Jacob Bernoulli: Superimposing God’s View Onto Probabilities

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On 16 August 1705, Jacob Bernoulli (1655–1705) passed away at Basel, Switzerland. Working with his younger brother Johann Bernoulli (1667–1748) at the University of Basel, he was known as a founder of the calculus of variations (a method for evaluating the action integral dl = √(dx²+dy²) for a small variation y→y+δy with l → l+ 𝒪(δy²)→l). He also contributed solutions to the Bernoulli differential equation, i.e. y’+P(x)y=Q(x)yⁿ, and outlined a solution to the ‘law of large numbers’ result in probability theory (related to the central limit theorem).

Jacob Bernoulli had initially studied theology and began work in ministry. Against the wishes of his father, Nicolaus Bernoulli (1623–1708), he sought out opportunities to learn mathematics and astronomy while travelling throughout Europe during 1676 to 1682. His theological background, nonetheless, was essential to his later work in mathematics.

“Jacob Bernoulli developed his art of conjecturing or doctrine of chances with the understanding that God has designed the universe to follow natural laws or regularities and that we only use ideas of chance where we lack knowledge of the underlying causes — not that these underlying causes do not in fact exist. To God everything is known and certain. In Bernoulli’s view, the law of large numbers shows that over the long run the underlying regularities of nature will manifest themselves. Finally, Bernoulli’s particular use of algebra and of the properties of binomial expansions to prove the lemmas that form the core of his demonstration of the law of large numbers fit with this ‘God’s eye’ view of the universe, in which everything is immediate and there is no scope for ordering into what is mathematically prior or posterior. Thus Jacob Bernoulli’s ideas about God and the world combine with his reliance on algebra in proving the law of large numbers to explain what has seemed so problematic to critics like Hacking about Bernoulli’s intended interpretation of his law of large numbers: why he ‘assumed’ the existence of a ratio of cases in his proof of the law of large numbers and nevertheless believed that the proof justified the use of observed frequencies to discover such ratios to a close approximation.”

Referenced:
Sylla, Edith Dudley. “Jacob Bernoulli on Analysis, Synthesis, and the Law of Large Numbers.” in Analysis and Synthesis in Mathematics: History and Philosophy. Vol. 196. Eds. Michael Otte and Marco Panza.(New York, NY: Springer Science & Business Media, 1997), 80-81. Images: Painting by Niklaus Bernoulli (1662-1716)Chart online.

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Edith Stein on Theology, Philosophy and Natural Sciences

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edith stein 03Edith Stein most likely died on 09 August 1942.  Stein was among the principle exponents of phenomenology and a pupil of Edmund Husserl and Max Scheler. Her journey as a philosopher was joined to that of a believer when she converted from Judaism, and then atheism, to faith in Christ. She later became a Carmelite nun and took the name Teresa Benedicta of the Cross. Due to her Jewish background, during the Nazi persecutions she fled to Holland where she was captured in 1942 and deported to Auschwitz. She died that same year in a gas chamber. Pope John Paul II declared her a patron saint of Europe. Among her works are The Phenomenology of Husserl and the Philosophy of St. Thomas Aquinas (1929), Finite and Eternal Being: An Attempt to Ascend to the Meaning of Being (posthumously published in 1950), and The Science of the Cross (also posthumously published in 1950.

“Revelation does not, by any means, provide us with all the knowledge that we can and would like to assimilate; rather, it leaves us much latitude for rational inquiry. Yet we find here positive facts and norms resting on a firm foundation, and many errors in theory and practice could be averted if this scriptural source were thoroughly utilized. Rightly understood and employed, the theological and philosophical approaches are not in competition; rather, they complete and influence each other (Credo ut intelligam. Fides quaerens intellectum).

“The philosophizing mind is challenged to make the realities of faith as intelligible as possible. On the other hand , these realities protect the mind from error, and they answer certain questions concerning matters of faith which reason must leave undecided. This is true also of the positive sciences occupied with identifying natural data.” – Edith Stein (in: Essays On Woman (The Collected Works of Edith Stein Book 2) (English Edition))

Johann Bernoulli: Mathematics + Theology

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On 06 August 1667, Johann Bernoulli (1667–1748) was born in Basel, Switzerland.

Working with his older brother Jacob Bernoulli (1655–1705) at the University of Basel, he was among the first mathematicians who understood and contributed to the new infinitesimal calculus of Gottfried Wilhelm von Leibniz (1646–1716). Among the original contributions credited to Johann were: the first statement of L’Hôpital’s rule (lim[f(x)/g(x)] = lim[f'(x)/g'(x)]), the catenary equation solution (gravitational force applied to non-taut chain) and the brachistochrone problem (path of shortest descent between two points).

