Bertram Brockhouse: Moral Implications of Material World


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On 13 October 2003, Bertram Brockhouse (1918 –2003) passed away in Hamilton, Ontario, Canada. He was co-awarded the 1994 Nobel Prize in Physics with Clifford Shull (1915–2001) “for pioneering contributions to the development of neutron scattering techniques for studies of condensed matter,” in particular “for the development of neutron spectroscopy.”

Prof. Brockhouse had thematically framed his Nobel Lecture around the conflict between whether physics was restricted to only a pragmatic materialism, or whether it allowed moral metaphors.

“The Grand Atlas comprises ‘maps’ of the world we live in, metaphorical maps which just might prove to be metaphysical, maps that link percepts with other percepts, by means of theory. On a pragmatic view, as on a religious view, theory and concepts are held in faith… Beyond that, theory and concepts go to constitute a language in which the scientistic matters at issue can be formulated and discussed.

“At a given epoch of the ‘state-of-the-art’ there are applications visible – technological or scientific applications – and also perhaps moral implications which go to forbid or enjoin them. And there can be metaphors visible, which modelled upon, may ultimately find places as theory held in faith, in the Grand Atlas. So that metaphors too are to be watched for their moral implications; nuclear fission, nuclear fusion are examples. Might it not be better that these notions never have been thought?

“In the world to which the Grand Atlas applies, there is an enduring tension: additional evidence increases the reasonableness of accepting the concepts as actual entities or even as moral, not merely mental, realities – but the burden of proof can always be shifted to the opposite side.”

Brockhouse, Bertram Neville. “Nobel Lecture: Slow Neutron Spectroscopy and the Grand Atlas of the Physical World.” Stockholm, Sweden. 8 Dec 1994.
Image: © TheFamousPeople(dot)com.


Piero della Francesca: Transcendental Beliefs


pierodellafrancescaautoritrattopresunto700On 12 October 1492, Piero della Francesca (1415–1492) died at Sansepolcro, Italy.

He was a Renaissance, humanistic painter of religious art, perhaps most known for the fresco cycle “History of the True Cross” at Chiesa de San Francesco, Arezzo, Italy. Additionally, he was an author of mathematical treatises on algebra, solid geometry and perspective geometry.

He is most known for having produced an illustrated translation of Archimedes’ complete works in the 1450s. Another early copy of Archimedes writings was featured at a recent exhibit the Walters Art Museum in Baltimore, MD, “The Archimedes Palimpsest Project” (2011-2012). This team had rediscovered an ancient manuscript of Archimedes which had been copied over in the 13th century for a prayer book by a monk in Jerusalem, Johannes Myronas (died ca.1229). Della Francesca’s translation of Archimedes’ complete works would be completed by the 1450s.

From the book Piero’s Light: In Search of Piero della Francesca: A Renaissance Painter and the Revolution in Art, Science and Religion (2014) by Larry Witham:

“Since the times of Piero, Platonism has offered a pathway through the great debates over art, religion, and science. It is a path filled with the pitfalls of dialectical thinking and the limits of Platonism puts on ultimate human knowledge. Being of this nature, the Platonist outlook requires a kind of ‘faith’ in the first principles of both religion and science. In the arts it requires a willing belief that we are responding to some kind of universal intuitions about beauty; in science it has been a faith in the rationality of the universe, thus putting Piero della Francesca at the fountainhead of these great issues since the Renaissance…

[T]he transcendental ideas of Platonism can be taken to mean the rationality, or mathematical nature, of the universe, or taken to mean the mind of God. In Piero we can find both, it seems. On one front, Piero’s paintings convey a sense that universal beauty, religious belief, and science can coexist on a relatively friendly terms. In a second line of attack, his work with mathematics foreshadows the modern world’s reliance on numbers and our continuing suspicion that somehow—and for some transcendental reason—the universe is rational. The universe is here for our minds to understand within the great Platonist limits of the sensible and intelligible powers of human perception… Having evolved out of Platonism, the continuing belief in intuition as a non-material quality in human life and human achievement suggests that there is something about the mind that is greater than its parts…

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David Gregory: Divine Providence and Human Progress


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On 10 October 1708, David Gregory (1659–1708) passed away in England. A mathematician and physicist on the faculties of the universities of Edinburgh and Oxford, he was known for his popularization of and commentary on the discoveries of Isaac Newton (1643–1727), published as ‘Astronomiae physicae et geometricae elementa,’ as well as other writings on mathematics.

His personal acquaintance with Newton enabled him to obtain some record of his religious views (conversation recorded 1705): —“The plain truth is, that he believes God to be omnipotent in the literal sense… for he supposes that as God is present in space where there is no body, he is present in space where a body is also present … What cause did the ancients assign to gravity? He believes that they reckoned God the cause of it, nothing else.”

