Procession of Female Saints (c. 504), Unknown.

 

"Procession of Female Saints" (c. 504), Unknown.

Magnificat November 2026

The mosaics of Ravenna and the communion of saints

This image of a procession of female martyrs is found at the Basilica of Saint Apollinaris in Ravenna, Italy, and it is one of the most stunning mosaics that comes to us from the early Church. The Basilica was finished at the beginning of the 6th century by Ostrogothic king Theodoric the Great and has undergone many renovations and name changes; this mosaic is one of the original decorations of the church.

The artistic style may strike us as Byzantine, that is, of eastern influence, but Ravenna at the time of the construction of this church was home to the Roman emperor. A strict East-West divide in artistic style does not come until much later in the history of Western art. The gold and glittering tiles are so striking that legend has it Saint Gregory the Great (r. 590–604) asked for the images to be darkened to ensure ­worshippers were not distracted. For us, in the month of November, these gilded figures serve as a wonderful starting point for contemplating the citizens of heaven—the saints—and our relationship to them.

 

Placement in the church

In order to understand the effect of this mosaic and its theological meaning, it is important to grasp its location in the church. The procession stretches the entire north wall of the church. If you stand at the door facing the altar in the basilica, this procession of female saints covers the left side and a procession of male saints covers the right side. The female saints process from an image of the port of Ravenna to an image of the Virgin Mary with Child and angels. They are led by the three Magi. The male saints process from an image of the palace in Ravenna to an image of Christ enthroned with angels. This arrangement will later become standard with images in eastern churches (Mary and Child on the left of the altar, Christ seated on the right, with saints on both sides).  

The location of these images reflects the actions of the worshippers during the liturgy. At this period, men and women occupied different sides of the church during worship. Standing was also the usual posture during the liturgy.

 

The liturgy as heavenly worship  

This beautiful mosaic teaches us in many ways about the communion of saints, liturgy, and everyday holiness.

First and foremost, the experience of worshipping in this space must have made the presence of the saints palpable. The golden aura and heavenly ­setting of the mosaics make visible the invisible setting of the liturgy. In the Mass, we truly participate in the worship of heaven and come into the presence of saints and angels. The mosaics express the truth of what we might not always sense: we are standing in heaven and in the company of heaven, or at least within its gates (cf. Psalms 122:2).

In particular, the mosaics make visible the invisible presence of the saints named in the Eucharistic prayer, who join in making the offering of the Mass. Many of the saints of the Roman canon are found in this mosaic. The Roman canon, which we refer to as Eucharistic Prayer I, was in use by the 6th ­century, ­although it was not fully set in the form that we know today until the 7th. On the women’s side, for example, you should see familiar names: Perpetua, Felicity, Agatha, Lucy, Agnes, Cecilia, and Anastasia. The fact that the saints are lined up, one after another, with little distinction between them is reminiscent of a list like the one we find in the Roman canon.

What is remarkable about these women is the kind of death they share—they are martyrs. The sacrifice that these women make, they who cast their crowns before the throne (Revelation 4:10), is that of their whole lives. Of the nature of Christian worship, Saint Augustine writes: “This is the sacrifice that the Church continually celebrates in the sacrament of the altar (which is well known to the faithful), where it is made plain to her that, in the offering she makes, she herself is offered.” In union with the one body of Christ, we become the offering that Christ is, as the martyrs well know.

The mosaic, therefore, is not just meant to overawe the worshipper with the heavenly presence of the saints or to heighten the majesty of the liturgy. It also calls each person to the holiness of these saints. In the images, the saints are literally traveling from the city of Ravenna to heaven—as mentioned above, the left procession begins at the port, and the right procession begins at the castle. Both processions arrive at the heavenly throne, the saints having won the race and obtained their crowns (cf. 1 Corinthians 9:24). These saints on the walls of the church stand beside and among the regular people—not merely at the front of the church. The summons is clear: Travel alongside these men and women, on the same road, so that you too may arrive not only at the Eucharistic altar but at the heavenly one, giving your life to God. The saints are worshipping with the people of Ravenna, standing in a Communion line alongside them so that all may come to the same resting place.

 

Elizabeth Klein

Associate professor of theology at the Augustine Institute in St. Louis, Missouri.

 

Procession of Female Saints (c. 504), Unknown, Basilica of Sant’Apollinare Nuovo, Ravenna, Italy. 

