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..
Saturday, November 22, 2008
/ / / (discrete) & ----- (continuous)
Wikipedia, mathematically speaking, has some things to say:
/ / /
Discrete mathematics, also called finite mathematics, is the study of mathematical structures that are fundamentally discrete, in the sense of not supporting or requiring the notion of continuity. Most, if not all, of the objects studied in finite mathematics are countable sets, such as integers, finite graphs, and formal languages. Discrete mathematics has become popular in recent decades because of its applications to computer science. Concepts and notations from discrete mathematics are useful to study or describe objects or problems in computer algorithms and programming languages.
-----
In mathematics, a continuous function is a function for which, intuitively, small changes in the input result in small changes in the output. Otherwise, a function is said to be discontinuous. A continuous function with a continuous inverse function is called bicontinuous. An intuitive though imprecise (and inexact) idea of continuity is given by the common statement that a continuous function is a function whose graph can be drawn without lifting the chalk from the blackboard.
Wednesday, November 19, 2008
Thom
NotesReneThom
Some main points about Thom
First, keep in mind that it is a theory of models – and this is always an interesting problem, which is how it takes up a model of meaning.
The general background to this is really biology: “a system of forms in evolution constitutes a formalizable process if . . . “
At the same time, we are talking about the sciences in general, hence the quote of D’ARchy Thompson. But note how that quote institutes one of the main problems of mathematics in the modern era, which is the study of patterns, as opposed to what we previously considered mathematical, that is the treatment of numbers.
Thompson makes this distinction between form and pattern explicity.
Then, note the title of the subchapters: Succession of form; Science, and the indeterminism of pheonena, Qualitative or quantitative, etc.
In otherwords Thom is pointing to a main problem which in a sense constitutes all scientific inquiry – foresee the change of form and “if possible,” explain it.
Its important to see how Thom introduces the notion of a model to formalize the space of change. And it is also important to understand that the model has two elements: topology and calculus. It is interesting in this to see him refer to Descartes and Newton in this context, specifically since it introduces the problem of the quantitative (Descartes and Newton) but in different ways. “Descartes, with his vortices, hi hooked atoms and the like explained everything and calculated nothing; Newton, wit hthe inverse square law of gravitation, acluated eeryting and explained nothing.”
The point his is really about how to quantify quality, how do you explain transformations in quality. “With the exception of the grandiose, profound, but rather vague ideas of Anaximander and Heraclitus, the fir pre-Coscrativ philosophers, all these thoereis rely on the experience of solid bodies in three-dimensional Euclidean space.” And, according to Thom, this is insufficient to explain the intensity of phenomena.
The then goes on to justify this problem of the formal model exactly by evacuating from it the Euclidean notion of space and of objects in space (recall our initial discussions of the ontological “limits” of Euclidean geometry). Hence the introduction of another, unlimited, formalizable space, which is topological – a manifold. “We therefore endeavor to free out intuition from three-dimensional experience and to use much more general, richer, dyamical contps, which will in fact be independe of the configuration spaces.” Keep in mind how architecture problematically exploits the topological model Thom introduces by the very fact that it returns it directly to Euclidean space.
Note that the catastrophe models that he elaborates are only local models, and there is no universal model. That’s one of the important distinctions from previous models. The second is that the model accounts for change, namely catastrophic change. This is what differential analysis (calculus) could not explain. Calculus treats of dynamical systems (which are continuous) and the rate of change as long as that change is continuous. But it cannot account for a discontinuous system.
Morphogenesis just is the discontinuity of a system.
It is that which leads to change, growth, and alteration.
Note how this notion, still based in mathematical physics, though now of a qualititative rather than quantitative stance, will constrast heavily with the algorithmic notions we are about to encounter.
Some main points about Thom
First, keep in mind that it is a theory of models – and this is always an interesting problem, which is how it takes up a model of meaning.
The general background to this is really biology: “a system of forms in evolution constitutes a formalizable process if . . . “
At the same time, we are talking about the sciences in general, hence the quote of D’ARchy Thompson. But note how that quote institutes one of the main problems of mathematics in the modern era, which is the study of patterns, as opposed to what we previously considered mathematical, that is the treatment of numbers.
Thompson makes this distinction between form and pattern explicity.
Then, note the title of the subchapters: Succession of form; Science, and the indeterminism of pheonena, Qualitative or quantitative, etc.
In otherwords Thom is pointing to a main problem which in a sense constitutes all scientific inquiry – foresee the change of form and “if possible,” explain it.
Its important to see how Thom introduces the notion of a model to formalize the space of change. And it is also important to understand that the model has two elements: topology and calculus. It is interesting in this to see him refer to Descartes and Newton in this context, specifically since it introduces the problem of the quantitative (Descartes and Newton) but in different ways. “Descartes, with his vortices, hi hooked atoms and the like explained everything and calculated nothing; Newton, wit hthe inverse square law of gravitation, acluated eeryting and explained nothing.”
The point his is really about how to quantify quality, how do you explain transformations in quality. “With the exception of the grandiose, profound, but rather vague ideas of Anaximander and Heraclitus, the fir pre-Coscrativ philosophers, all these thoereis rely on the experience of solid bodies in three-dimensional Euclidean space.” And, according to Thom, this is insufficient to explain the intensity of phenomena.
The then goes on to justify this problem of the formal model exactly by evacuating from it the Euclidean notion of space and of objects in space (recall our initial discussions of the ontological “limits” of Euclidean geometry). Hence the introduction of another, unlimited, formalizable space, which is topological – a manifold. “We therefore endeavor to free out intuition from three-dimensional experience and to use much more general, richer, dyamical contps, which will in fact be independe of the configuration spaces.” Keep in mind how architecture problematically exploits the topological model Thom introduces by the very fact that it returns it directly to Euclidean space.
Note that the catastrophe models that he elaborates are only local models, and there is no universal model. That’s one of the important distinctions from previous models. The second is that the model accounts for change, namely catastrophic change. This is what differential analysis (calculus) could not explain. Calculus treats of dynamical systems (which are continuous) and the rate of change as long as that change is continuous. But it cannot account for a discontinuous system.
Morphogenesis just is the discontinuity of a system.
It is that which leads to change, growth, and alteration.
Note how this notion, still based in mathematical physics, though now of a qualititative rather than quantitative stance, will constrast heavily with the algorithmic notions we are about to encounter.
Re: Seminar
maybe we should all just meet at our birthday party saturday night. you all thought deleuze wrote like he was drinking anyway, right . . .
On Wed, Nov 19, 2008 at 10:59 AM, Peter Macapia <peter.dora@tmo.blackberry.net> wrote:
Hi everyone, thanks for getting back to me. Renee has asked if we could meet any time after 5 on Sunday, that's fine with me, but not sure about the others, if that doesn't work, let's consider Saturday. Anyhow, yes, there is a 15 page paper due for the class. I mentioned it previously, but we've been focused primarily on the issues. The topic is architecture and toplogy. There is a lot of material to choose from. Let me know your ideas. As for the next set of readings I've adjusted them, but they are now on the server. Here's what we have for Sun (or Sat): a wrap up discussion of the digital toplogy material and intensity. I'd like you to read the Delanda essay for this Deleuze and genetic algorithm, Delanda essay for Modeling Software, and Wolfram essay how do simple programs behave. In addition I'd each of you to look up the terms "discrete" and "continuous" and write a very short blog entry on that. The readings for Tuesday are alos on the server and they are Chu and the Rocker essays.
Ok, thanks
P
Design Office for Research and Architecture
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Seminar
Hi everyone, thanks for getting back to me. Renee has asked if we could meet any time after 5 on Sunday, that's fine with me, but not sure about the others, if that doesn't work, let's consider Saturday. Anyhow, yes, there is a 15 page paper due for the class. I mentioned it previously, but we've been focused primarily on the issues. The topic is architecture and toplogy. There is a lot of material to choose from. Let me know your ideas. As for the next set of readings I've adjusted them, but they are now on the server. Here's what we have for Sun (or Sat): a wrap up discussion of the digital toplogy material and intensity. I'd like you to read the Delanda essay for this Deleuze and genetic algorithm, Delanda essay for Modeling Software, and Wolfram essay how do simple programs behave. In addition I'd each of you to look up the terms "discrete" and "continuous" and write a very short blog entry on that. The readings for Tuesday are alos on the server and they are Chu and the Rocker essays.
Ok, thanks
P
Design Office for Research and Architecture
68 Jay Street
Brooklyn, NY 11201
USA
646-575-2287
petermacapia@labdora.com
http://labdora.com/
http://atlas.labdora.com/
Ok, thanks
P
Design Office for Research and Architecture
68 Jay Street
Brooklyn, NY 11201
USA
646-575-2287
petermacapia@labdora.com
http://labdora.com/
http://atlas.labdora.com/
Tuesday, November 18, 2008
'n_10_city
Ok, I'm cheating because I read Peter's round-up post of everyone else's posts. I am also cheating because last class we made a lists of words and I shall now steal some lists of words from other people in the pursuit of defining intensity.
Besides the fact that he spells realization funny, CB is specifically chronicling the Arnhem Transfer Hall which he is consulting on with BvB (which is in fact the frontispiece of the BvB article). I would peg this quote directly as a Balmond definition of intensity when he looks ahead to “New Territories”:
“When [the] connectivity is seamless... zones of confluence, aggregations, overlaps and bandwidths, become a new language for structure.”
Within the topic of “Texture, Fields, and Techniques,” BvB speaks of various infrastructures (not purely structural) by saying:
“Infrastructural layers may be classified, calculated, and tested individually, then interwoven to achieve both effective flux and effective interaction.”
The GL article “Geometry in Time” defines his attitude clearly when he discusses all that 3d modeling and animation tools bring to architecture:
“The linkages between these characteristics of time, topology, and parameters combine to establish the virtual possibilities for designing in animate rather than static space.”
We discussed PE in a lot of detail already, but for Rebstock his definition of intensity would be derived from his definition of the fold:
“By introducing the concept of the fold as a nondialectical third condition, one which is between figure and ground yet reconstitutes the nature of both, it is possible to refocus or reframe what already exists in any site.”
And finally for RT, who is simply interested in advancing a mathematical theory, implies elements of intensity by the way in which he derives the construction of his model:
“From a macroscopic examination of the morphogenesis of a process and a local and global study of its singularities, we can try to reconstruct the dynamic that generates it.”
All in all a similar theme is the need to define a new (pick one): language, interaction, possibility, concept, or dynamic. Intensity could be viewed or defined within the framework of any of the preceding terms as a result of the “new.”
Intensity
I think its interesting given Daniel's take on Balmond, that intensity would have to be legible in the form of a curve. Daniel, is that what Balmond is after? Are there words, maybe other words that point to intensity? And its interesting that intensity, as per Eric's comment, is this interstitial condition, but I'm not sure what that means. I'm not sure what meaning he us giving the word intensity. Perhaps Adam's points can calrify some issues since at least as far as I can't tell, he is deriving it from a specific essay and developing a theory of intensity according to Lynn's argument. At the very least, its clear that there is something about the intensity of architecture's existence or manifestation and Lynn sees himself an advocate of that.
That strange thing is that like in Balmond, that intensity is somehow graphically shaped, by the figure of the curve, or the geometrical pattern.
