Kentucky Science Conversations – Professor Kate Bulinski writes a guest blog
This is the second “Kentucky Science Converstions” guest blog. As mentioned in last week’s post, Prof. Gerry Williger, an astronomer at the University of Louisville here in Kentucky, and Louisville’s Archbishop Joseph Kurtz set in motion a series of ongoing conversations about science. This conversation has included Williger, Kurtz, Tim Dowling, who studies planetary atmospheric dynamics at UofL, and Kate Bulinski, a geoscientist with the School of Environmental Studies at Bellarmine University in Louisville, and me. I of course had to encourage all of these folks to contribute posts to this blog.
Today we have a guest post from Professor Kate Bulinski, who is is an Associate Professor of Geosciences in the School of Environmental Studies at Bellarmine University. She received her B.S. in Geoscience from The Pennsylvania State University in 2002 and her Ph.D. in Geology from University of Cincinnati in 2008. In addition to teaching classes for undergraduate students each semester, she pursues paleontological research often involving her students. Her current research efforts are focused on the paleoecological relationships at the Devonian Falls of the Ohio coral fossil beds in Clarksville, Indiana. Most recently, she completed a sabbatical including two months of intensive field work there in the fall of 2017. She regularly conducts public outreach, particularly through paleontology education workshops for K-12 teachers and through Kentucky Interfaith Power and Light, an interfaith non-profit group that works with faith communities to respond to environmental concerns. As a product of these efforts she was awarded the Kentucky Academy of Science Excellence in Science Education and Outreach Award in the fall of 2017.
Professor Kate Bulinski, 31 Jul 2018
It may seem a little strange for a paleontologist to be contributing to an astronomy blog, but there is one factor that unites the two disciplines: the concept of deep time.
It is very difficult for humans to get a sense of the scope and scale of the age of the Earth and the universe. We have a tendency to think in terms of human time scales. To the average person, a few centuries is quite old, and in terms of the age of the Church, the time frame of a couple of millennia is ancient. For a paleontologist however, our time scales are framed by many millions if not billions of years of Earth history.
Taking this wide-angle view of the history of our planet gives me a very different perspective of humanity’s relationship to the Earth and, to borrow a phrase from Douglas Adams, makes me also think very differently about life, the universe, and everything.
When you begin to think like a paleontologist, you start to realize how the fossil record reveals a magnificent history of our planet. From the smallest microbes pumping oxygen into our early Precambrian atmosphere several billion years ago, to the advent of shelled ocean-dwelling creatures more than 500 million years before the present, one thing is clear: the evolution of life on our planet was a time-intensive enterprise. It is in this vast expanse of time that life responded to shifting climates, the movement of tectonic plates and the changes in ocean chemistry that produced the environments where some organisms thrived while others did not. Incredible episodes of ecological crisis and mass extinction unfolded on our planet long before mammals, let alone humans beings, existed.
When you begin to recognize the scope of these time scales, it is impossible not to feel incredibly humbled by the seeming insignificance of the human species as an inhabitant on the 4.6 billion-year-old Earth. It was an incredible responsibility for humans to inherit the charge to care for creation, and it was also a responsibility that I do not think we initially had the wisdom to properly cultivate. I believe we as humans are just now awakening to the horror of what our species has done to our beautiful planet in a geological blink of an eye. As a person of faith, it is impossible for me not to feel devastated when I see how the modern human being has abused our world.
There is no doubt that our use of the Earth’s resources has improved the human condition. The mining of metals and other earth materials have allowed us to create all kinds of buildings, infrastructure and goods that created the cities and towns where more than 7.5 billion people now live. Fossil fuels created economic prosperity, led to the industrialization of agriculture, and reduced hunger and poverty around the globe, in just a few human lifetimes. However, in that short span of time we filled our oceans with plastic, polluted our air and water supplies, and altered the composition of our atmosphere. We created the conditions in which people and the rest of creation are now suffering from illnesses stemming from pollution and the effects of more severe and frequent natural disasters associated with a changing climate.
Air pollution knows no boundaries. (Public Domain)
To me, there is no more important social justice concern to address because the call to care for our earth is also the call to care for all of humanity. Poverty, famine, illness and conflicts have all been documented to stem from the effects of environmental degradation, and therefore, if we wish to work to reduce human suffering, we need to work to solve environmental problems. It is in this spirit, of course, that Pope Francis wrote Laudato Si. He challenges us all to grapple with the extent to which humanity has altered the natural environment of the earth, and to examine what we can do to course-correct as a moral imperative. This is not an easy charge. Our modern world was built on the back of fossil fuels and mined materials. They literally infuse our lives, whether it is in the form of synthetic materials in our clothing, the pesticides and fertilizer used to grow our food, the incredible amount of disposable plastic packaging used with abandon in our consumer goods, the rare earth metals that are used to manufacture our cell phones or the way we generate electricity and power our transportation. We need to examine the entire system of how we manufacture, purchase, use and dispose of the materials in our life and ask ourselves if they are a reflection of what was meant when we were asked to care for creation.
Picture of the author in a rock quarry exposing fossiliferous Silurian-age rock (approximately 435 million years old).
As a thought experiment, I sometimes ask my students to contemplate what the fossil record of the 21st century would look like. Would we have layers of sediment embedded with plastic debris and electronic waste? Would we have strange isotopic signatures in the rocks as a result of the use of nuclear technology, the manufacturing of synthetic chemicals, and the burning of fossil fuels? What would future humans (or our evolutionary descendants!) have to say about this era of Earth history? And perhaps more importantly, what would God say about how we responded to the charge to care for creation and how we responded once we realized the mistakes we were making? These are all questions that I think are worthy to contemplate when we think about our place in time and in space. It is so easy to get wrapped up in the minutia of our daily lives but the world is so much bigger and older than all of that. We are a part of this great chain of being, and I hope beyond hope, God willing, that we can continue to be a part of that chain for many more millions of years to come.
Kentucky Science Conversations – Archbishop Joseph Kurtz writes a guest blog
Clips from local news coverage of the Archdiocese of Louisville’s solar panel array (WLKY, May 30, 2018).
I am happy to introduce to readers of The Catholic Astronomer a few guest bloggers. In September 2017, with astronomy “in the air” thanks to the August 2017 eclipse, my friend and colleague, Prof. Gerry Williger, an astronomer at the University of Louisville here in Kentucky, sent an invitation to Louisville’s Archbishop Joseph Kurtz to attend some of the talks that are part of the Public Astronomy Lecture Series hosted by UofL’s Department of Physics and Astronomy. Archbishop Kurtz got right back to Gerry, commenting on his own interest in astronomy, and suggesting that they get together to discuss their common interest. Gerry in turn suggested inviting me and Tim Dowling, who studies planetary atmospheric dynamics at UofL (and who has written a guest post for The Catholic Astronomer on the 2017 eclipse). Within a week or two the four of us were having our first meeting. Astronomy was the spark for this endeavor, but of course there is more to science than outer space, and so soon Archbishop Kurtz invited Kate Bulinski, a geoscientist with the School of Environmental Studies at Bellarmine University in Louisville to join us. The result of all this has been some delightfully nerdy conversations about science (and education, and people, and religion, and the new solar panel array on the archdiocesan offices, and more)! Of course, with such an interesting group, I had to encourage all of these folks to contribute posts to this blog.