"Memories of Rome: Raphael and Michelangelo contemplating Saint Peter’s Basilica in Rome" (1831), Carl Gustav Carus (1789–1869)

 "Memories of Rome: Raphael and Michelangelo contemplating Saint Peter’s Basilica in Rome" (1831), Carl Gustav Carus (1789–1869)

Magnificat November, 2026

There is one city in the world where, even before you set foot within its walls, it is the city itself that seizes you, enfolds you, and transfigures you. It is a city you will claim to have visited, whereas in truth it is she who will have unveiled to you the treasures of your inner life. As you walk her streets, thinking you are ­discovering her, it is she who will reveal your own soul to you.

Take your place on that hill overlooking Rome where the Romantic painter Carl Gustav Carus (1789–1869), a disciple of Friedrich, has set Raphael and Michelangelo.  Side by side with them, in the ­evening light, contemplate the Eternal City. You find ­yourself almost ­granted a vision, at the very spot where Chateaubriand, in the autumn of 1803, stopped, overwhelmed, and wrote, in his Memoirs from Beyond the Grave: “Rome appeared; I greeted her, this queen of the world. I greeted her as one greets a mother. I felt that I was only a traveler, but that my soul had just come home.”

In such a place, in such exalted company, you are no longer a tourist, nor even a contemplative pilgrim. For it is not you who contemplate Rome; it is Rome that searches your soul.

Twilight falls. The dust shimmers with light like the golden ­tesserae in the apses of the major basilicas. The shadows lengthen and sketch anew a majestic world in which the purposes of God are made manifest. Over Rome the light does not go out; it ­recollects itself. It grows more solemn, more interior. At the hour when the day itself is preparing to withdraw into its sanctuary, the sky becomes a vault. The moon is a lamp lit to mark the tabernacle where the daylight will come to rest. At this hour, in Rome, all creation becomes liturgy and sings Compline.

And behold: at the center of the painting, as at the ­center of the world, the dome of Saint Peter’s, in a soft blur of latent gray, rises from the mist of evening. It lifts toward heaven like ­incense of a pleasing fragrance. Raphael and Michelangelo gaze upon it. They behold the work their genius began, which ­others continued, and which the centuries will sanctify—until our own time: on November 18, 2026, Pope Leo XIV will celebrate an ­extraordinary Mass in the Basilica of Saint Peter in Rome to mark the four-­hundredth ­anniversary of its solemn consecration.

In communion with Raphael and Michelangelo as they ­contemplate the papal basilica at dusk, Carus seeks, with his brush, to celebrate “the inner conversion, the second birth,” that he himself experienced in Rome. It is this interior experience that his friend Goethe (1749–1832) so eloquently bears witness to with his pen when he writes, in his Italian Journey: “In this city where all ­contradictions are reconciled in beauty, I rediscovered what I had always carried within me without knowing it.”

In this twilight hour, the artist invites us to let ourselves be seized by Rome, the city that reveals to man the depths of his own soul: pagan Rome, ­glorious witness to the Gospel’s preparation; ­apostolic Rome, forever a ­fertile soil, made fruitful by the blood of the martyrs; Christian Rome, splendor of a universal Catholicity, ­living, ­visible, tangible; eternal Rome, divine mystery of unity, where human ­history and the history of ­salvation are wedded.

It is into this very story that Carus invites us to enter. His work is not simply a Romantic view of Rome, with two legendary artists contemplating their own work even before it has been raised from the ground. It is the story of a Christian artist’s soul, the story of a soul that longs to come home and that, in the light of the setting sun, discerns its mother, arms flung wide like Bernini’s colonnade, ready to welcome her child.

 

Pierre-Marie Dumont

Memories of Rome: Raphael and Michelangelo contemplating Saint Peter’s Basilica in Rome (1831), Carl Gustav Carus (1789–1869), German Museum of Romanticism, Goethe House, Frankfurt am Main, Germany.

Saint Francis Receives the Stigmata (detail, 1904), Maurice Denis (1870–1943)

 

"Eight Hundred Years On, Brother Sun Still Rises Every Morning"

October 2026 Magnificat

On Sunday, October 4, 2026, we celebrate the eight-hundredth anniversary of the death of Saint Francis of Assisi. This is why, on the cover of your Magnificat, we offer for your contemplation a monumental work by Maurice Denis: Saint Francis Receiving the Stigmata. Painted in 1904, when the “Nabi of the beautiful icons” was leaving behind the audacity of his youth for a more interior, more classical, more prayerful path, this work preserves the ­influence of Gauguin and Sérusier in a taste for flat areas of color, for rhythm, for chromatic order; but it now makes them subservient to a life choice. The artist is thirty-four; he does not renounce modernity: he baptizes it.

