CANON / QUANTUMETRIC

Takashi Yamaguchi

1  Introduction

In the movie "Space Force," a staff member who has been on Mars for many years, unable to return to Earth, has a conversation with Erin on Earth and finally says in tears. 'Let me tell you something. Tears float here. It's the same as on Earth, the same salty water as in the ocean. I miss the earth." 

This sentimental and casual line contains an important meaning. 
Life born on earth is at once part of the earth and part of the earth. In other words, in nature, all creation is finely related and continuous, like a nested structure, although the parts and the whole are inversely related to each other. 
The natural creation is thus also related to its environment, and is both whole and part. It is a molecular structure and has a canon that relates to matter in general. 
Architecture is also a creation. But architecture (especially contemporary architecture) is not like that. What is the difference? It seems to me that an important issue is hidden in this difference. 

Today, in all fields of scholarship, subdivisions are being created. However, each of these subdivisions does not intersect, but only sediments and accumulates, remaining in a stratum that has become rigid and fixed over time. The number of divisions of the subdivisions increases, moving toward the minuscule, which may be called differentiation in the sense of a willingness to let the exact characteristics at the minuscule point emerge. However, this differentiation, although it has a viewpoint from each minuscule point, still seems to be left in fragments. 
There is also a movement to grasp the whole by giving probabilistic approximations and fragmenting them and then aggregating them, without precisely scrutinizing the whole. This is so-called integration. 
The question arises as to whether the whole can really be grasped from the viewpoint of averaged fragments or from the viewpoint of aggregating approximated fragments. Such a question seems to me to be connected to the previous question. It seems to me that some important meaning is hidden in the derivative and integral, which are a set of parts and the whole.

This essay starts from a simple question that I have been asking myself, stemming from such a problem of differentiation and integration, and moves toward the disclosure of my own architectural theory. 
In particular, in the present age, the question of subjectivity is of particular interest. However, it is also a fact that, in denying the subject, the diversity of objects has been emphasized and the canon has been disregarded. 

Originally, canon was an ancient Greek architectural art meaning (standard). The sculptor Polykleitos linked sculptural creation to mathematical relationships based on his study of the proportionality of the human body. It also influenced music and the Christian concept of canon. In Western Europe, such canon has been emphasized.

Architecture is not merely the pursuit of a functional and beautiful stand-alone object, isolated and unrelated to the whole in itself. Architecture is the result of thought and the fruit of critique, but it is never independent of the whole. It is from this perspective that I would like to examine the concept of architecture for the next generation. 
First, as an introduction, I would like to begin with the worldview of the ancient Greeks. How did they view the world? Then, I would like to overview how derivatives and integrals were born in the development of mathematics, which later attempted to view the universe objectively. Then, we will understand that there existed the viewpoint of an architect, not of a scientist. With this as a starting point, I would like to begin this discourse.



2  Geometry and Motion

In ancient Greece, people sought geometry as the entity that constituted the world. They tried to grasp the world through perfect geometry represented by circles and spheres. 
In Aristotle's "Celestial Theory," the universe was divided into the celestial and the sublunar worlds. In the celestial world, there is neither creation nor annihilation, everything is regular, and motion is a perfect constant velocity circular motion. In addition to the conventional theory of the four elements, the so-called aether as the fifth element caused motion, and as the celestial motion of concentrically arranged circular motion, it indicated the perfection of the universe. 
In the sublunar world, everything is made of the four elements earth, water, air, and fire, and everything is created or annihilated by their union or separation. 
Motion in the lower lunar world is divided into "natural motion," which follows the nature of objects, and "forced motion," which occurs when an external force is applied to objects. Motion is associated with the elements that make up the world, and the four elements earth, water, air, and fire are assumed to produce linear motion. 
Each element had a unique place to occupy, which was thought to be a concentric spherical layer of earth, water, air, and fire, in that order, starting from the center of the earth. Natural motions in the terrestrial world, such as falling and rising, were also explained on the basis of the elements. Natural motion was understood as an objectivistic movement toward a unique field. In other words, the elements that make up the world have their own unique fields in which they should exist, and they arise by having a purpose to move toward their own unique fields. For example, earth, water, air, and fire all have a specific field, toward which earth moves downward, water flows sideways, air stays, and fire moves upward. 
Anything in motion must be moved by something. In other words, "forced motion" occurs when an external force is continuously applied. When the force is lost, the motion returns to its natural state (stillness). 
This ancient view of the universe was an ideological and geometrical worldview at a time when motion was not yet understood.

And it has been seen as really unmemorable from the modern point of view. This view of the world has been seen as inferior by the progressive history view from a physical perspective. Here, however, we do not take that view. 
Later, Johannes Kepler discovered the laws concerning the planets and made achievements in celestial theory based on the elliptical motion of the planets. But he too was fascinated by geometric entities. Influenced by Pythagorean and Neoplatonism, he held that the size of the orbits of the planets was determined by geometric entities called regular polyhedra, which are Platonic solids. He was adhering to the constructional nature of seeking mathematical entities of number, proportion, and geometry. In other words, there existed a consciousness that did not deviate from the principle of construction as a norm.  



3  Isaac Newton's arrival

This view of the universe as a geometric entity and the theory of motion were rejected with the advent of Isaac Newton. Newton thought in terms of the relationship between space and time in terms of velocity.
He did not make any hypotheses, and his theory was established by denying Aristotle's theory of purpose. In other words, he adopted the positivist attitude of seeking the truth by bypassing the search for the ultimate substance of things.
The differential and integral calculus discovered by Newton extracted the principles for describing the physical phenomenon of motion.
In Newton, the work of René Descartes is important as a foundation.
Descartes presented the concept of extension. All sensory things other than extension, such as firmness, weight, color, smell, etc., were dismissed in favor of pure, abstract materiality.
Furthermore, Descartes produced coordinates, and Newton's worldview is the inheritance and extension of this Cartesian grid created by Descartes. Newton uses this Cartesian grid to explain motion. He takes the viewpoint of the transcendent Absolute, which transcends the viewpoint of each individual human being, and aggregates and transforms each relative coordinate into an absolute coordinate, opening up absolute space and time. In other words, it is a completely independent and transcendent space and time that is unaffected by anything else. While he said he did not make any hypotheses, he assumed only one. Newton denied Aristotle's space and time, which held that time is caused by the motion of objects and that space does not exist independently of objects. Thus, space and time became a priori according to Newton.
Newton ceases to seek for entities and advances Descartes' concept of space to a transcendental absolute coordinate system, all for the description of motion. He affirms complete transcendence. The important thing to note here is that because he set up an absolute homogeneous space and time, he created a surveying concept in which entities with extended concepts are additively superimposed on abstract coordinates. The surveying concept was only possible with an unbiased space-time. This concept of surveying was possible because the cosmological model was not expressed as a geometry of entities, but was transformed into a platform of a transcendental absolute space that has no entities. It describes motion on that platform. Furthermore, the concept of surveying succeeded in making the quantity of human experience continuous with the infinite quantity of transcendental intuition, which Kant could not do. This is because the platform is a transcendental absolute space, which can also describe infinite quantities. This concept of surveying contributed greatly to the subsequent development of physics.
Thus, Newton's unique conception of absolute space and time was accepted as proof of God's existence, regardless of his intentions. Later, this homogeneity would become dogmatic, and would be precipitated as a problem to be solved in modernist architecture.



3.1 Concepts of Calculus

Both the derivative and the integral, by means of the concept of infinity, direct experience toward the transcendental concept of intuition. The derivative attempts to give authenticity to the concept of mean.
The derivative begins with the ratio that is the primitive of all things in the West: df(x)/dx, the ratio of minute parts. Mathematically, this ratio is the average of an instantaneous change, or slope. In kinematics, it is the ultimate average of the amount of change at each point, i.e., the velocity.
Aristotle's concept of motion, which had been a mystery until then, was made expressible by the derivative, which quantifies the instant. Differentiation also means viewing a curve as many straight lines. In other words, the focus is on the minuscule point of contact in the tangent line and attempts to converge from the attributes of the local neighborhood to the minuscule. From the viewpoint of the proximity, we move toward the microscopic viewpoint. In other words, it conceals potentiality at a point.
What is an integral? Integral begins with the product of minuscule parts, f(x)dx. Mathematically, it is the integration of an instant, i.e., a broadening that begins with a minute part, i.e., an area.
Kinematically, it is the accumulation of changes, i.e., positional energy.
Integration is the capture of the whole from its parts, i.e., the sum of its parts. And each part is not exact, but approximate. By infinitely dividing, it has a vector that continues to expand and extend from its neighborhood and has the property of moving from the parts to the whole.
Such an integrated whole already contains the attributes of each approximate part, that is, the approximate viewpoint. As the potential of such approximate viewpoints is infinitely subdivided and expanded into a whole of infinite sums, the number of viewpoints grows and the important focal points undergo a process of diffusion.
The question arises as to whether such averaged differentiation and the direction of product differentiation, an accumulation of approximations, capture the whole. There seems to be some important meaning hidden in the differentiation and integration, which is a set of averages and approximations.



