Maker, Monks, and Math: Getting People to See the Beauty Within

I’m a math major and a math tutor. In my three years of doing the latter, primarily focused on introductory calculus, I have struggled with how to explain the concepts and processes in an understandable way to my students. And it is a struggle because math has become so internal that it becomes hard to even see what would be difficult about it, especially with the straightforward processes of introductory calculus.

But beyond that, I want to show my students the beauty of mathematics. I loved math from a very young age, but it was not until I took classes here that I really understood the inner beauty, hidden from the world by proofs, technical definitions, and layers of abstraction. How do you show someone what makes Galois theory incredible or topology so interesting without immersing them in these technicalities?

As Christians, we are confronted with the same problem. Bringing someone to faith is an attempt to make them see the inner beauty of the story and how much better our lives are when living in faith. But, as we have already discussed in class, that’s difficult to do, especially when you’re so immersed in it. How do you externalize yourself from it to see it from a non-Christian perspective? How do you bring people in?

Christianity has the additional problem of faith. Nobody really rejects the reality of math; no matter how much someone may dislike it, he does not deny its truth. But that’s not the case with Christianity. Plenty of people will reject God even if the best arguments and evidence are brought to them. Faith is a decision we cannot make for someone else; to quote The Matrix (my favorite film), “I can only show you the door. You're the one that has to walk through it.”

So, with the problem established, we can ask the obvious question: how do we get people in the story? The answer? The same way we do with math.

What do most math classes consist of? Lectures and problem sets. In lectures, the teacher explains the information and usually goes through a few examples. In lower level math classes, those examples are generally computations, whereas in higher levels they are proving important results. Problem sets are where the knowledge is tested by going through computations individually or practicing with the definitions and theorems. In my experience, this is where the real learning happens, especially with proof-based math; I don’t really understand anything until I’ve worked with it directly. Thus, the practice improves my knowledge, allowing me to advance to new topics which I can then practice. It becomes cyclic. 

Likewise, Christian faith comes in two parts: knowledge and practice. The knowledge comes from reading the scriptures and listening to sermons, as one would expect, but also from making those arguments ourselves; the true test of understanding is whether you can explain it to someone else. The practice also comes in familiar forms, prayer and church attendance. Faith is not just about “knowing” Jesus is Lord but acting on that faith, to the best of your abilities. You cannot truly understand without the practice.

This is what the monks see. When looking at St. Benedict’s Rules for Monasteries, specifically Chapters 8 to 20, it details a thorough schedule for saying the entirety of the Psalms each week. The practice is vital to the monks and centers everything they do. The effect the practice has on one’s spirit is absolutely crucial; gathering together in praise of God, each and every day, and multiples times therein, allows for spiritual edification of potent strength.

And I can speak to this in my own practice. During my participation in Professor Fulton Brown’s prayer group, we have had many fluctuations in attendance. Sometimes, it has simply been the two of us; other times, we are joined by a larger group. And there is power in both. The larger group is great because we are able to gather in fellowship and raise our voices in praise to God. But the smaller group has its own quality, as I know that we gather every week, rain or shine (and I do mean that!), to come together and praise our Lord. No matter the circumstances, I count on gathering together, and I know my faith has grown stronger as a result of it.

Through their disciplined practice, then, the monks are able to see what they do. Bede’s On the Tabernacle or Gregory’s Moralia in Job are clearly the result of knowledge from practice. For example, consider this quote from Bede: “The width of the ark was one cubit on account of the dispensation of the Lord’s own charity, with which he took care to unite his elect in God” (Bede, 12). The symbolism Bede sees in the measurements of the ark is something that most would never notice, and something I admittedly struggled to understand the precise grounding of. It is only through the result of their practice that one could hope to understand the texts the way they do. And that is unique, among scholarly considerations, since it is not merely an object of study and knowledge, but also one of worship for those considering it. I do not worship math nor use it to worship in the way that I do with the Scriptures.