This large panel is one single breath, a breath of primordial light. Look how this dawn tears open the heavens, and how, in the morning of the world, everything is ablaze! Here is the earth offering itself to its rays: the hills, the trees, the rocks, the grasses, the distance; everything receives, everything responds. Everything calls forth thanksgiving.

And here is Francis, so small in this incandescent immensity. Yet small and meaningful, like a simple three-letter word: “Yes.” There he stands, on the very edge of the cliff of La Verna, as though at the end of the visible universe, offered to the Invisible, his arms outstretched in the form of a cross. And creation as a whole seems gathered behind him in order, with him, to become an offering. Francis has walked through this creation barefoot, almost for fear of wounding it. For he loved it as brothers and sisters love one ­another, finding his dearest confidants in fire and water, in the bird, in the wolf and the lamb. Creation, for him, is not an environment but a kinship. It is not matter for predation; it is God’s gift, an appeal to gratitude, a summons to praise.

This is what Maurice Denis renders so admirably: under his brush, our Mother Earth becomes a canticle and calls for our ­voices. And this both gently and powerfully challenges us. Praise and thanksgiving are the first act of justice towards reality. One who, in ­thanksgiving, calls all creatures his brothers and sisters, and the earth his mother—how could he devastate them? One who receives the world as a gift—how could he treat it as prey?

Yet let us follow Maurice Denis further still. For this light is not only cosmic: it is crucified. Brother Sun is not the pagan idol of a self-sufficient world; he is the sign of Another. His brightness ­descends, crosses space, and reaches the body of the poor man of Assisi. Francis no longer contemplates only the beauty of God in creatures; he receives in his own flesh the very form of Christ. The singer of nature becomes the Alter Christus, configured to him in whom all things were created, in heaven and on earth. Francis, who had embraced poverty, is now embraced by the cross. Thus, the stigmata are the burning signature of Christ at the bottom of a life made poor by having been entirely given.

I live, now not I, but Christ lives in me (Galatians 2:20). Jesus ­countersigns upon Francis what Francis had long since allowed Jesus to write in his deeds: poverty, gentleness, obedience, fraternity, mercy, self-gift to the very end. Before the crucified Jesus conformed Francis’ hands, feet, and side to his own, Francis had already conformed his whole life to that of Jesus.

Thus the two Francises become one: the poet of Brother Sun and the crucified one of Mount La Verna; the brother of all ­creatures and the brother of the suffering Christ; he who sings creation and he who bears in his flesh the new and eternal creation. The ­artist brings them both to light in a single dawn: nature receives its ­splendor from God, and man receives his splendor from Christ.

So let us allow this light to reach us, to bathe us, to transfigure us. Let us ask Francis to teach us the gaze that blesses, the poverty that sets free, the gentleness that disarms, the likeness to Christ that alone saves our lives and the world. Eight hundred years have passed, yet Brother Sun still rises. And holiness remains that reality beyond our strength, impossible to conquer, and yet so simple to receive and to offer: to become poor enough, fraternal enough, loving enough for God to sign, authenticate, and make effective his real presence in our lives.

Pierre-Marie Dumont

Saint Francis Receives the Stigmata (detail, 1904), Maurice Denis (1870–1943)

The Monk by the Sea (1808–1810), Caspar David Friedrich (1774–1840)

 

"The Monk by the Sea" (1808–1810), Caspar David Friedrich (1774–1840)

October 2026 Magnificat

From the relative safety of shore, a solitary figure surveys white-capped waters, brooding clouds, and a boundless sky. The horizon stretches unbroken before him; the heavens dominate his diminutive form. Though his religious garb suggests faith, his head and heart are level with the restless waves. He is a question—an image of existential longing. He is Caspar David Friedrich’s Monk by the Sea.

Viewing Friedrich’s art is like “eavesdropping on someone’s prayers” (Helmut Börsch-Supan). The artist’s devout Lutheran faith and ascetic lifestyle informed his landscapes—often populated by lone, faceless figures—with a reverential mood. Friedrich stood at the vanguard of German Romanticism, and his oeuvre echoes the movement’s firm conviction: “Nature is the living, ­visible garment of God” (Goethe, 1808). When criticized for eschewing traditional religious iconography in favor of landscape, the artist asserted the religious possibilities of the genre and his distinctively Christian approach.

From a tender age, Friedrich was captivated by the natural beauty of Rügen, an island near his hometown of Greifswald on the Baltic Sea. It was here that he first heard the shore sermons of Lutheran pastor Ludwig Gotthard Kosegarten, whose plein-air preaching to seasonal fishermen was accompanied by the “trumpets of the sea and the many-voiced pipe organ of the storm” (Kosegarten, Jucunde, 1803). The island’s austere coast—with its icy waters, bracing winds, and barren dunes—is the setting for Monk by the Sea.

