harnad@mind.UUCP (Stevan Harnad) (06/30/87)
In comp.ai.digest: Laws@STRIPE.SRI.COM (Ken Laws) asks re. "Fuzzy Symbolism": > Is a mechanical rubber penguin a penguin?... dead...dismembered > genetically damaged or altered...? When does a penguin embryo become > a penguin?... I can't unambiguously define the class of penguins, so > how can I be 100% certain that every penguin is a bird?... and even > that could change if scientists someday discover incontrovertible > evidence that penguins are really fish. In short, every category is a > graded one except for those that we postulate to be exact as part of > their defining characteristics. I think you're raising the right questions, but favoring the wrong answers. My response to this argument for graded or "fuzzy" category was that our representations are provisional and approximate. They converge on the features that will reliably sort members from nonmembers on the basis of the sample of confusable alternatives encountered to date. Being always provisional and approximate, they are always susceptible to revision should the context of confusable alternatives be widened. But look at the (not so hidden) essentialism in Ken's query: "how can I be 100% certain that every penguin is a bird?". I never promised that! We're not talking about ontological essences here, about the way things "really are," from the God's Eye" or omniscient point of view! We're just talking about how organisms and other devices can sort and label APPEARANCES as accurately as they do, given the feedback and experiential sample they get. And this sorting and labeling is provisional, based on approximate representations that pick out features that reliably handle the confusable alternatives sampled to date. All science can do is tighten the approximation by widening the alternatives (experimentally) or strengthening the features (theoretically). But provisionally, we do alright, and it's NOT because we sort things as being what they are as a matter of degree. A penguin is 100% a bird (on current evidence) -- no more or less a bird than a sparrow. If tomorrow we find instances that make it better to sort and label them as fish, then tomorrow's approximation will be better than today's, but they'll then be 100% fish, and so on. Note that I'm not denying that there are graded categories; just that these aren't them. Examples of graded categories are: big, intelligent, beautiful, feminine, etc. > You are entitled to such an opinion, of course, but I do not > accept the position as proven... (Why opinion, by the way, rather than hypothesis, on the evidence and logical considerations available? Nor will this hypothesis be proven: just supported by further evidence and analysis, or else supplanted by a rival hypothesis that accounts for the evidence better; or the hypothesis and its supporting arguments may be shown to be incoherent or imparsimonious...) > ...We do, of course, sort and categorize objects when forced to do so. > At the point of observable behavior, then, some kind of noninvertible > or symbolic categorization has taken place. Such behavior, however, > is distinct from any of the internal representations that produce it. > I can carry fuzzy and even conflicting representations until -- and > often long after -- the behavior is initiated. Even at the instant of > commitment, my representations need be unambiguous only in the > implicit sense that one interpretation is momentarily stronger than > the other -- if, indeed, the choice is not made at random. I can't follow some of this. Categorization is the performance capacity under discussion here. ("Force" has nothing to do with it!). And however accurately and reliably people can actually categorize things, THAT'S how accurately our models must be able to do it under the same conditions. If there's successful all-or-none performance, the representational model must be able to generate it. How can the behavior be "distinct from" the representations that produce it? This is not to say that representations will always be coherent, or even that incoherent representations can't sometimes generate correct categorization (up to a point). But I hardly think that the basis of the bulk of our reliable all-or-none sorting and labeling will turn out to be just a matter of momentary relative strengths -- or even chance -- among graded representations. I think probabilistic mechanisms are more likely to be involved in feature-finding in the training phase (category learning) rather than in the steady state phase, when a (provisional) performance asymptote has been reached. > It may also be true that I do reduce some representations to a single > neural firing or to some other unambiguous event -- e.g., when storing > a memory. I find this unlikely as a general model. Coarse coding, > graded or frequency encodings, and widespread activation seem better > models of what's going on. Symbolic reasoning exists in pure form > only on the printed page; our mental manipulation even of abstract > symbols is carried out with fuzzy reasoning apparatus. Some of this sounds like implementational considerations