Today we have the first of these new guest posts, a short post from Archbishop Kurtz. Pope Benedict XVI appointed Most Reverend Joseph E. Kurtz, D.D. as the fourth Archbishop and ninth bishop of the Archdiocese of Louisville on June 12, 2007. Before coming to Louisville, Archbishop Kurtz served as Bishop of Knoxville, Tennessee, from 1999 to 2007. If you are thinking that you know the name Kurtz, that may be because Archbishop Kurtz was Vice President of the United State Conference of Catholic Bishops (USCCB) from 2010 to 2013, President of the USCCB from 2013 to 2016, and currently serves as the chairman of the Committee for Religious Liberty, and in that capacity he serves on the administrative committee of the USCCB. And, most importantly of all, Archbishop Kurtz ranks among The Catholic Astronomer’s subscribers! Thus he gets the e-mails announcing the various posts (you can subscribe, too—no cost—see “Subscribe to this Blog” above). And so today he will have the odd experience of getting an e-mail announcing his own post.
Archbishop Joseph E. Kurtz, 6 Aug 2018
What a joy it is to be on the regular emails of the Vatican Observatory Blog. I have had an interest in faith and science since I was a boy. In recent days, much of what is written on this topic assumes that faith and science are opposed to one another. Instead, Saint John Paul II points out so well in his 1998 encyclical on the topic, Fides et Ratio, that faith complements science—leading the inquirer to greater and greater wonder and curiosity at the magnificence of God’s creation.
I was delighted about a year ago to meet with three scientists teaching at local universities in Louisville. They reached out to me in the hope that we might discuss the relationship between their Catholic faith and their professions. We have met three times and even added some others to the dialogue. Thus far it has been greatly enriching for me. While our purpose has been to talk and not to plan programs or events, already fruitful results are emerging on the horizon beyond our small group. At our next meeting, we are inviting two high school teachers from a local Catholic high school—one a theology teacher and the other a teacher of science—who have been collaborating to bring together the richness of both of their concentrations. These developments remind me of the Latin definition of theology as fides quaerens intellectum or “faith seeking understanding.” The history of theology clearly reveals that a lively faith does not shun the secular sciences but both learns from them and enriches them.
St. Macrina’s Discourse on Science and Technology
St. Macrina the Younger
St. Macrina the Younger has a fascinating fourth-century discourse on science and technology. Macrina, who lived from 330 to 379 A.D., was the sister of St. Basil the Great and St. Gregory of Nyssa, and the daughter of St. Emmelia, and the granddaughter of St. Macrina the Elder (saints run thick in that family). Her discourse on science and technology was recorded by St. Gregory: it was part of their dialogue that became Gregory’s On the Soul and the Resurrection.
Macrina discusses how we know more than just what our eyes show us, because through our minds we take what our eyes see and we reason and we calculate; and we come to know, for example, that the sun is far larger than the Earth (science), and how to create machinery that can even imitate human actions (technology). Check out what St. Macrina the Younger has to say—her discourse is available on the Vatican Observatory Faith and Science pages:
CLICK HERE for Macrina’s discourse on Science and Technology.
Mathematics Against the Multiverse in 1614 (re-run)
This is a "re-run" of a post that originally ran on May 11, 2016.
The most surprising things can be found in astronomy’s history—like “the multiverse,” that collection of parallel universes that is the central theme in Brian Greene’s 2011 book The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos. You might not expect to encounter a multiverse in an astronomy book from four hundred years ago, but in fact you will if you look through a 1614 book entitled Disquisitiones Mathematicae de Controversiis et Novitatibus Astronomicis (or Mathematical Disquisitions Concerning Astronomical Controversies and Novelties) written by Johann Georg Locher of Germany. The greatest claim to fame of Disquisitions is probably that Galileo made much sport of it in his 1632 Dialogue Concerning the Two Chief World Systems: Ptolemaic and Copernican. Locher was a student of Christoph Scheiner. Scheiner was an astronomer at the University of Ingolstadt, a Jesuit priest, and someone Galileo would eventually come into conflict with regarding sunspots. Disquisitions is only available in original form, in Latin. The noted historian of science Alexandre Koyré once wrote that “Since Galileo’s time no one ... has ever so much as looked at the Disquisitions,” and that even people who have cited it obviously borrowed from Galileo’s quotations of it in the Dialogue. This is all unfortunate, because Disquisitions contains much material worth reading, such as Locher’s discussion of the multiverse.
The discussion is very brief. He outlines the basic Aristotelian structure of the universe—earthly material at the center of the universe, with water on the earth and air above them both, and also fire. All this is contained within the embrace of the heavens, which are made of ether and comprise the bulk of the universe. Every material thing is found within this structure, he says. But then Locher notes that various people have opposed this idea—
| Etenim antiqui Philosophi ijdemque Mathematici plerique, Universum infinitum esse statuerunt, inque duas tribuerunt portiones, quarum alteram Mundum hunc aut Mundos fecerunt, singulos quidem finitos mole, infinitos tamen numero; alteram, quae extra Mundos vagaretur, infinitorum congeriem quandam atomorum, e quibus & mundi facti alerentur, & noui identidem fierent. | And as a matter of fact a good many philosophers and mathematicians of old have concluded that the Universe is infinite. They divide it into two portions. One is this World or rather the Worlds, each finite in size, yet all infinite in number. The other, which ranges beyond these Worlds, is a great chaos of infinite particles, from which both existing worlds might be nourished, and new worlds continually made. |
By “this World” Locher means this observable universe—our Earth and the heavens. He includes a fascinating, full-page illustration of this. In the illustration, the stars surround the system of Earth and planets. Locher says that because the exact arrangement of this system is in dispute (Disquisitions discusses both the Copernican system in which the Earth and planets circle the sun, and the Tychonic system—which Locher favors for scientific reasons—in which the sun, moon, and stars circle Earth while the planets circle the sun), he is leaving blank the space they would occupy. Then, surrounding the stars is the “infinite atomic chaos.” Locher’s idea of an atom is not the same as ours. He is envisioning the most elementary particles of matter, so this might be better rendered the “infinite particle chaos.”
Locher is clearly talking about the sort of ideas found in the ancient poem On the Nature of Things by Lucretius. Lucretius writes—
| Principio nobis in cunctas undique partes,/ Et latere ex utroque, infra, supraque per Omne/ Nulla est finis, uti docui; res ipsaque per se/ Vociferatur, & elucet natura profundi;/ Nullo jam pacto verisimile esse putandum est,/ (Cum quoquovorsus spatium vacet infinitum,/ Seminaque innumero numero summaque profunda/ Multimodis volitent aeterno percita motu);/ Hunc unum terrarum Orbem, coelumque creatum;/ Nil agere illa foris tot corpora materiai;/ Cum praesertim hic sit Natura factus, & ipsa/ Sponte sua forte offensando semina rerum/ Multimodis, temere, incassum, frustraque, coacta/ Tandem coierint ea, quae conjecta repente/ Magnarum rerum fierent exordia semper,/ Terrai, maris, & coeli, generisque animantum./ Quare etiam atque etiam tales fateare necesse est/ Esse alios alibi congressus materiai,/ Qualis hic est, avido complexu quem tenet aether. | The first point which I advance is, that in every direction around us, and on all sides, above and below, there is no limit through the whole of space, as I have demonstrated, and as the thing itself proclaims, and as the nature of the expanse makes manifest. But by no means can it be thought true—when infinite space lies open in every direction, and when particles countless in number, driven about by everlasting motion, fly through the void in manifold ways—that this one globe of the earth, and this one heaven, have been alone produced; and that those innumerable particles of matter beyond our sphere do nothing; especially when this world was made by Nature on her own, the particles jostling about in various ways, often brought together confusedly, ineffectually, and to no purpose, finally coalesced, thrown together suddenly, to ever become the beginnings of great things—of earth, sea, heaven, and race of animals. For which reason, it is necessary you admit, that again and again there be other combinations of matter in other places, such as is this universe which the ether holds in its vast embrace.* |
Lucretius goes on to say that these many universes not only form up from time to time spontaneously from the chaos, but that they also die off into the chaos (and indeed, the general deterioration of things these days—says Lucretius, two thousand years ago—indicates that our universe is already dissolving away).