Genesis

No topographical markers betray this location. Friedrich empties the canvas, distilling “into the most elemental pictorial language an experience of the natural world that…approaches the universal and the timeless” (Hokanson & Seidenstein, The Soul of Nature). This dearth of detail allows for a symbolic, spiritual reading of land, sea, and sky. Divorced from the particularities of place and time, these natural forces evoke the Genesis narrative—a recurring theme in Friedrich’s art.

Standing on the dry land (Genesis 1:9), the monk feels the mighty wind move over the darkened surface of the deep as leaden clouds remit to light (Genesis 1:2-3). He gazes out over God’s creation as if contemplating its origin: In the beginning, when God created the heavens and the earth—and the earth was without form or shape, with darkness over the abyss and a mighty wind sweeping over the waters—Then God said: Let there be light, and there was light (Genesis 1:1-3).

The watery chaos (Gn 1:2)—tĕhôm, in Hebrew—is associated with confusion and disturbance, ­potentiality and formlessness. A return to this ­primordial state implies movement from intelligibility to ­incoherence, form to fragmentation, life to death. The tĕhôm is a common Biblical metaphor for extreme affliction: Save me, God, for the waters have reached my neck. I have sunk into the mire of the deep, where there is no foothold. I have gone down to the watery depths; the flood overwhelms me (Psalm 69:1-2).

Existential angst

There is a profound, melancholic resonance between the monk and the sea. Hemmed in by a low horizon, the monk’s figure is framed by its turbulent waves—his robe shares their inky hue. Out of the depths (Psalm 130:1) he invokes the infinite, curved like a question mark below the vast sky.

Monk by the Sea was originally exhibited with its counterpart, Abbey in the Oakwood, a depiction of the monk’s burial. Silhouetted in the waning light, Gothic ruins tower over a cemetery, where oaks spread gnarled branches toward a crescent moon. The abbey, the trees, the moon—each more ancient than the last—highlight the transience of the monk’s life. In a similar vein, as Friedrich himself comments, any traces of the monk’s brief presence on the beach will be quickly erased by the wind.

In both paintings, the absence of perspectival markers creates an almost disorienting sense of incalculable space. Together, the pair suggests the monk’s feelings of insignificance amidst the immensity of space and time. His mortality seems to threaten a descent into the void. Existential angst wars with faith within.

The sublime

God’s response to existential distress often looks like a kind of re-creation. As Peter sinks in the Sea of Galilee, Christ repeats the pattern of Genesis, pulling the “rock”—the dry land—from the waters. Job—crying out, beset by suffering—receives an enigmatic reply from the midst of the whirlwind: Where were you when I founded the earth? (Job 38:4).

Here too, the monk’s attention is directed toward the grandeur of the created order—toward a perspective as high and as wide as the vast expanse of sky. He must see creation anew with the eyes of faith, and discern the divine within the very vastness that disturbs his spirit.

A quintessential example of the Romantic sublime, Monk by the Sea depicts an experience of the incomprehensible, even terrifying, force and immensity of nature. From the Latin sub—“up to”—and limen—“threshold”—it describes man’s fleeting brush with the far side of reason. Often eliciting wonder and awe, this intense confrontation can also lead to despair: feelings of personal insignificance and mortal dread. Approached in faith, however, it offers a thrilling glimpse of the Creator, whose intricate management of the universe overwhelms man’s faculties. This “sacred intuition,” says Friedrich, is “seen and recognized only in belief.”

While the monk’s frame is dwarfed by the heavens, so too is the narrow strip of sea, suggesting divine dominion over the forces of chaos that beset his soul. Isolated on desolate dunes, the monk anxiously considers his place within the cosmic order. Yet—far above him—calm light shines.

Amy Giuliano

Holds degrees in art history from Yale and theology from the Angelicum, Rome.

The Monk by the Sea (1808–1810), Caspar David Friedrich (1774–1840), Alte Nationalgalerie, Berlin. 

Saint Jerome in His Study (c. 1435), Jan van Eyck (c. 1390–1441)

"Saint Jerome in His Study" (c. 1435), Jan van Eyck (c. 1390–1441)

For centuries the Church has remained indebted to Saint Jerome, the 4th-century scholar and Doctor of the Church whose translation work made it possible for “the treasures of the Bible to be opened more lavishly, so that richer fare may be provided for the faithful at the table of God’s Word” (Sacrosanctum Concilium, 51). In his early-15th-century masterpiece Saint Jerome in His Study, the gifted Flemish painter Jan van Eyck offers a striking visual homily. A prominent figure in the Early Netherlandish painting school, van Eyck uses vibrant color, warm light, and rich symbolic details to evoke the power of God’s Word in the life and work of Saint Jerome.