rather than representational ones. The question was: Do all-or-none categories (such as "bird") have "defining" features that can be used to sort members from nonmembers at the level of accuracy (~100%) with which we sort? However they are coded, I claim that those features MUST exist in the inputs and must be detected and used by the categorizer. A penguin is not a bird as a matter of degree, and the features that reliably assign it to "bird" are not graded. Nor is "bird" a fuzzy category such as "birdlike." And, yes, symbolic representations are likely to be more apodictic (i.e., categorical) than nonsymbolic ones. -- Stevan Harnad (609) - 921 7771 {bellcore, psuvax1, seismo, rutgers, packard} !princeton!mind!harnad harnad%mind@princeton.csnet harnad@mind.Princeton.EDU
franka@mmintl.UUCP (Frank Adams) (07/02/87)
In article <936@mind.UUCP> harnad@mind.UUCP (Stevan Harnad) writes: |The question was: Do all-or-none categories (such as "bird") have "defining" |features that can be used to sort members from nonmembers at the level of |accuracy (~100%) with which we sort? However they are coded, I claim that |those features MUST exist in the inputs and must be detected and used by the |categorizer. A penguin is not a bird as a matter of degree, and the features |that reliably assign it to "bird" are not graded. I don't see how this follows. It is quite possible to make all-or-none judgements based on graded features. Thermostats, for example, do it all the time. People do, too. The examples which come to mind as being obviously in this category are all judgements of actions to take based on such features, not of categorization. But then, we don't understand how we categorize. But to take an example of categorizing based on a graded feature. Consider a typical, unadorned, wooden kitchen chair. We have no problem categorizing this as a "chair". Consider the same object, with no back. This is clearly categorized as a "stool", and not a "chair". Now vary the size of the back. With a one inch back, the object is clearly still a "stool"; with a ten inch back, it is clearly a "chair"; somewhere in between is an ambiguous point. I would assert that we *do*, in fact, make "all-or-none" type distinctions based precisely on graded distinctions. We have arbitrary (though vague) cut off points where we make the distinction; and those cut off points are chosen in such a way that ambiguous cases are rare to non-existent in our experience[1]. In short, I see nothing about "all-or-none" categories which is not explainable by arbitrary cutoffs of graded sensory data. --------------- [1] There are some categories where this strategy does not work. Colors are a good example of this -- they vary over all of their range, with no very rare points in it. In this case, we use instead the strategy of large overlapping ranges -- two people may disagree on whether a color should be described as "blue" or "green", but both will accept "blue-green" as a description. The same underlying strategy applies: avoid borderline situations. -- Frank Adams ihnp4!philabs!pwa-b!mmintl!franka Ashton-Tate 52 Oakland Ave North E. Hartford, CT 06108
harnad@mind.UUCP (Stevan Harnad) (07/03/87)
In Article 176-8 of comp.cog-eng: franka@mmintl.UUCP (Frank Adams) of Multimate International, E. Hartford, CT.writes: > I don't believe there are any truly "all-or-none" categories. There are > always, at least potentially, ambiguous cases... no "100% accuracy > every time"... how do you know that "graded" categories are less > fundamental than the other kind? On the face of it, this sounds self-contradictory, since you state that you don't believe "the other kind" exists. But let's talk common sense. Most of our object categories are indeed all-or-none, not graded. A penguin is not a bird as a matter of degree. It's a bird, period. And if we're capable of making that judgment reliably and categorically, then there must be something about our transactions with penguins that allows us to do so. In the case of sensory categories, I'm claiming that a sufficient set of sensory features is what allows as to make reliable all-or-none judgments; and in the case of higher-order categories, I claim they are grounded in the sensory ones (and their features). I don't deny that graded categories exist too (e.g., "big," "smart"), but those are not the ones under consideration here. And, yes, I hypothesize that all-or-none categories are more fundamental in the problem of categorization and its underlying mechanisms than graded categories. I also do not deny that regions of uncertainty (and even arbitrariness) -- natural and contrived -- exist, but I do not think that those regions are representative of the mechanisms underlying successful categorization. The book under discussion ("Categorical Perception: The Groundwork of Cognition") is concerned with the problem of how graded sensory continua become segmented into bounded all-or-none categories (e.g., colors, semitones). This is accomplished by establishing upper and lower thresholds for regions of the continuum. These thresholds, I must point out, are FEATURES, and