Okay. Now, this is not the lecture I will give. I just wanted to give you a few glimpses. I've been thinking about the relationship between architecture and philosophy and why architecture in particular, also from the perspective of metaphor, analogy, and bringing terminology and tools of thinking into abstract thinking into philosophy, actually originating out of terminology describing spatial relations and architectural relations. So I just want to mention this because the moment of deconstructivism was also this: why was somebody like Derrida interested in architecture? Because when we think very generally and abstractly about the world, about society, we use metaphors. For instance, when we describe social order, we are using metaphors of the spatial order, and it makes sense because society is ordered spatially, always already through the order of the city, and these became the diagrams of thinking society, the diagrams of thinking also other domains of abstract knowledge. And I want to show that, just in response, before I show you what the next stage might be. Let me just think.
Oh, again. Sorry. No, I can't click anything. Oh, I don't know why this mouse is not working. Oh, here, here. Okay. Cancel. Okay. So wait one second. So the deep-seated power of architectural tropes embedded in most general operations of logic and language poses a limited limiting frame or barrier to innovation. The transcendence of this frame is difficult because the very patterns of conception, clear and distinct thinking, are locked within that frame. So, for instance, yeah, so the conceptualizations of the various institutions that call for architectural translation into buildings are themselves already dependent on ancient conceptual architectures that in turn were abstracted from the built architectures through and within which the original formation of these institutions unfolded in the first place: the family, the school, the hospital, the palace, the city. So basically, every brief, if you receive a brief, it will have a list of spaces and diagrams. This is already spatialized. So it will be a well-structured list of contents with a series of chapters and chapter headings. There is, you know, the composition of the brief into paragraphs and subparagraphs. These are architectural orders. You know, a large container with subcontainers, singular headings, meaning doors into these, if you like, rooms. The schedule of accommodation is already a series of boxes within boxes and boxes next to boxes on the paper. You think this is just the content, but it already has a spatial order, a traditional architectural order in the very way we think. And that is so we have here relations of exclusion, inclusion, subsumption, one thing nests into another. One paragraph is a subparagraph of an overall chapter, etc. These logics are very simplistic and powerful architectures that come out of the built environment. So sequences also, you know, in space they become sequences in thinking, etc., etc. They are then recycled back to us. This is old architecture giving us a brief to generate. The problem is then we are likely to regenerate this kind of architecture. We're then building these chapters as floors or rooms, and that's the problem. And somebody, sorry, I have to go forward.
So deconstructivism was about breaking this up. It was the vehicle by which philosophy returned to its root in architecture in an effort to break this vicious circle of repetition through direct action in space. So we have to, if we continuously live in an order which only knows nesting one within another, you come into the campus, the campus has a number of buildings, then you go into the building, it has different floors. It's only one order of logic of ordering, nesting spaces within spaces or adjacencies. And deconstructivist architecture has totally new forms of ordering there for us. We can't use these categories. You can't describe, for instance, our buildings in these terms. Um, anyway, so that's why we needed the philosophy. And okay, I want to show you.
I mean, for instance, the most fundamental operation in any thinking and philosophy really is distinction. You have to separate. You know, a concept is a distinction. Inside versus outside, male versus female, animal versus plant, your tribe, my tribe. And the distinction is the most abstract move, the most generalized move of any thinking. And actually comes from drawing a distinction, building a wall, sorting different animal types into different cages, different tribes into different villages, different status groups into different, you know, male here, female there. This is where you embody these distinctions, and the concepts are built concepts. And then we are building out, they become analogies, metaphors. So that is the fundamental profound deep roots of all thinking: walls, fences, trenches, demarcating social identity. How do you fix this? By putting different things into different places. And so there is basically you have an inside and an outside. And then you also subdivide the inside further. And it's very deep, you know, these are logic diagrams, right? These are set theoretical Venn diagrams. And what is set theory? It is the deepest representation of all logic, and all mathematics can be founded on these operations: enclosure and subdivision. It's like so.