The multiverse, according to Locher and Lucretius. (Image composed from edited versions of Locher's diagram.)
Locher says, however, that truth and Christian philosophy demolished this fiction some time ago. He then proceeds to show how this is done. His method? Mathematical reasoning (despite his mention of “Christian philosophy” Locher makes no use of religion in his anti-multiverse arguments). He might not convince a modern mathematician who has the benefit of four more centuries of mathematical studies to look upon, but Locher believes that mathematical reasoning shows that physical infinitudes are unreasonable. He says he will provide just a brief discussion, and not a rigorous argument.
Locher’s discussion has multiple parts, and is not that brief, but it goes something like this: Imagine a line of alternating black and white segments of a given actual length, such as six inches, and that this line starts at A and extends infinitely to the right, in the direction of F. Then suppose the black segments are eliminated, and the whites collapsed to the left toward A. Is there now an infinite amount of space remaining to the right of the whites? That can’t be. You cannot start from A and reach the end of the infinite series of white segments. What if the whites were collapsed to the right? Would there be an infinite space in front of A in which to place the infinitude of black segments? Again, no.
Locher’s illustration of an infinite line extending to the right from A, broken into black and white segments.
Or suppose you were to pair off the blacks and whites, or group them into threesomes or foursomes. If the line consisted of a dozen six-inch segments, then there would be six pairs, four threesomes, or three foursomes. But if the line consists of infinitely many segments then it cannot divide into a finite number of pairs or threesomes or foursomes; it must divide into an infinite number of each. But it cannot divide into equal numbers of each, because there are by definition fewer foursomes than threesomes, etc. Does this mean one infinity is larger than another? Does all this not say that you can subtract an infinity from an infinity and get an infinity? In terms of actual things, like six-inch segments, how do you subtract infinitely many of something from anything and still have anything left over, let alone an infinity? Is this not contrary to the concept of “infinitely many,” and thus unreasonable?
Locher grants the idea of infinity, just not an actual physical infinitude. After all, he says, were there not mathematical infinities then the square roots of all numbers could be determined exactly. He says also to consider a quantity such as motion. Imagine motion being as slow as you want. Divide that in half, and you have slower. There is no limit to this—you can always divide and get a slower motion. So thus certain infinities do exist.
But Locher rejects any physical infinities, and he draws some interesting corollaries from this. Because of this, he says, the universe cannot have existed from eternity; and therefore it was brought into existence at some point in time; and therefore we know from evidence that almighty God, the author of the universe, exists; and the fables of the ancients, about the universe forming from the confluence of elementary particles, are destroyed. There is no infinite multiverse. However, he says the universe we do have is so vast that only God can truly measure and know it.
Nevertheless, Locher continues, despite human feebleness before such immensity, we do now have the telescope, and it has revealed so much we did not know before. And that is what the Disquisitions is mostly about, not the multiverse. But in 1614 the multiverse was being discussed.
*From Book II, 1059-1078. This is my translation, which is based on the translation by John Selby Watson. Here is a more poetic version, by John Mason Good:
And first, th' entire of things, above, below,
Search where thou wilt on every side alike
Spreads unconfined: this, as already taught,
Right reason proves, and many a clamorous fact.
Then deem not thou, since thus perpetual space
Flows infinite, and infinite the seeds
That, from exhaustless founts, in endless modes
Fly through the void, by endless motions urged,
Deem not this visual system of the heavens
Alone exists, unparalleled by aught,
And that all matter elsewhere sleeps supine.
Since too of its own nature the vast mass
Sprang forth spontaneous, rousing every power
To every mode of motion, rashly oft,
Oft vain and fruitless, till, at length, it formed
Th' unchanging rudiments of things sublime,
And heaven, and earth, and main, and mortals rose:—
Hence doubly flows it, other systems still,
Like ours, must deck the vast ethereal void,
Enfolded in its avaricious grasp.
Knowing the Moon’s Distance (re-run)
This is a "re-run" of a post that originally ran on March 24, 2016.
How do we know what we know in science?
What is the distance from the Earth to the moon? You can easily find that information using a smart phone and Google. Google says that distance is 238,900 miles.
Fine, but how do you know that value is right? Google’s business is not astronomical research. No doubt Google got the value from some “Scientific Authority.” Do you believe Google? Do you believe Scientific Authority? How do you know the moon isn’t just on some dome up there, way above the clouds? Seriously—how do you know? You may simply believe Authority, but plenty of people do not. Just recently [in early 2016] Neil deGrasse Tyson felt the need to respond to rapper B.o.B’s assertion that the world is flat, an idea no more absurd than the moon being on a dome above the clouds.
B.o.B (left); Neil deGrasse Tyson (right)
So how might people like B.o.B, who question Scientific Authority, verify the moon’s distance for themselves? After all, science is not supposed to be about accepting things on Authority. Science is supposed to be about testing, replicating, and verifying the results of others. And yes, it is in fact possible to verify the distance to the moon.
Imagine that you live in Grand Forks, ND, and you have a friend who lives a great distance due south of you, in Victoria, TX. You both have small telescopes and decent cameras. You both agree that at 10:00 PM tonight you will photograph the moon. But first, you each have to calibrate how many degrees the field of field of view of your camera-plus-telescope covers, so you can use it to make measurements of things in the sky.
How do you do this? You take a photo of a 1-foot ruler at a set distance away. Remember that the circumference C of a circle whose radius is R is given by the formula C=2πR. The length of a sector S of a circle marked out by some angle is a fraction of the circumference: S=(Angle/360o)C. For example, if the angle is 90 degrees, then you have a quarter circle and the sector length S is S=(90o/360o)C. That is (1/4)C, or 1/4 the circumference of a circle of radius R.
You want to determine what a degree is in your camera-plus-telescope. So, at what distance will the ruler need to be so that it measures 1 degree as seen in any pictures you take with your camera-plus-telescope? Using S=1 foot and Angle=1 degree, you go to your formulas:
S=(Angle/360o)C
1 ft=(1o/360o)C
C=360 ft
Next, to find the distance (which will be R):
C=2πR
360 ft=2πR
360 ft/2π=R=57.3 ft
Therefore if you set up the ruler 57.3 ft away and take a photo of it through your telescope, the length of the ruler will be 1 degree.
With the calibration complete, you and your friend proceed to take pictures of the moon tonight, with the results being as shown below. Note the difference between these two photos! The moon is not in the same place relative to the stars when seen from Grand Forks as when simultaneously seen from Victoria. Why not?
