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I was thinking about a way to memorize arbitrary sequences of digits by having the numbers actually represent a language, have a second meaning.

There are, presumably probably, infinite things the language of numbers could express.

One interesting property of this language unlike some human or programming languages is it is “total”: every possible arrangement of “letters” maps to an extension (its meaning, whatever the language represents).

I think there could be two primary focii in analyzing this.

One, the cognitive domain the arbitrary mathematical sequence maps to (sounds, colors, concepts, English words, other number sequences, shapes, or even all of the above?)

Two, the inherent mathematical structure or relationship between the sign and signified - is it the sum of the digits that determines its meaning? Is it a complex algorithm taking various functions on each incoming digit, individually? And so on.

I am just interested in any interesting number languages of any kind that have been developed in history. (Of course, we could start by thinking about ASCII-encoding and UTF-8, and maybe imagine how a base-10 encoding could map to some 10 fundamental elements of human communication, so as to always produce coherent, specific and meaningful concepts or sentences, no matter the choice of digits).

I personally like the idea of classifying all concepts by some well-known ontology and considering there to be 10 choices at each level. A level is like, a sub-concept in a hierarchy or taxonomy of concepts.

In other words, “178” could mean “crustacean”, because on level 1, we have 10 broad categories to classify all things in the universe as (exclusively or inclusively, I’m not sure if categories could overlap) - 1 is “life” - the next level subdivides life into types, so maybe 7 is “aquatic” - and then somehow 8 is the crustacean family. Another digit brings us more specific - 1785 is “Alaskan King Crab” (or something, for example).

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The big difficulty with an encoding like this is that the functional load is distributed very unevenly across the syllables. If you miss the sixth digit/syllable, that's not going to affect much. But if you misunderstand the first digit/syllable, now the entire meaning has gone awry! For human communication, it's best to distribute this functional load as evenly as possible, because speech is a very noisy channel. So these encodings don't tend to be very practical as languages.

But you can find some conlangs experimenting in this direction. The most famous is probably Solresol, which encodes everything in base seven (so that it can use the seven steps of a major scale or the seven classical colors). The encoding changes depending on the length of the word:

  • One- and two-note words are the most common function words
    • Two-note words with repeated notes are verb tenses
    • Two-note words without repeated notes generally come in pairs; reverse the order of notes to get the other element of a pair (like fasol "why" and solfa "because", or sido "same" and dosi "other")
  • Three-note words are the most common content words
    • Three-note words with a pair of repeated notes are the most common
    • If a three-note word has a clear opposite, reversing the order of the notes produces it
  • Four-note words are other content words
    • The combination of the first notes, and whether or not the word has a pair of repeated notes, sorts it into one of 14 categories
  • Five-note words are types of plants, animals, and minerals

The 14 categories don't have a consistent system of subcategorization, but it's a start!

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  • Wow, right on point, thanks. Commented Jun 24, 2023 at 3:31
  • What if the “load distribution” was a very specific object in the language, sort of like algorithms with checksums you can use to check if the message received was correct? Like, you take a “dense” language like Solresol, and apply a function to offset pre-calculated communication risk (ie, some mechanism to offset noise, various options, and to a precise, chosen degree). The language can state its own checksum formula in each message, maybe. Commented Jun 24, 2023 at 3:35

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