From edward.cherlin.sy.67@aya.yale.edu Sun May 05 13:00:16 2002 Return-Path: X-Sender: cherlin@pacbell.net X-Apparently-To: lojban@yahoogroups.com Received: (EGP: mail-8_0_3_2); 5 May 2002 20:00:16 -0000 Received: (qmail 57372 invoked from network); 5 May 2002 20:00:15 -0000 Received: from unknown (66.218.66.217) by m4.grp.scd.yahoo.com with QMQP; 5 May 2002 20:00:15 -0000 Received: from unknown (HELO mta6.snfc21.pbi.net) (206.13.28.240) by mta2.grp.scd.yahoo.com with SMTP; 5 May 2002 20:00:15 -0000 Received: from there ([216.102.199.245]) by mta6.snfc21.pbi.net (iPlanet Messaging Server 5.1 (built May 7 2001)) with SMTP id <0GVN00H2DM8F4Z@mta6.snfc21.pbi.net> for lojban@yahoogroups.com; Sun, 05 May 2002 13:00:15 -0700 (PDT) Date: Sun, 05 May 2002 13:00:14 -0700 Subject: Numbers and digits (was Re: bases) In-reply-to: To: lojban@yahoogroups.com Message-id: <0GVN00H2EM8F4Z@mta6.snfc21.pbi.net> Organization: Web for Humans MIME-version: 1.0 X-Mailer: KMail [version 1.3.2] Content-type: text/plain; charset=iso-8859-1 Content-transfer-encoding: quoted-printable References: X-eGroups-From: Edward Cherlin From: Edward Cherlin Reply-To: edward@webforhumans.com X-Yahoo-Group-Post: member; u=31895329 X-Yahoo-Profile: echerlin On Sunday 05 May 2002 11:53, And Rosta wrote: > > From: John Cowan [mailto:cowan@ccil.org] > > Sent: 11 November 2001 17:43 > > > > And Rosta scripsit: > > > And, similarly, just because Lojban has noncompositional words > > > for zero through to 15 does not mean Lojban by default uses > > > base 16. > > > > Note that dau does not represent the *number* 10, but the *digit* > > 10; a fine distinction, but important. > > What is the distinction? > > --And. It is the usual problem of use vs. mention. "li dau" uses the digit=20 "dau" in mentioning the number 10. We use digits and other elements, such as a negative sign, as part of=20 the representation of numbers that we wish to mention. It is=20 particularly easy to confuse the categories when talking about=20 single-digit numbers.=20 In the following, the form 'A' is a single character, and "A" is a=20 string containing one character. (This notation is well-known and=20 represents an essential distinction in many programming languages. It=20 is usually difficult to get it across to novices, for the same=20 reasons that sometimes make it difficult to explain the difference=20 between a digit and a number.) I differentiate numbers from=20 characters or strings with the prefix "number" or by their appearance=20 in a mathematical expression, and write numbers in decimal notation.=20 The representation of a number in a particular notation is not the=20 number. Thus ~("10" =3D 10) ~("0A" =3D 10) ~("dau" =3D 10) ~("pano" =3D 10) The digit '1' is not the number 1, and the digit "dau" is not the=20 number 10. The number 10 can be represented by the digit sequence=20 "dau" (containing one digit) in an appropriate context, such as=20 following "li". The number 160 can be represented by the digit=20 sequence "dauno" containing two digits. In this case, as in any=20 positional notation, a digit in the rightmost column represents a=20 certain value, and the same digit in the next column to the left=20 represents that value multiplied by the current base. Thus in=20 "dauno"(base 16), we can say that "dau" has as value the number 160,=20 but in "dauno"(base 12), its value is the number 120. "dau" is not=20 itself the number 10, or the number 160, or the number 120. It is a=20 digit representing those values and others in context. We can say that "dau" represents the number 10 in certain contexts,=20 as long as we are aware that this relationship is contextual, and not=20 one of identity. It is correct to say that the number represented by=20 the string "dau" is 10, but it is nonsense to say that "dau" is the=20 number 10. li dau du li pano //Correct in some contexts zo dau du li pano //Not just false; a category error --=20 Edward Cherlin Generalist "A knot! Oh, do let me help to undo it!" --Alice in Wonderland