A little blur, so I just turned them into black and white.
Thursday, February 19, 2009
Wednesday, February 11, 2009
smooth & striated - vs - the fold
I pulled the same conclusions as pawel from the smooth/striated text. deleuze describes the attributes of both spatial qualities, but argues that they are able to shift back and forth - striated to smooth and vice versa. so, one quality could not exist without the other, since they are definable by what they do and don't have in common.
the fold text was a little tougher to get through - perhaps its easier if one is already familiar with leibniz's work? deleuze explains the fold through the idea of a finite body being transformed through an infinite number of folds. the labyrinth he references is therefore not a system of lines, but one entity that is now able to create space. the process of folding is why organisms exist. it creates dimensionality (not in the metric sense, though). so, there is never a scenario of just one fold in matter. there are always multiple folds within folds.
this idea seems impossible to represent architecturally, as eisenman attempted. if one of the essential concepts is this immeasurable folding, there is no way to include so much detail in a built solution. and, the way that I understand the fold is that it isn't a quantifiable thing... it is a force acting on matter. seems like it's not enough to create only a structural iteration of the idea. does that mean that no designer will ever be able to capture it? there are a whole lot of them trying, at the moment.
how does the baroque house fit into all of this? I'm having trouble making that connection.
the fold text was a little tougher to get through - perhaps its easier if one is already familiar with leibniz's work? deleuze explains the fold through the idea of a finite body being transformed through an infinite number of folds. the labyrinth he references is therefore not a system of lines, but one entity that is now able to create space. the process of folding is why organisms exist. it creates dimensionality (not in the metric sense, though). so, there is never a scenario of just one fold in matter. there are always multiple folds within folds.
this idea seems impossible to represent architecturally, as eisenman attempted. if one of the essential concepts is this immeasurable folding, there is no way to include so much detail in a built solution. and, the way that I understand the fold is that it isn't a quantifiable thing... it is a force acting on matter. seems like it's not enough to create only a structural iteration of the idea. does that mean that no designer will ever be able to capture it? there are a whole lot of them trying, at the moment.
how does the baroque house fit into all of this? I'm having trouble making that connection.
Tuesday, February 10, 2009
models
Deleuze sets up five types of models to indentify two different kinds of spaces occurring in various conditions through the models he is describing; however distinct or separate those two spaces are: one being the smooth and the other striated, they always run into some kind of specific relationships, some kind of non/-measurable conditions . For one the smooth and striated are two not identical conditions but are fully dependent on each other`s evolution; they constantly transform between one another or how the author calls is – intertwine, and however different the intertwining is, the relationship between elements within each model is a dynamic one. I think he is saying that the smooth space needs the striated in order to become one or the other. It’s not necessarily a matter of conflicting or resolving conditions, more that these conditions will always exist, and there is a play in exchange of energy; no means of simple invention or mathematical solution, but means of unpredictability. This is how the organic has evolved from scattered nomad cave life to agglomerated self-organized/sustained cities, and it is rarely/never one or the other since the division line between the two spaces is very abstract.
Jan 27 blog: Contrasts Between Topology and Geometry
Euclid’s three categories of geometry are definitions, postulates and common notions. Definitions serve to describe the most basic geometric elements and the figures that can be constructed from them. The postulates describe specific relationships that exist among geometric figures, and the Common Notions are basic statements of equality.
Euclid seems to primarily concern himself with space that can be fully rationalized and physically measured. His notion of space is somewhat limited in that it only allows for the creation of space in two dimensions. Space is conceived of, and described by the vocabulary set forth in the definitions, postulates and common notions. He does not establish a means of describing space that exists outside his language of points, lines, planes and figures.
Barr defines geometry as the study of mathematical space. He defines topology as a type of geometry but states that it also encompasses other fields. The two differ in that geometric spaces must, by definition, be visually expressive. This is not necessary for a topological space. Typology provides the means of expression for figures that would, in geometry, be otherwise indescribable. It deals with rules of continuity rather than rules of form.
It becomes easy to see the differences between geometric and topological spaces when looking the example of the geometric and topological pentagon (pg. 12, fig. 14). A pentagon is defined geometrically as a polygon having five sides and five interior angles. However it talks nothing of the number of faces, vertices and edges. The topological pentagon is not a geometric pentagon because it does not have five interior angles, but it still can be classified as a pentagon because it retains the same number of faces, vertices and edges.
Eisenman rejects the traditional ideas of Cartesian geometry and instead favors the idea of the fold rather than the point. He is interested in the way that the fold can change and manipulate the existing relationships of the horizontal and vertical, and figure and ground. He favors the ideas of Deleuze and objectile, which imply continual variation through the fold. He is interested in its affect on the object / event relationship.
