Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!mnetor!seismo!husc6!Diamond!aweinste From: aweinste@Diamond.BBN.COM (Anders Weinstein) Newsgroups: net.ai,sci.electronics,net.cog-eng Subject: Re: The Analog/Digital Distinction: Soliciting Definitions Message-ID: <1625@Diamond.BBN.COM> Date: Mon, 27-Oct-86 17:06:14 EST Article-I.D.: Diamond.1625 Posted: Mon Oct 27 17:06:14 1986 Date-Received: Mon, 27-Oct-86 23:17:05 EST References: <7@mind.UUCP> Reply-To: aweinste@Diamond.BBN.COM (Anders Weinstein) Organization: BBN Labs, Cambridge, MA Lines: 62 Keywords: analog, digital, continuous, discrete, symbolic, nonsymbolic, numeric, representation, icon, image, visual, verbal Xref: mnetor net.ai:1246 sci.electronics:12 net.cog-eng:310 Philosopher Nelson Goodman has distinguishes analog from digital symbol systems in his book _Languages_of_Art_. The context is a technical investigation into the peculiar features of _notational_ systems in the arts; that is, systems like musical notation which are used to DEFINE a work of art by dividing the instances from the non-instances. The following excerpts contain the relevant definitions: (Warning--I've left out a lot of explanatory text and examples for brevity) The second requirement upon a notational scheme, then, is that the characters be _finitely_differentiated_, or _articulate_. It runs: For every two characters K and K' and every mark m that does not belong to both, determination that m does not belong to K or that m does not belong to K' is theoretically possible. ... A scheme is syntactically dense if it provides for infinitely many characters so ordered that between each two there is a third. ... When no insertion of other characters will thus destroy density, a scheme has no gaps and may be called _dense_throughout_. In what follows, "throughout" is often dropped as understood... [in footnote:] I shall call a scheme that contains no dense subscheme "completely discontinuous" or "discontinuous throughout". ... The final requirement [including others not quoted here] for a notational system is semantic finite differentiation; that is for every two characters K and K' such that their compliance classes are not identical and every object h that does not comply with both, determination that h does not comply with K or that h does not comply with K' must be theoretically possible. [defines 'semantically dense throughout' and 'semantically discontinuous' to parallel the syntactic definitions]. And his analog/digital distinction: A symbol _scheme_ is analog if syntactically dense; a _system_ is analog if syntactically and semantically dense. ... A digital scheme, in contrast, is discontinuous throughout; and in a digital system the characters of such a scheme are one-one correlated with compliance-classes of a similarly discontinous set. But discontinuity, though implied by, does not imply differentiation...To be digital, a system must be not merely discontinuous but _differentiated_ throughout, syntactically and semantically... If only thoroughly dense systems are analog, and only thoroughly differentiated ones are digital, many systems are of neither type. To summarize: when a dense language is used to represent a dense domain, the system is analog; when a discrete (Goodman's "discontinuous") and articulate language maps a discrete and articulate domain, the system is digital. Note that not all discrete languages are "articulate" in Goodman's sense: Consider a language with only two characters, one of which contains all straight marks not longer than one inch and the other of which contains all longer marks. This is discrete but not articulate, since no matter how precise our tests become, there will always be a mark (infinitely many, in fact) that cannot be judged to belong to one or the other character. For more explanation, consult the source directly (and not me). Anders Weinstein