The 18th century was a rich period in the history of science, including the publication of the final edition of Newton’s work, the acceptance of the Copernican system by the Church, and the active role of Jesuit observatories in observing the Transits of Venus. One hero of this era is Fr. Roger Boscovich, who (among his other accomplishments) first proposed the modern atomic theory of matter.
A Serious Meditation – from Benjamin Banneker’s 1793 Almanac
- Article
- 390 words
- General audiences
A discussion of a Christian’s duty, from the 1793 almanac published by the self-taught American astronomer Benjamin Banneker of Baltimore County, Maryland.
[Download PDF]Banneker-MEDITATION
Click here to access Banneker’s 1793 almanac, courtesy of the Smithsonian.
Accuracy of Solar Eclipse Observations Made by Jesuit Astronomers in China
- Article
- 10 pages
- University specialist level
A 1995 Journal for the History of Astronomy article by F. R. Stephenson and L. J. Fatoohi:
Abstract: During the seventeenth and eighteenth centuries, Jesuit astronomers at the Chinese court in Beijing observed many eclipses of the Sun and Moon. For most of these events the times of beginning, middle and end were measured and the magnitudes estimated. Summaries of virtually all of the observation made between A.D. 1644 and 1785 are still preserved. In this paper, that various solar eclipse measurements that the Jesuits made during the period are compared with computation based on modern solar and lunar ephemerides.
Click here to access this article via NASA ADS.
Click here to download a PDF of this article from NASA ADS.
Book: The Cambridge Concise History of Astronomy
Book- 380 pages
- High school students and above
As suggested by our research team. This description is from the publisher:
Astronomy is one of the oldest sciences, and one which has repeatedly led to fundamental changes in our view of the world. This book covers the history of our study of the cosmos from prehistory through to a survey of modern astronomy and astrophysics (sure to be of interest to future historians of twentieth-century astronomy). It does not attempt to cover everything, but deliberately concentrates on the important themes and topics. These include stellar astronomy in the seventeenth and eighteenth centuries, at the time subordinate to the study of the solar system, but the source of many important concepts in modern astronomy, and the Copernican revolution, which led to the challenge of ancient authorities in many areas, not just astronomy. This is an essential text for students of the history of science and for students of astronomy who require a historical background to their studies.
Click here for Table of Contents from Cambridge University Press.
Click here for an excerpt from Cambridge University Press.
Click here for a preview from Google Books.
Boscovich – his geodetic and cartographic studies
Article- 8 pages
- High school level and above
A heavily illustrated 2013 article by B. Crippa, V. Forcella, and L. Mussio, published in Memorie della Societa Astronomica Italiana Supplement, concerning the 18th-century Jesuit astronomer Roger Boscovich:
Abstract: The name of Ruggero Giuseppe Boscovich has many spellings: the Croatian Boscovič, linked to his Dalmatian origin, becomes Boscowich in German. Ruggero Giuseppe Boscovich lived and worked in many cities: Rome, Pavia, Venice, Paris, London, Warsaw, Saint Petersburg and Constantinople, where he carried out diplomatic missions. He was a Jesuit and studied mathematics, physics, astronomy, geodesy, and cartography. His studies in geodesy and cartography were developed in Italy: he measured the meridian between Rome and Rimini, he worked on the new map of the Papal State and he designed the Brera Observatory. In the first part of the present work, we present Boscovich’s activities from a chronological point of view. In the second part, we focus on two specific arguments, related to geodesy and cartography: the new map of the Papal State and an attempt to rebuild the associated triangulation.
Click here for this article from NASA ADS.
Click here to download a PDF of this article from Memorie della Societa Astronomica Italiana.