Then there are other possibilities, the tension between states of an undecideability. So its a kind of stress. Something poised between one moment and the next - which we talked about previously.
In van Berkel its a kind of generic, but at the very least involves evolution, od something constantly becoming.
Well, is there a correct way to use this term? I'm not sure. But that's not the point. One thing for sure is that each of these authors are placing on the table an agenda that takes into account various forms or kinds of intensities that can be experienced in actuality or conceptually - and that's just it, it can be experienced. Change, process, tramsformation, etc., each of these are rich in experience because they imply that something is in the process of happening.
This is not a typical notion in the history of architecture anymore than it was typical to make an ellipse and start generating dynamic movement in arcitecture in plan during the High Renaissance.
Our interest here is that each of the authors wants to claim this from an area within those things that constitute architecture's interiority. That last is Esienman's term. It has associations with Deconstruction and Derrida and refers to, among other things, a principal of its own speicif logics of organization that are constantly under erasure, being negoatiated, and seem always essential.
Anyhow, the readings are highly calculated in this way, because, as we'll see, the last set of readings point to a certain limit of the models of meaning that the authors are about to experience in the face of computation and algorithm. For, and this is the point, to argue for a dynamic model, continuous or discontinuous, is to argue essentially for an empirical model, it is to argue for mathematical phyics.
Clearly this isn't wrong.
But it is now out of date.
For years we have been entering a mew model, which is algorithmic and leads us to different possibilities. In order to understand this, clearly it is essentil to identify just what is the nature of the models of meaning in previous digital architecure.
Balmond is pointing one way out of this.
As one author said, we have left the great age of mathematical physics and entered the new one of alorithm
P
Design Office for Research and Architecture
68 Jay Street
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646-575-2287
petermacapia@labdora.com
http://labdora.com/
http://atlas.labdora.com/
"again, with more intensity"
I took a look again at the Balmond essay (since it was the only one that really resonated at all with me) and tried to prize out his notions of intensity. Most of the essay dealt with structural concerns, especially as it related to different patterns/requirements of circulation. I can see these clashing grids as a form of intensity, something that needs to be intelligently negotiated. Balmond also seemed concerned with retaining curvature, another concept that can be linked to intensity of form (especially if you think about all the math that goes into a complex curve...woo! intense!). But mostly it comes down to pattern, and intensity of connection. His final example of the braiding and interconnectedness of 'strands' began a whole other discussion of intensity.
A short essay on intensity
Last night, Peter Eisenmann told a crowd of young aspiring architects, “If you don’t know Maya and Rhino, I won’t hire you.” It was a bold statement from an aging architect summing up his lecture on how architecture has transitioned from Corbusier to Gehry. Eisenmann only traced “Ten Canonical” buildings and yet any student (or instructor) of architecture today can’t help but feel powerless in the wake these buildings of “undecidedness” that plague the critique process, buildings that in themselves provide inadequate justification to their fruition, taxonomy, or even quality. It is here, I contest, where theory nudges the lagging momentum. Perhaps it is in texts that architects will move forward in the days ahead of economic and design uncertainty.
Why invoke the Deleuzian Fold? The blob buildings are not catching on—at least not as planned. The word blob in architecture comports an insulting flavor. Lynn foresaw this and used blob in the title thus highlighting his own weakness (McCain’s choice of young Palin, anyone?) in an attempt to sooth the blob pejorative. And yet we are still faced with the critique’s criticism: how do I qualify this design?
We are truly dealing with blobs of simulated matter that have no place in a Cartesian geometry class. No matter what architecture you experience or admire, you cannot deny that we are in a place that does not design the way our instructors were taught. We don’t listen to the same music or wear their same clothes either. In the words of Eisenmann, nobody writes music for a harpsichord anymore. To write the music that people listen to, we need to play the instruments that they are listening to.
That is why.
You can’t be a Walter Gropius for very long. It’s almost a rule that the sequel can’t be 1.5X better than any original and usually is lucky to achieve .5X. Gropius got a dozen years teaching studios until someone else came along to “bigger and better” his work. Gehry is an obvious response to many things in architecture, his feature will not last long either.
And hey, just like these authors, I managed to write without using the word intensity as well. I don’t quite see how intensity has parallels in these readings. How is intensity via layer seen in Berkel? Where does Lynn point to intensity through force? And what does passé-partout mean? Intensity is a value in need of measurement. If any system were to make room for intensity as an idea, it seems like it would sit more appropriately on the geometry side of points, numbers, and real measurements. Topology has few qualitative attributes, at least compared to Cartesian geometry. [Unless you mean intensity as a default to measurement such as, “that cocaine was intense! I don’t what happened!” where intensity sort of bypasses qualitative analysis. But I don’t think this method works.] Am I wrong?
Why invoke the Deleuzian Fold? The blob buildings are not catching on—at least not as planned. The word blob in architecture comports an insulting flavor. Lynn foresaw this and used blob in the title thus highlighting his own weakness (McCain’s choice of young Palin, anyone?) in an attempt to sooth the blob pejorative. And yet we are still faced with the critique’s criticism: how do I qualify this design?
We are truly dealing with blobs of simulated matter that have no place in a Cartesian geometry class. No matter what architecture you experience or admire, you cannot deny that we are in a place that does not design the way our instructors were taught. We don’t listen to the same music or wear their same clothes either. In the words of Eisenmann, nobody writes music for a harpsichord anymore. To write the music that people listen to, we need to play the instruments that they are listening to.
That is why.
You can’t be a Walter Gropius for very long. It’s almost a rule that the sequel can’t be 1.5X better than any original and usually is lucky to achieve .5X. Gropius got a dozen years teaching studios until someone else came along to “bigger and better” his work. Gehry is an obvious response to many things in architecture, his feature will not last long either.
And hey, just like these authors, I managed to write without using the word intensity as well. I don’t quite see how intensity has parallels in these readings. How is intensity via layer seen in Berkel? Where does Lynn point to intensity through force? And what does passé-partout mean? Intensity is a value in need of measurement. If any system were to make room for intensity as an idea, it seems like it would sit more appropriately on the geometry side of points, numbers, and real measurements. Topology has few qualitative attributes, at least compared to Cartesian geometry. [Unless you mean intensity as a default to measurement such as, “that cocaine was intense! I don’t what happened!” where intensity sort of bypasses qualitative analysis. But I don’t think this method works.] Am I wrong?
Monday, November 17, 2008
why is topology groovy...
... and tectonics square. Greg Lynn in his article on blob tectonics starts answering this question by describing what a blob is, "Or should I say blobs, of all different sizes and shapes and irreducible typological essences." Here he hints on the relation of one to many, or singularity to intensity, on which he than elaborates while defining blobs. "The term BOLOB connotes a thing which is neither singular nor multiple but an intelligence that behaves as if it were singular and networked but in its form can become virtually infinitely multiplied and distributed." He invokes the emergent organizational system that both Deluze and Steven Johnson talk about in their work, the kind of singular organism that is not composed of one node but rather it is made up of intensities of many networked nodes.
Later in the article, the terms are paired up in similar fashion to how Ben van Berkel presents the opposition of modernist generic space vs. way cooler intensities of "spatial arrangements that follow the diving, swooping, zooming, slicing, folding motions" When Lynn brings up Liebniz's work the terms morph from wholes vs. intensities, to clear vs. vague, then into Cartesian "constitutive identity" vs. "changes in identities". Those, in turn, are quickly elaborated into "a series of continuous multiplicities and singularities" to finally become "an assemblage that behaves as singularity while remaining irreducible to any single simple organization." Lynn's describing his blobs as aggregate objects, or intensity objects that are "simultaneously singular in it's continuity and multiplicitous in its internal differentiation", so simply put groovy...
Later in the article, the terms are paired up in similar fashion to how Ben van Berkel presents the opposition of modernist generic space vs. way cooler intensities of "spatial arrangements that follow the diving, swooping, zooming, slicing, folding motions" When Lynn brings up Liebniz's work the terms morph from wholes vs. intensities, to clear vs. vague, then into Cartesian "constitutive identity" vs. "changes in identities". Those, in turn, are quickly elaborated into "a series of continuous multiplicities and singularities" to finally become "an assemblage that behaves as singularity while remaining irreducible to any single simple organization." Lynn's describing his blobs as aggregate objects, or intensity objects that are "simultaneously singular in it's continuity and multiplicitous in its internal differentiation", so simply put groovy...
Sunday, November 16, 2008
THOM :: intensity as morphogenetic states.
As topologically categorized by type of potential, as in those moments of transition between dynamic and static equilibriums, minima and maxima, continuous and discontinuous.
EISENMAN :: intensity of the passé-partout.
As the charged reframing, the in-between.
BALMOND :: intensity as organization.
Of flow. Through pattern and connectivity.
LYNN :: intensity through force.
Of movement, understood locally within contextual, global condition.
VAN BERKEL :: intensity via layering.
By mapping primary elements of construction, circulation and program.
As topologically categorized by type of potential, as in those moments of transition between dynamic and static equilibriums, minima and maxima, continuous and discontinuous.
EISENMAN :: intensity of the passé-partout.
As the charged reframing, the in-between.
BALMOND :: intensity as organization.
Of flow. Through pattern and connectivity.
LYNN :: intensity through force.
Of movement, understood locally within contextual, global condition.
VAN BERKEL :: intensity via layering.
By mapping primary elements of construction, circulation and program.
Tuesday, November 11, 2008
Intensity
We finished up today looking at a word that doesn't exactly have explicit existence in the texts we examined, and that was intensity.
Up until that point we were examining the work of Eisenman, van Berkel, Lynn, and Balmond and charting the consistency of terms like fluidity, movement, vector, dynamic, event, etc. All of these imply situations of change whether continuous or catastrophic.
There were some good problems; form os one of the categories of architecture's ontology, how does Lynn's essay make that specific? Event is an ethico-political and historic potentiality in Eisenman, but in what sense does the reframing of architecture lead to a critical attitude if that attitude is apropos of nothing in particular? The programmatic reconfiguration of space as always multiple in van Berkel leads to a transformation of the generic, but in what sense does that multiplicity change our understanding of the urban experience which in many ways already is multiple? Balmond for sure is maybe the most precise, situating all of this in a radical transformation of structure.
But then note how this precision also answers the problem for Lynn.
All of these essays are poised to attack Modernism and the legacy of Cartesianism and Euclidean geometry, all the while invoking the Fold from Deleuze and Catastrophe theory for Thom.
The question is why.
I'd like each of you to wanswer that by introducing a very very short essay on intensity using as precisely the words of these authors
Design Office for Research and Architecture
68 Jay Street
Brooklyn, NY 11201
USA
646-575-2287
petermacapia@labdora.com
http://labdora.com/
http://atlas.labdora.com/
Up until that point we were examining the work of Eisenman, van Berkel, Lynn, and Balmond and charting the consistency of terms like fluidity, movement, vector, dynamic, event, etc. All of these imply situations of change whether continuous or catastrophic.