they are detected by feature-detectors. The rest is a matter of grain: If you are speaking at the level of resolution of our sensory acuity (the "jnd" or just-noticeable-difference), then there is always a region of uncertainty at the border of a category, dependent on the accuracy and sensitivity of the threshold-detector. But discrimination grain is not the right level of analysis for questions about higher-order sensory categories, and all-or-none categorization in general. The case for the putative "gradedness" of "penguin"'s membership in the category "bird" is surely not being based on the limits of sensory acuity. If it is, I'll concede at once, and add that that sort of gradedness is trivial; the categorization problem is concerned with identification grain, not discrimination grain. All categories will of course be fuzzy at the limits of our sensory resolution capacity. My own grounding hypothesis BEGINS with bounded sensory categories (modulo threshold uncertainty) and attempts to ground the rest of our category hierarchy bottom-up on those. Finally, as I've stressed in responses to others, there's one other form of category uncertainty I'm quite prepared to concede, but that likewise fails to imply that category membership is a matter of degree: All categories -- true graded ones as well as all-or-none ones -- are provisional and approximate, relative to the context of interconfusable members and nonmembers that have been sampled to date. If the sample ever turns out to have been nonrepresentative, the feature-set that was sufficient to generate successful sorting in the old context must be revised and updated to handle the new, wider context. Anomalies and ambiguities that had never occurred before must now be handled. But what happens next (if all-or-none sorting performance can be successfully re-attained at all) is just the same as with the initial category learning in the old context: A set of features must be found that is sufficient to subserve correct performance in the extended context. The approximation must be tightened. This open-endedness of all of our categories, however, is really just a symptom of inductive risk rather than of graded representations. > "Analog" means "invertible". The invertible properties of a > representation are those properties which it preserves...[This > sounds] tautologically true of *all* representations. For the reply to this, see my response to Cugini, whose criticism you cite. Sensory icons need only be invertible with the discriminable properties of the sensory projection. There is no circularity in this. And in a dedicated system invertibility at various stages may well be a matter of degree, but this has nothing to do with the issue of graded/nongraded category membership, which is much more concerned with selective NONinvertibility. > It is quite possible to make all-or-none judgements based on graded > features [e.g., thermostats] Apart from (1) thresholds (which are features, and which I discussed earlier), (2) probabilistic features so robust as to be effectively all-or-none, and (3) gerrymandered examples (usually playing on the finiteness of the cases sampled, and the underdetermination of the winning feature set), can you give examples? > "chair"... with no back... [is a] "stool"... Now vary the size > of the back The linguist Labov, with examples such as cup/bowl, specialized in finding graded regions for seemingly all-or-none categories. Categorization is always a context-dependent, "compared-to-what" task . Features must reliably sort the members from the nonmembers they can be confused with. Sometimes nature cooperates and gives us natural discontinuities (horses could have graded continuously into zebras). Where she does not, we have only one recourse left: an all-or-none sensory threshold at some point in the continuum. One can always generate a real or hypothetical continuum that would foil our current feature-detectors and necessitate a threshold-detector. Such cases are only interesting if they are representative of the actual context of confusable alternatives that our category representation must resolve. Otherwise they are not informative about our actual current (provisional) feature-set. > I see nothing about "all-or-none" categories which is not explainable > by arbitrary cutoffs of graded sensory data... [and] avoid[ing] > borderline situations. Neither do I. (Most feature-detection problems, by the way, do not arise from the need to place thresholds along true continua, but from the problem of underdetermination: there are so many features that it is hard to find a set that will reliably sort the confusable alternatives into their proper all-or-none categories.) -- Stevan Harnad (609) - 921 7771 {bellcore, psuvax1, seismo, rutgers, packard} !princeton!mind!harnad harnad%mind@princeton.csnet harnad@mind.Princeton.EDU
sher@rochester.arpa (David Sher) (07/05/87)
