Johannes Stöffler: Reformational Astrology and the Gregorian Calendar


On 16 February 1531, Johannes Stöffler (1452–1531) passed away in Tübingen, Germany. Educated at the Blaubeuren Monastery school and at the University of Ingolstadt, he was a German instrument-builder, astrologer, mathematician, and priest. His published works included Almanach (1499), Elucidatio fabricae ususque astrolabii (1512), Astrolabiumsschrift (1513), Tabulae astronomicae (1514), Calendarium Romanum magnum (1518), Ephemeriden (1531), Commentary on the Sphaera of pseudo-Proclus (posthumous, 1534). He was buried in Collegiate Church (Stiftskirche) in Tübingen.

From the compendium Geographers: Biobibliographical Studies (Ed. T.W. Freeman, 2015):

“[D]uring his work as a clergyman, even with his additional duties later as the dean of the national chapter of Ehingen, he used well, true to his status as a private scholar, to undertake intensive mathematical studies and research. He performed astronomical observations of his own and calculated, on the basis of Ptolemy’s world conception, the daily planetary constellations including the sun and the moon, for a period of over thirty years in advance (1499–1531); in his own workshop he made several celestial globes, in all probability one terrestrial globe, and also sundials and excellent mechanical astronomical clocks. By these feats he achieved, in the course of approximately twenty years, the qualifications of a major authority in the mathematical/astronomical field.

“Stöffler saw himself primarily as a Christian astrologer… His astrological researches led him to turn away from ancient traditions and brought him to a view of the reality, indeed the validity, of his own standpoint. Stöffler went beyond astrology to become a mathematical astronomer. By patient calculations he uncovered the reasons for the mistakes of the ancient Church that caused the controversy about Easter. Though anxious to avoid conflict with ecclesiastical authorities, he developed principles for a new determination of the date of Easter. When in 1582 Pope Gregory XIII finally accomplished the overdue reformation of the calendar, Stöffler’s research was a decisive influence on all essential points. Stöffler’s geography can be understood, to a great extent, in the light of astrology. Since the latter, besides depending on the celestial movements, also requires the knowledge of longitudinal/temporal differentials he could not avoid dealing with the determination of geographical coordinates by astronomical measurement… In principle, like Ptolemy, he contended that it was the mission of geographia to portray the world as far as it is inhabited or known.

“Stöffler remained linked to the classical world concept, in all scientific ideas and, as an eminent astronomer, astrologer and geographer, he accomplished a great deal, though of a nature (as least in geography) that still glorified Antiquity, in spite of considerable corrections and critical comments. Nevertheless he promoted (mainly through his students) the development of geography to a level that would not have been possible without his efforts… By his outlook on the Maker’s works in Creation, he had probably personally endowed Melanchthon with the natural piety that later became the germ of the latter’s own theologically (in effect Lutheran) orientated geography.

“When Stöffler’s influence as a geographer, with the fading concept of the geocentric world concept, declined, even though his accomplishments in geography, astrology and calendar-making were still appreciated, he disappeared from the memory of the geographical world … As one of the leading geographers of his era, this unassuming scientist from Tübingen is still waiting for a more just appreciation of his merits.

—Hoheisel, Karl. “Johannes Stöffler (1452–1531).” in Geographers: Biobibliographical Studies. Vol. 12. Ed. Thomas Walter Freeman. (London, UK: Bloomsbury Publishing, 2015), 123-124; 125-126.
Images: Deutsche FotothekHimmelsglobus by Johannes Stöffler (1493); Landesmuseum Württemberg, Stuttgart.


Fr. Roger Joseph Boscovich: Quantum Theory


boscovich 1

On 13 February 1787, Fr. Roger Joseph Boscovich (1711–1787) passed away in Milan, Italy. Educated at the Collegium Romanum (1740), he was a Croatian mathematician, physicist, astronomer, philosopher, theologian, poet, and diplomat. The Boscovich crater on the moon is named in his honor. His theory of atomic resonant modes in discrete quanta was influential in the development of modern QM theory.