There were some good problems; form os one of the categories of architecture's ontology, how does Lynn's essay make that specific? Event is an ethico-political and historic potentiality in Eisenman, but in what sense does the reframing of architecture lead to a critical attitude if that attitude is apropos of nothing in particular? The programmatic reconfiguration of space as always multiple in van Berkel leads to a transformation of the generic, but in what sense does that multiplicity change our understanding of the urban experience which in many ways already is multiple? Balmond for sure is maybe the most precise, situating all of this in a radical transformation of structure.
But then note how this precision also answers the problem for Lynn.
All of these essays are poised to attack Modernism and the legacy of Cartesianism and Euclidean geometry, all the while invoking the Fold from Deleuze and Catastrophe theory for Thom.
The question is why.
I'd like each of you to wanswer that by introducing a very very short essay on intensity using as precisely the words of these authors
Design Office for Research and Architecture
68 Jay Street
Brooklyn, NY 11201
USA
646-575-2287
petermacapia@labdora.com
http://labdora.com/
http://atlas.labdora.com/
Saturday, November 8, 2008
MORPHOGENESIS…
Rene Thom’s reading has become much more accessible because of the previous readings we have done. Most specifically, by deciphering Deleuze and his use of Thom’s ideas, we are able to better appreciate the subtle spatial implications of “morphogenesis”, forms of “becoming” and qualitative and quantitative properties relationship to metric and non-metric properties.
In attempting to map the “succession of form” Rene introduces a series of models evolved from recent developments in topology and differential geometry. When discussing the models, Rene points out the shortcomings of both qualitative and quantitative results in earlier models. He explains how quantitative results cannot explain a “car trip” and how at the same time qualitative results are “insufficient” because they “rely on the experience of solid bodies in three dimensional Euclidean space”.
So…In order to explore “succession of form” and to reconcile these terms, Rene introduces dynamical models that are not based in Euclidean space and metric quantities (not modeling form) but are based on degrees of freedom, discontinuities, and relational functions (modeling relationships, events, changes and possibilities). Rene uses topology and differential analysis as the basis for multi-dimensional models that can yield rigorous while at the same time, qualitative results.
So it seems the big idea here is seems to fit right in with what we have been talking about. The idea here seems to the connection between the “form” and the “processes” that led to the form. Rene introduces models that allow us to explore this same “plane of possibility”. When we begin to see “form” as a simple “crystallization” of processes we are able to gain much insight into the genesis of past present and future matter both organic and inorganic.
It seems clear how Deleuze builds upon some of these concepts when he described the “new status of the object”. It also seems clear how that these are exactly the issues that a whole group of architects and designers seem to be addressing. From Greg Lynn to Eisenman, these designers are considering form in a manner that relates to philosophical foundations of genesis and universal understanding.
Rene Thom’s reading has become much more accessible because of the previous readings we have done. Most specifically, by deciphering Deleuze and his use of Thom’s ideas, we are able to better appreciate the subtle spatial implications of “morphogenesis”, forms of “becoming” and qualitative and quantitative properties relationship to metric and non-metric properties.
In attempting to map the “succession of form” Rene introduces a series of models evolved from recent developments in topology and differential geometry. When discussing the models, Rene points out the shortcomings of both qualitative and quantitative results in earlier models. He explains how quantitative results cannot explain a “car trip” and how at the same time qualitative results are “insufficient” because they “rely on the experience of solid bodies in three dimensional Euclidean space”.
So…In order to explore “succession of form” and to reconcile these terms, Rene introduces dynamical models that are not based in Euclidean space and metric quantities (not modeling form) but are based on degrees of freedom, discontinuities, and relational functions (modeling relationships, events, changes and possibilities). Rene uses topology and differential analysis as the basis for multi-dimensional models that can yield rigorous while at the same time, qualitative results.
So it seems the big idea here is seems to fit right in with what we have been talking about. The idea here seems to the connection between the “form” and the “processes” that led to the form. Rene introduces models that allow us to explore this same “plane of possibility”. When we begin to see “form” as a simple “crystallization” of processes we are able to gain much insight into the genesis of past present and future matter both organic and inorganic.
It seems clear how Deleuze builds upon some of these concepts when he described the “new status of the object”. It also seems clear how that these are exactly the issues that a whole group of architects and designers seem to be addressing. From Greg Lynn to Eisenman, these designers are considering form in a manner that relates to philosophical foundations of genesis and universal understanding.
the problem (again) of space
01. the quality vs quanity conversation
02. the local vs global condition
From Euclid’s problematic attempt at space, the issue here is not so much about defining that which constitutes space, but characterizing it. Thom gives us catastrophe theory. Balmond and (especially) Lynn argue again and again for a closer attention to the potential energies already available.
Balmond “To spend energy on promoting a free-shape only to forget its interior meaning and call on structure, late, to prop up the surface, seems a wasted opportunity”
Lynn “to reconcieve motion as force rather than as a sequence of frames”
It’s the Thom/Eisenman/Lynn—all of them—addressing the grain of sand that starts the landslide, the hull of the boat in the sea (we owe a lot to the nautical world, no?)
Then the local/global situation is essentially the one of emergence. Eisenman talks about it as the passé-partout, a "kind of reframing that can never be neutral". Dealing with more than the sum of the parts. Thom talks about the same local conditions birthing different outcomes based on unseen conditional factors. Lynn reference’s Yoh’s work that “complicates the distinctions between a global system and local components”.
In the end I think Lynn is right to point out that, since the “perhaps more than any other discipline, the negotiation between construction and abstract concepts has been the responsibility of the architect”, these threads remain the ones rewoven again and again.
02. the local vs global condition
From Euclid’s problematic attempt at space, the issue here is not so much about defining that which constitutes space, but characterizing it. Thom gives us catastrophe theory. Balmond and (especially) Lynn argue again and again for a closer attention to the potential energies already available.
Balmond “To spend energy on promoting a free-shape only to forget its interior meaning and call on structure, late, to prop up the surface, seems a wasted opportunity”
Lynn “to reconcieve motion as force rather than as a sequence of frames”
It’s the Thom/Eisenman/Lynn—all of them—addressing the grain of sand that starts the landslide, the hull of the boat in the sea (we owe a lot to the nautical world, no?)
Then the local/global situation is essentially the one of emergence. Eisenman talks about it as the passé-partout, a "kind of reframing that can never be neutral". Dealing with more than the sum of the parts. Thom talks about the same local conditions birthing different outcomes based on unseen conditional factors. Lynn reference’s Yoh’s work that “complicates the distinctions between a global system and local components”.
In the end I think Lynn is right to point out that, since the “perhaps more than any other discipline, the negotiation between construction and abstract concepts has been the responsibility of the architect”, these threads remain the ones rewoven again and again.
the simplest elementary catastrope
The idea of various surfaces representing catastrophe behaviors is quite compelling. It's nice that they gave them names, such as the butterfly catastrophe. Though the most basic catastrophe is called the fold, surly Eisenman is not saying he literally based his Rebstock Masterplan on such a specific type of mathematical representation. Just as when Deleuze speaks of the fold, he's using it as a metaphor or framework to talk about (basically) everything else. Temporal modulation of space, continual variation of matter, singularities and repressed immanent conditions of existing urbanism = the fold = a way of projecting new social organizations into an existing urban environment. I follow. But, sadly, I don't know enough about his actual Rebstock proposal to know if he pulled it off.
I found some images of the project, but from a site in Spanish. As Eisenman himself said, he likes to enter competitions, but would rather not win because then he has to build something. Was the formulation of his Rebstock masterplan conceived as a way to advance his theories/agenda? Does it matter if that was the case? Where does this proposal fall within the realm of other fold (or topological?) projects, historically speaking?
Friday, November 7, 2008
Thom/Eisenman
The issue of qualitative vs quantitative is to me one of most interesting aspects of Thom's catastrophe theory. It might be because his explanation of that aspect seemed very clear next to the deeply elaborated mathematically talk on the structural stability of form. Interestingly, while describing qualitative aspects Thom resorts to psychology, and intuition as arguments to use it in his mathematical model. In his example where a theoretical process is graphed along with two graphs of the recreated mathematical formulas, the one quantitatively closer is clearly a worse representation of the original proses - to a intuitively thinking person. "A natural tendency of mind" to put qualitative result over quantitative
As to the catastrophe theory itself, it was hidden deep under the math formulas of Thom's text. As far as I could gather from outside sources, it has more to do with mathematical description and analysis of events and dynamical systems than with geometry, although Thom elaborates on it in form and structural stability. It is more intuitive for me to think of it in terms of processes or systems that are affected by their evolution and their influencing parameters to produce a "disastrous effect" of "dicontinuity", or jumping the fold.
the catastrophe theory is suggested by Peter Eisenman as one of solutions to dealing with architecture in the age of mediation. He argues that the condition of the world today calls for departing from architecture based on Cartesian rationalism to one based on fold. Since Thom's theory combines fold and event it is best suited for such move. The fold is not simply reinterpretation of plan or section but a condition that exists in between others, for Eisenman - a new direction.
As to the catastrophe theory itself, it was hidden deep under the math formulas of Thom's text. As far as I could gather from outside sources, it has more to do with mathematical description and analysis of events and dynamical systems than with geometry, although Thom elaborates on it in form and structural stability. It is more intuitive for me to think of it in terms of processes or systems that are affected by their evolution and their influencing parameters to produce a "disastrous effect" of "dicontinuity", or jumping the fold.
the catastrophe theory is suggested by Peter Eisenman as one of solutions to dealing with architecture in the age of mediation. He argues that the condition of the world today calls for departing from architecture based on Cartesian rationalism to one based on fold. Since Thom's theory combines fold and event it is best suited for such move. The fold is not simply reinterpretation of plan or section but a condition that exists in between others, for Eisenman - a new direction.
catastrophe
My reaction to Rene Thom's article can be summed up with an equation. If you take the degree of complexity of his argument, d, and multiply it by the combination of my understanding of the principles, U, and the new model of meaning he is establishing (M), you can find the state of my brain after reading the article, or b. Thus, when completed, i felt d(U+M)=b.
Ok, I got that out of the way. In all seriousness, Thom had devised a new way of talking about continuity and space in a qualitative, rather than quantitative sense, something quite foreign to mathematics. It was difficult to really decipher what it is he was saying between all of the equations, but the other writing (The Elementary Catastrophes, author unknown?) cleared a few things up, defining catastrophe theory in terms of physics, or at least setting up a physical analog (the metal clicker) to better explain the principles. However, the graphing of the more complicated behaviors started to melt my brain a bit.
Eisenman sees the potential in this catastrophe viewpoint as a way to redifine the purpose of architecture, a response to media saturation and the shortening of our collective attention spans, arguing that architecture is less about space now and more about event. I'm not sure I wholly agree with him on this, but I can see how he might get excited about the potential within the theory.
Ok, I got that out of the way. In all seriousness, Thom had devised a new way of talking about continuity and space in a qualitative, rather than quantitative sense, something quite foreign to mathematics. It was difficult to really decipher what it is he was saying between all of the equations, but the other writing (The Elementary Catastrophes, author unknown?) cleared a few things up, defining catastrophe theory in terms of physics, or at least setting up a physical analog (the metal clicker) to better explain the principles. However, the graphing of the more complicated behaviors started to melt my brain a bit.
Eisenman sees the potential in this catastrophe viewpoint as a way to redifine the purpose of architecture, a response to media saturation and the shortening of our collective attention spans, arguing that architecture is less about space now and more about event. I'm not sure I wholly agree with him on this, but I can see how he might get excited about the potential within the theory.