Speaking again from personal experience, I have experienced something similar, though on a much smaller scale. When we first started I would trip over the words and was still learning their cadence. But now that we have practiced together for five quarters (and counting!), Psalm 94 has become known to me in a way it was not before. Lines like “make a joyful noise to him with psalms” (Psalm 94:2) have taken on a new meaning as we do that weekly, or “To day if you shall hear his voice, harden not your hearts” (Psalm 94:8) feels like reaching out to those around us as we pray in the Quad. I had not really thought about it before my reflection in class, but I realize that I understand them differently now versus when we started.

Thus, just as in math, faith comes through knowledge and practice, and they act cyclically: practice gives way to greater knowledge, and the deeper understanding brings a deeper faith and better knowledge.

Thus, let us return to the original question: how do we bring people into the faith, to see its inner beauty? There is not a perfect answer, since faith is a personal choice that we cannot control. But, for both ourselves and for others, we must both share and participate in knowledge, the intellectual grounds of faith, but also practice our faith to the best of our abilities. In trying to demonstrate the inner beauty of the story and of faith, both are necessary and cannot be substituted.

I will conclude with a question, then, that I do not have a proper answer to: considering the benefits the monks reap from their practice, why don’t we all become monks?

—Chad Berkich

The Meaning of Chanting

    The most important issue raised in our previous class – for me – was the reconciliation of Benedict 1-10 with Benedict 11-20; that is, what was the relationship between the practices of the monastic community (the ‘rule’) and the chanting of psalms?
    We must begin by understanding that the psalms represented an overwhelming majority of all words that the monks ever spoke in the monastery. Benedict wrote that the monks should speak “gently and without laughter, humbly and seriously, in few and sensible words” (Benedict 7) and that “permission to speak should rarely be granted even to perfect disciples” (Benedict 6). Benedict believed that excess speech, even in ‘edifying conversation’, represented a source of sin (Benedict 6). It was therefore necessary for the monk to purify his speech of excesses and to reduce it only to the necessities of his religious obligations.
    We must then understand the importance of this practice for the monks’ spiritual cultivation; the central idea here is conforming the internal spirit to the will of God through external practice. For example, “if the disciple obeys with an ill will and murmurs, not necessarily with his lips but simply in his heart, then even though he fulfil the command yet his work will not be acceptable to God, who sees that his heart is murmuring” (Benedict 5). That is, external obedience to the rule, for example, would not be ‘acceptable to God’ unless it was accompanied by internal, spiritual obedience to God’s will. The monk must therefore learn not to ‘murmur’ in his acquiescence to the will of God internally by molding his spirit through external behavior, for example by resigning himself to not protest the commands of the abbot (externally, or ‘on the lips’).
    Similarly, Benedict developed an analogy between the abolition of the monk’s personal will with respect to the abbot, and the abolition of his personal will with respect to God. The monks, “not living according to their own choice nor obeying their own desires and pleasures but walking by another’s judgment and command, they dwell in monasteries and desire to have an Abbot over them” (Benedict 5). Similarly, they were expected to emulate the Lord’s proclamation that “I have come not to do My own will, but the will of Him who sent Me”. Just as the monk was expected to abandon his external work in the monastery, ‘leaving it unfinished’, whenever summoned by the abbot to do his will, so he was expected to ‘forsake his own [internal] will’ whenever summoned by God to do his will.
    The psalms played a central role in this process, because the external purification of sin from speech was meant to cultivate the internal purification of sin from the mind, just as external humility by not ‘murmuring on the lips’ was meant to cultivate internal humility by not ‘murmuring in the heart’ (Benedict 5). This was achieved by molding the internal voice through constant repetition of the external voice. It seems, therefore, that Benedict 1-10 represents the literal rule of the monastic community, while Benedict 11-20 represents the rule of the psalms; or, the rule of the mind that constant repetition of the psalms was meant to install.
    Thus, the key idea of the rule in general was to form the mind according to the demands of religion through external practice. The act of external reconciliation with the will of the abbot would thereby inculcate an internal reconciliation with the will of God. The quintessential act of external obedience is silence, and the monks were almost entirely silent when they were not chanting the psalms, which would have thus formed their minds significantly in the mold of the psalms. Of course, the content of their chants was not chosen arbitrarily; it must have been meant to harmonize one’s external practice, and thereby assimilate one’s internal will, with the will of God.
    So, it is finally necessary to investigate how the specific content of the psalms must have been thought to achieve this end. Psalm 94, with which the monks always began their daily chants, offers such an insight. The speaker implores the singers, “To day if you shall hear his voice, harden not your hearts”. Likewise, “Come let us adore and fall down: and weep before the Lord that made us”, and “let us praise the Lord with joy”. The psalms call their singers to humility and obedience, and were thus an appropriate medium for the monks’ rare speech.
    There is also a curious interplay here between the first and second person pronouns: in some places, the psalm calls ‘us’; in other places, ‘you’. We might justifiably wonder how each individual monk conceptualized the speaker at any particular moment, and perhaps we can speculate on it here. Suppose that each call to obedience would have been spoken internally as well as externally: the monk, repeating these words day after day, would have had them stamped on his internal voice. The external repetition of the words would therefore not have precluded a simultaneous internal repetition. However, we should recall that the process of internal conformity to external practice was designed to assimilate the individual will of each monk to the will of God. Thus, as the psalms called each singer to obedience, as in ‘harden not your hearts’ or ‘let us praise the Lord’, the monk’s own internal voice (or will) was replaced by the voice (or will) of God. At the same time, the monk would have naturally assimilated the external words to his internal will. Obedience would therefore have become a nearly spontaneous act for the monk: given that his will was ultimately assimilated to the will of God and that his internal voice became indelibly stamped with the psalms, the call to obedience would have issued from within, and the monk would have become a speaker of the psalms both literally and spiritually. 