4  Pre-Differentiation and Integration

Let us now look at a certain beautiful Western European city.
The subject of this view is not a specific city of choice. Let us assume a fictitious city, emphasizing and generalizing its characteristics.
This assumed city is filled with canon and historicity, so that even new constructions are built in the face of past history. The architecture is also built in subtle coordination with the urban context, but the most important fact is that this beautiful city is composed of an accumulation of architectural elements, which are the smallest parts of the city. The architecture of this city exists in a canon built on the mathematical relationships of ratio and geometry. The concept of infinity contained in the golden rectangle, the ratio of spacing between columns, and the ratio of width to height are the basis of composition in architecture. This means that the basic concepts of differentiation and integration are already included. Ratio is the basis of differentiation, and the concept of infinity is the basis of differentiation and integration. For example, the golden ratio represents God's providence that moves toward the maximum and the minimum, and that seeks to transcend the human world and continue into the infinite universe. Furthermore, in an attempt to fill everything in a building with divine providence, the building is constructed with symmetria, in which the parts and the whole are divisible by integers. Therefore, the architecture has an interest in detail.
Subdivision is fundamental in so-called architectural generation. Each mathematically subdivided part of a building is related to other parts and is generated in mathematical consistency with the building as a whole. Such mathematical consistency constitutes a mirror-image relationship with the surrounding area. In this way, the relationship between the buildings and their neighbors is adjusted, and the surrounding area, and even the city as a whole, is continuously connected. This indicates that this entire city retains a process of subdivision and superposition that can be described as pre-differentiation and integration.
This makes it possible to generate mathematically across all scales. Thus, universalization is ensured, self-referentiality is possible, and as a result, historical context can be generated through the repetition and multiplication of similarities.
Furthermore, in this city, the volume is flat and expansive, and symmetrical centripetal spaces exist here and there. The city has a certain dimensional system based on the proportion of the Vitruvian body, which forms a flat volume with a certain height. Architecture and cities are also considered as canonical mathematical volumes that are continuous with the human body. In general, Western European cities are built on such a mathematical volume, which guarantees their extended constructiveness.
There are not only squares as external spaces, but also spaces as internal spaces with the symmetry of cathedrals. There is also the linear space of the street. These spaces are clearly separated from the volume of the building. The non-touchable space is continuous with the touchable volume and is Gestaltically reversible. The two are topologically continuous throughout the city, even though they are inverted. In this city, there exists a mathematical nature as such a canon. Because such normative mathematical similarity exists in the city, the city has a clear context and maintains a beautiful aspect. It is not that beauty exists in a city because beautiful buildings are individually arranged in an additive manner. In the creation of a city, symmetry and proportionality as a system of pre-differentiation and product differentiation, based on canon, are the requirements for the creation of a unified beauty.
Because of the strong dominance of such a mathematical construction of the city, it is not possible to easily erect buildings that deviate from the mathematical context. This is because it would create an ugly dissonance. The same is true of music. There is a definite canon. Music, which began with Pythagorean proportions, is also mathematically structured, so any whimsical deviation would be ugly.



5  Introduction of the concept of infinity

Let's take a look at the modern city. It is characterized by verticality, as symbolized and represented by Manhattan in New York City. Verticality is an expression of so-called capitalism. The excessive desire of capitalism has led to the vertical expansion of the volume of office buildings. Excess invites the concept of infinity into the concept of subdivision and superposition, and shifts the concept of pre-derivative and pre-integral into differentiation and integration. Then, a new phenomenon emerges, backed by this new concept of differentiation and integration. In other words, problems that had been confined to the concepts of pre-derivative and pre-integral are brought to the fore.

Only the height parameter of this system expands abnormally and sweeps skywardNote 1). This system uses technology as a means to an end, but at the same time represents technology. Capitalism averages and approximates everything and tries to control people on a common platform. Based on the homogeneous absolute space originated by Newton, the units of space are created based on a congruent grid that can be formed anywhere, eliminating unique fields. The whole is constructed by averaging through differentiation and integrating it. This expanding system swallows everything. In other words, architecture based on a homogeneous grid that emphasizes economic efficiency is being built all over the world. It is a system in which man's diverse and miscellaneous desires are averaged and differentiated as a form by the capitalist system, and then integrated excessively only in the direction of height by a program that is organized in an approximate manner. Instead of the standard volume and space based on the human body as indicated by Vitruvius, floor units standardized by economic efficiency are uniformly piled up and extended vertically in an abnormal manner. There exists a power that breaks down even traditional canonical forms. This is a world of distorted integration that can only be achieved through technology driven by capitalism. A world in which the oppression of average verticality has been expanded will emerge.

Jacques Lacan, in his psychoanalysis, divides desire into three categories. Namely
Desire (besoin): a bodily reaction to sustain life, a basic need.
Demande: a desire sought in the form of a signifier, linguistically segmented.
Desire (désir): something that is constituted in the cleavage between desire and demand.
According to this definition, demand (demande) is increasingly linguistic, and today, with the language of global capitalism, the rift between desire (besoin) and demand (demande) is wide open, and desire (désir) is becoming over-constituted and bloated in this rift. Furthermore, desires (désir) are beginning to be manipulated by information technology. Architecture begins to be generated based on such desires (désir). This is why contemporary architecture and cities are beginning to transform.
Here the bi-directional vectorial thinking of differentiation and integration, while very important for the generation of architecture and cities, can become a mere device to accelerate desire, and is complicit in what is hasty and careless. In current architectural design, the relationship between the part and the whole is governed by the easily controlled approximate framework of the mean. As Gottfried Leibniz detested, there is an attempt to universally extend the Newtonian world (congruence through homogeneous grid) in which everything is homogeneous and full.
It can be said that the liberation of human desire for excessive profit has turned diverse cultures and histories toward uniformity and simplification of man himself. Modernism was such a trend. Modernist architecture has become a servant of the technology that accelerates desire. However, architecture was supposed to transcend this framework and build a new generative system that embraces diversity.

Mies van der Rohe seems to occupy an important position in this architectural direction, presenting some thought-provoking concepts. I would like to discuss it in detail below.



6  Mies van der Rohe's place in contemporary architecture

Modernization is an enormous energy that expands as new production continues to emerge; even the subject is positioned as an entity that is fully integrated into this process.
Mies already existed as the discoverer and practitioner of the principles of modernism. Whether he was aware of it or not, the existence of the SUBJECT was retreating into the background, about to be engulfed by the flow of modernization.



6.1  Differentiation and Integration in Mies' Work

Sprouting of programmatic form generation
Modernity always seeks to create the "new," and there exists a logic that seeks to dismantle the various forms that have been generated in the past. At the same time, modernism is also a process of homogenization that makes everything flat and interchangeable. Mies departs from Newtonian absolute space, which defines the universality of distance and the absoluteness of position, and the thought of Newtonian differentiation and integration is at the root of his thinking.
Le Corbusier sought fertility by accumulating componentized and discontinuous spaces. Mies, however, paradoxically achieved spatial fertility by simplifying the space to a flat plane, through the various perspectives it encompasses.



