Today I am happy to introduce another guest blogger here at Sacred Space Astronomy: Karen Shadle, Director of Worship for the Archdiocese of Louisville Kentucky. Long-time readers of this blog may remember a post about Msgr. Bouchet’s telescope and Tim Tomes. Tomes is now the archivist and historian for the Archdiocese. He encouraged Shadle to contact me after reading an article on moveable feasts that she had written for her column in The Record, the Archdiocesan newspaper. This post is adapted from that article. Karen Shadle is a musicologist with a Ph.D. from the University of North Carolina at Chapel Hill. She specializes in the history of sacred music in the United States and is an accomplished organist, pianist, and choir director. She lives in Louisville with her husband and two children.
Karen Shadle, 23 Jan 2020
“Alexa, when is Easter?” I asked, pre-stressing for what will be a very busy spring in the Archdiocese of Louisville.
“Easter is Sunday, April 12,” the digital assistant chirped back.
Unlike Christmas, which we know happens on December 25th every year, Easter in the Roman Church moves around from year to year. It occurs on the first Sunday after the first full moon after the vernal equinox. The vernal equinox, which is the official beginning of spring in the Northern Hemisphere, is the date on which the center of the sun is directly above the earth’s equator, when day and night are of equal length.
“Equinox” combines the Latin words aequus (equal) and nox (night). I don’t know about you, but the long stretches of winter darkness seem to weigh me down. On many days, it is dark when I leave for work and dark when I come home! The vernal equinox is an exciting turning point where we can all look forward to long days that culminate in sunlit summer evenings.
The vernal equinox always occurs somewhere in the range of March 19-21, but it can vary a bit depending on where you live in your specific time zones, leap year calculus, the slight tilt of the earth, and some other astronomical math that I don’t understand. (I am a liturgist and definitely NOT an astronomer!) At the Council of Nicaea in 325, the Church declared that March 21 would be fixed as the “ecclesiastical approximation” of the vernal equinox in order to simplify things somewhat. Therefore, Easter in the Roman church can be as early as March 22 or as late as April 25.
Why is Easter’s date tied to the moon and the sun to begin with? We know from scripture that Jesus rose from the tomb early on the first Sunday following the feast of Passover. The Jewish calendar is partly lunar and partly solar. Its months are either 29 or 30 days, corresponding to a roughly 29.5-day lunar cycle. Its years are either 12 or 13 months, corresponding to a roughly 12.4-month solar cycle. Passover should ordinarily correspond with a full moon on the 15th of the month of Nisan. However, because we are not dealing with whole numbers, the month-moon cycles often get slightly out of sync before lining back up again. Because of this, the Jewish rabbis would sometimes have to announce when Passover would be celebrated in a given year. This is how we derive the tradition of calculating Easter.
None of this matters much in the age of Alexa, Google, Siri, and the others. Calendars are ubiquitous, and we trust their calculations without thinking. However, there was a time when the announcement of the date of Easter was of great practical and spiritual importance to the Christian people.
There is a very beautiful and very optional liturgical rite of the Proclamation of the Date of Easter, which can be inserted into Mass at the Solemnity of the Epiphany. This feast is traditionally celebrated on the 12th day after Christmas (January 6) and marks the arrival of the Magi bearing gifts for the newborn King. In the United States, Epiphany is moved to a Sunday (between January 2-8) so that it can be more readily celebrated by the faithful.
At the Epiphany Mass after the homily or after the communion rite, a deacon or cantor chants the proclamation:
Noveritis, fratres carissimi, quod annuente Dei misericordia, sicut de Nativitate Domini nostri iesu Christi gavisi sumus, ita et de Resurrectione eiusdem salvatoris nostri gaudium vobis annuntiamus.
Know, dear brothers and sisters, that, as we have rejoiced at the Nativity of our Lord Jesus Christ, so by leave of God's mercy we announce to you also the joy of his Resurrection, who is our Savior.
Die sexta et vigesima februarii erit dies Cinerum, et initium ieiunii sacratissimæ Quadragesimæ.
On the twenty-sixth day of February will fall Ash Wednesday, and the beginning of the fast of the most sacred Lenten season.
Die duodecima aprilis sanctum Pascha Domini nostri Iesu Christi cum gaudio celebrabitis.
On the twelfth day of April you will celebrate with joy Easter Day, the Paschal feast of our Lord Jesus Christ.
Die una et vigesima maii erit Ascensio Domini nostri Iesu Christi.
On the twenty-first day of May will be the Ascension of our Lord Jesus Christ.
Die una et trigesima maii festum Pentecostes.
On the thirty-first day of May, the feast of Pentecost.
Die undecima iunii festum sanctissimi Corporis et sanguinis Christi.
On the fourteenth day of June, the feast of the Most Holy Body and Blood of Christ.
Die undetrigesima novembris dominica prima Adventus Domini nostri Iesu Christi, cui sit honor et gloria, in sæcula sæculorum. Amen.
On the twenty-ninth day of November, the First Sunday of the Advent of our Lord Jesus Christ, to whom is honor and glory for ever and ever. Amen.
(The dates here are the dates for 2020.) Through the rhythms of times and seasons we celebrate the mysteries of salvation. We are a pilgrim Church, and Jesus Christ is the Lord of all time and history. Like the sun in the sky, God illuminates all that is known.
The Proclamation of the Date of Easter on Epiphany is an ancient tradition that is somewhat obscure and rarely used in modern liturgy, perhaps for good reason. On a practical level, Christians no longer need to wait for an announcement or scribble down a list of the important moveable feasts of the year. Nevertheless, I’m glad the Proclamation persists as an option. I might even encourage a renaissance. It’s a beautiful reminder of the centrality of the resurrection of Jesus in the rhythm of our lives. Most everything that the church does revolves around Easter, and so should our lives of faith.
There are many ways to mark time in a year. Farmers use the seasons, accountants use fiscal quarters, sports fans use the team schedule, and teachers use semesters. Christians mark time by Easter. From Easter’s placement, the rest of the liturgical year falls into place. As we turn the page to a new year, let us all reorient ourselves to the cross.
Dates of moveable feasts for the year 2020 (arrows) as calculated by the Jesuit astronomer Christopher Clavius, four centuries ago. From his 1603 Romani calendarii a Gregorio XIII. Click here to see the whole page, courtesy of Google Books.
Entirely by coincidence, another person from the Diocese of Louisville has been writing on the proclamation of the date of Easter: Fr. Steven Reeves, associate pastor at Saint Boniface and Saint Patrick churches in Louisville. Click here to see his take on the subject.
The 1990s TV show Star Trek: Deep Space Nine (DS9 for short) is a favorite of the Graney family. DS9 featured lots of those extraterrestrial non-human intelligent life forms so common to Science Fiction: Cardassians, Klingons, Bajorans. But these extraterrestrials were just humans in make-up. By this I don’t just mean that the Klingon or Bajoran characters were played by human actors wearing rubber “ears” or “brow ridges”; I mean that these characters were essentially human. Their cultures might have been different, but they acted like human beings.
DS9 did attempt to develop extraterrestrials that were less “human” and more “alien”. They did this via “The Dominion”, the overwhelmingly powerful kingdom of a race of fluid creatures called “Founders”. The Founders manufactured two races to serve them: the “Vorta”, who were managers and diplomats; and the “Jem’Hadar”, who were soldiers. The Jem’Hadar were “hatched out of a vat”, fed intravenously, grew to maturity within days, and lived only a few years. They were fighters by instinct. They neither ate, nor drank, nor begat children. By genetically programmed instinct they obeyed the Vorta, and venerated the Founders as gods. The Jem’Hadar were the soulless minions of the Founders—manufactured, instinct-driven, utterly disposable killers. They were perhaps DS9’s most convincing effort at inventing truly non-human extraterrestrials.
