Kindle Notes & Highlights
Luigi Giussani clarifies what is at stake by insisting that “to educate means to help the human soul enter into the totality of the real.”3
Modern culture has disenchanted the world by disenchanting numbers. For us, numbers are about quantity and control, not quality and contemplation.
Education is our path to true humanity and wisdom.
There is a structural flaw in our education that we need to overcome. It is related to a profound malaise in our civilization, which by progressive stages has slipped into a way of thinking and living that is dualistic in character. The divisions between arts and sciences, between faith and reason, between nature and grace, have a common root.
We need to retrace our steps, to find the “wisdom we have lost in knowledge,” the “knowledge we have lost in information” (T. S. Eliot).
As our own eyes reveal every day, the universe is beautiful. It has majesty, order, and loveliness;3 these three types of beauty are precisely what scientists themselves love to discover in the world.
The following points may serve to sum up the thrust of the book. The way we educate is the way we pass on or transform our culture. It carries within it a message about our values, priorities, and the way we structure the world. The fragmentation of education into disciplines teaches us that the world is made of bits we can use and consume as we choose. This fragmentation is a denial of ultimate meaning. Contemporary education therefore tends to the elimination of meaning—except in the sense of a meaning that we impose by force upon the world. The keys to meaning are (and always have been)
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The world is a fabric woven of mysteries, and a mystery is a provocation to our humanity that cannot be dissolved by googling a few more bits of information.
The “circle of learning” (from which we get our word encyclopedia) was systematized into nine fields of study by the Roman Marcus Varro in the first century after Christ, and refined by Augustine, Boethius,8 and Cassiodorus into a list of seven divided into two groups. The first group, the trivium (three ways), consisted of: grammar rhetoric dialectic
The second group comprised the quadrivium (or the four ways) of sacred sciences known as the artes reales, or physicae. These were the disciplines by which Plato believed the inner vision of the soul could be awakened: arithmetic geometry astronomy
music
arithmetic being pure number, geometry number in space, music number in time, and astronomy number in both space and time.
Classical educational ideals and literacy were preserved through the dark ages after the fall of Roman civilization within oases provided by the Benedictine and other monasteries.
technological progress made in the Servile Arts, also known as the Mechanical Arts, coupled with the new notion that the purpose of “science” was to be useful—which had come to mean obtaining power over nature rather than wisdom17—was to reshape the world in ways that the ancient and medieval authors could hardly have conceived.
The purpose of an education is not merely to communicate information, let alone current scientific opinion, nor to train future workers and managers. It is to teach the ability to think, discriminate, speak, and write, and, along with this, the ability to perceive the inner, connecting principles, the intrinsic relations, the logoi, of creation, which the ancient Christian Pythagorean tradition (right through the medieval period) understood in terms of number and cosmic harmony.
Beauty is the radiance of the true and the good, and it is what attracts us to both.
the power to reveal truth in the very act of creating.
We have bemoaned the compartmentalization that thrusts the two ways of looking at the world into separate boxes. But the greatest scientists have never ceased to be motivated by the desire to find beauty in their equations, and their breakthroughs are often the result of an intuition, or an imaginative leap.
Theology, for example, relies particularly on the method of analogy. Theologians make statements about God, relying on a similarity between Creator and created, despite the overarching difference in the nature of being.
In this case the difference is greater than any similarity, but at least something meaningful can be affirmed. We can say God “wishes” or “intends” a particular outcome (such as the salvation of humanity) because the words as applied to human beings gesture in the direction of some truth about God, and are endorsed by their occurrence in scripture where God reveals something of himself in terms we can understand
The assumption of this system of education was that by learning to understand the harmonies of the cosmos, our minds would be raised toward God, in whom we could find the unity from which all these harmonies derive: Dante’s “love that moves the sun and the other stars.”
our present education tends to eliminate the contemplative or qualitative dimension of mathematics altogether, reducing everything to sheer quantity.
The invention of zero, like that of the wheel, was one of the turning points in the history of civilization. It radically simplified the process of calculation, since a set of nine symbols could be rearranged to make numbers of any size by attributing a value to their position in the composite (without zero it would not have been possible to distinguish between 45, 405, and 40,050).
The solar year, for example, like the lunar month, is not a rational multiple of a day. If it were precisely 365.25 days, as we were told in school, then astronomical events related to the apparent position of the sun would repeat precisely over that period, and the year and the day would be back in step at exactly the same point. “So nothing ever repeats exactly. Calendars therefore have to make compromises, and it is the history of those compromises in different cultures that has led to a plethora of calendar systems.”20
Irrationals cannot be used to count things, but are encountered in relationships between things that can be counted.
When one thing is compared to another we call the relationship a ratio (it is this word from which we derive the word “rationality”).
Slightly more sophisticated is a proportion, or analogy, which is based on the comparison of one ratio with another (A to B is like C to D), especially when there is a common term linking the two ratios that acts as a mediator between them (A to B is like B to C).
