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From the President

Dear Reader,

This issue of our bulletin includes articles that show two sides of the imagination. Senior Fellow Erik Ellis expresses why as a humanist scholar he values how the Quadrivium provides an objective basis for understanding and instantiating beauty, while Emily Kwilinski writes of the joys she has found as an adult in returning to the imaginative literature of her youth (we include a few selections from Lucy Maud Montgomery’s Anne of Green Gables series to give you a taste). 

The Quadrivium has been much on my mind of late. I am writing this introductory note from the Pascal Instituut in Leiden in the Netherlands. As with our Boethius Fellows, Jeff Lehman and I are beginning a second year of teaching the Quadrivium to a small group of very bright students working towards PhDs in a Great Books program. We have begun each year with a week of in-person classes, grounding our teacher/student relations in personal interaction that is impossible with Zoom meetings alone. We have broken bread together, while having conversations that range from Leiden’s dramatic fight for independence in the 1570s to the character of Cassius in Julius Caesar, to whether equality of opportunity is a good to be desired or perhaps a justice to be insisted upon. 

In a walking conversation (almost everyone bikes or walks in the cities here), Dean Gerard Versluis noted that, inspired by programs like that of St. John’s College in Annapolis, their curriculum includes mathematics and literature. This has caused them difficulties in recruiting students, who are often eager to study philosophy and theology but wonder why they should be required to take courses in subject areas they consider irrelevant. There are many things we can say to explain this, but often the proof is in the pudding. I loved hearing from Femke Heijmans, one of our students, who expressed her amazement at how much she learned from last year’s study of Euclid, but even more at her realization of how much, much more there is to know than she will ever be able to. 

The same question came up in one of the several academic retreats I led for teachers this summer. The three-day program of integrated learning includes a session in which participants prepare to publicly present Euclid’s demonstration of how to bisect an angle without using a protractor. In the midst of some energetic discussion to understand the arguments and entertain other ways, one participant raised the question, “But what use is all this?” Some participants excitedly pointed out that they had been enjoying a palpable experience of learning to use reason. I invited them to imagine how vastly different their life would be if they had been trained so that they could habitually reproduce even difficult geometrical demonstrations clearly, orderly, and intelligently. 

These are among the profound effects that the Quadrivium has traditionally had on students and continues to have today on liberal arts students fortunate enough to be required to develop their powers of mathematical thinking. The Boethius Institute is in a privileged position to promote the inclusion of the Quadrivium in today’s classical liberal arts renewal, and it will be a primary focus of our efforts in the next few years. 

In other news, the Augustine Institute graduate school, home base for Jeff Lehman and myself, moved over the summer to a beautiful new campus in St. Louis. This threw a wrench into our plans to host several events this summer, but will provide outstanding opportunities in the near future. We hope to welcome you there in the future. 

From a Review of A Brief Quadrivium and Teaching the Quadrivium: A Guide for Instructors

by Senior Fellow Dr. Erik Ellis

From a review of A Brief Quadrivium and Teaching the Quadrivium: A Guide for Instructors originally published in Principia 3, no. 1 (2024)

Classical educators know that the canon of the liberal arts numbers seven, but very few of us make much progress beyond the trivium before we jump headfirst into philosophy. We approach advanced mathematics through the modern canon of algebra, geometry, trigonometry, and calculus, not the four arts of the quadrivium—geometry, arithmetic, music, and astronomy. Even the one common term, geometry, means different things. For most of us, it is something like applied algebra. The minority who have gone through Euclid will know that the classical art of geometry uses no numbers at all, only proportion. If we have some direct knowledge of the quadrivium this is only very rarely because we studied them as they are. We tend to learn about them, presenting them either as primitive (and therefore obsolete) forms of the STEM fields, or as a few wonder-inspiring diagrams of the golden ratio projected onto the masterpieces of the Old Masters sandwiched between sessions of mathematics classes hardly distinct from those offered in non-classical educational settings—two excellent starting places are Gary B. Meisner’s Golden Ratio and Mirana Lundy’s Quadrivum. In the end, if the quadrivium enters into our thinking or our teaching, it is at second or third hand, and we and our students at best come to appreciate its historical presence in the past of Western culture without acquiring the intellectual character or skills that would enable us to use the quadrivium productively in our own attempts to make the world more beautiful.