From a young age, Jerome (c. 347–420) was immersed in the study of literature and languages. Not long after his baptism in 366, he placed his significant linguistic and literary talents at the service of the Word of God. He lived an ascetic life of study and prayer in a continuous lectio divina, reading and contemplating God’s Word. The fruit of his long years of study was the collection of original and revised Latin translations known as the Vulgate, which became the official Latin text of Scripture.

Feasting at the table of God’s word

Jan van Eyck places Saint Jerome in the corner of a warm interior space where he is seated at an ornate desk covered with a deep green tablecloth. The delicately carved high-back seat suggests a cathedra, a bishop’s liturgical chair. Jerome is clothed in a vibrant red robe and a red hat or galero, a medieval headdress worn by cardinals. The saintly scholar’s head is inclined in deep contemplation of God’s Word.

With his right hand, Jerome gently touches the pages of Scripture. One can feel the movement of the sacred text as the living Word of God. In a blue curtained niche behind him are recessed shelves with large and small reference books and an astrolabe, an astronomical instrument used to chart the stars. Green and red bead tassels indicating his cardinal rank hang nearby. And on top of a white jar labeled “TYRIRICA,” thought to be an antidote to physical or spiritual poisons, is a pomegranate, a symbol of Christ’s Resurrection. The dark glass bottle near the sacred text reflects light streaming in from the high upper left window. This subtle glimmer of reflected light evokes the light of the Holy Spirit who inspires Jerome’s study and contemplation of God’s Word.

A large hourglass on the table in front of Saint Jerome suggests the gradual passage of time and human mortality. On the folded letter, in plain sight, is a clear salutation, addressed to an unnamed cardinal. Historians suggest it refers to Cardinal Niccolò Albergati, patron and friend of van Eyck, who may have commissioned and owned this exquisite painting. In the lower right corner, a crouched lion alludes to the legend that Saint Jerome extracted a thorn from the paw of the animal, who became his lifelong companion.

Jesus, the living and incarnate Word

“Ignorance of the Scriptures is ignorance of Christ.” These words attributed to Saint Jerome direct our gaze to Jesus Christ, who stands at the heart of Sacred Scripture. And what may we learn from Saint Jerome today? “This above all: to love the Word of God in Sacred Scripture…. It is important that every Christian live in contact and in personal dialogue with the Word of God…. On the one hand, it must be a truly personal dialogue because God speaks with each one of us through Sacred Scripture and it has a message for each one of us. We must not read Sacred Scripture as a word of the past, but as the Word of God that is also addressed to us” (Pope Benedict XVI).

Moreover, Pope Benedict continues, “although it is a personal Word, it is also a Word that builds community, builds the Church. We must therefore read it in communion with the living Church.” Saint Jerome reminds us that “human opinions come and go. What is very modern today will be very antiquated tomorrow. On the other hand, the Word of God is the Word of eternal life, it bears within it eternity and is valid for ever. By carrying the Word of God within us, we therefore carry within us eternity, eternal life.”

Jem Sullivan, Ph.D.

Associate professor in the School of Theology and Religious Studies at The Catholic University of America and the author of Way of Beauty: Rekindling Eucharistic Amazement with Visio Divina (Our Sunday Visitor).

 

Saint Jerome in His Study (c. 1435), Jan van Eyck (c. 1390–1441), Detroit Institute of Arts. ©  Detroit Institute of Arts / Bridgeman Images.

The Creation (c. 1480–1490)

"The Little Rabbit That Chose the Better Part"

Magnificat September 2026

From September 1 to October 4, the feast of Saint Francis of Assisi—in 2026 we mark the eighth centenary of his death—the Church leads us into the Season of Creation. In the spirit of this season, we contemplate this illumination painted around 1480, which comes to us from the close of the Middle Ages, when the image, with its poetic and symbolic language, sets us before the very foreground of the creative act.

And now, behold

See how everything begins, not in matter, but in glory. There is not a primordial chaos; there is gold. This burning sheet, silent, sovereign, does not represent a thing, but the glory of Being. Gold, here, is the radiance of glory; it is light before it has encountered any obstacle; it is the first morning of the world, even before the dawn has received a name. God said, “Let there be light!” ( Genesis 1:3 )

The gold background does not merely fill the image; it grounds it. It does not decorate the world; it proclaims its source, its life, and its fulfilment. It is the signature of uncreated light. It is the first day that endures beneath all days. It is the Let there be light that never ceases to resound. It is the brightness before the sun, the brightness of God, the brightness of the light that does not wane, the radiance of divine glory, by which creation is a transfiguration.

