Re: [lojban] New PA-proposal

[Pierre Abbat <phma@phma.optus.nu>]

On Thursday 17 November 2011 04:40:07 Jakob Nissen wrote:
> Firstly, I'd like to say that neither am I member of the BPFK or
> anything like that, nor do I have insight in the formal grammar of
> Lojban, since I know very little about programming or computer
> language.
> What I do know, though, are the goals and ambitions of the language,
> and to a large extend, what makes good Lojban good and bad Lojban bad.
> Recently, I went through the grammar of the PA-selma'o. and discovered
> to my horror how bad it is now. The day after, I began writing a
> proposal for a new PA-grammar, if not to change anything directly,
> then at least to begin a debate on how to improve this big and broken
> part of cmavo-space.
>
> Klaku’s number proposal:
> The number system of Lojban simply doesn’t work. Due to historical
> reason (I’ve been told), it was decided to let all numbers work the
> same way in the grammar, make no distinction between the selma’o of
> the different PA, and allow any string of PA to be grammatical.
> Furthermore, today, all numbers are grouped from left to right.
> This is not satisfactory. While it grammatically allows all thinkable
> number constructs, the grammar of the numbers do not in any way
> correspond to the way the numbers actually interact. This means that:
> 1) Strings of PA which make absolutely no sense are grammatical (like
> {li pai ra’e xo pi pi}) and
> 2) Strings of PA which makes sense are parsed wrongly, leading to
> confusing results (like {li rau su’o pa}, which is parsed {li <rau
> su’o> pa}).
> This is bad. In short, the grammar of numbers might be internally
> consistent, but it does not relate to the language, and therefore
> seems like a “black hole”, where anything goes in the grammar.
>
> Proposed changes
> Therefore, I propose to rearrange the words in the different PA as
> follows in order to allow for at least a minimum of usable grammar in
> numbers:
> 1)	The new PA1 should contain {xo}, and all members of the current PA1
> and PA2. These constructs are mathematically exact digits, which can
> be combined to form number strings.
> 2)	The new PA2 should contain {du'e, mo'a, rau, ro, so'a, so'e, so'i.
> so'o, so'u and no'o (and {xo’e}, in the number sense)}. These numbers
> are inexact or subjective, always are their own number string, but can
> appear before or after any number in order to give additional
> information about it.
> 3)	The new PA3 should contain {ce'i, ma'u, me'i, ni'u. za'u, da'a,
> su'e, su'o, ka'o and fi’u}. These take the next number string or
> PA3+number string (with right-grouping rules) and modify it into a new
> number. The grammar of {fi’u} is changed: it can now only express 1/n.
> In order to express a/n, use {a pi’i fi’u n}. They all should work
> without having a number after them, in that case, the number should be
> a default.

Changing "fi'u" like this breaks existing text. Also, "fi'u", in current 
usage, is meaningful at the end of a number string; it denotes the golden 
ratio. li fi'u vu'u fi'u fi'u du li pa.

"ce'i" followed by a cardinal number means a transfinite cardinal. How would 
you denote transfinite ordinals?

> 4)	The new PA4 should contain {pi’e and ki’o}, and can appear at any
> time, in any number string, any amount of times. They sever the number
> string, but {ki’o} allows two adjectent number strings to “fuse”
> together again. When several PA4 are put together, the number string
> {no no no} is assumed to be between them.

"pi'e" has two distinct uses: separating numbers which have only a vague 
notion of relative significance, such as year, month, and day or parts of a 
continued fraction, and separating digits in a base greater than 16. Hours, 
minutes, and seconds can be interpreted either way, except when a time ends 
in "pi'e nono pi'e xano" (a leap second). We may need to introduce a new 
cmavo for one of these uses.

In base 16, "no no no no" should be assumed to be between two "ki'o". If it's 
an IPv6 address, multiple copies of "no no no no" can be between them (if 
there's any ambiguity in where to put the 0000 strings, the IPv6 address is 
invalid).

> 5)	The new PA5 should contain {ra’e, pi and ji’i}, and can appear once
> in each number string. The grammar of {ji’i} is changed for this
> purpose: the construct {ji’i ni’u/ma’u} no longer tell us whether
> there have been “rounded up” or “rounded down”. Alone, it means works
> as a number on it own, and tells us the other number strings are
> approximate. For “typical number”, use {no’o}. For elliptical number,
> I suggest the experimental cmavo {xo’e}. If no part of a string is
> placed before {pi} or {ra’e}, the default is 0.

There may be usages in which each section between two "pi'e" can have "pi" in 
it. I don't know what they are though.

"ra'e" normally follows "pi", but when talking about p-adic numbers, "ra'e" 
precedes "pi", and the sequence of digits preceding "ra'e" is repeated. How 
would you interpret "pira'e" or "ra'epi" with no digits?

> 6)	The new PA6  should contain {pai, te’o and tu’o}. These are full
> numbers and can be modified by PA3 and PA4, but no other.
> Dealing with problems this gives us:
> 1)	How is PA6+{ki’o} defined?
> a)	It’s not, sorry. It should be grammatical, though.
> 2)	How does PA6 work with PA5?
> a)	{ji’i} works with all numbers. {pi te’o} is “0.271828…”, similar
> with {pai}. {ra’e} is not defined with any number from PA6.

I consider "pi te'o" and "pi pai" to be nonsense.

Pierre

-- 
Don't buy a French car in Holland. It may be a citroen.

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