Sunday, May 4, 2008

Euclidean Geometry in the Core Curriculum – an Epic Study…

Very few schools are quite like the University of Dallas. In fact, no school is quite like the University of Dallas. A school where advanced technology is secretly frowned upon and long skirts and bowties are main-stream, UD – a contained, almost secret, bubble of classical knowledge within the modern world – is a place like no other. Boasting a Core Curriculum incorporating classic novels and solid Theological Truth, coupled with a wide range of History, Logic, and Philosophy courses, the University of Dallas seeks to train students to think independently. Striving to impress an understanding of things of both the old and new worlds in hopes that graduates will go out into the world integrating their newfound understanding of Truth into their jobs, classrooms, independent businesses, and daily lives, the University of Dallas is tag-lined as “the place for independent thinkers.” The mission statement claims:
“The University of Dallas is a Catholic institution that seeks to educate its students to develop the intellectual and moral virtues, to prepare themselves for life and work, and to become leaders in the community. Through intensive teaching, interactive discourse, and critical analysis, the university pursues truth, virtue, and wisdom in the liberal arts and professional studies.”

Embedded within the unique tradition of the University of Dallas is the Core Curriculum. Utilizing, first and foremost, ancient thought, the Core provides a solid foundation for students and professors to maintain a concrete basis for academic thought and growth. Very distinctive to UD, the Core is designed to present what the best learners of the past have already discovered. In studying these concepts, students are able to further engage in dialogue and continue their search for Truth. Over the course of two years, students take over 60 credit hours that are part of the Core. With the courses constantly building upon one another, the very first Literary Traditions class somehow connects to the very last Philosophy, History, or Theology course. As the Core classes are taken, a student’s knowledge is constantly expanding, allowing the serious student to be treated with respect and dignity as information is presented that is truly vital to their growth in the intellectual and academic world. Incorporating important texts such as Homer’s Iliad and Odyssey, Aquinas’ Summa Theologiae, Plato’s Republic, Kennan’s American Diplomacy, Henry Adam’s autobiography and study of the American culture, the writings of Shakespeare, Augustine’s Confessions, Dante’s Divine Comedy, and numerous other works that provide a glimpse into the minds of profoundly influential thinkers, no book can be excluded because each presents a different concept that is most necessary to preserving the ideals of the University. Included within this Core curriculum is a most vital Mathematics course that studies the first thoughts of an ancient Greek mathematician, Euclid.

Considered the “Father of Geometry,” Euclid of Alexandria lived in the time of Ptolemy the First, about 323 BC to 283 BC. Very little is known about Euclid’s actual life, but many assume that he studied at Plato’s Academy in Greece and was very active in the Library at Alexandria. It is Euclid’s Elements that makes him the patriarch of mathematics. The first single, logically coherent framework of mathematical thought, the Elements included a series of precise mathematical proofs that still hold over 23 centuries later. The first math textbook, probably dreaded by all students who came in contact with it, presented a method that taught how to incorporate a small set of axioms in proving a series of propositions (theorems) that were derived from these axioms. Explaining plane geometry, axiomatic systems, and solid geometry of three dimensions, Euclid eventually extended his mathematical thought to a finite number of dimensions, establishing the Elements as the unparalleled text that would lead to the number theory of modern mathematics today.

The basic purpose of Euclid’s geometrical methods was and is, quite simply, to draw conclusions after certain information is given. This simple deduction process, one that most people are taught in the early days of elementary school, is absolutely essential to basic thought processes. When information is presented one must be able to infer that the said information will lead to certain actions happening or particular concepts being true. For example: Jane knows the refrigerator is broken, and because the milk she bought at the store will sour if she leaves it in a hot refrigerator, she decides to put the gallon of milk in her neighbor’s refrigerator until she can get her own fixed. On the mathematical level of Euclid, this very simple deduction process is incorporated when proving the existence of points, lines, points of intersection, etc. In short, it is Euclid’s Elements - a mathematical text integrated into the Core Curriculum at the University of Dallas - that introduced and preserved the deductive thought process into the intellectual world.