And here, at the threshold of the world, is the uncreated Light, ­begotten of uncreated Light, the first-born before all creation. Look: all things are created through him and for him (Col 1:15-17). See how, even before the creation of man and woman, it is a human figure that, rightly, the ­illuminator gives us to contemplate. Yet it is not the venerable old man representing the Father in so many images: it is a young man. Yes, it is indeed he: it is already Christ—before Bethlehem, before Nazareth, ­before the Jordan, before the cross, before the empty tomb—Christ in his creative eternity: the Word.

For when Scripture narrates the work of the six days, it is marked by this decisive formula: God said. God speaks, and it is done. God creates by his Word. Now the Word of God is not a breath lost in the air: it is Someone. He is the Son, the Only-Begotten, the Image of the invisible God, the One in whom all things were created. (Colossians 1:15–16 )

The hand that speaks

Thus the illuminator has clothed him with all his signs. First, his youth: not the passing testimony of his age, but the eternal newness of the Son. His blue halo rayed with gold: the blue of the heavenly heights, the gold of glory, of the light that does not dim. His crown consecrates him King of the universe, but with a disconcerting kingship: he does not ascend the throne to dominate others; he will descend from it in order to raise them to it; he does not have subjects under his feet, but brothers and sisters whose feet he will wash; he does not weigh upon humanity with his divine omnipotence; out of love, he will become man so that man may become God.

And precisely his red mantle, which covers his heavenly blue tunic, speaks of his ardent Love, of his life given, of his blood ­already ­mysteriously poured out in the very dawn of creation. And his hands! The right hand is the hand of the Pantocrator, the hand of Christ the Almighty: the hand that speaks, the creative hand that says Fiat and it is done. The left hand is open: it also speaks, it says: Father, thy will be done. (Matthew 6:10)

Thus, through the image, the artist makes us see the Word as he unfolds his creative power. In the upper right, here is the ­firmament of the second day, spread out like a great blue mantle in which the clouds dispense the freshness of the first morning. In this sky are kindled the lights of the fourth day. That they have a face is not naïveté, it is a poetic language:

Praise to you, my Lord, for all creation,

Most specially our noble Brother Sun,

Bringing the day by which you grant us light.

 

Pierre-Marie Dumont

The Creation (c. 1480–1490), illumination from Ms 101, fol. 7, Getty Museum, Los Angeles. Image: Courtesy of Getty’s Open Content Program.

American Paleobotanist 🇺🇸 👨‍🔬 Ralph Works Chaney (August 24, 1890 – March 3, 1971)

 

From McGraw-Hill encyclopedia of science and technology. McGraw-Hill Modern Men of Science; 426 Leading Contemporary Scientists Presented by the Editors of the McGraw-Hill Encyclopedia of Science and Technology. McGraw-Hill, 1966.

CHANEY, Ralph Works

American paleobotanist

Born August 24, 1890, Chicago, Illinois, USA

Died March 3, 1971, Berkeley, California, USA

In his study of Tertiary forests, Chaney developed a dynamic approach based upon close resemblances between plants of the past and those now living.  He considered plant fossils as representatives of the vegetation of their day, in contrast to their study as individual specimens whose structure or phylogeny is the primary concern of many paleobotanists.

Chaney's familiarity with living plants influenced his emphasis on similarities rather than on differences in designating fossil species.

But he did not use modern specific names for plants older than Pleistocene, arguing that the incompleteness of their record did not justify assuming that there had been no changes of specific rank since Tertiary time. Firmly believing that taxonomy should be a tool rather than a burden, he set up stratigraphic species where differences in size or other minor characters could be detected in rocks of different ages. In like manner he tended to establish geographic species for similar plants separated by ocean or climatic barriers. Recognition of elements whose fossils had close living equivalents in major areas did much to clarify areal and systematic relationships of fossil plants to each other and to those that have survived in modern forests.

Chaney's collecting procedure required handling of large numbers of specimens, so that variations within designated fossil species could be compared with those of related living plants. A census taken in the field showed which species were abundant near sites of deposition, and perhaps suggested more remote habitats in adjacent uplands for sparsely represented plants.