This is due to reasons both theoretical and practical. Many who would never question the enduring value of the arts of grammar, logic, or rhetoric struggle to see how the historically constructed quadrivium could be of any more than historical interest to contemporary educators. A deeper problem is that since antiquity these arts have been debased and abused, such that Latin dictionaries list “astrologer or wizard” as the second definition of the noun mathematicus. For such reasons, Plato’s Timaeus and Boethius’ De Arithmetica tend to be reserved for those undertaking advanced studies of those authors, and the immense influence exerted by these texts on Western culture is often presented as a curiosity or problem rather than as a fact whose recovery might lead to fresh insight in the present.

It comes as no surprise that our inability to accommodate pre-Copernican astronomy and pre-Cartesian mathematics (with the notable exception of Euclid) to our narrative of scientific revolution and progress has not led many of us to develop classroom resources that would give our students access to these traditions and help them develop the skills the arts promise to impart. Green Lion Press, whose edition of Euclid is no doubt well known to many readers of Principia, follows a grand narrative of the “Scientific Revolution” to a great extent in their offerings, providing the text editions that make it possible for students in great books programs to re-create the discoveries of Kepler, Newton, Lavoisier, and Faraday. When I met Howard Fisher, an associate editor at Green Lion Press, I asked him why they do not offer editions of Aristoxenus, Boethius, or other “quadrivial” authors. He told me there is no editorial policy against it, and in fact, they would if they could. The problem, he said, is a lack of editors. Would I like, he added, to try my hand at doing it myself?

Fortunately for me, a humanist who has not yet mastered the arts of number, Peter Ulrickson has provided the sort of book I have long imagined but not had the skill to write. A Brief Quadrivium divides the four arts into a thirty-week curriculum, distributed approximately equally across geometry, arithmetic, music, and astronomy, ending with three brief chapters that consider the quadrivium’s relationship to modern physics, mathematics, and music theory and its propaedeutic role in “preparing us to seek the highest, unchanging things.” Upon completion of the curriculum, students will not only have been exposed to wonder, but they will also have laid the foundation of a detailed, technical knowledge of the quadrivium that they can use both to understand the nature of reality and to produce works of art, in the Aristotelian sense, imitating nature to bring order to chaos and instantiate beauty in the world.

A key component of Ulrickson’s presentation is the continuity of the quadrivium and the trivium as two parts of a whole, as opposed to the modern division of the disciplines into arts and sciences. An excellent example of this in practice is Ulrickson’s gentle but persistent and effective explanation and use of technical terminology. Relying on a philosophy of language based in Aristotelian ideas that recognizes the adaequatio of words, concepts, and things and the status of each of the components of the quadrivium as stable and articulated technai, Ulrickson provides readers with an account of terms like “definition,” “lemma,” “proposition,” and “conjecture” and encourages them to build up familiarity with them. Those who, like me, have made the transition from “literary studies” to the “trivium,” who have come to appreciate the precision that training in the arts of language can bring to conversations about the great ideas, will be pleased to ground their developing knowledge of the quadrivium in this system of language. Properly technical language is not jargon; it is rather a key constitutive element of the knowledge and practice of the art, and Ulrickson presents this in a compelling way that will resonate with classical educators.

Rediscovering Classic Children’s Literature as an Adult

by Emily Kwilinski

C.S. Lewis dedicates his classic The Lion, the Witch, and the Wardrobe to his goddaughter Lucy with the following words: 

I wrote this story for you, but when I began it I had not realized that girls grow quicker than books. As a result you are already too old for fairy tales, and by the time it is printed and bound you will be older still. But some day you will be old enough to start reading fairy tales again. 

