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..

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”?

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.

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”

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.”

...

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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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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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..

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.

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.

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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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.

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.