Boscovich and the Brera Observatory
Article- 10 pages
- University level
A 2013 article by Elio Antonello of the Istituto Nazionale di Astrofisica – Osservatorio Astronomico di Brera in Italy, published in Memorie della Societa Astronomica Italiana Supplement, concerning the 18th-century Jesuit astronomer Roger Boscovich:
Abstract: In the mid 18th century both theoretical and practical astronomy were cultivated in Milan by Barnabites and Jesuits. In 1763 Boscovich was appointed to the chair of mathematics of the University of Pavia in the Duchy of Milan, and the following year he designed an observatory for the Jesuit Collegium of Brera in Milan. The Specola was built in 1765 and it became quickly one of the main european observatories. We discuss the relation between Boscovich and Brera in the framework of a short biography. An account is given of the initial research activity in the Specola, of the departure of Boscovich from Milan in 1773 and his coming back just before his death.
Click here for this article from NASA ADS.
Click here to download a PDF of this article from Memorie della Societa Astronomica Italiana.
Boscovich, the discovery of Uranus and his inclination to theoretical astronomy
Article- 8 pages
- University level
A 2013 article by L. Guzzardi, published in Memorie della Societa Astronomica Italiana Supplement, concerning the 18th-century Jesuit astronomer Roger Boscovich:
Abstract: On March 13th 1781 Frederick William Herschel observed a bizarre celestial body moving in the sky. Retrospectively, that astral body was not at all new at that point. It was observed by a number of astronomers since the end of 17th century (and maybe earlier). But they failed to find out its motion and catalogued it as a fixed star – each time a different one. On the other hand, Herschel realized it was moving, and catalogued it as a comet. That news of a new finding in the sky rapidly spread throughout Europe, and after some months the `Herschel’s comet’ was correctly recognized as a new planet, which will be named Uranus. The present paper assumes the event of the discovery of Uranus and the assessment of its planetary nature as a system of complicated, interrelated processes which involved a number of actors in the 17th-century astronomical community. In this framework, the role of the Dalmatian-born Jesuit scientist Ruggiero G. Boscovich is emphasized and the meaning of this discovery is discussed as an example of his interest in theoretical research more than in observational science.
Click here for this article from NASA ADS.
Click here to download a PDF of this article from Memorie della Societa Astronomica Italiana.
Copernicus and the “High Seas”
Article (blog post series)- 3600 words
- General audiences
In this series of posts, written for The Catholic Astronomer blog, Christopher Graney discusses “Two Spheres Theory” regarding the shape and composition of the Earth. The Two Spheres Theory was a medieval idea that came to be taken as scientific evidence for existence of, and direct action in the world of, God. However, the Two Spheres Theory was soundly disproven by, among other things, Christopher Columbus’s voyage to the lands now known as the Americas.
Click here to read Part II of this series.
Emilie Du Châtelet on the existence of God
- Article
- 6 pages
- High school level and above
Gabrielle Émilie Le Tonnelier de Breteuil, Marquise Du Châtelet, wrote, among other things, a translation and commentary on Isaac Newton’s Principia (published posthumously in 1759), and a physics textbook for her son, entitled Institutions de Physique (Foundations of Physics, published in 1740). The second chapter of this textbook was addressed to the question of God’s existence.
[Download PDF]
DuChatelet-On-Existence-God
Pope Benedict XIV – Benedict’s Patronage of Learned Women
Article (book chapter)- 20 pages
- University level
“Benedict’s Patronage of Learned Women”, by Marta Cavazza of the University of Bologna, is a chapter in Benedict XIV and the Enlightenment: Art, Science, and Spirituality, a collection of essays concerning the mid-eighteenth-century papacy of Benedict XIV (Prospero Lorenzo Lambertini), published by the University of Toronto Press. Cavazza writes:
[A] handful of women… received public recognition in eighteen-century Italy, especially in Bologna, for their philosophical [scientific], mathematical, and anatomical knowledge. The instigator and director of these events was in most cases Benedict XIV… [who] used his moral authority and his sovereign power to encourage and reward women who excelled in the fields of philosophy and medicine, helping them obtain public honours and academic positions that were reserved for men during that era… They became “a symbol of the successes of the Bolognese science” chiefly thanks to Benedict XIV’s patronage. The connection between the promotion of modern science and not only the recognition of the intellectual dignity of women, but also the legitimation of a role for them within cultural institutions (almost) equal to that of men, was undoubtedly one of the most original and progressive features of Pope Lambertini’s reformist engagement, an engagement carried on the the context of the brief season of the Catholic Enlightenment, not by chance coincident with his pontificate.