In article <967@mind.UUCP> harnad@mind.UUCP (Stevan Harnad) writes: > >Most of our object categories are indeed all-or-none, not graded. A >penguin is not a bird as a matter of degree. It's a bird, period. Just for the record is this an off hand statement or are you speaking as an expert when you say most of our categories are all or none. Do you have some psychology experiments that measure the size of human category spaces and using a metric on them shows that most categories are of this form? Can I quote you on this? Personally I have trouble imagining how to test such a claim but psychologists are clever fellows. -- -David Sher sher@rochester { seismo , allegra }!al A: stwter s
harnad@mind.UUCP (Stevan Harnad) (07/05/87)
In Article 185 of comp.cog-eng sher@rochester.arpa (David Sher) of U of Rochester, CS Dept, Rochester, NY responded as follows to my claim that "Most of our object categories are indeed all-or-none, not graded. A penguin is not a bird as a matter of degree. It's a bird, period." -- > Personally I have trouble imagining how to test such a claim... Try sampling concrete nouns in a dictionary. -- Stevan Harnad (609) - 921 7771 {bellcore, psuvax1, seismo, rutgers, packard} !princeton!mind!harnad harnad%mind@princeton.csnet harnad@mind.Princeton.EDU
dmark@sunybcs.uucp (David M. Mark) (07/08/87)
In article <974@mind.UUCP> harnad@mind.UUCP (Stevan Harnad) writes: > > >In Article 185 of comp.cog-eng sher@rochester.arpa (David Sher) of U of >Rochester, CS Dept, Rochester, NY responded as follows to my claim that >"Most of our object categories are indeed all-or-none, not graded. A penguin >is not a bird as a matter of degree. It's a bird, period." -- > >> Personally I have trouble imagining how to test such a claim... > >Try sampling concrete nouns in a dictionary. Well, a dictionary may not always be a good authority fro this sort of thing. Last semester I led a graduate Geography seminar on the topic: "What is a map?" If you check out dictionaries, the definitions seem unambiguous, non-fuzzy, concrete. Even the question may seem foolish, since "map" probably is a "basic-level" object/concept. However, we conducted a number of experiments and found many ambiguous stimuli near the boundary of the concept "map". Air photos and satellite images are an excellent example: they fit the dictionary definition, and some people feel very strongly that they *are* maps, others sharply reject that claim, etc. Museum floor plans, topographic cross-profiles, digital cartographic data files on tape, verbal driving directions for navigation, etc., are just some examples of the ambiguous ("fuzzy"?) boundary of the concept to which the English word "map" correctly applies. I strongly suspect that "map" is not unique in this regard!
smoliar@vaxa.isi.edu (Stephen Smoliar) (07/10/87)
In article <3930@sunybcs.UUCP> dmark@marvin.UUCP (David M. Mark) writes: > we conducted >a number of experiments and found many ambiguous stimuli near the boundary >of the concept "map". Air photos and satellite images are an excellent >example: they fit the dictionary definition, and some people feel very >strongly that they *are* maps, others sharply reject that claim, etc. >Museum floor plans, topographic cross-profiles, digital cartographic >data files on tape, verbal driving directions for navigation, etc., are >just some examples of the ambiguous ("fuzzy"?) boundary of the concept >to which the English word "map" correctly applies. I strongly suspect >that "map" is not unique in this regard! Indeed, it almost seems as if "What is a map?" is not really the appropriate question. The better question might be "What can be used as a map?" or perhaps "How can I use a FOO as a map?" Furthermore, I agree that "map" is probably not unique. There are probably any number of bindings for BAR for which "What is a BAR?" runs into similar difficulty and for which "How can I use a FOO as a BAR?" is the more useful question. One candidate I might propose to discuss along these lines is the concept of "algorithm." There are any number of entities which might be regarded as being used as algorithms, ranging from Julia Child's recipies to chromosomes. It would seem that any desire to classify such entities as algorithms is only valuable to the extent that we are interested in the algorithmic properties such entities possess. For example, we might be interested in the nature of recipes which incorporate "while loops" because we are concerned with how such loops terminate. In an earlier posting, Harnad gave the example of how we classify works of art according to particular styles. Such classifications may also be susceptible to this intermediate level of interpretation. Thus, you may or may not choose to view a particular tapestry as an allegory. You may or may not choose to view it as a pastoral. Such decisions influence the way you see it and "parse" it as part of your artistic appreciation, regardless of whether or not your particular view coincides with that of the creator! I suspect there is a considerable amount of such relativity in the way we detect categories. That relativity is guided not by what the categories are or what their features are but by how we intend to put those categories to use. (In other words, the issue isn't "What features are present?" but "What features do we want to be present?")