Simulated moon photographs taken from Grand Forks, ND (left) and Victoria, TX (right). Simulation made using the Stellarium planetarium software.
The answer is parallax. As shown in the figure below, observers at two different locations A and B on Earth will see celestial objects in different positions against the stars. And this is very cool. Why? Because parallax means we can do triangulation—we can use angles to measure distances.
Object 1 appears among the stars at A1 as seen by an observer on Earth at A, but it appears at B1 as seen by an observer at B. The difference between the two positions is the parallax of the object. Object 2 is more distant from Earth and thus has a lesser parallax—there is a lesser difference in the positions of Object 2 as seen by the two observers.
Let’s superimpose a sector of a circle on our parallax diagram, as seen below. We make point A be Victoria, point B be Grand Forks, and Object 2 be the moon. Now, the sector angle between A and B is the same as the angle between the different moon positions on the sky, A2 and B2, as seen from Victoria and Grand Forks.
Using your calibration ruler and the photo software on your computer, you measure the moon to have a diameter of 0.92” on your photos. This turns out to be half the length that your calibration ruler measures in photos, so 0.92” translates into the diameter of the moon being 0.5 degrees. This 0.5 degree value happens to agree with what you have read from The Scientific Authorities! So far, so good.
Now you use the photo software to overlay the two pictures. To measure the angle between the two moon positions, you find a small, distinct feature on the moon (arrowed in green below) and use it to measure the difference in the moon’s position. You find it moved 0.07” horizontally, and 0.52” vertically. Since the Pythagorean Theorem says a2+b2=c2, you can calculate the total distance it moved: 0.52469”. At 1 degree for 0.92”, that translates into 0.28516 degrees.
Photos of the moon from Grand Forks and Victoria overlaid.
Measuring the difference in the moon’s position using a distinct feature on the lunar surface—a small dark spot.
The next thing you need is the distance from A to B—the
distance from Grand Forks to Victoria. You refuse to accept anything on Authority, so you decide to bicycle from Grand Forks to Victoria. You outfit the bike with a precision odometer you personally calibrated to ensure that it measures distance correctly. You follow the most direct route, even taking walking paths if need be. You discount the mileage of any side trips. And, after a month-long cycling trip, your odometer tells you that the distance from Grand Forks to Victoria is 1408 miles.
Now you know the distance from A to B on the sector is S=1408 miles, and the sector angle is 0.28516 degrees. Back to the equations to determine the sector’s radius R, which is the distance from Object 2 (the moon) to A or B:
S=(Angle/360o)C=(Angle/360o)2πR
1408 miles=(0.28516o/360o)2πR
R=(360o/0.28516o)(1408 miles/2π)=282,900 miles
Ta-da! You and your friend have just calculated the distance to the moon. 282,900 miles is not the same as Google’s 238,900, but it is definitely “in the ball park.” And, you made a lot of approximations in your work. You ignored the differences between the distances measured from A to B across the curved surface of the Earth vs. along the sector of the circle centered on the moon. Your picture overlay and picture distance measurements were crude. Your route was not direct—every turn and jog would lengthen the A-B distance (and likewise make your calculated R too large). The moon was high in the sky when you took the pictures, but not directly overhead like in the parallax diagram. There was much room for improvement in your work. Yet nonetheless your value for the moon’s distance generally agrees with Google’s—to within 20%! And you measured that distance entirely on your own. You relied on no Authority. You used only a phone camera, a small telescope, a ruler, and a bicycle. And you used one other very important thing: you used reason to determine the distance to the moon.
Triangulation is an old method of measuring distances. Note that the two key measurements involved in it are the distance between A and B, and the angle. These measurements can be made without any modern technology. In the 16th century, before even the telescope had been invented, Tycho Brahe made angle measurements to accuracies of better than 1/30 the diameter of the moon by means of instruments that were essentially giant protractors. Brahe could have told you the distance to the moon through triangulation.
Left—Tycho Brahe. Right—An illustration of Tycho’s astronomical instruments, all of which are angle-measuring devices of one sort or another.
A table from Giovanni Battista Riccioli’s 1651 Almagestum Novum giving parallax and distance information for the moon, according to various astronomers dating all the way back to Hipparchus in antiquity (Tycho Brahe included). Average distances range from 56 to 77 times the radius of Earth, or 224,000 to 308,000 miles. The result discussed here fits right into this range.
Note also that, at least in principle, the distance to any object in the heavens might be measured this way. In fact, triangulation is the only direct method of measuring distances to most things in space. The problem is that the farther the object in question, the smaller the angle (as seen with Object 1 and Object 2 in the parallax diagram), and if the angle is too small it will be impossible to measure. Brahe actually tried to measure the distance to Mars this way in an effort to test whether Copernicus was right in his ideas about the universe, but could not get good enough measurements.
This is how we know stuff in astronomy. We know through reason—through observations, measurements, and calculations. It makes sense. You can try it for yourself. Enjoy the ride!
The Mound, the Fort, and the Church: The Trees Speak to Science (Part II)
How old is Serpent Mound, a Native American monument notable in part for its astronomical alignments? Last week we saw how E. G. Squier and E. H. Davis argued that the Native American works that they surveyed in the 1840’s had to be many centuries old, by reason of the trees growing on those works. However, you may recall from my post of three weeks ago that the Ohio History Connection (formerly the Ohio Historical Society), who operates the Serpent Mounds site, states that—
Thousands of years ago, Native Ohioans populated the landscape with mounds and massive earthworks. In the late 19th century, Harvard University archaeologist Frederic Ward Putnam excavated Serpent Mound, but he found no artifacts in the Serpent that might allow archaeologists to assign it to a particular culture. Based largely on the nearby presence of Adena burial mounds, later archaeologists attributed the effigy to the Adena culture that flourished from 800 B.C. to A.D. 100. This theory on the site’s origin was accepted until a 1991 site excavation used radiocarbon dating to determine that the mound was approximately 900 years old. This would suggest that the builders of the Serpent belonged to the Fort Ancient culture (A.D. 1000–1500). In 2014, another team of archaeologists presented new radiocarbon dates for the Serpent suggesting that it was built by the Adena culture at around 300 B.C. More work is needed to clarify the age of Serpent Mound.
Those age estimates vary wildly. The Ohio History Connection is making no statement at all regarding the age of Serpent Mound, other than that more work is needed on the matter. There is apparently no persuasive argument for the age of Serpent Mound.
Frederic Ward Putnam wrote about Serpent Mound in an article entitled “The Serpent Mound of Ohio”, published in the April 1890 issue of The Century Illustrated Monthly Magazine. Putnam described how, in September 1883, he and four other archaeologists visited the Serpent. He described the area as being covered with brush when he visited, but not so much brush that he could not see what was there. In fact, he wrote that on the evening that he arrived at the Serpent, he made arrangements with a Mr. Lovett, the owner of the land, to have the place cleared of underbrush so that they could see the entire Serpent, and that by noon the next day it had been roughly cleared, and—
...the view thus obtained of the serpent and the egg—as the oval work in front of its jaws has been called—led to a still stronger desire to know more, and a resolve to do all in my power to preserve this singular structure, which seemed so strangely transplanted from the mythology of the East.