Both Lord Kelvin in Lectures on Molecular Dynamics and the Theory of Light (1904) and J.J. Thomson in The Corpuscular Theory of Matter (1907) made reference to the atomic theory of Boscovich; these are full text books on google.books:

Fr. Boscovich in Lord Kelvin’s book (1904):
Fr. Boscovich in J.J. Thomson’s book (1907):

Around the time that J.J. Thomson had deduced the charge/mass ratio of the electron and outlined the +/- “plum pudding atomic model,” his lab was joined by Fr. Henry Vincent Gill, SJ (1872–1945), a Jesuit who had completed his masters of physics degree at the Catholic University of Louvain in the 1890s and took up residence at Cavendish Lab from 1906 to 1908. Quote: “The son of H.J. Gill, head of the publishing firm, M. H. Gill & Son, Henry was educated at Clongowes Wood College and University College Dublin. He possessed an acumen for mathematics and science and studied in Louvain and under Professor J.J. Thompson, Cavendish Laboratories, Cambridge (1906-1908). Fr. Gill had a special interest in seismography: ‘Experiments with Spinning Tops to Illustrate Earthquake Reactions’ was the title of a lecture given by Henry Gill at the Cavendish Laboratory, 16 June 1908.”

An article in the The Mathematics Teacher 61:2 (1968), pp. 167-175, argues how Fr. Gill’s later work on the history of science was foundational to the interpretation of Thomson’s early experiments. Specifically, Fr. Gill’s writings on the historical development of atomic theory and the work Fr. Roger Boscovich SJ, a book Fr. Gill asserted had exerted a definitive influence on the atomic view of matter as being composed of points in a vacuum, interacting via forces comparable to quantized modes (normal eigenmodes) of a compressible spring.

Another source states: “Therefore, bearing in mind that in the period 1903-1907 ‘J.J. Thomson deducted his hypothesis directly from the Theory and curve of Boscovich, and showed that the notion of ‘allowed’ and ‘forbidden’ orbits follows from it,’ Gill points out that Boscovich made an ‘essential element of the modern concept of the atom’ and ‘where Boscovich planted two hundred years ago others have reaped.’ Hence, Gill called this model ‘The Boscovich-Thomson’ atom and indicates that ‘when the history of atomic theory is being written, it is right that the part played by Father Roger Boscovich should not be overlooked.’”

Irish Jesuits Album. “Fr. Henry Gill S.J., M.C., D.S.O.” Acct:
Fitzpatrick, Mary M., and Antonietta Fitzpatrick. “Roger Joseph Boscovich Forerunner of Modern Atomic Theory.” The Mathematics Teacher (1968): 167-175.
Stoiljkovich, Dragoslav. Roger Boscovich: The Founder of Modern Science. Trans. Roger Anderton (Petnica, Serbia: Petnica Science Center, 2010), 4-4.

Lawrence Joseph Henderson – Anthropic Principle: Cosmos Created for Human Life (‘Anthropos’)


lawrence joseph henderson 2.jpg

On 10 February 1942, Lawrence Joseph Henderson (1878–1942) passed away in Cambridge, MA.

Educated at Harvard Medical School (MD, 1902), he was known for the Henderson–Hasselbalch equation (pH = pKₐ + log₁₀ ([A]/[HA])), which is used to calculate the pH of a buffered solution. The standard Henderson–Hasselbalch equation for the pH of a one-buffer solution can be generalized for ≥2 buffers, viz. pH = pKₐ + log₁₀ ([A]/[HA]) (one buffer); pH = pKₐ + log₁₀ ([CB] / ([CA]-[CB]) ) (two buffers).

lawrence joseph henderson books

Prof. Henderson had also authored several texts on the philosophical and scientific basis of the anthropic principle, including The Fitness of the Environment (1913) and The Order of Nature (1917). The first of these texts had included quoted passages on the theological views of William Whewell (1794–1866), Francis Bacon (1561–1626), Josiah Parsons Cooke (1827–1894), Henri-Louis Bergson (1859–1941) and others. It concluded with the reflection.

“The properties of matter and the course of cosmic evolution are now seen to be intimately related to the structure of the living being and to its activities; they become therefore, far more important in biology than has been previously suspected. For the whole evolutionary process, both cosmic and organic, is one, and the biologist may now rightly regard the universe in its very essence as biocentric.”

His Harvard University remembrance noted:

“…A member of the Faculties of Arts and Sciences and of Medicine as head of the Fatigue Laboratory, and as Chairman of the Society of Fellows, he exemplified that breadth of scholarship which overlaps artificial departmental barriers; and his work was animated by a consuming interest in the social implications of science and education. In the Society of Fellows, which brings together a group concerned with independent studies in a variety of fields, he found a congenial outlet for his catholic interest in scholarship and in young men seriously devoted to its pursuit.”

Righetti, Pier Giorgio. Immobilized pH gradients: Theory and Methodology. Vol. 3. (Amsterdam, NL: Elsevier, 1990), 55-56.
Henderson, Lawrence J. The Fitness of the Environment. (New York, NY: MacMillan Co., 1913), 312.
“Report of the President of Harvard College and Reports of Departments,” 1943 Edition. (Cambridge, MA: Harvard University Press, 1943), 26.
Image: Painting by Kenneth Frazier (1867–1949) (© Harvard Art Museum).

