Subject: Re: [lojban] I almost caught the train

From: "Bob LeChevalier (lojbab)" <[email-masked]>
Date: Tue, 13 Mar 2001 05:48:58 -0500

At 08:22 PM 03/12/2001 -0500, [email-masked] wrote:
>In a message dated 3/12/2001 6:00:28 PM Central Standard Time,
>[email-masked] writes:
>><There is no grammar for numbers so that is a string of 4
>>digits, the first of which is large.>
>
>Ambigous: "there is no grammar for numbers. Therefore, panono is a string
>of four digits, the first of which is large.

so'apanono, not panono

> The first part of this is false, I hope,

Numbers are read as a string of digits in order. If you want to call that 
a grammar, there is one, but there are only informal conventions (typically 
those of modern mathematics) and not rules for interpreting a string of digits.

>and the second in this context, seems to mean there cannot be
>grammatical numbers more than a digit long, especially if the first is
>large(r than the rest?).

No, so'a in a string of digits is going to be large-for-a-digit, perhaps in 
base 10 an 8 or a 9.

>"No part of the grammar of numbers allows a number to be a string of digits,
>if the first is large"

Did I say this? I was trying to say that we haven't defined any grammar to 
interpret such a string, nor any conventions.

> I suppose "large" in both these cases means something
>special, in this case PA4?
>Somehow, I had the notion that "at least 100" was {su'o panono}

That is how I would read it. though I would write the su'o together with 
the panono in a single word. The space implies they are separate 
words/concepts, but grammatically they are not.

>I now gather that it is {panono su'o}.

I'm not sure how I would take panonosu'o. Your way might be plausible, but 
a 4 digit interpretation with the 4th digit non-zero is also plausible.

> So, "almost 100" is going to be {panono so'a}

To me, that looks like 1008-1009, in base 10.

><>I have no suggestion for "barely over 100" off the top of mu head.
>
>panoso'u>
>But then {panonosu'o} means "a whole lot more than a thousand" or some such,
>and the other PA+PA4 get really weird.

PA+PA4 is not a convention we see in math notations, to my knowledge.

><soso'a or even soda'a
>
>or if you want the base n solution, da'ada'a
>
>I might also try panononi'u,>
>I'm lost. What does "all except 9" or "almost 9" have to do with the cases
>and what does?

The first could be read "ninety-largish.

The second could be read "all-but-one-ty all-but-one", where all but one in 
a digits context must implicitly be the base number minus one. True, by 
one convention of interpreting da'a, it could also mean all-but 
(all-but-one), but that is the same as "one".

>What does "all except all except" have to do with base n?
>and -100 with anything.

No that is 100-minus.

>Except that they all show that the PA4s go at the right end.

PA4 can go at either end. But how do you interpret it?

The answer is to remember that PA in a string of numbers is a digit. or 
perhaps a local digit-operator where the former makes no sense.

ro as a trailing digit is plausibly the base number; thus soro is 
"ninety-all" or "ninety-ten" = 100.

"roso" has by usage been given a conventional interpretation "all nine", 
though perhaps that should be roboi so, except that this makes the grammar 
explicitly two separate digits, which don't always interact in the way we 
might expect based on usage before a sumti (the five, fifty-five gallon 
drums example of classic Loglan 1 is muboi mumu lo dekpu lante).

da'a is "all but", defaulting to all-but-one. As a digit therefore it must 
be one less than the base number. As a first digit, it has a special 
convention like ro does.

so'a thru so'u as digits I think of as descending approximate numbers - in 
base ten, something like 8-9, 6-8, 4-6, 2-4, 1-2.

su'e has a conventional interpretation if it precedes a number - at most 
that number; as a trailing or medial digit, I can imagine a few mutually 
inconsistent uses.

su'o would be in the same boat, except that it's default value is "at least 
some" and not "at least none" and thus it is not an exact mirror of su'e 
but of da'a, so as a digit it means "1 or more", and this makes sense in a 
medial or trailing position, while allowing it in the leading position to 
be interpreted as su'o[number].

du'e and mo'u and rau don't fit any standard mathematical interpretation as 
digits in a string. What digit-value could they mean in terms of 
base-notation systems? I thus might try to use them attitudinally on 
another number either preceding or following it: sodu'e is "nine, and that 
is too much".

ji'i on the other hand does have a standard notational usage, often written 
as "~", so "ji'iso" is "~9" or approximately nine. I once or twice have 
seen the approximately sign also used interdigitally to show where exact 
numbers separate from the approximation (i.e. to communicate significant 
figures), so I would read "panoji'ipa" as "101" with only the first two 
digits significant/certain and the last digit a guesstimate. Trailing, 
ji'i could either mean that all the digits are significant, and/or that the 
whole number is an approximation, which is the same thing as ji'i
preceding.

I think that covers all the PA4s, as I would try to use them. None are set 
in stone unless they appear in the Book, but they seem to be plausible 
interpretations of a digit with an inexact value.

The hard ones aren't the PA4s, but rather the PA5s. What might "papaipa" 
mean? Who knows?

lojbab
--
lojbab [email-masked]
Bob LeChevalier, President, The Logical Language Group, Inc.
2904 Beau Lane, Fairfax VA 22031-1303 USA 703-385-0273
Artificial language Loglan/Lojban: http://www.lojban.org