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Yet I want to call this process of increasingly clarifying concepts and making distinctions conceptual technology. And conceptual technology is the "product" that philosophy has to offer other fields, to improve them both academically and practically.

Certainly conceptual clarity is useful in making models (e.g. understanding that the species concept is vague in an evolutionary model affects the form and use of the model). But how can a model of some phenomenon (e.g. of evolution of species or liquidity) impact our understanding of that concept (e.g. liquidity) or its properties (like vagueness). Think also about the evolution of the moral experience: how does the evolutionary explanation for our moral reactions and experiences affect our understanding of morality as a philosophical notion? In general, it is indisputable that clearer concepts can lead to better science, but the impact of more refined science on philosophy is much less clear.

The way I usually think about this is that once it is possible to build a model or perform an experiment on some phenomenon, then most of the philosophical work on that phenomenon must have already been done. Our understanding of the concept of liquidity is not complete, and though many experiments utilize liquids and the fluid properties of liquids, there are no tests that I can think of to distinguish features of the liquidity (how liquid it is). But on further thought there are things like viscosity, pressure, throughput, laminar vs turbulent flow, etc. We can test for these features of liquids without understanding what it really means to be a liquid or makes something a liquid. There is a real sense in which these feature are part of what it means to be a liquid and how liquidy something is.

But in our philosophical understanding of liquidity, the scientific facts of flow and pressure and viscosity seem unhelpful. The concept of liquidity includes these features, but our understanding of liquidity as a concept doesn't seem helped much by knowing (for example) the viscosity variation under different temperatures and pressures. Our normative concepts seem unaffected by any account of the evolutionary fitness of certain reactions to behaviors. Our philosophical questions seem to be about exactly those things that we can't collect data about. But that's jumping to the conclusion.

I am more and more convinced that if you have a philosophical question, and you can build a model to test it, then you didn't really have a philosophical question. If, on the other hand, you think that making a philosophical distinction can improve some scientific result, then of course you could make a model to test that by making different distinctions in the models. And what I really want to think more about it, can we have two theories about some phenomenon, build different models of that phenomena, and then the results of those models refines our concepts of how things work?]]> Philosophy xml-rss2.php?itemid=84 Thu, 17 May 2012 07:31:12 -0500 xml-rss2.php?itemid=83 level of organization. This is an epistemic notion because it relates to what we can capture in models, not to the structure of reality. Hierarchies of scale are a mixed ontological and epistemic notion: the levels are still based on what people can discern, but there is an added ontological assumption that a higher level exhaustively includes the elements of a lower level. Now I will show why levels of organization, not hierarchies, are the domains and ranges of scientifically useful reduction and emergence relationships. One way to think about this is to separate strict hierarchies from roughly hierarchal organization. If one goes strict than phenomena at any level can be broken down into phenomena at any lower level. We can loosen this requirement by only requiring that the part-whole relationships follow an ordering even if not every level has the same descriptive power with respect to every other level. That's an improvement because it allows for cases like the following: A is higher than B which is higher than C. A cannot be reduced to B, but both A and B can be reduced to C.

Although, consider that we may conclude that this relationship among A, B and C implies that A isn't really higher than B, though they are both higher than C. If we find some level D that is between A and B such that A can be reduced to D, and D to B, then doesn't that also imply that A can be reduced to B via D? Seems so. When people/scientists consider this issue, their notion of levels seems to be limited to constitution: what parts make up the whole in a physical sense. And as long as we are talking about physical objects in the world, the part-whole relationships keeps looking strictly hierarchal.

But now consider this: bodies are objects, cells are objects; and since bodies are higher up on the hierarchy, bodies are made up of cells. But bodies are not made of just cells. There is water and nutrients and other chemicals in a body that are not parts of (or even inside) cells. And these molecules are at a completely different scale than cells – in fact cells are made up of (reducible to) these very objects. So this is a case in which bodies and cells can both be reduced to molecules, but bodies cannot be reduced (in the ontological sense) to only things at the cellular level. This is so even though a body contains all the molecules that its cells are made of...the cells are a proper subset of the body. But we can pull this same trick again and point out that there are parts necessary for the body that are not part of any molecule, but are rather in the domain of submolecular physics. We can always do this, and there is always going to be something missing.

This leads us to the issues that there is no lowest level and that no science is complete, but these are not the current topic. I'm more interested in taking this toward part-whole relationships that are not constitution. Translating phenomena from one level to another is typically a lossy compression, some of the details are left out. This is true whether one is translating macro to micro or micro to macro. But here comes the real kicker, the phenomena we are translating are not always objects.

