On Jun 12, 2011, at 4:13 PM, Danny Ayers wrote: >>> (there will be some isomorphism between a thing and a description of a >>> thing, right? >> >> Absolutely not. Descriptions are not in any way isomorphic to the things >> they describe. (OK, some 'diagrammatic' representations can be claimed to >> be, eg in cartography, but even those cases don't stand up to careful >> analysis. in fact.) > > Beh! Some isomorphism is all I ask for. Take your height and shoe size > - those numeric descriptions will correspond 1:1 with aspects of the > reality. Keep going to a waxwork model of you, the path you walked in > the park this afternoon - are you suggesting there's no isomorphism?
Yes, in fact I am *denying* there is *any* isomorphism. What structures are you intending to appeal to when you say 'isomorphic'? Do you see reality as being some kind of giant category? Or what? Lets suppose that the interpretation/denotation/semantic/reference mapping goes from the representation to the reality. (Since its an isomorphism, it should be invertible, so this is an arbitrary choice, right?) Call this mapping ref, so X ref Y means that Y is one way reality might be assuming X is true, when X is used as a representation. First point: for descriptions, ref is a Galois mapping, which means that when X gets larger - when the representation says more about the reality - then Y, the number of ways that the reality can be, gets smaller. The more you say, the more tightly you constrain the ways the world can be. This is exactly the opposite from how an isomorphism would behave. Next point: there can indeed be correspondences between the syntactic structure of a description and the aspects of reality it describes. Your example of the path I walked would be one, if you were to draw the path on an accurate map. But this is completely hostage to the map being **accurate**. If I used a not-to-scale sketch map, then no, you don't get isomorphism. Yet it seems to me that these two cases, the real map and a sketch map, both seem to work in the same kind of semantic way. So this explanation of how they work cannot depend on there being an isomorphism. Maybe there is a kind of homomorphism, but even that is kind of hard to make work. What it seems to be is more like, the map projection function is a homomorphism of the entire mapped terrain, and then marks or symbols on the map indicate terrain location by inverting this projection morphism and asserting an existential to the effect that the thing described is contained in that back-projected space in the terrain from space occupied by the mark or symbol in the map space. But I don't think all this is really germane to the http-range-14 issue. The point there is, does the URI refer to something like a representation (information resource, website, document, RDF graph, whatever) or something which definitely canNOT be sent over a wire? > >> ** To illustrate. Someone goes to a website about dogs, likes one of the >> dogs, and buys it on-line. He goes to collect the dog, the shopkeeper gives >> him a photograph of the dog. Um, Where is the dog? Right there, says the >> seller, pointing to the photograph. That isn't good enough. The seller >> mutters a bit, goes into the back room, comes back with a much larger, >> crisper, glossier picture, says, is that enough of the dog for you? But the >> customer still isn't satisfied. The seller finds a flash card with an >> hour-long HD movie of the dog, and even offers, if the customer is willing >> to wait a week or two, to have a short novel written by a well-known author >> entirely about the dog. But the customer still isn't happy. The seller is at >> his wits end, because he just doesn't know how to satisfy this customer. >> What else can I do? He asks. I don't have any better representations of the >> dog than these. So the customer says, look, I want the *actual dog*, not a >> representation of a dog. Its not a matter of getting me more information >> about the dog; I want the actual, smelly animal. And the seller says, what >> do you mean, an "actual dog"? We just deal in **representations** of dogs. >> There's no such thing as an actual dog. Surely you knew that when you looked >> at our website? > > Lovely imagery, thanks Pat. > > But replace "a novel written by a dog" for "dog" in the above. Why > should the concept of a document be fundamentally any different from > the concept of a dog, hence representations of a document and > representations of a dog? I dont follow your point here. If you mean, a document is just as real as a dog, I agree. So? But if you mean, there is no basic difference between a document and a dog, I disagree. And so does my cat. > Ok, you can squeeze something over the wire > that represents "a novel written by a dog" but you (probably) can't > squeeze a "dog" over, but that's just a limitation of the protocol. So improved software engineering will enable us to teleport dogs over the internet? Come on, you don't actually believe this. Pat > There's equally an *actual* document (as a bunch of bits) and an > *actual* dog (as a bunch of cells). > > Cheers, > Danny. > > -- > http://danny.ayers.name > ------------------------------------------------------------ IHMC (850)434 8903 or (650)494 3973 40 South Alcaniz St. (850)202 4416 office Pensacola (850)202 4440 fax FL 32502 (850)291 0667 mobile phayesAT-SIGNihmc.us http://www.ihmc.us/users/phayes