Click here for a preview of this article, courtesy of Google Books.
The Madras Observatory: from Jesuit cooperation to British rule
Article 1000 words General Audiences An article published in Aeon in 2017 by Blake Smith, a PhD candidate in history at Northwestern University in Illinois and the School for Advanced Studies in the Social Sciences in Paris. Click here to access this article directly from Aeon. The Madras Observatory offers little to the visitor’s eye. Stone slabs and broken pillars lie ignored in a fenced-off section of a local weather centre in the southern Indian city of Chennai. Few tourists venture out to see the ruins of the 18th-century complex. On the other side of the subcontinent, in northern Indian cities such as New Delhi, Varanasi and Jaipur, remains of the Jantar Mantars, vast astronomical stations, are far more popular attractions. Built in the same century as the Madras Observatory, their stark geometric structures, with looming proportions and vibrant colours, make for mandatory stops on travellers’ itineraries. Yet it is the Madras Observatory, and not the spectacular Jantar Mantars, that … Continue reading →
Laura Maria Caterina Bassi of Bologna
Articles (two)- 29 pages; 32 pages
- High school level and above
Laura Maria Caterina Bassi (1711-1778) of Bologna, Italy is often identified as being the first woman to earn a doctoral degree and the first to be a university professor (where she eventually became the highest paid member of the faculty). Bassi showed great talent when she was young, and became something of a celebrity in Bologna when she earned her first degree. She was awarded a position at the University of Bologna that was somewhat honorary, but managed to eventually turn that into a full position as professor of physics. Bologna’s Archbishop, Prospero Lambertini, supported Bassi (and encouraged other women to pursue higher education in science)—support that became more valuable as Lambertini became Cardinal and then Pope Benedict XIV. Bassi’s drive and persistence is reflected in the words of someone involved in considering her request to be made a professor:
finally to satisfy, if one ever can, the demands of Signora Laura Bassi who, although she has no right to be admitted among the Professors of the Institute, nevertheless has asked for this well over three Years, having nurtured some hope of this more than once…. she is a celebrated Woman known to the entire Republic of Letters, who truly brings great honor to her Patria, thus it seems that [her request] merits benign attention.
Laura Bassi accomplished her work in the realm of science while also being a wife, and mother of eight children (some sources report twelve children).
The following two articles are available electronically via JSTOR—many libraries provide free access to services, such as JSTOR, that can be used to download the full text of these papers:
Click here to access “Science as a Career in Enlightenment Italy: The Strategies of Laura Bassi,” by Paula Findlen (Isis: Journal of the History of Science Society, 1993, vol. 84, pg. 441-469). This article contains illustrations and focuses primarily on Bassi and her life.
Click here to access “The Desire to Contribute: An Eighteenth-Century Italian Woman of Science,” by Gabriella Berti Logan (American Historical Review, June 1994, pg. 785-812). This article has a stronger focus on Bassi’s scientific work.
Boscovich – his geodetic and cartographic studies
- Article
- 8 pages
- High school level and above
A heavily illustrated 2013 article by B. Crippa, V. Forcella, and L. Mussio, published in Memorie della Societa Astronomica Italiana Supplement, concerning the 18th-century Jesuit astronomer Roger Boscovich:
Abstract: The name of Ruggero Giuseppe Boscovich has many spellings: the Croatian Boscovič, linked to his Dalmatian origin, becomes Boscowich in German. Ruggero Giuseppe Boscovich lived and worked in many cities: Rome, Pavia, Venice, Paris, London, Warsaw, Saint Petersburg and Constantinople, where he carried out diplomatic missions. He was a Jesuit and studied mathematics, physics, astronomy, geodesy, and cartography. His studies in geodesy and cartography were developed in Italy: he measured the meridian between Rome and Rimini, he worked on the new map of the Papal State and he designed the Brera Observatory. In the first part of the present work, we present Boscovich’s activities from a chronological point of view. In the second part, we focus on two specific arguments, related to geodesy and cartography: the new map of the Papal State and an attempt to rebuild the associated triangulation.