Friday, October 31, 2008
Eiseman, Folding, Rebstock
warning: this is the first day this month that I haven't had coffee.. :(
To some extent, Eiseman is saying that architecture can now experience that shift in The Wizard of Oz when color came into view. Actually, he means something much deeper (I hope), almost another dimension but by the last page he leaves me highly skeptical, unconvinced, and worried that he is recycling too much of his jargon.
Maybe working with ideas such as the fold will enlighten us architects. His portrayal of the Rock Show struck a key of interest and the sound bite surely hits home especially with the herd mentality to summarizing your blog posts with a single, encapsulating image. Are we architects destined to obey this fad? Must we create experiences, animations, temporal systems while neglecting the building, the bricks, the rain? I hate to think we are shackled to figure ground drawings however to say that design is a non-dialectic process seems renascent of the pessimistic post-modernists. "But as in most disciplines," he leaves us with "they are no longer thought to explain the complexity of phenomena." Thanks for getting somewhere with your article, Eiseman.
And of all cities to analyze, he picks the absolute deadville of a town in Germany, Frankfurt, where even the old folks go mad with boredom. The only successful thing that city ever did was suck up my ATM card and whimper, "Es tut mir leid.."
I can see why we are reading the piece: someone turns his back on Cartesian rationalism. However, it doesn't take a fold to re-articulate "a new relationship between vertical and horizontal or between figure and ground." The color blue could do just fine: it's not black or white, figure or ground. Or maybe even crumpling up the article, toss it in the waste basket. How's that for revealing "other conditions that may always haven been immanent or repressed in" me. Slight shift on context, but at least you get what Iam trying to say.
"The fold can then be used as both a formal device and as a way of projecting new social organizations into an existing urban environment." What does it mean to project new social organizations into existing urban environments? If it means "the library needs to go over there," so be it. If it means, "I am a wizard who can magically orchestrate social interactions despite existing conditions," then I get a little lost.
sorry if you had to read this..
To some extent, Eiseman is saying that architecture can now experience that shift in The Wizard of Oz when color came into view. Actually, he means something much deeper (I hope), almost another dimension but by the last page he leaves me highly skeptical, unconvinced, and worried that he is recycling too much of his jargon.
Maybe working with ideas such as the fold will enlighten us architects. His portrayal of the Rock Show struck a key of interest and the sound bite surely hits home especially with the herd mentality to summarizing your blog posts with a single, encapsulating image. Are we architects destined to obey this fad? Must we create experiences, animations, temporal systems while neglecting the building, the bricks, the rain? I hate to think we are shackled to figure ground drawings however to say that design is a non-dialectic process seems renascent of the pessimistic post-modernists. "But as in most disciplines," he leaves us with "they are no longer thought to explain the complexity of phenomena." Thanks for getting somewhere with your article, Eiseman.
And of all cities to analyze, he picks the absolute deadville of a town in Germany, Frankfurt, where even the old folks go mad with boredom. The only successful thing that city ever did was suck up my ATM card and whimper, "Es tut mir leid.."
I can see why we are reading the piece: someone turns his back on Cartesian rationalism. However, it doesn't take a fold to re-articulate "a new relationship between vertical and horizontal or between figure and ground." The color blue could do just fine: it's not black or white, figure or ground. Or maybe even crumpling up the article, toss it in the waste basket. How's that for revealing "other conditions that may always haven been immanent or repressed in" me. Slight shift on context, but at least you get what Iam trying to say.
"The fold can then be used as both a formal device and as a way of projecting new social organizations into an existing urban environment." What does it mean to project new social organizations into existing urban environments? If it means "the library needs to go over there," so be it. If it means, "I am a wizard who can magically orchestrate social interactions despite existing conditions," then I get a little lost.
sorry if you had to read this..
Wednesday, October 29, 2008
REBSTOCK MASTERPLAN…
Reframing the idea of figure ground in order to gain a more rich sense of context. Eisenman follows Deleuzian thinking and continues with the development of the “objectile” as something not concerned with “essential form” but with an “event”. This event relates back to the “dilating” and “folding” of matter discussed in “Pleats of Matter”.
In the Rebstock Park Master plan, Eisenman borrows the concept of the fold to integrate figure and ground, subject and object, plan and section. He uses the fold and the dimensionality of the edge, or the continuity of the surface as a way to reframe relationships such as “old and new, transport and arrival, and commerce and housing”. He compares the fold to the “mat in a picture frame” underscoring its ability to connect the two worlds of the tangible and the intangible, subject and object and seen and unseen.
Eisenman also introduces the mathematics of Rene Thom and catastrophe theory. Using Thom’s seven elementary events, Eisenman discusses, what I believe is, a sort of event plane, whose virtual curvature maps events, possibilities and processes. This type of mapping would be a complex series of nonlinear relationships rather than a sort of Cartesian rational 1 to 1 mapping.
If I understand correctly, there would be folds in this surface that would connect unforeseen possibilities and events. It is within the folds that all of the possibilities of becoming are hidden, what Deleuze called the “meanders and detours”. Eisenman explains, “The fold, then, becomes the site of all the repressed immanent conditions of existing urbanism”. This sounds like Deleuze’s butterfly and caterpillar.
And again I cannot help but to think of the tools we use, Maya, Max, Animations, Etc…From fluid dynamics to particle systems and even splines, our tools embody, and are used to explore, this new sense of the “objectile” and “event”…Our pursuit of physical form dabbles in a metaphysical philosophy of being and becoming…Digging it!
I have not read Greg Lynn but maybe this is partially why the curve is “groovy”?
In the Rebstock Park Master plan, Eisenman borrows the concept of the fold to integrate figure and ground, subject and object, plan and section. He uses the fold and the dimensionality of the edge, or the continuity of the surface as a way to reframe relationships such as “old and new, transport and arrival, and commerce and housing”. He compares the fold to the “mat in a picture frame” underscoring its ability to connect the two worlds of the tangible and the intangible, subject and object and seen and unseen.
Eisenman also introduces the mathematics of Rene Thom and catastrophe theory. Using Thom’s seven elementary events, Eisenman discusses, what I believe is, a sort of event plane, whose virtual curvature maps events, possibilities and processes. This type of mapping would be a complex series of nonlinear relationships rather than a sort of Cartesian rational 1 to 1 mapping.
If I understand correctly, there would be folds in this surface that would connect unforeseen possibilities and events. It is within the folds that all of the possibilities of becoming are hidden, what Deleuze called the “meanders and detours”. Eisenman explains, “The fold, then, becomes the site of all the repressed immanent conditions of existing urbanism”. This sounds like Deleuze’s butterfly and caterpillar.
And again I cannot help but to think of the tools we use, Maya, Max, Animations, Etc…From fluid dynamics to particle systems and even splines, our tools embody, and are used to explore, this new sense of the “objectile” and “event”…Our pursuit of physical form dabbles in a metaphysical philosophy of being and becoming…Digging it!
I have not read Greg Lynn but maybe this is partially why the curve is “groovy”?
THE SMOOTH AND THE STRIATED…
It seems that Deleuze is establishing the Universe as a sort of continuum,
differentiated by folds and perhaps intensities and densities. He explains, “Development does not go from smaller to greater things through growth or augmentation, but from the general to the specific, through differentiations of an initially undifferentiated field either under the action of exterior surroundings or under the influence of internal forces that are directive.” One can already envision a sort of material infinity, made up of, say, fabric that infinitely pleats and folds upon itself. Zoom in and out and out and all we see is varying patterns of material made up of points, lines and folds.
Following this logic, in order to really make sense of all of this, in order to really gain insight from this vision of the universe, we would have to closely examine the finest element of the fabric and also the widest view of the material. We would want to look at the fold and the fabric composition and patterning at a variety of scales. We would want to look for consistencies and differences. Enter the smooth and the striated, a way of examining and comparing the points, splines and nurbs surfaces that make up the fabric of existence? Wow.
When we zoom in so far as to inhabit the fibers we see the material is composed in two ways, the smooth and the striated or the felt and the fabric. The spaces created by these two compositions are described as sedentary and nomadic. We also see that these two compositions are generally contiguous. They are not generally stitched together but are usually intertwined, as the fibers of one dematerialize or grow into the fibers of the other. As it turns out there are all sort of variations in this fabric from densities of weaving to intensities in the fibers in the felt and to patchwork integrations.
As we traveled through the material and through the universe, zooming in and out, we would also see that the smooth and striated fibers would take on many forms and create many types of space. They would create patterns like stone and water and folds like sound waves and wind. We could always zoom in or zoom out and see the folds and material consistency as related and describable as some combination of smooth and striated, nomadic and sedentary.
Traveling through the universe and through the material, Deleuze chooses to move through some of the more complex and illusive of spaces. It would be comparable to move through the physical space of table salt where cubic fibers aggregate to make the material or through the space of molecules where chemicals bond to create the material.
Instead, Deleuze moves to spaces that are more intangible and ambiguous, where the distinction between smooth and striated becomes blurry in notably more interesting. In order to show how all spaces can be thought of in this way, Deleuze starts with simple spaces, the space of fabric, the space of sound waves and then moves into more complex spaces, the space of water, the space of mathematics, the space of art.
The idea here seems to be to be to think about these phenomena and objects as spaces and intensities within and around the fabric and as part of this same universal continuum made distinct by their expression of differentiation in consistency and patterning.
Deleuze uses these spaces to describe the universe and in so doing, implicitly employs principles from mathematics to make differentiations in the patterning and consistency mentioned above. It only makes sense. If the universe can be expressed through the weaving of lines and the creation of complex systems of interconnected networks, mathematics seems like the most appropriate tool to explore and to begin to understand these universal patterns.
differentiated by folds and perhaps intensities and densities. He explains, “Development does not go from smaller to greater things through growth or augmentation, but from the general to the specific, through differentiations of an initially undifferentiated field either under the action of exterior surroundings or under the influence of internal forces that are directive.” One can already envision a sort of material infinity, made up of, say, fabric that infinitely pleats and folds upon itself. Zoom in and out and out and all we see is varying patterns of material made up of points, lines and folds.
Following this logic, in order to really make sense of all of this, in order to really gain insight from this vision of the universe, we would have to closely examine the finest element of the fabric and also the widest view of the material. We would want to look at the fold and the fabric composition and patterning at a variety of scales. We would want to look for consistencies and differences. Enter the smooth and the striated, a way of examining and comparing the points, splines and nurbs surfaces that make up the fabric of existence? Wow.
When we zoom in so far as to inhabit the fibers we see the material is composed in two ways, the smooth and the striated or the felt and the fabric. The spaces created by these two compositions are described as sedentary and nomadic. We also see that these two compositions are generally contiguous. They are not generally stitched together but are usually intertwined, as the fibers of one dematerialize or grow into the fibers of the other. As it turns out there are all sort of variations in this fabric from densities of weaving to intensities in the fibers in the felt and to patchwork integrations.
As we traveled through the material and through the universe, zooming in and out, we would also see that the smooth and striated fibers would take on many forms and create many types of space. They would create patterns like stone and water and folds like sound waves and wind. We could always zoom in or zoom out and see the folds and material consistency as related and describable as some combination of smooth and striated, nomadic and sedentary.