Claude Bernard: Common Ground for the Metaphysician, Scholastic & Experimentalist?


claude bernard

On 10 February 1878, Claude Bernard (1813–1878) passed away in Paris, France. Educated at University of Paris (MD, 1839), he was a French physiologist whose discoveries included: 1) that secretions of the pancreatic gland were involved in digestion; 2) the enzymatic function of the liver was to form ‘glycogen’ from blood glucose; and 3) the role of the vaso-motor system to regulate blood vessel dilation and contraction. During these researches, he also studied heat regulation in the body and invented the term “milieu intérieur,” now known as “homeostasis.”

A recent book notes: “Upon his death on February 10, 1878, Bernard received a state funeral – the first French scientist to be so honored. The procession ended at Pere Lachaise cemetery, and Gustave Flaubert described it later with a touch of irony as ‘religious and very beautiful.’ Bernard was an agnostic.” (J.G. Simmons, 2000)

Another article reports that, after his education at the Jesuit school of Villefranche, quote:

“he drifted into what would have been simple materialism only for the saving grace of his own utter sanity, his active imagination, and the unconscious influence of early training. During his most successful years of scientific investigation, wrapped up in his experiments and their suggestions, Bernard was drawn far away from the spiritual side of things. This partial view of man and nature could not endure, however. In an article on Bernard in the Revue des Questions scientifiques for April 1880, Father G. Hahn S.J., says of him: ‘A man of such uprightness of character could not be allowed to persist to the end in this restless scepticism. His mental condition was really a kind of vertigo caused by the depths of nature that he saw all around him. At the threshold of eternity he came back to his true self and his good sense triumphed. The great physiologist died a true Christian.’”

From an 1865 book by Claude Bernard.

“Man is by nature metaphysical and proud… Hence it follows that the experimental method is by no means primitive or natural to man, and that only after lengthy wanderings in theological and scholastic discussion has he recognized at last the sterility of his efforts in this direction…Yet for all that, the method of work of the human mind is not changed at bottom. The metaphysician, the scholastic, and the experimenter all work with an a priori idea. The difference is that the scholastic imposes his idea as an absolute truth which he has found, and from which he then deduces consequences by logic alone. The more modest experimenter, on the other hand, states an idea as a question, as an interpretative, more or less probable anticipation of nature, from which he logically deduces consequences which, moment by moment, he confronts with reality by means of experiment. He advanced, thus, from partial to more general truths, but without ever daring to assert that he has grasped the absolute truth.”

Simmons, John G. Doctors and Discoveries: Lives That Created Today’s Medicine. (Boston, MA: Houghton Mifflin Harcourt. 2000), 17.
Walsh, James J. “Claude Bernard: The Physiologist.” The Catholic World. Vol. LXXI, No. 424 (July, 1900), 525.
Bernard, Claude. An Introduction to the Study of Experimental Medicine. Trans. H.C. Greene. (New York, NY: Henry Schuman, 1865), 27. Full text at: Book cover:

G. H. Hardy: The Landscape of Mathematics


Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was a mathematician who contributed to number theory and mathematical analysis. He was also instrumental in bringing attention to the work of Srinivasa Ramanujan (1887–1920), an Indian mathematician who compiled nearly 3,900 results in mathematical identities and equations, many original and others new derivations of previously known results.

While Hardy had rejected his parents’ religion while an undergrad at Cambridge, he was recorded as having found some common ground with Ramanujan’s pantheistic beliefs:

“In 1914 Ramanujan arrived in England. So far as Hardy could detect (though in this respect I should not trust his insight far) Ramanujan, despite the difficulties of breaking the caste proscriptions, did not believe much in theological doctrine, except for a vague pantheistic benevolence, any more than Hardy did himself.

Later in life, he would also admit some of the strengths of the Christian religion.

“That lunch time, he had no leisure for eating: he was writing postcards (postcards and telegrams were his favourite means of communication) to each of his clerical friends. But in his war against God and God’s surrogates, victory was not all on one side. On a quiet and lovely May evening at Fenner’s, round about the same period, the chimes of six o’clock fell across the ground. ‘It’s rather unfortunate,’ said Hardy simply, ‘that some of the happiest hours of my life should have been spent within sound of a Roman Catholic church’.”