Henry Stratakis-Allen

Journeys Into Knowledge

    Lately, I've been thinking about journeys. Alfred the Great traveled to Italy as a young boy to be knighted by Pope Leo IV. The panels Bede observed at Monkwearmouth-Jarrow were brought from Rome. The Greek litany in King Athelstan's psalter is the result of the travels undertaken by Israel of Trier, according to Michael Wood in The Story of a Book. Wood writes that the journey embarked upon by British Christians to Rome "reestablished their links with Rome," which was their "spiritual heartland" (Wood 181). Journeys, then, have been integral to the story we are following in this course.

Route undertaken from Canterbury to Rome by Cristina Menghini

    Yet, as we brought up in class on Thursday, medieval monks like Bede spent their time ensconced in monasteries, practicing the strict daily schedule we read about in St. Benedict's Rule for Monasteries. At the beginning of class on Thursday we asked how Bede and his contemporaries knew about the symbolism of the tabernacle and the veil. What led them to this knowledge, in the absence of regular communication with Rome? For monks who spent their lives in monasteries, how did they connect with their "spiritual heartland" while staying put?

    The methods used by the monks to embark upon their spiritual journey did not require them to physically travel anywhere. Journeys, even if they entail moving from place to place, are not only physical. There are some voyages that we know so well we can run through them in our minds. My most familiar journey is the short, hour-long car ride from my home in Albuquerque, New Mexico, to my grandfather's house in Santa Fe, which I have undertaken regularly since before I can remember. Since being in college, though, I have physically undertaken this journey only twice. Despite a reduction in frequency, however, I can recall every brown, shrub-covered hill that rises to the sides of I-25, and every shady spot where snow stays all winter, refusing to melt. My mental recollections of this trip have become just as vivid as what I experienced when actually undertaking the journey. 

    Characteristic of my journey, and most, is a change in surroundings. You begin in one place and end up in another, progressing through different landscapes, physical conditions, and mental states. One can embark upon a journey, I believe, by progressing through a multitude of experiences that change your mental or spiritual state. To me, the opening of a book like the Codex Amiatinus and the recitation of psalms mimic the change in surroundings that is experienced during physical travel. As mentioned in class, upon opening the Codex Amiatinus one immediately sees the purple pages and is welcomed into the mystery of the tabernacle. The illustrations on the pages and the artful script serve not only to convey ideas or stories but to embody the glory of God---the reader can "see" God as Moses did on the mountaintop. To turn through the book, whether reading the words or appreciating its appearance, is to journey into the holy of holies. The physical book provides you with a changing visual experience which, along with the story told in the text, lets you into the spiritual realm. Turning through the Codex Amiatinus or other holy manuscripts, which medieval monks like Bede may have done, provided a journey into the spiritual that was just as, if not more, meaningful than a physical journey to the spiritual homeland of Rome.