Traveling through the universe and through the material, Deleuze chooses to move through some of the more complex and illusive of spaces. It would be comparable to move through the physical space of table salt where cubic fibers aggregate to make the material or through the space of molecules where chemicals bond to create the material.
Instead, Deleuze moves to spaces that are more intangible and ambiguous, where the distinction between smooth and striated becomes blurry in notably more interesting. In order to show how all spaces can be thought of in this way, Deleuze starts with simple spaces, the space of fabric, the space of sound waves and then moves into more complex spaces, the space of water, the space of mathematics, the space of art.
The idea here seems to be to be to think about these phenomena and objects as spaces and intensities within and around the fabric and as part of this same universal continuum made distinct by their expression of differentiation in consistency and patterning.
Deleuze uses these spaces to describe the universe and in so doing, implicitly employs principles from mathematics to make differentiations in the patterning and consistency mentioned above. It only makes sense. If the universe can be expressed through the weaving of lines and the creation of complex systems of interconnected networks, mathematics seems like the most appropriate tool to explore and to begin to understand these universal patterns.
THE PLEATS OF MATTER…
Better late than never...I hope.
This reading seems to be describing at an interconnected universe held together by “folds”. This universe includes, I believe, includes all material and immaterial, organic and inorganic matter. It is made of Souls and Stones alike. Deleuze makes a distinction between the two “floors” of matter in the universe and uses Baroque architecture and mathematics as a way of thinking about the connectedness of these two “floors”.
I think that with Deleuze-the interconnected nature of these worlds allows us to examine physical artifacts and relate them to metaphysical concepts. The reading is not necessarily about the physicality of the fold or about Baroque architecture, but more about how these resonate with a new conception of the universe and the object/subject.Deleuze always leaves me feeling like the shaping of matter is deeply wrought with metaphysical implications.
“The world was thought to have an infinite number of floors, with a stairway
that descends and ascends…but the Baroque contribution is a world with only
two floors, separated by a fold that echoes itself, arching from the two sides
according to a different order”
that descends and ascends…but the Baroque contribution is a world with only
two floors, separated by a fold that echoes itself, arching from the two sides
according to a different order”
Deleuze discusses the concept of “viewpoint” and the transformation of the subject to the object. This is another example of the “two floors” concept. He explains how perspective was seen by some as a tool to connect these two worlds, there by embodying some sort of relativism. But in fact perspective clearly embodies a “pluralism” that disconnects the two worlds. Perspective relies on a singular “point of view” while Deleuze argues that “There are many points of view-whose distance is in each case indivisible” So there are infinite viewpoints and an infinity of connected matter to be viewed. This conception of the universe makes perspective seem like a tool incapable of expressing the complexity of connectedness of these two worlds.
The “fold” is also a way of describing the capacities and tendencies of matter. Potential for variation is folded within matter. Deleuze explains how the butterfly is not different from the caterpillar but how they are one singular creature folded together. This invokes the idea of time and evolution and questions the notion of the plutonic object, which seems to be trying to freeze this evolutionary fold into a static singularity.
In terms of math, it seems implicitly tied into all of this. If all matter, organic and inorganic, physical and metaphysical is tied together through a series of folds and differentiations it seems critical to think about curves and trajectories. It seems that curvature and continuity are taking the place of Boolean logic. “To unfold is to increase and to fold is to diminish, to reduce” this is reminiscent of fractal geometry.
In fact through out the article Deleuze is referring to Leibniz, Descartes and other thinkers such as Heinrich Wolfflin, all of which have had immense impact on the field of mathematics and design. It is a widely held belief that mathematics tends to explain much of the physical world around us and that there is some universal truth found in mathematics that goes beyond our physical world. If we think that 2+2 always equals 4 whether we believe it or not, (which soap bubbles, gravity, and nautilus shells among other things, seem to indicate) then we agree that mathematics is a sort of existential truth. There is physical world and a …dare I say it… metaphysical world. Hence, the two floors, linked by a fold, a curve-a mathematical phenomena. All of this does make me think of Maya, splines, fractals, particles, networks, and their metaphysical implications. Hmm…
Also, of course in the article there is a lot of formal language that seems of particular interest to the architect and designer. There is all of this formal description of Baroque architecture - separation of facade, spongy, flattening of pediment, etc…There is discussion of how matter finds form through elastic and plastic forces and a description of the fold as the smallest element of matter and the point as a simple “extremity of the line”. Deleuze introduces Leibnez’s concepts of families of curves. Three types of points are distinguished, the point of inflection, the point of position, and the point of inclusion. Their counterparts, “explication, complication and implication” form the “triad of the fold”.
I could never summarize what I believe to be the subtleties and rich tangential nature of this reading but most obviously stated and most obviously relevant to our field is the changing status of the object. Deleuze makes (sort of) clear for all of us…
“The new status of the object, the objectile, is inseparable from the different layers that are dilating, like so many occasions for meanders and detours. In relation to the many folds that it is capable of becoming, matter becomes a matter of expression.”
...
Tuesday, October 21, 2008
Models
It seems maybe not so fortuitous that in the Smooth and the Striated we come up against - once again - this question of space. Indeed it begins with an oposition (but should we really call it that) between a kind of Cartesianism and something else, something less predictable. An polarization announced already at the beginning of the fold. Here at least wind the question of model explict. And of course multiple. There is not one. And yet a mathematics (trajectory, continuous varation, etc) runs through the text as a kind of spine, from one model to the next. Is this then a master model? Is it a conceptual scaffolding? What is compared to what? Stasis and mobility. For a start.
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Friday, October 17, 2008
Everywher
I like the kind of swift grab-all style of your comments Eric. And you'er right D covers much ground. But you also put your finger on something kind of important: is this mere metaphor? Pick out a passage for us to review on Tues.
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Thursday, October 16, 2008
I read "nomad" and got excited. Then I came to "religion," "war machine," and was on the edge of my seat. When I read Mongol, I jumped for joy like no Deluezing reader ever has. All these issues are right up my alley and not so common in architecture. By the end of the article, however, I was at the back of my chair trying as hard as I could to figure out how he was using mathematics.
Deleuze jumps around a lot in this text. I give him immediate credit for inserting social issues but they are so watered down in all the analogies they become distracting. He compares the striation to geology, organisms, fabrics, human anatomy, composers and more all while insisting on Greek language lessons. He seems to be munching through ideas like breakfast cereal.
He is either covering way too much ground or he just can't nail down what he is trying to say. (I will recant this statement after a few more readings.)
Deleuze had some very interesting tangents. For instance, "composers do not hear; they have close-range hearing, whereas listeners hear from a distance. Even writers write with short-term memory, whereas readers are assumed to be endowed with long-term memory." Woa. He gets into some great ideas pertaining to scale, point of view, orientation. His notion of the sea also paints an eloquent picture of complexity in common notions of striation. He really has me when he talks about bearings and fabric and yet I get confused again when he brings up the Mongols and nomads. I think a discussion of this reading would do me a lot of good.
I'll read through it a few more times and get back..
Deleuze jumps around a lot in this text. I give him immediate credit for inserting social issues but they are so watered down in all the analogies they become distracting. He compares the striation to geology, organisms, fabrics, human anatomy, composers and more all while insisting on Greek language lessons. He seems to be munching through ideas like breakfast cereal.
He is either covering way too much ground or he just can't nail down what he is trying to say. (I will recant this statement after a few more readings.)
Deleuze had some very interesting tangents. For instance, "composers do not hear; they have close-range hearing, whereas listeners hear from a distance. Even writers write with short-term memory, whereas readers are assumed to be endowed with long-term memory." Woa. He gets into some great ideas pertaining to scale, point of view, orientation. His notion of the sea also paints an eloquent picture of complexity in common notions of striation. He really has me when he talks about bearings and fabric and yet I get confused again when he brings up the Mongols and nomads. I think a discussion of this reading would do me a lot of good.
I'll read through it a few more times and get back..
Wednesday, October 15, 2008
Comment for Adam
The response is interesting and in light of one Deleuze's books logique de sens, not far off target in terms of Deleuze's multiplicity. Deleuze for instance was very interested in Lewis Carroll's work on mathematics and his book Alice in Wonderland. I like the notion of a kind of delirium. I'm not sure though delusional is something he is offering as an alternative form of thinking. Difficult as the texts are, they still offer one interesting insight into our problem: namely, how far can the use of a mathematical model travel?
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delusionalDeluze
And that is to say I'm not quite sure if he makes me more delusional than his text is or the other way around. Than again, delusions, or thought disturbances are to be expected when math (the concrete science) moves into calculus, and is used to describe limits and attempts to describe infinity (the unknown, the untouchable, the elusive, the angst evoking). is Deluze delusional talking about the "Soul of point, line, surface, or the fold"? He sure is eloquent in the logic of his model. He is reaching all the way to Greek roots when he makes a move from the imperfect physical point "neither atom, nor Cartesian point - elastic point-fold," to idealistic mathematical point "rigorous without being exact". He follows the logic with Euclidean strictness and set of basic parameters where point describes extremities of lines. Though his model is broader, including vectors, magnitudes, movement, force, and direction. so far so good. But wait, now that seems to transform the point into "the metaphysical point," or the soul, or the subject. Now while I can follow each little step, this general move is something I still have to digest. how exactly did we move form the physical to ideal to now "a point of view" or "a point of inclusion"?
I find both texts dualistically very stimulating and discouraging. But my mind too ventures off while reading, sometime stimulated by the multitude of ideas and possibilities he opens (especially in the smooth & striated), and other times just finding it difficult to follow the condensation of his lifes' work seemingly neatly packed in every few lines.
I find both texts dualistically very stimulating and discouraging. But my mind too ventures off while reading, sometime stimulated by the multitude of ideas and possibilities he opens (especially in the smooth & striated), and other times just finding it difficult to follow the condensation of his lifes' work seemingly neatly packed in every few lines.
deleuze, mathematical model
Ugh.
Ok, I made it through most of this and was able to absorb a very small amount. I often found my mind wandering while my eyes ran over the words. However, I think I found a section that deals with what Peter was asking us to look for (not that I found it particularly clear).
In The Folds In The Soul, Deleuze gets heavy into mathematical language in talking about "inflection," or the fundamental component (the atom) of a fold. He breaks it down into three types, vectorial (symmetrical/orthogonal/tangential), projective (defined by hidden parameters), and infitely variable (like fractals).
Ok, I think I'm following.
He then goes into irrational numbers, talks about limits (yay Calculus!), and then I get a bit lost again.
"When mathematics assumes variation as its objective, the notion of function tends to be extracted, but the notion of objective also changes and becomes functional."
I'm looking forward to reading someone else.
Ok, I made it through most of this and was able to absorb a very small amount. I often found my mind wandering while my eyes ran over the words. However, I think I found a section that deals with what Peter was asking us to look for (not that I found it particularly clear).
In The Folds In The Soul, Deleuze gets heavy into mathematical language in talking about "inflection," or the fundamental component (the atom) of a fold. He breaks it down into three types, vectorial (symmetrical/orthogonal/tangential), projective (defined by hidden parameters), and infitely variable (like fractals).
Ok, I think I'm following.