And this is these were not invented. The form of the city, the bounding of a realm, is not something you think first and then do. It's to make a separate, you stabilize something. The circular form is the most efficient natural form. If you try to enclose something and make it super long and squiggly, it's difficult to defend. It's very expensive, vulnerable. So nobody invented this. The circle is fundamental, a material necessity. And how do you grow? Series of concentric circles. So the form of the city is a natural crystallization of ordering moves. But then this diagram of concentric circles, in the Renaissance for the first time when you draw a city, you draw that but much rigorized. And then this diagram becomes the thinking matrix of many other things, as I will demonstrate to you. Okay. So when science starts, the science of zoology, where you distinguish different plants, it starts like this. You just put them in different places. It's like the garden where you plant. Here you plant the tomatoes. Here you have the potatoes. Here you have the chickens, animals. And this classification is first of all a physical act, and then it becomes a conceptual reference of that. Then you can stick a label on this, then you can draw it. So the science of zoology is based on physical classification, physical fencing, then drawing this like the Renaissance drew the city later, and then you get more complicated nesting. And these diagrams are at the very heart of the science of biology or let's say zoology, and they are architectures, fundamental and profoundly the architectures. So, and this is nearly the only move we've had for thousands of years.
Bounding a realm and then subdividing it with basically that nesting logic. And that's also a classification system is nothing but a thinking system. And if you pick up any textbook, any science, the book is a representation of that. It's that bounded thing and inside it has chapters and subchapters. That's the way you can order, the only way you order a whole science. You know, you have these different subdisciplines and then the sub within this and then different theories within this, and the book content list is structured like this. And that's the most general overview conceptualization. Your map of the science is a simple, very simple architecture, and it's like this. And so when you in the Renaissance when science is starting, these ordering of the instruments of categories, it is like the tool cabinet of the handicraft person. This is a sorting matrix. If you go now to a museum, how do you build a collection? It is, you know, the archaeology museum. It's these shelves. They become diagrams. They become filing cabinets. They become libraries. That's the way we think. We think architecturally. There's no other way of thinking. Language itself is operating like this. And order is a place for everything and everything in its place. And look at this, top right.
So in the Renaissance, when you have the first proper science and books about certain domains, for instance here an ethics, the system of virtues and vices. How do you think about it? You take the city plan because nothing else. You have no other thinking tool than the city map when you can then kind of segment it, a hierarchy of central and less central and segmentation. The system of virtues, the system of vices. Um, can't see. And what is the image of the cosmos when you want to think? It's again the city, which nobody invented. We generated the city gradually, building out from a circle which is the necessary bounding, the most efficient material bounding the container extension, and then we draw it, and then that's everything we want to understand. Understanding means fitting the domain of knowledge into the city diagram. There's no other way of thinking. That's my challenge here. Thinking the cosmos, center, periphery, upside down also in three dimensions. So what is this? 1582? It's a memory system. It's a kind of map of all human knowledge.
And it's obsessive. There is only one way to systematize knowledge. It's drawing it into the city map and symmetry and proportion. There are other diagrams, and I don't have that here, but Immanuel Kant is reflecting in the 18th century, a few hundred years later, on the, he's trying to make the map of our mental faculties, the fundamental categories by which we order our thinking. His drawing, I wish I had this here, but it's a classical architecture. It has four points. It has two symmetry axes. It's completely symmetrical. It has four headings. So it's substance, causality, relation, and quantity, four. And each has three subcategories. And that's the systematic system of all judgments, all types of thoughts fits into a Villa Rotunda plan. And that's his idea of how you know that this is systematic. Systematic knowledge is simply he wants to have the symmetry axis and he wants to have under each heading three subcategories. It's obsessive. But since up to this time all architecture which wasn't thrown together like a crazy village was that, and this became the only diagram, and that's why it's interesting. When architecture suddenly breaks through this, it's exciting for philosophers because we keep habituated into this logic of containment, of symmetry, of repetition through our architectures. Ah, here it is. I didn't.