And yet, that effort was not so convincing. Once DS9 began to feature episodes with one-on-one interactions with the Jem’Hadar, they started to seem less soulless. They understood the world around them. They were aware, for example, about what their Vorta superiors were up to, even though the Vorta dismissed them as non-persons. They could control their instinct to fight, and could even work with adversaries, if their mission required them to do so. They accepted their role in “the order of things”, and did the jobs they were created to do. The lead character in DS9, Captain Benjamin Sisko, ended up describing them as “professionals”. When he had a platoon of Jem’Hadar surrounded, he called for a truce and tried to negotiate a surrender so as to avoid massacring them. The Jem’Hadar leader respectfully declined—it was not in the “order of things” for them to surrender—and, when the truce was over, led a final, hopeless charge against Sisko’s forces. And so DS9’s Jem’Hadar ended up being rather human; not soulless minions after all.
This focus on being human is a theme in the long-lived Star Trek franchise. One of its most famous characters, Mr. Spock, was a Vulcan who often disdained human emotions and ideas. In the movie Star Trek: The Wrath of Khan, he gives his life to save the starship Enterprise, because “the needs of the many outweigh the needs of the few, or the one”. His Captain, Kirk, eulogies him by saying, “Of all the souls I have encountered in my travels, his was the most… human.”
Likewise, consider the Marvel movie Guardians of the Galaxy, and the character of Groot. Groot is truly a non-human alien, a walking plant who can say little more than “I am Groot”. But Groot, like Spock, sacrifices himself to save his Guardians teammates because, as he so eloquently puts it, “We are Groot”. In the world of Science Fiction, even a plant seems to have a human soul.
Then consider all the Science Fiction replicants, droids, artificial intelligences, clones, and whatnot who all manage to have souls, or appearances thereof. We humans have been most willing to grant, through Science Fiction, souls or humanity to non-humans. Thus it may surprise readers of Sacred Space Astronomy to learn that we humans have been very willing to deny, through Science itself, souls or humanity to actual human beings.
The story of Science’s role in denying humanity to human beings is told in the book Adam’s Ancestors, by David N. Livingstone (an entry on the V.O. Faith and Science pages—click here for it). The book is about the idea of “pre-Adamites”: “people” postulated to have existed prior to Adam. I use quotation marks here because usually the pre-Adamites were assumed to be not truly human—not “true men”, to use the language of the time. The true men were the Sons of Adam and Daughters of Eve (to borrow the phrasing of C. S. Lewis’s The Lion, the Witch, and the Wardrobe). The others were sort of like Vulcans, or even the Jem’Hadar—aliens who might have no souls.
The idea of the pre-Adamite is an old one. Livingstone describes it as having been fed through two principle roots. One of those roots is the diversity and wide distribution of people in the world. Originally that diversity was the stuff of legend. The ancient author Pliny the Elder had written about all sorts of strange “people”—people with one leg and a giant foot, people with a single eye, people with dog heads, people with no heads at all and faces in their chests, and so forth. Scholars for centuries took Pliny at his word.
Pliny’s strange beings, from Sebastian Münster’s Cosmographia of 1544
Pliny’s strange people even appear in Shakespeare:
It was my hint to speak—such was my process—
And of the Cannibals that each other eat,
The Anthropophagi, and men whose heads
Do grow beneath their shoulders.
[Othello, Act I, scene iii]
Scholars wondered whether creatures such as these, who were certainly as weird as any Klingon, could be Sons of Adam and Daughters of Eve.
Then, as the world was more widely explored, people were found living in lands that were far separated from the world of Europe-Asia-Africa by vast spans of water. How could such widely dispersed peoples, speaking widely differing languages, all have come from the one family line of Adam? And what of people who claimed long histories, like the Egyptians or the Chinese? Surely all this could be explained more easily by having some other beginning to at least some of humanity than just Adam and Eve in the Garden of Eden.
The second root feeding the pre-Adamite idea was a discomfort with difficult passages in Genesis. Consider Genesis 4, for example. Cain, upon being sent away to the land of Nod by God for the murder of Abel, expresses fear that anyone who saw him would kill him:
Cain said to the Lord: “My punishment is too great to bear. Look, you have now banished me from the ground. I must avoid you and be a constant wanderer on the earth. Anyone may kill me at sight.”
Since only Adam, Eve, Cain, and the now-dead Abel had been mentioned thus far, whom did Cain fear? And then Genesis mentions Cain’s wife. Where did she come from? Surely all this could be explained more easily by having some other beginning to at least some of humanity than just Adam and Eve in the Garden of Eden.
But when it is assumed that there is some other beginning to at least some of humanity, the idea that all people are Sons of Adam and Daughters of Eve—all of one family—is lost. And when that is lost, then we can start making the claim that this group of people are “true men”, while that group of people are just soulless animals—just sorts of apes who happen to have a more human-like shape—like Jem’Hadar (as DS9 originally envisioned them).
Usually the groups being labelled as soulless have been those with darker skins; usually, but not always. The Irish, for example, were often included as being among the “lesser races”. As Thomas Cahill pointed out in his How the Irish Saved Civilization, they were the “white chimpanzees”, “incapable of civilization”.
Adam’s Ancestors documents lots of comparisons of people to apes, and lots of scientific efforts to quantify to what extent different groups of people differed from “true men”. Social scientists went about quantifying humans with measurements of differing cranial capacities, differing language structures, and the differing distributions of people and of apes. They insisted that these different groups that they saw were different species. This was illustrated by the supposed infertility of (at least over a number of generations), and weakness of, “hybrid” offspring of “mixed race” couples. These scientists experienced resistance from those who insisted for religious reasons that all peoples were brothers and sisters in the family of Adam—all Sons of Adam and Daughters of Eve.
An article from the May 1865 issue of The Anthropological Review provides an illustration of all this (as there is a “faith versus science” element in this, Sacred Space Astronomy readers will not be surprised to find a Galileo reference here):
Everywhere the supremacy of facts is now recognised, and the only loyalty even professed by the more advanced minds is not a faithful adherence to tradition, but unswerving fealty to the truth. The battle fought and won by astronomy in the days of Galileo, was in truth but the beginning of the war, and alone would have proved utterly inadequate to teach men of science their strength, or theologians their weakness. This was shown in the reception accorded to geology, whose stupendous revelations from the page of nature were long expected to bend to a written record. It is still shown in the criticisms provoked in certain quarters by anthropological investigations. We are free to speculate on the age of rocks, and even to inquire into the succession of plants and animals; but man is a sacred, and, therefore, a forbidden subject. His origin, antiquity, and special relationships have all been settled by a tribunal that laughs at induction, and treats opposing facts with derision.... Till very recently, even the greatest minds bowed in submissive silence to this unreasoning despotism. However free and untrammeled in other provinces of investigation, they paused upon the threshold of man. He was an exceptional instance in the grand scheme of creation, an isolated phenomenon in the great plan of nature, to make free with whom, after the ordinary fashion of inductive inquiry, was little other than an act of open and scandalous impiety.... On special difference as attaching to brown and white bears, and of organic diversity in relation to African and Asiatic elephants, it was quite lawful to dilate, but an Esquimaux and a European, a Negro and a Persian, were to be invariably treated as of one species. Freedom of inquiry ceased with man....
It is in relation to this most important question, freedom of inquiry, and we may add, liberty of speech, on the part of men of science, that the anthropological societies now rising in various parts of Europe are doing such good service to the cause of truth. Composed of the most advanced minds in the countries where they are respectively organised, these bodies present a barrier to fanaticism, and ensure freedom of inquiry and discussion, at least within the limits of their own meetings, and in the pages of their own publications.... For let us not deceive ourselves; the public, even the educated public, are still unprepared for the full reception of the truth as it is in nature, on the subject of man. They want our statements to be toned down, and our conclusions to be modified into accordance with their limited ideas, ere they will give us a favourable or even an unprejudiced hearing. They have not yet given up their idols. They are still under the dominion of traditional ideas, and in plain language, are too much the slaves of authority to listen without fear to the echoes of a freeman's voice.... Hence, then, the necessity for effective organisation on the part of anthropological inquirers, not merely for the purpose of ensuring freedom of discussion among themselves, but also with the equally important object of supporting a literature devoted to the statement of facts, and the utterance of conclusions too far in advance of existing opinion for their easy reception by the general public, and yet eminently calculated to promote the cause of anthropological inquiry....