He then goes into irrational numbers, talks about limits (yay Calculus!), and then I get a bit lost again.
"When mathematics assumes variation as its objective, the notion of function tends to be extracted, but the notion of objective also changes and becomes functional."
I'm looking forward to reading someone else.
Sunday, October 12, 2008
Models of meaning
Our discussion last Tuesday examined a few issues at stake between Vitruvius, Boullee, and Durand. Keep in mind that Vitruvius stands in the history of Western arch as the first systematic exposition of arch Principals. And please also keep in my mind what is at stake in the articulation of Principals and what a principal is in the notion of a system. Its first major use comes of course in the work of Aristotle who used it to systematize philosophy.
In Vitruvius one od the first principles is of course symmetry and it is connected with a number of paradigmatic uses of mathematics in architecture, such as perfect geometrical figures (circle and square), ideal ratios, harmony and proportion. These elements to repeat hang together as if on a chain (they are NECESSARILY connected). The importance of course is a metaphysical lesson, not a contingent value; symmetry and it attendant terms point to Nature and man's relation in an ideal essentialist manner. So, the term is abstract and ideal but nonetheless a powerful notion of the idea of perfection in architecture. The ideality of this is that a) it is a gemoetrical notion embodies in the circle and the square and b) timeless and univseral (in a platonic sense). That then is one kind of invocation of mathematics and geometry - their uses MEANS a certain formal coherence in architecture. There is another discussion of the use of mathematics and geometry in architecture which comes at the end and that involves entasis, wherein although a temple might actually use ideal mathematics its actual appearance will not cohere with the perfection of the idea since our eyes and physical material existence are not perfect.
Thus a different use of mathematics enters which we can call instrumental and which in no way we can isolate as a principal since it doesn't of necessity lead to any Principal but merely corrects our experience of it. It is just a way to get a job done.
Are these two uses in conflict? Are they coherently aligned? Doesn't the introduction of an instrumental use of mathematics call into question the ideality of mathematics in architecture?
At any rate we may want to remember that Gothic architecture which shares so much with the history of Northern European "barbarian" art was dismissed throughout hsitory because it failed to achieve the quality of geometrical purity found in the GrecoRoman tradition. (Interestingly, Leibniz's curve was often alligned with the barbaric curve of the gothic arch). It was seen as vulgar, a sentiment which Eisenman still shares today because it was more of a material contingent system (think here of Gaudi"s funicular chains as an example-they output geometry as an effect of gravity on the network of chains). The Gothic system actually uses much in the plan dimension of the ideality of mathematics from the grecoroman tradition, but not in elevation and section. There all geometry derives from experimentation.
At any rate, back to models of meaning. When we read Boullee he talks about symmetry in many senses consisten with Vitruvius - and of course he is entirely aware of this ideality. At the same time as a models of perfection he is modernizing it in relation to a theory of sensation as and I pointed out this is what accounts for the notion of irregularity. Regardless, at stake again is symmetry and geometry as a model of meaning. When we get to Durand, that model entirely shifts. And to make a long story short, Durand kind of inflates the ideal and the instrumental by saying that sysmmetry is an economic function.
Ok, so what does all this imply? Well, for one when we use a geopmtrical model in the history of architecture we are often introducing a model of meaning. Mathematics and geometry are not simply tools. Ok, we get that. We alrwady know that. For another, it clarifies the distinction between a principlaed use and a contingent use. And finally, that the meaning of the model is just in fact how it is used.
Now we are and have been asking about toplogy as in so many different ways different from geometry and looking at what possibilities it holds for architecture.
We've looked at it in a kind technical sense and now with Deleuze we are looking at how it emerged as a model of meaning.
Firsyt let us note that Deleuze and Bernard Cache stand as essential references in the emergence of digital design (the first iteration of computational architecture that allowed for complexity). Without Deleuze no Greg Lynn or Eisenman, for example. But in order to see what this means in theuir work let us first take a glimpse at Deleuze'
The first thing we can note, right of the bat is the idea of the fold, and the opposition between the curve of Leibniz who introduces a new mathematical system and Descartes's whose system is still tied to a notion of stasis. Despite my poor skills at teaching mathematics I think you got the point: calculus deals with change and variation, it deals with motion and time, and it deals with therefor events.
We will discuss this more on Tuesday next week but meanwhile please finish your examination of both texts and write an entry for the blog about a specific moment in which Deleuze is using mathematics as a model of meaning and try and write something explicit about what that model is mathematically ( eg if he is talking about curves or vectors or whatevr)
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Monday, October 6, 2008
if it ain't baroque...
Only when Deleuze is summarizing things (at the end) do I have any sort of a vague notion of what was contained in the preceding 30 pages. So let's discuss the end where he lays out six points relating to the fold and my attempt at a translation of the various representations of the fold contained therein:
1. The fold: as a condition of continuity and infinity.
2. The inside and the outside: a separation and division.
3. The high and the low: a dialectic condition.
4. The unfold: not the act, but rather the lack of a fold.
5. Textures: a multiplicity of folds.
6. The paradigm: the framework within which the fold is considered.
In this case, Leibniz and the Baroque are the framework of choice for his entire discussion. I think the above needs to be expanded upon considerably, but it's a beginning.
1. The fold: as a condition of continuity and infinity.
2. The inside and the outside: a separation and division.
3. The high and the low: a dialectic condition.
4. The unfold: not the act, but rather the lack of a fold.
5. Textures: a multiplicity of folds.
6. The paradigm: the framework within which the fold is considered.
In this case, Leibniz and the Baroque are the framework of choice for his entire discussion. I think the above needs to be expanded upon considerably, but it's a beginning.
Wednesday, October 1, 2008
better late...
I'm not cheating because I haven't yet read what anyone else posted, but I'll still issue my comments on the general question (as I recall) from last class, "What does mathematics have to do with architecture?" in relation to the viewpoints presented in the readings. A pseudo-summary first...
Vitruvius:
A codified characterization and description of the temple form derived from his study of Greek architecture. It is significant that Chapter 1 is titled "First Principles of Symmetry." Also significant is the “foot” which becomes a base unit of measure, derived from the proportions of the human body which, as it has come from Nature, is perfect.
Boullee:
He is recounting a conversation which, presumably, he was present at. The question posed for discussion is, “Are the basic principles of architecture derived from Nature?” People relate to the “human condition” thus anything that is symmetrical and proportional is pleasing to the eye.
Durand:
He summarizes the works of Vitruvius and Laugier (imitation of the human body and the hut, respectively) then politely disagrees with their conclusions. “Fitness and economy,” are the principles that must be met. Economy is further characterized by symmetry, regularity and simplicity.
It would seem there is something about symmetry, whether it is a means to an end (Durand) or it is the means (everyone else). There is an instinctive beauty that is universally perceived in that which is symmetrical. In our “universe” we also relate most readily to Nature (with a capital “N”) where symmetry is ever-present. In mathematics symmetry is a basic property of pure geometrical shapes (i.e. the circle, the square, etc.). It is not much of a leap to presume a correlation between such geometry and nature with symmetry as a common thread.
Here's my favorite quote:
“If we imagine a Palace with an off-centre front projection, with no symmetry and with windows set at varying intervals and different heights, the overall impression would be one of confusion and it is certain that to our eyes such a building would be both hideous and intolerable.” -Boullee
Take that Frank Gehry.
Vitruvius:
A codified characterization and description of the temple form derived from his study of Greek architecture. It is significant that Chapter 1 is titled "First Principles of Symmetry." Also significant is the “foot” which becomes a base unit of measure, derived from the proportions of the human body which, as it has come from Nature, is perfect.
Boullee:
He is recounting a conversation which, presumably, he was present at. The question posed for discussion is, “Are the basic principles of architecture derived from Nature?” People relate to the “human condition” thus anything that is symmetrical and proportional is pleasing to the eye.
Durand:
He summarizes the works of Vitruvius and Laugier (imitation of the human body and the hut, respectively) then politely disagrees with their conclusions. “Fitness and economy,” are the principles that must be met. Economy is further characterized by symmetry, regularity and simplicity.
It would seem there is something about symmetry, whether it is a means to an end (Durand) or it is the means (everyone else). There is an instinctive beauty that is universally perceived in that which is symmetrical. In our “universe” we also relate most readily to Nature (with a capital “N”) where symmetry is ever-present. In mathematics symmetry is a basic property of pure geometrical shapes (i.e. the circle, the square, etc.). It is not much of a leap to presume a correlation between such geometry and nature with symmetry as a common thread.
Here's my favorite quote:
“If we imagine a Palace with an off-centre front projection, with no symmetry and with windows set at varying intervals and different heights, the overall impression would be one of confusion and it is certain that to our eyes such a building would be both hideous and intolerable.” -Boullee
Take that Frank Gehry.
Tuesday, September 30, 2008
And finally
So this is what we have in Vitruvius - things like models of meaning, the figure of the human, ideal proportions, harmony, etc. They all fit nicely along a chain. Symmetry is part of the foundation. Why should anything be symmetrical? And so in the first part we have these idealizations of math and geometry. So many. They all go together in the name of perfection. But then at the end, there is something else. He asks us to consider distorting the perfect geometry so that it will appear perfect when we see it. And that is because even if a line is straight, if it is long, it will appear curved - so let's correct that. But now thye question is whther this conflicts with the first use of mathematics and geometry? Is it the same kind of use?
And Durand, who was a student of Boullee, will say that symmetry is important because it is economical. This is a different model than Boullee surely. Everyone I think understood that. Your comments were clear.
(Sure, some might argue whether symmetry is a geometrical or mathematical term - I would say so, but you can debate it)
And now, finally, the point of these readings, at least one of them. Was to distinguish and get clear that mathematics and geometry just do offer us models of meaning. And we use those models in various ways. But also, a model is a kind of idealization - things ought to be this way, this is how we should understand the nature of things, etc.
And that is quite different than an instrumental use which says, in order to measure the length of this or that piece do the following . . .
So, we use mathematics (including geometry and toplogy) in ideal and instrumental ways. Only that we often find them in conflict. For reference see my discussion with Alejandro in Log 3.
So, for toplogy, I want you to see it as something architects have offered up as a model of meaning. And see what kind of model it is.
Only that we needed to have a grasp of what that means in architecture and the three readings were a way of getting to that problem.
In his essay, a plea for Euclid, Cache discusses this problem of the toplogical model. Things do have to be built in Euclidean space. But that doesn't necessarily devalue the usefulness of the topological model. It just makes us critical in an insightful way. Not negative, just insightful.
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What is a model?
So we use models. How do these function? What do we do with them? A model of meaning gives us a reference for how we ought to understand the nature of things. Think of Lacan's diagram of the self. Think of Freud's mystic writing pad. Think of Kepler's model of the universe, or Descarte's. Now think of how architects have used various models of meaning from mathematics. That's all I'm asking you to do. Just see how they use it. And then look for contradictions. Not in order to confute them, but to recognize that is one of the things we do. It just is.
Try going to studio with a mayline, or a fist full of watercolor markers and tell your instructor "I'm going to do it this way, hell with Maya.". Try modeling your project in just cubes of foam and say "Hell with curves and nurbs"
Tell me what the response is.
