From cbmvax!uunet!cuvma.bitnet!LOJBAN Mon Jan 27 17:01:38 1992 Return-Path: Received: by snark.thyrsus.com (/\==/\ Smail3.1.21.1 #21.19) id ; Mon, 27 Jan 92 17:01 EST Received: by cbmvax.cbm.commodore.com (5.57/UUCP-Project/Commodore 2/8/91) id AA06585; Mon, 27 Jan 92 16:59:09 EST Received: from rutgers.edu by relay1.UU.NET with SMTP (5.61/UUNET-internet-primary) id AA11815; Mon, 27 Jan 92 15:42:09 -0500 Received: from cbmvax.UUCP by rutgers.edu (5.59/SMI4.0/RU1.4/3.08) with UUCP id AA25938; Mon, 27 Jan 92 14:40:25 EST Received: by cbmvax.cbm.commodore.com (5.57/UUCP-Project/Commodore 2/8/91) id AA29280; Mon, 27 Jan 92 14:19:22 EST Received: from CUVMB.COLUMBIA.EDU (via uunet.UU.NET) by relay1.UU.NET with SMTP (5.61/UUNET-internet-primary) id AA25765; Mon, 27 Jan 92 13:30:22 -0500 Message-Id: <9201271830.AA25765@relay1.UU.NET> Received: from CUVMB.COLUMBIA.EDU by CUVMB.COLUMBIA.EDU (IBM VM SMTP R1.2.1) with BSMTP id 4855; Mon, 27 Jan 92 13:29:07 EST Received: by CUVMB (Mailer R2.07) id 9829; Mon, 27 Jan 92 13:28:17 EST Date: Mon, 27 Jan 1992 13:18:00 EST Reply-To: "61510::GILSON" Sender: Lojban list From: "61510::GILSON" Subject: numeral strings X-To: lojban To: John Cowan Status: RO John Cowan writes: >It is common in mathematics to write "2pi" to represent 2 times pi. Lojbab >has it that the corresponding numeral string: > re pai > 2 pi >should also mean 2 times pi in Lojban. My view is that since Lojban does not >allow you to omit multiplication operators in general -- for example: > (m + n)(m + n) >is > vei my. su'i ny. ve'o pi'i ve'i my. su'i ny. ve'o > ( m + n ) * ( m + n ) >and it is ungrammatical to omit the "pi'i" -- it follows that: > 2 pi >must be > re pi'i pai > 2 * pi >and simple "re pai" has no defined meaning. This principle may be extended >to other analogous cases. >Argument pro: not allowing implied operators in numeral strings will tend >to prevent confusion (why is "2 pi" = "2 * pi" whereas "23" = "2 * 10 + 3"?) >and will allow expansion space, as undefined number strings may be put to >newly devised uses if not pre-empted for things that can be said otherwise. >Argument con: "re pai" is shorter and (having the syntax of a number) can >be used in places where a full mathematical expression cannot. Expressions >other than simple numbers must be parenthesized when used as quantifiers, so >"2 pi people" requires a "vei" (left parenthesis) in front of the expression >"2 times pi". >Special note on "imaginary i": I am willing to allow a special role to >"ka'o", the cmavo for "i", because "3+4i" can reasonably be thought of as >a conventional way of notating the point <3,4> on the complex plane, rather >than as a multiplication by "i" and an addition. I do not believe this >argument carries over to "2 pi" or "2 e". I myself could live with either option (because the two arguments pro and con carry about the same weight with me), but the one thing I would object to strongly is distinguishing "imaginary i" from such constants as pi and e. While 3+4i can be defined without reference to multiplication by i and an addition, in my own mind anyway, the _algebraic_ meaning of 3+4i is exactly the same as 3+4x with x=i. Bruce