So, this is another of Kant's. Everything in Kant's Critique of Pure Reason looks like Villa Rotunda, let's say, the most ordered of all architectures, the classical architecture. And that's I think is very symmetry and completeness as qualities of thought. He wouldn't accept that if it was asymmetric then it can't be the truth. The truth must be like that. And of course looking back now it seems absurd. It's the formal a priori coming out of architecture into all thinking anyway, but also so we have this category of nesting classification. The other thing we have is network. Even to this day, if you look at any science diagram, any science diagram, it's boxes within boxes and maybe lines connecting boxes. These kind of relation diagrams, flow diagrams, where do they come from? Pathways. So we have boundaries and then we have pathways, and we can draw them and rationalize them and architecturalize them, and then we get nodes and connections. The whole science of network theory, graph theory, any diagram in science fits into this category or fits into the nesting category. Can you see the obsession? How much we are dependent on physical spatial logics which we then emerge. Nobody designed that. Then we draw and design. This is a city plan. Cutting these pathways and then making a drawing and then using that drawing as a thinking tool. That's abstract thinking is totally dependent on architecture. But this architecture wasn't invented. It just emerges and then we kind of bring it into architecture. Finally, look at this. And what are these? They're just networks of pathways. We have nothing else up to recently.
So now that's why I was so excited about on the right hand side. These are the two topics: boundaries within boundaries within boundaries and networks, usually kind of branching networks. That's Chris Alexander. The breakthrough is this. Nobody has used, very rarely and hardly ever you see these kind of diagrams. But it's extremely important. Some elements might be in more than one subset. Subsets could overlap. Overlap is a mental operation. And networks could be less ordered than grids or branching. They could be more complex and there could be multiple paths. So that was a breakthrough. These should be very common in science. But since all buildings are like cities are like this, we didn't have that. And the revelation here is we have to go there with architecture. Social organization is more complex. We have overlap. You can be part of many circles, many competencies, many teams and disciplines. Overlap is a social reality. Let's build this and let's think it and let's diagram it. And so, but still again, space syntax is only based on this. Social network theory. This is sociology when it wants to clarify, summarize, what does it use? Path network. Have nothing else to go by anyway. And so, and I want to bring in.
And the whole of mathematics can be founded on set theory. All mathematics can be brought back to set theory. What is set theory? It's this, it's architectures. But they have of course doing overlap and Boolean algebra. I feel like anyway, there's interesting things that systems of language, they all build their own architectures. And there's French, okay, French, German, Danish, Italian. This means tree, wood, forest. There's no, you can't translate these because they have dissected the world differently. So when you, each language makes cuts. The world is infinitely complex. When you put a language, you're putting in distinction. You draw a cut here, but each language draws these cuts somewhere else. If they were drawing the same cut, then you can just swap out the label. Tree is Baum, but they haven't cut it the same way. So that means literally you cannot translate. That's why it's interesting. What is, how do the Chinese translate? They don't have the same concepts. They have set these distinctions which emerge out of practice, out of routine differently. That means absolute untranslatability, no matter what you try, because the geometry of the language system of distinction is different. You know, you could classify the animal kingdom in various ways. Amphibian versus reptile versus this, you know, concept. So if you do that in different ways and languages have done that, you cannot translate anyway.
So I just wanted to show that the kind of architecture of modernism was already breaking the classical mold that you allow yourself to organize. If you would look at any social organization of the 19th century, obsessively symmetry, it's crazy. But asymmetric they couldn't tolerate. That means the system isn't systematic. There's something wrong. It's out of balance. It's out of whack. We've, you know, modernity, we managed to have a social organization which is asymmetric, but it's still nested tree. And we have these kind of, we tolerate these kind of architecture. We tolerate these kind of institutions. But by the way, in the 70s and 80s you wanted something else. They never have overlap. And that's where we, for instance, this is a typical modernist. You allow asymmetry, but you have each part is separate and internally repetitive. And here we said, okay, why we let them fuse? We have these zones of overlap and interpenetration and no longer repetition but gradients really. This is a very old project anyway.
