(2) Thinking is where architecture originates; drawing is the first step in its realization. Drawing is the wellspring for the idea of building. In the light of Goedel's Proof, the idea of reason is called into questioned and intuition gain credence and validity. Freehand drawing is examined in the context of contemporary conditions and an argument is presented that posits freehand drawing as an essential means of understanding important intuitive forces that, in conjunction with rationalism, are implicit to the process of design. Rationalism and intuition are parallel themes that may sometimes contradict but must dramatically combine if critically challenging results are expected.

(3) The topic of drawing and intuition is one that must be argued for and made accessible because too often intuition is overlooked and pushed aside in favor of the more easily explained rational and economic processes. We often go to extremes in presenting data, information, and diagrams to explain or at least prove to ourselves the necessity of reason, with little or no acknowledgement of the intuitive. But rationalism is inherently incomplete. If either rationalism or intuition is pursued to their extreme positions then one's results will be suspect. In concert, rationalism and intuition are equally important and vital to making architecture. Given this, I assert that drawing is a vital and accessible means of working intuitively and consequently it contributes to the success of making architecture. Quite simply, freehand drawing is essential to an architect's acquisition of knowledge.

I. Goedel's Proof

"What makes the desert beautiful is that somewhere it hides a well."
Antoine de Saint-Exupery

(5) Geometry is based upon deductive reasoning. This method of thought is founded upon the idea of axioms or postulates that must be accepted a priori, or without proof, in order to derive a set of theorems. An example of an axiom is: only a single, straight line can be drawn through two points. Axiomatic thought is a method created by the Greeks to establish conclusions based upon "explicit, logical proof." This method survived essentially intact until the twentieth century, and remains a critical means for understanding our world and almost every facet of it. This process is vital because it eliminates the tendency of the human mind to judge or evaluate simply through observation and instead posits the idea that a proof, or logical sequence of events, must occur repetitively before the results can be verified, known, and ultimately believed. Consider that if a projectile is launched from a certain point at a fixed rate, then it can be predicted where it will land. Such "if/then" rules put before us a series of seemingly limitless possible consequences. In its more pure form this model of thought represents, perhaps, the conception closest to perfection known and is, for many, God, because what makes the idea of logic beautiful is consistency. Logic exists outside the realm of language, culture, place and time. In essence, logic knows no boundary and burden; it simply is.

(6) Goedel's argument, however, challenges logic's basic concept of consistency. Based upon the idea of consistency, mathematics (and its armatures: science and technology) have become increasingly abstract. This abstract complexity poses a serious problem, one that Newman and Nagel characterize in the following terms:

"which is the question of whether a given set of postulates (axioms) can serve as a foundation of a system that is internally consistent, so that no mutually contradictory theorems can be deduced from the postulates. In other words, given any complex set of propositions can the proof be complete?"

(7) They observe further "that the axioms are interpreted by models composed of an infinite number of elements. This makes it impossible to encompass the models in a finite number of observations; hence the truth of the axioms themselves is subject to doubt"^Ref.1. Thus an increasingly larger number of axioms can effectively prove an increasingly larger number of theorems. Given a climate of thought that assumes that all circumstance and phenomena can eventually be understood and proven with number and formula, Goedel's revelation is enormous. He simply proves this assumption false, and concludes the axiomatic method has limits. As Nagel and Newman say,

"he proved that it is impossible to establish the internal logical consistency of a very large class of deductive systems -- elementary arithmetic, for example -- unless one adopts principles of reasoning so complex that their internal consistency is as open to doubt as that of the systems themselves. In light of these conclusions, no final systematization of many important areas of mathematics is attainable, and no impeccable guarantee can be given that many significant branches of mathematical thought are entirely free of internal contradiction." ^Ref.2

(8) With Goedel's proof, doubt has not only been introduced but verified. No longer can we believe science will ultimately find all solutions to all problems. Simply, Goedel discovered a virus in the system. His work attacks the idea that one holistic paradigm of thought is possible. Consequently, another god was destroyed.

(9) But Nagel and Newman, being mathematicians, cannot assault their deity so easily. They conclude, "Goedel's proof should not be construed as an invitation to despair or as an excuse for mystery -- mongering or that there are truths which are forever incapable of becoming known, or that a 'mystic' intuition must replace cogent proof." At once they confirm the fact that Goedel has undermined an entire system of thought but they never quite admit mathematics is entirely subject to doubt. Their conclusion acknowledges a genuine fear we all seem to possess even to the point of slandering intuition and intuitive thought with words such as "mystery-mongering." One can easily feel their angst and fright concerning what might occur if mysticism were to again become pervasive. But this fear characterizes the modern condition and points toward an important area of concern.