Squier and Davis’s illustration of Serpent Mound, from their book Ancient Monuments of the Mississippi Valley: Comprising the Results of Extensive Original Surveys and Explorations. Squier and Davis wrote regarding the Serpent that “No plan or description has hitherto been published; nor does the fact of its existence appear to have been known beyond the secluded vicinity in which it occurs.”
So, there were no trees on the Serpent in 1883. However, Putnam writes that—
When Squier and Davis, after their survey in 1846, gave to the world the first account of this earthwork, it was covered with a thick forest, from which many a noble tree has been cut, as indicated by stumps still standing at the time of our visit. Thirteen or fourteen years after their visit a tornado swept its path directly along the serpent hill, and with the exception of a few saplings the forest was laid low. This led to clearing the land, and to the cultivation for a few years of the portion occupied by the serpent. Nature soon covered the scars with a protecting sod, which was followed by a growth of sumach, redbud, and briers.
But in fact Squier and Davis (who we met last week) did not report that the Serpent was covered with a thick forest. They made no mention of forest in their description of the place, and noted no forest in their illustration of it. They did mention forest at other Native American structures. Some examples:
All around are scattered the trunks of immense trees, in every stage of decay; the entire forest presenting an appearance of the highest antiquity [“‘Fort Hill,’ Highland County, Ohio”]....
Most of the wall, and a large portion of the area, are still covered with a heavy primitive forest. Trees of the largest size grow on the line, twisting their roots among the stones, some of which are firmly imbedded in their trunks [“Stone work, near Bourneville, Ross County, Ohio”]....
It is covered with a primitive forest of oak, hickory, and locust, of the same character with the surrounding forests [“Fortified hill, Butler County, Ohio”]....
I am going to speculate now: I am skeptical that Serpent Mound was ever heavily forested. The mound structure is long but the mound itself is not that large—just a few feet high—and it is not made of rock, but rather mostly clay. If a large forest grew up on Serpent Mound—a forest of the sort that grew on ‘Fort Hill’ (see Part I of this post from last week)—then surely the falling of trees would have ripped up the mound, and it would not have been so intact as it was in 1846, or in 1883, or as it is today. And had a tornado passed through, tearing up an ancient forest in the manner Putnam claimed, surely that would have damaged the mound greatly, on account of the great falling trees pulling up vast chunks of the ground, all at the same time.
Fallen trees in the forest on the ‘Fort Hill’ construction in Ohio, and the earth they pulled up in falling.
My speculation is that Serpent Mound was built or actively maintained by Native Americans who lived in that area much later than Squier and Davis or Putnam thought. Nineteenth century Americans (not of Native ancestry) tended to consider the people who they had displaced as not being builders of big structures. Putnam himself refers to
...the scattered bands of the last century [who] made their habitation on the spot, probably without any legendary knowledge or thought of the earlier worshipers at the shrine, over grown and half hidden by a forest which seventy years ago was of the same character as that on all the hills about.
In Putnam’s view, the more recent Native Americans were just a people who dwelt among the ruins of works built by others, not a people who built great works themselves. I speculate that he was not inclined to consider that more recent people built Serpent Mound, or at least maintained it up until some point in the more recent past—recent enough that no impressive forest of ancient, large trees greeted Squier and Davis in 1846. There may have been trees there in 1846—Putnam noted stumps, after all—but they were a relatively recent second growth.
But such speculations aside, the point here is that there is a reason that the Ohio History Connection has so little to say about how old Serpent Mound is! Sometimes science can tell us things with great precision, as illustrated by the sun in St. Louis Bertrand Church. Sometimes science cannot tell us things with great precision, but still presents to us a highly persuasive argument, as illustrated by the trees at ‘Fort Hill’. And sometimes science can only tell us that “more work is needed to clarify” the matter in question—and the matter may in fact never be clarified.
The Mound, the Fort, and the Church: The Trees Speak to Science (Part I)
My post from two weeks ago discussed Serpent Mound, a large Native American monument, and the possible astronomical alignments in the mound, and really how uncertain is the question of those astronomical alignments. As the Ohio History Connection (formerly the Ohio Historical Society) says—
Due to the short sight lines and the inability to define precise alignments... it may not be possible to determine whether the builders of the Serpent really intended it to be aligned to either the sun or the moon.
A montage of representations depicting both the Native Americans who built the places in Ohio such as Serpent Mound and the structures that they built. These images are details from larger works (see the Ancient Ohio Art series and the Appalachian Forest Museum) depicting activities at various Ohio locations.
Then last week’s post featured “astronomical alignments” in St. Louis Bertrand Church in my home town of Louisville, Kentucky, and how reliable the calculations and repeatable the results are regarding the position of the sun shining into that church (or into anything else). Not much is uncertain in that case. One nice thing about astronomy is just how reliable and repeatable it can be in so many cases—science at its cleanest and brightest: here are my calculations; here are my results; you do the same calculations; you make the same observations; you will see the same things; you will get the same results; we will be in complete agreement; there will be no dispute.
But not all science is so clean and shiny. Oftentimes things are much more muddled and uncertain and open to interpretation. Let’s consider the science behind the age of Serpent Mound. How might that age be determined?
Serpent Mound today.
Illustrations of Serpent Mound from an 1890 article by Frederic Ward Putnam in The Century magazine.
G. Squier and E. H. Davis first discussed Serpent Mound in their 1848 book entitled Ancient Monuments of the Mississippi Valley: Comprising the Results of Extensive Original Surveys and Explorations, published by the Smithsonian Institution. Consider their discussion of the “Fort Hill” Native American structure in Highland County, Ohio, which they surveyed in 1846, and of its age.
This work... is universally known as “Fort Hill,” though no better entitled to the name than many others of similar character. The defences occupy the summit of a hill, which is elevated five hundred feet above the bed of Brush creek at its base [the same creek that passes Serpent Mound some miles to the south].... lts sides are steep and precipitous; and, except at one or two points, if not absolutely inaccessible, extremely difficult of ascent. The points most easy of access are at the southern and northern angles, and may be reached on horseback. The top of the hill is level, and has an area of not far from fifty acres, which is covered with a heavy primitive forest of gigantic trees. One of these, a chestnut, standing on the embankment... measures twenty-one feet in circumference; another, an oak, which also stood on the wall... though now fallen and much decayed, still measures twenty-three feet in circumference. All around are scattered the trunks of immense trees, in every stage of decay; the entire forest presenting an appearance of the highest antiquity.
Squier and Davis’s illustration of “Fort Hill”.
Thus much for its natural features. Running along the edge of the hill is an embankment of mingled earth and stone, interrupted at intervals by gateways. Interior to this is a ditch, from which the material composing the wall was taken. The length of the wall is eight thousand two hundred and twenty-four feet, or something over a mile and a half. In height, measuring from the bottom of the ditch, it varies from six to ten feet, though at some places it rises to the height of fifteen feet.... [T]he degree of skill displayed and the amount of labor expended in constructing its artificial defences, challenge our admiration, and excite our surprise. With all the facilities and numerous mechanical appliances of the present day, the construction of a work of this magnitude would be no insignificant undertaking. And when we reflect how comparatively rude, at the best, must have been the means at the command of the people who raised this monument, we are prepared to estimate the value which they placed upon the objects sought in its erection, and also to form some conclusion respecting the number and character of the people themselves....