So, so this is then you jump to something like this. Suddenly instead of set series, circles within circles or even just overlapping circles, you have now degrees of belonging, separation, fusion. How much do these two are in one group? How much are they separate? And so basically set theory becomes fuzzy logic. The boundaries are open. They are blurred. They are both you have here in these diagrams. You have both overlap and fuzziness. You can be in many sets at the same time with different degrees depending on your centrality position. So there's a much more intricate and sophisticated representation of some logic, some order. And you should order complex social environments like this with more repertoire. But we still have an a priori. We don't do random things. That's not order. But now we not only do nesting with sharp boundaries. We do overlap, interpenetration, negative Booleans. And we're doing it not with sharp but with degrees of belonging. And as you know, fuzzy logic was required to deliver for something like pattern recognition. A lot of AI operations. Logic used to be sharp Aristotelian logic, set theory. You're either an element or not. You're either a subset or not, complementary, etc. And this logic, this mathematics, was running against the wall when it came to certain capacities. And fuzzy logic, everybody understood, allowed us a huge leap forward in technology. All pattern recognition is fuzzy logic based. And just as an example, this means this logic is superior, is more sophisticated, and therefore I want to build, I, we should live in this logic. Architecture has to become fuzzy logic. That's the project, let's say, of.
And also like this, this radical idea that you not have one pattern and another one next, that you inter, you have multiple reference systems operating on the same substrate, on the same logic, on the same audience, on the same space. That's a dramatic increase of information richness and power of ordering. Because when you put your finger in there, you could be, if I'm here, I'm in several places. I'm in the circle. I'm on that squiggly line. I'm on XY pavilion. I'm simultaneously placed multiple times, and that's powerful rather than having to choose. I'm either here or there and have only one set of system. I'm only part of one system and I have to choose. No, you don't have to choose. Layer them in. That's also when you write a text, when you describe a society, when you describe a science, you can layer it in. It's not that you have to make a choice and have only, but also you can live like this. The city can be like this. The space shouldn't be like this. The architecture can be like this. So and in the city it's like this. People living, this is a map. It's a certain territory. There are different populations living there. Some populations always go to the local village. They never go to the city. They only know they're close to here, here, here. There's another group of people, white collar professionals. They never go between here. They don't know. They only know where they are relative to this. So these two populations have different maps of reference, different connections, different relations, and they exist and overlap in the same space. So it's a social reality. But our diagrams, our architectures, they're asking us to choose. They're asking us to only impose one order. But we should have multiple simultaneous orders. So this idea of simultaneity anyway.
So these are the kind of things I wanted to bring in. I had another lecture prepared, but because of the challenge of architecture and philosophy, architecture and the fundamental principle of thinking and of logic, and that we can expand logic from a simple Aristotelian logic to a kind of probabilistic and fuzzy logic, multi-reference logic, complex network logic, etc., rather than just grids, and that this is why, you know, and Deleuze for instance was interested when he talks about smooth versus striated space. Striated space is the hardline distinctions, and he said no, we don't want that, we want smooth, we are more or less in many places and we shift gradually from one to the other. That's like soft logic, that's fuzzy logic. And so these philosophers came in to help architecture to expand our thinking, and then we make it manifest in the world. But the philosophers were interested in architects because here they can basically help us break up old dysfunctional logics, old dysfunctional philosophical thinking, and expand our mind because the mind is a collective mind which comes out of practice. It's not all here and then we do it. We reflect, we absorb, we grab and learn and then reapply. That's why, you know, basically you could say yes, there are these metaphors: beg, grab, conceive, you know, grasping means understanding. These are etymological kind of roots, but I'm showing the kind of physical spatial architectural roots because we, the language evolves in the built environment we construct, which is always a constructed environment, never a wilderness. A constructed environment means it has already always already classified, distinguished, and connected the different domains and elements. Anyway, that's my pitch on that one. And this is the kind of, yeah, the opposite of this order is not chaos but sophisticated multi-layered, fine-tuned simultaneity of many orders. That's the pitch. Thank you.