6.2　Barcelona Pavilion　1928-29 

There is no classicist relationship here. Classicism here means that the relationship between materials, structure, and tectonics is tightly segmented. The Barcelona Pavilion is only a flat surface, and it is completed by sweeping it. The architecture can be grasped only from the information on the plan. The cross section is only a parameter. It is a kind of design method that leaves the parameters to the plan as if it were given a height. In this sense, it can be said to be the starting point for the mathematical generation of forms by computer programs that would come later.
Each freestanding wall is dematerialized and mapped with a material. The wall as a surface is freestanding. It is the freestanding wall that has lost its meaning, and there is no wall of traditional composition. There is no wall as a support of power. There is only a cut-out constructivist wall. There are only points, lines, and surfaces as elements of architecture in which glass, floors, ceilings, and walls are abstracted. It is not so much ambivalent to classicism, which uses the column as its criterion, but rather it has moved away from the classical framework and is something completely different. It is not so much a functional program as it is the very program by which space is produced. It can be said to encompass the multipurpose space as a functional program. It is not creating a homogeneous space, a multipurpose space as a program.
Furthermore, while departing from Romantic Classicism, he broke away and created an image of Suprematism, presenting the ideality of the plane. It is neither a framework nor a grid, but a space in which a plane is parametrically swept vertically. Transparency emerges through the absoluteness of the plane. The cross section is hidden behind as a parameter. With the absence of such a cross-section, there is no concept of a beam, but a series of abstract surfaces. The plane is important, and the ideational is lodged in the plane. Thus, the plane is a purified entity. The cross-section is merely a parameter that lurks behind and complements it. It can be said that Mies adheres to the principle of the plane even more strictly than Le Corbusier's domino system. Note 2)
There is, however, an underlying Newtonian differential and integral thinking. It is the act of differentiating the whole in proximate time. Then, what has been differentiated is now integrated. In this process, the nearby time is transformed into a neutral time with universality. In such an act lurks a uniquely programmed integration. The planar fragment of solidified time is made integral, and the object is generated by the parameters of only the time flowing in the neighborhood. In other words, it is a parameterization of the plane and a mapping to the surface. In the process of Newtonian differentiation and product differentiation, anything that is not easy to manipulate is discarded. The existence of the subject as an intelligence that incorporates temporality from the distant past, like Peter Eisenman, has evaporated, and even the reason for the existence of the object has evaporated, so there is no temporality as criticality. The existence of the subject as an intelligence that incorporates the temporality from the object has evaporated, and even the reason for the existence of the object has evaporated. In other words, it is the germ of the program, and in the sense that it is programmed without regard to questions about the subject or object, it can be said to be the origin that influenced the program fundamentalismNote 3) that emerged later.



 6.3  Glass skyscraper

This project was undertaken when Mies began working as an individual, and it was to determine the direction he would take in the future. As can be seen in these works, the flat surface is raised as it is. In both cases, the cross-section is not altered, but the shape of the plane is changed. The flat surface has broken free from the spell of grid and has become a flat shape that expands around crystalline shapes and flowing curves.

Even if we take into account the technological constraints of the time that led to this cross-sectional form, the fact that the subsequent Barcelona Pavilion and the Farnsworth House were built on a scale that was hardly subject to such technological constraints, and yet used the same technique, makes it possible to understand that the building emerged from a more conceptual elaboration. The fact that the building is built in the same way as the Barcelona Pavilion and the Farnsworth House, which are on a scale that is hardly constrained by such technological constraints, is understandable. In other words, it is a Newtonian differentiation and integration. We can read a conceptual attempt to hide the existence of the cross section in the background and treat it as a parameter. In this sense, we can recognize a part of such conceptual exploration in these glass skyscraper projects.
Mies reduced everything to the plane. This is in stark contrast to Le Corbusier, who believed that the plane should control architecture. Mies simply reduced all architectural mobility to the programmatic mobility of the sweep. He did not see architecture as being filled with energy and mobility, as Le Corbusier did. In this sense, Mies's planes can be said to be programmatic planes, leaning toward and transcending Newtonian absolute space. He made the plane into a device with cross-sectional parameters, reducing all of architecture to a parametric program. 



6.4  The Hidden Problems in Mies' Architecture

From the Problem of Temporality to the Problem of Critique　
Mies only created an object that existed only in the neighborhood of temporality. He succeeded in establishing an aesthetic object, but failed to impart a criticality that is important for architecture. 



6.5  Program Issues

Mies' architecture connects to the problem of programs in our time. This is because the program introduces proximate temporality, but does not take into account the entire past time of anteriority.
Focusing only on proximate time means giving in to the control of functionality, which in turn leads to giving in to capitalism. This trend leads to programs, which are increasingly unrelated to interiority and criticality.
This leads to the idea of architecture as projection. In other words, the search for the interiority of architecture is abandoned in favor of the mapping of the exterior onto architecture. In other words, it is a break with time from the past. The past exists only as an archive. There is no criticality in this. If the past is sealed up as an archive only, it will only be forgotten. If so, is it good for the past to be placed under the control of technology that reuses it with AI? I don't see the SUBJECT there. Mies' consciousness only moves solemnly toward an artisanal tectonic in nearby temporality.
Such a movement goes beyond Mies' tectonic consciousness and turns into a plastic programmatic fundamentalism. There, canom no longer exists, but rather becomes a movement to deny it. It was a movement that flowed from Le Corbusier's concept of plasticity, but it was also a movement that was at the mercy of new technologies.

Here, we would like to present a different perspective from Newton's. This is the thought of Leibniz, who proposed derivatives and integrals at the same time. Although they opened the same mathematical achievement of differential and integral calculus, Leibniz's ideological stance was different from that of Newton's.



7  Gottfried Leibniz's Point of View

Leibniz's approach was different from Newton's. Like Newton, Leibniz did not simply immerse himself in the mathematical world, but was imbued with a fertile criticality.
Witnessing the end of the Western medieval system centered on the Holy Roman Empire and the Pope due to the Thirty Years' War, Leibniz chose to search for divine providence to unify the world for the salvation of people's spirit. There existed a desire for the ultimate form of things. He sought a subdivided geometry that led to the ultimate substance. He sought a subdivided geometry that led to the ultimate substance, the monad.



 7.1  Leibniz's monad

Leibniz believed that the world is composed of monads that arrive at microscopic units that cannot be further subdivided.
In other words, Leibniz sought God's providence as a map of the ultimate microscopic units of subdivision and invented derivatives and integrals.
The monad was a further mastery of the unity of the maximum and the minimum in which God's providence is continuous from the part to the whole, going infinitely toward the infinite, and seeking the ultimate perfection of continuous non-contradiction. The monad was an attempt to explain the world in terms of the monad, the order of absolute entities, as this monad would unify the world with true order and reveal the existence of God.
The monad is the smallest entity that has no concept of extension. In it exists the power to bring everything out. Leibniz is poised to keep the world in the smallest unit that has the power to open up.
Leibniz says of monads that "spontaneity in the precise sense of the word is common to all simple entities, including ourselves..." note 4).
Leibniz tried to place the metaphysics of God at the root of the laws of nature. It focused on matter. He put a spiritual entity, the soul or monad, at the root of matter, and set forth a metaphysics in which the entire universe was expressed in itself.
What is important is the focus on substance, which Newton denied, and on the "force" of spontaneity.
In space as a container, there is no independent thing, but the thing itself, and all of its successive series. In other words, Leibniz denied Newton's transcendental absolute space and time itself.
Gilles Deleuze describes the world that Leibniz opens as "an infinite curve tangent to innumerable curves at innumerable points, a curve with only one variable, a converging series of all series." Note 5).
This is Leibniz's concept of the derivative. It comes as close as it can, but it does not vanish into the infinitesimal beyond. It is a series of infinitely continuous units that remain at the smallest unit. This is because Leibniz was searching for the entity that produces force.



 7.2  A shift in the way we perceive space

Leibniz's view of space was different from Newton's. In all things, it was the exact opposite.
Newton assumed the antecedence of absolute space and time as a priori in order to describe motion. This is because motion is described in coordinate space and the concept of time is a priori to explain motion.
Leibniz, however, rejects the assumption of the pre-existence of transcendental time and space.
Leibniz says, "Space, time, and expanse are always in the world, not the other way around." Note 6) 　
In Leibniz, the world is not something in which space and time are prior and things are placed after them. On the contrary, time and space exist in a world full of things.
Deleuze explains this by saying, "It is not that the given is in the space, but rather the space is in the given. Space and time are in the given." (Note 7).
In other words, in Leibniz's thought, we find an attitude of will that seeks the expression of the power of space, rather than in the direction of assuming an a priori and transcendent time and space, such as Newton's absolute space, and describing mobility under this assumption. Space itself is assumed to have relations that are full of order. Moreover, the relations are the manifestation of differentiation, which is the source of generation. In other words, for space, Newton was describing motion, while Leibniz was seeking a principle of generation of motion that goes beyond description. Therefore, he rejected Newton's absolute space on the grounds that it is not a simple absolute space in which only homogeneity, which lacks differentiation, expands infinitely.
Newton considered space merely as a criterion for reducing motion to physics. That criterion contributed greatly to becoming the basis for pioneering physics later on. At the same time, however, it was a simplification of homogeneity that discarded the richness of reality. This is what influenced modernist architecture.
While Newton's approach to differentiation and integration was a tool of physics, Leibniz's was a proof of God, seeking the source or location of force. And the idea was pregnant with an important seed that would open an era. It is opened by Deleuze.