I’m not sure I ever reached an age when I considered myself “too old for fairy tales,” but there have certainly been seasons in which other things seemed more important. Pursuing an English major and Classical Education minor at a liberal arts college, I was up to my eyes in Aquinas and Aristotle, Faulkner and de Tocqueville. My dorm room was infested with Greek flashcards. Books that I had read, highlighted, and tabbed piled up—books that I hadn’t read piled up higher. (I used to joke that the only thing I got from my English major was a stronger grasp of how many things I had not read.) 

Counterintuitively, it was around that time that I started picking up my childhood books again. Not only the fairy tales like The Hobbit and The Lion, the Witch, and the Wardrobe, but also the books that had taught me, as a girl, what girlhood was: Anne of Green Gables, Emily of New Moon, A Little Princess, The Secret Garden. I developed a habit of reading a few chapters of these long-forgotten childhood classics before I fell asleep at night. Somehow, I knew it was precisely what I needed. Over the years, I have turned to children’s literature again and again, and developed more articulate ideas on why this practice was so fruitful.

Children’s literature is simple. 

I first started reading children’s books because they were the books I had on hand, and they didn’t feel intimidating. Their simple language was easy to read after a day of slogging away at a medieval theology paper in the library. I already knew what was going to happen in these books, and that was somehow soothing, making them perfect bedtime reading.

Many of us have favorite books from childhood we’d love to revisit, or childhood classics we never got to read. Unlike some other classics we may wish we had read (War and Peace is my personal nemesis), children’s literature is easy to “catch up on.” If you have your own children, you can even read books with them that you wish you had read yourself, enriching both your and their experience. 

In its simplicity, children’s literature reminds us that literature does not need to be complex and wordy in order to have deep reservoirs of meaning. Especially those of us who dwell in lofty academic spheres sometimes need this reminder—the simplest way of saying something is often the best way. 

Children’s literature is (or should be) moral. 

Admittedly, children’s literature, especially the classics, can be a tiny bit moralistic. Often the lessons meant to be drawn from it—being happy without wealth, for example, or caring for those around us—can be a little bit on-the-nose.

But when I returned to children’s literature as an adult, I felt that touch of moralism was a good corrective. Sara Crewe’s patience in A Little Princess, the healing powers of human connection as depicted in The Secret Garden, Anne Shirley’s indefatigable enthusiasm—I felt all these traits reawakening my desire for a beautiful life, just as they are meant to do for children. It was a fruitful moment to reflect on the woman I had meant to become when I had been formed by these incredible characters—and the woman I was actually becoming. 

I certainly don’t think all literature should be as morally simple as these “fairy tales” and formative children’s books. But it can be helpful to return to the basic categories of good and evil as they are laid out in the books we read to children—if only because they can help us discern good and evil in other books, and even in our own lives. It’s easy for me, as an adult sophisticate, to justify my impatience or envy or discontent. But when I’m faced with a children’s book that explains in simple and compelling terms that it is better to be patient and kind and grateful, I have to feel a little silly. I knew as a child that these things were true, and I know it as an adult too. 

Children’s literature awakens our wonder for life. 

When we are children, everything is new. It is always funny to me to revisit a book I read as a young child and understand a turn of phrase or description that I never understood before, because I didn’t have enough context for it. More frequently, though, reading children’s literature renews my wonder at life because it affords the perspective of a child who is experiencing it all for the very first time.

Whether it is Mary running all over the garden with Dickon and discovering that the rose bushes are alive underneath all their old, rotten branches, or Anne accidentally dyeing her hair green, or Polly and Digory exploring the rafters of a whole row of houses, children’s literature reminds me that life is extremely interesting, after all. It can be easy to forget this in the daily slog of adulthood, when one day seems very much like another. In a children’s book, every day is a new step in an adventure. 

Over the years, my own adventure has led me through a master’s in theology and a Ph.D. in Theology, the Imagination, and the Arts, and now I’m lucky enough to be reading “fairy tales again” as part of my daily work.

As a reading guide for an app called Read With Me, I’m currently taking a group of people through Frances Hodgson Burnett’s The Secret Garden, a classic I’ve read many times. Still, every day new things jump off the pages. If you want to make reading children’s literature a part of your life, you’d be welcome to join us. I’m also including a list of my favorite children’s classics, both those that are well-known and those that are a bit less well-known, if you want to build a children’s literature reading practice of your own! 

