Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!utgpu!water!watmath!clyde!rutgers!princeton!mind!harnad From: harnad@mind.UUCP Newsgroups: comp.ai,comp.cog-eng Subject: Re: The symbol grounding problem (Reply to Ken Laws on ailist) Message-ID: <849@mind.UUCP> Date: Mon, 15-Jun-87 09:23:35 EDT Article-I.D.: mind.849 Posted: Mon Jun 15 09:23:35 1987 Date-Received: Wed, 17-Jun-87 01:10:47 EDT References: <764@mind.UUCP> <768@mind.UUCP> <770@mind.UUCP> <6174@diamond.BBN.COM> <847@mind.UUCP> Organization: Cognitive Science, Princeton University Lines: 70 Xref: utgpu comp.ai:493 comp.cog-eng:120 Summary: On physically invertible encoding/decoding schemes Ken Laws on ailist@Stripe.SRI.Com writes: > Consider a "hash transformation" that maps a set of "intuitively > meaningful" numeric symbols to a set of seemingly random binary codes. > Suppose that the transformation can be computed by some [horrendous] > information-preserving mapping of the reals to the reals. Now, the > hash function satisfies my notion of an analog transformation (in the > signal-processing sense). When applied to my discrete input set, > however, the mapping does not seem to be analog (in the sense of > preserving isomorphic relationships between pairs -- or higher > orders -- of symbolic codes). Since information has not been lost, > however, it should be possible to define "relational functions" that > are analogous to "adjacency" and other properties in the original > domain. Once this is done, surely the binary codes must be viewed > as isomorphic to the original symbols rather than just "standing for > them". I don't think I disagree with this. Don't forget that I bit the bullet on some surprising consequences of taking my invertibility criterion for an analog transform seriously. As long as the requisite information-preserving mapping or "relational function" is in the head of the human interpreter, you do not have an invertible (hence analog) transformation. But as soon as the inverse function is wired in physically, producing a dedicated invertible transformation, you do have invertibility, even if a lot of the stuff in between is as discrete, digital and binary as it can be. I'm not unaware of this counterintuitive property of the invertibility criterion -- or even of the possibility that it may ultimately do it in as an attempt to capture the essential feature of an analog transform in general. Invertibility could fail to capture the standard A/D distinction, but may be important in the special case of mind-modeling. Or it could turn out not to be useful at all. (Although Ken Laws's point seems to strengthen rather than weaken my criterion, unless I've misunderstood.) Note, however, that what I've said about the grounding problem and the role of nonsymbolic representations (analog and categorical) would stand independently of my particular criterion for analog; substituting a more standard one leaves just about all of the argument intact. Some of the prior commentators (not Ken Laws) haven't noticed that, criticizing invertibility as a criterion for analog and thinking that they were criticizing the symbol grounding problem. > The "information" in a signal is a function of your methods for > extracting and interpreting the information. Likewise the "analog > nature" of an information-preserving transformation is a function > of your methods for decoding the analog relationships. I completely agree. But to get the requisite causality I'm looking for, the information must be interpretation-independent. Physical invertibility seems to give you that, even if it's generated by hardwiring the encryption/decryption (encoding/decoding) scheme underlying the interpretation into a dedicated system. > Perhaps [information theorists] have too limited (or general!) > a view of information, but they have certainly considered your > problem of decoding signal shape (as opposed to detecting modulation > patterns)... I am sure that methods for decoding both discrete and > continuous information in continuous signals are well studied. I would be interested to hear from those who are familiar with such work. It may be that some of it is relevant to cognitive and neural modeling and even the symbol grounding problems under discussion here. -- Stevan Harnad (609) - 921 7771 {bellcore, psuvax1, seismo, rutgers, packard} !princeton!mind!harnad harnad%mind@princeton.csnet harnad@mind.Princeton.EDU