Quote from “A Treatise of Practical Geometry: In Three Parts” (published 1684) by David Gregory:

“In short, it seems to have been the intention of Divine Providence, that mankind should be, as far as possible, self taught; that we should attain to every thing excellent and useful as the result of our own experience and observation; that our judgments should be formed by the appearances which are presented to them, and our hearts instructed by their own feelings … A variety of useful lessons may be learned from our attention to the conduct of Divine Providence respecting us. When history and experience demonstrate the uniform method of Divine Providence to have been what has been above represented, let us learn from it to be content with the natural, though slow progress we are in to a more perfect state.”

Osler, Margaret J., ed. Rethinking the Scientific Revolution. (Cambridge, UK: Cambridge Univ., 2000), 292.
Gregory, David. A Treatise of Practical Geometry: In Three Parts. (London, GB: Hamilton, Balfour, and Neil, 1761), 171-172. Image: Portrait by George Jamesone.

Max Planck: Faith is Indispensable for Scientists


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On 4 October 1947, Max Planck (1858–1947) died at Göttingen, Germany. A German theoretical physicist, his earliest work was on the subject of thermodynamics, an interest he acquired from his studies under Kirchhoff, whom he greatly admired, and very considerably from reading R. Clausius’ publications. He published papers on entropy, on thermoelectricity and on the theory of dilute solutions.

Experimental observations on the wavelength distribution of the energy emitted by a black body as a function of temperature were at variance with the predictions of classical physics. Planck was able to deduce the relationship between the energy and the frequency of radiation. In a paper published in 1900, he announced his derivation of the relationship: this was based on the revolutionary idea that the energy emitted by a resonator could only take on discrete values or quanta. The energy for a resonator of frequency v is hv where h is a universal constant, now called Planck’s constant.

This was not only Planck’s most important work but also marked a turning point in the history of physics. The importance of the discovery, with its far-reaching effect on classical physics, was not appreciated at first. However the evidence for its validity gradually became overwhelming as its application accounted for many discrepancies between observed phenomena and classical theory. Among these applications and developments may be mentioned Einstein’s explanation of the photoelectric effect.

In 1918, he won the Nobel Prize in Physics for his development of quantum theory. Planck’s constant is named for him, a foundation of quantum formulation. He was revered by his colleagues not only for the importance of his discoveries but for his great personal qualities. He also organized conferences and authored philosophical works, among them Science and Faith (1930) and Where is Science Going? (1932).

Albert Einstein stated his appreciation on the occasion of Planck’s 60th birthday in 1918 with these words:

“The longing to behold this pre-established harmony [from Leibnitz] is the source of the inexhaustible patience and perseverance with which Planck has devoted himself, as we see, to the most general problems of our science, refusing to let himself be diverted to more grateful and more easily attained ends. I have often heard colleagues try to attribute this attitude of his to extraordinary will-power and discipline — wrongly, in my opinion. The state of mind which enables a man to do work of this kind is akin to that of the religious worshiper or the lover; the daily effort comes from no deliberate intention or program, but straight from the heart. There he sits, our beloved Planck, and smiles inside himself at my childish playing-about with the lantern of Diogenes. Our affection for him needs no threadbare explanation. May the love of science continue to illumine his path in the future and lead him to the solution of the most important problem in present-day physics, which he has himself posed and done so much to solve. May he succeed in uniting quantum theory with electrodynamics and mechanics in a single logical system.”

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Svante Arrhenius: Envisioning the Destinies of the Stars


Svante Arrhenius 2On 02 October 1927, Svante August Arrhenius (1859–1927) passed away in Stockholm, Sweden.

He was a physical chemist as well as a historian & philosopher of science, most known for his characterization of the Boltzmann transition rate of a chemical reaction, the Arrhenius equation k=A*Exp[-Eₐ/kᵦT]. For his work, he won the 1903 Nobel Prize in Chemistry “in recognition of the extraordinary services he has rendered to the advancement of chemistry by his electrolytic theory of dissociation.”

He was also the author of several books on religious traditions and their beliefs regarding the origins of the cosmos: The Destinies of the Stars (GP Putnam’s Sons, 1918); and The Life of the Universe as Conceived by Man from the Earliest Ages to the Present Time. Vols I-II (Harper & Brothers, 1909). From The Destinies of the Stars (1918):

The ancients believed that the fates of men could be read in the stars and this faith persisted with the power of religion until a few centuries ago. It was shared by the foremost astronomers, pre-eminently by Tycho Brahe, who endeavoured to support it through his investigations. Traces are yet to be found in popular conceptions. These ideas have been verified today in a certain sense although with a wholly different meaning than held by our forefathers. The planets do tell us the conditions that existed on the Earth at the first dawn of life and we can also draw from them a prediction of the fate that once, after millions of years perhaps, will befall the latter descendants of present generations.

