I wrote: > I made up the following list of "The Three Laws of Models."
1. No model can be an exact representation of the complexities of empirical reality. 2. The predictions implied by any model vary as the assumptions change. 3. No model applies to answer all questions (to predict in all domains) because no model can tell the whole story.< I am sorry, but I didn't put this into context (of the book I'm writing). In trying to do social research, there are three stages: (a) abstraction: simplifying the blooming, buzzing complexities of the empirical world in order to understand it (or rather, that element of the world you want to understand); (b) theory: a specific understanding of the world, emphasizing (theoretical) causation links (which need not be simple or linear, and might be structural) between events that the author of the theory thinks are most important; and (c) model: a statement of the theory using math, graphs, pictures, and/or words made in order to communicate the theory to others, to test its internal cohesion (getting the story straight), and to verify its consistency with perceived empirical reality. Max quotes: "Models are to be used, not believed." -- Henri Theil That's right. It's a big mistake to confuse the map (the model) with the territory, to reify the model. That seems the gist of my first "law." It's a great quote. Dan writes: >Maybe, "No model is universal even within its particularity (including this one)"?< I don't understand this, Dan. I wasn't presenting an actual model. It was more of an abstraction. Ian writes: >The terms and inferences of models may not be commensurable with similar models [underdetermination of theory by evidence, intertranslatability [!!!] and all that; see http://ndpr.nd.edu/review.cfm?id=9304 and the book itself for more....Ian] < I'd have to read the book. The review seems written by a jargon-lover, who doesn't like to link abstract concepts to concrete exemplars. Too abstract for me. But of course, that's because he's presenting something like a model himself, i.e., an abstract picture of the book, which itself is an abstract story. This should not be surprising, since that's what book reviews do. Doyle Saylor quotes me: "No model applies to answer all questions (to predict in all domains) because no model can tell the whole story." and says: >... I assume you for some reason think a GUT (Grand Unified Theory) is not attainable?< Maybe in the domain in which it is supposed to apply. (I don't know enough physics to say either way.) But it wouldn't apply, say, to understanding economics, sociology, psychology, or for that matter, chemistry and biology. I don't think anyone can reduce society to biology or biology to chemistry or chemistry to physics. In any event, if I understand it, the GUT is a theory. The actual specification of that theory -- the model -- may not fit the actual world very well. The point of seeking it would be to find a model that fits the empirical world better than previous ones. He quotes me again: "No model can be an exact representation of the complexities of empirical reality." and writes: >The presumption here is that we are talking 'mathematical' model.< No, as I made clear above, I was not referring to merely mathematical models. There are verbal models. By their very nature, all models involve abstraction -- simplification -- and thus leave empirical stuff out. So they do not correspond to the complexities of empirical reality. >You do not make a distinction between a model and paradigm. So this is very vague about what you mean.< A paradigm is 20 cents. More seriously, a paradigm is very different from a model (at least for the way I use the word). A paradigm -- or research program -- involves a general vision of how the empirical world works that is applied as part of the process of understanding it. (Neoclassical economists, for example, would like to understand the world totally in terms of unique and stable equilibria, as in a simple market.) It's a little bit like a street-light, which shows up certain aspects of empirical reality, but may be totally wrong for the purpose at hand: remember the story of the drunk looking for his car keys under the street-light (even though he lost them in a dark alley) because "that's where the light is better." A research program might be thought of as a mega- or über-model. However, entire paradigms are almost never communicated completely to others. Nor are the internal consistency or the empirical fit ever tested for a research program as a whole. This testing seems impossible. Only the pieces (the models) can be contrasted/compared with empirical reality. One paradigm might do better than another if its pieces pass empirical tests better than the other, but that doesn't "prove" or "disprove" it as much as suggest that it is more productive of insights. >Is a photograph of a space a model?< No. It's a kind of data. Like all data, it is limited in its representation of the real world that lies behind our perceptions of it. But it's not a "mental picture" the way a model is. In some ways, however, a photograph is a mixture of data and a model, since the photographer has a major effect on the appearance of the picture. But it's not a model as I use that word. But the example does point up an important aspect of data: the nature of (almost?) all data is infused with and affected by pre-existing theory. By the way, in case anyone was wondering, I wasn't talking about Tyra Banks either. Doug quotes: "The SLB [Sharpe-Lintner-Black capital asset pricing] model is just a model and so surely false." - Eugene Fama Like a map, it is false as a picture of the details of the territory, but like a map it might be useful as a tool for getting where people want to go. I don't know enough about that specific model to say anything about its validity or lack thereof. Doug also quotes the Maestro: "It doesn't, however, induce us to then conclude that, if the model doesn't forecast - which implies that it has not captured the appropriate structure - we nonetheless tend to use the structure of the model to do analysis and draw significant conclusions about how the inner workings of relationships occur even though the coefficients which we're employing clearly don't forecast anything worthwhile." - Alan Greenspan huh? AG is ambiguous, as usual. (He should have played the "Sphinx" in the movie "Mystery Men." Maybe in the stage version?) Isn't there a "not" missing somewhere in there? Robert writes: >Asimov later added a fourth, which he decided he had to call the "zeroth law."< According to the Wikipedia, the three laws of robotics are: > 1. A robot may not injure a human being or, through inaction, allow a human > being to come to harm. >2. A robot must obey orders given to it by human beings, except where such orders would conflict with the First Law. >3. A robot must protect its own existence as long as such protection does not conflict with the First or Second Law.< The "zeroeth law" is that: > "A robot may not harm humanity, or, by inaction, allow humanity to come to > harm"; the rest of the laws are modified sequentially to acknowledge this.< A lot of Asimov's robot stories are about how these "laws" fail to solve all problems with robots. -- Jim Devine / "Segui il tuo corso, e lascia dir le genti." (Go your own way and let people talk.) -- Karl, paraphrasing Dante.