His work in mathematics had brought some opposition from both Cartesian philosophers and Calvinistic philosophers alike, to which Johann responded with a pamplet wherein he stated: “All my life I have professed my Reformed Christian belief, which I still do… [yet] he would have me pass for an unorthodox believer, a very heretic; indeed very wickedly he seeks to make me an abomination to the world, and to expose me to the vengeance of both the powers that be and the common people…”

A historian summarizes Johann Bernoulli’s theological views which enabled him to reconcile his faith with the discoveries he made in calculus:

By entangling math with divinity, implying that math and God were one, anyone who opposed one defied the other… God was the world’s greatest mathematician. As he examined the infinitely small, Johann was enraptured by the incredible, and both his imagination and philosophy widened, leading to his conclusion that ‘the omnipotence of God in the smallest of things is inexhaustible and infinite.’ Furthermore, he infused math with spirituality, associating the concept of the infinitely large with ‘the truly terrible number at which reason is silent and that appears to approach eternity, disappears into it and is nothing in comparison with eternity, which absorbs and devours all things, as if it were only one year, one month, one day, one single hour, one single minute, and this moment that is now past.’ Yet it was not merely one branch of math that was divine but all of it. The ‘universal eloquence of mathematics…penetrate[d] the essence of nature.’ Johann’s philosophical treatment of a scientific craft truly distinguishes his work from other 17th-century peers.”

A collection of letters between Johann Bernoulli and Leibniz was published as Commercium philosophicum et mathematicum in 1745. He was buried at Peterskirche (St. Peter’s Church) in Basel, Switzerland.

Referenced:
O’Connor, John J. and Roberson, Edmund F. “Johann Bernoulli.” The MacTutor History of Mathematics Archive.
Hoon, Callie Phui-Yen. “Johann Bernoulli: Calculus’s Éminence Grise.” Concord Review (2015): 35. Image: Portrait by Johann Rudolf Huber, circa 1740.

Christians are Anti-Science? or: Jesuit Astronomers

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35 moon craters

There are 35 moon craters (or even more!) that have been named to honor Jesuit scientists. These are the ones portrayed here on our blog:

We also provide information on two great companions of Matteo Ricci in the China mission, another Jesuit: Johann Adam Schall von Bell, SJ: Jesuit missionary who was appointed a Mandarin on the official Chinese calendar reform; and a convert to the Catholic faith: Xu “Paul” Guangqi: a governor, agricultural scientist and mathematician.

And there is more: a few days ago, we shared on facebook and twitter this image prepared by the Vatican Observatory astronomer Br. Bob Macke SJ on a selection of asteroids named for Jesuits:

The Vatican Observatory has a blog: https://www.vofoundation.org/blog/ and can be found on twitter under @VaticanObserv. 

Joseph LeConte: Evolution and its Relation to Religious Thought

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On 06 July 1901, Joseph LeConte (1823–1901) passed away at Yosemite Valley, CA.

After studying at Franklin College in Athens, GA, and the New York College of Physicians and Surgeons, NY, LeConte made his first expedition as a biologist with his cousin, John Lawrence LeConte (1825–1883), traveling over a thousand miles along the Upper Mississippi River in a birchbark canoe in 1844. This experience led him to study for a second graduate degree in the natural sciences, completed in 1851, under the guidance of notable American biologist Louis Agassiz (1807–1873) at Harvard University.

Teaching at the University of South Carolina during Civil War and encountering various hardships, he moved to the University of California, Berkeley in 1868, where he worked with John Muir (1838–1914) and helped establish the Sierra Club. His published works included scientific papers on geology and ecology, and the textbooks Elements of Geology (1878), Religion and Science (1874), and Evolution and its Relation to Religious Thought (1888).

“… evolution is the process by which the Divine plan is carried out. These two views, that which refers phenomena directly back to the primal intelligence, & that which refers them back to secondary & intermediate causes have always existed and will always exist. They do not exclude each other. They are two formulas for the same thing; the one the formula of religion, the other the formula of science. The one formula is an expression of the domain of faith, the other of the domain of knowledge…

“We see around us everywhere invariable laws. Now, intelligence in the presence of invariable laws, or acting through invariable laws, can attain results only by contrivance. It is impossible that there should be invariable laws without contrivance, or contrivance without invariable laws. We are hampered, conditioned, limited on every side, by the inviolable laws of Nature, and, in order to attain results, we are compelled to resort to indirect methods, to mechanical and other contrivances, in accordance with these laws… Now, Deity himself, if He acts by laws, must bring about results by what seem to us contrivances. Shall we then speak of Him, the unconditioned, as conditioned by the laws of Nature? With our limited faculties, we cannot do otherwise. We cannot speak of Him, we cannot even think of Him except under conditions. But, observe the difference betwixt Him and us, in this regard.

