tlhIngan-Hol Archive: Sun Oct 08 00:07:01 2000
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RE: math questions / speculations (longish)
ja' De'vID:
>Okrand renders "2 + 1" as /wa' boq cha'/ and "two allies with one".
>You're reading /cha' boq wa'/ backwards.
I'm reading it as "one allies with two". That's not backwards; that's
exactly what it says when translated into literal English. Based on the
meanings of the terms "addend" and "augend", and the customary way to
represent addition using those terms, I maintain that {cha' boq wa'} means
the same thing as "2 + 1".
But, again, if you keep trying to say that I've got it backwards, I must
point out to you, again, that Okrand tells us that the numbers can go in
either order for addition without changing the situation. "2 + 1" and "1 +
2" both add up to the same value. So it's both pointless and irrelevant to
insist that one of them is "more correct" than the other based on what
English has to say. I think it's infinitely more productive to analyze
Klingon mathematics based on what *Klingon* has to say.
>I stand by my statement that /cha' boq wa'. mI'vam boq wej./
>represents 3 + (1 + 2).
I really can't see how you can come to that conclusion unless you take the
complete pair of Klingon statements and read them from right to left.
You're acting as if Klingon grammar is a simple reversal of English, but
that's not really the case. Within a clause, subjects and objects are
"backwards", but Klingon clauses tend to go in the same order as English,
and Klingon sentences *certainly* go in the same order as English.
{cha' boq wa'. mI'vam boq wej.} That's two sentences. First, one allies
with two. Then three allies with the result. The number "3" quite clearly
enters the situation *after* one has considered the addition of "1" to "2".
>MO himself gives "2 + 1" as an example; it is /wa' boq cha'/.
>
>/cha' boq wa'/ would therefore be "1 + 2". Yes, /cha' boq wa'/
>means "one allies with two"; but "one" is already there, and
>then it allies with "two" (which joins it) -- not the other way
>around. You're getting mixed up because you expect the thing
>that is the subject of /boq/ to be the one that "joins" the
>equation, i.e. at the right. This is what you would expect in
>"English" mathematics. But it's precisely the other way around
>in Klingon; the thing doing the "allying" is already there, and
>is joined by its ally. The order of operation is backwards.
>That's what I'm pointing out.
I disagree completely. Again, consider subtraction. The subject of the
verb {boqHa'} is what *leaves* the alliance; there can be no argument on
that point. That's a pretty strong indication that the subject of {boq} is
what *joins* an alliance.
I'm not basing anything on what I expect from English arithmetic. I'm
basing everything on what I know and what I observe and what I deduce about
Klingon grammar. You're getting "mixed up" because Okrand gave {cha' boq
wa'} as the Klingon translation for "1 + 2" and only later pointed out that
the order of the numbers doesn't matter. But he also gives {QaghmeylIj
tIchID, yIyoH} as the Klingon translation for "have the courage to admit
your mistakes," and he gives {batlh qelDI' tlhIngan, lumbe'} as the Klingon
translation for "a Klingon does not postpone a matter of honor." You can't
use translations as a valid basis for deciding what Klingon does and does
not do.
>> {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.
>
>Now try: /loS boq cha'. mI'vam boq wa'./ Applying the definition
>of addition given in HQ, this is 1 + (2 + 4). This is backwards
>from the order for subtraction. I'm not trying to be purposely
>difficult or inconsistent; I'm just following the rules as laid out.
No rules have been "laid out" for anything like this! The definition of
addition doesn't say how to chain operations, or how to group them, or even
if grouping is a valid concept for addition.
>> 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'},
>
>I'm not *assuming* that; I'm starting with the *given* in HQ that
>/wa' boq cha'/ is "2 + 1". What turns things around in my head to
>put the "1" at the beginning is the same bleddy thing that turned
>things around in MO's head to put the "1" at the end of "2 + 1"
>for /wa' boq cha'/. Don't blame me; I didn't make up the rule.
You're *assuming* that it's a direct mapping, without considering the given
fact that the order of the numbers in addition can be swapped without
consequence.
>I would agree, except that the actual examples that are given by
>MO contradict this. "4 + 3" is rendered by MO as /wej boq loS/.
And "cold warriors" is rendered as {Suvrupbogh SuvwI'pu'}. Later
commentary makes clear that the Klingon phrase indeed literally means
"warriors who are ready to fight," just as later commentary makes clear
that addition doesn't necessarily have to have the numbers in a particular
order.
>> 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.
>
>Except that I'm not the one who decided on the order of the operands.
>MO decided that, and I'm just following the recipe.
He didn't "decide" the order. Indeed, he specifically said that the order
of the numbers for addition isn't important.
>If you read the
>article carefully and look at the given examples, you'll see that I'm
>being very consistent with MO's examples.
Being consistent with examples is fine, as long as you don't try to extend
those examples past where they stop. Okrand's examples stop with two
numbers and one sentence. Trying to use them to show how three numbers and
two sentences work is not justified.
>The same distinction doesn't
>work for subtraction, because the order of the operands is flipped
>between addition and subtraction.
The order of operands for addition is up for grabs. I prefer to choose the
interpretation of order that goes along with the meaning of the words used
to describe the operation, not the interpretation of order that defies the
meaning but instead tries to mirror the English.
>maHvaD chovnatlhmey nunobpu' *matlh. chovnatlhmeyvam yIqImqa'qu'!
chovnatlhmey vIbuSchu'taH. chovnatlhmey neH vIchov. mughmeH mIw vISaHbe'.
>> I see the whole thing as entirely consistent. Which I actually
>> find rather surprising. :-)
>
>You see the whole thing as entirely consistent because you're
>reading your Terran expectations back into it! {{=)
I'm disregarding all Terran influences completely, and basing my
interpretations exclusively on the Klingon examples given.
Since anything more I said would be repetition of prior statements, I will
stop.
-- ghunchu'wI' 'utlh