Zompist Bboard Again

Much has been written about how languages form the familiar counting numbers. But it recently occurred to me that I have never read anything about how languages form fractional or real numbers. English adds "point" to the whole number portion and simply lists the digits, but this seems obviously a case of the written form transferred into speech. Do other languages have their own methods?

malloc wrote: ↑Tue Jul 04, 2023 8:26 pm English adds "point" to the whole number portion and simply lists the digits

Does it? Of course this is the case when reading out a written number, but when actually talking about fractions it seems to be more usual to say the number of fractions: ‘one half’, ‘three quarters’, ‘nine tenths’.

bradrn wrote: ↑Tue Jul 04, 2023 8:46 pmDoes it? Of course this is the case when reading out a written number, but when actually talking about fractions it seems to be more usual to say the number of fractions: ‘one half’, ‘three quarters’, ‘nine tenths’.

Well ok, but I was thinking of numbers like 3.14159... and so forth. Fractions are indeed a counterexample but using fractions for every non-integral number seems rather cumbersome. Imagine saying "three and fourteen thousand one hundred fifty nine hundred thousandths".

malloc wrote: ↑Tue Jul 04, 2023 8:51 pm

bradrn wrote: ↑Tue Jul 04, 2023 8:46 pmDoes it? Of course this is the case when reading out a written number, but when actually talking about fractions it seems to be more usual to say the number of fractions: ‘one half’, ‘three quarters’, ‘nine tenths’.

Well ok, but I was thinking of numbers like 3.14159... and so forth. Fractions are indeed a counterexample but using fractions for every non-integral number seems rather cumbersome. Imagine saying "three and fourteen thousand one hundred fifty nine hundred thousandths".

I think most languages don’t even have a way of referring to irrational numbers.

malloc wrote: ↑Tue Jul 04, 2023 8:26 pm Much has been written about how languages form the familiar counting numbers. But it recently occurred to me that I have never read anything about how languages form fractional or real numbers. English adds "point" to the whole number portion and simply lists the digits, but this seems obviously a case of the written form transferred into speech. Do other languages have their own methods?

George Ifrah's The Universal History of Numbers would be my go-to reference on this.

I found some info on this while researching my books. E.g. in Akkadian, you wrote down the base-60 digits. A number like 4,15,34,38 could be a whole number, or 4*60 + 15 and a fraction, or 4 and a fraction, etc. We don't know how these were spoken out loud and whether that caused problems.

In Ancient Egyptian, the preferred way to write a rational number was to use reciprocals only. E.g. they would rather not say 2/5, but express this as 1/3 + 1/15.

malloc wrote: ↑Tue Jul 04, 2023 8:51 pm

bradrn wrote: ↑Tue Jul 04, 2023 8:46 pmDoes it? Of course this is the case when reading out a written number, but when actually talking about fractions it seems to be more usual to say the number of fractions: ‘one half’, ‘three quarters’, ‘nine tenths’.

Well ok, but I was thinking of numbers like 3.14159... and so forth. Fractions are indeed a counterexample but using fractions for every non-integral number seems rather cumbersome. Imagine saying "three and fourteen thousand one hundred fifty nine hundred thousandths".

Well, when you're selling your crops, that number (or anything along those fractional lines) doesn't really crop up much, does it? On the other hand, where did the name "Pi" come from?

keenir wrote: ↑Tue Jul 04, 2023 11:50 pm On the other hand, where did the name "Pi" come from?

Euler, if I recall correctly.

EDIT: yes.

bradrn wrote: ↑Tue Jul 04, 2023 11:54 pm

keenir wrote: ↑Tue Jul 04, 2023 11:50 pm On the other hand, where did the name "Pi" come from?

Euler, if I recall correctly.

EDIT: yes.

On one hand: Thank you.

On the other hand: drat, I was hoping the discussion could use it as an example of fractions (etc) taking their names from the vernacular of their day. (though, at the time, Greek was something the upper classes of Europe were expected to be able to speak/read)

On the gripping hand: thank you.

bradrn wrote: ↑Tue Jul 04, 2023 11:54 pm

keenir wrote: ↑Tue Jul 04, 2023 11:50 pm On the other hand, where did the name "Pi" come from?

Euler, if I recall correctly.

EDIT: yes.

Er, that link doesn't say that Euler came up with pi, he popularized it. William Jones had used pi in our sense in 1706. Earlier mathematicians used pi for the circumference.

zompist wrote: ↑Wed Jul 05, 2023 12:12 am

bradrn wrote: ↑Tue Jul 04, 2023 11:54 pm

keenir wrote: ↑Tue Jul 04, 2023 11:50 pm On the other hand, where did the name "Pi" come from?

Euler, if I recall correctly.

EDIT: yes.

Er, that link doesn't say that Euler came up with pi, he popularized it. William Jones had used pi in our sense in 1706. Earlier mathematicians used pi for the circumference.

Ah, sorry, I skimmed it too quickly. Still, keenir got the point I was making.