7.3  Gilles Deleuze's Eye

Deleuze focuses on Leibniz's emphasis on difference.
In "Difference and Repetition," Deleuze thoroughly rejects "sameness" and pursues an understanding of the world through "difference.
Deleuze says, "It is in repetition that what is repeated is formed and yet hidden." Note 8) 
Deleuze focuses on the possibility of something being generated through endless repetition. That something is difference, and he overlaps the mechanism that produces it with Leibniz's monad and emphasizes it.
Deleuze was interested not in Newton's transcendental world, where derivatives and integrals were transcribed to describe motion, but in Leibniz's monad, which captures force as the source from which motion is expressed.

In any case, it was true that the differential and integral calculus, unlike the static geometry established by the old static and perfect mathematical proportions, brought infinite temporality into proportion and shifted it to a new world of parameters. This prompted a shift from the static world of balance and harmony of the Renaissance style to the changing dynamic world of movement. Its influence was felt throughout the arts, giving rise to the "distorted pearl" of Baroque art.



7.4  Discovery of a new subject-subject

Deleuze published his important book "The Folds: Leibniz and the Baroque" in 1988.
The Baroque is an endless process of folding the folds, and folding them again, and adding folds on top of folds, and folds on top of folds, and so on. The baroque line is an infinite number of folds. Note 9)
According to Deleuze, "the ideal generative element of the fold is inflexion. Inflexion is an intrinsic singularity (une singularité intinsèque), a pure "event" (le pur Evénement) concerning lines and points, and a "potentiality" (le Virtuel), in particular, an ideality (l'idéalité). It is important to note that the refraction "is not inside the world. It is the "world" (le Monde) itself, rather than its beginning.
Deleuze focuses on the monad that moves toward minute entities and paraphrases the world in terms of the monad.
According to Deleuze, "the ideologically emergent element of the fold is inflexion. In other words, the continually folding folds generate inflexion and form the world. Inflexion itself is a world of dynamic change. The world is understood as an event. In other words, the world is transformed from a static "object" to a dynamically changing "event.
The baroque is merely a representation of the distortion of refraction caused by such dynamic change. Deleuze's "folds" are precisely such distortions. He reads this newly emerged world of baroque distortion not as a single complete geometrical plane, as in the past, but as intricate folds with multiple surfaces folded into each other. It was something that was more in keeping with Leibniz's thinking, and not Newton's transcendental and homogeneous coordinate space.
Thus, Deleuze, through Leibniz's monad, presents the concept of the "folds," the field of difference, as a further disruption of the absolute, homogenized world that emerged after the disruption of the classical, complete, centripetal world. He presented the "folds" as a field of difference where new creations are generated, rather than the neutral Newtonian absolute space where fertile meanings dissipate and disappear. The fertile thing in which concealment and disclosure are intertwined was undoubtedly the folds.

Deleuze describes the SUBJECT.
"...it is also called perspective. This is what the rationale for perspective is. Perspectivism does not imply a dependence on a predetermined subject. On the contrary, what comes to the point of view, or rather what remains in the point of view, is the subject. ...In other words, the subject (sujet) is not something that is subservient, but, as Whitehead puts it, a "self-transcendent superjet." Note 11)

Deleuze uses the concept of perspective to depict the figure of the subject. In other words, the concept of perspective does not mean that the viewpoint of the subject is predetermined and viewed. On the contrary, what falls from the world viewed at the point of view constitutes the subject. In other words, it shows the reversal that what gathers at the viewpoint is what constitutes the subject. The subject (sujet) is not something that is placed below, but is a "self-transcendent state" (superjet), as Whitehead puts it.
In other words, Deleuze takes the view that the subject is what is constituted.

And perception is data for the grasping subject. It is so not in the sense that this subject suffers a passive effect=result, but on the contrary it is so in the sense that it actualizes the latent and, thanks to its spontaneity, objectifies the latent." Note 12) 

The subject is folded and mutated in the folds.
The subject does not exist beforehand. Assuming that various realities are grasped and integrated, various perspectives are called upon, and the subject is composed, then perception is the collection of data, and the subject is the place where the data is collected.
The subject is the movement itself that constantly collects new data, rewrites them, and projects them into the future while referring to the past. This indicates that the concept of "subject" has gone beyond the old concept of the human subject, and has become a concept that is close to the program.

Thus, the mighty SUBJECT was reviewed by Deleuze, and it was shown that the world is no longer produced by irradiation from the mighty SUBJECT.
Deleuze saw in Leibniz's thought this dynamics of difference. Here, the world no longer has the absoluteness of the existence of a transcendent subject, nor is it a static, homogeneous field in which objects exist, but a field of chains of "events" filled with a dynamic flux of energy, full of differences.

This posed certain problems, since it advanced the negation of the canon; it solved the problem of the SUBJECT, but at the same time it reduced the status of the SUBJECT and focused on the PROGRAM alone. Although it is now possible to supplement the movement as a fluid, it is flawed by an overconfidence in the program. This awareness leads to an easy dependence on and connection with computer technology, destroying the canon of architecture. Furthermore, in Japan, we can see a reversal of the situation, where the market principle of capitalism uplifts authorship, indicating that the twisted subject destroys the "canon.
In response to these issues, I would like to clarify my own concept of architecture in order to express my own position. As an architect, not a critic, I feel it is my responsibility to present my own architectural concept.



8  Background of own architectural concept

I would like to discuss the state of the subject, which emerges as the next problematic issue in my own projects, and touch on my own concept of architecture. It is a transformation of the structural relationship between subject and object, and concerns a manifold that can move. It is a life form that can respond to any situation of externality and can be transformed in a variety of ways. I would like to discuss such a concept.

The origin of my architectural concept was based on neoclassicism. It was a quest for monumentality and perfect geometry. At that time, I believed that the mission of architecture was to concretize idealistic abstraction. The plane, he believed, was to be the ideal horizon, and it had to be perfectly structured with thorough consistency and mathematical proportionality. He also saw the cross-section as the ideal abstraction that emerges as space. As a student, he created "The Awakening of A Bao a Ku," a work associated with a phantom in Jorge Luis Borges's "Dictionary of Phantoms.

Beneath the "Tower of Victory" lies A Bao A Qu, and the phantom awakens when someone begins to climb the spiral staircase to the rooftop. A Bao Ah Coo catches the shadow of the person and follows him or her up the spiral staircase. The transparent figure of the phantom increases in color and brilliance with each step, and when the top step is reached, A Bao a Coo appears in its full glory. However, when a person has climbed to the top of the "Tower of Victory," he or she will reach nirvana and will not cast any shadow. In other words, since A Bao Ah Koo cannot see the shadow, it cannot catch the person and therefore cannot ascend to the rooftop.

The A Bao A Qu, unable to attain perfection, is plagued with anguish, and its color, luster, and body fade away. As soon as the person who had been ascending begins to descend, a-ba-o-a-qû immediately tumbles to the lowest level.

The Awakening of A Bao A Qu was about the conflicting sorrows of those who advance toward the ideal of nirvana and the anguish of the phantoms who follow them.

Traces of conflicting thoughts appear in this drawing. Oddly enough, in retrospect, there is not a perfect consistency, but rather an eroticism that partially disrupts the consistency, and on the other hand, there are glimpses of a consciousness that tries to disrupts the consistency. In other words, while pursuing canon, there was a mixture of wills that did not want to be taken in by it. This mixture of opposing wills is the starting point of my architecture.

Next are Void Centers and Cyberspace as Reference Space, two submissions to the International Competition for Urban Development in Spreebogen, Berlin. These were the inflection point of his own architectural concept.