Galba A XVIII or The Athelstan Psalter

    The monks, however, spent most of their days reciting psalms rather than flipping through books. The recitation of psalms daily, in a specific order, served a similar but more powerful purpose for the monks than looking at a manuscript. To chant the psalms, like turning the pages of the Codex, is to enter into the mystery of God. In their recitation, the monks embark upon a spiritual journey. What separates this journey from that undertaken when reading a book is that chanting the Psalms is an active, participatory event while reading is passive. You devote very little physical energy to reading. When reading the Codex, the main entrance into the tabernacle comes from the passive, sensory experience of viewing the purple pages. When reciting psalms in a monastery, however, a monk would have had both the passive sensory experience of hearing the psalms from his brothers around him and reciting the psalms himself. He would not only listen but participate in the creation of the sound and rhythm. Active participation in this recitation mimics the physical act of undertaking the journey to Rome.

    The organization of the psalms, too, contributes to the journey embarked upon by the monks every day. Benedict says, in chapter 13 of Rule for Monasteries, that on weekdays the Morning Office should begin with Psalm 66 followed by Psalm 50. Since I am writing this on a Friday, we will follow Benedict's direction and follow Psalm 50 with Psalms 75 and 91. This selection of four psalms takes us through praying for God's favor (Ps 66), repenting for sin (Ps 50), telling of God's protection of His Church (Ps 75), and praising God (Ps 91). These are followed by the "psalms of praise" along with additional hymns, litanies, and canticles. In reciting these psalms one is taken through different spiritual landscapes, encountering different features of the Lord: His grace, His mercy, His protection. Different psalms are chosen for each day of the week, taking the one who recites them through a different progression of events and, therefore, a different journey upon each recitation. 

    The recitations, however, occur on a cycle: one set of psalms during one part of the day and certain psalms for each day of the week. A monk who spent his entire life in a monastery knew the psalms by heart. We tend to think of journeys in terms of what we get out of them, and we often tie this newfound knowledge to the experience of a new place or path. When deciding where to travel we would rather see new places than return to a place we have already been. How, then, can the journey that is reciting the psalms continue to be enlightening when undertaken so often? In class, we recognized that the constant recitation of psalms through a monk's life would lead him to deeper contemplation of God's mystery, why? The interesting thing about journeys is that when one path is undertaken often, the memories of past trips begin to blur together, engaging in conversation with each other across time. When I drive from Albuquerque to Santa Fe I am reminded of times forgotten and gain knowledge about myself through the comparison of present and past. If the recitation of the psalms is a journey, then, the value of it lies in the repetition, for through repetition a monk engaged in conversation not only with the material but also with his memories of reciting the material and all the questions this material triggered throughout his time engaging with it. Through this conversation, the monk traveled deeper into the mystery. The more often the journey is undertaken the more there is to discover. Just as travelers to Rome returned with artwork, books, and ideas, so too did monks like Bede return from their daily recitations with knowledge and questions concerning the divine.

-Aethelryth (AB)

The Sacred in Time and Space

Throughout the readings for Thursday’s class and during our discussion, I felt that we touched on the motif of the sacred in both time and space repeatedly. The Romanian author Mircea Eliade (who was, interestingly enough, formerly employed by the University of Chicago) also touches on these ideas, noting that every religion and every individual treats certain spaces and segments of time as qualitatively different and more important than other spaces and segments which are quantitatively identical; that is to say, for example, that a church, even if it occupies the same amount of space as a warehouse, holds greater psychological and metaphysical importance in the minds of Christians. I would like to discuss some of the cases in which the sacred appeared in our discussion and how this sacredness causes a ‘narrativization’ of our lives.