[The theory of development of man is] purely a question of science, and as such its decision must be left to those who are prepared to investigate the subject through the evidence of fact rather than the authority of dogma. Once for all, then, let us clearly understand that theologians as such, have nothing to do with this great controversy; their attempted meddling with which is an impertinence that the dignity of science can afford to treat with the silent contempt it so richly deserves.
The same article includes references to the superiority of Caucasians, such as—
man, even in his highest existent form, the Caucasian, is still but an initial type, only in the process of emergence... while the inferior races, more especially the negroid, are still absolutely embryonic.
—as well as this reference to—
the true man, by which we mean the large-brained and small-mouthed Caucasian.
And there is this, on “hybrids”—
When we consider that in this way every healthy and rightly-constituted organism, when of pure type and on its own site, is in perfect harmony with itself, that all its powers and functions are perfectly balanced, and that the whole is in due relationship to the atmospheric and telluric forces by which it is surrounded, we shall cease to wonder at the unhealthiness and ultimate infertility of most hybrids, in whom this fine balance is lost, and who are in a sense the product of a generative chaos, that is, of conflicting forces, not constituted by Nature for harmonious conjunction.
In the October issue of this journal for that same year we find a writer declaring that Egypt was not an “African” civilization, on the basis of certain people being supposedly incapable of civilization—
And let it also be fearlessly announced by anthropologists, that a purely Negroid type, though they had possessed twenty Egypts for twice ten thousand years, would never have raised the magnificent piles of Luxor and Carnac.... The time has now assuredly come, when the accepted fallacies of a learned barbarism should succumb to the clear demonstrations of inductive science, and racial facts be championed to their appropriate place, as among the most important and reliable data upon which history, more especially that of the earlier ages, can be based.
Meanwhile, in the February issue we find a description of the “true Celt”, noting that—
it has been generally assumed that one well defined form of head is recognisable as characteristic of the true Celt. Dr. Morton, in defining the Celtic family, says: “They have the head rather elongated, and the forehead narrow and but slightly arched. The brow is low, straight and bushy; the eyes and hair are light, the nose and mouth large, and the cheek-bones high. The general contour of the face is angular and the expression harsh.” Dr. J. Aitken Meigs... remarks: “No. 1356—a cast of the skull of one of the ancient Celtic race of Ireland—appears to me the most typical in the Irish group. This head, the largest in the group, is very long, clumsy, and massive in its general appearance. The forehead is low, broad, and ponderous; the occiput heavy and very protuberant.”
Of course, today’s science has completely overthrown this nineteenth-century science and the idea of pre-Adamites, much as today’s science has completely overthrown the Aristotelian theory that said that the Earth lies at rest in the center of the universe because gravity is the tendency of certain materials toward the center of the universe. Indeed, the material quoted above is today viewed as utterly disgraceful. Today science tells us that all human beings appear to be descended from one common origin. Scientists now speak, for example, of DNA evidence pointing to the existence of a “mitochondrial Eve” for all humanity. The idea that there are different species of human beings—some of which are “true men”, and others of which are distinctly not—and that “hybrids” of these differing “species” are unhealthy and ultimately infertile—is now scientifically unsupportable, to put it mildly. Science tells us now that there is one human race; we are all one family. But that is not what science said in 1865.
Science of course changes. But wrongness about the nature of gravity is a much different thing from wrongness about person X and person Y being of two species, one superior, one inferior—one perhaps with a soul, the other perhaps not—the marital union of which will yield unhealthy and ultimately infertile offspring. And science was not just wrong here, but obstinately wrong. People have long recognized what it means to be human. The writers of Star Trek or Guardians of the Galaxy were hardly the first to be unable to envision any sort of true gradations of humanity:
I think the king is but a man, as I
am: the violet smells to him as it doth to me: the
element shows to him as it doth to me; all his
senses have but human conditions: his ceremonies
laid by, in his nakedness he appears but a man; and
though his affections are higher mounted than ours,
yet, when they stoop, they stoop with the like
wing. Therefore when he sees reason of fears, as we
do, his fears, out of doubt, be of the same relish
as ours are.
[Henry V, Act IV, scene i]
And let us not forget those theologians whose impertinent meddling science supposedly could afford to treat with silent contempt. Nor let us forget those people who might not have been “theologians”, but who adhered to the traditional reading of Genesis, rejected the idea of pre-Adamites, and thus maintained that all people were of one family: Sons of Adam and Daughters of Eve. They may have kept in mind Revelation 7—
After this I had a vision of a great multitude, which no one could count, from every nation, race, people, and tongue. They stood before the throne and before the Lamb, wearing white robes and holding palm branches in their hands…. Then one of the elders spoke up and said to me, “Who are these wearing white robes, and where did they come from?” I said to him, “My lord, you are the one who knows.” He said to me, “These are the ones who have survived the time of great distress; they have washed their robes and made them white in the blood of the Lamb. For this reason they stand before God’s throne and worship him day and night in his temple. The one who sits on the throne will shelter them. They will not hunger or thirst anymore, nor will the sun or any heat strike them. For the Lamb who is in the center of the throne will shepherd them and lead them to springs of life-giving water, and God will wipe away every tear from their eyes.”
In other words, some people knew, on faith, and perhaps on the same common sense that Shakespeare and Star Trek seem to share, what “the most advanced minds of science” failed to grasp via the “evidence of fact” and “demonstrations of inductive science”: that people who looked different were still “men and brothers”. These people knew that man is indeed a sacred subject, and that to forget that is to head toward very dark places. It does not require the most advanced mind to know this. No doubt that is why even Groot and the Jem’Hadar seem to be simply human souls in heavy make-up.
This is a “nerdy” story about some of the real minutia of writing and publishing in the academic world. I am only going to subject subscribers to Sacred Space Astronomy to it.
Writers need editors. A weakness of blogs like this one is that we writers can just dump on you readers whatever we want. We do not have an editor who makes sure that what we write makes sense, reads well, etc. We can ask each other for help, or we can ask others to edit our writing (I often ask my wife to read over my posts), but we can also just drop something on the blog.
Editors help. Some famous editors have passed away in recent months, and their passing is noticed by the literary world (click here or here for examples). Of course, sometimes editors make changes that writers do not want. But, since editors usually have the final say, the writers usually have to go along with it.
“How can I?” replied she; “there’s no fitting your figure. At one time you’re a New Moon, and at another you’re a Full Moon; and between whiles you’re neither one nor the other.”
Illustration from the Jones-Chesterton volume of Aesop's fables.
The Frogs’ Complaint Against the Sun
Once upon a time the Sun was about to take to himself a wife. The Frogs in terror all raised their voices to the skies, and Jupiter, disturbed by the noise, asked them what they were croaking about. They replied, “The Sun is bad enough even while he is single, drying up our marshes with his heat as he does. But what will become of us if he marries and begets other Suns?”
There was once an Astronomer whose habit it was to go out at night and observe the stars. One night, as he was walking about outside the town gates, gazing up absorbed into the sky and not looking where he was going, he fell into a dry well. As he lay there groaning, some one passing by heard him, and, coming to the edge of the well, looked down and, on learning what had happened, said, “If you really mean to say that you were looking so hard at the sky that you didn’t even see where your feet were carrying you along the ground, it appears to me that you deserve all you've got.”
Astronomers certainly get no sympathy from Aesop! (Of course, almost no one gets any sympathy from anyone in those fables.)
I picked up a used copy of Aesop and read it in bits and pieces. When I came across the astronomy fables, I thought that they would be something of interest to readers of Sacred Space Astronomy—and that they would be something for this blog that was fun and completely different!
