Category Archives: Mathematics

More Serious Sirius Business

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My post last week was about brilliant Sirius, which turns out to be a double star, comprised of a much brighter Sirius A, and a faint Sirius B.  We saw how the motions of these stars, seen in the video below, told us that the Sirius system was 8.6 light years away, and had 20+ times the sun’s luminosity.  The motion of Sirius B orbiting around Sirius A takes 50 years to complete.  The video below shows a little more than two complete orbits of Sirius B about Sirius A, from approximately 2020 to approximately 2154.  The video is a simulation, and presents what you would see if you had a very good telescope aimed at the exact same point in the sky for all that time. If the telescope is instead aimed at Sirius A, then the motion of Sirius B becomes a textbook case of an orbit—Kepler’s laws of orbital motion in action, as can be seen in … Continue reading →

A Serious Sirius Business

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The brightest star* in the sky, Sirius, the Dog Star, was the subject of a nice, short article in the March 2020 issue of Sky & Telescope magazine.  The article noted that Sirius is a double star: the Sirius that we point to in the night sky (what astronomers call “Sirius A”) is orbited by a faint companion star (“Sirius B”).  Sirius B is most difficult to see through a telescope, owing to the brightness of Sirius A—but it can be spotted, and even photographed. The motion of Sirius B around Sirius A can also be spotted.  Observe Sirius with a good telescope over a period of 50 years and you will see Sirius B complete one orbit.  The video below shows a little more than two complete orbits of Sirius B about Sirius A, from approximately 2020 to approximately 2154.  This video is a simulation made with the app Celestia.  It shows what you would see if you had … Continue reading →

Cutting Up: Math through Eyes of a Mathematician

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Over time I have had the pleasure of introducing to readers of Sacred Space Astronomy guest bloggers who are scientists, bishops, and worship directors.  Now I am pleased to introduce a mathematician.  Jeffrey Diller is Professor of Mathematics at the University of Notre Dame (currently on leave, having finished up a term as chairperson of the Department of Mathematics there).  He studies dynamical systems that arise in a complex analysis context.  He also teaches: he was awarded the Fr. James L. Schilts, C.S.C./Doris and Eugene Leonard Teaching Award at Notre Dame in 2012, the Joyce/Kaneb Award for Undergraduate Teaching in 2015, 2008, and 2003.  Since I have been running a series of posts on the topic of mathematics, I wanted a mathematician to give a mathematician’ s perspective on what is great, and what is appealing, about mathematics.  Jeff tells me that he became interested in the topic of this post in part out of his recent experience as coordinator … Continue reading →

Fr. Grienberger the Astronomer, and his Homemade Pi

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Today is “Pi Day”! This post is part of a series of posts on Pi, infinity, and other things mathematical. Click here for the series. What is Pi (π)?  We celebrate “Pi Day” on March 14 (3/14).  That is because Pi is (roughly) 3.14.  Indeed, I scheduled this post to appear at 1:59 AM, because Pi is (a little less roughly) 3.14159!  How nerdy can a guy get? So Pi is a mathematical idea that has its own day.  That is good, because astronomy involves a lot of mathematical ideas.  But still, what is Pi, and how do we know what it is? This question started bugging me after I bought my previous laptop.  For some reason the calculator “app” on this laptop was striking in a way that older calculator apps were not.  Perhaps this is because the new app was large and bold.  But at any rate, note how the button for π (that is, Pi) on the … Continue reading →

Religious Scientists: Canon Nicolaus Copernicus (1473-1543); Heliocentricism

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This entry is part 13 of 15 in the series Religious Scientists of the Catholic Church

When the name Copernicus is mentioned, what often comes to mind is the role that his heliocentric theory played in the Galileo affair. This creates the false impression of Copernicus as a controversial figure at loggerheads with Church authority. In reality, Copernicus was himself a Church figure. He was a canon (a church administrative role that at the time required ordination to minor orders) at his uncle’s diocese in Warmia. He held a doctorate in canon law. When his heliocentric system was presented to Pope Clement VII in 1533, it was favorably and enthusiastically received. Cardinal von Schoenberg of Capua encouraged him in a letter to promulgate the theory widely. In the seventy years after the publication of De Revolutionibus (until Galileo published his Siderius Nuncius) Copernicus’ work saw almost no objections on theological grounds. Biographical Sketch: Mikołaj Kopernik was born in Toruń in modern-day Poland on (it is believed) February 19, 1473. His father was a copper merchant, and … Continue reading →

The Infinite – Faith and Math (re-run)

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This post is a re-run of a post that originally ran in August, 2018. This post is part of a series of posts on Pi, infinity, and other things mathematical. Click here for the series. 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 … Continue reading →

Blaise Pascal and his Wager

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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’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 … Continue reading →

Religious Scientists: Sr. Mary Kenneth Keller B.V.M. (1913-1985) – Computer Science

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This entry is part 11 of 15 in the series Religious Scientists of the Catholic Church

When I was little, my dad bought an Apple II+ computer.  Every Christmas, my uncle would send us a pack of computer games on 5.25-inch floppy disks. We spent countless hours playing those games on its primitive green pixelated screen.  It was fun to play games made by somebody else, but even better was when I learned to make the computer do what I wanted it to do, with a little programming.  I learned a very simple computer language called Beginner’s All-purpose Symbolic Instruction Code, or BASIC.  With it, I made my own games, limited only by my imagination and skill.  For the freedom that programming in BASIC gave me, I have to thank a nun: Sr. Mary Kenneth Keller. Biographical Sketch: She was born Evelyn Marie Keller on Dec 17, 1913 (different sources disagree on this date) in Cleveland, Ohio. In 1932, she joined the Sisters of Charity of the Blessed Virgin Mary, where she took the name Mary … Continue reading →

Blaise Pascal: to God through Math

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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 … Continue reading →

Religious Scientists: Fr. Roger Boscovich S.J., F.R.S. (1711-1787) – Atomic Theory

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This entry is part 10 of 15 in the series Religious Scientists of the Catholic Church

Fr. Roger Joseph Boscovich S.J. was one of the last great polymaths. His areas of study and work include physics, mathematics, atomic theory, celestial mechanics, geodesy, philosophy, theology, architecture, poetry, and more. Biographical Sketch Ruđer Josip Bošković was born May 18, 1711 to a merchant family in Dubrovnik, in what is today Croatia.  He attended the Jesuit school in Dubrovnik. In 1725, he traveled to Rome to study at the Roman College, and in 1731 entered the Jesuit order. He was ordained a priest in 1744. He showed aptitude for mathematics and the natural sciences, and from 1740-1759 served as a professor of mathematics at the Roman College.  It is during this time that he made many of his more significant scientific contributions.  In 1742, Pope Benedict XIV requested Boscovich’s input on a little problem. The dome of St. Peter’s Basilica was developing cracks.  Boscovich recommended securing the dome with iron bands, which was then implemented successfully. This led him … Continue reading →