LouisKatz | Main / ShapeAndNumber

While I am a strong proponent of the school of art described by the following statements: Aesthetics is for the artist as ornithology is for the birds (Barnet Newman) and Talking about Music is like Dancing about architecture (Lori Anderson), I concede that at times one must talk, must think in concrete ideas, and must even delve into the question of what is beautiful or what is beauty.

When you name something, you delineate it, separate it from the rest of creations. Naming creates edges where none existed before. Naming takes the analog universe and digitizes it. It is a process that simplifies and gives us models.

Unfortunately names takes away as they gives, the remove the conception of the whole, and delude us into thinking or acting like there is a delineation between yellow and green or sweet and sour. But in order to use our conscious intellect, we need to name. To deny naming, to live wholely in the intuitive seems unworkable and unwise (see Blink).

 I absolutely do not believe in absolutes and people are  either dualists, or they are not.

They say a picture is worth a thousand words. It is an obviously untrue statement, but it sets us on a course of understanding. You can't tell a picture, and no number of words adequately transcribes one. Our visual, nonverbal understanding of shape, form, and curves is incredible subtle but it clumsy. It generally has few concrete concepts and its lack of delineations, of names, makes discussion of forms difficult at best.

Ceramics is a field that often attracts those who find math uninteresting, or those who fear it, the numeraphobes. Due to the way our classrooms are structured we learn that the study of numbers is a separate subject from the rest of creation. By the age of 15 most of us just put up with its study in school. Few of us grasp its applicability to everyday events, objects, and ideas.

Each branch of mathematics that we learn as children has a different sort of relationship to the real world and is useful in different ways; geometry, algebra, trigonometry, and calculus. It is calculus that can help us with naming, delineating, subjegating form and shape. Calculus provides us with tools, words and concepts.

When you learn calculus one of the first things you learn is how to take derivatives of equations. Equations are numerical descriptions of shapes. The derivative describes the shape or equation the derivative is taken from in a way that gives a road to understanding.

If you have a curve and an equation that describes it, the first derivative gives you an equation, or shape that describes the slope of the original curve. As the slope (rise/run) increases the first derivative increases. The slope describes how the shape changes over time or over the horizontal axis.

A critical point is the point where the derivative of the function is 0 or does not exist

Discontinuities in the first derivative aka immediate changes in slope. Increasing slope vs decreasing.

Positive vs negative slope.

Second derivative, aka derivative of derivative. Rate of change in the change in slope.

Second derivative discontinuities. Transitions( my word) Second derivative going positive to negative. Inflection.

Louis