Now. Ask your instructor: "But really, what is a surface as opposed to a plane? What is a curved surface and what is a spline?". Or if they are using grids, ask them about those. Ask why you have to conceive of geometry in the way they are asking you to. Just ask.
It should be an interesting conversation.
And maybe they'll give you models of meaning. Maybe
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Try going to studio with a mayline, or a fist full of watercolor markers and tell your instructor "I'm going to do it this way, hell with Maya.". Try modeling your project in just cubes of foam and say "Hell with curves and nurbs"
Tell me what the response is.
Now. Ask your instructor: "But really, what is a surface as opposed to a plane? What is a curved surface and what is a spline?". Or if they are using grids, ask them about those. Ask why you have to conceive of geometry in the way they are asking you to. Just ask.
It should be an interesting conversation.
And maybe they'll give you models of meaning. Maybe
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Whar is space?
Or more precisely where?
No, the readings don't really touch on that issue. But its an interesting question. Let me put it this way; what enables us to talk about space? I mean, where do we point to and what do we use TO talk about it? Someone might say; Well, I just see it here, its all around me. And I walk through it, and so on. And that might be perfectly fine. And we might accept that. But what does it mean "I see . . ."? In what sense is that automatically meaningful? How do I know by what you say, that we see the same things. And now you might resort to physiology, and psychology, or some other discipline.
But would that be enough? I mean, would that be sufficient for architecture? Would psychology or physiology or anthropology give us the authority to say what it means to see space? To give us a definition? And what about mathematics or philosophy? Each discipline, each author might give us a model, a model of meaning to make clear what space is, what it means to KNOW it.
Can you have, for example, I private language that only you understand? This comes from Wittgenstein. Would it be a language?
Could you say what space is only because you experience it? Would that be the foundation of your knowledge? Then would it be possible to say WE have a concept of space?
Do we "know" the earth is round? That the sun is the center of this solar system? Etc.
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No, the readings don't really touch on that issue. But its an interesting question. Let me put it this way; what enables us to talk about space? I mean, where do we point to and what do we use TO talk about it? Someone might say; Well, I just see it here, its all around me. And I walk through it, and so on. And that might be perfectly fine. And we might accept that. But what does it mean "I see . . ."? In what sense is that automatically meaningful? How do I know by what you say, that we see the same things. And now you might resort to physiology, and psychology, or some other discipline.
But would that be enough? I mean, would that be sufficient for architecture? Would psychology or physiology or anthropology give us the authority to say what it means to see space? To give us a definition? And what about mathematics or philosophy? Each discipline, each author might give us a model, a model of meaning to make clear what space is, what it means to KNOW it.
Can you have, for example, I private language that only you understand? This comes from Wittgenstein. Would it be a language?
Could you say what space is only because you experience it? Would that be the foundation of your knowledge? Then would it be possible to say WE have a concept of space?
Do we "know" the earth is round? That the sun is the center of this solar system? Etc.
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divine being?
Interesting that none of the readings really talk much about “SPACE”. Boulee discusses at length the transcendent quality of masterful use of geometry and the reliance on nature as the source of all inspiration (I’m not necessarily buying all of this), but he never really discusses any quality of space. Also there seems to be missing a criticality. Boulee simply accepts geometries, specifically the sphere, as a pure and perfect form. Does this mean, as architects, that if we simply erect spheres we are creating in the order of the “Divine Being”. Personally I see some controversy with spheres and question their use in an architectural context. Surely there is something more to architecture than “geometrical perfection”. Is this really how we perceive space and value buildings; simply by their “clarity, regularity and symmetry”??? Boy that building was….perfectly symmetrical…it really took my breath away. “Symmetry is pleasing because it is the image of clarity and because the mind, which is always seeking understanding, easily accepts and grasps all that is symmetrical”-Montesquieu. “Weary of the mute sterility of irregular volumes, I proceeded to study regular volumes” How banal and dismissive this sounds. Aren’t we, in fact, finding out new phenomena in neural science, self-organization and complexity? Our understanding of “the mind” is changing and so should our use of it. Boulee seems naive and outdated in his simplistic acceptance of geometrical forms as a model for meaning. Hasn’t science, technology and modernity moved us a little further than this?
Durand strikes a little closer to home for me. The ideal form in architecture does not seem to be based on the primitive hut and the human body was not the proportional system employed to design Greek columns. Good. “FITNESS” Good. This does not mean that architecture does not have meaning. It just indicates that its meaning might not be derived through imitation and use of symbols. Where Boulee tends to talk about Math as a way for our work to gain meaning, Durand talks of math in terms of metrics and dimensions not in terms of transcending meaning. Durand is looking beyond implied meaning into the nuts and bolts. He looks at (1)the objects that architecture uses (2) the combination of these elements and (3) the alliance of these combinations in a composition of a specific building. There is nothing here about implied legitimacy because of the choice of objects, Durand would not reel over the sphere the way Boulee has. For Durand the choice of elements is only 1 part of the equation.Opinion-We are searching for meaning in our work and in our use of geometry- I would like to think that our understanding of the world and ourselves has mutated and hopefully matured over the last several millennium. I would think, intuitively, that we have more to learn and it is only through critical use and study of math that we will develop more and deeper meaning. Or maybe we can just keep making cenotaphs and placing temple fronts on banks without question, confident in its antiquated and implied meaning.
Durand strikes a little closer to home for me. The ideal form in architecture does not seem to be based on the primitive hut and the human body was not the proportional system employed to design Greek columns. Good. “FITNESS” Good. This does not mean that architecture does not have meaning. It just indicates that its meaning might not be derived through imitation and use of symbols. Where Boulee tends to talk about Math as a way for our work to gain meaning, Durand talks of math in terms of metrics and dimensions not in terms of transcending meaning. Durand is looking beyond implied meaning into the nuts and bolts. He looks at (1)the objects that architecture uses (2) the combination of these elements and (3) the alliance of these combinations in a composition of a specific building. There is nothing here about implied legitimacy because of the choice of objects, Durand would not reel over the sphere the way Boulee has. For Durand the choice of elements is only 1 part of the equation.Opinion-We are searching for meaning in our work and in our use of geometry- I would like to think that our understanding of the world and ourselves has mutated and hopefully matured over the last several millennium. I would think, intuitively, that we have more to learn and it is only through critical use and study of math that we will develop more and deeper meaning. Or maybe we can just keep making cenotaphs and placing temple fronts on banks without question, confident in its antiquated and implied meaning.
Monday, September 29, 2008
v+b+d
of note on Vitruvius :: Quite obvious is his insistence on both symmetry and proportion. But he’s not talking about proportion as a truth in a purely mathematical way. He writes about columns perceived as proportional from the angle of the viewer. Which means his in an interpreted mathematics, not a universal reality inherent in the geometric proportion itself, but one which respects, and maybe even needs, a context.
for Boulee :: He’s the strongest voice for symmetry, with a nod to proportion but not as priority. And while I can’t claim to know how far the comparison would carry, Boulee’s talk of the impossibility of pure invention of form (the comments regarding Perault’s argument), did remind me of the way Plato treats the term equality in Phaedos. While Durand clearly is the grander champion of economy, Boulee does, if indirectly, borrow Durand’s soapbox for a moment to reinforce his own by arguing that symmetry is that which the eye easily understands. I don’t think it too far a stretch to see this as an example of what Durand calls the “love of comfort and dislike of all exertion.”
Durand :: Instead of starting his categories with the geometric associations Vitruvius and Boulee both marry to symmetry and proportion, Durand seems much more interested in topological relationships. His call for “fitness” defines the formal requirements of a building by their behaviors, their events, their program*, instead of the categories of columns by height and feet as proportional measuring sticks.
*I can’t help but think of Koolhaas, particularly the TED talk by Josh Prince-Ramus on their Lousiville project :: http://www.ted.com/index.php/talks/joshua_prince_ramus_on_seattle_s_library.html
for Boulee :: He’s the strongest voice for symmetry, with a nod to proportion but not as priority. And while I can’t claim to know how far the comparison would carry, Boulee’s talk of the impossibility of pure invention of form (the comments regarding Perault’s argument), did remind me of the way Plato treats the term equality in Phaedos. While Durand clearly is the grander champion of economy, Boulee does, if indirectly, borrow Durand’s soapbox for a moment to reinforce his own by arguing that symmetry is that which the eye easily understands. I don’t think it too far a stretch to see this as an example of what Durand calls the “love of comfort and dislike of all exertion.”
Durand :: Instead of starting his categories with the geometric associations Vitruvius and Boulee both marry to symmetry and proportion, Durand seems much more interested in topological relationships. His call for “fitness” defines the formal requirements of a building by their behaviors, their events, their program*, instead of the categories of columns by height and feet as proportional measuring sticks.
*I can’t help but think of Koolhaas, particularly the TED talk by Josh Prince-Ramus on their Lousiville project :: http://www.ted.com/index.php/talks/joshua_prince_ramus_on_seattle_s_library.html
vitruvius - boullee - durand
Vitruvius definitely uses mathematics to idealize architecture as it relates to natural form, namely the human body. Proportion and symmetry come from the relationships of the body (digits, palms, feet, etc.). He also brings in numerology, the sacredness and/or perfectness of certain numbers (also based on nature and the body). He lays out applications of math in the thickness and spacing of columns, based on proportions (still based on nature). Value is applied to "perfect" symmetry.
Boullee also cites nature as the generator of perfection, but in terms of regularity, symmetry, and variety. Proportion is the combination of these three elements, once more relating to the "human organism." Very much along the same lines as Vitruvius, proportions and harmony are derived from nature and symmetry is "the image of order and perfection."
As Eric pointed out, Durand steps away from (and even criticizes) the reliance on natural form as inspiration, using mathematics in a more practical way. As an architect (and builder) he is more concerned with how regularity of form is more easily constructable, and thus more economical. He also uses mathematical reasoning in arranging building elements to establish a richer experience.
Boullee also cites nature as the generator of perfection, but in terms of regularity, symmetry, and variety. Proportion is the combination of these three elements, once more relating to the "human organism." Very much along the same lines as Vitruvius, proportions and harmony are derived from nature and symmetry is "the image of order and perfection."
As Eric pointed out, Durand steps away from (and even criticizes) the reliance on natural form as inspiration, using mathematics in a more practical way. As an architect (and builder) he is more concerned with how regularity of form is more easily constructable, and thus more economical. He also uses mathematical reasoning in arranging building elements to establish a richer experience.
Reaction to Readings
These readings really took me back in time. A time where Architecture was perfect (Vitruvius), where the follies of the mind were simplified by true natural beauty (Boullee), and then Durand. It seems to me like Boullee and Vitruvius had many things in common: they were both utopian, they both built this road to architectural superlatives. How they used mathematics is less obvious. Their system of dialectics parallels geometry, a sort of progression from simple to complex, yet this was not necessarily laid down heavy in the readings.
Boullee used geometry to legitimatize architecture. Meanwhile, it's difficult to follow anyone who states, "Weary of the mute sterility of irregular volumes.." When he begins the next sentence with, "An irregular volume is composed of a multitude of planes," Maya quickly comes to mind, as do NURBS surfaces, and it becomes clear that we have a much varied respect for the perfection of shapes. Math, I guess, is a tool for determining symmetry which leads to order which finishes with clarity.
