Re: [FRIAM] basin filling
On 04/16/2014 10:48 AM, Marcus G. Daniels wrote: What is the question here? What are the historical conditions that lead to one or the other forming? How to destabilize such a social system? An answer to the latter is to vote for progressive candidates, seems to me, and let (Glen's) `database' grow from those experiences. Try stuff, and collectively learn from those experiences.. Well, for me -- and I think what Steve was arguing for that lead to Roger's criticism, I'd like to be able to ask the question of whether any of them [pat|mat|ky|*]riarchy arise naturally at all... or even regardless of equivocation around natural, whether some of them arise more frequently than others. But especially, I'd like to ask questions surrounding their strength. Haphazardly trying stuff is great and I fully support it. ;-) But it would be better to know how _hard_ you have to try in order to escape, say, patriarchy. I'd also like to know their positions relative to one another (mostly distance between them). If we push too hard against patriarchy are we more likely to land in a kyriarchy than a matriarchy? Can we maintain the system between attractors? Or are they too densely packed so that the slightest perturbation sends us hurtling into the nearest neighbor? Perhaps we could engineer it to flit between 2 or more of them with delicately timed tweaks? But it's also possible that these systems aren't attractors at all... perhaps the state space is relatively isotropic and being stuck in any one region really is a matter of a few gamers (lineages of gamers) keeping it there? To my mind, we won't make any progress on this sort of thing until we make a serious effort to define the space, which means building a schema that credibly captures enough of the salient variables. The spaces spanned by tiny bases like just money (or a similarly small set like money and family) are just too _ideal_. They aren't rich enough analogs to give us any insight into the real space to which they refer. -- ⇒⇐ glen 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 21:37 -0600, Steve Smith wrote: 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)? You expect people to think and you also intend to model them with particles? Anyway, depends if you want to illustrate results in social science or do social science. 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
On 04/15/2014 08:37 PM, Steve Smith wrote: 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's no reason why we wouldn't pursue both qualitative and quantitative models. I find myself arguing for the idea that all quant models are preceded by qual models anyway. It's a straightforward extension of the philosophical problem of degree vs. kind (for those of us who think philosophy is useless). I think the notion of an attractor survives the dimensionality problem. It seems clear that patriarchy is a stable attractor. I don't know why, of course. But we can speculate then try to hone the speculation into hypotheses that can be tested qual, first, and quant for those that survive long enough. Qualitatively, we can test your (1) by translation across geography. Do white males get all the goodies in, say, Peru? How about the Central African Republic? Etc. On 04/15/2014 03:52 PM, Marcus G. Daniels wrote: A master equation for an economic system will be high dimensional. I think the concept of a master equation is inscription error. If you look hard enough for such an equation, you will find one. But it may be illusory, which means whatever you find will break for inexplicable reasons, until you find the new one or go with an equation-free approach. 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). It's not clear to me that time spent with family is antithetic to time spent at work. There's a long tradition of combining the two... just look at the Koch brothers... or the Bush dynasty. ;-) The curse of high dimensionality is even worse than you've mentioned so far in that we have no idea which variables are identical, equivalent, dependent, and independent. Indeed, anything we _name_ a variable is suspect. But none of this should stop anyone with the energy and interest. All we need do is hone speculation down to a falsifiable model, falsify it, log it in the database, and iterate. The trick is that the _database_ sucks. We don't keep track of how well/poorly our models are doing. E.g. this was in the news recently: Everything Is Permitted? People Intuitively Judge Immorality as Representative of Atheists http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0092302 And this was cited as evidence the author (Gervais) is biased: Mentalizing Deficits Constrain Belief in a Personal God http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0036880 These aren't just qualitative models but it's super easy to criticize the choices they made in quantification. Why? Because the database sucks. 