lishka@uwslh.UUCP (Christopher Lishka) (07/13/87)
In article <3930@sunybcs.UUCP> dmark@marvin.UUCP (David M. Mark) writes: >In article <974@mind.UUCP> harnad@mind.UUCP (Stevan Harnad) writes: >> >> >>In Article 185 of comp.cog-eng sher@rochester.arpa (David Sher) of U of >>Rochester, CS Dept, Rochester, NY responded as follows to my claim that >>"Most of our object categories are indeed all-or-none, not graded. A penguin >>is not a bird as a matter of degree. It's a bird, period." -- >> >>> Personally I have trouble imagining how to test such a claim... >> >>Try sampling concrete nouns in a dictionary. > >Well, a dictionary may not always be a good authority for this sort of >thing. I don't want to start a huge discussion on a related topic, but I guess I'll throw in my two-cents worth. Mr. Harnad states that one should try sampling concrete nouns in a dictionary. It seems to me that a short while ago there was some discussion around the country as to what a dictionary's purpose actually is, to which a prominent authority on the subject replied that a dictionary is *only* a description of what people are commonly using certain words for. Now, one upshot of this seems to be that a dictionary, in the end, is NOT a final authority on many words (if not all of them included). It can only provide a current description of what the public in general is using the word for. In the case of some words, many people will use them for many different things. This may be one reason for the problems with the word 'map.' In the case of a penguin, scientifically it is considered a bird. I consider it a bird, although a penguin certainly does not fly in the air. However, if every English-speaking person except a few, say myself and Mr. Harnad, suddenly decided to think of a penguin as something other than a bird, than a dictionary's description would need to be changed, for myself and Mr. Harnad would be far outweighed. I suspect that the dictionary would have some entry as to the historical meaning of 'penguin' (i.e. a penguin used to be considered a bird, but now it is something else). However, since a dictionary is supposed to be descriptive of a language in its current usage, the entry for penguin would have to be modified. Which brings me to my point. Given that a dictionary is a descriptive tool that seeks to give a good view of a language as it is currently being used, can it really be used as a final authority? My feeling is no; just look at all the different uses of a certain word among your friends, not to mention the entire state you live in, not to mention your continent, not to mention the entire English-speaking population of the world. Holy cow! You've suddenly got a lot of little differences in meaning for a certain word. Not to mention slang and local terms (e.g. has anyone ever heard of the word 'bubbler?' It means a 'Water Fountain' here in Wisconsin, but you'd be surprised how many people don't know this term). In this case you can only look at words as a 'graded' term, not an all-or-none term if you are using a dictionary as the basis for a definition. Sure, if you want to use a scientific definition for penguin, go ahead...since science seems to seek to be unambiguos (unlike general spoken language), then you will have a better all-or-none description. But I don't think you can go about using a dictionary, which is a descriptive tool, as an all-or-none decisive authority on what a word means. If I remember back to a Linguistics course I took, this is the same difference as denotation vs. connotation. A couple notes: if you notice above (and right here), I use the word 'you' (as a technical writer would use the word 'one') to refer to a person in general (i.e. the reader). This is not generally accepted as proper English by the people who seek to define proper English, but it is the term that is used by most people that I have known (here in Wisconsin). It seems to me that this is further evidence of my argument above, because I do not think twice in using this term 'you;' it is how I was raised. Also, please don't start a discussion on language in this group unless it pertains to A.I. (and in some case it does); I just felt that someone ought to speak up on the ambiguity of words, and how to different people there might be problems with using a dictionary as a basis for judgement. If you want to continue this discussion, please e-mail me, and I will respond in a decent amount of time (after I cool off in the case of flames ;-) -- Chris Lishka /lishka@uwslh.uucp Wisconsin State Lab of Hygiene <-lishka%uwslh.uucp@rsch.wisc.edu \{seismo, harvard,topaz,...}!uwvax!uwslh!lishka