Click here for this article from NASA ADS.
Click here to download a PDF of this article from Memorie della Societa Astronomica Italiana.
Searching the Heavens and the Earth: The History of Jesuit Observatories [with book reviews]
Book- 369 pages
- University level
Searching the Heavens and the Earth: The History of Jesuit Observatories, is a 2003 book by Agustín Udías, S. J. of the Department of Geophysics and Meteorology, Universidad Complutenese (Madrid, Spain). From the publisher:
Jesuits established a large number of astronomical, geophysical and meteorological observatories during the 17th and 18th centuries and again during the 19th and 20th centuries throughout the world. The history of these observatories has never been published in a complete form. Many early European astronomical observatories were established in Jesuit colleges.
During the 17th and 18th centuries Jesuits were the first western scientists to enter into contact with China and India. It was through them that western astronomy was first introduced in these countries. They made early astronomical observations in India and China and they directed for 150 years the Imperial Observatory of Beijing.
In the 19th and 20th centuries a new set of observatories were established. Besides astronomy these now included meteorology and geophysics. Jesuits established some of the earliest observatories in Africa, South America and the Far East.
Jesuit observatories constitute an often forgotten chapter of the history of these sciences.
Click here for more information, including a brief preview, from the publisher (Springer).
Click here for a substantial preview from Google Books.
Below are two reviews of this book by astronomers with the Vatican Observatory:
- Book review by Fr. Sabinao Maffeo, S. J., in the Journal for the History of Astronomy, 2005 (PDF, courtesy of NASA ADS).
- Book review by Br. Guy Consolmagno, S. J., in the Archivum Historicum Societatis Iesu, 2007 (PDF).
Copernicus and the “High Seas”
- Article (blog post series)
- 3600 words
- General audiences
In this series of posts, written for The Catholic Astronomer blog, Christopher Graney discusses “Two Spheres Theory” regarding the shape and composition of the Earth. The Two Spheres Theory was a medieval idea that came to be taken as scientific evidence for existence of, and direct action in the world of, God. However, the Two Spheres Theory was soundly disproven by, among other things, Christopher Columbus’s voyage to the lands now known as the Americas.
Click here to read Part II of this series.
Boscovich and the Brera Observatory
- Article
- 10 pages
- University level
A 2013 article by Elio Antonello of the Istituto Nazionale di Astrofisica – Osservatorio Astronomico di Brera in Italy, published in Memorie della Societa Astronomica Italiana Supplement, concerning the 18th-century Jesuit astronomer Roger Boscovich:
Abstract: In the mid 18th century both theoretical and practical astronomy were cultivated in Milan by Barnabites and Jesuits. In 1763 Boscovich was appointed to the chair of mathematics of the University of Pavia in the Duchy of Milan, and the following year he designed an observatory for the Jesuit Collegium of Brera in Milan. The Specola was built in 1765 and it became quickly one of the main european observatories. We discuss the relation between Boscovich and Brera in the framework of a short biography. An account is given of the initial research activity in the Specola, of the departure of Boscovich from Milan in 1773 and his coming back just before his death.
Click here for this article from NASA ADS.
Click here to download a PDF of this article from Memorie della Societa Astronomica Italiana.
Boscovich, the discovery of Uranus and his inclination to theoretical astronomy
- Article
- 8 pages
- University level
A 2013 article by L. Guzzardi, published in Memorie della Societa Astronomica Italiana Supplement, concerning the 18th-century Jesuit astronomer Roger Boscovich:
Abstract: On March 13th 1781 Frederick William Herschel observed a bizarre celestial body moving in the sky. Retrospectively, that astral body was not at all new at that point. It was observed by a number of astronomers since the end of 17th century (and maybe earlier). But they failed to find out its motion and catalogued it as a fixed star – each time a different one. On the other hand, Herschel realized it was moving, and catalogued it as a comet. That news of a new finding in the sky rapidly spread throughout Europe, and after some months the `Herschel’s comet’ was correctly recognized as a new planet, which will be named Uranus. The present paper assumes the event of the discovery of Uranus and the assessment of its planetary nature as a system of complicated, interrelated processes which involved a number of actors in the 17th-century astronomical community. In this framework, the role of the Dalmatian-born Jesuit scientist Ruggiero G. Boscovich is emphasized and the meaning of this discovery is discussed as an example of his interest in theoretical research more than in observational science.