Both Leonardo da Vinci and Piet Mondrian used such rectangles frequently in their paintings, and the ratio itself can be found governing the lengths of sections in many Beethoven movements.
We have to recall that mathematics begins not just with counting, but also with measuring. To perform an act of measuring one has to do two things. One has to count, but one also has to compare one thing with another (for example a ruler or measuring tape).
It turns out by a remarkable coincidence that this “Logos line” is linked to the circle by a number associated above all with the creation of the world by God in the book of Genesis: the number 7. For if we multiply our Logos line by 7 we obtain a close approximation of the circumference of the circle (the exact multiplier is more like 7.025).
But it seems to me there is another reason why this number is only approximate, and this reason touches on the deepest mystery revealed by Christianity. Mediation between heaven and earth is accomplished by the seven sacraments issuing from the actions of the Logos during his life on earth, echoing the seven mystical days of creation.28
it seems justifiable to speculate that it is because the mediation of the God-Man will always leave room for the vital but infinitesimal human contribution, our free cooperation with grace.
This is the tiny and indispensable human contribution needed if heaven is truly to descend to earth, and earth finally to be integrated with the everlasting Trinity.
How will the reformers react to this bit?
As Josef Pieper argues, the reduction of the liberal to the servile arts would mean the proletarianization of the world.
At the heart of any culture worthy of the name is not work but leisure, schole in Greek, a word that lies at the root of the English word “school.”
The “purpose” of the quadrivium was to prepare us to contemplate God in an ordered fashion, to take delight in the source of all truth, beauty, and goodness, while the purpose of the trivium was to prepare us for the quadrivium. The “purpose” of the Liberal Arts is therefore to purify the soul, to discipline the attention so that it becomes capable of devotion to God; that is, prayer.
Harmony—the perceived agreement or “concord” between different frequencies—was first analyzed mathematically by Pythagoras.
In the twelfth century, at the cathedral of Notre Dame in Paris, a musical revolution took place expressing the genius of the new Gothic architecture in the world of sound: the monastic plainchant, with its single line of text, became polyphonic. Now two or even four different voice parts could overlap and interweave, making harmony together.
As plainchant and drone gave way to polyphony and chords, Pythagorean music theory evolved too.
Twelve perfect fifths are almost but not exactly equal to seven perfect octaves, and the Pythagorean comma is the amount of the discrepancy.
There is also a close parallel between sound and light. In Sanskrit the roots of the words for “shine” and “sound” are the same, and in modern physics both are forms of vibration.
Haydn linked each instrument in the orchestra to a distinct color (the trumpet scarlet, the flute sky blue, and so on),
According to the English composer John Tavener (b. 1944), all music already exists. When God created the world he created everything. It’s up to us as artists to find that music. Of course that’s an exhausting experience, but you have to rid yourself of any preconceived idea about what music is; rid yourself of the idea that you have to struggle over note rows, or with sonata form, or the humanist bugbear, development. Music just is. It exists. If you have ears to hear, you’ll hear it! . . . I believe we are incarnated in the image of God in this world in order for us to re-find that heavenly
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The practical implications were summarized in 1989 by HRH Prince Charles in a book called A Vision of Britain.19 His ten perennial principles for good architecture and town planning based on the concept of service and a sensitivity to the human meaning of buildings were as follows: Place. By this he meant be sensitive to location and setting. One place is not the same as another. “Don’t rape the landscape.” Hierarchy. The composition of a building should lead the eye to its most important elements. “If a building can’t express itself, how can we understand it?” Scale. “Buildings must relate
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Michael S. Rose has attempted a summary of the principles of church architecture, reducing them to three in particular, which he calls Verticality, Permanence, and Iconography.20
In the case of Verticality Rose believes that “the massing of volumes upward . . . most readily creates an atmosphere of transcendence and, in turn, enables man to create a building that expresses a sense of the spiritual and the heavenly.”
The second of Rose’s principles, Permanence, involves a similar use of the “fourth dimension,” time. The transcendence of time by eternity, and by Christ as the incarnation of eternity in time, is suggested by the stability and durability of the church. An effective church building is a manifestation of tradition, and tradition is more than just the dead accumulation of custom; it is a living organism that overcomes time and death by a process of continual regeneration and gradual creative development.
The third law of church architecture is Iconography, by which Rose means the capacity of the building to convey meaning not only by its overall form, but by the details of its composition and adornment.
According to Rudolf Wittkower, medieval architects tended to build on geometrical principles, using circles, squares, triangles, and pentagons, whereas Renaissance architects preferred arithmetical principles, epitomized in the simple ratios of the musical scale.
They understood—and the earlier church fathers may have understood even better—that Adam’s role in the cosmos was a priestly and mediatory one from the beginning. That role had been restored in Christ, who by assuming human nature had in a way assumed the whole of nature by taking on a body.