A flock (e.g. of birds) is an object at the macrolevel, and flocks are made up of birds (which makes it look like an ontological hierarchy), but the flock object is clearly not reducible to its constituent bird-object parts alone. The behaviors of the birds are a crucial feature of the flock object-phenomenon, but behaviors are not part of ontology. Thus when we are talking about emergence and reduction of phenomena we must go beyond just ontology and therefore beyond the notion of constitutional hierarchy. (Note: I wonder if this is all that is supposed to be meant by the slogan "More than the sum of its parts.")

When we develop a translation between phenomenon A and phenomenon B, it is sometimes the case that some of the objects of B are some of the parts of A. In this case a translation from A to B is called a reduction and a translation from B to A is called an emergence. I identify/define the levels of organization as the ranking of all ontologies that figure into a reduction or emergence relation. Thus the levels will not be strictly hierarchical. The levels will be refined and filled in as new models/theories demonstrate new reduction/emergence relationships. And although any particular translation is between two levels, there may actually be a continuum of levels.

(Afterthought: I want to be clear that some people may use the word 'hierarchy' to mean what I refer to as a level of organization. That is, they may not subscribe to the ontological requirement, or the demand that each layer can be losslessly described at each other, but refer to the levels as hierarchies. Fine. I don't care about which words people use. This isn't a semantic issue. The truth is that some very good scientists are not comfortable with these concepts, and have never even considered the differences. It is likely that many people's concepts of reduction and emergence include the ontological requirements of complete hierarchies, and they do not distinguish between applying them to the world or to models. Disabusing people of this sloppy usage is part of the point.)]]> Philosophy xml-rss2.php?itemid=83 Tue, 6 Mar 2012 07:34:25 -0500 xml-rss2.php?itemid=82
For the robust/vulnerable dichotomy we can take the human body as clear example of a complex system. It is extremely robust to certain insults, like the removal of a limb or a lung, which are large and disruptive, but can be dealt with. On the other hand, there are some specific regions in the brain and heart where the removal of just a cubic millimeter of tissue results in the immediate death of the individual. Given an average body mass of 70kg, that's just 1/70,000,000 of the total volume. That sounds like a fragile system to me. We can contrast that to a society of 70 million people that can survive the loss of any, and perhaps any quarter, of its population.

We can say that a system is robust with respect to some property (like being alive or perpetuating) when that system has that property over a large proportion of changes; i.e. the overall likelihood that the system will have that property is high. And we can say that a system is vulnerable to a particular change if the likelihood of loosing that property is high for such changes (and fragile if it vulnerable to at least one change). And from these definitions it is clear that a system can be both robust and fragile (with respect to some property). However, this does not mean that every system is equally robust and vulnerable…or robust and vulnerable through the same sorts of changes. Differences in robustness and vulnerability characteristics can be used to establish equivalence classes of system dynamics and thus allow us to categorize systems (or at least models of systems) by how they change over time.

Instead of offering exact criteria for systems to be complex, the style has shifted to listing some common features of complex systems, and features of systems that make them complex. Robustness is typically on these lists, but vulnerability is typically not. Part of the reason is political; practitioners of complexity science want to make it sound good. A better reason is that it's the complexity of the system that makes it robust, but systems are vulnerable where the complexity fades. For example, brains and hearts and eyes are very specific, optimized organs that are more like designed systems and less like self-organizing systems than other tissues, and that's why they suffer from single-point failures.

This is merely an unsatisfactory ad hoc rationalization to justify the connection between complexity and robustness; i.e. it's a political explanation. The truth is that at the current state of the art, robustness applies to some complex and some non complex systems, and fails to apply to others. Until some specific mechanistic connection between the complexity of systems (measured somehow) and their robustness and vulnerability characteristics is established in a general way, the claims are mere rhetoric. And furthermore, once this work is done, I'm sure we will find that robustness is neither a necessary nor sufficient feature for systems to be complex (or vice versa). It is a contingent property, and working out when systems are and are not robust will be interesting and difficult research.

Finally, the claims relating robustness to complexity often make unfair use of the lack of specificity of the two terms. My research on formalizing robustness has revealed that there are many distinct meanings that, though related, indicate very specific dynamics. A property can be maintained without being lost, regained if lost, obtained if not present, or present over a large proportion of possible futures (among others). Saying that a system is robust, without specifying the way in which it is robust, offers little to no insight into the relationship of that property and system dynamics.