• The Hobbit
• The Chronicles of Narnia 
• Winnie the Pooh
• An Episode of Sparrows 
• Little Women
• Little Men
• Pollyanna
• Caddie Woodlawn
• Anne of Green Gables (and series) 
• Emily of New Moon 
• A Little Princess
• The Secret Garden 
• The Lost Prince
• Swallows and Amazons
• The Wind in the Willows
• The Princess and the Goblin
• A Girl of the Limberlost
• Charlotte’s Web
• Little House on the Prairie
• Heidi
• Peter Pan
• Around the World in Eighty Days
• Railway Children
• Five Children and It
• The Little Prince
• Pippi Longstocking
• The Great Adventures of Sherlock Holmes
• Hans Christian Andersen’s Fairy Tales
• The Blue Fairy Book
• The Adventures of Tom Sawyer

Excerpts from Anne of Green Gables

by Lucy Maud Montgomery

From Anne of Green Gables, Chapter 35

Then, almost before anybody realized it, spring had come; out in Avonlea the Mayflowers were peeping pinkly out on the sere barrens where snow-wreaths lingered; and the "mist of green" was on the woods and in the valleys. But in Charlottetown harassed Queen's students thought and talked only of examinations.

"It doesn't seem possible that the term is nearly over," said Anne. "Why, last fall it seemed so long to look forward to — a whole winter of studies and classes. And here we are, with the exams looming up next week. Girls, sometimes I feel as if those exams meant everything, but when I look at the big buds swelling on those chestnut trees and the misty blue air at the end of the streets they don't seem half so important."

Jane and Ruby and Josie, who had dropped in, did not take this view of it. To them the coming examinations were constantly very important indeed — far more important than chestnut buds or Maytime hazes. It was all very well for Anne, who was sure of passing at least, to have her moments of belittling them, but when your whole future depended on them — as the girls truly thought theirs did — you could not regard them philosophically.

"I've lost seven pounds in the last two weeks," sighed Jane. "It's no use to say don't worry. I WILL worry. Worrying helps you some — it seems as if you were doing something when you're worrying. It would be dreadful if I failed to get my license after going to Queen's all winter and spending so much money."

"I don't care," said Josie Pye. "If I don't pass this year I'm coming back next. My father can afford to send me. Anne, Frank Stockley says that Professor Tremaine said Gilbert Blythe was sure to get the medal and that Emily Clay would likely win the Avery scholarship."

"That may make me feel badly tomorrow, Josie," laughed Anne, "but just now I honestly feel that as long as I know the violets are coming out all purple down in the hollow below Green Gables and that little ferns are poking their heads up in Lovers' Lane, it's not a great deal of difference whether I win the Avery or not. I've done my best and I begin to understand what is meant by the 'joy of the strife.' Next to trying and winning, the best thing is trying and failing. Girls, don't talk about exams! Look at that arch of pale green sky over those houses and picture to yourself what it must look like over the purply-dark beech-woods back of Avonlea."

"What are you going to wear for commencement, Jane?" asked Ruby practically.

Jane and Josie both answered at once and the chatter drifted into a side eddy of fashions. But Anne, with her elbows on the window sill, her soft cheek laid against her clasped hands, and her eyes filled with visions, looked out unheedingly across city roof and spire to that glorious dome of sunset sky and wove her dreams of a possible future from the golden tissue of youth's own optimism. All the Beyond was hers with its possibilities lurking rosily in the oncoming years — each year a rose of promise to be woven into an immortal chaplet.

From Anne of the Island, Chapter XIV. (Two young women face the reality of death.)

THE SUMMONS

Anne was sitting with Ruby Gillis in the Gillis’ garden after the day had crept lingeringly through it and was gone. It had been a warm, smoky summer afternoon. The world was in a splendor of out-flowering. The idle valleys were full of hazes. The woodways were pranked with shadows and the fields with the purple of the asters.