Click here for this article from NASA ADS.
Click here to download a PDF of this article from Memorie della Societa Astronomica Italiana.
Jesuit Science
- Article and Video
- 750 words (article), 1 hour (video)
- General audiences
Br. Guy Consolmagno, S. J., an astronomer with the Vatican Observatory, discusses Jesuits and their many contributions to science in an article and in a talk (on video). Br. Consolmagno notes:
A Jesuit scientist, supported by the order, is often not tied to a three-year funding cycle or six-year tenure review. Thus we have the time – it may take decades – to catalogue double stars, seismic velocities, or patterns in climate or terrestrial magnetic fields. Jesuits, for instance, invented the basic taxonomy of the plants of India. But this sort of science often meant that their work was unappreciated by their immediate peers. Famously in the 19th century the Whig historian and politician Thomas Macaulay sneered that the Jesuits “appear to have discovered the precise point to which intellectual culture can be carried without risk of intellectual emancipation” and that being a Jesuit “has a tendency to suffocate, rather than to develop, original genius.”
Tradition and Today: Religion and Science
- Article (PDF)
- 12 pages
- University and higher level
Fr. George V. Coyne, S. J., Director of the Vatican Observatory from 1978 to 2006, presents four case histories which indicate that the relationship between religion and science has, in the course of three centuries, passed from one of conflict to one of compatible openness and dialogue, to show that the natural sciences have played a significant role in helping to establish the kind of dialogue that is absolutely necessary for the enrichment of the multifaceted aspects of human culture, whether traditional or modern. He argues that the approach of science to religion in each of these periods can be characterized respectively as: (l) temptress, (2) antagonist, (3) enlightened teacher, (4) partner in dialogue.
[Download PDF]
Sci-Rel_4_epochs
A Serious Meditation – from Benjamin Banneker’s 1793 Almanac
- Article
- 390 words
- General audiences
A discussion of a Christian’s duty, from the 1793 almanac published by the self-taught American astronomer Benjamin Banneker of Baltimore County, Maryland.
[Download PDF]Banneker-MEDITATION
Click here to access Banneker’s 1793 almanac, courtesy of the Smithsonian.
Emilie Du Châtelet on the existence of God
- Article
- 6 pages
- High school level and above
Gabrielle Émilie Le Tonnelier de Breteuil, Marquise Du Châtelet, wrote, among other things, a translation and commentary on Isaac Newton’s Principia (published posthumously in 1759), and a physics textbook for her son, entitled Institutions de Physique (Foundations of Physics, published in 1740). The second chapter of this textbook was addressed to the question of God’s existence.
[Download PDF]
DuChatelet-On-Existence-God
Isaac Newton – Two books relating to religion
Books (two)- 376 pages;
- University level
Isaac Newton, one of the most prominent scientific figures in history, is often said to have written more about theology than about mathematics and physics. However, his views on the nature of God were unorthodox, and much of what he wrote regarding matters relating to religion was never published. However, his Chronology of Ancient Kingdoms was published in 1728. It contains material such as Newton’s diagram of the Temple of Solomon, shown here. Newton’s Observations upon the Prophecies of Daniel and the Apocalypse of St. John, was published posthumously in 1733 and is another example of Newton’s writing on matters relating to religion.
Click here for Chronology, courtesy of Erara.
