At 04:30 PM 9/28/01 -0400, pycyn@aol.com wrote:
In a message dated 9/28/2001 2:34:31 PM Central Daylight Time, jimc@MATH.UCLA.EDU writes:To me it seems rather inelegant that a language feature fails to function in the absence of a default radix. For example, if you were a rabid dozenal fanatic (or hex :-), would you want to be forced to specify the radix of your own favorite number system in that depraved base X (ten)? Or, stretching the point rather more than seems justified, perhaps if you were a heptapus you could not manage base ten, and it's nasty and dumb to shut the heptapi out of the Lojban world just over the radix.xod, too: <10 is the default earth human base, and the one shared by the six cultures that contributed gismu! No other apology is needed. The "cultulrally neutral" (retarded) solution is to issue the base number in base one.>The situation of heptapodes reminds us, as xod does again, that the choice of the default base is out of our hands (snrk!). Rationality has no power against 10 (or more) millennia of counting on fingers (yes, I know about binary counts, but people don't count that way). The fingerless three base, the shorthanded four base and the two handed eight base have all passed away, along with the scholarly 12 and 60 and 13 and 20 and 18 and Lord knows what else. All downed by the digits. so we offer the possibility of using others, but we do so in the context of human reality. As for (yuck, ptui) hex, the very computers which are its main source of appeal make it it unnecessary, since they convert any system into any other system with such great ease.
More importantly, the grammar of MEX is not intended to be, nor can it be "elegant", and still meet the requirement specification of representing all forms of written symbolic notation. Various mathematicians (and logicians) use the notation system for all manner of contradictory purposes, and it was a difficult stretch in order to come up with a grammar that could EXPRESS the full range of what expressions are used to express in the unrestricted world of notational systems, then make it LALR1.
What we came up with is workable if not elegant for the most common mathematical notation used, that of standard constant base arithmetic and algebra. Every bell and whistle that might be appended to that core system is potentially a system-breaker, and we chose not to worry about it because there was no solution. Mathematical notation is inherently ambiguous, in that most notations do not presume to require express use of priority markings if the default order of operations rules are in use. But calculator notation usually ignores standard order of operations without marking it. (Lojban allows you to expressly parenthesize everything for non-ambiguity, and the book probably is written with this as a standard, but we recognized that in normal usage of Mex there would be times when the Lojban would - and would have to - merely represent the written notation evaluated under the norms for that notation, parsing rules be damned).
lojbab -- lojbab lojbab@lojban.org 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