tlhIngan-Hol Archive: Sun Oct 01 19:10:34 2000

Back to archive top level

To this year's listing



[Date Prev][Date Next][Thread Prev][Thread Next]

RE: math questions / speculations (longish)



ja' De'vID:
>If I were to say, "one plus two; that number plus three", in
>English, it would be interpreted as (1 + 2) + 3.

Agreed.

>But if I were to say, as you did above, /cha' boq wa'. mI'vam
>boq wej./, that would be 3 + (1 + 2).

Disagreed.  I'm not sure why you're reading it backwards.  It's actually
extremely similar to the English rendering.  "One allies with two; three
allies with this number."  It sure seems like (2 + 1) + 3 to me.

>The grammar given
>seems to be /*augend* boq *addend*; chen *sum*/, whereas
>in English we would say "addend plus augend equals sum".

I think you'd better slow down and reread the descriptions in HolQeD.  If
by "addend" you mean the number that's there to begin with, and by "augend"
you mean the amount by which the "addend" is being increased, then it's
quite obvious to me that you're interpreting the Klingon pattern backwards.

Look at {cha' boq wa'} "one allies with two".  "Two" is already there.
"One" allies with it, increasing the value.  Using what I think is your
terminology, {*addend* boq *augend*}.

But when talking about addition, there is no relevant distinction between
the two roles; everything is an "addend".  Let's try subtraction instead,
where the order *does* make a difference.

{wej boqHa' cha'} "Two dis-allies from three."  "Three" is there.  "Two"
takes away from it, decreasing the value.  The second number is the
"subtrahend", if I have the terminology correct.

{loS boqHa' cha'. mI'vam boqHa' wa'.) "Two dis-allies from four. One
dis-allies from this number."  I can interpret this only as (4 - 2) - 1.

>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.

You're almost certainly wrong.  There's no grammatical justification for
"chaining" verbs like that.  The wording might end up along those lines,
with suitable agreement of what the object of the subsequent verb is
supposed to be and with suitable agreement of the punctuation conventions,
but the grammar itself cannot support multiple main verbs in a single
sentence.

>But this would come across to
>me as "two plus three; one plus that", or 1 + (2 + 3).

What is it that turns things around in your head to put the "1" at the
beginning when the "one" starts out at the end?  It looks like you're
assuming "one plus two" maps directly to {cha' boq wa'}, but that attempted
mapping completely misses the fact that "plus" is not a verb in English,
thus "one" is not the subject and "two" is not the object.  Based on the
meaning "allies with" and the order of things when subtracting, I'd say
that the actual numbers end up going in the same order in Klingon as they
do in English.

>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...

I fail to see the relevance of prefix or postfix notation here.  We're not
talking about mathematical notations at all; we're talking about the way
the language talks about the operations.  And Klingon's grammar is at least
as "infix" as English is here.

>I could, I suppose, say /cha' boq wa'.  wej boq mI'vam./
>to specify (1 + 2) + 3.

Now I'm really confused.  If you're going to make a distinction based on
the position of the numbers in addition, you really ought to do it in such
a way as to make the same distinction work for subtraction as well.  Since
your understanding of addition in Klingon seems at odds what I think is
blindingly obvious, I don't think I'll have much useful to say about your
interpretations of multiplication or division in Klingon

>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)

However, I *will* say something about your understanding of multiplication
in English. :-)  In 2 x 3 = 6, the multiplier is 2 and the multiplicand is
3.

>In Klingon,
>*augend* boq *addend*; chen *sum* ("reverse" from English)

I think you have the Klingon labels reversed.

>*minuend* boqHa' *subtrahend*; chen *difference* ("same" as English)
>*multiplicant*-logh boq'egh *multiplier*; chen *product* ("same" as English)

You definitely have the *English* labels reversed.

>*divisor* boqHa''egh *divident*; chen *quotient* ("reverse" from English)

This isn't bad at all.  By my understanding of what the {boq} verb does,
sentences involving addition and subtraction end up with the numbers in
essentially the same order as the customary Terran mathematical notation.
Sentences involving multiplication and division, being repeated addition or
subtraction, also fit the pattern well by putting the number begin added or
subtracted as the subject of the verb.

I see the whole thing as entirely consistent.  Which I actually find rather
surprising. :-)


-- ghunchu'wI' 'utlh




Back to archive top level