8.1  Void Centers / 1992

In 1988, an international theoretical research group was formed to design architecture through telecommunications, where members existed apart from each other.
The group was called ARX. The official name was ARchiteXture ( ARX ), a term coined from the words architecture, texture, and text, expressing ARX's own conception of architecture as a language, a fabric that is deployed in a global network. Multiple subjects are melted down. This was to deconstruct the old concept of authorship. To communicate repeatedly in an accelerated state, beyond the normal body speed. Furthermore, the form is melted down among the constituent members.
ARX took the concept of plural logic one step further and established this idea as a design process. The idea was then layered into a single project that was the brainchild of multiple members from different cultures. The result of the project was not the total product of compromise, but rather cracks, imbalances, and differences that revealed the differences between the beauty and richness of a multicultural society.
In 1992, the multiple-subjects telecommunicatively interpenetrating method won the International Competition for Urban Development of Berlin Spreebogen, embodying the theory of ARX.
The concept of the competition proposal was filled with many ideas. De-centrism, deconstruction of the concept of authorship, and juxtaposition of a group of subjects with different cultures and thoughts existing in the same time but in different places. Continuity between interiority and exteriority, between interiority and exteriority, by setting up a common denominator that intersects the city. The competition proposal was based on an attempt to create a diagram that extracts temporality, and to insert parameters into the diagram.
Architecturally, the competition proposal decenters and diverges the fragments generated by the diagram. The relationship that intersects the city is intervened as a diagram, and the architectural and urban structure is generated by the parameters. The motivation of the site, which is pregnant with temporality, was extracted.



8.2  Cyberspace space as a reference space

I recognize the Cyberspace as Reference Space text as the origin of quantum generation, the concept of generation by intelligent particles, and as a development of the subject-object problem. It was also a precursor to today's concepts of mirror worlds and metaverse.
In an attempt to focus on the relationship between the present author, the subject, and the object, the precipitated subject received from the past, we propose an autonomous program that acts as an agent with a perspective of otherness. This autonomous program is presented as an intervening reference space between subject and object. It stores the precipitation of the relationship between the various conditions of externality and the architectural object as a possible form of future orientation that is not repression.
Living organisms materialize information in the molecular structure of genes. In other words, the organism is under the spell of hardware. Humans, however, have acquired not materialization but virtuality created by electronic networks. In other words, we have succeeded in separating information from matter. The diagram started out as a two-dimensional diagram, but it has gone beyond three dimensions to become a multidimensional matrix that includes temporality and stores information. It is not a determined and fixed program, but also an autonomously modifiable program.
Here, we are formulating a reference space with AI as an agent. This reference space goes beyond the standardization that simply collecting big data is good enough, and aims to intervene between subject and object.
The real world and the virtual world are located in a mirror-image relationship, and in response to each other, each becomes continuous. The flow of continuity also occurs between the real and the virtual. This is what this project demonstrated.



9  Influence of Deleuze/Guattari's concept of the "abstract machine"

The concept of diagram has evolved through J.N.L. Durand, Le Corbusier, Mies, and Eisenman. After Eisenman, however, Deleuze/Guattari's concept of the "abstract machine" had a major influence on the development of the concept of the "diagram," which is the concept of architecture as an adaptation to social and external conditions. The optimistic aspect of incorporating externalities into the architectural program and projecting it into the future was emphasized, and a new position of "programmatic principle" emerged. The position of programmatic principles emerges. This is the position of auto-poiesis, which erases the subject as a human being and automatically generates architecture. Curiously, architects from Eisenman onward have been moving forward without a sense of crisis or questioning these developments. They have simply reversed the position of subject and object and their dominant relationship. The next generation will overreact to this part of the movement and forget the existence of the subject, i.e., human existence itself.
My concept of architecture is a resistance to this movement.



9.1  Formulation of SUBJECT as intelligence

Architecture is established in a certain site, and there is always an external environment surrounding the site, so even if the architecture is generated by a wonderful program as desired by programmatic fundamentalists, it is still affected by externalities, and the question of how interiority can be reconciled with externalities remains. The question of how interiority can be reconciled with exteriority remains. Traditionally, architecture created by interiority has been questioned in relation to exteriority through the principle of de athesis, or place. However, this concept of place has become a thing of the past. The externality and interiority of architecture must be made continuous, but we must depart from the traditional position of regarding externality as authentic. Such a position cannot capture the new creations of architecture, but rather creates new oppressions. Rather than reverting to a traditional sense of place, we must consider how to relate interiority to exteriority.
Eisenman's work shifts the issue further in a highly intellectual direction, in the vein of Rowe. Because Eisenman formulated the SUBJECT as an intellect, he had to assume ANTERIORITY as the totality of knowledge precipitated in history and INTERIORITY existing inside architecture. In the course of my research, I came to the conclusion that what Eisenman saw as interiority may in fact have been an illusion of conscious abstraction created by the subject. Eisenman's diagram was established by the existence of the subject, which sharpened his intellect. It expressed the beauty of criticism and the spark of intelligence, but it was difficult for ordinary people to understand, and it did not have universality. It was also the exact opposite of the black box of the SUBJECT of Tadao Ando's intuition and sensibility, yet it existed on the two sides of the same plane. However, the formulation of the existence of the SUBJECT as an intellect, rather than a sensibility, emphasized an attitude of looking at the culture and history behind the establishment of architecture, and made it possible to escape from the control of the client's desires.
My conception of architecture was a continuation of Ando's and Eisenman's conception of the subject. It is based on the assumption of conscious abstraction created by the subject as intellect. While architecture is founded on the subject as intellect, it goes beyond that and moves in the direction of recovering elements other than conscious abstraction. This leads to the question of how to perceive the human being before asking the question of how to perceive architecture. In the classical conception, human beings were considered in terms of dimensions, in terms of number-ratio relationships. This led to the search for a continuity with the universe of the maximal and the minimal. This is because they sought a theistic view of the universe under the absolute transcendent called God. However, man is depriving God of His place. Man had to inherit the rational characteristics of the absolute transcendent. Thus, he established a being who possessed rational intelligence as the source of all-seeing power and applied it to man. Eisenman's architecture exists along these lines. However, such an image of man was clearly biased. It concentrates a powerful centrality on the subject that controls poiesis. The reaction to weaken it was the movement of Deleuze and others. The movement is toward excesses that erase the subject. The next generation is at the mercy of these movements, and tries to leave poiesis to the program. But these directions are also excessive. I would like to break out of this impasse by rethinking human existence as a unified entity, rather than as a biased aspect of intellect and sensibility. Rather than viewing human beings only in terms of their intellect, I seek to uncover other elements and attempt to solve the problem from there. This is the totality of intuition, emotion, and the body, which has not yet become an emotion. We accept these physicalities as they are and connect them to architecture. By doing so, interiority will break out of the black box of Eisenman's intellect, and humans will be able to connect to architecture. This also relates to the problem of the SUBJECT as intuition, which is Ando's starting point.
My attempt is to explore the factors that support the creation of such architecture. Eisenman's direction of making the invisible visible by grouping it under the category of motivation was a precursor to the recognition of the importance of passion. We must further extend the concept of architecture.



9.2  The Role of architecture

Screening by the outside world (otherness, externality)
The problem is that architecture itself is subordinated to or indifferent to the complex human activities in which it is based, even though the foundation of architecture is placed in the midst of such complex human activities. Particularly in Japan, where the pursuit of functionality and economy is fundamental, there is a marked indulgence in the play of form, materiality, and detailing as a form of resistance to such subordination. An important problem for architecture today is that the foundation of architecture itself has moved beyond modern rationalism and has been placed under the control of an even more global capitalism. It has been convinced that architecture's role is to faithfully implement global diversity beyond the desires of society and man. The situation created by this pressure to perform is becoming truly unstoppable.
The forms generated by a program can produce an almost infinite number of variations, depending on the algorithms of its relationships. In the case of living organisms, natural selection can sift through them. In architecture, however, such feedback is rarely provided, and is impossible.
Screening by the outside world emerges as a complement to such architectures' own defects. However, such a thing does not exist today.
It is important to extract and inherit the anteriority of the place where architecture is inserted as a canon. Otherwise, architecture will become like a cancerous cell that destroys the sense of place that has been cultivated over the years.
In the future, it will be necessary to confront existing ARCHITECTURE as a subsystem, an entity that compensates for such deficiencies. The existence of another ARCHITECTURE as an agent, as a being from the standpoint of history, culture, and human beings themselves. These two need to exist and be confronted. They are separate from the old ARCHITECTURE and exist as avatars. Furthermore, they open the possibility for a new ARCHITECTURE as the basic mother by fusing them together.