The European languages I know seem to treat digits like English, with the caveat that many use a comma where English has a point. E.g. in German pi = 3,14159... drei Komma eins vier eins fünf neun...
Colloquially, the first two positions after the comma are often read as one two-digit number (3,14 = drei Komma vierzehn), although math teachers try their darndest to suppress that.
English has specific forms for fractions up to "quarter", and uses ordinal numbers ("fifth", "sixth", etc.) after that. German has specific forms for all fractions, formed with the suffix -(s)tel for the regular ones, so 1/23456 is ein dreiundzwanzigtausendvierhundertfünfundsechzigstel*1), while other languages use ordinals also for the fractions of 2,3,4, although many languages have a specific word for "half".
*) The ordinal is "23456." dreiundzwanzigtausendvierhundertfünfundsechzigste
Russian works basically like English with regards to these matters, only that it also uses the comma instead of the point.

bradrn wrote: ↑Wed Jul 05, 2023 2:25 am

zompist wrote: ↑Wed Jul 05, 2023 12:12 am William Jones had used pi in our sense in 1706. Earlier mathematicians used pi for the circumference.

Ah, sorry, I skimmed it too quickly. Still, keenir got the point I was making.

BTW, fun fact.... That name rang a bell, and that William Jones is the father of the William Jones who is famous for positing the Indo-European family in 1786.

hwhatting wrote: ↑Wed May 31, 2023 11:40 am

MacAnDàil wrote: ↑Tue May 30, 2023 8:09 am According to Alexander MacBain’s An Etymological Dictionary of the Gaelic Language
For Welsh, I hereby refer to the following dictionary:
https://www.welsh-dictionary.ac.uk/

No serious linguist relies on McBain anymore; it's long outdated and contains a lot of speculative and nowadays rejected etymologies. The only reason it's still regularly referred to, mostly by amateurs, is that it's out of copyright and you can get reprints cheaply. I also have it at home, but would never rely on it. GPC is a much better source.

Coming back to this because I realise I am not sure of the better alternative: which sources are best on Gaelic etymology?

Surprisingly enough, the Ithkuil website only discusses natural numbers (and zero) with no explanation for fractions or real numbers, let alone complex ones. Considering the nature of the project, I would have expected mechanisms for handling pretty much every kind of number known, including stuff like quaternions and p-adics.

MacAnDàil wrote: ↑Thu Jul 06, 2023 1:35 am Coming back to this because I realise I am not sure of the better alternative: which sources are best on Gaelic etymology?

I don't think that there is anything more up-to-date specifically on Gaelic, but I'm also not really looking into Gaelic etymologies most of the times. My interests in Celtic are mostly Continental Celtic, and Proto-Celtic as far as it's relevant for PIE reconstruction; for the latter, there is Matasovič's "Etymological Dictionary of Proto-Celtic" (there are copies floating on the internet), but it normally only quotes Irish for Goidelic. There's also Martina Lucht's dissertation on the basic lexicon of Old Irish, but it again only quotes Irish forms for the modern language. Classical works like LEIA or Pedersen are more grounded in IE linguistics and in philology than McBain, but one can hardly call them up-to-date anymore, and they also don't focus on Gaelic. So all these works are useful only if you want the etymology for a Gaelic word that's also attested in Irish.

hwhatting wrote: ↑Sun Jul 09, 2023 4:00 am

MacAnDàil wrote: ↑Thu Jul 06, 2023 1:35 am Coming back to this because I realise I am not sure of the better alternative: which sources are best on Gaelic etymology?

I don't think that there is anything more up-to-date specifically on Gaelic, but I'm also not really looking into Gaelic etymologies most of the times. My interests in Celtic are mostly Continental Celtic, and Proto-Celtic as far as it's relevant for PIE reconstruction; for the latter, there is Matasovič's "Etymological Dictionary of Proto-Celtic" (there are copies floating on the internet), but it normally only quotes Irish for Goidelic. There's also Martina Lucht's dissertation on the basic lexicon of Old Irish, but it again only quotes Irish forms for the modern language. Classical works like LEIA or Pedersen are more grounded in IE linguistics and in philology than McBain, but one can hardly call them up-to-date anymore, and they also don't focus on Gaelic. So all these works are useful only if you want the etymology for a Gaelic word that's also attested in Irish.

Thank you for your answer, though it is a shame that there is little for Scottish Gaelic and I can't seem to access the link you sent.

MacAnDàil wrote: ↑Wed Jul 12, 2023 8:40 am

Thank you for your answer, though it is a shame that there is little for Scottish Gaelic and I can't seem to access the link you sent.
[/quote]
You're welcome. I re-checked the link and it's working fine for me; maybe this alternative version works?
https://nbn-resolving.org/urn:nbnhbz:5-11426

I was looking up the Latin -que and -ve suffixes today – the ones which mean 'and' and 'or' because I'm basically stealing it for a conlang. I'm not all that familiar with Romance languages though and I was wondering if these actually persisted into any modern languages?

Jonlang wrote: ↑Wed Jul 12, 2023 12:02 pm I was looking up the Latin -que and -ve suffixes today – the ones which mean 'and' and 'or' because I'm basically stealing it for a conlang. I'm not all that familiar with Romance languages though and I was wondering if these actually persisted into any modern languages?

Pedantic note: they’re clitics, not suffixes. (Well, not actually so pedantic — it explains why they have more resemblance to other words than to suffixes, insofar as there’s a difference.)

Jonlang wrote: ↑Wed Jul 12, 2023 12:02 pm I was looking up the Latin -que and -ve suffixes today – the ones which mean 'and' and 'or' because I'm basically stealing it for a conlang. I'm not all that familiar with Romance languages though and I was wondering if these actually persisted into any modern languages?

As far as I know, no, they didn't. (NB: in Latin, they sometimes became fixed parts of conjunctions or adverbs like denique "finally, at last"; namque "for"; it's possible that they survived in descendants of such adverbs or conjunctions, although I can't remember any such cases right now.)