Why might a person see great intrinsic value in mathematical knowledge? Why might a person be a “math nerd”? Consider this lengthy quotation, from a piece written by Fr. Ron Rolheiser that was published in The Record (the newspaper of the Archdiocese of Louisville, Kentucky) some time ago,* in which Fr. Rolheiser reflects upon the words of a woman who had gone through a profound spiritual experience:
What she remembers most and most wants to share with others is this: “I learned that God is very close. We have no idea how close God is to us. God is closer to us than we ever imagine!” Her experience has left her forever branded with a sense of God’s warmth, love, and welcome, but what’s left the deepest brand of all inside her is the sense of God’s closeness. I was struck by this because, like millions of others, I generally don’t feel that closeness, or at least don’t feel it very affectively or imaginatively. God can seem pretty far away, abstract and impersonal, a Deity with millions of things to worry about without having to worry about the minutiae of my small life. Moreover, as Christians, we believe that God is infinite and ineffable. This means that while we can know God, we can never imagine God. Given that truth, it makes it even harder for us to imagine that the infinite Creator and Sustainer of all things is intimately and personally present inside us, worrying with, sharing our heartaches, and knowing our most guarded feelings. Compounding this is the fact that whenever we do try to imagine God’s person our imaginations come up against the unimaginable. For example, try to imagine this: There are billions of persons on this earth and billions more have lived on this earth before us. At this very minute, thousands of people are being born, thousands are dying, thousands are sinning, thousands are doing virtuous acts, thousands are making love, thousands are experiencing violence, thousands are feeling their hearts swelling with joy, all of this part of trillions upon trillions of phenomena. How can one heart, one mind, one person be consciously on top of all of this and so fully aware and empathetic that no hair falls from our heads or sparrow from the sky without this person taking notice? It’s impossible to imagine, pure and simple, and that’s part of the very definition of God. How can God be as close to us as we are to ourselves?
The woman had approached Rolheiser spontaneously, wanting to communicate God’s closeness. Rolheiser, in contrast, finds it hard “to imagine that the infinite Creator and Sustainer of all things is intimately and personally present”.
Infinity is a mathematical concept of sorts. It cannot be directly expressed, but it can be studied by a certain process of imagining a progression of simple calculations. For example, consider simple division, say 100 divided by 2: 100/2 = 50. Now let us divide 100 by a larger number, such as 5: 100/5 = 20. Dividing by a larger number (5 rather than 2) yields a smaller result (20 rather than 50). Now let us extend this to dividing 100 by progressively larger and larger numbers: 100/10 = 10; 100/50 = 2; 100/100 = 1; 100/500 = 0.5; 100/1000 = 0.1; 100/10,000 = 0.01. Dividing by progressively larger and larger numbers yields progressively smaller and smaller results. So while we cannot actually divide 100 by infinity, we can imagine that as we increase the dividing number more and more, the result will be smaller and smaller still; thus we can say that as the dividing number heads up toward infinity, the number resulting from the division heads down toward zero. And thus in some sense, 100 divided by infinity is zero.
Now let us go the other direction, and divide 100 into some other number. Let’s divide 100 into 20: 20/100 = 0.2. Now let’s divide 100 into something larger, like 400: 400/100 = 4. Let’s keep dividing 100 into larger and larger numbers: 1000/100 = 10; 40,000/100 = 400; 10,000,000/100 = 100,000. Dividing 100 into progressively larger and larger numbers yields progressively larger and larger results. Thus while we cannot actually divide 100 into infinity, we can imagine that as we divide 100 into increasingly larger numbers, the result will be larger and larger, so that we can say that as the number being divided heads up toward infinity, the number resulting from the division also heads up toward infinity. And thus in some sense, infinity divided by 100 is infinity. And this does not change if, instead of dividing our various numbers by 100, we instead divide by 200, or by 10,000, or by a billion, or by an umpteen gazillion. Our “math nerd” fact for the day: Infinity divided by any number is infinity.
(This is not something new in mathematics. Johann Georg Locher and his mentor, Fr. Christoph Scheiner, S.J.—both math nerds to some extent—wrote about infinity at some length in their 1614 book Mathematical Disquisitions. It was not new stuff then, either.)
So, if there is an infinite Creator and Sustainer of all things, it makes no difference whether there are billions of persons on this earth, with thousands of people being born, dying, sinning, etc. every minute. It makes no difference that there are trillions upon trillions of phenomena (indeed, far more than that). We human beings each have a finite amount of time and attention to divide among the things we have to do or keep track of, so that the more things we have the less we can focus on each. However, an infinite Creator and Sustainer of all things has an infinity to divide, and our brief study of mathematics has shown us that infinity divided by any number, is infinity. Therefore that infinite Creator and Sustainer of all things can focus an infinity of attention on a hair that falls from your head, or a sparrow that falls from the sky. Our knowledge of mathematics helps us to understand that the infinite Creator and Sustainer of all things really will be intimately and personally present. If there is an infinite Creator and Sustainer of all things, that infinite Creator and Sustainer of all things knows each of us, has more time for us, and is closer to us, than we know and have time for and are close to ourselves—infinitely more. For the person who believes that an infinite Creator and Sustainer of all things exists, a “nerdy” knowledge of mathematics can help him or her to understand how that infinite Creator and Sustainer of all things can know and care about a hair or sparrow.
It is socially acceptable, even among educated people, to be ignorant of mathematics, and even to dismiss it as being beyond explanation and beyond interest—as being the province of the nerds who can wrap their minds around such things. However, knowledge of math is valuable and worthwhile in so many ways, including, as we see here, in ways related to faith. This is important even to those who might not believe that an infinite Creator and Sustainer of all things exists—at least if they care about math and science and related “STEM” areas of knowledge, and about knowledge and education in general. In the U.S., at least, students go into debt for education, and there is increasing pressure within the world of education to engage students and to do everything possible to ensure that students are successful and that they do not accumulate debt yet no degrees. So what in fact will engage people? Some will be engaged by math because they love math; others because they believe knowledge of math will help in getting a good job. But to engage a diverse audience of people means to consider what a diverse audience finds engaging and wants to really know. So often, the subject of knowledge that really engages a broad swath of people—that makes people want to spontaneously come forward to share what they know with others—is faith. As I have discussed in the past, the future is full of people of faith; full of people who have a strong reason to see a great intrinsic value in mathematical knowledge, to be attracted to nerdy mathematical thought because through it they can understand how God can be close.
*November 30, 2017 edition of the Record, page 5—click here. Also available on Fr. Rolheiser’s website—click here for the website.
There were two bald eagles soaring over the Ohio River in Louisville, Kentucky one Saturday this past October. My wife and I saw them while we were taking a walk on a brisk, fall day. They were wheeling far overhead in a perfect azure sky. It was October 12. The eagles were not soaring over some remote part of the Ohio River—they were on the river where it passes right between the downtowns of Louisville on one side, and Jeffersonville, Indiana on the other. Below the eagles were bridges, boats, cars, buildings, parks, and lots of people out enjoying the day.
The first time I ever saw a bald eagle in the wild was also on the Ohio River. This was in the early 2000s, when my family was exploring a remote area west of Leavenworth, Indiana. Then, a few years later, when my college’s observatory was located in Otter Creek Park, on the river well south-east of Louisville, everyone at the park was thrilled to discover a nesting pair of bald eagles on the river there. The eagles were a big deal. The location of the nest was not widely discussed, for fear that it would draw enough sightseers that the eagles would be disturbed and leave. A few years after that, there were bald eagles hanging around the Farnsley-Moremen Landing, a historic home and park on the river in the south-eastern outskirts of Louisville. My family had come to visit the park, and we noticed a crowd of people with telescopes, binoculars, and cameras. The eagles seemed not to care.
Seeing bald eagles near Louisville: from left to right, Leavenworth, Indiana; Otter Creek Park; Farnsley-Moremen Landing; downtown.
When I was a kid, if Kentuckians wanted to see bald eagles, they went to some place else—like Alaska. I remember hearing one of my relatives talk about seeing bald eagles in Alaska. If you wanted to see an eagle soaring overhead in Kentucky, your best bet was the constellation Aquila. Even hawks were not common in developed areas.
The constellation Aquila the eagle, per the Stellarium planetarium app.