A standard section was set up in the John Day Basin of eastern Oregon, where abundant and well-preserved fossils occurred in stratigraphic sequence. Successive floras showed differences in composition, and Chaney noted a progressive reduction in size and texture of leaves. This provided a basis for dating the floras of other areas, and for their assignment to the same stage in the Tertiary sequence if they occurred in the same general latitude.

Quantitative appraisal of leaf characters provided a basis for estimating Tertiary climates. Large, thick, camptodrome-veined leaves now characterize the evergreen forests of the tropics, while trees of higher latitudes are largely deciduous, with smaller, thinner leaves, and craspedodrime venation. The change in leaf characters from Lower to Upper Tertiary shows a response to progressive changes toward the cooler and drier climate of our day.

Chaney pointed out that the temperate Eocene plants of Alaska did not appear in Oregon until Oligocene time, and that subtropical Eocene plants of Oregon have survived only in low latitudes. He suggested the term "geoflora" for groups of plants in mass migration; the Arcto-Tertiary Geoflora has maintained itself with only minor changes in composition since the Eocene, during which time its distribution has been shifted from Alaska southward across the United States. The Neotropical-Tertiary Geoflora has moved from Washington and Oregon into Mexico and Central America.  Recognition of a deciduous conifer, Metasequoia, as a fossil by S. Miki in 1941, and its almost contemporary discovery as a living tree by T. Wang in central China, has done much to confirm the concept of geofloras. Chaney had previously predicted that a fossil "redwood" might be discovered, with a deciduous habit suited to occurrence at high latitudes. He visited the natural occurrence of Metasequoia in 1948 to determine that its associates were members of the Arcto-Tertiary Geoflora, and revised the fossil records of several members of the Taxodiaceae.

Most fossil floras contain plants that lived at low to middle altitudes. Chaney suggested that since the lapse rate corresponds to successively lower temperatures at higher latitudes, an Eocene flora living near  sea level in Alaska may have had a counterpart in the mountains of Oregon; its absence or scant representation in the Oregon Eocene was to be expected in view  of its remoteness from sites of deposition, but we could reconstruct such a montane flora by studying floras of similar age in deposits to the north. An early elaboration of this concept led to his suggestion that angiosperms may have had their origin at high altitudes during the Jurassic period, although they first appeared in the fossil record in Cretaceous time.

While there has been well-defined latitudinal control of forest distribution during the Tertiary period, Chaney noted significant departures. A given flora lived farther south with increasing distance from the Pacific Coast; it ranged far to the north across ocean basins. Plotting the occurrence of Eocene floras across North America and Eurasia, he showed that lines connecting similar floras (isoflors) followed the paths of modern isotherms and of major forest types. He concluded that Eocene position of continents and oceans in relation to each other and to the axis of rotation was essentially the same as it is today. This placed the burden of proof on advocates of continental drift and polar migrations during later geologic time.

A descendant of pioneer Illinois farmers, Chaney majored successively in zoology, botany, and geology at the University of Chicago, where he received his B.S. in geology in 1912 and his Ph.D. in paleontology in 1919. Several years of high-school and university teaching (State University of Iowa) preceded his appointment in 1922 as research associate of the Carnegie Institution of Washington; he retired in 1957.  From 1930 until 1957, he was also professor of paleontology at the University of California, Berkeley.  He carried on field work widely in the Americas and Asia. During World War II he set aside his paleobotanical work to become assistant director of the University's Radiation Laboratory in an administrative capacity. He was elected to the National Academy of Sciences in 1947.

For background information see Paleobotany in the McGraw-Hill Encyclopedia of Science and Technologu.

American mathematician Salomon Bochner 👨‍🏫 🇺🇸 (20 August 1899 – 2 May 1982)

From McGraw-Hill encyclopedia of science and technology. McGraw-Hill Modern Men of Science; 426 Leading Contemporary Scientists Presented by the Editors of the McGraw-Hill Encyclopedia of Science and Technology. McGraw-Hill, 1966.

BOCHNER, Salomon

American mathematician

Born August 20, 1899, Cracow, Poland (then Austria-Hungary)

Died 2 May 1982 Houston, Texas  

Bochner's achievements were mainly in the field of harmonic or Fourier analysis, that is, in the theory of representation of general functions by trigonometric series, trigonometric integrals, and more comprehensive expansions. But he was also active in the theory of functions of several complex variables, especially on Cauchy formulas, and on functions in tubular domains, which latter topic has applications to hyperbolic differential equations and to problems in quantum field theory. In differential geometry he introduced a general topic that goes under the name "curvature and Betti numbers."

