Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!mnetor!seismo!rutgers!princeton!mind!harnad From: harnad@mind.UUCP (Stevan Harnad) Newsgroups: comp.ai,comp.cog-eng Subject: Re: The symbol grounding problem Message-ID: <792@mind.UUCP> Date: Fri, 29-May-87 11:27:31 EDT Article-I.D.: mind.792 Posted: Fri May 29 11:27:31 1987 Date-Received: Sun, 31-May-87 03:25:30 EDT References: <764@mind.UUCP> <768@mind.UUCP> <770@mind.UUCP> <6174@diamond.BBN.COM> <6211@diamond.BBN.COM> Organization: Cognitive Science, Princeton University Lines: 95 Keywords: icons, categories, symbols, grounding Summary: Why physical invertibility may be important in cognitive modeling Xref: mnetor comp.ai:466 comp.cog-eng:107 aweinste@Diamond.BBN.COM (Anders Weinstein) of BBN Laboratories, Inc., Cambridge, MA writes: > invertibility has essentially *nothing* to do with the difference > between analog and digital representation according to anybody's > intuitive use of the terms... A blurry image is uncontroversially > an analog or "iconic" representation, yet it is non-invertible; > a digital recording of sound in the audible range is surely an A/D > transformation, yet it is completely invertible. [I]nvertibility... > [only] indicates whether... the transformation preserves or loses > information in the technical sense. But loss of information is... > possible in any of the 4 cases... A/D, A/A, D/A, D/D... > I admit I don't know what the qualifier means in your criterion > of "physical invertibility"; perhaps this alters the case. I admit that the physical-invertibility criterion is controversial and in the end may prove to be unsatisfactory in delimiting a counterpart of the technical A/D distinction that will be useful in formulating models of internal representation in cognitive science. The underlying idea is this: There are two stages of A/D even in the technical sense. Signal quantization (making a continuous signal discrete) and symbolization (assigning names and addresses to the discrete "chunks"). Unless the original signal is already discrete, the quantization phase involves a loss of information. Some regions of input variation will not be retrievable from the quantized image. The transformation is many-to-fewer instead of one-to-one. A many-to-few mapping cannot be inverted so as to recover the entire original signal. Now I conjecture that it is this physical invertibility -- the possibility of recovering all the original information -- that may be critical in cognitive representations. I agree that there may be information loss in A/A transformations (e.g., smoothing, blurring or loss of some dimensions of variation), but then the image is simply *not analog in the properties that have been lost*! It is only an analog of what it preserves, not what it fails to preserve. A strong motivation for giving invertibility a central role in cognitive representations has to do with the second stage of A/D conversion: symbolization. The "symbol grounding problem" that has been under discussion here concerns the fact that symbol systems depend for their "meanings" on only one of two possibilities: One is an interpretation supplied by human users -- "`Squiggle' means `animal' and `Squoggle' means `has four legs'" -- and the other is a physical, causal connection with the objects to which the symbols refer. The first source of "meaning" is not suitable for cognitive modeling, for obvious reasons (the meaning must be intrinsic and self-contained, not dependent on human mental mediation). The second has a surprising consequence, one that is either valid and instructive about cognitive representations (as I tentatively believe it is), or else a symptom of the wrong-headedness of this approach to the grounding problem, and the inadequacy of the invertibility criterion. The surprising consequence is that a "dedicated system" -- one that is hard-wired to its transducers and effectors (and hence their interactions with objects in the world) may be significantly different from the very *same* system as an isolated symbol-manipulating module, cut off from its peripherals -- different in certain respects that could be critical to cognitive modeling (and cognitive modeling only). The dedicated system can be regarded as "analog" in the input signal properties that are physically recoverable, even if there have been (dedicated) "digital" stages of processing in between. This would only be true of dedicated systems, and would cease to be true as soon as you severed their physical connection to their peripherals. This physical invertibility criterion would be of no interest whatever to ordinary technical signal processing work in engineering. (It may even be a strategic error to keep using the engineering "A/D" terminology for what might only bear a metaphorical relation to it.) The potential relevance of the physical invertibility criterion would only be to cognitive modeling, especially in the constrain that a grounded symbol system must be *nonmodular* -- i.e., it must be hybrid symbolic/nonsymbolic. The reason I have hypothesized that symbolic representations in cognition must be grounded nonmodularly in nonsymbolic representations (iconic and categorical ones) is based in part on the conjecture that the physical invertibility of input information in a dedicated system may play a crucial role in successful cognitive modeling (as described in the book under discussion: "Categorical Perception: The Groundwork of Cognition," Cambridge University Press 1987). Of course, selective *noninvertibility* -- as in categorizing by ignoring some differences and not others -- plays an equally crucial complementary role. The reason the invertibility must be physical rather than merely formal or conceptual is to make sure the system is grounded rather than hanging by a skyhook from people's mental interpretations. -- Stevan Harnad (609) - 921 7771 {bellcore, psuvax1, seismo, rutgers, packard} !princeton!mind!harnad harnad%mind@princeton.csnet harnad@mind.Princeton.EDU