Architecture possesses a ground, an essential ground, that cannot be further simplified or argued against. An axiom, accepted as self-evident. It is a ground other than beauty — not beauty, but that upon which beauty depends, and by which it is judged — other than symmetry, but that which symmetry measures and upon which it depends, other than order, which refers beyond that essential ground to something larger. This ground is resident in each smallest incident of architecture, something that each incident owns as evidence of its presence as architecture, rather than anything that might be imposed upon it.
This is the ground, medium and context for thought-about-architectural-form. The ground, medium and context for thought-about-architectural-form is the logical and artistic possibility of there being (unitary) wholeness or completeness; its gravity (in both senses: as a field of influence and effect of the responsibility conveyed by its sheer importance) is the will-to-completion that gives that possibility a direction, universally assumed of stuff that is neither unitary or whole; and its satisfaction is both the achievement of that wholeness or its sophisticated frustration.
Like the case with language, where a grounding in difference is revealed reductively through a consideration of the smallest possible unit, the phoneme, but the possibility of satisfaction in meaning is found at the higher level of the words these phonemes build up, in architecture the status of this ground, also apparent at the smallest scale, is most clearly seen before the ultimate reduction: the brick does not count as architecture, but the arch might. This ground of architecture may be revealed through conversation; Kahn asks the phoneme what it likes, and it says it likes a word. The smallest division of the work in which the effect of the ground is discernable is already a system.
The system reveals itself as a unit with the elimination of other topo-logical possibilities. As Occam’s razor strips away superfluity, the system is revealed and in the process naturally separates away from others as a unique resolution of the forces contributing to and contesting that system’s completion. The distillation is not endless; since the final unit is still understood as a system, the irreducible end of the process still leaves something that could be understood in physical terms as composed. Were it not for this, there would be no grain to the system, no form of gravity to drive it out of the entropic stasis that a reduction all the way to self-satisfied atoms would produce. In formal terms it is the simplest state of a condition recognizable as complete, but which harbors still in this completion the possibility of non-completion. And in this possibility exists the lines of force that constitute the gravity of the field.
Underlying this is an even more fundamental orientation to a world made up of things, for those to whom architecture has meaning. As architecture makes no sense outside reference to embodiment, the topo-logical system/unit must possess three-dimensionality or be representative of a three dimensional entity. The gesture, for example, is not a system until fleshed out, given a body, embodied.
The simplest example of a system unit, reduced all the way according to the possibilities available in a three-dimensional event space, is the sphere, which immediately evolves within architecture to the more pragmatic, or aggregate-able, system-izable, form of the cube, usually associated with the brick or dressed block (and it is here that architecture also finds its pragmatic roots — not just in a necessary relationship to building, but also in this final irreducibility of its topo-logical sources). The rectangularity of the standard brick is itself already a step away from a pragmatically absolute reduction to the cube. Even the simplest of these system units carries this history in it and the working of that gravity in this history. The possibility of that history’s reversal, that is, the possibility of being less than a brick at this most pragmatically reduced level, spawns the magnetic force impelling the systems at all scales to completion.
The energy latent in this drive to completion is due to the repression at the most reduced level of the possibility of that “prior” or yet more reduced state of satisfaction, through completion: the cube or sphere. This refusal of stasis sets the whole field of forces in motion. Another way to view this is that the brick or block’s rectangular proportions are already the result of influences exerted on the more neutrally inflected cube, drawing or forcing its elongation in a single direction. Further, the adherence of that elongation to the rectangular, drawing the cube out specifically along the lines inherent in the cube, is further evidence of the rectangular solid’s non-reduced state, since this faithfulness to the geometry of the cube itself reveals an acknowledgement of that prior system. The repose of the golden section rectangle might be argued to be an exception, since it seems to embody already a level of stasis that need not repress the will to a greater repose in the cube, but the golden section is as easily understood as enjoying a state of repose arrived at after an operation performed on a cube.
Though elements as basic as the cube are the building blocks of all more complex systems, they are in themselves uninteresting except as the anchor or starting point for the universal compulsion to completion that operates in any topo-logical field — that is, any intentional array of form. They are not to be understood like the atoms or molecules or computational units that miraculously make up more complex forms through the operation of some algorithm upon otherwise inert, expectant matter. The compulsion to completion, which animates all formal manipulation and development, varies in its nature with each system that feels it and demonstrates its effects. The trajectory and force of the will to completion is determined in each case by the subject systems that embody it, and varies with those systems. Thus the variety of effects evident in the world of form and the reason why the ultimate reduction of the idea of the system to the limited number of platonic solids is useless. It is useless because historically unexampled and uninteresting. This is not to say that a greatly reduced minimalism couldn’t be imagined that took its inspiration at this level, but this has not yet happened and it would be a great challenge for such an enterprise to cope with the complexity of reality.
Because the will-to-completion is inherently selfish and form takes up space, the topo-logical space is characterized by competition. The particular angle or trajectory taken by the will-to-completion stipulating the particularity of the system is also the drive behind the particularity of the various systems and their component unit’s relation to each other within the system and to other systems. The designer inserts herself into the picture at this point, as the sponsor and adjudicator of that competition. Depending on the awareness with which this insertion is made, design is either the discovery of the rules of this competition or the writing of them, and thus the analysis of the forms that dictate these rules or the creation of forms that follow from such rules.