The evidence of antiquity afforded by the aspect of the forest, is worthy of more than a passing notice. Actual examination showed the existence of not far from two hundred annual rings or layers to the foot, in the large chestnut-tree already mentioned, now standing upon the entrenchments. This would give nearly six hundred years as the age of the tree. If to this we add the probable period intervening from the time of the building of the work to its abandonment, and the subsequent period up to its invasion by the forest, we are led irresistibly to the conclusion, that it has an antiquity of at least one thousand years. But when we notice, all around us, the crumbling trunks of trees half hidden in the accumulating soil, we are induced to fix upon an antiquity still more remote.
A large tree (but not 20+ feet in circumference) growing atop the wall at Fort Hill. This photo was taken at approximately the location indicated by the orange dot seen in the Squier and Davis figure above.
The forest at Fort Hill is still relatively undisturbed, and still boasts plenty of “crumbling trunks” of large old fallen trees. This photo was taken at approximately the location indicated by the blue dot seen in the Squier and Davis figure above.
This seems pretty reasonable, does it not? Squier and Davis presumably had a tool like a “hole saw” with which they could extract a bore sample from the chestnut tree. They counted the rings in and measured the length of the sample to determine 200 annual rings per foot within the tree’s trunk. The trunk measured 21 feet in circumference, so its radius was 21 ft/(2*pi) = 3.34 ft. That value times 200 yields 668 years—they are erring on the side of caution by giving 600 years as the upper limit on the tree’s age. The structure upon which the tree was growing must therefore have been well over 600 years old. Recall that they were doing this estimate in the 1840s, so today the Fort Hill structure would be well over 750 years in age by this estimate.
Squier and Davis note that, regarding “the antiquity of the ancient monuments... no attempt to fix their date accurately can, from the circumstances of the case, be successful. The most that can be done is to arrive at approximate results.” They know that the calculations here will not have anything like the accuracy and precision of the calculations regarding the sun in St. Louis Bertrand Church that we discussed last week.
However, Squier and Davis note a second important way of checking the age of these Native American structures, apart from tree rings—namely, that the forest that covers places like Fort Hill looks just like the rest of the forest in Ohio (in the late 1840s). They write that the Native American structures
are covered with primitive forests, in no way distinguishable from those which surround them.... Some of the trees of these forests have a positive antiquity of from six to eight hundred years [as measured by tree rings]... But, as already observed, the forests covering these works correspond in all respects with the surrounding forests; the same varieties of trees are found, in the same proportions, and they have a like primitive aspect.
Squier and Davis then quote U.S. President William Henry Harrison (of Ohio, who died in 1841), who had explained the logic of this in a talk to the Historical Society of Ohio:
The process by which nature restores the forest to its original state, after being once cleared, is extremely slow. The rich lands of the West are, indeed, soon covered again, but the character of the growth is entirely different, and continues so for a long period. In several places upon the Ohio, and upon the farm which I occupy, clearings were made in the first settlement of the country and subsequently abandoned and suffered to grow up. Some of these new forests are now sure of fifty years’ growth, but they have made so little progress towards attaining the appearance of the immediately contiguous forest, as to induce any man of reflection to determine that at least ten times fifty years must elapse before their complete assimilation can be effected. We find in the ancient works all that variety of trees which give such unrivalled beauty to our forests, in natural proportions. The first growth on the same kind of land, once cleared and then abandoned to nature, on the contrary, is nearly homogeneous, often stinted to one or two, at most three kinds of timber. If the ground has been cultivated, the yellow locust will thickly spring up; if not cultivated, the black and white walnut will be the prevailing growth.... Of what immense age then must be the works so often referred to, covered as they are by at least the second growth, after the primitive forest state was regained?
And so we see the logic of the argument put forth by Squier and Davis in the 1840s as to why the Native American monuments that they surveyed had to be many centuries old. This science is not so clean and bright as the sun-in-St.-Louis-Bertrand stuff discussed in last week’s post. Still, can we dispute their conclusions? It would seem that no one could disagree with their assessment of the age of Fort Hill.
But does that assessment work for Serpent Mound? Maybe not... but that will have to wait for next week’s post.
The Light of Truth
St. Louis Bertrand Church in Louisville, Kentucky, courtesy of Google Streetview.
My post for last week discussed Serpent Mound in Ohio, and possible astronomical alignments present in that Native American monument. Today is the Autumnal Equinox—one of the days that supposedly is marked by the bends in Serpent Mound—so I am sticking with the theme of astronomical alignments. It turns out that astronomical alignments can be found in all sorts of places, if you think to look for them.
A friend of mine, Justin Elliott, is the sort of person who thinks to look for them. He and his family regularly attend either the 9:00 AM or 10:30 AM Mass at St. Louis Bertrand Church in my hometown of Louisville. Perhaps because Justin grew up attending a “megachurch” that is relatively plain compared to St. Louis Bertrand, or perhaps because he has read too many mystery books to his own children, or perhaps because he watched too many movies of the “Indiana Jones” or “DaVinci Code” genres, Justin has a fascination with the ornate interior of the church, and how the light shining through the stained glass windows plays across all the various features within the interior.
The interior of St. Louis Bertrand Church. Note the large baldachino over the altar.
This past winter Justin and I got into a discussion about the light from one particular window: a round window located in the center of the front wall of the church; a window that bears the word “Veritas”—“Truth”. Would the light shining through “Truth” ever beam down upon key interior features—upon the tabernacle? upon the crucifix? upon the center of the main aisle?—all in true Hollywood style, so that at that key “Moment of Truth” the hero or heroine would be able to “decipher the clue” and “solve the riddle”.
The ‘Veritas’ Window at St. Louis Bertrand.
Deep in winter, when this discussion began, the Light of Truth was illuminating nothing but a relatively bare wall of the nave of St. Louis Bertrand. However, the position of the sun changes over the course of a year. If we knew where the sun needed to be for the Light of Truth to hit various interior features of the church, and we had some measurements of the church, we could make some predictions about where the Light of Truth might land, and when. Thanks to modern technology, the measurements and calculations needed to determine all this are much less tedious than they would have been “back in the day”. Indeed, we were able to sit down and rough out the calculations in an evening in Justin’s living room, with Justin’s children milling about, no doubt marveling at the level of nerd-dom on display, with laptops running Google maps and the Stellarium planetarium app, and papers with scribbled calculations and diagrams scattered all about the coffee table.
For the Light of Truth to beam right down the center of the nave of the church and strike the tabernacle, the crucifix, or the center of the main aisle, the azimuth angle of the sun (that is, its position along the horizon) would have to be such that the sun was shining directly onto the front of the church building. St. Louis Bertrand faces East, mostly—we found that it actually faces about eight degrees South of East, because Louisville’s grid of streets is not exactly oriented with the cardinal NSEW directions.
St. Louis Bertrand Church is oriented so that it faces about 8° S of E.
Thus we had to look for when the sun would have an azimuth of eight degrees South of East and be above the horizon. That would not occur until early March. Then we had to figure out the vertical or altitude angle needed for the sun to shine in onto a notable feature within the church—the baldachino, for example, one of the higher large interior features, and thus one of the first things that would be illuminated by the Light of Truth. To do this we had to estimate the height of the ‘Veritas’ window above the floor of the church, and the height of the baldachino, and do a little trigonometry to work out the required solar altitude angle.
The ‘Veritas’ window, seen from outside.