To create this intellectual world so necessary for the preservation of a functioning society, a liberal arts education must be instituted and fostered. For a liberal arts education to truly work, students must immerse themselves in an environment where conversations can be made with the thinkers of the ancient world. Just as the numerous dialogues of Plato were written as a conversation between a superior thinker and an inferior pupil, so too must the University experience be an exchange between the minds of old and the fresh young minds anxiously anticipating the molding of their untainted thought. Therefore, this education is more than a student sitting within a classroom, drearily taking notes and regurgitating information weeks later on a monstrously huge exam. This education is training the student to be modest and bold, unpretentious and daring. Students must humble themselves enough to quiet their restless thought so the established thinkers of the ancient world can penetrate their minds, yet they must also take these thoughts and use them to break away from the noise of the modern world. There can be no compromising of this concept, simply because it is what makes a liberal arts education truly liberal; that is to say, completely open to the thoughts of others, but aware of the necessity of implementing these thoughts into a world so often polluted with the thoughtlessness, the cheapness, of contemporary thought. It is, in short, a return to the old world in order that the new world exists as a Truth filled society.

This concept of a liberal arts education is exactly what the University of Dallas strives for, and often accomplishes, every day. The University of Dallas maintains that it is “committed to the study and development of the western tradition of liberal education, and the Catholic intellectual tradition,” as well as being guided by “principles of learning that acknowledge transcendent standards of truth and excellence that are themselves objects of inquiry and research.” Quite simply, UD hopes to foster an understanding of the liberal arts and the teachings of the Roman Catholic Church while also striving to study the Truths of the world that surpass the merely physical. On a very basic level of explanation, the University of Dallas is built on the concept that seeking answers -investigating ancient and modern thought – will lead to complete enlightenment and understanding of Truth. A liberal arts education is, as Dr. Leo Strauss of the University of Chicago says, “an education in culture, of culture.”

Thus, the liberal arts education – the education that guides students through the ancient minds so that their modern minds might function in accord with Truth – cannot exist without the Core curriculum placed at the very center of the UD education. Without four required English classes taking students through the most primary novels and poems since the first words were written on any page, without four History courses guiding students through the events of the European and American worlds, without three Philosophy classes incorporating the most basic and most advanced thoughts of those who questioned ‘why?”, without two Theology courses studying the Biblical texts and the Theological traditions of the western world no student, at least no self-respecting student, would gain the knowledge necessary to survive in the harried intellectual world of today. But before any of these courses can be taken – before Homer can be read, Dante studied, and Plato exhorted upon, before Henry Adams can be critiqued, Hopkins analyzed, and Augustine pored over – a class is vital, absolutely necessary, for the young, inquiring mind, Euclid must be examined. The Elements must sit first on any liberal arts student’s shelf, to be perused frequently, to be pondered regularly, to be considered habitually. Deductive thought is essential for the liberal arts student, simply because if they are to engage in the conversation necessary with the ancient thinkers then they must be able to draw conclusions from what they discover in order that they implement the thoughts of those who have come before.

Edna St. Vincent Millay, an American poet greatly influenced by Shakespeare and Milton, wrote:
Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.

O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.

Her point, quite simply…Only Euclid, the Greek mathematician so keen on presenting deductive thought by way of axioms proving theorems, has truly seen beauty. Only this pupil of Plato’s prodigies has experienced that which is truly glorious, because only he has pondered the things that are and the things that could be. No one else, neither then nor now, has had the privilege of seeing the beautiful for what it truly is – an unabashed, most spectacular gift from the Heavens themselves.

It is only the student committed to the study of Euclid that will advance within this world. Only the man, woman, or child dedicated to the deductive thought process that will have the chance to encounter the splendid things of the world. It is the UD student’s study of Euclidean Geometry - the examination of Euclid of Alexandria’s Elements - that will lead their minds to magnificent discoveries, allowing them to, again and again, encounter Truth.
QED