9.3  Movement from SUBJECT-centeredness to OBJECT-centeredness

In response to the movement from subject-centrism to object-centrism in contemporary Western philosophy, the contemporary architectural consciousness also responds to this trend. The arguments of Eisenman and Rem Koolhaas should be understood in this context. It is important to review the relationship between subject and object. Architecture has too often believed in a single world with an all-encompassing hierarchy supported by a strong subject.
Such a worldview frees the object from the confines of composition and relationships, and forces us to reexamine how we relate to the subject. The composition and relationships of the object are not the original form of the object, but are something that is added by human beings. This is the flip side of Kant's correlativism, a worldview in which we think we understand the object through the filter of the subject, but in reality we cannot approach the "thing itself.
Basically, architecture, as its etymology suggests, is concerned with technology. architecture, which has emphasized the status of the subject and has not acknowledged its limitations, is moving toward the domination of the object by technology. As a result, architecture, as an entity that surpasses humans, has the potential to undermine human existence. It is becoming more and more detached from human beings, and is suppressing human beings themselves. Computational technology is a double-edged sword, and it is fraught with ambivalent problems. The subject-object problem is latent in these problems and will emerge as an important issue in the future. It is time for us to seriously consider the subject-object problem.
What would it be like if the subject and object were all on equal footing?



9.4  Subjectivity Issues

Architecture was originally a form, a "structure. But what is a fluid existence that departs from this, that does not fix any function, that does not represent anything, as a body of energy? The abstract machine accelerates this. It is because the object acquires temporality and becomes a fluid, ever-changing life form. It has the danger of becoming a distorted life form that denies the subject to recognize and critique, and has only desires that exclude the act of recognition.
We are moving from machines to life, but life is not a rough mechanism like a machine, because it is fundamentally based on quantum relationships. It is known to be generated from a fairly minuscule world. In that sense, the parametric program is only sketchy.
What is important is a perspective that tries to resist being characterized as a focus from which all the actions of an individual seem to aggregate, as Deleuze describes in "A Thousand Plateaus." It is a denial of the system itself, in which everything seems to be attributed to the individual or individuals. Capitalism can be said to be founded on such a system of subjectification. A society in which systems that identify the individual are ubiquitously in place further accelerates "constant management in an open environment. Deleuze's concern was how to create the subject as a focal point of "resistance" by turning back and redirecting external forces, how to resist the forces of identification as individuals, as individuals, and how to embody within individuals and individuals the "right to difference, mutation, and transformation. It was about how to resist the forces that sought to identify us as individuals and as individuals, and how to embody within us the "right to difference, mutation and transformation. It is a denial of a fictional system that appears to emanate from the individual as an imaginary image, and it is a denial of capitalism's bloating of the SUBJECT, never simply a denial of the existence of the SUBJECT itself.
The programmatic fundamentalism and object regressionism attempt to go beyond this Deleuzean consciousness to the elimination of the human being as a SUBJECT, but such a direction seems to be wrong. The attitude of trying to reach a conclusion hastily without examining the subjectivity issue is a hidden danger of moving in the wrong direction.
At no time is it more important than today to rethink architectural theory and philosophical conceptions of subjectivity.



10  Own architectural concept

My own basic architectural concepts can be summarized in the following eight categories.

1 quantumetric/segmentmetric
2 robotectonic
3 de-centralism　 
4 con-jectivsm  
5 bio-multiplicity 
6 negotiation/intervening 
7 post-vitruvian physicality
8 provisionality

We would like to discuss these architectural concepts in detail, including background information.



10.1  Quantumetric・Segmentmetric（Quantum generation and segmental generation）

Here, as a new concept of architectural generation, we propose the concept of expressing kinetic energy by the flow and density of the distribution and arrangement of volume and space and functions of point sets and segment sets by their connected, discrete, and coarse and dense distributions.

This proposal is an extension of Eisenman's proposal of the diagram, in which the SUBJECT generates the OBJECT as a VOLUMETRIC, internal, dynamic entity, but different from the concept that remained in motion between each VOLUME divided into parts.
With Eisenman, Le Corbusier's VOLUME was redefined and became an entity with a vector of force. This goes beyond the mere act of looking at a discontinuous, coagulated, tangible OBJECT, and impregnates the consciousness that space has energy. To take it one step further, this concept of volume has the potential to open up to a continuum with energy density.
The opportunity for this begins with Le Corbusier's implication of volume as a gas, rather than a fixed solid. In this sense, Le Corbusier's concept of volume was an important consciousness, and he deserves much credit for it. The kinetic energy that generates such architecture flows throughout the building, causing the edges and surfaces that define the building's limits to disappear. It also allows the flow of generative energy of the externality context to be absorbed into the interior of the building.
This conception goes beyond the fixed object of the Newtonian worldview. The fixed object is advanced to Le Corbusier's concept of volume, which is developed through the dynamics of Eisenman's volumetric volume, and seeks to open up a more dynamic world in the direction of making the volume particulate. In other words, the concept of quantumetric transforms the volume into a discrete energy density, assumes it, makes it more kinetic, and completely transforms its quality. Individual objects are subdivided as particles, and the totality of particles is defined as a form that constitutes itself as an intelligent agent.
Ultimately, it aims to control motility, which assumes quantum behavior that is connected to human consciousness and preconsciousness. It is to extract information emitted by the body, such as brain waves, body temperature, skin currents, and changes in respiration and heart rate, and convert it into energy density. We believe it should be extended to non-human life. By doing so, it reconstructs volume and space.
Segmentmetric is the generation of segments of greater dimension than particles, and is included in the quantum metric concept.
This is a concept in which each function is not aggregated into an elementalist unit and made into parts, but the volume itself is decomposed as a neutral particle, and the whole is composed by the recombination and redistribution of each particle through intelligent movement based on the robotectonic concept. The perception of volume is now quantum, which is very different from the conventional rigid one. At that time, our awareness of the object will also change, and we will no longer be able to distinguish between the classical dichotomy of subject and object.



10.2  Robotectonic

The subject is no longer a strong will or intellect in accordance with the Western tradition, but a complex aggregate of physicality and object groups, which, as an agent, further filters the whole, is imbued with temporality, and is transformed by the quantumetric. It is a fusion of the human body, the subject group, and the object group. Here, there is no subject formulated as absolute intelligence. In other words, the classical worldview as an interiority found in the subject is dismantled, and a new composite interiority emerges, generating a fluid architecture without edges that is topologically continuous with the exteriority. This generative process eliminates the very problem of standardization that Eisenman fears. Furthermore, the criticality is no longer owned by the subject, but is outside the framework of intellectual ownership. The aesthetic and instantaneous solution of the shimmering critique by the past subject disappears, and the complex aggregate itself, topologically continuous inside and outside, embraces temporality, discovers all things, and formulates a loose solution that is possible.
Such a solution method is based on the concept of nonlinear generation, in which the subject does not linearly manipulate the object as in the volumetric method, but the segment group itself, which is an individual component with a brain, changes its arrangement while measuring its surroundings. Such a sequence of flow will be performed by robotectonic, a concept combining the words "robotics" and "tectonic," in which each component or matter is joined and unjoined by an agent with a brain, and the joining method is changed to a robotic one by the agent with a brain. The whole is composed by the interrelationships. This is the very life-like movement that embodies both abstraction and concreteness, virtuality and reality, which is contained in the nonlinearized system.
The object concept acquires this fluidity, transforms from machine to life, dismantles the Western subject, and opens up human existence itself.
My research activities to date have been conducted with this direction in mind.



10.3  De-centralism

It is the successor to Eisenman's thinking, but its basic position is different. Eisenman tries to preserve the old consciousness of the SUBJECT. My idea is to go beyond Eisenman's consciousness and further consider the state of the SUBJECT. In anticipation of the coming network society, I anticipate that the existence of the subject itself will change, and that poiesis will transform the meaning of maintaining the old form. For me, an important early architectural conception was around the issue of the SUBJECT, the deconstruction of the concept of authorship and the melting down of the individual SUBJECT. This was the concept I described at the time of ARX's formation, and it was also the concept of Void Centers. It was a superposition of perspectives across points of view. The superimposition of thoughts from different perspectives is intended to dismantle the centrality and centrism of the subject. It is not comprehensive. It does not deny confusion and friction, but on the contrary, it denies a scheduled direction. It seeks to liberate standardized, mundane, and repressed thinking. However, as a basic stance, it does not seek to erase the subject, as in the case of programmatic fundamentalism.
De-centrism is a criticism of the idea that information, wealth, and power are concentrated in a single point, and it is also a criticism of the power of the creator. The only absolute in the Western Middle Ages was God. God ruled over all and was considered the absolute creator. During the Renaissance, man assumed the role of creative agent from God. The Renaissance was a time when centrism should be dismantled through the denial of an absolute God. Instead, man assumed the status of an absolute God. With the advent of modern thought, through a further process of diversity, the subject is being de-centered and is moving toward melting and dispersing. Yet many architects still cling to the centralism of the past. Even though they know it is impossible, they cling to the afterimage of the past, and make decisions based on the pretense of a centralized subject. This is a correction of such excessive SUBJECTS.