While we were at it, we could figure out just how far down the aisle of the church the Light of Truth would shine. The sun would achieve its maximum altitude angle, and thus would shine most steeply into the church and put the Light of Truth at its furthest point up the aisle, at around the summer solstice.
Did the calculations work? They certainly did. The Light of Truth was cast exactly as expected, at exactly the times calculated. Shown here are photos taken on Sunday, March 18, one of the earliest dates in 2018 when the sun first achieved the vertical altitude and the eight degree South of East azimuth needed to start illuminating the top of the baldachino; and on Sunday, June 17, near the summer solstice. The sun shining through the ‘Veritas’ window cast a blue-green circle of light that was plainly visible to those looking for it.
The ‘Light of Truth’ (blue-green circle of light, cast by the ‘Veritas’ winow) illuminating the top of the baldachino, on March 18, at about quarter of 9 AM. Click the image to enlarge.
The ‘Light of Truth’ illuminating the aisle near the back of church, on June 17. This sequence of photos shows the blue-green circle moving across the aisle in the minutes prior to 10:30 AM. The light actually reached the center of the aisle for the ‘Moment of Truth’ at just about 10:30 AM. Click the image to enlarge.
The elevation of the sun on March 18 and June 17 (simulated pictures). Both pictures show the sun when it has an azimuth angle of 8° S of E.
Diagram illustrating the path of the sun’s rays through the ‘Veritas’ window on both dates at the ‘Moment of Truth’ when the sun had an azimuth angle of 8° S of E and thus was shining straight down the nave of the church.
There are a number of items of note here. The first is that the ‘Light of Truth’ behaved exactly as calculated. It hit the center line of the church (corresponding to the sun hitting the eight degree azimuth angle) exactly at the expected times, at least to within the uncertainty involved in trying to figure out just when that ‘Moment of Truth’ was, since the blue-green circle of light did not have well-defined edges.
The second is that every March 18 the light passing through the ‘Veritas’ window will hit the center of the top of the baldachino in the manner seen here, and every June 17 it will hit the center of the aisle in the manner seen here, and it will do so at the same times. Indeed, as the days pass from the 18th of March to the 17th of June, day by day the location where that blue-green circle of light crosses the center will slowly descend the baldachino, passing over the crucifix and the tabernacle and the altar, and then it will slowly walk down the aisle toward the back of church. It will then return the way it came, day by day, during the second half of June and on into July, August, September, and October. Each day within that span of time from mid-March through early October—be that day the Feast of the Annunciation, or of St. Athanasius, or of the Most Sacred Heart of Jesus, or Sts. Joachim and Anne, or the Transfiguration, or St. Teresa of Calcutta—has its own ‘Moment of Truth’ and its own point at which the ‘Light of Truth’ strikes (just as occurs at the Kentucky Vietnam Veterans’ Memorial in Frankfort, Kentucky—a phenomenon discussed in another post).*
Between the 18th of March and the 17th of June, with each passing day the point at which the blue-green circle of light cast by the ‘Veritas’ window strikes the baldachino moves a little lower, and then walks down the aisle toward the back of church. The March 18 position is indicated by the pink arrow, the June 17 by the green.
A graph of the time at which the circle of light cast by the ‘Veritas’ window shines straight down the nave of church over the course of the year. Times are Eastern Daylight Time, and only Sundays are plotted. From early October to early March the sun is not in position to shine straight down the nave.
The last item of note is the dramatic beauty found at the ‘Moment of Truth’. The ‘Veritas’ window is located atop many other windows in the front wall of the church, and at that moment when the light from the sun pours through the ‘Veritas’ window straight down the nave of the church, the light from the sun pours through all those windows straight down the nave of the church. The effect can be quite stunning, and right at that key moment when the hero or heroine would be able to decipher that clue and solve that riddle—just like Hollywood would want it. A priest with a sense of the dramatic might similarly be able to time a Mass on a particular feast day to take advantage of the effect.
Many churches probably see similar effects at differing times of the year—and this stuff is not limited to churches, either. All that is required is the right window placement and the right building orientation, and you too will have your own calendar-marking astronomical alignments to study.
Light from the ‘Veritas’ window and other windows, at the ‘Moment of Truth’ on June 17. Note the red bands from other windows. Compare to the picture of the windows earlier in this post.
*This is true under the Gregorian calendar, which is effectively synched to the sun. The Julian calendar, which preceded the Gregorian, “drifted” slightly, so that over time the position of the sun on given days changed, with consequences for the date of Easter. Lunar calendars, such the Jewish, Islamic, Chinese and many other eastern calendars, are not synched to the sun at all.
Astronomy in Art & Architecture: Serpent Mound, Ohio
If you have been reading The Catholic Astronomer for a while, you might be familiar with these “Astronomy in Art & Architecture” posts (click here for all of them). This one is the first to feature ancient art!
Serpent Mound in south-central Ohio is a pretty cool place. It is a Native American monument that sits on a high ridge at the junction of two creeks, with steep drop-offs and even abrupt cliffs on either side. According to The Ohio History Connection (formerly the Ohio Historical Society), who operates the site—
Serpent Mound is an internationally known National Historic Landmark built by the ancient American Indian cultures of Ohio. It is an effigy mound (a mound in the shape of an animal) representing a snake with a curled tail. Nearby are three burial mounds—two created by the Adena culture (800 B.C.–A.D. 100), and one by the Fort Ancient culture (A.D. 1000–1650).
Thousands of years ago, Native Ohioans populated the landscape with mounds and massive earthworks. In the late 19th century, Harvard University archaeologist Frederic Ward Putnam excavated Serpent Mound, but he found no artifacts in the Serpent that might allow archaeologists to assign it to a particular culture. Based largely on the nearby presence of Adena burial mounds, later archaeologists attributed the effigy to the Adena culture that flourished from 800 B.C. to A.D. 100. This theory on the site’s origin was accepted until a 1991 site excavation used radiocarbon dating to determine that the mound was approximately 900 years old. This would suggest that the builders of the Serpent belonged to the Fort Ancient culture (A.D. 1000–1500). In 2014, another team of archaeologists presented new radiocarbon dates for the Serpent suggesting that it was built by the Adena culture at around 300 B.C. More work is needed to clarify the age of Serpent Mound.
Illustrations of Serpent Mound from an 1890 article by Frederic Ward Putnam in The Century magazine.
Serpent Mound today.
One of the claims about Serpent Mound is that its builders aligned it with the setting of the sun at the summer solstice, and with the rising of the sun at both summer and winter solstices, and at the equinoxes, too. The head certainly is oriented toward the general direction of the summer solstice setting sun, but this lengthy mound is built on rolling terrain, and there are no precise marker points built into any part of it, so the rising sun alignments are vague. As The Ohio History Connection says—
Due to the short sight lines and the inability to define precise alignments... it may not be possible to determine whether the builders of the Serpent really intended it to be aligned to either the sun or the moon.
Plaque discussing the possible astronomical significance of Serpent Mound.
The supposed alignments of the mound.
A montage of representations depicting both the Native Americans who built the places in Ohio such as Serpent Mound and the structures that they built. These images are details from larger works (see the Ancient Ohio Art series and the Appalachian Forest Museum) depicting activities at various Ohio locations.
