NEW Pathway: “Of Looking on Beauty Bare: An Unhurried Study of Euclid’s Elements.”
The Founders’ Education Series: The Quadrivium
“Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace…”
-Edna St. Vincent Millay
“I had not imagined that there was anything so delicious in the world.”
– Bertrand Russell
For those interested in joining the FREE Euclid seminar on September 14th, scroll down to the bottom of the page for the simple sign-up form.
Regular Pathway Start date: Monday, October 9th (daytime) OR Thursday
October 12th (evening)
Option 1: Mondays, 12 pm EST/11 Central, 9 Pacific
Option 2: Thursday evenings, 9pm EST/8 pm Central/6 pm Pacific.
Meeting Frequency: Weekly
Session length: 1.25 hours
Instructors: David Saussy
Pathway Duration: Open, Quarterly
Cost: $250 subscription per quarter (3 months of weekly sessions), with all-access pass to any other slow reading courses.
The Design of the Pathway, “Of Looking on Beauty Bare: A Study of Euclid’s Elements”
Euclid’s great Thirteen Books of the Elements has suffered a peculiar fate in the modern world. On the one hand, his thinking forms in a certain way one indisputable foundation of modern thought (especially his Fifth Book, which presents what later came to be known as a “theory of ratios”). Not only is the formalized language of modern mathematics rooted in a certain interpretation of Euclid, but Euclid is even is used as a foil, over against modern ideas are presented. Sooner or later, the attentive modern reader will come across critics of a so-called “Euclidean space”, as if it were perfectly evident what that is.
On the other hand, we don’t know actually know Euclid’s thinking. Even though it is relatively easy to get a hold of a copy of Euclid’s Elements, his work is foreign to us. We only see Euclid through the lens of familiar conceptions that do little justice to the original. The most common geometry lessons in high school present Euclid in an algebraic manner, which is to say not on Euclid’s own terms. What we call “Euclidean space” is in fact ‘algebraized’ space, space interpreted through the presuppositions entailed in Algebraic analysis.
Yet what are Euclid’s own terms? Something astonishingly approachable. Those of us who come to Euclid, as readers of the original in translation, often have the experience of delight mingled with a touch of bitter disappointment. It is not unusual to feel robbed of something that could have been our own long before. We are now accustomed learning a ‘mathematical language’ in school, but Euclid’s proofs require not a special separate language to learn, but rather our own natural intuitions of space, form and relationships. We have everything we need already to come to the study of the forms and ratios in Euclid. No wonder the Greek word for learning in fact is the root of our word “mathematics”, as if to say, what is to be learned in Euclid is most approachable and learnable matter of all.
It is well known that Abraham Lincoln spent much time with Euclid in his younger years, and we might even discern something of the rigor of Euclid in Lincoln’s thought, for example in his Cooper Union address, or the debates with Steven Douglass (known as the Lincoln-Douglass Debates). There is a reason why Lincoln might have spent so much time with Euclid. Not only is Euclid beautiful, but from Euclid we can learn, in a way like no other, what makes a good argument (or a bad one).
If you are wondering about the intellectual climate of our time – namely what is wrong with it – a fruitful place to spend time (that doesn’t involve hand-wringing but pleasure and satisfaction of sinking your teeth into something substantial) is Euclid’s Elements. A study of Euclid could be the business not of a few specialists, but of all educated people everywhere, or all people seeking an education – which as we know, in truth, is a task for a lifetime.
Our work is to learn how to talk and think about what we see unfolding in Euclid’s Elements. We will start slowly with Book I, the definitions and common notions and postulates. We will move as slowly – or as quickly – as our group is capable of doing. No prior experience in Euclid or the history of mathematics is required. Everyone possesses what is needed already.
Who is it for?
- All those who wish to get acquainted with a forgotten source of western thought, as we encounter it through reflections on Euclid and our own experience.
- Those who “hated” math or think they are “not mathematical” in school.
- Anyone educated in modern mathematics, who would like to investigate the history of mathematics, through direct contact with the primary sources (rather than through the secondary or intermediary sources).
- Someone looking to fill the blanks missing in their own education, which have likely overlooked classical sources.
- Someone who has spent time with Euclid, but not enough time – would like to revisit, and take their time unconstrained by academic calendars.
What is the aim of a conversation (what learning experience should I expect)?
Our approach to Euclid will be conversational rather than lecture. Serious conversation allows discussants to meet the Euclidean text on the basis of discussants’ own questions – thus promoting a more active and intimate relationship to the material, not to mention a better understanding of it.
Conversation aims for reflective understanding of Euclid based upon a sustained work with the text. There are no tests in this learn pathway. Some supporting essays may be offered to help develop an understanding of the difference between ancient and modern mathematics and its relationship to human thought in general. The primary focus of this pathway is the building of reflective understanding based on direct engagement with the text, rather than amassing facts and historical data outside our reflections.
Euclid’s work elegantly builds a succession of theorems on the basis of primary definitions. To each one of the theorems is offered a “proof”, which demonstrates the truth of the theorem on the basis of the foundational definitions, common notions and postulates, as well as preceding theorems. Most of us encountered the “Pythagorean theorem” in school in an algebraic formula, but this algebraized interpretation strips away the originality and fullness of Euclid’s actual thinking. As we read Book I, you will get to see that theorem in its authentic form – the 47th proposition, built upon preceding insights and axioms.
Not all the proofs we encounter are entirely convincing, at least not at first; and this is a question which will engage us in a lively way. What is a proof? What would we find convincing in a proof? How does demonstration work exactly? What does it mean to make an argument? What is the mode of being of these mathematical objects – points, lines, circles, triangles etc. ?
As a matter of reading most actively, and getting the most of our engagement, we can take turns demonstrating theorems. This means that you try to follow in the footsteps of Euclid’s proofs, by showing all the steps he takes setting out the figure and unpacking the relationships, leading the final conclusion. If you try to do this without the aid of notes or the book, you develop a skill that you can’t get in any other way. You’ll find your mind sharpened, and your ability to think and talk though complex arguments improved.
Books and Resources
Euclid Elements, Green Lion Press; First Edition (January 1, 2002)
Interested to see what a seminar on Euclid is like? Sign up below and join us for a free introductory seminar on Euclid.
When: Thursday, September 14th, 9 pm EST, 8 pm Central
Discussion Focus: Book 1: Definitions, Common Notions and Postulates. Bring your questions!
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