laporta@apollo.UUCP (07/14/87)
In article <245@uwslh.UUCP> lishka@uwslh.UUCP (Christopher Lishka) writes: >Given that a dictionary is a descriptive >tool that seeks to give a good view of a language as it is currently being >used, can it really be used as a final authority? My feeling is no; SUMMARY (1) You are absolutely right. There is no 'final authority' because language changes even as one tries to pin it down, with a dictionary, for example. (2) AI programs designed to 'understand' natural language must include an encyclopedic as well as a lexicological (dictionary) competence. (3) The nonexistence to date of perfect artificial understanders of natural language should not be surprising, given the enormity of the task of constructing an artificial encyclopedic competence. (4) The encyclopedia in this instance must grow with the language, preserving past states, simulating present states, and predicting future states. ELABORATION Tackling (2) first: While dictionary definitions are helpful guides in some respects, the nature of linguistic competence is encyclopedic rather than lexicological. For instance, you might hear someone say: Because I was going to give a cocktail party, I went to the mall to buy whiskey, peanuts, and motor oil. A lexicological competence would deem this sentence grammatical and unremarkably consistent, since 'mall' includes the availability of all the items mentioned. An encyclopedic competence, on the other hand, would mark this sentence as strange, since 'motor oil' is not a part of 'cocktail party,' unless, I suppose, you were willing to assume that some of the guests needed mechanical, not social, lubrication. Even this conjecture is unlikely, however, because 'cocktail party' includes humans consuming alcoholic beverages. A case of Billy Beer at the local Exxon is not a cocktail party. Car mechanics do not come to work in little black dresses. An encyclopedic competence is able (a) to isolate the assumptions an utterance requires for coherence, (b) to rank their probability, and (c) thus to evaluate the coherence of the utterance as a whole. Further, 'encyclopedic' in this context includes more than is found in the _Brittanica_. A humorist might write (in the character of a droll garage mechanic) about a parley to negotiate sale of a gas station. He decides to provide a little festive atmosphere by bringing along some beer. But even this hypothesis doesn't eliminate all strangeness: why is the mechanic buying motor oil at the supermarket? Certainly he could get a better price from his distributor. This sentence is a mine of linguistics lessons, but the above should be enough to suggest my point. Encyclopedic competence, however provided, (scripts or semantically marked graphs of words, to give two examples which are not mutually exclusive) is crucial to understanding even the topic of an utterance. The wider question evolves from (1) ... : Language is an elaboration of symbols which refer to other symbols. The 'last stop' (the boundary of semiotic analysis, not the the boundary of the linguistic process itself in actual beings or machines) is the connection of certain signs to 'cultural units.' These pieces of memory are what ground symbol nets to whatever they are grounded upon. (I prefer Harnad's formulation, but that is not crucial for this discussion.) When Og the Caveman remembers one morning the shape of the stone that he used as a scraper yesterday, a cultural unit exists, and stones of that shape are the first signs dependent upon it. To oversimplify, the process continues infinitely as signs are connected to other signs, new cultural units are formed, signs modify other signs, etc. ... and concludes with (3) and (4): Meaning is 'slippery' because language changes as it is used. A historically amnesiac encyclopedic competence for 1980 would mark as improbable sentences used daily at American slave auctions of the 1840's. SOURCE NOTE: Nearly everything I have said here has been elaborated by Umberto Eco in his book 'A Theory of Semiotics' and subsequent writings.
