FORM-MAKING

FORM-MAKING
Architects, artist, and designers are form-makers. We also desire a sense of order, an idea of arranging the space around us so that we can experience it. Early on in history, Math has been the ideal calculation to solve the order of the world, starting with the Greeks, as a way to make sense of the surroundings one lived in. The precise knowledge of mathematics to provide an identity to define the forms in the natural world, eventually led to these ideals being placed back on the structures we were to live in. Since we build alongside nature, a sense of harmony should exist. Architecture begun to see the order of buildings which in turn represented a harmony with the landscape.

COGITO ERGO SUM
As Reneé Descartes states, "Cogito ergo Sum,"
a french philosopher & mathematician / 1596-1650, coined the phrase that would be the trademark for many others to follow suit in its statement.

“I think, therefore I am.”

Thinking is used as a source to claim that we exist. If you can think it, it is believed to exist. If you are thinking, then you exist. There are thoughts, and thoughts cannot exist without the brain, we we must exist, therefore “we are.”
But since we don't habit our minds, form-making represents our thoughts into creation.

The human senses validate the experience of the object. To bring these two aspects, the mind-to think, and the body-to experience is what develops an a way of existing (in architecture.)

Descartes also goes to say the that visual simplification is a way for us to understand the world with clarity and distinction in our mind.
What is clear to that of a physical object should be as clear to that which is in the mind. If we see a square, we should also be able to see a square in our mind.

Descartes goes to also state that mathematics and geometrical ideas is clear and distinct knowledge (which can be transferred into ordering our surroundings.)

Once again, a square in your mind, if you are thinking it with with clarity and distinction, will be a square when you create its existence. But to know what a square is, you will need tools to help create this form.

TOOLS and TECHNOLOGY
allow for the expression of forms and space to be rendered onto paper or the computer. Notice, that the tools we use all lead back to the cartesian coordinates and the rendering of dynamic symmetry. The horizontal and vertical axes will become a constant in rendering design and the fundamental knowledge in form-making. Tools and technology are what shape architecture. As technology becomes sophisticated, so does its tools. But the cartesian coordinate grid remains.

Pure forms are created from a compass, T-square and 30-60 and 45 degree triangles. Non-traditional or complex forms that need major computation form the cartesian grid can be developed on the computer.

DYNAMIC SYMMETRY
Mathematics is a universal language. Greeks were the first to recognize its distinction. Enter Pythagoras (c.550-500BC), who states that the "visible world is merely an illusion that hides the real mathematical reality of things. Mathematics exist separately from human beings and is prior to the creation of the universe itself. This platonist view of mathematics "pre-existing" and is the real truth to the universe has been used rigorously in architecture as way of solving our visual perception of spaces, mathematical formulas in the form of lines and shapes, and its positioning in space.
The Golden Section or Golden Rectangle became an instrument in defining size and shape in both the floor plan, sections, and the elevations of a building.
After its disappearance in use, Dynamic Symmetry came later in 1920 by way of Jay Hambidge, an author and teacher, as a revival to the use of geometric harmony with nature, and emphasized the use of the diagonal as a way to develop the 'dynamic' process of form making. Dynamic Symmetry shows the description of a square.

Think it as I describe it.

“The square is a very simple shape. It is contained by four straight lines of equal length joined together by four right angles. It appears rigid, uncompromising and empty, but it is on the contrary, an expression of unity. When it is understood, the empty space and its shape becomes more than a graphic element, it will generate the basic elements of design.”

Once it is created, our experience allows us to define it in the world, and we can apply complexity through the use of our human experience with it. Take for example the true quantifiable properties of material things, i.e. length, width, height, size, shape, position, etc. but never of properties such as smell and or touch. We can only experience these senses and cannot be quantifiable.

It is a system that with the use of the technology, both hand drawn and digital means can allow us to look more in depth on the world we exist in.

As Descartes points out; because we have thought of it with our clear understanding and use of mathematics, then it begins to exist. From this, existence beckons experience. One can say that because we have caused it to exist in the world of perception, by way of formulating drawings or software to represent its form, we must now understand the experience. With experience, the use of the human senses, we are confronted with the use of complexity, our senses are not only visual. When we combined these two efforts together, simplicity and complexity, architecture becomes "real." Imagination allow for it to exist and we allow our senses to experience its existence.

CARTESIAN COORDINATES
Descartes also developed the convention of Cartesian Coordinates, representing unknowns in values of x, y, and z and knowns as a,b, and c. In its basic and simple point of view, we can reference the world with the horizontal and the vertical. We branch out from this position once we validate its relationship to this x, y axis. If we begin to look at a grid system, the world can now be seen through the horizontal and vertical, and location with the the 2-d and 3-d realms. We have the ability to record the idea in all points of view, the floor plan, the elevation, and the section. Spatial depth can be recorded in terms of perspective and axonometric views, and difference in scale. In this viewpoint we are able to position ourselves in space on any plane and relate ourselves to the ground.

"The whole is greater than the sum of its parts." Gestalt Principle

SIMPLICITY TO COMPLEXITY
Simplicity is not only in its form, but also in its expression. Simplicity is defined as the absence of luxury and ornament and clarity of expression. Complexity what is to follow.

Precedence in Architecture
Plan to Section Plan to Elevation
As a formative idea, the relationship of a plan to a section or an elevation entails design by using an identifiable correlation between the horizontal and vertical configurations of the building. Embodied in this is the linking of the two realms so that decisions in one arena determine or influence the form of the other.

Analysis -
Structure, Natural Light, Massing, Plan to Section, Unit to Whole, Circulation, Repetitive to Unique, Geometry, Symmetry and Balance, Additive & Subtractive, Hierarchy, Parti

Le Corbusier

Gunnar Asplund

Robert Venturi

Formative Ideas -
is a concept which can be used to influence or give form to design. The ideas offer ways to organize decisions, to provide order, and to consciously generate form. By engaging one formative idea instead of another, one begins to determine the formal result and the manner in which it will differ from other configurations. The use of different ordering ideas may generate different results.
We will look at the following: Geometry, Geometric Derivatives, Equal, Transition, Rotate, Shift, Overlap

IN SUMMARY
Mathematics is science. Science is Reliable. Mathematics is reliable knowledge.
It cannot be interpreted in any other way other that its self-evident axioms, i.e. parallel lines never meet, the shortest distance between two points is a straight line. We obtain a great deal of reliable knowledge through the use of mathematics. These are rules that apply in the realm of architecture.

Experience is sensory. Our senses remember. Our memories develop experiential knowledge.

These two forms of knowledge define architecture to one that is both simplex and complex at the same time. We do not live in caverns of geometry alone. It is through our daily lives and personal interactions that define the spaces we live in. Geometry may gives us an initial spatial position to our place, but it is up to our experience, and our moving bodies to provide it with the experience that can reshape its geometry to accommodate our current viewpoints, our current lifestyles, and our current themes that we investigate and explore. As we begin to create a memory of ideas that shape our daily existence, we slowly develop the complexity forms will need in a changing society.

FORM MAKERS
Andy Goldsworthy - sculptor