Anne had given up a moonlight drive to the White Sands beach that she might spend the evening with Ruby. She had so spent many evenings that summer, although she often wondered what good it did any one, and sometimes went home deciding that she could not go again.

Ruby grew paler as the summer waned; the White Sands school was given up—“her father thought it better that she shouldn’t teach till New Year’s”—and the fancy work she loved oftener and oftener fell from hands grown too weary for it. But she was always gay, always hopeful, always chattering and whispering of her beaux, and their rivalries and despairs. It was this that made Anne’s visits hard for her. What had once been silly or amusing was gruesome, now; it was death peering through a wilful mask of life. Yet Ruby seemed to cling to her, and never let her go until she had promised to come again soon. Mrs. Lynde grumbled about Anne’s frequent visits, and declared she would catch consumption; even Marilla was dubious.

“Every time you go to see Ruby you come home looking tired out,” she said.

“It’s so very sad and dreadful,” said Anne in a low tone. “Ruby doesn’t seem to realize her condition in the least. And yet I somehow feel she needs help—craves it—and I want to give it to her and can’t. All the time I’m with her I feel as if I were watching her struggle with an invisible foe—trying to push it back with such feeble resistance as she has. That is why I come home tired.”

But tonight Anne did not feel this so keenly. Ruby was strangely quiet. She said not a word about parties and drives and dresses and “fellows.” She lay in the hammock, with her untouched work beside her, and a white shawl wrapped about her thin shoulders. Her long yellow braids of hair—how Anne had envied those beautiful braids in old schooldays!—lay on either side of her. She had taken the pins out—they made her head ache, she said. The hectic flush was gone for the time, leaving her pale and childlike.

The moon rose in the silvery sky, empearling the clouds around her. Below, the pond shimmered in its hazy radiance. Just beyond the Gillis homestead was the church, with the old graveyard beside it. The moonlight shone on the white stones, bringing them out in clear-cut relief against the dark trees behind.

“How strange the graveyard looks by moonlight!” said Ruby suddenly. “How ghostly!” she shuddered. “Anne, it won’t be long now before I’ll be lying over there. You and Diana and all the rest will be going about, full of life—and I’ll be there—in the old graveyard—dead!”

The surprise of it bewildered Anne. For a few moments she could not speak.

“You know it’s so, don’t you?” said Ruby insistently.

“Yes, I know,” answered Anne in a low tone. “Dear Ruby, I know.”

“Everybody knows it,” said Ruby bitterly. “I know it—I’ve known it all summer, though I wouldn’t give in. And, oh, Anne”—she reached out and caught Anne’s hand pleadingly, impulsively—“I don’t want to die. I’m afraid to die.”

“Why should you be afraid, Ruby?“ asked Anne quietly.

“Because—because—oh, I’m not afraid but that I’ll go to heaven, Anne. I’m a church member. But—it’ll be all so different. I think—and think—and I get so frightened—and—and—homesick. Heaven must be very beautiful, of course, the Bible says so—but, Anne, it won’t be what I’ve been used to.”

Through Anne’s mind drifted an intrusive recollection of a funny story she had heard Philippa Gordon tell—the story of some old man who had said very much the same thing about the world to come. It had sounded funny then—she remembered how she and Priscilla had laughed over it. But it did not seem in the least humorous now, coming from Ruby’s pale, trembling lips. It was sad, tragic—and true! Heaven could not be what Ruby had been used to. There had been nothing in her gay, frivolous life, her shallow ideals and aspirations, to fit her for that great change, or make the life to come seem to her anything but alien and unreal and undesirable. Anne wondered helplessly what she could say that would help her. Could she say anything? “I think, Ruby,” she began hesitatingly—for it was difficult for Anne to speak to any one of the deepest thoughts of her heart, or the new ideas that had vaguely begun to shape themselves in her mind, concerning the great mysteries of life here and hereafter, superseding her old childish conceptions, and it was hardest of all to speak of them to such as Ruby Gillis—“I think, perhaps, we have very mistaken ideas about heaven—what it is and what it holds for us. I don’t think it can be so very different from life here as most people seem to think. I believe we’ll just go on living, a good deal as we live here—and be ourselves just the same—only it will be easier to be good and to—follow the highest. All the hindrances and perplexities will be taken away, and we shall see clearly. Don’t be afraid, Ruby.”