Some philosophical and theological reflections from his 1922 address to the British Association:

“A chair may be a collection of whirling atoms, or an idea in the mind of God. It is not my business to suggest that one account of it is obviously more plausible than the other. Whatever the merits of either of them may be, neither draws its inspiration from the suggestions of common-sense. Neither the philosophers, nor the physicists themselves, have ever put forward any very convincing account of what physical reality is, or of how the physicist passes, from the confused mass of fact or sensation with which he starts, to the construction of the objects which he classifies as real. We cannot be said, therefore, to know what the subject-matter of physics is; but this need not prevent us from understanding the task which a physicist is trying to perform. That, clearly, is to correlate the incoherent body of facts confronting him with some definite and orderly scheme of abstract relations, the kind of scheme, in short, which he can only borrow from mathematics.

“The function of a mathematician, then, is simply to observe the facts about his own hard and intricate system of reality, that astonishingly beautiful complex of logical relations which forms the subject-matter of his science, as if he were an explorer looking at a distant range of mountains, and to record the results of his observations in a series of maps, each of which is a branch of pure mathematics. Many of these maps have been completed, while in others, and these, naturally, the most interesting, there are vast uncharted regions. Some, it seems, have some relevance to the structure of the physical world, while others have no such tangible application. Among them there is perhaps none quite so fascinating, with quite the same astonishing contrasts of sharp outline and mysterious shade, as that which constitutes the theory of numbers.g.h. hardy 3

“The positive integers do not lie, like the logical foundations of mathematics, in the hardly visible distance, nor in the uncomfortably tangled foreground, like the immediate data of the physical world, but at a decent middle distance, where the outlines are clear and yet some element of mystery remains. There is no one so blind that he does not see them, and no one so sharp-sighted that his vision does not fail; they stand there a continual and inevitable challenge to the curiosity of every healthy mind. I have merely directed your attention for a moment to a few of the less immediately conspicuous features of the landscape, in the hope that I might sharpen your curiosity a little, and that some of you perhaps might feel tempted to walk a little nearer and take a rather closer view.”

—Hardy, Godfrey Harold. A Mathematician’s Apology. (Cambridge, GB: Cambridge University Press, 1992), 35, 21.
Hardy, Godfrey H. “The Theory of Numbers.” Nature 2759.110(1922): 381-385.
Image from the film: The Man Who Knew Infinity (Warner Bros., IFC Films, 2015).

Pope em. Benedict XVI on Creation


PB16 on creation 2013-02-06

On 06 February 2013, Pope Benedict XVI dedicated one of his last audiences to the topic of creation:

“But our question today is: in the age of science and technology, does it still make sense to speak of creation? How should we understand the Genesis narratives? The Bible is not intended as a natural science manual; its intention instead is to teach us the authentic and profound truth of things. The fundamental truth that the Genesis stories reveal to us is that the world is not a collection of contrasting forces, but has its origin and its stability in the Logos, in God’s eternal Reason, who continues to sustain the universe. There is a plan for the world that arises from this Reason, from the creating Spirit. Believing that such a reality is behind all this, illuminates every aspect of life and gives us the courage to face the adventure of life with confidence and hope.”

You can read the whole text here.

Oliver Heaviside: Justification of Faith



On 03 February 1925, Oliver Heaviside (1850–1925) passed away in Torquay, England. A significant physicist and mathematician, he is known for his re-formulation of Maxwell’s field equations in terms of electric and magnetic forces and energy flux, work adapting complex analysis to electrodynamics and a formulation of vector analysis.

Regarding Maxwell’s equations, one historian of physics notes (T. Bearden): “Maxwell’s vector equations taught in university are actually Heaviside’s truncated equations, and are only a simplified version of what Maxwell originally wrote…Maxwell’s original theory is 20 equations in 20 unknowns. The theory was later truncated by Maxwell himself on the insistence of his editor, and then particularly by Heaviside, Gibbs, and Hertz after Maxwell’s death.”

His text Electromagnetic Theory (originally published 1912) includes an interesting use of the Reformation-era theological concept of “justification by works.”

“The justification of faith is by work, for the process works. If it failed, then we should have to find some other way.”

…Perhaps this might give new meaning to the popular physics meme interpreting Genesis 1:

“And God said … ∯ E da = Q/εₒ; ∯ Bda = 0; ∮Eds = d/dt∯Bda; ∮Bds = μₒ∯Jda + εₒ,μₒ d/dt∮Eds … and there was light.”

“Maxwell-Heaviside theory of electrodynamics.” Tom Bearden Website.
Heaviside, Oliver. Electromagnetic Theory, Volume 3. (New York, NY: Cosimo Books, 2008), 219. Image: © OliverHeaviside(dot)com.