tlhIngan-Hol Archive: Wed Mar 20 08:02:47 1996

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Re: Fractions



>Date: Wed, 20 Mar 1996 00:34:04 -0800
>From: [email protected] (Terrence Donnelly)

>   I recall a discussion about fractions a while back.  I don't 
>remember what the result was, but I don't think we reached any 
>conclusion.

>Anyway, I was reading about Egyptian math the other day and I got a 
>wild idea.  It seems that Egyptians used something called "unit 
>fractions", which can only have a numerator of 1 (the denominator 
>can be anything).  To indicate fractions with other numerators, you 
>have to add unit fractions: 2/3 = 1/3 + 1/3; 3/4 = 1/2 + 1/4; 5/7 = 
>1/3 + 1/3 + 1/21, etc.

Actually, one of your examples is a classic non-example.  Ancient Egyptians
used only unit fractions, true, EXCEPT for one case: there is a case of 2/3
being recorded as 2/3 and not as 1/2+1/6 (as would probably have been
expected.  I don't think they tended to add like fractions).

>I though maybe Klingon worked this way too.  I noticed that the 
>word {bID} is defined as 'half', and not 'one-half', so maybe it's 
>a unit fraction.  Then I got to thinking, maybe {bID} just means 
>'fraction' (in the same way that {maH} means 'tens').  Maybe 'half' 
>is properly *{cha'bID}, but klingons know by convention that {bID} 
>by itself is equivalent to *{cha'bID}.  Then we could have 
>*{wejbID}, *{loghbID}, etc.

>As I recall, the big problem with fractions was indicating 
>numerators and keeping fractions distinct from whole numbers in the 
>same phrase.  With unit fractions, we wouldn't have to; the 
>fraction is always a single distinct number word.  Ex: 5-1/5 = {jav 
>javbID}.

>It's totally unsupportable, I know, but it's very late and at the 
>moment it seems like a neat idea.

Yeah, it is interesting... and wholly unsupportable, as you said.
Basically you're postulating that bID means "reciprocal", with really NO
support at all.  There has already been speculation that "-vI'" does that,
since we have "vatlhvI'"=="percent", which is 1/100.  There's certainly
more support for -vI' than bID (why contract *cha'bID to bID and leave no
other evidence?), and there's nowhere near enough support for -vI' either.
Oh well...  It's an idea.  I would like to see a good way to do fractions.

>-- ter'eS


~mark


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