Complexity is even more vague, and identifying what characteristics make systems complex is fraught with confusion. Something like: collections of at least an intermediate number of components that interact in such a way that self-organization and/or adaptation is possible in some situations. If that's the kind of thing that people mean by "complex system", then certainly it is folly to claim that such systems will be robust in general, or that robust systems will be complex in the sense of satisfying that loose definition. My guess is that people who consent (or acquiesce) to claims that complex systems are robust will retract their support when expressed in these more detailed (but equally vague) terms.

So it seems that under closer inspection complex systems are no more characterized by their robustness than their fragility, contrary to many unfounded claims made by practitioners of complex systems modeling, and expounders of complexity theory. This makes our whole field seem unscientific and foolish. For the field to mature we need specific, testable, and falsifiable claims about the relationships of system properties like interaction structure, scale, rates of change, behavior rule types, etc. and properties of system dynamics such as tipping points, robustness, path dependence, and adaptability. I've started on some of this work with my measures of some of these phenomena, but the scale of this project is science-wide. Building and using the appropriate formal tools is an important first step, but it is even more crucial to convince people of the importance of thinking and speaking clearly on these issues. ]]> Philosophy xml-rss2.php?itemid=82 Wed, 22 Feb 2012 07:14:09 -0500 xml-rss2.php?itemid=81 here]]> Commentary xml-rss2.php?itemid=81 Mon, 30 Jan 2012 20:37:16 -0500 xml-rss2.php?itemid=80 their website. ]]> Commentary xml-rss2.php?itemid=80 Wed, 18 Jan 2012 02:07:19 -0500 xml-rss2.php?itemid=79 equilibrium distribution. An example of an equilibrium distribution used commonly in Markov modeling is when the percentages of agents in each state remains constant although individual agents continue to transition from one state to another. This is not what I mean by process equilibrium, though it's a closer idea. An equilibrium distribution of this sort implies a cycling of the states, and the process by which this is achieved is static. This is certainly important, even for complexity analysis, but it doesn’t describe the process itself equilibrating.

A standing wave at first seems to be a similar concept to the equilibrium distribution. These are stereotypical emergent phenomena (and while this may not guarantee that it's a complex system, let go ahead and say that it is) in which the parts are continuously churning though the aggregate pattern is constant. Holding the water flow rate and rock locations constant, the wave phenomenon seems to be in equilibrium…so isn't that a complex system in equilibrium? No. It's the water particles that compose the complex system from which the wave emerges, and the water particles are not in equilibrium. Sloppy term usage can get one in trouble with these sorts of things, so let's be extra careful. When aggregate properties are constant through changes in the micro components that is not equilibrium; that's simply identifying a robust higher-level (aka emergent) phenomenon.

The concept of process equilibrium relates the concept of equilibrium analysis (and its partner concepts) to the processes themselves. Two different interpretations naturally come to mind: 1) the actual rules used by agents stop changing even though a mechanism exists through which they could change, or 2) the process (e.g. the set of agent actions) always stays the same although individual agents may change their actions (e.g. because they switch roles). The first interpretation is analogous to a stable state, but it's stability in the enacted process. The second is analogous to a stable distribution, but of actions instead of states.

These rule-related interpretations are perhaps novel, but they are not a far stretch and have probably already been explored to some degree. My thinking is that in some models the sets of behavior rules accessible to agents are constant and in some models the agents have the capability to change their behavior rules (through other rules, or indirectly by changing the context of future behaviors). If the behavior rules can’t change then the system is always in process equilibrium and that’s trivial and uninteresting. But if the agents can learn or adapt then the behavior rules can change; and if at some point the rules being used stop changing, then that’s interesting. If agents can learn but stop learning to do new things, or they can adapt but no longer do so, then that's a kind of system stability that we'd like to capture but aren't generally. The second type demonstrates a system-wide co-adaptation of behaviors…everything is still acting, perhaps even constantly changing their actual actions each time step, but the rule set becomes frozen through internal dynamics.

But we can capture behavior rules in many ways. In the Game of Life the agents can’t change their rules, but we can track which rules are actually used by each cell and mark when that set of actually used rules stop changing…or changes in cycles. Such tracking could distinguish configurations that create perpetual novelty from ones that repeat, and how long that cycle is. However, this is treating the used behavior rule as a property of each agent at each time-slice of the model…again falling into static thinking. That's not anything new.