The fact is, the spur of high ground on which the serpent sits is oriented toward the setting summer solstice sun. So, maybe the builders ended up with that alignment by accident. Or, maybe they chose that piece of ground purposefully: they found a piece of dramatically elevated land with an alignment toward the solstice sun, and they decided that it was a special place and chose to build the serpent there. This is something about which no one really knows anything for certain, other than that here is a very large, very cool piece of Native American art, and it does seem to have a solstice alignment.
The tail of the serpent.
Dude, my Mom wrote me a physics book, and now I gotta read it!
Take a look at a couple of entries from the Vatican Observatory Faith and Science pages, both pertaining to the Institutions de physique written by Gabrielle Émilie Le Tonnelier de Breteuil, marquise du Châtelet. Du Châtelet wrote the book for her son (who of course then had to read a physics book his Mom wrote—homeschooling Moms, take note!). It is an early physics textbook, so to speak, that covers Newtonian physics (she published it in 1740). It also contains material related to astronomy. And Du Châtelet made the second chapter of Institutions on the existence of God—not something you are likely to find in a physics textbook today.
Click here and here for the Faith and Science entries on Du Châtelet, including a partial translation of that second chapter proof of the existence of God.
Left - frontispiece illustration from Institutions de physique. Center - Du Châtelet. Right - illustration for the second chapter on the existence of God.
A group of faculty and students at the University of Notre Dame have been working for four years to create a complete translation of Institutions. A conference was held at Notre Dame this year to celebrate completion of their work. The complete translation (in various formats—not published) is available through the website of Katherine Brading, who led this project (but is now at Duke University). Click here for their complete translation of the second chapter.
The Infinite – Faith and Math
Illustration from an argument on infinity in Johann Georg Locher's 1614 book, Mathematical Disquisitions.
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 months 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 discussed in my last post, 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.
Seeing Too Many Enemies of Science in a Faith-Full World
Planet Earth is a world of the faith-full. And, it seems Earth is likely to become yet more faith-full during the next few decades. The scientific community will have to embrace that faith-full world if it wants a scientifically literate world.
The Pew results. Click image to enlarge.
A few years ago the Pew Research Center published an article entitled “The Future of World Religions: Population Growth Projections, 2010-2050” that projected the growth of various religious groups. Their projections, among religions, were for Christians and Hindus to maintain their share of the world’s population, for Muslims to grow substantially, and for Buddhists and Folk Religions to shrink. However, Pew projected the overall share of the world’s population that identifies with a religion to grow—from 83.6% of the world’s population in 2010, to 86.8% in 2050—as the religiously unaffiliated, which includes atheists and agnostics, drops from 16.4% of the population today to 13.2% in 2050. Pew notes that while there is a belief among some that increasing economic development will result in increasing religious disaffiliation, that is the experience only within certain countries. Pew writes—
There is little evidence of economic development leading to religious disaffiliation in Muslim-majority countries. In Hindu-majority India, religious affiliation remains nearly universal despite rapid social and economic change. And in China, religious affiliation—though very difficult to measure—may be rising along with economic development.
Pew notes that China is currently home to a large population of religiously unaffiliated, but if Christianity expands at the rate some experts predict, the world’s percentage of Christians may be higher than Pew projects—and the percentage of religiously unaffiliated, lower.
So if the scientific community wants a scientifically literate world, we will have to reach a faith-full world. Unfortunately, the scientific community can seem a little lost on this point. Consider, for example, the title of the 2016 book by Jerry Coyne, an evolutionary biologist from the University of Chicago: Faith Versus Fact: Why Science and Religion Are Incompatible. I thought of this again while paging though the Spring 2018 issue of the SPS Observer, the magazine of the Society of Physics Students, published by the American Institute of Physics. Within that issue was a short opinion piece by Don Lincoln, Senior Scientist at Fermilab, entitled, “To the Ramparts: Defending Science!”, itself part of a larger section entitled “Exploring Science Communication and Policy”. Lincoln writes—
There is a cultural war going on for the soul of America, and you are a soldier. That might seem to be an overly martial metaphor, but bear with me. On the one side, there are the voices of reason and science, guided by logic and with a deep respect for the interplay between mathematics, modeling, and empiricism. On the other side are those who reject the tools that have advanced our understanding of the universe. They are the antivaxxers and flat-earthers, the homeopaths and climate-change deniers.... There’s astrology, creation science, and zero-point energy.... The forces of pseudoscience have always been among us. But the internet has given them a larger voice than before and allowed them to grow their communities. With increased voice comes increased influence.
Click image to enlarge.
Lincoln is telling today’s young scientists to think of too many people as being enemies. He puts too many people on the other side of the ramparts. Flat-earth-ism, astrology, and creationism (to stick with astronomy-related things Lincoln mentions) are not all of a piece.*
Flat-earth stuff is simply naked ignorance, and it always has been. No one ever in human history, who bothered to take the least trouble to look, ever thought that the Earth is flat. Aristotle knew the Earth is round, and he was not the first to figure that out. The roundness of Earth is obvious to anyone who pays any attention.
By contrast, plenty of distinguished thinkers over a vast span of centuries believed in astrology. Johannes Kepler, one of my favorite people to talk about on this blog, did, and he is one of history’s A-list scientists. Astrology has not withstood the test of time. It fails as a science. But, unlike flat-earth-ism, it was once sort of defended by reasonable people.
Creationism is different still. One can reasonably argue that the universe was created by God relatively recently, and that God simply chose to create a mature universe that appears to science to have vast age, just as God chose to create Adam as a mature man who, were some scientist around to examine him, would have appeared much older than he was—and science cannot challenge this any more that it can challenge the claim that God created the universe this morning with the appearance of vast age. Kepler believed that the universe was 6,000 years old. Kepler was a voice of reason and science, guided by logic and with a deep respect for the interplay between mathematics, modeling, and empiricism, but his faith meant a lot to him. Even were he made aware of modern scientific discoveries, he might have still affirmed as a matter of faith the idea of a recently created universe.
Faith means a lot to many, many people, and among people of faith there is a deep intellectual tradition of reason and logic and science. And, according to Pew’s projections, faith-full people are only going to become a bigger part of the population of this planet. Science absolutely, positively does not want to be putting them, or any noticeable fraction of them, on the other side of the ramparts with the Flat-Earth know-nothings. Science cannot afford to be so exclusionary and opposed to diversity of thought as to accept declarations that science and religion are incompatible; it cannot afford to be in battle with any noticeable fraction of a group that makes up 80+% of the world’s population and growing. On the contrary, the scientific community must work to ensure that there is no opposition between faith and science, that no one gets the message that science is more the business of people from Norway than people from Nigeria (Christianity, for example, often being cited as declining in Scandinavia and growing in Africa). Call it Celebrating Diversity. Call it wanting the largest possible pool of scientific talent. Call it recognizing demographic reality. Regardless of what we call it, we need to make sure that the only people on the other side of the ramparts are those who really do have no commerce with reason and logic.
And guess what? The Vatican Observatory is doing exactly the sort of thing that the scientific community ought to be doing! So, support science! Support inclusivity! Support more people thinking that they can be a part of the scientific enterprise! Support the V.O., and particularly the Vatican Advanced Technology Telescope!—click here. Someone has to be doing science with an eye to an increasingly faith-full world.
*Lincoln does use the term “creation science”, so he may be referring to efforts to argue that the Earth does not even appear to be old as measured by science, efforts which tend more toward the flat-earth mentality, but without his having explicitly drawn this distinction I suspect most readers will think of creationism in general when they read his piece.