Wikipedia:Reference desk/Archives/Mathematics/2021 March 23

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March 23

Lets imagine we apply the concept of radix economy to a sillabary language, what would be the amount of sillables with most radix economy?

There are languages that instead of symbols for letters, there are only symbols for syllabes, so there is no letter only syllabes. Imagine we applied the concept of radix economy to that, what would be the amount of syllabes with most radix economy?179.180.30.203 (talk) 22:03, 23 March 2021 (UTC)

A radix economy quantifies a cost, so less is better. I see a definition for the radix economy of a symbolic numeral in a given base, such as decimal or binary. I do not understand how to apply the concept to a language.  --Lambiam 01:20, 24 March 2021 (UTC)

Radix economy talks about amount of digits needed to write a number and the amount of unique digits you have, you could just change that to amount of syllabes to write some word (assuming any combination of syllabes is possible) and the amount of unique syllabes are using.2804:7F2:68C:C9BA:814D:3BE9:3AC3:5E4D (talk) 00:13, 25 March 2021 (UTC)

I guess the question is, what is the fewest number of graphemes possible in a syllabary (as opposed to an abugida). But the question doesn't make sense to me. The necessary number of graphemes is exactly equal to the number of possible syllables in the language, which will obviously depend on the language. For example, Chinese has a little over 400 possible syllables, while English has over 15,000. (Of course neither of these languages is normally written in a syllabary.) CodeTalker (talk) 19:14, 24 March 2021 (UTC)

It is also not perfectly clear what a "syllabary language" is. Mycenaean Greek was written with a syllabary, known as Linear B. In its reconstruction, the language has a larger arsenal of syllables than the number of syllabic signs of the script; the mapping from spoken syllable to sign is not injective. For example, sper (as in sper.ma) and p^he (as in the name i.p^he.me.de.ja) are both represented by the sign 𐀠. One could similarly design a syllabary for English with far fewer than 15,000 signs. Someone designing a conlang could construct all words from just two syllables, such as the nuclear syllables ⟨i⟩ and ⟨o⟩.  --Lambiam 21:15, 24 March 2021 (UTC)

I suppose the OP has in mind generating a lexicon from a fixed, presumably rather small, set of syllables. The radix economy is something like $WS{\frac {\log W}{\log S}}$ where W is the number of words (perhaps weighted by frequency of use) and S is the number of syllables. Factoring out $W\log W$, because you don't get to change that, leaves ${\frac {S}{\log S}}$, which has a minimum at e. Hm, not very helpful. —Tamfang (talk) 03:57, 30 March 2021 (UTC)

Since S is a whole number, the minimum is attained at 3, which is about a 5.5% improvement over a two-syllable language.  --Lambiam 09:44, 30 March 2021 (UTC)