tlhIngan-Hol Archive: Fri Sep 29 18:49:22 2000
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RE: math questions / speculations (longish)
- From: [email protected]
- Subject: RE: math questions / speculations (longish)
- Date: Fri, 29 Sep 2000 21:46:04 -0400 (EDT)
De'vID:
> > I'm assuming that the
> > math verbs (/boq/, etc.) follow the same grammar as other verbs.
>
> > For example,
>
> > 1 + 2 + 3 = ...
> > */wej boq cha' boq wa'/ or
> > */wej boq cha' 'e' boq wa'/?
>
> > Which one is more grammatically proper, given what we know of
> > Klingon grammar? Or do we not know how to chain this type of
> > sentence at all?
SarrIS:
> bIQaghlaw'. cha' boq wa'. mI'vam boq wej. chen jav.
Qatlh mIwvam. 'IHbe' mIwvam. nom *mI'tlhegh chenmoHlaHbe' vay'.
[*/mI'tlhegh/ "mathematical equation/formula", after the manner
of /mu'tlhegh/ "sentence".]
> latlh mIw:
>
> wa' cha' je boq wej. chen jav.
mu'tlheghvam lI' law' vebHa'bogh mu'tlhegh lI' puS. mI'mey
law' chelmeH, ngeD Qu':
wa' cha' wej loS vagh jav Soch chorgh Hut je boq wa'maH;
chen vaghmaH vagh. maj.
> > Another interesting thing is that Klingon grammar seems to
> > enforce a right-first interpretation, i.e.
>
> > 1 + 2 + 3 would be interpreted as 1 + (2 + 3), rather than
> > (1 + 2) + 3 as in English/Earth mathematics.
>
> qatlh qechvam Danaj? not qechvam chup HolQeD.
If I were to say, "one plus two; that number plus three", in
English, it would be interpreted as (1 + 2) + 3.
But if I were to say, as you did above, /cha' boq wa'. mI'vam
boq wej./, that would be 3 + (1 + 2). The grammar given
seems to be /*augend* boq *addend*; chen *sum*/, whereas
in English we would say "addend plus augend equals sum".
If there were a way to chain multiple additions (e.g. as in
English "one plus two plus three..."), I was speculating
that the grammar might be */wej boq cha' boq wa'/. I'm
probably wrong about this. But this would come across to
me as "two plus three; one plus that", or 1 + (2 + 3).
Maybe I'm thinking too hard about this, but what I'm getting
at here is like the difference between Polish and reverse
Polish notation. Polish notation is when you put the
operator before the operands, e.g. for 1 + 2, write + 1 2.
So, for multiple additions, you'd write + + 1 2 3. This
is naturally (1 + 2) + 3.
But for reverse Polish notation, you write the operands
first and the operator last. e.g. for 1 + 2, write 1 2 +.
To add 1 and 2 and 3, you'd do 1 2 3 + +. However, this
naturally enforces 1 + (2 + 3). The reversal in grammar
between English and Klingon seems to me to suggest the
same kind of relationship between Polish notation and
reverse Polish notation mathematics.
(Neither is more "correct" than the other, mathematically
speaking; we just prefer left-first precedence because
English speakers, and probably speakers of most human
languages, find it more natural. Maybe someone who knows
a human language where O comes before S can comment on how
that affects the order of operation in mathematics.)
I could, I suppose, say /cha' boq wa'. wej boq mI'vam./
to specify (1 + 2) + 3. It seems a terribly clunky way to
do things, especially if I have to add a list. Maybe I
can clip. First, I can probably drop the /-vam/, because
it's obviously /mI'/ refers to the previous sum. Then
I can replace the /mI'/ with an implicit /'oH/ and drop that
as well.
/cha' boq wa'. wej boq. loS boq. vagh boq.../
"One plus two, plus three, plus four, plus five..."
maj. It's as efficient as the English.
Actually... it might be even better:
(((3 + (1 + 2)) + 4) + 5)...
/cha' boq wa'. boq wej. loS boq. vagh boq.../
Dun! This is really cool, if it's legal. {{=)
> > If I were to say:
>
> > 2 + 5 x 3 = ?
> > /cha' boq vagh boq'egh wej; chen nuq?/
> > (assuming this is legal)
DopDaq qul yIchenmoH QobDI' ghu'. I forgot the /-logh/ on the /vagh/.
> bIQaghlaw'. yIQIm:
>
> (2+5)*3
> vagh boq cha'. wejlogh boq'egh mI'vam.
I'm nitpicking, but the formula given in HolQeD is
/*multiplicand*-logh boq'egh *multiplier*; chen *product*/
e.g. "2 x 3 = 6" is /cha'logh boq'egh wej; chen jav/
So, what you wrote would be 3 * (2 + 5). According to HolQeD,
(2 + 5) * 3 would be /vagh boq cha'. mI'vamlogh(?) boq'egh wej./
I'm not sure if MO intended this, but the order of specifying
the operators is quite mixed up when compared to English.
In English,
addend + augend = sum
minuend - subtrahend = difference
multiplicand * multiplier = product
dividend / divisor = quotient (+ remainder)
In Klingon,
*augend* boq *addend*; chen *sum* ("reverse" from English)
*minuend* boqHa' *subtrahend*; chen *difference* ("same" as English)
*multiplicant*-logh boq'egh *multiplier*; chen *product* ("same" as English)
*divisor* boqHa''egh *divident*; chen *quotient* ("reverse" from English)
I may be nitpicking. I realize that MO's background is linguistics,
but I'm an engineer with a background in math, so maybe I'm picking
up on something he didn't intend. But it makes a big difference to
the order of operation when you begin chaining these things.
The haphazard (from a human point of view) way that Klingon math
operators order their operands are naturally going to impose a
different order of operation than "human" mathematics.
> wejlogh boq'egh vagh boqpu'bogh cha'.
> wejlogh boq'egh boqchuqpu'bogh cha' vagh je.
Ouch. jIwuQ.
> 2+(5*3)
> cha' boq vaghlogh boq'eghpu'bogh wej.
(5 * 3) + 2... pIm. loQ pIm, 'ach pIm.
You want /vaghlogh boq'eghpu'bogh wej boq cha'/ for 2+(5*3). See
what I mean about the order of operation being messed up from
English?
> mIwwIj DaparHa''a'?
vIparHa'bej. tlhIngan Hol lo'lu'taHvIS, reH qaq mu'tlhegh mach.
> SarrIn
(p.s. You alternated between SarrIn and SarrIS in your messages.
Which one is it?)
--
De'vID
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