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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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.





Design Office for Research and Architecture

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petermacapia@labdora.com

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