Today you can be right smack in the center of Kentucky’s largest urban area and look up to see a pair of bald eagles while taking a stroll in a park. And the parks of the city are full of hawks and owls. Peregrine falcons rest on bridges over the Ohio River.
When I was young, I read that the presence or absence of “apex predators” like the bald eagle—king of the sky, the biggest, baddest thing on wings—was an indication of the health of an ecosystem. The fact that there were no eagles was a sign of bad ecological health; toxins in the environment worked their way up the food chain, and apex predators, who ate things that ate the toxins, could not survive. I have seen the eagles return over my lifetime. And I have seen the return of hawks and falcons and owls (the park near my house is full of hooting at night). And of impressively antlered bucks, standing alongside roads and bike trails and paths (or along the river in central Louisville) and watching people and cars go by. And of flocks of wild turkey. And of elk and bear in Kentucky’s more mountainous regions. None of these were to be found when I was a kid.
So I understand those in my state who might take a skeptical view toward claims that the Earth is in environmental peril. They might hear a statement like this, which came from NPR’s Rachel Martin on “Morning Edition” one day in October—
The threat from climate change is so massive, so apocalyptic, it can be hard to wrap your head around. [October 16, 2019]
—and they might say, “Really? Tell that to the eagles.” Is it unreasonable for skeptics to react with disbelief to statements like this when it seems like the environment is rapidly regaining ground, right before their eyes? Or consider this statement:
The earth, our home, is beginning to look more and more like an immense pile of filth.
That is from Pope Francis (Laudato Si, paragraph 21; also June 18, 2015 @Pontifex). Again, might not a skeptic from Kentucky legitimately scoff?—especially one who recalls that, not so long ago, what you saw when you looked up to the sky from downtown Louisville was likely to be a filthy, polluted, yellow sky, and not eagles soaring in an azure sky? ‘More and more like a pile of filth?’ Tell that to the eagles. Perhaps, our skeptic might say, the Vatican is making the same sort of mistake that it made when it opposed the Copernican theory: offering opinions on matters of science in which further information might yet come forth.
Moreover, our skeptic might say, Kentucky is not a wealthy state. Kentucky needs economic growth to improve the lives of Kentuckians—to provide jobs, education, and opportunities, and to have less people hopeless and addicted to opiates. Our skeptic might even think we have already given up too much for those soaring eagles.
But there is another story about October and soaring in Louisville, Kentucky. A week prior to that brisk fall day with the eagles soaring in the perfect sky, something else was soaring: the temperature. The first days of October saw temperatures in the upper 90s (°F) / mid-upper 30s (°C). Temperature records were shattered. Existing high temperature records were topped by 5°F / 3°C. This followed a September that itself shattered high-temperature records, and that was nearly devoid of rain. High 90s is hot in Louisville, even in July. But high 90s in late September and early October? When the days are shorter than the nights? With no rain, the grass brown, and plants wilting? Perhaps the word “apocalyptic” does come to mind. Happily, the rain came, and the temperatures fell, so that by October 12 we had a perfect, brisk fall day to see those eagles.
The theory behind human-caused climate change is not complex: the idea is that human activity is altering the composition of Earth’s atmosphere, and altering it in such a way as to cause it to retain heat more efficiently. The theory is not new. In 1866 Fr. Angelo Secchi, a pioneer in astrophysics who is considered a key figure in the development of the Vatican Observatory, wrote that,
Definitely we are facing a climate change, due to human activity such as deforestation and the introduction of artificial sources of heat [i.e. burning fuels].
Measurements indicate that indeed the composition of the atmosphere is changing in a manner consistent with what would be expected from deforestation and the burning of fuels, both of which release carbon into the air. And various measurements indicate that the Earth is warming, as would be expected from the measured changes in the atmosphere.
The theory makes sense, but I have discussed in previous posts how a resident of Kentucky (click here) or Wisconsin (click here) might have grounds for skepticism about any claimed warming. What is more, science can be a tricky business. When the Vatican rejected the Copernican theory, it could certainly cite powerful scientific arguments, and prominent scientific authority (i.e. Tycho Brahe) against any motion of the Earth. No doubt the Vatican folks from that time who were involved would be rather surprised to see how things turned out. The science of Earth’s motion changed. As Br. Guy often points out in talks, what is in science books changes: a biology textbook from a century ago will not serve you so well today.
And yet, our Kentucky skeptic has seen high 90s in October. Recall the post from last week on Pascal’s Wager. Blaise Pascal, a man of solid faith, is considered a sort of founding figure of decision theory—the science of how to weigh risks and rewards in order to make rational choices. In Pascal’s case, the choice was whether or not to believe that God exists. Our Kentucky skeptic might consider a sort of Pascal’s Wager on whether or not to believe that climate change exists. Pascal argued that to decide to believe that God exists is a low-risk, high-reward proposition. To our skeptic, to choose to believe that climate change exists is probably not such an easy choice.
Suppose our Kentucky skeptic believes authority, believes the climate scientists, and accepts the existence of climate change. Thus, despite those eagles soaring in Kentucky’s own perfect October skies, our Kentucky skeptic accepts the idea of impending environmental apocalypse. Suppose furthermore that our skeptic endorses actions to mitigate climate change, actions that in fact do hurt Kentuckians economically. And suppose the authorities turn out to be wrong. Will the judgment of our skeptic’s children and grandchildren not be that our erstwhile skeptic was a fool for caving in to ‘the hype’ when our skeptic could see eagles soaring overhead in a perfect fall sky?
Now suppose our skeptic staunchly continues to reject the existence of climate change, despite authority, despite the scientists—and despite high 90s in October on our skeptic’s own home turf. Suppose our skeptic cites the economy and the soaring eagles, and dismisses the soaring temperatures as a fluke—another bit of crazy Kentucky weather (they say that if you don’t like the weather in Kentucky, wait five minutes, and it will be something different). But then, suppose that the next freak heat wave and drought hits, not in the fall, but in the heat of the summer. Suppose the mid-summer high temperature records are shattered as thoroughly as the October records were shattered, and the drought is as long, or longer, than it was this fall. If the temperature in the heat of the summer is continually breaking 110°F, and crops are failing, and animals dying, and water is severely rationed, and industry and the economy are severely curtailed, and the lush Kentucky landscape is brown and devastated, will the judgment of our skeptic’s children and grandchildren not be that our skeptic was a fool?—a fool who not only ignored authority, but who also ignored the personal experience of October 2019’s soaring temperatures?
I am not saying that these scenarios are realistic. I am not saying that the economy and the environment are in fact necessarily opposed. I am saying that, when I see those soaring eagles, I can see where a climate skeptic might be coming from. But when I see those soaring temperatures, I think that skeptical outlook involves a lot of risk. Blaise Pascal, where are you?
This pair of eagles is just upriver from downtown Louisville:
Check out Blaise Pascal’s Wager on the Vatican Observatory Faith and Science site (click here for it).
If you like math and science it is likely that you have encountered Blaise Pascal (1623-1662). Perhaps you learned about Pascal’s Principle of hydraulics in a physical science class, or in an engineering technology class where you learned about machines that use hydraulics. Or maybe you read about his work with measuring atmospheric pressure, and how he found that as he ascended a mountain the pressure he measured grew less and less. You might have encountered Pascal’s Triangle in a math class.
Pascal and Pascal's Triangle
Pascal’s Wager involves matters of faith—sort of. The Wager is an argument that it is reasonable to seek to believe in God. “Seek”, because the Wager is directed to the person who neither believes nor is inclined to believe. The Wager argues that a person risks little, and gains much, by choosing to seek belief in God. It is all about balancing risk and reward, and apparently Pascal is viewed by some as a sort of founding figure of decision theory—the science of balancing risks and rewards to arrive at good decisions. Surely gamblers beat Pascal to this idea by centuries, if not millennia—and Pascal says as much in the Wager. But apparently Pascal was the first to write about it.
The Wager is not about belief itself. Pascal uses the idea of a wager only to lead an intelligent non-believer, who has no inclination toward belief, to the point of seeing that belief is rational. But Pascal writes that tightly-reasoned proofs are not what leads people to God, and he does not urge the non-believer to pursue them. We know God only by Jesus Christ, Pascal says, and those who have claimed to know God, and to prove God without Jesus Christ, have offered little.