(10) Goedel's proof calls to light the notion of absurdity. Mathematicians use a concept called reductio ad absurdum ^Ref.3 which is a method of proving that, if a proposition in question is not true, an absurdity results. This is one of the central themes of the twentieth-century philosophy as evidenced most completely by Albert Camus and is pervasive throughout modern philosophy.

(11) The arguments set forth by many twentieth-century philosophers, including Goedel, carefully use logic to disprove logic and thereby set into motion a perpetual paradox. There is no solution to this paradox given our current conditions, but there is a means of stepping outside the argument where one can fully sense the totality of the situation and consequently begin to describe it. This stepping aside is the intuitive, inductive, view. One does not have to participate fully in the event to understand the event. At some point one must feel the circumstances as well as think them. Many philosophers carefully avoid the intuitive, sensual role of irrational thought because intuition is the origin of all proven or unproven assumptions. Goedel's argument, however, recognizes that to acknowledge intuition is to acknowledge the irrational as the basis for all rational thought.

(12) Yet it is only through intuitive, empirical, and inductive means that we can begin to see. It is the role of the artist to enlighten. It is the method of the artist to feel.

II. The Body and the Builder

"By nature architecture must begin in the realm of the imagination and journey to the real."
John Hejduk

(14) But the human mind, being a complex system of thought, inexplicably cannot accept this simplicity and we crave more. Why, for example, do cathedrals exist? They are often three or four times as tall as they need be and use very expensive materials. Why are some buildings of brick and mortar, others of steel and glass? Obvious as these questions may seem, the answers is extremely complex. No clear answer ever emerges, especially when one adds to the aesthetic equation issues of history, culture, and time. More and more ideas are piled on to the heap in such a way that the original intent is lost. To regress, we build in order to solve problems concerning the human body. Be it a problem of sickness or a problem of comfort, the body is central to the purpose. Consequently, the idea of logic and rational necessity is more easily understood architecturally when couched in terms of function and need. Complexity arises because the body is not only an end, or a problem solved, but it is also a means, or a method of solution. When we speak of means we address the idea of education, where method becomes one with necessity.

(15) One of the earliest practitioners of architecture to write about his subject was Vitruvius. In his treatise, The Ten Books of Architecture, he grounds his entire thesis in education ^Ref.4. He succinctly states that both practical knowledge and theory are required to "attain object and carry authority." Consequently we see built before us that which we have created. Vitruvius then adds a curious caveat when he stated, "In all matters, but particularly in architecture, there are these two points: the thing signified, and that which gives its significance. That which is signified is the subject of which we may be speaking; and that which gives significance is a demonstration of scientific principles." This statement is important because it places before us the idea that two separate and distinct ideas are contained within one object: the human body. We both think and act. Our physicality determines both the built and imagined. When working in harmony with the other the results are, quoting Vitruvius, "firmness, commodity and delight." In effect, what Vitruvius did was to place architecture in the realm of psychology, and psychology is ultimately of the body. So what does this mean? In order to learn to design we must think and do. We must have ideas that can be built and we must have buildings that can be understood and explained to a large number of people. To facilitate this learning knowledge must be acquired physically. Learning, then, is first a physical act. Mixing mortar and picking up bricks becomes equally important to picking up a book and comprehending words. In the origins of the human mind, the signifier and the signified coexist. Immediately after realization, they are split, like atoms, into the physical and mental, keeping in mind each are contained within the realm of one body. One simply cannot be relegated to the passive role of observer and expect to understand how or why something exists. To completely understand architecture we must participate with it, just as to completely to understand philosophy we must live it. It does not matter which comes first, thinking or doing; we must do both. We must think and act.

(16) Let us now address the contemporary role of the architect as practitioner and examine how the ideas of doing and thinking are manifested in current conditions. Most specifically two primary concerns are examined in the process of how architecture is made. The first is physicality of the body; the second addresses the role of intuition and the fear of the irrational.

(17) In an architect's office one finds a world of drafting stations, computer terminals, meeting rooms, and racks of reference books. Upon entering the space where buildings are drawn and produced, there is very little evidence of the enormous complexity of what goes on in this largely bureaucratic process. As a rule, less than half of the total billable hours that comprise a project are spent doing drawings. Most time is spent in a conference room negotiating with clients, bankers, developers, contractors, and an assorted committee of lesser players. Once a contract has been signed and a schedule set, the primary conditions that determine whether or not a building will exist have already been determined. In a typical scheme of events, design and design development will account for approximately twenty to twenty-five percent of the total expenditure of time. This figure, by some accounts, is high. Economics and bottom line decisions account for most time spent. This is our reality and, hence, all architects must confront this to survive. What, then, are the salient characteristics of this process? Primarily, the methods and techniques used in bidding, negotiation, documentation, and administration are rational, calculated, scientific decisions that leave nothing to doubt and nothing to chance. As evidenced earlier, the rational thought process is inherently flawed. Truth can never be fully ascertained and no system is beyond reproach. If we continue to produce construction based largely upon rational, economic decisions, the built environment will become increasingly more banal. Intuitive decision-making must be acknowledged and allowed to flourish if architecture is going to remove itself from the rut. Intuition is needed to give architecture meaning; and economics cannot be the driving determinant if architecture is to have substance. We cannot continue to base our decisions solely on life-cycle depreciations and actuarial tables. The profession is editing the imagination from the process of making architecture and the ability, or even desire, to dream is no longer pertinent because how can one bill a client for such thoughts. Yet dreams are where architecture begins and these origins are inherently important.