10.4  con-jectivism・bio-multiplicity （New subject-object relationships and biodiversity）

The diagram is both a projection of the world onto the cutting plane of the present and an abstraction of complex events. It can also be called a diagrammatics that acts on intuitive consciousness. It is necessary to describe the historical significance of the diagram as something that cuts out the world and discloses a cross-section of it through intuitive awareness. While a program implies the act of making, i.e., the integration of all information toward production, the diagram, on the contrary, indicates the perception of the world and the act of organizing complex and intertwined information. Moreover, beyond organizing, it can be said to have the magical power to interpret and transform the world itself. The artist's will is incorporated in the process of organizing the information, and the world can be twisted according to the artist's will. The problem with the diagram is that it is static. Is there no problem in cutting off a world that is constantly changing and projecting it onto a static screen? The problem is that it is possible for the will of the creator to creep in under the guise of an objective observer.
An algorithm is a set of instructions given by a human being for a computer to execute. It can describe the problem as if it were being solved by a human. It can also be described in such a way that a computer can understand it.
The linguistic clarity of the description opens up the possibility of not only describing the steps of the problem, but also exchanging solutions with other "agents" in the subsequent process. In the computer world, agents are computers themselves. An algorithm is an intermediary between human thought and the computational power of the computer. There are two aspects of algorithms that serve as such an interpreter. On the one hand, it is a means of instructing the computer how to solve a problem, and on the other hand, it is the human thought itself translated into the form of an algorithm.
In Eisenman, the intelligence of the subject was read from the object as a diagram and attempted to be stored in the object. What was read and stored was the canon and creativity. In the near future, with the advent of advanced technology, we can expect to see an environment that goes beyond singularity. In such a future, it is expected that further intervening entities will emerge between the subject and object, without relying solely on the subject. This is a departure from the Western worldview of dichotomies. It is a departure from the Kantian worldview and an acceleration in the direction proposed by Deleuze, i.e., the possibility will open up for the subject and object to become completely mixed and integrated without hierarchy. I do not deny the existence of such an entity, but rather believe that it should be actively incorporated into the creative process.
Graham Herman's object-oriented ontology holds that chance events will always occur due to something of which the SUBJECT is unaware. The subject has a depth that can never be plumbed by any point of view and is retreated from all relations.
In other words, the inevitability of chance. The world is ruled by chance, and we are aware of it. The presentation of this concept itself allows us to understand how the West has been caught in a Kantian spell. It is a departure from the Kantian world in which everything exists through the SUBJECT. All objects are ontologically equivalent, and all objects and subjects are on an equal footing. However, the song is not only about free diversity, but must be based on the canon in anteriority.

The two disassemblages that Herman describes are the result of technology, and as can be understood from the fact that the word "architecture" is derived from the word "techné," it is the fate of architecture itself, in which technology intervenes. In other words, it is also true that technology has been used to manipulate objects.
Poiesis is different from cognition. The architecture that controls poiesis will have to deal with this problem carefully.

In this context, con-jectivism must be defined.
I propose the concept that the subject and object are not bound by a domination relation, but that the object itself has intelligence and is transformed by its interaction with the subject's collective. This position is also a critique of the current tendency toward object-centrism. It is not a reactionary attempt to return to the subject-centeredness of the past, but rather a demand to not forget the existence of the creator, the human being. It is also a concept that establishes human existence.
My basic stance is the denial of the relationship that creates hierarchy in the object through the subject's powerful dominance.

Herman denied this as "upward dismantling" and "downward dismantling," but I believe that for architecture, which is deeply imbued with technology, objects must be dismantled, and each time they are dismantled, the relationship between them must be reassembled.
This is in line with the quantum theory position. When we observe, everything is fixed, but before that, everything is in a state of ambiguous superposition, i.e., everything is undetermined, free, and dismantled.

The object group should be a transformation of its own structural form, which opens to all kinds of relations, rather than being reduced to a mere atomistic approach or to instrumental relations fixed by the subject, as Herman fears. Moreover, it is a transformation to a structure that can be called a dynamic quantum structure. The structure is static, but it is a structure that can move. This is what prepares it as a structure that can respond to any external situation and can be transformed into anything. Instead of having a relationship formulated in advance for the purpose of the subject, and constructing the object in a fixed relationship with a hierarchy, the object is opened as purposeless, and prepared for anything.

The bio-multiplicity I propose is defined as something vital beyond Deleuze's multiplicité. Deleuze says, "This variety of persistence can never be confused with the many, much less the unity of persistence with the one." However, bio-multiplicity goes beyond Deleuze's emphasis on the diversity and unity of persistence, and combines quantum and robotic qualities, as described below, and even traverses not only real space but also virtual space, traveling between time and space, between the real and the virtual, and between the real and the virtual. It is a concept that traverses the duality of time and space, the real and the virtual. Humans have stored their genetic information in the DNA in their bodies, but the fact that it is now possible to store information in a world beyond the real world opens up a new era. The real world is continuous on a platform beyond the metaverse and the digital twin. In other words, we have a continuous continuity beyond reality, and robot technology makes it possible to realize it, to penetrate both the real and virtual worlds, and to change freely into the future, with an orientation toward more continuous and continuous fluidity.



10.5  Negotiation・Intervening

From de-centralism came a shift in thinking toward seeking an exchange between virtuality and materiality, one that seeks to transcend the old sense of place by layering immaterial space over real space with the project Cyberspace as Reference Space.
In the course of discussions with Jacques Derrida, Eisenman realized that he should go beyond Plato's chora and prepare another intervening space. By doing so, he went beyond classical place-ness. From Casa Guardiola to the Revstock Park project, he grafted anteriority into the present.
Eisenman's concept of inclusivity is very important for contemporary architecture. Architecture has been assumed to be directly inserted into time, the present, and into the site. This creates only a binary relationship to time and place, creating edges in relation to the surroundings and the past, and rejecting smooth continuity. Eisenman transformed such compositions. Eisenman found a way out of the conventional Western dichotomous world. He transcended the rigid dichotomies that even Derrida could not overcome. Furthermore, Eisenman combined criticality and interventionism to create his own style. Still, however, Eisenman remained an attempt within real space.
As a further extension of Eisenman's thinking, I will attempt to intervene the virtual world full of imagination and images into the real space and make the two continuous. I believe that this will dismantle the classical sense of place and make it possible to impregnate real space with free creativity.
In other words, I am trying to inherit Eisenman's concept of inclusivity and extend it to all things that are dichotomous. I assume the existence of intervening agents, such as the opposition between virtuality and materiality, between the interiority of corporeality and exteriority, and so on. Such an agent attempts to ensure an edgeless continuity that transcends oppositional structures. We believe that the problem of human existence dominated by capitalism can also be solved by resolving the binary opposition structure. In other words, we must break away from the oppositional structure of two choices: subordination or domination.



