Re: [FRIAM] basin filling
Marcus - I understand that pre-inventing Psychohistory (ala Asimov) is an out-of-reach task. Predictive models in general are hard, and as you say, this one has deeply compounded problems of dimensionality and testability, etc. What I'm seeking are notional models with more acknowledgement of the complexities and maybe a qualitative hint toward any first or second order "unintended consequences" they might hint at. Familiar, brutally simple models are on the order of: 1. White Males get all the goodies, everyone else gets bupkis. 2. The rich get richer. There is plenty of anecdotal evidence that both of these are basically true in many contexts, but I don't think they help us do much except *maybe* continue/restart/accelerate "affirmative action" programs and/or sharpen the blade on the guillotine (for the rich). A *notional* model helps people think about the problem space, and not just people with a strong technical understanding of the problem space. The public is trained to look for simple, linear relationships between things and zeroth order effects, I'm just calling for the development of a broader and deeper description of these very relevant problems. Is it possible that we might operate with more hope, more earnestness, maybe even less cynicism if we had models that suggested nonlinear response curves and "tipping points" (as Malcom Gladwell popularized)? We might avoid problems such as are described in Susan Faludi's "Backlash" and "Stiffed" where the most well intentioned reactions to first order symptoms of inequality have lead to various unexpected results that undermined the original intentions of the actions. Just my $.02 - Steve On Tue, 2014-04-15 at 13:53 -0600, Steve Smith wrote: I believe that our "common understanding" of such problems as gender/race inequalities tends to be too "simple" which might explain why progress in the domain is both slow and somewhat herky-jerky. A master equation for an economic system will be high dimensional. For example, every person has assets to track over time. There are many-to-many economic transactions that explode the state space. Forget about geometry you can visualize. And a lot of the variables are not going to be independent. Time spent at work and time spent with family will be t and (1-t). Income will be correlated with t (paid by the hour). To get at gender culture things various stateful things like affinity to peers and family need to be quantifiable somehow. Are love and hate a linear scale or logarithmic? Maybe it is more like a step function? And how do you validate these system evolution models? You might be able to give someone a million dollars but you can't easily take it away, or spontaneously make a janitor a medical doctor or get most people to agree to change their sex. The experiments that would be illuminating can't be done for practical or ethical reasons. It's a curse of dimensionality in spades, and only by contrasting Billions and Billions of different policy systems could one hope to get good enough statistics to say that a hypothetical master equation was or was not at work in the real world. Marcus FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
Re: [FRIAM] basin filling
On Tue, 2014-04-15 at 13:53 -0600, Steve Smith wrote: > I believe that our "common understanding" of such problems as > gender/race inequalities tends to be too "simple" which might explain > why progress in the domain is both slow and somewhat herky-jerky. A master equation for an economic system will be high dimensional. For example, every person has assets to track over time. There are many-to-many economic transactions that explode the state space. Forget about geometry you can visualize. And a lot of the variables are not going to be independent. Time spent at work and time spent with family will be t and (1-t). Income will be correlated with t (paid by the hour). To get at gender culture things various stateful things like affinity to peers and family need to be quantifiable somehow. Are love and hate a linear scale or logarithmic? Maybe it is more like a step function? And how do you validate these system evolution models? You might be able to give someone a million dollars but you can't easily take it away, or spontaneously make a janitor a medical doctor or get most people to agree to change their sex. The experiments that would be illuminating can't be done for practical or ethical reasons. It's a curse of dimensionality in spades, and only by contrasting Billions and Billions of different policy systems could one hope to get good enough statistics to say that a hypothetical master equation was or was not at work in the real world. Marcus FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
Re: [FRIAM] basin filling
Nick - ... It offers a picture of a three dimensional structure as a model for goings-on in an N dimensional space. Not at all clear to me that the intuitions drawn from a three dimensional model have any use at all in n-dimensional space. Reread Edwin Abbot Abbot's "Flatland: a Romance in Many Dimensions" ? There are qualitatively new properties that appear in higher dimensional space which in fact are hard to think about in lower dimensional spaces. Very specifically, 0-D space has no "room" for distinct objects... go to 1-D and you can now have objects which are located uniquely along the "number line"... go to 2-D space and said objects can now have relations with eachother (connections as in a graph or network) other than those "adjacent" along the number line in 3-D you find that you can make those same *connections* arbitrarily without having "edge" crossings (e.g. a road network requires over/underpasses to avoid crossings while in principle the flight paths of aircars do not). In the case of an N-Dimensional manifold and 2D surfaces embedded in a 3D space... the idea of a "basin of attraction" is intuitive if we use the landscape metaphor to think about it. In a hydrological landscape (watershed) we have the concept of "drainage basins" which are fairly easy for people to apprehend but invoke all kinds of other thoughts which are *not* necessarily relevant to the problem at hand. For example, there is not really a concept of "flow" within the basin, nor is there one of "erosion" *of* the basin, nor is there an idea of "filling" (like a lake) which is apt to the problem. I have always been persuaded that a model that requires a model to make it intelligible is no model at all. I mean, either a model is sufficient to bring a phenomenon within the range of some set of useful intuitions, or it is of no value. In the above example, the 2D surface in a 3D model with 2D bounded regions is a valuable *model* of the mathematical abstraction involved. We *add* the landscape metaphor to it to make it more usefully familiar. If we see the "surface" as a complex of "watersheds", it is perhaps a quicker if not more accurate way to explain the situation. As usual, our language can help or hinder our understanding. In this case, what we mean by "model" and how that relates to "metaphor". I usually think of *mathematical* models, I suspect you think of *conceptual* models and I'm not sure how you use *metaphor* in this case, perhaps you don't if you are thinking strictly in the sense of a literary metaphor. I use metaphor specifically to be a complex analogy between one domain (target) and another (source). Both domains are ultimately "models" in the sense that the map is *never* the territory.Ideally, the target domain is a very simple abstraction of the territory in question. In our example above... the "territory" is the socioeconomic status of populations and the "map" is a set of points embedded in the parameter space (age, race, gender, income, education, ) along with an Evolution Function, or essentially the "local" rules (in time) for how an individual "moves" through that space. For example, individuals educational level is a monitonically increasing function with time while their income and assets may trend that way but are NOT strictly monotonic (take a cut in pay, spend savings, etc.). To *then* translate that geometric description into a more familiar one (watershed), adds a level of familiarity to anyone with limited experience with such geometric spaces but at the same time, it adds potentially unwanted/irrelevant/distracting properties to the understanding/discussion. So... said simply, I think we "layer" models (both mathematical and conceptual) all the time for various reasons, but when we actually shift to *metaphorical* descriptions to make them more intuitively accessible (especially to laypersons) we also risk *mis*understandings. I too, look forward to other folks weighing in from other perspectives. I believe that our "common understanding" of such problems as gender/race inequalities tends to be too "simple" which might explain why progress in the domain is both slow and somewhat herky-jerky. - Steve FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