“In one respect the dreams of our ancestors have not proved true, namely, with reference to the habitability of the other globes in our solar system. According to the great Kant, conditions on the wandering stars outside of the Earth’s orbit were so favourable to life that their inhabitants ought to have reached a far higher development than beings on the Earth. The last remnant of this conception lives in the speculations about the marvellously proficient engineers who built the magnificent system of giant canals on Mars. A thorough critique has demonstrated that any other planet in our solar system hardly can offer an abode for higher beings, except this very Earth, which therefore justly may be called ‘the best of worlds’ among those that we know…”

For additional perspectives on these topics, visit our webpages for:

“Svante Arrhenius.” Wikipedia. Wikimedia Foundation.
— Arrhenius, Svante. The Destinies of the Stars. (New York, NY: GP Putnam’s Sons, 1918), 254-255.  Image: Portrait of Arrhenius by Almar Bech (1935–)

Guido Grandi: Mathematics at the Monastery? — Graphing with Parametric Co-ordinates


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On 01 October 1671, Dom Guido Grandi  (1671–1742) was born in Cremona, Italy.

He was a Camaldolese priest, professor of mathematics and engineering at the University of Pisa, as well as a Fellow of the Royal Society. While studying at the Jesuit college in Cremona, Italy, he was first introduced to the mathematical ideas of Fr. Giovanni Saccheri (1667–1733), known for his writings on non-Euclidean geometry.  After entering the Camaldolese order, he continued to discuss topics in geometry, calculus and gravity with Jesuit Fr. Tommaso Ceva (1648–1737).

Through this network of mathematicians and scientists, he was able to be sent  complimentary copies of the Principia Mathematica and Optics from Isaac Newton (1642–1727). As a translator, he is most known for introducing the calculus work of Gottfried Wilhelm Leibniz (1646–1716) to Italy, for which Leibniz personally thanked him. His writings later inspired Maria Gaetana Agnesi (1718–1799) to publish her own works in mathematics. Grandi’s original study of the parametric rose curve rhodonea is now known as Grandi’s rose @:

Video caption: “In the video schedules of polar functions of a type of r=sin (kz) are shown. They are still called Grandi’s roses, in honor of the Italian mathematician Guido Grandi (XVIII ). ”

With Tommaso Bonaventuri (?–1731) and Benedetto Bresciani (1658–1740), he published a 3-volume edition of the works of Galileo Galilei (1718). Later in his career, he carried out research on hydraulics throughout Rome and was called to serve as an adviser to Pope Clement XII. He was buried at the Camaldolese monastery church in a tomb made by sculptor Giovanni Baratta (1670–1747) with an inscription from Father A. Forzoni, one of Grandi’s students.

O’Connor, John J. and Roberson, Edmund F. “Luigi Guido Grandi.” The MacTutor History of Mathematics Archive. Image: Portrait online.

Ismaël Bullialdus: Theoretical Inverse-Square Law


bullialdus painting

On 28 September 1605, Ismaël Bullialdus (1605–1694) was born in Loudun, France.

He was a French Catholic priest (raised in a Calvinist family/ ordained a Catholic priest at 26 years old), who worked as a mathematician and physicist, and who is today most remembered as the so-called “finder, not the keeper, of the inverse-square law.”

As noted in the book Gravitation and Cosmology (Wiley & Sons, 1972) by Dr. Steven Weinberg, 1979 Nobel Laureate in Physics, professor at University of Texas at Austin.

“The first suggestion of an inverse-square law may have been made around 1640 by Ismaël Bullialdus (1605–1694). However, it was certainly Newton who in 1665 or 1666 first deduced the inverse-square law from observations.”

Original text:

“Virtus autem illa, qua Sol prehendit seu harpagat planetas, corporalis quae ipsi pro manibus est, lineis rectis in omnem mundi amplitudinem emissa quasi species solis cum illius corpore rotatur: cum ergo sit corporalis imminuitur, & extenuatur in maiori spatio & intervallo, ratio autem huius imminutionis eadem est, ac luminus, in ratione nempe dupla intervallorum, sed eversa.”

Translated at MacTutor History Archives:

“As for the power by which the Sun seizes or holds the planets, and which, being corporeal, functions in the manner of hands, it is emitted in straight lines throughout the whole extent of the world, and like the species of the Sun, it turns with the body of the Sun; now, seeing that it is corporeal, it becomes weaker and attenuated at a greater distance or interval, and the ratio of its decrease in strength is the same as in the case of light, namely, the duplicate proportion, but inversely, of the distances [that is, 1/d²].”

Weinberg, Steven. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. (Hoboken, NJ: John Wiley & Sons., 1972), 13.
Bullialdus, Ismaël. Astronomia Philolaica. (1645), Bk I, Ch. XII.
O’Connor, John J. and Roberson, Edmund F. “Ismael Boulliau,” The MacTutor History of Mathematics Archive.