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CONLANG  December 2013, Week 3

CONLANG December 2013, Week 3

Subject:

Re: Numbers, Counting, and Arithmetic

From:

Alex Fink <[log in to unmask]>

Reply-To:

Constructed Languages List <[log in to unmask]>

Date:

Thu, 19 Dec 2013 01:03:26 -0500

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (71 lines)

Triple-barreled response.

On Tue, 17 Dec 2013 19:44:40 -0500, Zach Wellstood <[log in to unmask]> wrote:

>So if I have 8 graham crackers now:
>
>latłalayaa tłar lu'alár.
>three-INAN INSTR ABSTR-IMMED-APPLIC-be.five.DIR
>= 8 (lit, "it is five with three")

In view of your examples below, how do you distinguish addition from multiplication when just one of them is happening?  That is, how do you tell 8 from 15?

>Now we have an issue with multiplication. Right now I have a temporary
>system/idea in the works where everything's basically the same, you just
>add the multiplier and add "and" to the phrase. It works like this:
>[multiplier] [addition]=and [base]:
>
>(again using all the same morphology)
>latłalayaá sayalayaa'i tłar lu'alár.
>three-INAN one-INAN=and INSTR ABSTR-IMM-APPLIC-be.five.DIR
>= 16 (lit, "it is five with three and one")
>
>To be honest, I like how this works, but it means that large integers
>require many embedded clauses (not even phrases, full clauses!).

In particular it comes out center-embedded!  Ordinarily you'd expect that to lead to severe processing dysfluency, if not outright improcessability, beyond about three digits or so.  But given the fact that any largish number without zeros(?) will end ending with a constant string "be.five be.25 be.125 be.625...", which you therefore don't have to pay attention to, this might not be so bad (though I agree it would probably call for abbreviation in use).  If zeros do cause gaps in this string which you have to pay attention to, that gets harder again.  

>It is definitely unwieldy (I still don't know how to say 465)

Is this another manifestation of the problem with zeroes, or something else?


On Wed, 18 Dec 2013 11:29:41 -0500, C. Brickner <[log in to unmask]> wrote:

>---- Original Message -----
>From: "C. Brickner" <[log in to unmask]>
>To: [log in to unmask]
>Sent: Wednesday, December 18, 2013 11:21:18 AM
>Subject: Re: Numbers, Counting, and Arithmetic
>
>First off, multiplication is just a shortcut to addition, so that 5*3 is
>the same as 5+5+5, "add 5 to itself 3 times," or "repeat 5 thrice." There's
>no rule that says a language has to use a parallel shortcut (if there was,
>we'd break it).
>_______________________________
>
>Math is definitely not my strong suit, but shouldn't that be "add 5 to itself 2 times"?  If I add 5 to itself once, the result is 10; if I add 5 to itself twice, the result is 15.  Some might say that the first addition is 5 itself, but if I add 5 to itself 0 times the result is 5 and I haven't really added anything.
>
>More than willing to be enlightened!
>
>Charlie
>______________________________
>
>On further thought: yes, 15 is 5 3 times: here's 5, here's 10, here's 15.  But is having 5 3 times the same as adding 5 3 times?  Here's 5. I add the first 5, here's 10.  I add the second 5, here's 15.  If I add a 3rd 5, the result is 20.  I can't add just 5.  Addition means 5 + x, in this case.  If x=5, then I get 5, 5 + x, 5 + 2x.  Two additions.

These off-by-one considerations remind me of a commonish construction in number systems in natlangs which I think is underappreciated: whereas an ordinary base-5 system (say) would express 17 (say) as 3*5 + 2, based on "three" and "two", another alternative is to express it as "two on the way to the fourth five" and thus based on "four" and "two".  Looks a little less tidy, arithmetically; one has to write 17 = (4-1)*5 + 2, where the -1 is just an invariant part of the formula.  


On Tue, 17 Dec 2013 20:03:51 -0500, Matthew George <[log in to unmask]> wrote:

>A lot of languages find it convenient just to list the digits in sequence
>("four two").  I suggest finding a way to pull that off.

Dò they?  In English the main instance in which we do this is for numeric codes or identifiers of various sorts.  (My phone number may as well be thought of as the sequence "zero, seven, four, six, three, ..." rather than the single quantity "seven billion, four hundred sixty-three million, and change".)  Numbers that actually refer to quantities aren't read one digit at a time.

Takasugi Shinji's pages
  http://www.sf.airnet.ne.jp/~ts/language/number/tongan.html
suggest that Tongan actually dòes simply read lists of digits out generally, but I've always wanted independent confirmation of this, in case this data is actually reallu just a numeric code reading style of some sort.  (Also I must disagree with Shinji that this is the sỳmplest possible number system, at least if "most transparent" is any component of "simplest": I can't get from "seven five" to "75" by arithmetic without knowing that I have to throw a multiplier of ten in there, a ten whose morphological expression is zero.)

Alex

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