Durand is sort of the grey goose. He tackles the five orders of architecture, Vitruvius & Boullee as well, by challenging established principles and at times by simply saying they are wrong (love the footnotes). Architecture to Durand is not imitation based on nature. Instead, he focuses on fitness and economy. He states, "The more symetrical, regular, and simple the building is, the less costly it becomes." The dispositions of the architect come together to make a good building. Durand doesn't use math the same way the others did. He uses math more passively while he critiques previous authors. I get a hint of Maya as well when he states, "Furthermore, is not such a model even more defective than the copy," and remember all the times I've tried to duplicate or copy things in my scene and everything gets screwy. Is he saying that non-geometric shapes have a history as opposed to definite location in space?
I realize I am just brushing the surface. The question, how do they use math, is not as clear as it was in Barr or Euclid. Knowing the discussion leans towards topology, we can only insert ideas and extract pieces of understanding.
Boullee used geometry to legitimatize architecture. Meanwhile, it's difficult to follow anyone who states, "Weary of the mute sterility of irregular volumes.." When he begins the next sentence with, "An irregular volume is composed of a multitude of planes," Maya quickly comes to mind, as do NURBS surfaces, and it becomes clear that we have a much varied respect for the perfection of shapes. Math, I guess, is a tool for determining symmetry which leads to order which finishes with clarity.
Durand is sort of the grey goose. He tackles the five orders of architecture, Vitruvius & Boullee as well, by challenging established principles and at times by simply saying they are wrong (love the footnotes). Architecture to Durand is not imitation based on nature. Instead, he focuses on fitness and economy. He states, "The more symetrical, regular, and simple the building is, the less costly it becomes." The dispositions of the architect come together to make a good building. Durand doesn't use math the same way the others did. He uses math more passively while he critiques previous authors. I get a hint of Maya as well when he states, "Furthermore, is not such a model even more defective than the copy," and remember all the times I've tried to duplicate or copy things in my scene and everything gets screwy. Is he saying that non-geometric shapes have a history as opposed to definite location in space?
I realize I am just brushing the surface. The question, how do they use math, is not as clear as it was in Barr or Euclid. Knowing the discussion leans towards topology, we can only insert ideas and extract pieces of understanding.
Saturday, September 27, 2008
Readings
The assignment is the assignment. Whatever comments want to be thrown out is fine, but do the assignment. Daniel, thanks for the post - I'm not sure either Durand or Boulle are doing topology. But that's an interesting point. Consider again we are asking a question about how architects use mathematics and are we clear on that? Look at how Vitruvius, Durand, and Boullee idealize geometry in different way, look at how they use the term symmetry. They are all talking about geometry. In vitruvius there is an interesting contradiction and there is one between Boullee and Durand, to all: the comments posted here are comments meant to address the assignments and the readings primarily. Do that first, them maybe the rant will have value. Maybe. Ok, so Daniel, good, go back and look up the word symmetry - how do they use it? (And yes, with respect to Durand, he is anticipating something about computation, but we'll take a closer look at that later.). Thanks p
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http://labdora.com/
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initial reaction to the readings
The Durand reading starts to imply a topological investigation of the orders of columns while questioning the initial reasoning behind the forms. Boullee starts to explore the topology of solids (whether he thought of it in those terms or not), pulling out their attributes of regularity, symmetry, and variety. Both writings start to touch on ideas that we've discussed, but beyond that I'm not sure the relevance aside from "hey look, these guys kinda got it, maybe."
Friday, September 26, 2008
The Value of a system..
I previously commented on the value of Topology, or more specifically, the lack of value in a system so myopic. I can't help but feel like I started a war of sorts between geometry and topology. I found myself defending geometry, or at least its relevance, while it was systematically challenged by the class discussion. In this war, I noticed an interesting relationship between these two factions: you can't dis one without using it. It was like Delanda's class where he kept using Ratified Generalities in order to show how worthless ratified generalities were. Was I taking crazy pills in class or did I stumble upon an insight: geometry and topology are complimentary, or rather, one surely supports the other in a tower of knowledge. If we remove geometry, topology collapses.
Topology will not get us anywhere without geometry. That bottle flying through the air follows a perfect arch, also created when you squash a circle. If you remove that arch, you are left with relationships. Relationships have no meaning without corresponding subjects.
Is anybody else picking up on this quasi-meaningless battle that I just invented?
If I could address Universality: To me, the study of anything universal is in the psychology realm. Freud, Jung perhaps can teach us something, but does architecture
or even mathematics belong there? I would say no. We bought mathematical universals in "Contact" with Jodie Foster, and left it there. Does a certain part of the brain correspond to feelings, sure. Can you condition a monkey to use a computer, why not? But does red, white, and blue make one feel patriotic? Do buildings with the Golden Section calm one's senses? If you dig a hole, dig another hole next to it, then put them together, do you get two holes? No. Not here, and certainly not everywhere.
Do we have any psychology majors out there? I wouldn't imagine we do, under my personal stereotypes. They search for commonalities, truths, universals. I happen to be an Anthropology major where we almost inherently search for differences. We find and place value in plurality, human interactions, in relationships.. And here I circle back again. This may not be as clear to you as it is to me, but perhaps topology is the study of intricacies that are too human (for lack of better term) to be universal. What if psychology is to geometry what anthropology is to topology? I don't care that you salivate when you smell beef. I am absolutely fascinated over avuncular disparities in Mongolian nomads (anyone want to read my dissertation?) To be sure, Peter may flick his nose at a circle or square and yet spend weeks infatuating over mugs and donuts. So maybe we don't have to dismiss geometry or even assign values to anything. Maybe we can agree that it is simply more interesting to step past universals and into something more contingent, more organic, more ...?
Am I taking crazy pills?
Tuesday, September 23, 2008
functions
Today we discussed a couple of issues. We are considering what topology allows us to consider as a logic of organization difficult if not impossible to conceive with just geometrical concepts and tools. One way of looking at this is ontologically -- and that only means the way in which something is said to exist. If i asked you to describe this water bottle, this seems non-controversial: it has such and such geometrical properties, such and such measurements, and so on. But now i throw the water bottle and ask you to describe it mathematically. All of sudden geometry seems insufficient and we need another mathematical tool to describe the arc of its movement. As Eric pointed out, that would imply the introduction of time, the change of position, etc. It would imply calculus. In order to mathematically describe the bottle being thrown, we’d have to introduce the mathematics of calculus. But note: there are also two different ontologies here. The thing qua thing -- that is the object as such as static. Then there is the thing qua event -- the bottle moving through the air. Renee: Good point, once we draw the trajectory we reintroduce geometry, we reintroduce a geometrical artifact, a curve – but also note that the curve would not have the curvature without calculus. This also plays into our discussion of diagrams. The curve is a description of the behavior, it is a diagram. The curve doesn’t necessarily describe the arc of movement, though it could – what it describes the rate of change, as long as it is continous. Here’s an interesting question: if I draw the bottle in two dimensions using geometry am I making a diagram? Ok, so, what I am asking you to consider is the nature of a diagram and how it can be used to describe the behavior of events. If we consider Plato’s ontology in relation to the Meno and the Phaedo, the highest form of existence is really ideas and forms: Eidos/Form. The discussion of Equality in the Phaedo, and Beauty and the rest in Meno are discussion about Universal Principals which we know only as pure souls but which we have the capacity to recollect. As humans we acquire knowledge through experience, but this is contingent – not universal. The mathematical demonstration in Plato then belongs to a kind of Ideality – things like geometry are Universal facts, they are not contingent on our experience: they transcend it. Mathematics as always been thought of in these terms and architecture has continuously purchased Uinversal principals of meaning through using such models. This is partially what I mean by a model of meaning. Le Corbusier’s use of the golden ratio and the modular are such examples. Ok, now consider the example from Bentham’s Panopticon and Foucault’s discussion of it as a function of a function. It is a diagram of relations of force. The incredible thing is that it doesn’t have any particular formation as, say geometrical object or space – it is a way of networking and creating space. Deleuze thought that this was important: a diagram is not a thing, but a series of relations through which things come into being. They are more event-related. And this is also why he is critical of the Platonist tradition and offers an important reading of ontology through Stoic ontology and the way in which it privilages events over things or ideas. So, one way to consider the problem of what is topology is to consider it as having a different form of existence than objects. This does not define it, but helps clarify and distinguish it from geometry. When you eat and apple there is an apple and then there are a series of processes that convert that apple into something else. We can consider these functions – could we say the functions map the apple on to other functions, nourishment, energy, etc? Well, at least we could say the entire digestive process of which there a numerous different events is not really a visible process – its visibility is not the same as seeing the apple. But we could diagram those functions and consider their topological properties – that is their forms of continuity. And this might now help – we can’t really see as diagram as a thing, but rather as something that relates, that networks a series of functions. So it is not a picture of a thing so much as a state of affairs and in that sense has to be abstract. When Choisy discovered the principle of asymmetry in the Acropolis and introduced into architectural notation for the first time a vector describing the arc and movement of the spectator he was introducing a new ontological concept in architecture – the experience of walking through the site, not just seeing the building as such, and this is what accounted for the odd juxtaposition of the buildings. Le Corbusier took this diagram and turned it into the architectural promenade of which there are now countless variations of which Koolhaas’s work is just one. Here is a case in which a notion of organization had to take on features of topology (that is continuity of functions movement, building, space, time, position, etc.) through the logic of the diagram. What this introcued to architecture was the concept of the event. Tschumi’s work is principally based on this. It is principally diagrammatic.
Sunday, September 21, 2008
Biology
Foucault makes an important reference to Cuvier's taxonomic reorganization of species according to a topology of functions. Note that the section in The Order of Things has to do with Modernity and an epistemological shift in which knowledge and discourse (how we see and what we say) move from a representational logic to an anlytical one. That is, that which constitutes the order of the world is no longer understandable on the level of representational comparisons.
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Design Office for Research and Architecture
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Question
Under what conditions does a mathematical model become explicit in architecture?
Design Office for Research and Architecture
68 Jay Street
Brooklyn, NY 11201
USA
646-575-2287
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http://labdora.com/
http://atlas.labdora.com/
Design Office for Research and Architecture
68 Jay Street
Brooklyn, NY 11201
USA
646-575-2287
petermacapia@labdora.com
http://labdora.com/
http://atlas.labdora.com/
sweeping up
We also need to understand -- at least confront a very basic and very complicated problem: architecture's use of mathematics. Is it so simple that we just use mathematics? I mean, is it clear how we use it? Ok among the texts i am uploading for you, and you'll have email note about the ftp site, is Plato's Phaedo. Look at passage 75 for this coming week and read maybe a bit before and after. Consider the use of "Equal." Could the term, and the concepts to which it applies be replaced with, say, Triangle, or Square? Think also of the following: is there something beyond the world of flux? In otherwords, is all knowldge experiential? How do we have knowledge of things like geometry? And now ask yourself whether the fact that a triangle always has 180 degrees when you add the interior angles is a fact of our experience or something transcendent of that? And what is the implication? All of this has to do with the Platonic theory of Forms, what these share with ideality and mathematics and the strange problems we have in architecture when we talk about the use of mathematics. in the following week we will look at Vitruvius, Boullee and Durand to see that problem in relief
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