This may occur unconsciously. Indeed, the only contemporary instance, by PDE as a critical activity, would suggest that it has generally been unconscious. But this does not in itself invalidate the proposition that what is being described here and will be investigated later has not in fact informed the best work through history. It will be found when not declared and judged when it has been.
The sense of a will-to-completion that underlies topo-logical value is the product of the human empathetic/projective engagement with the stuff of experience. The human experience as a body in space has been exteriorized in a common sense that views both physical and non-physical (conceptual, metaphorical — metaphor is a machine) relationships mechanically, as the interaction of bodies in space. Indeed, the idea of relationship itself is underwritten by a prior sense of divisibility that can be attributed to the human physical experience.
History told from the perspective of a topo-logic will be seen to proceed from a naïve discovery or statement of some originary topo-logical problem, such as that buried within Brunelleschi’s archeological revival of Roman Classicism and its difficulties reconciling trabiated and mural tectonics, to a gradual recognition and working through of the topo-logical resolution of that problem (with perhaps a dawning awareness of the impossibility of a final solution) with ever greater and more subtle or complex (and in view of that impossibility, necessarily tragic) sophistication in the handling of the conflict: from primitive to classical and then, if its impossibility is accepted, into mannerism. Such a history can be told from the straight perspective, interior to the style and the problem that is set by the initial topo-logical irresolution and its attempted solutions, and the logic that develops as the system; or the story can be told critically, from an external perspective that appreciates the provisional nature of that problem. The first history will find a high point in the classical state of the style, the second in its mannerist phase, both claiming a superior understanding of the problem and its conditions for solution. The critical history will assume the impossibility of solution, but lose therefore the extra brilliance that the traditional history will enjoy in its tragic belief in eventual solution, or, rather, in the denial of that impossibility.
A history told from a topo-logical viewpoint will be unfashionably teleological. This is excused, though — actually demanded — by the clear direction of the will-to-completion underlying it. As the originary problem is worked out through the development of the style, the same imputation of direction that allows the distinction between a primitive and classical phase of a style to be tolerated is made of the topo-logical system. In fact, it is the more basic topo-logical distinction promoted by the particular trajectory of the will-to-completion that allows the more refined, or at least removed, stylistic distinctions to be made.
“Style” can be considered derivative of the challenge posed to the will-to-completion by a particular originary topo-logical problem. This problem has here-to-fore been expressed, if at all, in tectonic terms. The discourse of tectonics is at pains to elevate itself from discussions of construction or structure without relying too heavily on a potentially trivializing relation to aesthetics. The appreciation of topo-logical value fills this missing dimension in tectonic discourse. The expressive dimension of structure or construction — the sense of appropriate proportion or the good detail, the “telltale detail,” the satisfyingly evident resolution of forces — with which tectonics concerns itself, is ultimately understood topo-logically.
The tendency in analyzing work from the topo-logical perspective will be to criticize imperfect resolution. This carries the implicit assumption of the intentional fallacy, that the author of the work must have intended better resolution and failed, must have been working with this issue in mind. While it is a tenet of the topo-logic game that practitioners through history have acted with conscious or unconscious appreciation of the issues it dramatizes, it leaves open the degree to which they have bound themselves to it or understood the specific problem their work exemplifies. Indeed, this difference is where style comes from, since if everyone everywhere always pushed the work to the most perfect or complete resolution of any particular problem, everything would look the same and probably tend across the board to look like simple cubes. So, the fact that Mies has wideflange columns disappearing into the ground without any sort of base, which from the standpoint of topo-logical ideality is imperfect (truncating the columns without respect for their own requirements or desires), does not mean that Mies had erred. Rather, the analysis might consider that instance as a clue to understanding the particular Miesian attitude toward the issue of truncation. Such an approach would look for other instances of the condition in the work, such as the corner condition at the IIT classrooms, and try to build from them all a general statement about this specific challenge. This general account might then shed light on other individual topo-logical situations evident in the oeuvre. Here the psychology attending the will-to-completion might also be introduced, to explain the documented system — if in fact there is enough consistency among the various instances to add up to a system. The resolution might be seen as frustrated or contested, the irresolution as dutiful or resigned.
This obvious personification/projection is (according to Lakoff and Johnson) not only warranted, but necessary. And certainly it is supported by the history and continuing practice of the profession. Kahn’s conversation with the brick is far from the only instance, and indeed remains a constant illustration of the way the building is typically ascribed desire in discussions of ongoing design by practitioners.
Because of that intimate connection with the psychology of the author, this sort of analysis can be supplemented and extended with the other kinds of speculation common to historiography. While the topo-logical perspective claims for itself a right to autonomy, in fact the only dimension of the architectural discussion that may make this claim (except, maybe, tectonics), it need not be confined by this essential nature to dry discussions of form alone. The form it discusses is inherently motivated — by the will-to-completion and then by the incidents and accidents to which that will is specifically subjected in the particularities of the work and the course of design.