Click here to check out the full text of Pascal’s Wager, from the VO Faith and Science pages. I wager you will find it interesting!
This post is part of a series of posts on Pi, infinity, and other things mathematical. Click here for the series.
Tomorrow (January 5) is Perihelion Day! The Earth journeys around the sun in an orbit that is ever-so-slightly elliptical (the elliptical nature of the orbit is so mild that the orbit basically looks like a circle that is slightly off-center from the sun). This means that the distance between the sun and the Earth varies over the course of a year. Today is the day on which that distance is a minimum, and the technical term for the point of minimum distance between the Earth and sun is “perihelion.”
Today is also the day of the brightest sun of the year. Since the distance to the sun is a minimum then the apparent size of the sun in the sky is a maximum (of course, as with the much-ballyhooed “Super Moons” that we hear about all the time, this effect is not very great).
The apparent size of the sun as seen from Earth at perihelion (left) and six months later, at “aphelion” (right). Images created with Stellarium.
A thing I like to point out about perihelion is that it is a true Global Event. Regardless of creed, calendar, or hemisphere, everyone everywhere on Earth experiences perihelion tomorrow. So wish everyone you meet, and even all your social media friends from around the world, a “Pleasant Perihelion”! It is the globally inclusive greeting!
When the Earth is at perihelion, it moves the fastest in its orbit. Thus you could even wish everyone a “Pleasant Perihelion and a Happy Maximum Orbital Velocity Day”. Earth is moving fastest because an orbit is essentially a fall; the Earth is falling toward the sun on account of gravity. And this faster motion at perihelion turns out to have an effect on daylight.
The Earth orbits the sun because it is essentially falling toward the sun by reason of the sun’s gravity. Here the elliptical nature of Earth’s orbit is shown greatly exaggerated. As the Earth travels from P, the perihelion point, toward A, the point of greatest distance from the sun (the “aphelion” point), it moves against the pull of the sun’s gravity, and so it loses speed—just like a ball that is thrown upward loses speed as it moves against the pull of Earth’s gravity. Then as the Earth moves from A toward P, it moves with the pull of the sun, and gains speed—just like the ball gains speed as it falls back to earth. Image from University of Nebraska-Lincoln.
We have daylight and darkness, day and night, because Earth rotates on its own axis. We think of that rotation as being one “day”—24 hours—but in fact the time of rotation is 23 hours and 56 minutes. That is, if you observe a star that is directly overhead one night, you will find the same star to be overhead again 23 hours and 56 minutes later.
The time for a person at A to be carried around the Earth by its rotation one time with respect to a star is 23 hours, 56 minutes.
So what about the 24 hour day, you ask? Imagine that the Earth journeyed around the sun in a perfectly circular orbit, always moving at the same speed along that orbit. Now imagine two people on opposite sides of the earth. Person A observes a certain star being directly overhead. At the same time, person B observes the sun being directly overhead (person B would be experiencing the “mid-day” point, halfway between sunrise and sunset).
In this diagram the Earth's rotational motion on its own axis is indicated by the red arrow, while its orbital revolution about the sun is indicated by the green arrow.
Now we wait 23 hours and 56 minutes until the star is overhead again for A. But during that time the Earth moves along its orbit, from position 1 to position 2 as shown below. The star is so far away that this motion does not matter. But the motion does matter in the case of the sun. Therefore, as seen below, when the Earth is at position 2 and the star is overhead again for person A, the sun is not yet overhead for person B. The earth has to turn a little more—four minutes more, so that B is at B'—in order for the sun to be overhead for B. Thus a “day” measured by the sun is 24 hours while a “day” measured by the stars is 23 hours and 56 minutes.
Now remember that the Earth’s orbit is not a perfect circle; the Earth does not always move at the same speed along its orbit. When the Earth is moving faster (like when near perihelion) it will move farther along its orbit during a given period of time. The distance between 1 and 2 in the above diagram will be greater. Therefore, the Earth will have to turn still more to reach point B' so that the sun is overhead for B. And therefore mid-day will arrive a little late.
This is why in the northern hemisphere the darkest evening of the year of was in early December, even though the shortest day was at the solstice on December 21 (and in the southern hemisphere the brightest morning was in early December even though the longest day was at the solstice). As the Earth approached perihelion and moved faster in its orbit, mid-day began to arrive late at a rate that exceeded the rate at which the days were changing in length. Because of the perihelion’s effect on mid-day, the period of daylight was drifting backwards against the clock, making the evenings brighter (and the mornings darker) than they would be if Earth were in a perfectly circular orbit. The perihelion daylight drift occurs in both hemispheres.
So it is perihelion that is behind the strange business of daylight and the solstice that we encountered in the December 7 and December 21 posts! Of course we have one more point to cover in all this—the date of the northern hemisphere’s darkest morning and the southern hemisphere’s brightest evening. That is also about now. The table below shows sunrise times at Castel Gandolfo (home of the Vatican Observatory).
The sun rises today at 7:36 AM there, and this is basically the latest sunrise (give or take some seconds). Note how there exists a period, from roughly December 29 through January 10, in which the sun rise time is largely unchanging at 7:36, even though the day length is getting longer with each passing day. Between December 21 (when the solstice occurred) and now the perihelion drift had been winning out over the changing length of daylight itself, but that is now coming to an end. From now forward through early June, northern hemisphere dwellers will see the days growing longer, and both the mornings and evenings growing brighter; southern hemisphere dwellers will see just the reverse on all accounts—shortening days, darkening mornings, darkening evenings. (All the data here is from Date and Time.)
One final note: I learned about the solstice and the daylight not through a study of astronomy; rather I learned about it firsthand when my son started taking a bus to school. The bus came at a set time in the morning. At the start of the school year (in late August), my son caught that morning bus in broad daylight. As the semester progressed the mornings grew darker. By December it was dark and gloomy when my son caught that bus. I knew the days would grow longer after the December solstice, so I assumed that when Christmas break ended in January we would see brighter mornings. I was wrong! And disappointed. When school resumed after New Year’s, the mornings were darker than ever. Not until February did the mornings start to brighten appreciably, yet it was obvious well before then that the evenings had brightened a lot. Trying to understand why in January my son was standing in the dark when waiting for his morning bus is what led me to investigate and understand the solstice and the daylight.
The universe indeed holds surprises for those who are attentive to it. Many of these surprises require no advanced degrees or Advanced Technology Telescopes or other specialized knowledge or equipment. Sometimes, all they require is a regular bus ride.
There is something whose existence is known to many, but that is infinite, and thus ultimately unknowable. In the words of one person who has studied this thing extensively, exploring it is similar to exploring the universe. We can learn more and more about it, and yet, because it is infinite, what we learn amounts to nothing in comparison to what there is to learn.
The thing I am talking about here is pi (π): the ratio of the circumference of a circle to its diameter, as in C = πD. The mathematician David Chudnovsky, who developed algorithms for calculating pi to billions of digits, made the comparison between it and the universe.
Mathematics is a form of knowledge that is terribly undervalued today. Try saying something really favorable about mathematics to a group of people. See what reaction you get. Even highly-educated people feel free to talk about how they do not like math or are not good at math. They might be able to expound on Shakespeare or abstract art, but basic algebra is beyond them. Jimmy Buffett even wrote a song called “Math Suks!”, as you can see below (note that the lyrics are not entirely inoffensive, and, worse yet, may prompt nearby listeners, even highly educated ones over the age of 14, to start chanting “Math Suks!”). Buffett’s song even got coverage in the journal Science.
But math helps us to see things we might not otherwise see, and mathematics is true and universal. A line and a circle will intersect in at most two points, and that is true, period. It is true whether you are a man or a woman, whether you are a Russian or a Brazilian, whether you are an artist or an engineer. Indeed, it has generally been assumed that, were we ever to make contact with an intelligent extraterrestrial species (that is, space aliens), mathematics would form the basis for a means of universal communication, because mathematics would be true, even for space aliens. Even space aliens who were unlike us in every conceivable way would understand what pi is. There is even a book about math called How Not to be Wrong (because you will not be wrong if you reason mathematically, because mathematics is true).