“I can’t help it,” said Ruby pitifully. “Even if what you say about heaven is true—and you can’t be sure—it may be only that imagination of yours—it won’t be just the same. It can’t be. I want to go on living here. I’m so young, Anne. I haven’t had my life. I’ve fought so hard to live—and it isn’t any use—I have to die—and leave everything I care for.” Anne sat in a pain that was almost intolerable. She could not tell comforting falsehoods; and all that Ruby said was so horribly true. She was leaving everything she cared for. She had laid up her treasures on earth only; she had lived solely for the little things of life—the things that pass—forgetting the great things that go onward into eternity, bridging the gulf between the two lives and making of death a mere passing from one dwelling to the other—from twilight to unclouded day. God would take care of her there—Anne believed—she would learn—but now it was no wonder her soul clung, in blind helplessness, to the only things she knew and loved.

Ruby raised herself on her arm and lifted up her bright, beautiful blue eyes to the moonlit skies.

“I want to live,” she said, in a trembling voice. “I want to live like other girls. I—I want to be married, Anne—and—and—have little children. You know I always loved babies, Anne. I couldn’t say this to any one but you. I know you understand. And then poor Herb—he—he loves me and I love him, Anne. The others meant nothing to me, but he does—and if I could live I would be his wife and be so happy. Oh, Anne, it’s hard.”

Ruby sank back on her pillows and sobbed convulsively. Anne pressed her hand in an agony of sympathy—silent sympathy, which perhaps helped Ruby more than broken, imperfect words could have done; for presently she grew calmer and her sobs ceased.

“I’m glad I’ve told you this, Anne,” she whispered. “It has helped me just to say it all out. I’ve wanted to all summer—every time you came. I wanted to talk it over with you—but I couldn’t. It seemed as if it would make death so sure if I said I was going to die, or if any one else said it or hinted it. I wouldn’t say it, or even think it. In the daytime, when people were around me and everything was cheerful, it wasn’t so hard to keep from thinking of it. But in the night, when I couldn’t sleep—it was so dreadful, Anne. I couldn’t get away from it then. Death just came and stared me in the face, until I got so frightened I could have screamed.”

“But you won’t be frightened any more, Ruby, will you? You’ll be brave, and believe that all is going to be well with you.”

“I’ll try. I’ll think over what you have said, and try to believe it. And you’ll come up as often as you can, won’t you, Anne?”

“Yes, dear.”

“It—it won’t be very long now, Anne. I feel sure of that. And I’d rather have you than any one else. I always liked you best of all the girls I went to school with. You were never jealous, or mean, like some of them were. Poor Em White was up to see me yesterday. You remember Em and I were such chums for three years when we went to school? And then we quarrelled the time of the school concert. We’ve never spoken to each other since. Wasn’t it silly? Anything like that seems silly now. But Em and I made up the old quarrel yesterday. She said she’d have spoken years ago, only she thought I wouldn’t. And I never spoke to her because I was sure she wouldn’t speak to me. Isn’t it strange how people misunderstand each other, Anne?”

“Most of the trouble in life comes from misunderstanding, I think,” said Anne. “I must go now, Ruby. It’s getting late—and you shouldn’t be out in the damp.”

“You’ll come up soon again.”

“Yes, very soon. And if there’s anything I can do to help you I’ll be so glad.”

“I know. You have helped me already. Nothing seems quite so dreadful now. Good night, Anne.”

“Good night, dear.”

Anne walked home very slowly in the moonlight. The evening had changed something for her. Life held a different meaning, a deeper purpose. On the surface it would go on just the same; but the deeps had been stirred. It must not be with her as with poor butterfly Ruby. When she came to the end of one life it must not be to face the next with the shrinking terror of something wholly different—something for which accustomed thought and ideal and aspiration had unfitted her. The little things of life, sweet and excellent in their place, must not be the things lived for; the highest must be sought and followed; the life of heaven must be begun here on earth.