So now we’re going to step it up one level. We’re going to take the set of deployable behavior rules as the unit of analysis here. This means that as long as the set of rules that agents can use continues to change then the system is not in process equilibrium. This concept of process equilibrium then becomes a way to analyze contingent behavior capabilities. It draws a line between doing something different only in different environments and being able to do something different with the same input at a later time. What I'd like to do is run the analogy one more step higher to separate learning and adaptation along another line. Perhaps define "learning" as being able to change the deployable behavior rules via a fixed set of update rules and define "adapting" as being able to change the updating rules. Then process equilibrium of the process equilibrium would also allow us to measure how adaptive a system is and identify systems that start out adaptive but sometimes converge into simpler learning dynamics…and when and why this happens.

There are some problems with this proposal, I think. One is that it isn't clear that adapting should be altering learning rules rather than being a different way to alter behavior rules directly. Perhaps the difference between learning and adapting is how the behavior rules change rather than which rules change. In my workshops I tell the story that a learning traffic light accepts the meaning of the red, yellow, and green and determines when and how long to shine each light. An adapting traffic light might add a different color or shine two at once or other such alterations to actual behaviors. No matter the difference between learning and adapting, they are both rule-driven activities separate from the behavior rules and thus the process equilibrium still does its first-tier work.]]> Methodology xml-rss2.php?itemid=79 Mon, 9 Jan 2012 07:13:17 -0500 xml-rss2.php?itemid=78 My approach to develop a meta-structure into which each type of belief may be translated. I imagine this meta-structure will be a matrix with entries corresponding to primary beliefs, confidence in those beliefs (secondary beliefs), and credence values (weights) for the aspects of the belief which can incorporate (at least) probabilities, fuzziness, and uncertainty. All updating/combining happens with these meta-structures, and what needs to be developed is the formally and conceptually proper method for operating on these matrices. The updated belief values can then be translated into any of the included belief measures…with the proper caveats for information loss and augmentation. For example, if one converts a Dempster-Shafer value into a probability, then it must also be augmented by an uncertainty level to maintain that information.

The point is to make a formalism that works in the sense of being able to translate and combine the disparate types in a way that is consistent and conceptually coherent. These two aspects feed off each other. There are many ways the math can be done, so the epistemology comes in to narrow the scope. And the epistemology does not designate a single formal approach, but the conversions and combinations have to be commutative, associative, etc. thus our understanding of these distinct belief concepts is improved through the mathematical effort.

Applications for such a capability are easy to come by: data fusion, situational awareness, information networks, and semantic webs to name the most obvious ones. I'm going to begin with just Boolean-style truth; i.e. whether (and how much) something is true, or is an X, or has property Y, etc. It may be directly extendable to categorical data in which a discreet distributions of truth values across categories is more appropriate. This includes multi-valued logics, multi-item identification, … more than a binary evaluation. Then on to continuous multi to complete the generalization.

If you, or somebody you know, is already working on such a thing, or have advice to give on dangerous territory, or you want to jump on board with this project, feel free to contact me.]]> Methodology xml-rss2.php?itemid=78 Thu, 5 Jan 2012 02:41:56 -0500 xml-rss2.php?itemid=77
d2(P,Q) = sqrt( (xP – xQ)^2 + (yP – yQ)^2 )

My non-dyadic distance function is just the sum of the distances from each point to the centroid. For the three-point example this comes to:

d3(A,B,C) = d2(A,M) + d2(B,M) + d2(C,M)

Naturally we can extend this to any number of points, and in any number of dimensions. This measure is always greater or equal to 0 because it is the sum of three measures that each is greater than or equal to 0, thus satisfying condition (1). The order of the three terms clearly doesn't affect the result, so it is symmetric as well.

The triangle inequality is that the sum of the distances between P and Q through the point R is greater than or equal to the distance directly from P and Q; i.e. the direct path is the shortest path; i.e. there are no shorter paths. This feature is also preserved by my measure because the centroid is identified such that it is indeed the minimum distance point from all the other points. One can work out the proofs for all these features quite simply…that just leads up to the interesting part.

Given those features, this generalized distance function over sets of more than two points is a metric. And if it's a metric then it defines a topological space, and if that's correct, is the topological space different from the one that the standard distance function generates? If so, what do open and closed mean on that space? How can we define Cauchy sequences that converge? There are lots of mathematical things to explore. Probably somebody has done all this already, but I couldn't find it because it's probably called something different.