Blaise Pascal would not have agreed with Jimmy Buffett.
Blaise Pascal, the French mathematician and scientist who lived from 1623 to 1662 (and whose hydraulic principle is studied by students in physical science classes everywhere), argued that understanding a bit about math helps us to see something about God. Pascal was a man of faith. He wrote,
The number 1, joined to infinity, adds nothing to it, no more than one foot to an infinite measure. The finite is annihilated in the presence of the infinite, and becomes a pure nothing. So our spirit before God, so our justice before divine justice. There is not so great a disproportion between our justice and that of God, as between 1 and infinity....
We know that there is an infinite, and are ignorant of its nature. As we know it to be false that numbers are finite, it is therefore true that there is an infinity in number. But we do not know what it is. It is false that it is even, it is false that it is odd; for the addition of 1 can make no change in its nature. Yet it is a number, and every number is odd or even (this is certainly true of every finite number). So we may well know that there is a God without knowing what He is.
Thus Pascal found that a few simple ideas from mathematics—the ideas of a finite number and of the infinity of all numbers, the ideas of odd and of even—were sufficient to point toward God. So, if you are like Buffett and think you don’t like math, well, this isSacred Space Astronomy: take an interest in math from the standpoint of religion, then. This post is the first of a number of posts, both new and re-runs, that will feature mathematics, pi, infinity, and Blaise Pascal.
This post is part of a series of posts on Pi, infinity, and other things mathematical. Click here for the series.
Today is the day of the December solstice in Louisville, Kentucky, where I live! This is the day on which the sun reaches its southernmost point in its yearly journey through the stars (as seen from Earth), and the precise moment at which the sun reaches that point is 11:19 PM for people in Louisville. But this moment occurs at 5:19 AM at Castel Gandolfo, the Vatican Observatory's headquarters. So in Italy, the solstice is on the 22nd in the early morning, while in Louisville the solstice is on the 21st at 11:19 PM.
Since the sun is now at its southernmost point, then, in the northern hemisphere, where the Vatican Observatory's telescopes are all located, the maximum daily altitude that the sun reaches (when it is at the point halfway between rising and setting) is the lowest of the whole year. The length of the sun’s day-long arc above the horizon is therefore shortest. Consequently, the length of time that the sun is above the horizon is shortest, and the duration of daylight is shortest. A sun that is low in the sky and not up for very long will not warm things much. Thus in the northern hemisphere the December solstice is the “winter” solstice.
The sun rises in the east and sets in the west. The time between one rising and the next is 24 hours, and the sun’s motion across the sky is always at the same rate. Thus when the sun is lower in the sky (blue dashed line) its path is shorter, and it is above the horizon for less time, than when it is higher in the sky (gray dashed line).
Of course the situation in the southern hemisphere is just the opposite: the sun’s maximum daily altitude, the length of the sun’s arc above the horizon, and the duration of daylight are all greatest. A sun that is high in the sky and up for a long time warms things quite well. Thus in the southern hemisphere this is the “summer” solstice.
Check out the table below, which is for Castel Gandolfo. Note the sunrise time, sunset time, and day length. You will see that the day length is indeed the shortest now, at 9 hr, 8 min, 38 sec, but the time of sunset is actually getting progressively later (as was discussed in the post from two weeks ago: click here for it).
From early December through now, the days have been getting shorter, but the sun has been setting later, meaning that the evenings have been getting brighter. Of course, the only way that could happen is if the mornings are losing daylight faster than the evenings are gaining daylight. Now the days will start getting longer, but the mornings are still going to get darker for a while. It is just that now the mornings will lose daylight slower than the evenings will gain daylight. We will find out why all this happens soon enough, but for now, just keep an eye on the sky, and watch how things change in the morning and the evening.
All data in these posts are based on sunrise and sunset times provided by Date and Time.
I am pleased to introduce another “Kentucky Science Conversations” guest blogger: Gerry Williger, an astronomer at the University of Louisville here in Kentucky. Gerry is the one whose efforts started the Kentucky Science Conversations with Louisville’s Archbishop Joseph Kurtz, that also involved Tim Dowling, Kate Bulinski, and me. Dowling, Bulinksi, and Archbishop Kurtz have all written guest blogs for The Catholic Astronomer-Sacred Space Astronomy, so Gerry’ s post here rounds out the group.
Gerry Williger got his Bachelor’s degree at Ohio State, then did a PhD at the University of Cambridge, England funded by a Marshall Scholarship. His thesis was on numerical simulations of intergalactic gas clouds, under Bob Carswell. He then worked as a post-doc at Cerro Tololo Inter-American Observatory in Chile, where he switched from doing theoretical work to observations, and followed that up with a post-doc at Max-Planck-Institut für Astronomie in Heidelberg. After eleven years abroad, he returned to the US to work on the Hubble Space Telescope Imaging Spectrograph team at NASA Goddard Space Flight Center and with the Far Ultraviolet Spectroscopic Explorer satellite team at Johns Hopkins University, both in Maryland. He took up a faculty job at the University of Louisville in 2005, where he teaches and continues to do research on observations of intergalactic gas and also protoplanetary disks (baby solar systems). During sabbaticals/leave, he worked for two years at the Université de Nice, France and most recently at Konkoly Observatory in Hungary on a Fulbright Fellowship.
Gerry Williger, 4 Nov 2019
Public outreach in science is important. We professional scientists usually rely on others for financial support to support our work to “push back the frontiers of knowledge”. Up to World War II, this was generally done with private funds. In the sixteenth century, Tycho Brahe had King Frederick II and Emperor Rudolph II as patrons. In the nineteenth century, William Parsons, the third Earl of Rosse, self-funded his astronomical work and the construction of the largest telescope in the world at the time, the 1.8 m diameter "Leviathan of Parsonstown" in Ireland. Learned societies like the National Geographic Society (founded in 1888) also funded research using private funds. After World War II, many governments realized that it was in the public interest to fund scientific research, and consequently most of the scientific research done today is funded by taxes from the public via organizations including NASA, ESA, the National Science Foundation and the European Southern Observatory.
Public enthusiasm really can have influence on the support (or non-support) of publicly funded scientific research. One example is from 1970, when NASA cancelled three moon landings: Apollo 18, 19 and 20. The budget was probably a primary consideration. However, an additional factor may have played a role: declining public support. NASA planetary curation scientist David R. Williams was quoted as saying, “The whole world was glued to Apollo 11. But by the time they got to 16 and 17 the general public just wasn't that interested anymore.” On the plus side, in 2004 the final shuttle mission to service the Hubble Space Telescope was cancelled by the then-NASA Administrator Sean O'Keefe. Several members of Congress, including Sen. Barbara Mikulski, fought with much public support (including thousands of letters from American schoolchildren) to get the servicing mission restored. In 2005, Mike Griffin became the NASA Administrator, and approved a new servicing mission, which significantly extended the operational life of the telescope. From these examples, public support of science does indeed make a difference. However, it takes strong and continuous efforts, usually done by scientists and teachers, to educate the public to keep the enthusiasm level for science high in the face of other topics competing for attention and the media news cycle. This can be done by reaching large numbers of people through the media, as pioneered by Jacques Cousteau, Carl Sagan and Stephen Hawking, and continued today by Sir David Attenborough, Brian Green and Neil Tyson. However, most public outreach is done by everyday scientists in small groups, whether in classrooms, planetariums, eclipse picnics—or even pubs.
I first became aware of the need for public outreach while in graduate school at the Institute of Astronomy in Cambridge, England, and felt it more and more as my career progressed. With the encouragement of my fellow graduate students, I started out public outreach by speaking in a school in Cambridge. At the request of my director, Bob Williams (a great believer in public outreach), I branched out to doing media interviews in La Serena, Chile. It motivated me to work on my Spanish! I made a small contribution to the annual open house at Max-Planck-Institut für Astronomie in Heidelberg, which is a good tradition in many institutes and universities, and spoke to more school groups while working at NASA and Johns Hopkins University in Maryland. I learned that many people, both students and adults, are interested in space exploration and our universe, and their enthusiasm gave me the energy to volunteer my time.