laporta@apollo.uucp (John X. Laporta) (07/15/87)
In article <3183@venera.isi.edu> smoliar@vaxa.isi.edu.UUCP (Stephen Smoliar) writes: >There are probably any number of bindings for BAR for which "What is a BAR?" runs >into ... difficulty and for which "How can I use a FOO as a BAR?" is the more useful >question. > >In an earlier posting, Harnad gave the example of how we classify works of >art ... Such classifications may also be susceptible to this intermediate level of >interpretation. Thus, you may or may not choose to view a particular tapestry >as an allegory ... [or] as a pastoral. Such decisions influence the way you see it and >"parse" it as part of your artistic appreciation, regardless of whether or not your >particular view coincides with that of the creator! > >I suspect there is a considerable amount of such relativity in the way we >detect categories. That relativity is guided not by what the categories >are or what their features are but by how we intend to put those >categories to use. (In other words, the issue isn't "What features >are present?" but "What features do we want to be present?") Umberto Eco writes in "Euge`ne Sue and _Les Myste`res de Paris_" about this problem. Sue was a sort of gentleman pornographer in post-Napoleonic France. One of his series, about a character like the Shadow who worked revenge on decadent aristocratic evildoers, with a lot of bodice-ripping along the way, caught on with the newly literate general working public. They consumed his book in vast quantities and took it as a call to arms so seriously that Paris was barricaded by people inspired by it. A sex-and-violence pornographic thriller became a call to political reform and the return of morality. The relevant semiotic category is "closure." Rougly speaking, a closed work is one that uses a tight code to tell a tale to an audience sharply defined by their sharing of that code. Superman Comics is an example of a closed work. (There is an entertaining study somewhere of explanations offered by New Guinean tribesmen of a Superman Comic.) Closed works don't ring, so to speak, with the resonance of the entire semiotic continuum, while open works do. Closed works are thus easily subject to gross misinterpretation by readers who don't share the code in which those works are written. Open works, on the other hand, enforce their own interpretation. While there is drift over time in these interpretations, it is far smaller than the vastly divergent interpretations offered of closed works by varying interpreters in the same era. Open works connect to the entire semiotic continuum - indeed, the (broadly) rhetorical methods (tropoi) they use bespeak a purpose of educating the reader about the subjects (topoi) they treat. _Remembrance of Things Past_ is an example of an open work. While a great deal of unfamiliar material and controversial analysis is offered to any reader of those 3000 pages, the mere act of reading them enforces what is, for the purpose of semiotics, a uniform interpretation (read disambiguated topical hypothesis). It is very easy to 'use' a closed work by correlating the elements of an external symbol system with the opaque code the work presents. Of course, if the 'grounding' of one's symbol system bears no relation to that which the work employs, one is just as much 'used' by the work as a consequence. (Imagine, for example, using a rectangular bar of plastic explosive as a straightedge.) It is far more difficult to impose an arbitrary interpretation on an open work, since it contains material that tends to contradict incorrect or incomplete hypotheses about its topos. For example, while we are 'told' that Superman comes from the planet Krypton, etc., we learn by watching Marcel what his origins are, and while Superman comes as a given from space, Marcel's character defines itself in our consciousness by our 'observation' of his life. Furthermore, while Superman is always Superman, Marcel has an origin and a destiny. Marcel changes with time, he breaks with Albertine; Superman always almost, but actually never marries Lois Lane. (Spiderman's recent marriage to Mary Jane is an interesting twist. Certainly by comparison with Superman's, Spiderman's story is an open work.) Historians who based hypotheses about 20th century American atittudes on an analysis of Superman comics would have to confirm them by considerable reference to external sources, while students of early 20th century France would likely use _Remembrance of Things Past_ to confirm their ideas. IN SUMMARY: The relativity of categorization is an inverse index of the 'openness' of the thing categorized. Dr. Morbius in "Forbidden Planet" was able to divine the purpose of Krell instrumentation because the science on which it was founded, while more advanced than his own, shared the same basis in physical reality and hypothesis testing. The space-given monolith in "2001" is indecipherable (a real 'black box', but with undefined input and output), and thus can be 'used' for any purpose at all.