First, we repeatedly discussed the layout of the Tabernacle Tent, with reference to a specific Medieval diagram. The diagram demonstrates that the tent is composed of two distinct parts - an outer area (the Holy Place) enclosing a second, smaller area (where the Ark of the Covenant is kept). This layout on its own, introduces a narrative element. The tent is first introduced to us as a mystery, into which we cannot see at all. Our culture, family, etc. will presumably have informed us that this is an important place. However, once inside, the mystery only deepens, as we are exposed to new information - there is yet another tent inside, into which only certain people - namely, priests -  can go. The Tabernacle tent serves to illustrate both an example of a sacred space and to introduce one kind of narrative - the mysterious narrative - in which information is slowly given to us which often only adds to our confusion and desire to know. As an aside, the layout of Carolingian monasteries, which we discussed in class, also exemplify a Tabernacle Tent-like layout, in which the church lies inside the wall of the monastery, which itself is a kind of sacred envelopment.

Second, we have discussed over multiple classes the importance and meaning of books - specifically in relation to their use as ‘conversion devices’ for Pagan England but also in general. The book, I think, serves as an unusual but interesting instance of the exact same phenomenon as the Tabernacle Tent. The St. Augustine Gospels, which we have looked at, is sacred in that it has great historical and religious significance, making it more important than, say, a rock of the same size and weight. Furthermore, like all books, it exemplifies the mysterious narrative discussed above. It does not, unlike a scroll or a painting, make all of its contents known right away. On the contrary, one has to actively seek out the information contained in it, with each new page revealing something new, but also encouraging further reading.

Third, to come to the main topic of Thursday’s class, the Psalms, we encounter both a different type of sacrality and of narrative. We discussed how chanting/singing the Psalms was a staple of monastery life for Benedictine monks around the time of Charlemagne. These Psalms were to be memorized and were always sung at a particular time of day. Here, we see a clear example of sacred time - the time in which the Psalms are sung, although quantitatively unremarkable with reference to, for instance, lunchtime, carry a far weightier load, in that skipping lunch means a few hours of extra hungriness, whereas skipping the singing of the Psalms might place a monk in both terrestrial and spiritual trouble. However, this example also presents a different kind of narrative - the unmysterious narrative. The singing of the Psalms forms a narrative in the sense that it is a kind of rock or anchor for the ‘story’ of the day and is unmysterious in that memorized lines are simply repeated - everyone involved already knows what is going to happen. 

So, what do we make of all of this? What’s the point of the mysterious and the unmysterious narrative? What do they tell us about ourselves and our understanding of the world? While I don’t pretend to have the answers to these questions, I can offer my best guess. I think that these two kinds of narratives reflect the two parts of what it means for something to be sacred. For something to be sacred it must, of course, be known, and therefore unmysterious, so that it can be distinguished from other things. However, sacredness also indicates mystery for a couple reasons worth discussing. First, there’s the mystery of what it even means for something to be sacred from a pure biological or materialist level - what evolutionary reason do we have to view two things with equal utility for our survival (a church and a warehouse, for example) as deeply different? I think that even someone who had never been exposed to Christianity, or religion at all, could tell you that the church is the more important building. But why? There is also a second, and less interesting reason, that mystery inspires sacrality, which is simply speculation. Without full knowledge or understanding one’s mind (and some people’s minds more than others) tends to wander, developing theories and generally keeping one occupied with what the secret could be rather than on the mundane; in other words, mysterious things are just more interesting than mundane, known things and will be conferred some importance for that reason alone. Sacredness is mysterious and vice versa.

—LM

The Tabernacle on my Bookshelf

There have been two times in my life where I was simultaneously in complete awe and terror. First was when I had the privilege of being in Normandy, France for the 75th anniversary of D-Day. That day I was standing at the top of the hill that looked down on Omaha beach. The sense of awe and terror realizing what happened just below me 75 years ago was something that I never experienced before or have not since until March 26, when I saw the image below. You open the book and are confronted with the beautiful page, and then you turn it and pass through the veil and into the tabernacle.