When I arrived as a faculty member at the University of Louisville and worked for two years as a faculty member at Université de Nice, France, my public outreach experience gave me a good springboard to teach astronomy as a basic science requirement. I continued with some public outreach, especially for events like the 2006/2012 Venus transits and the 2017 solar eclipse, and organized an annual public endowed astronomy lecture for a number of years. There are only a half dozen professional astronomers in Louisville (including Chris Graney and Tim Dowling), and I very much appreciate the work that local amateur societies do to help us professionals teach the public about scientific discoveries and engender their enthusiasm for learning.
However, I noticed that many outreach efforts were focused on schools, and wished that there would be something more for adults to continue their learning. At the same time as I was growing in my astronomy career, I was also growing in my faith. In particular, young adult groups in Heidelberg, Maryland, Louisville and Nice exposed me to non-traditional, community-centered learning experiences including Theology on Tap. I loved the idea of “taking theology to the people”, and thought of how it must have been two thousand years ago when Jesus and the early disciples would speak in public about theology. In Nice, I also saw “Science Café”, which looked like a powerful way to reach adults with continuing science education, and to encourage contacts with scientists on a human level. In Louisville, medical school researchers organize life sciences talks in a pub downtown with 80-100 people in attendance.
After seeing successful public science talks in cafés/pubs, hearing how public outreach helped build up the astronomy program at Ohio University, and noting the level of enthusiasm in Louisville with our annual endowed astronomy lecture, I suggested to my colleagues, Lutz Haberzettl and Jim Lauroesch, that we organize monthly public astronomy lectures starting in 2015. We held them on weekday evenings in our science building in a 200 seat lecture hall, advertised via community channels and to high school science teachers, and had variable success. We averaged perhaps twenty people, many of whom were students looking for extra credit in their astronomy classes. Sometimes our own campus parking service would ticket members of the local astronomy club for coming a few minutes before the parking restrictions were lifted. We were frustrated by the low attendance.
With the support of the local astronomical society and inspired by Theology on Tap, I looked for a pub to host our lectures. Luckily, I found one by tasting a beer called “Path of Totality Black Ale”. The owner loved astronomy and was looking forward to the 2017 eclipse! We moved there in September 2017 and had good success: our attendance increased to 30-40 per month, and we had many more townspeople in the audience.
Left: A talk at Monnik Beer Co. in Louisville, Kentucky, on the universe as portrayed in the Star Wars movies. Monnik is a pub/restaurant, so younger attendees are welcome. Right: Lutz Haberzettl and Gerry Williger at Monnik.
Monnik advertising a talk on “Alcohol and Other Important Molecules in the Universe”. The abstract for the talk included “Drink in the information about it and other organic molecules, which are important to the formation of stars, planets and indeed to potential life itself.”
Talks in pubs are wonderful. People are relaxed, our numbers are high enough for good atmosphere but not so high that discussion is limited, and we reach members of the public we otherwise would not find. People are happy to come because when they are not listening to a talk, they can eat, drink and enjoy themselves on their own. It’s a way of “inviting people to the table”, with no strings attached.
In the meantime, I heard about a movement called “Astronomy on Tap” (AoT), which started in New York around 2014. It is an umbrella organization which advertises public astronomy talks in non-academic venues, and gives tremendous freedom to local “branches” to tailor the format to local conditions. I checked them out, and after discovering their flexibility, began to consult with their organizers and advertise our talks on their website astronomyontap.org. Currently, AoT is held in a few dozen cities across North America and Europe, and has had trial runs in South America and Asia. In some cities, hundreds of people attend. Although it is difficult to know the exact numbers, it is clear that thousands of members of the public are engaging in lifelong learning by having science brought to them.
Two experiences arose because of our public talks in Louisville. First, I invited our local bishop to our endowed lecture series a couple of years ago, citing both the relationship between astronomy and theology and the contributions to science by the Vatican Observatory and from other religious. I even offered to discuss science and religion with him. I did not expect an answer, but got quite a surprise when Archbishop Joseph Kurtz wrote to me and said that although he could not make the public talk, he would love to have a discussion with me. At that point, I wondered whether I was up to the task alone, and called upon two other Catholic astronomers in town, Chris Graney and Tim Dowling, to round out our conversation. Our first meeting went swimmingly, and Archbishop Kurtz invited us back for quasi-monthly discussions about various topics of science and science education in Catholic schools, including an analysis of “Fides et Ratio” by Pope John Paul II. I had never read an encyclical before, but gained much appreciation for his scholarship after going through the work. There are indeed many points of common interest between science and religion, and it is well worth it for scientists, religious and the lay community in either sense to explore them.
I had a second enterprise spring from setting up AoT in Louisville. I applied for a Fulbright Fellowship to do research in Budapest, Hungary in 2018-19. There is a wonderful research group on proto-planetary disks (baby solar systems) there, and I wanted to improve my knowledge of the language and culture in the country where my parents were born. Fulbright Fellows are expected to do public outreach in their host countries, so I proposed to found Astronomy on Tap in Budapest. A colleague, Jacob White, co-founded it with me in January 2019 and helped to recruit other organizers, and AoT-Budapest has been going well ever since. The story of my year by the Danube and the consequent professional and personal growth will be a good subject for my next blog.
Photos of Astronomy on Tap in Budapest. Gerry Williger is standing in the photo at left; Jacob White is to his right.
Illustration from 1923 edition of Robert Frost's New Hampshire: A Poem with Notes and Grace Notes
Whose woods these are I think I know. His house is in the village though; He will not see me stopping here To watch his woods fill up with snow.
My little horse must think it queer To stop without a farmhouse near Between the woods and frozen lake The darkest evening of the year.
He gives his harness bells a shake To ask if there is some mistake. The only other sound’s the sweep Of easy wind and downy flake.
The woods are lovely, dark and deep, But I have promises to keep, And miles to go before I sleep, And miles to go before I sleep.
It is the darkest evening of the year! You probably know about the December 21 solstice—it is the “winter solstice” in the northern hemisphere, and the “summer solstice” in the southern hemisphere. In the northern hemisphere the December 21 solstice is the shortest day of the year; in the southern hemisphere it is the longest day. But you may not know about certain curious things that take place around the December solstice.
One of those things is that, while in the northern hemisphere the solstice is indeed the shortest day of the year, early December marks the “darkest evening” of the year. That’s right, the earliest sunset occurs more or less this evening. From here on the sun starts setting later each night. Check out the table below, which is for Castel Gandolfo (home of the Vatican Observatory). The sun sets tonight at 4:38 pm there. Note how the sun never sets any earlier, and starts setting later by the 14th of December. And yet the length of the day keeps getting shorter. (If we want to pick nits here, perhaps tonight is not the darkest evening of the year. That might be actually be in a couple of days. But the difference is mere seconds.)
Indeed, as the graph below shows, by the time of the solstice there will be several minutes more daylight in the evening than there are right now in early December. (All data in these posts are based on sunrise and sunset times provided by Date and Time.) That is despite the fact that the day length is actually getting shorter between now and the solstice. If there is more daylight in the evening, but less daylight overall, then what is happening? The answer is that between now and the solstice we lose daylight in the morning faster than we gain it in the evening.
Likewise, in the southern hemisphere the solstice is indeed the longest day of the year, but the brightest morning of the year is in early December. By the time the solstice arrives there will be several minutes less of morning daylight than there are right now.
We will get to the explanation for all this in a future post. For now, just observe it. See for yourself that it is true. Keep your eye on the sunset (if you dwell in the northern hemisphere) or on the sunrise (if you dwell in the southern hemisphere). Watch the evening brighten, northerners, even as the shortest day approaches. Watch the morning darken, southerners, even as the longest day approaches. The universe holds surprises for those who are attentive to it.