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? You don't need occult qualities like love and hate. There are plenty of almost-quantified qualities to consider first. Things like the Happy Planet Index or the Narcissistic Personality Index are in that fuzzy border and could be used to accrue falsified models. (Things like the Gini index may help with Steve's model (2).) The experiments that would be illuminating can't be done for practical or ethical reasons. It's true that the experiments that would be _ultimately_ illuminating can't be done. But there are those that could be _somewhat_ illuminating... and I argue that there are lots of psych, social, ecological, neuro, and biological experiments that are currently being done that help, even with the gender inequality problem. But again, why can't we _relate_ these results into some more complex, systemic models? ... because the database sucks. -- ⇒⇐ glen 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
I think the notion of an attractor survives the dimensionality problem. It seems clear that patriarchy is a stable attractor. I don't know why, of course. Because it is by definition? If people are persuaded or forced to participate in matriarchy, patriarchy, or kyriarchy then it continues (obviously). What is the question here? What are the historical conditions that lead to one or the other forming? How to destabilize such a social system? An answer to the latter is to vote for progressive candidates, seems to me, and let (Glen's) `database' grow from those experiences. Try stuff, and collectively learn from those experiences.. 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
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
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 04/14/2014 09:38 AM, Nick Thompson wrote: If we were dedicated to filling that basin, what would that look like? It would look like an understanding of merit and reward that addressed as many dimensions of a human and its environment as possible. Something like the ontologies I posted would be a good start. -- ⇒⇐ glen 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 Mon, 2014-04-14 at 10:05 -0700, glen wrote: On 04/14/2014 09:38 AM, Nick Thompson wrote: If we were dedicated to filling that basin, what would that look like? It would look like an understanding of merit and reward that addressed as many dimensions of a human and its environment as possible. Something like the ontologies I posted would be a good start. I've seen this sort of thing used before for threat evaluation. In that context they identified the resources that a bad guy could use to accomplish a set of bad things, with the related workflow for each one, and the (alternative) dependencies for those workflows. Then one tries to work through the combinatorics brute force to see what links are most crucial for maximizing the probability of success for various bad goals. (And then take some action to ensure that the links can be cut in the real world.) Here it is the opposite -- replacing bad things with desired things. It means being very clear on the relationships between dependencies (or to represent uncertain mappings somehow), which has yet to occur in this discussion. And perhaps harder, to admit that the things you cherish are nothing more than a node on a graph. :-) 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
On 04/14/2014 11:41 AM, Marcus G. Daniels wrote: I've seen this sort of thing used before for threat evaluation. In that context they identified the resources that a bad guy could use to accomplish a set of bad things, with the related workflow for each one, and the (alternative) dependencies for those workflows. Then one tries to work through the combinatorics brute force to see what links are most crucial for maximizing the probability of success for various bad goals. (And then take some action to ensure that the links can be cut in the real world.) Yep. I also think that simply defining the problem, way before getting to enough clarity for brute force, would go a long way to clarifying the silly arguments we get in today. I think if job reqs and candidate employees simply familiarized themselves with these ontologies as they considered hiring or taking a new position, that simple consideration would go a long way toward more rationality. And I'd be gobsmacked if any of our legislators thought about this stuff with such ontologies in front of them. Here it is the opposite -- replacing bad things with desired things. It means being very clear on the relationships between dependencies (or to represent uncertain mappings somehow), which has yet to occur in this discussion. And perhaps harder, to admit that the things you cherish are nothing more than a node on a graph. :-) Having worked on an human resources capital management application, in a company that was bought and cannibalized, I had a good opportunity to experience, first hand, the distance between an idealized human resource and actual humans. Oddly enough, it just convinced me that we could flesh out the schema and populate such a database (here in the 1st world, anyway) far enough to accommodate brute force if we only had the energy/desire/political will. But then I start feeling like a dirty communist and have to go chop some firewood or practice takedown/assembly of my 9mm ... with some Ted Nugent playing at 11. ;-) -- ⇒⇐ glen 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