He also is interested in the ways that the fold can be applied to Thom’s catastrophe theory. He explains that in catastrophe theory, a grain of sand that appears to cause a landslide is really not the cause at all, but rather the cause exists within the conditions of the entire structure. The fold in relation to architecture is similar in that it can serve as the unseen force that explains abrupt changes in form as well as in urban conditions. He sees enormous potential in the fold as a way to reinterpret and reframe what exists as well as connect the old and the new. He sees it both as a potential formal device as well as the way to transform architecture and urbanism from static objects to meaningful events.
Euclid seems to primarily concern himself with space that can be fully rationalized and physically measured. His notion of space is somewhat limited in that it only allows for the creation of space in two dimensions. Space is conceived of, and described by the vocabulary set forth in the definitions, postulates and common notions. He does not establish a means of describing space that exists outside his language of points, lines, planes and figures.
Barr defines geometry as the study of mathematical space. He defines topology as a type of geometry but states that it also encompasses other fields. The two differ in that geometric spaces must, by definition, be visually expressive. This is not necessary for a topological space. Typology provides the means of expression for figures that would, in geometry, be otherwise indescribable. It deals with rules of continuity rather than rules of form.
It becomes easy to see the differences between geometric and topological spaces when looking the example of the geometric and topological pentagon (pg. 12, fig. 14). A pentagon is defined geometrically as a polygon having five sides and five interior angles. However it talks nothing of the number of faces, vertices and edges. The topological pentagon is not a geometric pentagon because it does not have five interior angles, but it still can be classified as a pentagon because it retains the same number of faces, vertices and edges.
Eisenman rejects the traditional ideas of Cartesian geometry and instead favors the idea of the fold rather than the point. He is interested in the way that the fold can change and manipulate the existing relationships of the horizontal and vertical, and figure and ground. He favors the ideas of Deleuze and objectile, which imply continual variation through the fold. He is interested in its affect on the object / event relationship.
He also is interested in the ways that the fold can be applied to Thom’s catastrophe theory. He explains that in catastrophe theory, a grain of sand that appears to cause a landslide is really not the cause at all, but rather the cause exists within the conditions of the entire structure. The fold in relation to architecture is similar in that it can serve as the unseen force that explains abrupt changes in form as well as in urban conditions. He sees enormous potential in the fold as a way to reinterpret and reframe what exists as well as connect the old and the new. He sees it both as a potential formal device as well as the way to transform architecture and urbanism from static objects to meaningful events.
Wednesday, February 4, 2009
Tuesday, February 3, 2009
Summary Session 2 Conflicts
Vitruvius, Boulee, Durand, Eisenman
Deleuze, Rene Thom, Leibniz
Deleuze, Rene Thom, Leibniz
Problems of models of meaning
Conflicts between models of meaning.
We covered a lot today, bu we'll continue tor return many times to these examples of conflicts. Remember that architecture never ceases to make ambitious claims about its use of mathematics and geometry. And out first example points to a conflict between ideality and instrumentality in Vitruvius.
Its what I would call an internal conflict since the presumed idealization of mathematical and geometrical concepts is followed at the end of the chapter with a declaration of a reparative instrumental geometry. Symmetry is of course one of the priciples.
It is also a principle in Boullee and Durand. Their drawings point to rather different and I would say conflictual notions of architecture's use of geometry. For Boullee geometry and the example of the sphere embody Nature and Man's principles in perfect harmony. Geometry is both thing and symbol. In Durand, it is quite instrumental and if there is anything significant about symmetry it is because its an economic principle. In Durand's case furthermore we have a "method" that for the first time is analytical, probing, and generative.
First there is a grammatical spreadsheet of possibilities of primitive combinations. In subsequent illustrations of the Precis these develop into various syntactical formations. They become propositions about buildings.
I would say already JNL Durand is protocomputational.
We also looked at mathematical systems and certain differences, such as those betweem geometry and topology. And between those and the Cartesian coordinate system and Calculus and Catastrophe theory.
We looked at Eisenman's conflict with Euclidean Geometry and Cartesian space and his introduction of the Fold, Leibniz, Catastrophe theory and R thom, via Deleuze and Greg Lynn. Here one of the things at stake is the introduction of the ontology of events rather than the ontology of discrete forms.
Catastrophe theory combines calculus and the continuous variation/rates of change with topology. Its interest is to quantify qualitative states of change which calculus can't do on its own.
Ok, so this now becomes a new model but does so by showing the insufficiency of previous (Modernist) models. It is a kind of fifactic conflict. For the next blog please just read the two essays by Deleuze and identify how he uses models of meaning.
I want us to thoroughly distinguish between uses of computation for design and computation as a generative system.
In every case we see historically we have various modifications in geometry being applied to geometry and the transformation of design. With the algorithm and computation proper we've hit a limit since we are now no longer dealing with geometry and in fact I woud say possibly not even mathematics.
One last conflict. Eisenman like many others during the 90s takes the figure of the catastrophe fold and literraly transposes to the cartesian grid. Well, what's wrong with that? A lot. But for one, and promarily, the image of the catastrophe fold is a diagram - its not a thing. Esienman makes it a thing. A thingy! Punk.
Ok, hope this helps.
Peace out
P
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