(18) The second important concern in the methods and manners of making architecture is the role of the human body in the production of both drawings and construction. Due largely to economics and time, the process of making architecture has more to do with assembly than with making. We take a kit of parts offered through catalogues, then pick, choose, and document this process before sending something out for bid. What occurs outside the office is nominally a process of shipping and connecting parts until the building is complete, ribbons are cut, and it's a done deal. What should occur in the office is in the nature of drawing. Traditionally, office drawings have been hand- produced sheets that inherently called attention to a level of craft -- craft being an acquired skill gained through only hours of labor extended over years of practice. Quite literally, drawing has been a hands-on experience that necessarily puts the human body into an active role of production. This process has existed intact for many centuries and has served us well. But, as we are wont to do, we are liable to subject this process to revision. Indeed, we find computers and computer-aided drafting taking an increasing role in the production of architectural drawings. Once a database of details has been stored on a computer disc, the architectural "draftsman" increasingly becomes an assembler of various unrelated pieces until they become a unified whole. This method will continue to grow in importance because it is efficient and profitable.

(19) What are the implications for an architecture of meaning and substance? Unless the computer is placed into a role subservient to the dreams and imagination of the designer the products we construct will continue to be increasingly more banal, owing much to the rational necessity of economics and very little to the thoughts, hopes and dreams of our culture and civilization. We must find ways to activate the physicality of the body and the critical nature of its irrational, intuitive imagination.

III. Knowledge, Symbol, Thought

"And yet what they are looking for could be found in one single rose, or in a little water... but the eyes are blind. One must look with the heart...."
Antoine de Saint-Exupery

(20) It is in this perspective that drawing appears essential to an architect's acquisition of knowledge. It confirms reality and consequently confirms existence. Very few activities do this -- very few indeed among those involved in the process of architecture. To make a drawing with one's hands activates the imagination and stirs the transient qualities of the human mind to create and find spiritual presence. Perhaps it is the incompleteness that is craved; a direct link to the question of the here and now. Computer screens, like televisions, beckon us to a world of electronic displacement where the role of artistic expression is suppressed or, worse, polished to a fine and precise level of order that will guarantee commercial success. It is no wonder this electronic artifice is so important because our world has largely been voided of meaning except for what someone tells us on television. What exists? What is truth? If it is not on television then it must not be real. We have created a culture in which Batman, Superman, and Elvis are as real as this building we inhabit.

(21) Or are they? If we accept the premise that reality is that which can be known through all the senses, i.e., the human body as a whole, then these characters become nothing more than meaningless thoughts. Paul Ricoeur's writings speak of the idea that "the symbol precedes the thought." This statement acknowledges that an object exists first as an object then as a descriptive thought, i.e., language. Our media world reverses this process by telling us the language, or descriptive thought, exists first and the symbol is a secondary conclusion. In this context, nothing is real but what we think. Imagination is distorted and symbols no longer have meaning except to serve the media-maker.

(22) Artistic expression; making art; using one's hands and body to shape a real and vital material, resists this tendency. Craft calls into question the material and the intent of the maker. Skill gained through this direct contact is meaningful; it describes time; it leaves behind a history of itself within and inherent to the process. For an architect, drawing with one's hand without the aid of a ruler or straight edge or fine line pencil necessarily connects one first to the symbolic thought and second to the means by which it exists. The origin has meaning. With meaning, culture is completed. We can have a history once more.

Concluding Remarks

(23) We must not allow the idea of rational necessity to control the building process. The computer cannot be thought of simply as a tool for producing more work, faster. Computer technology must be made subservient to the imagination so that mere cause/effect schemes are not the only products. We must seek out new, and perhaps undiscovered, methods that acknowledge the human body and its intuitive understanding of phenomena.

(24) The challenge is to convince our colleagues in related disciplines of the importance of these issues: there is more to building than mere necessity and more to knowledge than merely thinking.

Ref.1: Ernest Nagel and James R. Newman, Goedel's Proof (New York: New York University Press, 1958).

Ref.2: Ibid.

Ref.3: Horblit, Marcus and Kaj L. Nielsen, Plane Geometry Problems with Solutions (New York: Barnes & Noble, 1970).

Ref.4: Vitruvius, The Ten Books of Architecture (New York: Dover, 1960).

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