10.6  post-vitruvian physicality

In turn, Western architecture has been based on the proportional and geometric system of the body. Under this Vitruvian corporeality, with the body as the center, the body is continuous to the cosmic world. The body is a continuum of two directions: the direction of expansion in the form of the maximal and the direction of contraction in the form of the minimal. Space is created by transforming the number ratio of the body into the physical substance of dimensions. Every detail of architecture is a reproduction and continuation of these physical dimensions. Beauty in the Western world was positioned as formality, totality, and logic, beginning with the number ratio. Such thinking contributed to the formation of ordered cities by canon.
However, this pushed the human body into the Euclidean geometrical world and limited human existence. To confine man to a perfect geometrical world would also lead to an excessive demand for reason alone. By nature, human beings are not only numerical and geometrical beings, but also possess things that fall short of those standards. I am interested in developing a view of the characteristics of the human body that goes beyond dimensions. The human body has diverse and rich characteristics beyond its external dimensions, such as weak electric currents flowing through the skin, brain waves traveling through the brain, body temperature, respiration, heart rate, and so on. The concept is oriented toward using sensing technology to seek a continuum of these characteristics into architecture.
This opens up the possibility of a transition from a volume confined and solidified by traditional edges and surfaces to an unrestricted, continuous existence. The "consciousness" that has controlled isolated and discontinuous architecture will have to be transformed.
Such structures have microscopic relationships and seek to be structured in quantum terms.
The old architectural form of existence is being transformed: the subject goes beyond abstractly composing the object, and the object itself adapts to its changing environment. Naturally, the existence of human beings as subjects is important. However, the coming SUBJECT is not a fictional SUBJECT created by the West as an intelligent being in the image of God. It is, as a matter of course, a subject that not only includes consciousness, but also comes from inside the body and is the primordial subject of human beings before it is yet to be constructed as consciousness. It must encompass not only human consciousness, but also the primordial wholeness of the human being, which is obtained by sensing brain waves, weak electric currents flowing through the skin, body temperature, sweat, respiration, heartbeat, and so on.
With such an all-encompassing subject at its core, we must seek a "vital variety" that can respond to and transform any situation of externality.



10.7  Provisionality

It is time to question the decision-making process itself. We take the linear decision-making process for granted, but we should rethink it.

The following issues were raised at the time the ARX was established.
The increasing speed of information exchange has led to a dislocation of the act of transmission, so that it is no longer possible to convey precise meaning. Instead of concepts such as precision, logicality, and integration, concepts such as alteration, mutation, and transformation are more straightforward in dealing with this situation."
Such an awareness will encourage a change in the way decisions are made.
Already objects are no longer distorted, complete entities, transmitted through digital technologies that can process large amounts of data. Quantum computers will further increase computing speed and throughput, making it possible to represent the object as something beyond classical geometry. It is palpable to the object as the oscillating thing implied by Le Corbusier, and is going beyond even the classical linearity of production, in which the object is generated as a result of the decisions made by the diagram as a diagrammatic representation. This leads to the questioning of the act of decision-making itself. The traditional act of decision-making has been eroded by the development of technology capable of processing large amounts of data, and the very basis of the act of decision-making itself is crumbling. (For example, the sketch, which is an expression of the decision act in the territory dominated by the subject, has already become obsolete in the sense that it erases all possibilities other than the decision.)
In other words, the traditional relationship between the SUBJECT and the OBJECT with respect to the act of decision must be rethought. Until now, the object has been uniquely determined by the mighty power of the subject. In modernism, this determination has been made under the cloak of a pretense of objectivity. In this sense, modernism can be called an architectural movement that constructed a concept of generation based on such deceptively objective determinism.
The flow of microscopic time is not in one direction. In quantum theory, the symmetry of time has been discovered. In other words, linear time flowing in one direction should be understood as a classical concept.

It has been discovered that an electron is in a "superposition state" of "upward spin state" and "downward spin state," and although it is not known which state it is in until it is observed, it goes from the "superposition state" to one of the two definite states when it is observed.
Niels Bohr and his colleagues interpreted this problem as a probabilistic one. This raises an important question. The existence of the decision itself is questioned. We have understood the world to be determined and progressing one by one over time. This assumption has collapsed. It is also a questioning of the progressivity of time.
Two particles in an entanglement relationship, no matter how far apart, are correlated at the same time. In other words, the distinction between remote and near disappears. Distance disappears.
Until the advent of quantum mechanics, the reality of objects was thought to be objective, independent of observation. However, it is dependent on observation. In other words, the relationship between SUBJECT and OBJECT must be reconsidered.
In the macro world, the flow of time proceeds only in one direction, from the past to the future. Such an asymmetrical "arrow of time," or directionality of time, exists. In the microscopic world, however, spatial movement exhibits symmetry in any direction: forward, backward, left, right, up, and down.
The Newtonian world is nothing but the extension of the narrow experience of human cognition to the realm of the divine. The object that appears before our eyes is merely an approximation of our experience of space and time from an absolutized perspective. It is merely the perspective of a human being who has closed his eyes to the possibilities of existing time and space.
Such phenomena cannot be captured by the conventional concepts of entity, identity, and time. Furthermore, beyond the issue of observation, they are also connected to the mechanisms of consciousness and memory, in other words, they foreshadow the existence of a relationship with the subject. In other words, it can be said that even the concepts of "subject" and "object" are being confronted with change.
In quantum mechanics, there is no physical means of distinguishing "this" from "that. In other words, individual identity cannot be established. In other words, everything is connected in a sea of relationships without distinction. The new situation in quantum mechanics forces us to dismantle not only the concepts of space and time that we know, but also the concepts of subject and object.

The concepts of time and space are based on "self-identity" and "linear causality. The law of causality presupposes linear time.
The world that is founded on the a priori assumption that everything has "self-identity" and "determinacy through linear causality" is collapsing.
The dichotomous act of one-way linear temporality of decision ignores and erases many important possibilities to be considered. To decide on something is to erase all other possibilities, and there is oppression on the time axis. Therefore, to reserve something tentatively, without making a decision, leads to many possibilities remaining to be considered and to increase the potential. With quantum theory, linear causality and determinism were rejected. It is an ambivalence governed by the probability of superposition. This is in conjunction with the quantum position. Everything is only fixed when the observation is determined. Before that, everything is usually in a state of undetermined and ambiguous superposition.
Furthermore, at the micro level, there is a symmetry of time. Therefore, the absoluteness of determinism by linear causality must be rethought. There is a need for a change in the very nature of determinism itself.
I will attempt to replace the traditional dichotomous principle of determination with a tentative principle of multinomial parallel reservation. By doing so, I hope to scoop up the many possibilities that are being erased in the selection process.
Until now, it has been believed in the continuity of sequential decision-making acts that the next decision-making act cannot be executed without the accumulation of past decisions in chronological order. We must break away from this linear continuity of sequential decision-making acts and transform them into a parallel continuity in which the decision-making acts at each point in time on the time axis can flow backward, making the uniquely decisive act tentative. A process that preserves only topological relationships can preserve possibilities. Computer technology is capable of storing such processes and will be able to open up new differentiation and product differentiation possibilities. The static diagram of Eisenman and Koolhaas, as a diagrammatic representation, is a definitive cutoff of the world, a uniquely deterministic process. We believe that we should transform the decision-making process of the continuity of such uniquely determining sequential decision-making acts. It is also important that the flow of time of the completion of the OBJECT does not interfere with the continuity of time of the continuous thinking of the SUBJECT. Time should be understood as having multiplicity and flowing in parallel, encompassing all possibilities. My visionality (provisional continuity) is presented under this conception of time. It occupies the most important place in my concept of architecture.



10.8  subject-object problem

The following diagram is a map of my architectural concepts arranged in relation to each other. The development from Le Corbusier's plan to Eisenman's volumetric. It also shows my own prediction for the direction of architecture in the future. The horizontal axis represents the time axis. The upper and lower parts juxtapose the virtual and real worlds; the relationships between con-jectivism, bio-multiplicity, subobjectivism, virtual, and real are expressed on the left side. In the middle, the relationship between metric and tectonic of the old architecture is shown. The vector from metric to parametric on the real side, and then to robotectonic and quantumetric on the virtual side is shown. Then, by crossing from robotectonic and quantumetric on the virtual side to the real side, the transformation process of new architecture, which is extended from the old architecture that existed only on the real side to the virtual side, is shown. The process of transformation of the new architecture is shown.

（機械による自動翻訳）










Takashi Yamaguchi/Architect, Architectural Theorist

President of the Takashi Yamaguchi Architectural Institute. D. in Architecture, Graduate School of Engineering, Kyoto University. After working at Tadao Ando Architectural Institute, he became independent in 1988, when he formed the research group ARX with his partner Peter Eisenman and theorists from Columbia University, and began design activities through telecommunication on a network, aiming to "deconstruct the subject". Invited artists from France, Italy, Germany, Finland, Romania, Peru, and China have exhibited with ARX. He has lectured and taught design at the Université de l'Architecture de Paris La Villette, Politecnico di Milano, Tsinghua University, Princeton University, MIT, and others. He has been a visiting scholar at Harvard University, a visiting professor at Columbia University, and a visiting scholar at the University of Tokyo.