Click here for Observations, courtesy of Archive.org
Book: The Cambridge Concise History of Astronomy
- Book
- 380 pages
- High school students and above
As suggested by our research team. This description is from the publisher:
Astronomy is one of the oldest sciences, and one which has repeatedly led to fundamental changes in our view of the world. This book covers the history of our study of the cosmos from prehistory through to a survey of modern astronomy and astrophysics (sure to be of interest to future historians of twentieth-century astronomy). It does not attempt to cover everything, but deliberately concentrates on the important themes and topics. These include stellar astronomy in the seventeenth and eighteenth centuries, at the time subordinate to the study of the solar system, but the source of many important concepts in modern astronomy, and the Copernican revolution, which led to the challenge of ancient authorities in many areas, not just astronomy. This is an essential text for students of the history of science and for students of astronomy who require a historical background to their studies.
Click here for Table of Contents from Cambridge University Press.
Click here for an excerpt from Cambridge University Press.
Click here for a preview from Google Books.
Isaac Newton – The ‘General Scholium’ of the Principia
Book chapter- 5 pages
- University level
Isaac Newton, for his Mathematical Principles of Natural Philosophy, arguably the most important work of science ever produced (first published in 1687), wrote a ‘General Scholium’ which discusses the solar system and the physics behind the solar system as the work of God. Newton is often said to have written more about theology than about mathematics and physics, although his views on the nature of God were unorthodox and much of what he wrote regarding matters relating to religion was never published. From the ‘General Scholium’:
This most beautiful System of the Sun, Planets, and Comets, could only proceed from the counsel and dominion of an intelligent and powerful being. And if the fixed Stars are the centers of other like systems, these, being form’d by the like wise counsel, must be all subject to the dominion of One; especially since the light of the fixed Stars is of the same nature with the light of the Sun, and from every system light passes into all the other systems. And lest the systems of the fixed Stars should, by their gravity, fall on each other mutually, he hath placed those Systems at immense distances from one another.
This Being governs all things, not as the soul of the world, but as Lord over all: And on account of his dominion he is wont to be called Lord God παντοκράτωρ [Pantokrator], or Universal Ruler. For God is a relative word, and has a respect to servants; and Deity is the dominion of God, not over his own body, as those imagine who fancy God to be the soul of the world, but over servants. The supreme God is a Being eternal, infinite, absolutely perfect; but a being, however perfect, without dominion, cannot be said to be Lord God; for we say, my God, your God, the God of Israel, the God of Gods, and Lord of Lords; but we do not say, my Eternal, your Eternal, the Eternal of Israel, the Eternal of Gods; we do not say, my Infinite, or my Perfect: These are titles which have no respect to servants. The word God usually signifies Lord; but every lord is not a God. It is the dominion of a spiritual being which constitutes a God; a true, supreme, or imaginary dominion makes a true, supreme, or imaginary God. And from his true dominion it follows that the true God is a Living, Intelligent, and Powerful Being; and, from his other perfections, that he is Supreme or most Perfect. He is Eternal and Infinite, Omnipotent and Omniscient; that is, his duration reaches from Eternity to Eternity; his presence from Infinity to Infinity; he governs all things, and knows all things that are or can be done. He is not Eternity and Infinity, but Eternal and Infinite; he is not Duration and Space, but he endures and is present. He endures forever, and is every where present; and, by existing always and every where, he constitutes Duration and Space.
Telescopes: Through the Looking Glass
Book- 234 pages
- General audiences
This book by Marvin Bolt was published in 2009, the year of the 400th anniversary of Galileo’s use of the telescope. It provides a readable history of the telescope by way of highlighting items that are on exhibit in the “Telescopes: Through the Looking Glass” exhibit at the Adler Planetarium in Chicago. Scattered throughout this beautifully illustrated book can be found references to the works of various clerics, such as Bartholomaeus Anglicus (1203-1274), Ferdinand Verbiest (1623-1688), Francesco Bianchini (1662-1729), and others. Those planning a visit to the Adler might enjoy a look through this book in advance.