“These laws of Nature, which condition man, are external to him, and therefore, in the nature of a law of necessity. But, to the Deity, they are not external; they are the laws of his own being—they are the modes of operation of his own will, perfect, because He is perfect, invariable, because He is unchangeable. Thus, then, the laws of Nature are to Him not a law of necessity, but a law of freedom.”

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Georges Lemaitre – the Big Bang Cosmology and its metaphysical implications (II)

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This is the second of two part. You can read the first part here.

Lemaitre‘s Cosmology and Stephen Gould’s NOMA

NOMA stands for Non-Overlapping Magisteria, meaning that science and religion simply should not or do not overlap. Therefore, there is only one responsible level of explanation at a given time, either the scientific one, for example, when it comes to evolution, fossils, molecular genetics, or the religious one, which helps to understand what the meaning of life is, whether there is a soul, and Heaven. (This is of course simplistic). NOMA can be criticized, just because there are overlaps, especially when it comes to us humans: just that he can think about abstract concepts such as NOMA suggests that there is something that exceeds the purely materialistic sphere of science. While Christians complain that NOMA gives science too much competence (“it is always religion that has to give way”), Atheists see in NOMA a cheap excuse to introduce a bit of religion through the back door.

While NOMA wants to achieve a mere juxtaposition, that is not one of Lemaitre’s goals. He is concerned with the clear separation of the categories “physics” (meaning all scientifically detectable things) and “meta-physics”, and both categories (or levels) must not be blurred or mixed. He is firmly anchored in the Thomistic viewpoint, which distinguishes between the first cause (God) and the second causes (the creatures in the broadest sense), which act according to their inherent (and ultimately God-given) qualities and possibilities.

Lemaitre sees both categories simultaneously present:

“Physics does not exclude Providence. Nothing happens without its order or permission, even if this gentle action is not miraculous. Evolution, whether of the universe or of the living world, could be made at random by quantum leaps or mutations. Nevertheless, this chance has, from a superior point of view, been directed towards a goal. For us Christians, it was oriented towards the appearance of life. In what was done, there was life, intelligence and life was light in man and finally in humanity by the incarnation of the Man-God: the true light that illuminated our darkness.

Chance does not exclude Providence. Perhaps chance provides the strokes mysteriously actuated by Providence.” [5]

God’s providential actions will not be rendered superfluous or non-existent due to scientific insights. But Providence remains often hidden to us, similarly as God Himself remains “a hidden God”

“Truly, you are a God who hides himself” (Is 45:15)

God is hidden behind and in His creation. He is a “hidden God”, transcending all our knowledge and cognition. “Truly, you are a God who hides himself“, as we read in Isaiah [Is 45:15].  We will find this term and concept often in Lemaitre’s writings. Already in 1931, Lemaitre writes:

“I think that everyone who believes in a supreme being supporting every being and every acting, believes also that God is essentially hidden and may be glad to see how present physics provides a veil hiding the creation”.

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Peter Guthrie Tait: Unseen Universe

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On 04 July 1901, Peter Guthrie Tait (1831–1901) died. He was a mathematical physicist known for his research on ‘knot theory’ and graph theory (Tait’s disproven conjecture stated that every 3-connected planar cubic graph had a path that passed through each vertex point only once), as well as additional mathematical research on quaternions, a number system that extends the complex number into three dimensions. These are defined as:tait 1

with the property:

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Many years later (1924), it was found in quantum mechanics that the spin state of electrons depends on the properties of quaternions. This research was published by Wolfgang Ernst Pauli (1900–1958).

Tait also researched the properties of the ozone layer and diatomic molecules in the presence of electrical discharge. He was the author of Elementary Treatise on Quaternions (1867), Treatise on Natural Philosophy, co-authored with Lord Kelvin (1824–1907) and Introduction to Quaternions (1873).

His book, The Unseen Universe: Or, Physical Speculations on a Future State (1875), co-authored with Balfour Stewart (1828–1887), had evinced his belief in the infinite divisibility of the continuum—“Indeed we are entire believers in the infinite depth of nature… To our minds it appears no less false to pronounce eternal that aggregation we call the atom, than it would be to pronounce eternal that aggregation we call the Sun. All this follows from the principle of Continuity, in virtue of which we make scientific progress in the knowledge of things and which leads us, whatever state of things we contemplate, to look for its antecedent in some previous state of things also in the Universe.” The quoted text above is from pages xiv-xv.

Referenced:
Stewart, Balfour and P.G. Tait. The Unseen Universe: Or, Physical Speculations on a Future State. (London, GB: MacMillan & Co., 1875), xiv-xv. Image: ART UK, Cambridge.