Re: [lojban] Re: New PA-proposal

["Mark E. Shoulson" <mark@kli.org>]

The situation in PA seems to be sort of a cop-out: "Whatever, look, it's 
a bag of words, let the higher level (semantics) sort it out." We could 
have done the same with the grammar as a whole, probably, but what would 
that have accomplished?

Thus klaku, from the proposal:
> 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.
So this defines {pai} and {te'o} in terms of their radix expansions. {pi 
pai} is {pai}/10, and if we were working in another base, it would be 
{pai}/B (for base B). I started writing this to say this is a terrible 
idea, but there is some consistency to it: {pi re} is {re}/10, etc. 
Whenever you move the {pi} around, you multiply/divide by the radix. 
Now, this reasoning would also lead to {pai no} equalling 10π and so on, 
where you would probably rightly say they can't join this way. (which 
makes me start thinking of having cmavo defined purely in terms of 
moving the radix point... You don't need one for moving it to the left, 
because numbers can't be infinite to the left and we can say {pi no no 
pai} and so on for moving it more places, but you'd need one for the 
right... Yeah, we could speak in terms of explicitly exponentiating the 
radix... OK, yeah, I know, I'm rambling and these aren't good ideas. 
Just stuff that hit me when trying to say this was a bad idea and 
discovering it might not be.)

> a)	All number strings then refer to the same number, describing it in
> different ways. This means you can say something wrong. ({li pai su'o
> vo} refers to "pi, which is more than 4", for instance.)

I think this is likely a bad idea, and will lead to trouble. Might 
prefer to just forbid more than one "number string" per number, or else 
come up with... a better meaning for it. We already have (enough) ways 
to indicate incidental relative clauses, etc. Maybe adjacent number 
strings have explicit multiplication between them, like in ordinary math 
notation (bad idea). Or maybe PA1 are really complete number strings, 
and for number strings x and y, {x y} means "x times the radix, plus y." 
That would yield a nice consistent meaning for how PA1 works as well as 
a meaning for other adjacent number strings--albeit a fairly useless 
meaning. Not a great solution either.

I'm not sure how happy I'd be with "messin' with th' established order 
o' things," especially considering the usage breakage involved. But 
that's another matter, and I could be convinced; I'm just looking at the 
idea on its own.

~mark

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