A distance measure like this can work as a spatial measure of clustering within communities, and even help identify community structure in spatial agent-based models...this is called "k-means clustering". It can also be used to analyze and compare multidimensional data across data sets in a simple nonparametric way. For this statistical application, it's actually similar to variance of least-squared error measures, and is certainly in the class of dispersion measures. For me, the next step would be to prove the mathematical properties...whether it's a metric and, if so, what are the properties of the space it defines? Has anybody seen this done already? ]]> Methodology xml-rss2.php?itemid=77 Thu, 15 Dec 2011 23:37:07 -0500 xml-rss2.php?itemid=76
The "problem" with adapting measures of network structure to layered networks is that there are multiple ways in which (for example) betweenness can be adapted to take account for the edge variety, and each one now measures something different and they might all be useful in some context. And we must consider the possibility that adapting methods for layered networks will inspire us to invent novel measures…structural properties that have never before been calculated.

Let's first consider the base case in which all our nodes are of the same type (e.g. people, so we're not yet going into k-partite territory with multiple edge types). Well, we already have some of these measures worked out for bipartite graphs, so if there were two types of edge we can take the dual of the graph (convert the nodes to edges, and edges to nodes) to convert our multilayered network into a network with multiple node types instead of edge types. That won't be a bipartite graph (usually) since we wouldn't expect the layered connections in a network to obey the connection restrictions of bipartitism, but some of the insights from bipartite measures may prove helpful. This dual conversion works for any number of layers (and types of nodes too), but there are lots of details to work out in such a transformation (e.g. dealing with self-edges, structure preservation, interpretation of measures taken on the converted graph for the original network), and that is the subject of a different post.

For now, I plan to build a Netlogo code example that includes a layered network. Probably I'll use something like the communication example because one type (vision) is directional and the other (hearing) is symmetric. And some other example in which different resources flow along different connections. Recommendations for research models with layered networks (existing ones to code up or an idea for a cool one to research) are welcome.]]> Methodology xml-rss2.php?itemid=76 Wed, 14 Dec 2011 19:54:43 -0500 xml-rss2.php?itemid=75 The dominant discrete geometry for 2D simulation environments is the square grid; mostly because it's the default and conceptually and methodologically simple. There are, however, some advantages to using a hexagonal grid in 2D: hexes also tessellate (tile) in two dimensions and the centers of all six neighboring hexes are equidistant (see Hex in Netlogo). In three dimensions, however, only the cube tessellates and hence the corner effects are inescapable…until now! By considering discrete geometries as networks of connections, it is possible to build a 3D hexagonal-like (actually dodecahedral) geometry in which all neighbors are equidistant. The problem with square grids in 2D is that the corner spaces (in a Moore neighborhood) are sqrt 2 (1.41421356) further away than the horizontal and vertical spaces. In the hex grid all the immediate neighboring cells are the same distance apart. However, the more general problem doesn't completely go away, it just gets pushed back one step. The reason that it's only delayed is that the hex grid preserves neighbor distances only up to distance one. The diagram shows that neighbors two steps away can be either distance 2 or sqrt 3 (1.73205081) depending on the path. This is exactly the right thing if interaction can only happen with immediate neighbors (as is often the case, for example in cellular automata), and it's still an improvement overall. Now we can extend this benefit to 3D worlds.

The 3D version of the hex-like geometry creates a 2D hexagonal grid along three axes, but those axes are not orthogonal. Each space has 12 neighboring spaces (see figure). The generated tiling uses irregular polygons, but they are equal volume and repeat with periods 1, 2, and 3 depending on the axis (for example, along one direction they just repeat, in another direction they repeat every other space, and in the third axis direction they repeat every three spaces). Thus, to get a wrapping space to tile properly one has to build it out of 1x2x3 sized blocks in the appropriate way...which is quite easily done, but restricts the viable world dimensions.

You get a closer look at the top example image I generated of a 6x6x6 wrapping 3D hex world here. My next step is to create all the necessary helper functions so that agents can move around such a world and refer to neighbors in an intuitive (for the programmer) way. If you have any particular application for which you think this helpful, let me know and I can create a demo of the technique for that purpose as part of the 3DHex code example. Advice for a better name for the dodecahedral geometry than "dodecahedral" or "3D Hex-like" is welcome too.]]> Methodology xml-rss2.php?itemid=75 Sun, 11 Dec 2011 13:22:47 -0500