In physics and technology many phenomena are viewed as "waves" (which subsumes "vibrations" or "oscillations"); there are waves in acoustics, hydronamics, electrodynamics, optics, and quantum mechanics, among others. Invariably, a "general" wave is an additive, finite or infinite, superposition of "simple" waves, a simple wave being one with a specific single "frequency" is associable; also invariably, in each context there is a certain "typical" case, in which all occurring frequencies are integer-values multiples of a single one, which is then the smallest one. This skeletal "sameness" within physical contexts of different provenance, especially the sameness of the "typical" case, is brought about by the fact that, in each case, a certain function f(x), the wave function (say on an interval of length 2π), is represented as a series, with constant coefficients, of the "simple" functions { sin nx, cos nx } or, in the complex version, of the "simple" functions  { e^imx }. This mathematical expansion is of course independent of the physical interpretation in which the function f(x) may be involved.

Another "typical" case arises if, as J.B. Fourier did in the early 19th century, we vary the interval over which f(x) is defined, and then let the length of the interval tend to infinity. This replaces the trigonometric series by a trigonometric integral, that is, the Fourier coefficients by a certain function, say 𝝋(ɑ), which is called the Fourier transform of f(x). Now the relation between between f(x) and its transform 𝝋(ɑ) is a "dual" or "reciprocal" one, meaning that f(x) can be reobtained from 𝝋(ɑ) in more or less the same manner as 𝝋(ɑ) was obtained from f(x). After lying dormant for the better part of a century, this duality began to be studied in earnest at the beginning of the 20th century. The principle underlying it is so general and comprehensive that the awareness and presence of it was felt in ever wider and ever more numerous areas of mathematics and physics. For instance, if formulated in a suitably comprehensive version, this duality subsumes the de Broglie duality between waves and corpuscles.

A new event occurred in the early 1920s when the mathematician Harold Bohr (younger brother of the physicist Niels Bohr) introduced, on -∞ < x < ∞, so-called almost periodic functions (which had been foreshadowed as far back as in the mechanics of Lagrange), each of which has a "discrete" Fourier expansion, in which however the "frequencies" λ , which occur in the "simple" functions { e^iλx }, can be arbitrary real numbers, with no requirement at all of commensurateness between any two of them.

Bochner soon introduced an algorithmic summability process, the so-called Bochner-Fejer process, which makes it just as easy to handle the Fourier expansion of almost periodic functions-for any type of almost periodicity, however general-as the customary case of periodic functions. Furthermore, Bochner gave an entirely different characterization of the class of almost periodic function on the line, namely, by a certain topological property of compactness. It was this alternate definition that afterwards enabled John von Neumann to extend almost periodicity from the euclidean line to other group spaces.

In the field of Fourier integrals, Bochner found a much applied criterion for a continuous complex-valued function 𝝋(ɑ) to be representable as Fourier-Stieltjes integral 

𝝋(ɑ) = ∫ e^iaxdF(x)

in which dF ≥ 0. For this to be possible it is not only  necessary but also sufficient that 𝝋(ɑ) be positive-definite, meaning that for any finitely many points ɑ₁,…, ɑ_n , and complex constants  c₁,…, c_n , there is:

𝚺   (p,q=1…n) c_pc_q𝝋 (ɑ_p-ɑ_q ) ≥ 0

This criterion has several applications in the theory of probability; it is also usable for the derivation of the spectral representation of a self-adjoint operator in Hilbert space; and it has been generalized and applied to functions on topological group spaces.

Bochner was also a precursor in the theory of the so-called Schwartz distributions in that he introduced generalized Fourier transforms for functions that do not grow faster at infinity than a power of x.

After attending high school in Berlin, Bochner studied mathematics at the University of Berlin, terminating with a Ph.D. in 1921. In 1924-26 he studied, partly as a fellow of the International Education Board, with Harold Bohr in Copenhagen, and with G. H. Hardy and J. E. Littlewood in Oxford and Cambridge. In 1926-33 he was lecturer at the University of Munich, where he wrote his first book on Fourier integrals. In 1933 he joined the mathematics department of Princeton University and in 1951 became Henry Burchardt Fine Professor there. He was elected to the National Academy of Sciences in 1950.

Bochner wrote "Several Complex Variables" (1948), "Fourier Transforms" (1949), "Curvature and Betti Numbers" (1953), "Harmonic Analysis and the Theory of Probability" (1955), "Fourier Integrals" (1959), and "The Role of Mathematics in the Rise of Science" (1966).

For background information see "Analysis of Variance"; "Fourier Series and Integrals"; "Integral Transform" in the McGraw-Hill Encyclopedia of Science and Technology.