Codex Amiatinus. Image Link

The Book this page is in gives us an image of God for us to behold, that will not be seen in full until the unveiling. This sense of mystery that the nature of books have, also provides us a sense of the Author of the book that we are looking at. Bede says, "For while we are in this life, we never manage perfectly to love God for his own sake, or to comprehend the love that God has for us (Bede, 13)." The Author is mysterious to us just like his book. Though different writers and thinkers have been wrestling with the problem of how to read and interpret the Bible, and the mystery it contains. This is complicated because if you are a believer then this is not simply just a book that gives the reader some guidelines in order to be happy, but that God literally authored the text that we have the privilege of seeing. But how do we go about reading it?

Firstly, we must ask for the Lord's assistance in the act of reading, understanding, and instructing people in the Bible (Bede, 1). This is sort of a strange idea, 'I must ask the Author of this text to help me understand the text, so I can be in his presence. But then how do I ask him to begin with, if I do not know who He is?' Maybe, this is where the pictures, icons, play a role, which allows us to see what is to be adored (Gregory the Great). The brave reader undergoing this joyful challenge also needs to familiarize themselves with the historical context and topography the story is being told from (Bede, 1). Think of Tolkien's map of Middle-Earth being on the pages before the story even starts. It allows the reader to put themselves into the world. I know where Frodo is and where he needs to go, and why he chose the path that he did because I know what the world, he is in looks like. Similarly, the places being discussed in the Bible are real and you and I can physically go there. I cannot go to Rohan, no matter how much I really want to. This is linked to what C.S Lewis said in Myth Became Fact, "It happens - at a particular date, in a particular place, followed by definable historical consequences. We pass from a Balder or an Osiris, dying nobody knows when or where, to a historical Person crucified (it is all in order) under Pontius Pilate (Lewis, 141)." The story the Bible tells is anchored in time, place, and Person; we can interact with it!

Mount Sinai (aka Mount My Measure) taken from Google Maps. Image Link

Like I said previously the Bible is not like other books. This means I cannot, or at the very least should not, read it like other books. Sure, you can just open it up at Genesis and read until you complete Revelation like any other book, but that does not seem to be the best way to behold the glory that the book contains. We can see this clearly reading Bede's text On the Tabernacle, that he does not think this is the best way either. Continuously throughout Bede's writing, he explains the verses on the tabernacle with references to the New Testament, particularly the Gospels. The tabernacle points to something that has yet to occur: the Incarnation (Bede, 2). This leads to the idea that the Bible is in constant communication with itself, and I will not pretend to be smart enough to attempt an understanding of that. Bede is smart enough, "The two testaments can be figured through the two cherubim; one of them proclaims the incarnation of the Lord as future, the other as having been accomplished. They look toward one another because they do not disagree with one another at all in the attestation of truth which they preach (Bede, 18)." Just as the Book talks to itself, the people that read it also talk about the book. The most obvious example is the footnotes that Bede utilizes. While many of them are citing other parts of the Bible, some are referencing other writers as well such as Pope Gregory the Great and Saint Jerome. This implies that one is not supposed to be left to their own devices when reading the Bible but rely on those that have come before in order to be better instructed in the meaning of the text.

Bible Cross-References. Image Link

Besides focusing on the historical authenticity of the text, the reader must keep an out out for the symbolism that fills the story and shows us what we are now supposed to do once we have heard the story. Bede again points us to the connection between the Old Testament and the New Testament, when he explains the story of Moses going up the mountain to receive the law from God, and that he should go down and teach the Israelites at the bottom of the hill all that Moses learned. Compare this with the New Testament story that it points to, Jesus goes up on the mountain and does not call one person to teach but all twelve apostles, as well as the crowds that followed. For the law that Jesus was teaching is not just for the Israelites but for all people, speaking many different languages to bring it to all the corners of the world (Bede, 2). 

-- L. O'Connor Jelenik

Bede, & Holder, A. G. (1994). Book One. In Bede: On the Tabernacle (pp. 1–27). essay, Liverpool University Press. 

Lewis, C. S., & Walmsley, L. (2000). Myth Became Fact. In Essay Collection and Other Short Pieces (pp. 138–142). essay, Harper Collins. 

Pope Gregory the Great. (600, October). Letter to Serenus of Marseilles.