \to 32 \to 27 \to 22 \to 17 \to 12 \to 7 \to 2 \to 1 \to 0$$

We pull out 5s until we cannot any more. Then we pull out 1s. There are 9 steps.

Homework: Reduce 9 using the same procedure.

Answer 2

For reference, the Greek numerals

Ancient Greeks used an ingenious system for writing numbers; they used for this purpose the letters of the Greek alphabet, as follows:

• The eastern (Ionic) form of the alphabet has twenty-four letters, as we all know: ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ; but ...

• The western form of the alphabet has two more letters:

  • wau Ϝ, and
  • qoppa Ϙ;

• And in very olden days (old even from the point of view of Classical Ancient Greece), in Ionia they had a letter which in later days they called sampi ϡ. (When it actually was used as a letter in the mists of time its name was san and its shape was something like Ͳ.)

This makes a total of 27 available letters, in alphabetical order ΑΒΓΔΕϜΖΗΘΙΚΛΜΝΞΟΠϘΡΣΤΥΦΧΨΩϡ. They used them to represent units, tens, and hundreds:

• ΑΒΓΔΕϜΖΗΘ represented 1 2 3 4 5 6 7 8 9.
• ΙΚΛΜΝΞΟΠϘ represented 10 20 30 40 50 60 70 80 90.
• ΡΣΤΥΦΧΨΩϡ represented 100 200 300 400 500 600 700 800 900.

All in all a number such as 314 would have been written ΤΙΔ´. Modern Greeks still use this system for the same purposes that in languages using the Latin alphabet we use Roman numerals; to distinguish letters-as-digits from letters-as-letters, they have a special symbol called keraia ´ which they put after the sequence of letters used as digits. (In the Antiquity, the keraia was used to denote the inverse of a number, so that for example Ζ´ meant 1/7.)

^{In modern usage, the letter wau is long forgotten, and for 6 they use a medieval symbol called stigma ϛ; and the letter qoppa has changed its shape to Ϟ, making it difficult to see its relationship with Latin Q.}

Other similar systems

• The Hebrews copied this system at some point after Alexander the Great spread Greek culture far and wide and the Hellenistic civilization ruled supreme in the classical world. The Hebrew alphabet has only 22 letters; the units are represented by the first 9 letters, the tens by the next 9, and the hundreds are more complicated: 100, 200, 300 and 400 have their own letters, and 500, 600, 700, 800 and 900 are represented as 100+400, 200+400 and so on.

• When the Slavic language acquired its own alphabet based on the Greek alphabet, it had the opposite problem: it had too many letters. 27 of those letters are used in the same way as the corresponding Greek letters, and the rest are simply not used for writing numbers.

  ^{Note 1: Modern Slavic languages do not use the ancient Slavic numerals. At all. They use Arabic numerals, and in very rare situations Roman numerals. Do no write ФПЅ and expect a Russian to understand 586. (The Ѕ is the Cyrillic letter dzelo, which a modern Russian wouldn't even recognize as a Cyrillic letter at all, it having been abolished by Emperor Peter the Great in 1708.) This system went out of fashion in the 18th century.}

  ^{Note 2: But a small shard of this system remains in the colloquial names of the letters И (derived from Greek eta Η) "octal I" and Ї (derived from Greek iota Ι) "decimal I".}