Today we clarified some of the issues around the difference between extensive and intensive properties. Extensive and intensive are different ways of conceiving of property. Fro Delanda it is differences in intesive properites that drive change and therefore organization and therefor form. In Wolfram change is manifest in . . . ?Here it is not so clear that we can say something remotely similar. And yet the type of change, that is, symmetry breaking, is just as phenomenal. The difference between the two authors just I'd this: Delanda is referring to thermodynamic process and in biology toplogical and chemical properties but in Wolfram change is an expression of the iteration of the rules. That seems confounding.
For next week we are going to act out the differences between the two systems; this time in terms of emergence and complexity as well as symmetry-breaking. I'l put on the server Philip Ball for those working on the side of physics and dynamical systems. For those working on the computational side use Casti.
Please send me a paragraph of what interests you in terms of the course, one of the readings, or a contemporary problem, and I'll reply with a topic and brief strategy for your final paper that will be based on a question.
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Tuesday, November 25, 2008
COMPLEXITY
Greg Lynn states, “The difference between the reductive tendencies of Cartesianism and the unfolding logic of Leibniz is that reductivism is expedient and crude compared with the creative, vital elegance of combinatorial multiplicity.” I love it.
Anyway, DeLanda, Casti, Wolfram and Lynn explore the issue of complexity. These authors seem to be on the same boat but on different sides of it. While it seems to me that there are similarities in the ways that they perceive and strive for complexity, there are also differences. It seems that emergence is of priority for each. One underlying difference though is in the way that emergence….emerges. LOL.
For DL it seems to always be about generational reproduction with the author creating complex and clever inputs and sorting and eliminating outputs, a glorified breeder. It seems that for Wolfram and Casti, the complexity achieved by CA and other such phenomena relies only on simple rules and simple outputs. The complexity and reproduction of the system relies on internal logic not external forces. None of the above mentioned authors seem to be as form hungry as Lynn. He discusses a model of complexity that relates directly to Leibniz. Complexity seems to be achieved through interaction and interconnectedness, “combinatorial multiplicities” and the intensities of “singularities”.
Anyway, DeLanda, Casti, Wolfram and Lynn explore the issue of complexity. These authors seem to be on the same boat but on different sides of it. While it seems to me that there are similarities in the ways that they perceive and strive for complexity, there are also differences. It seems that emergence is of priority for each. One underlying difference though is in the way that emergence….emerges. LOL.
For DL it seems to always be about generational reproduction with the author creating complex and clever inputs and sorting and eliminating outputs, a glorified breeder. It seems that for Wolfram and Casti, the complexity achieved by CA and other such phenomena relies only on simple rules and simple outputs. The complexity and reproduction of the system relies on internal logic not external forces. None of the above mentioned authors seem to be as form hungry as Lynn. He discusses a model of complexity that relates directly to Leibniz. Complexity seems to be achieved through interaction and interconnectedness, “combinatorial multiplicities” and the intensities of “singularities”.
INTENSITY
It seems that the whole name the game here, is Intensive properties. Extensive properties are basically that which are rationally divisible. Length, width, mass, these are divisible properties and are extensive. Temperature is not divisible and is not extensive. Neither is pressure, speed, or force. These properties are only modified by actions not by Boolean operations. This seems to go back to metric and non-metric properties.
Anyway. Intensive properties are what we seem to be after here the mapping and relating to critically understood phenomena or event. Matter then, is in a constant state of becoming and the “building” or “blob” or physical manifestation of a manifold diagram, becomes a result of its own multidimensional topological diagram. So then Intensities, of phenomena, of patterning, of matter are what drives forms. Intensive pressures seem to form matter and extensive properties are then used to measure and quantify this matter.
Anyway. Intensive properties are what we seem to be after here the mapping and relating to critically understood phenomena or event. Matter then, is in a constant state of becoming and the “building” or “blob” or physical manifestation of a manifold diagram, becomes a result of its own multidimensional topological diagram. So then Intensities, of phenomena, of patterning, of matter are what drives forms. Intensive pressures seem to form matter and extensive properties are then used to measure and quantify this matter.
Delanda's Intensity
When I heard Delanda speaking about intensity he also mentioned critical mass. When the temperature of water reaches a certain point it changes state. There is something more critical occurring at 32 than at 42 deg F. If extensive relationships are measurable, quantifiable, then there can be moments in that quantification where the quality is measurable, thus the moment of intensity. Is that a legitimate reading? Intensities occur through extensive relationships at key moments? Intensity is then the dependent variable while extensities are independent?
Delanda v. Wolfram
Delanda and Wolfram are almost temporally opposed when it comes to the notion of intensity. Delanda cites the medieval philosophical concept of intensive vs. extensive thinking to explain the difference between that which can be subdivided and that which cannot (intensive being the latter). He further points out that since differences in intensity can have the ability of canceling each other out, they can drive change in a system and ultimately become a productive force.
Wolfram never really uses the word intensity (or intense, or intensive), but the notion underlies his description of his cellular automata. His tipping point is sneakier to find, but there is a moment when particular rules create something completely unexpected and unpredictable. It could be said that the point at which the rule becomes unquantifiable is a moment of intensity.
Delanda sees intensity as a defined property. Wolfram sees it as a happy accident.
Wolfram never really uses the word intensity (or intense, or intensive), but the notion underlies his description of his cellular automata. His tipping point is sneakier to find, but there is a moment when particular rules create something completely unexpected and unpredictable. It could be said that the point at which the rule becomes unquantifiable is a moment of intensity.
Delanda sees intensity as a defined property. Wolfram sees it as a happy accident.
Sunday, November 23, 2008
Differentiation
In reading the DeLanda essays on Deleuze, both the case for modeling software and the essay for Deleuze and genetic algorithm, DeLanda seems to reintroduce the idea of a dynamical system consistent with basic notions of thermodynamics, mathematical physics, change, etc. But when he gets to the very idea of genetic algorithm what does he actually say about algorithm? What for him is aglorithmic and where is it operative in his discussion? Now, compare this, also with Wolfram's essay in which he discusses complexity in terms of algorithm or primitive computational rules.
Here's a question i'd like you to answer by Tuesday: both authors discuss complexity and transformation and change -- in a sense, they both point to the notion of intensity as a point in which one system flips over into a different organization -- but what is the difference between the way in which they present this?
Think of how this relates to the quesiton of the dsicrete and the continuous.
Here's a question i'd like you to answer by Tuesday: both authors discuss complexity and transformation and change -- in a sense, they both point to the notion of intensity as a point in which one system flips over into a different organization -- but what is the difference between the way in which they present this?
Think of how this relates to the quesiton of the dsicrete and the continuous.
Discrete and Continuous
Discrete is a form of mathematics and a ring setting on my phone. Synonyms that come to mind: subtle, passive, separated, finite, limited.
Continuous can be seen as the opposite. Synonyms include topology, morphing, articulated, connected. It seems that "continuous" is not as mathematical as discrete and in our topology/euclidean geometry binary, it doesn't quite work out as a ying and a yang. Discrete and continuous sound more like a ying and a yong, if that means anything.
Somehow, discrete seems more accurate in our dialogue while continuous being too general.
I am looking into the words perhaps a little too much, but looking nonetheless..
Continuous can be seen as the opposite. Synonyms include topology, morphing, articulated, connected. It seems that "continuous" is not as mathematical as discrete and in our topology/euclidean geometry binary, it doesn't quite work out as a ying and a yang. Discrete and continuous sound more like a ying and a yong, if that means anything.
Somehow, discrete seems more accurate in our dialogue while continuous being too general.
I am looking into the words perhaps a little too much, but looking nonetheless..
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