From the publisher, Adler Planetarium:
Through the Looking Glass celebrates the 400th anniversary of the telescope and the 2009 International Year of Astronomy. This exhibition catalogue focuses on ninety-nine artifacts from the Adler Planetarium’s world-class collection of historic telescopes. From the simple lenses of the world’s earliest telescopes 400 years ago to the complex computer-driven mirrors of current telescopes, these tools have gathered information about our nearest astronomical neighbors and the most distant objects in the universe. Through the Looking Glass examines this story through select rare books, works on paper, telescopes, and other instruments from the Adler Planetarium’s collection. Introductory paragraphs provide background information for each of four time periods, with each section featuring artifact entries that describe each object’s place in the fascinating history of the telescope. Telescope-makers intended for their work to be looked at as well as looked through. With this catalogue, readers can enjoy the craftsmanship of telescope-making over the centuries, and catch a glimpse of their importance and of the significant discoveries they enabled.
Click here for a preview of Telescopes: Through the Looking Glass.
Adler Planetarium website for the exhibit entitled “Telescopes: Through the Looking Glass”—click here.
George Berkeley – The Analyst; The Defence of Free-Thinking in Mathematics
Books (two)- 94 pages; 70 pages
- University level with knowledge of Calculus
George Berkeley’s 1734 The Analyst; or, A Discourse Addressed to an Infidel Mathematician criticizes how mathematicians thought regarding the “Method of Fluxions” (in modern terms, “Calculus”) of Isaac Newton, especially when some of those mathematicians were “infidels” (atheists) who criticized theological thought. Thus the title page of The Analyst quotes the Book of Matthew: “First cast out the beam out of thine own Eye; and then shalt thou see clearly to cast out the mote out of thy brother’s eye [7:5, KJV].”
Berkeley, a bishop in the Church of Ireland, acknowledges that Fluxions is “the general Key, by help whereof the modern Mathematicians unlock the secrets of Geometry, and consequently of Nature…. [and] that which hath enabled them so remarkably to outgo the Ancients in discovering Theorems and solving Problems….” However, Fluxions relies on concepts of infinity, applied repeatedly, and “to conceive a Quantity infinitely small… is, I confess, above my Capacity. But to conceive a Part of such infinitely small Quantity, that shall be still infinitely less than it… is, I suspect, an infinite Difficulty to any Man whatsoever….”
A major point of Berkeley’s is the idea of a second or third or fourth fluxion—called today a second, third, or fourth derivative. A derivative is a slope at some certain point—a point being infinitesimal in nature. Berkeley raises the conceptual problem of a slope within that slope, and then within that, and so on? Such things, he says, are nevertheless accepted by the same people who demand rigorous evidence in theology, and who claim to only believe what evidence they can see:
He who can digest a second or third Fluxion, a second or third Difference, need not, methinks, be squeamish about any Point in Divinity…. [W]ith what appearance of Reason shall any Man presume to say, that Mysteries may not be Objects of Faith, at the same time that he himself admits such obscure Mysteries to be the Object of Science?
Thus Berkeley argues that atheist mathematicians, who are so particular about points of religion, are more lax about their own field, submitting to authority, taking things on trust, and believing things that cannot be seen and mysteries that cannot be conceived. They have obstructions in their own eyes that they should look to cast out.
Berkeley’s 1735 A Defence of Free-Thinking in Mathematics responds to criticism of The Analyst. Berkeley emphasizes his interest in Truth, as he sees it, as opposed to the interest in Authority of the Infidel/atheist Mathematician. He asserts that the issue is not whether the “Method of Fluxions” is functionally useful, but whether the concepts in it are conceivable and solid, or whether mathematicians essentially accept it on faith based in its usefulness and in the reputation of Newton. Berkeley writes:
There are too many that deride Mysteries, and yet admire Fluxions; who yield that Faith to a mere Mortal, which they deny to Jesus Christ, whose Religion they make it their Study and Business to discredit…. I endeavour to shew, that such Men are defective in Point of Reason and Judgment, and that they do the very Thing they would seem to despise.
Stephen Mason, in his 1962 A History of the Sciences, credits Berkeley’s work with stimulating British mathematicians to inquire into the logical foundations of Calculus, and to place it upon a more secure foundation.
Click here to read The Analyst, courtesy of Archive.org.
Click here to read a 1901 re-publication of The Analyst, courtesy of Google Books.
Click here to read Defence, courtesy of Erara.
Click here to read a 1901 re-publication of Defence, courtesy of Google Books.