Wise Nick - As usual, I got my ears boxed on the substance, but everybody gave me a pass on the use of the metaphor, attractor and basin. It's been quite a while since I read any complexity literature and nearly as long since a complexity topic has graced these pages. So, I am wondering, if any of you would care to advise me on how to use that metaphor properly. If we were dedicated to filling that basin, what would that look like?What does this systems talk contribute to a discussion, other than a whiff of modernity? Would I have said less or more if I had suggested that we alter the incentives surrounding childcare for men and women, or the like. By all means, let's return to considering the phenomena in question (Openness vs Inequality) using the tools of complexity theory. In particular, of the socio-economic status of individuals within our system when engaged in one or more of the obvious Open Systems that are popularly included in western (and especially US culture) and specifically the global communication/information network comprised mainly of the Internet but also Cell Networks, Publishing and other Media Networks, and perhaps even outliers like HAM or CB radio and real-world public events such as meetings, conferences, public protests (e.g. Occupy), Democratic Processes, and the Marketplace. If we consider each individual over time as occupying a point in this space (a given gender, age, salary, net worth, educational-level, employment status, group-affiliations, etc.), and their being an Evolution function (F(t,_v)) which describes how that individual moves in phase space, then perhaps we can recognize and describe various point, line(Orbit), area(basin) and volume (in N-dimensions) attractors. Following Glen's criticism of the Landscape Metaphor, I will add that terms such as orbit (celestial navigation?) and basin are useful for their familiarity, but are very limited. In particular (no ear-boxing intended) I don't think the idea of Filling a Basin is apt... but ignoring that misleading aspect of the landscape metaphor, I think your point can be used to talk about exploring the adjacent possibles to F(t,_v) (name them Fn(t,_v) which might be alternative rule-sets (social, regulatory, religious, ???) whose attractors are more equal across the identified qualites of Gender, Race, and Sexual_Orientation (GRS). This opens the question of what means more equal?. I suppose first we need to identify what we are measuring... perhaps salary is key, maybe accumulated wealth/assets is another measure many follow, maybe social status (within what group? how broad?), maybe access to *other* resources besides $$? Some would include other features such as (likelyhood of being sexually harrassed, murdered, or raped). Once we identify that, then I suppose that we are interested in Fn(t,_v) whose attractors, when projected into the dimensions being valued, show no correlation with GRS? G, R and S, for our purposes are characterized by small integer sets (G cardinality of 2 or 3 or 4 or 5 or 6 if we differentiate between trans in each direction and hermaphrodite and maybe Neuter?) and (R cardinality of 2, 3, or 18,973 depending on how distinctive we want to be at which point it seems like R has smeared into Ethnicity and even Tribal/Clan/Family distinctions?) and S (roughly the cardinality of GxG?). I can't tell if modeling these things more formally will help understanding, but perhaps? I suspect that *equality* is not precisely what we seek.. but maybe there are other properties of the phase space and the attractors which we would like to find?The term Class in popular discussion seems apt. As is often the case with *any* system, thoughtful, informed, motivated modeling of the domain often helps us understand things which were a puzzle before, and sometimes even solve the implied problems that were represented in our puzzlement. In this case, what resources or experiences do SWMs have access to which non-SWMs do not (as easily?) and/or how can we change F(t,_v), or more to the point, choose from an infinite set of Fn(t,_v) which match the criteria we seek... and EVEN more to the point what does the space of Fn(t,_v) look like, what are the adjacent possibles to our current F(t,_v) and can we imagine or prescribe an evolution from Fo(t,_v) TO a desired Fn(t,_v)? Just to be difficult or oblique, let me close with a highly figurative allusion to a familiar children's allegorical tale: If Jack and Jill go up the hill (Landscape metaphor) to fetch a pail of water (seeking a more equitable Fn(t,_v) for all) then must Jack fall down,and break his crown? And if so, what does that mean? A fall from grace of the SWM? And must Jill also therefore come tumbling after?If figurative speech using metaphor is risky, I suppose turning a simple children's fairytale into an allegory for modern socioeconomic