Newton’s Apple and Other Myths about Science
- Book
- 304 pages
- High school level and above
This 2015 book, published by Harvard University Press (HUP) and edited in part by Ronald Numbers, is a follow-up to the 2009 book Galileo Goes to Jail and Other Myths about Science and Religion which was also published by HUP and edited by Numbers. From HUP:
A falling apple inspired Isaac Newton’s insight into the law of gravity—or so the story goes. Is it true? Perhaps not. But the more intriguing question is why such stories endure as explanations of how science happens. Newton’s Apple and Other Myths about Science brushes away popular misconceptions to provide a clearer picture of great scientific breakthroughs from ancient times to the present. Among the myths refuted in this volume is the idea that no science was done in the Dark Ages, that alchemy and astrology were purely superstitious pursuits, that fear of public reaction alone led Darwin to delay publishing his theory of evolution, and that Gregor Mendel was far ahead of his time as a pioneer of genetics. Several twentieth-century myths about particle physics, Einstein’s theory of relativity, and more are discredited here as well. In addition, a number of broad generalizations about science go under the microscope of history: the notion that religion impeded science, that scientists typically adhere to a codified “scientific method,” and that a bright line can be drawn between legitimate science and pseudoscience. Edited by Ronald Numbers and Kostas Kampourakis, Newton’s Apple and Other Myths about Science debunks the widespread belief that science advances when individual geniuses experience “Eureka!” moments and suddenly comprehend what those around them could never imagine. Science has always been a cooperative enterprise of dedicated, fallible human beings, for whom context, collaboration, and sheer good luck are the essential elements of discovery.
Click here for additional information from the publisher.
Click here for a preview from Google Books.
Galileo Goes to Jail and Other Myths about Science and Religion
- Book
- 320 pages
- High school level and above
This 2009 book, edited by Ronald Numbers, contains much that will be of interest to many readers. From the publisher, Harvard University Press:
If we want nonscientists and opinion-makers in the press, the lab, and the pulpit to take a fresh look at the relationship between science and religion, Ronald L. Numbers suggests that we must first dispense with the hoary myths that have masqueraded too long as historical truths. Until about the 1970s, the dominant narrative in the history of science had long been that of science triumphant, and science at war with religion. But a new generation of historians both of science and of the church began to examine episodes in the history of science and religion through the values and knowledge of the actors themselves. Now Ronald Numbers has recruited the leading scholars in this new history of science to puncture the myths, from Galileo’s incarceration to Darwin’s deathbed conversion to Einstein’s belief in a personal God who “didn’t play dice with the universe.” The picture of science and religion at each other’s throats persists in mainstream media and scholarly journals, but each chapter in Galileo Goes to Jail shows how much we have to gain by seeing beyond the myths.
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Pope Benedict XIV – Benedict’s Patronage of Learned Women
- Article (book chapter)
- 20 pages
- University level
“Benedict’s Patronage of Learned Women”, by Marta Cavazza of the University of Bologna, is a chapter in Benedict XIV and the Enlightenment: Art, Science, and Spirituality, a collection of essays concerning the mid-eighteenth-century papacy of Benedict XIV (Prospero Lorenzo Lambertini), published by the University of Toronto Press. Cavazza writes:
[A] handful of women… received public recognition in eighteen-century Italy, especially in Bologna, for their philosophical [scientific], mathematical, and anatomical knowledge. The instigator and director of these events was in most cases Benedict XIV… [who] used his moral authority and his sovereign power to encourage and reward women who excelled in the fields of philosophy and medicine, helping them obtain public honours and academic positions that were reserved for men during that era… They became “a symbol of the successes of the Bolognese science” chiefly thanks to Benedict XIV’s patronage. The connection between the promotion of modern science and not only the recognition of the intellectual dignity of women, but also the legitimation of a role for them within cultural institutions (almost) equal to that of men, was undoubtedly one of the most original and progressive features of Pope Lambertini’s reformist engagement, an engagement carried on the the context of the brief season of the Catholic Enlightenment, not by chance coincident with his pontificate.
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