Re: [FRIAM] basin filling
Steve, Glen, Marcus, I am liking these responses. Thankyou for giving the question your all. I am not sure I am man enough to respond usefully to them, but they are causing me to think. One thing that they make evident is a way in which basin is a metaphor that I had not thought of. 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. 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. Well, as I say: thank you. I hope others will pitch in. N Nicholas S. Thompson Emeritus Professor of Psychology and Biology Clark University http://home.earthlink.net/~nickthompson/naturaldesigns/ http://home.earthlink.net/~nickthompson/naturaldesigns/ From: Friam [mailto:friam-boun...@redfish.com] On Behalf Of Steve Smith Sent: Monday, April 14, 2014 2:45 PM To: The Friday Morning Applied Complexity Coffee Group Subject: Re: [FRIAM] basin filling Wise Nick - As usual, I got my ears boxed on the substance, but everybody gave me a pass on the use of the metaphor, attractor and basin. It's been quite a while since I read any complexity literature and nearly as long since a complexity topic has graced these pages. So, I am wondering, if any of you would care to advise me on how to use that metaphor properly. If we were dedicated to filling that basin, what would that look like?What does this systems talk contribute to a discussion, other than a whiff of modernity? Would I have said less or more if I had suggested that we alter the incentives surrounding childcare for men and women, or the like. By all means, let's return to considering the phenomena in question (Openness vs Inequality) using the tools of complexity theory. In particular, of the socio-economic status of individuals within our system when engaged in one or more of the obvious Open Systems that are popularly included in western (and especially US culture) and specifically the global communication/information network comprised mainly of the Internet but also Cell Networks, Publishing and other Media Networks, and perhaps even outliers like HAM or CB radio and real-world public events such as meetings, conferences, public protests (e.g. Occupy), Democratic Processes, and the Marketplace. If we consider each individual over time as occupying a point in this space (a given gender, age, salary, net worth, educational-level, employment status, group-affiliations, etc.), and their being an Evolution function (F(t,_v)) which describes how that individual moves in phase space, then perhaps we can recognize and describe various point, line(Orbit), area(basin) and volume (in N-dimensions) attractors. Following Glen's criticism of the Landscape Metaphor, I will add that terms such as orbit (celestial navigation?) and basin are useful for their familiarity, but are very limited. In particular (no ear-boxing intended) I don't think the idea of Filling a Basin is apt... but ignoring that misleading aspect of the landscape metaphor, I think your point can be used to talk about exploring the adjacent possibles to F(t,_v) (name them Fn(t,_v) which might be alternative rule-sets (social, regulatory, religious, ???) whose attractors are more equal across the identified qualites of Gender, Race, and Sexual_Orientation (GRS). This opens the question of what means more equal?. I suppose first we need to identify what we are measuring... perhaps salary is key, maybe accumulated wealth/assets is another measure many follow, maybe social status (within what group? how broad?), maybe access to *other* resources besides $$? Some would include other features such as (likelyhood of being sexually harrassed, murdered, or raped). Once we identify that, then I suppose that we are interested in Fn(t,_v) whose attractors, when projected into the dimensions being valued, show no correlation with GRS? G, R and S, for our purposes are characterized by small integer sets (G cardinality of 2 or 3 or 4 or 5 or 6 if we differentiate between trans in each direction and hermaphrodite and maybe Neuter?) and (R cardinality of 2, 3, or 18,973 depending on how distinctive we want to be at which point it seems like R has smeared into Ethnicity and even Tribal/Clan/Family distinctions?) and S (roughly the cardinality of GxG?). I can't tell if modeling these things more formally will help understanding, but perhaps? I suspect that *equality* is not precisely what we seek.. but maybe there are other properties of the phase space and the attractors which we would like to find?The term Class in popular discussion seems apt. As is often the case with *any
