13. Newton’s Optics

I’ve just finished reading selections from another work by Sir Isaac Newton, Optics, guided by what Mortimer J. Adler and Peter Wolff say about it in Foundations of Science and Mathematics, Reading Plan 3 of Encyclopedia Britannica’s The Great Ideas Program (Encyclopedia Britannica, 1960). In the Reading Plan Mortimer J. Adler and Peter Wolff (I) compare the methods used by Newton in Mathematical Principles and Optics; (II) examine the law of reflection and the law of refraction; (III) consider the corpuscular and wave theories of light; and (IV) pose and discuss three questions. Here I’ll compare the methods used by Newton (summarizes I), outline the parts of Optics assigned for reading in Foundations of Science and Mathematics (includes II and III), compare the corpuscular and wave theories of light (summarizes III), and pose the questions asked in IV. For a sketch of Newton’s life see https://opentheism.wordpress.com/2019/07/12/12-newtons-mathematical-principles-of-natural-philosophy/.

The Methods Used by Newton
Both of the works of Newton considered in my readings from Great Books of the Western World, Mathematical Principles of Natural Philosophy (https://opentheism.wordpress.com/2019/07/12/12-newtons-mathematical-principles-of-natural-philosophy/) and Optics, follow the pattern of Euclid’s Elements (https://opentheism.wordpress.com/2018/04/06/1-2-euclids-elements/): they begin with definitions, axioms, and postulates and then they present a series of propositions. However they differ considerably from each other in method. Mathematical Principles is a work in mathematical physics, characterized by the mathematical development of certain tentative formulations. Optics is a work in experimental physics, characterized by the experimental development of certain general principles.
All three works employ axioms, but they are of different kinds. The axioms in Elements are self-evident truths that are universally applicable. The axioms in Mathematical Principles state the very general Laws of Motion, which form the basis of the entire science of dynamics. The axioms in Optics just state what was generally accepted in the science of optics around the year 1700.
All three works present propositions, but again they are of different kinds. The propositions in Elements and Mathematical Principles state conclusions that are to be demonstrated from general principles. Optics state principles that have been found as the result of making experiments and observations and drawing general conclusions from them by induction.
[The above is based on part I of Adler and Wolff’s guide to Optics (Foundations of Science and Mathematics, pages 181-184).]

Optics
This is an outline of the parts of Optics assigned for reading in Foundations of Science and Mathematics: Book I, Part I, Definitions, Axioms, Propositions 1-2; Book III, Part I, Queries 27-31.DEFINITIONS
Newton defines eight terms. If I use a term which you don’t know the meaning of, please ask me its meaning and if it’s a term which Newton defines, I’ll give you his definition of it.AXIOMS
Newton gives eight axioms. I’ll give here just the three which Adler and Wolff explain or refer to in Part II of their guide to Optics (Foundations of Science and Mathematics, pages 184-186).
II. The angle of reflexion is equal to the angle of incidence.
IV. Refraction out of the rarer medium into the denser is made towards the perpendicular; that is, so that the angle of refraction be less than the angle of incidence.
V. The sine of incidence is either accurately or very nearly in a given ratio to the sign of refraction.
PROPOSITIONS
Newton presents 39 propositions but only the first two are assigned for reading in Foundations of Science and Mathematics. They are:
1. Lights which differ in colour, differ also in degrees of refrangibility. [Under Definitions, Newton defines refrangibility of rays of light as “their disposition to be refracted or turned out of their way in passing out of one transparent body or medium into another” (Optics in Great Books of the Western World, Encyclopedia Britannica, 1952, volume 34, page 379).]
2. The light of the Sun consists of rays differently refrangible.
QUERIES
In conjunction with presenting the 39 propositions, Newton makes 38 observations. After making them, he planned to repeat most of them and to make more to determine how rays of light are bent in their passage by bodies. However he was interrupted and instead proposed some queries to assist others in their search. The last five of his 31 queries are assigned for reading in Foundations of Science and Mathematics. They are:
27. Are not all hypotheses erroneous which have hitherto been invented for explaining the phenomena of light, by new modifications of the rays?
28. Are not all hypotheses erroneous in which light is supposed to consist in pressure or motion, propagated through a liquid fluid?
29. Are not the rays of light very small bodies emitted from shining substances?
30. Are not gross bodies and light convertible into one another, and may not bodies receive much of their activity from the particles of light which enter their composition?
31. Have not the small particles of bodies certain powers, virtues, or forces, by which they act at a distance, not only upon the rays of light for reflecting, refracting, and inflecting them, but also upon one another for producing a great part of the phenomena of Nature?
Adler and Wolff consider these queries in their III, which I summarize below.

The Corpuscular and Wave Theories of Light
In Query 29 (see above) Newton refers to the corpuscular theory of light, adding, “For such bodies will pass through uniform mediums in rights lines without bending into the shadow, which is the nature of the rays of light.” Adler and Wolff observe that this characteristic of light is easily explained by the corpuscular theory of light but gives some difficulty to its great rival, the wave theory of light, which will be encountered in the next reading in this series.
One consequence of the corpuscular theory is that light travels more swiftly in a denser than in a rarer medium. However according to the wave theory light travels more rapidly in a rarer medium than in a denser one. In 1850 Foucault performed an experiment which showed that the speed of light is greater in air than in water, thus supporting the wave theory. However since then additional phenomena have been discovered which cannot be reconciled with the wave theory. Thus the nature of light is still in doubt.

Questions about the Reading
1. What is the method employed by Newton to prove the axioms in the Optics?
2. How does the law of refraction explain the bent appearance of a stick in water?
3. Are there any practical consequences of the different refrangibility [capability of being refracted] of light rays of different color?

9. Montaigne’s The Essays

I’ve finally read another selection assigned in Religion and Theology, Reading Plan 4 of Encyclopedia Britannica’s The Great Ideas Program—Michel de Montaigne’s The Essays. It was my second look at a selection of Montaigne’s essays in my current reading from The Great Books of the Western World guided by The Great Ideas Program. The first was when I was working through Reading Plan 1, A General Introduction to the Great Books and to a Liberal Education. I introduced my report on that reading with this quotation from The New Encyclopedia Britannica: “In the 20th century, [Montaigne] is fully recognized in all his aspects as a great writer, and his public is worldwide. Most of his readers see him as friend, mentor, and master of the essay, of the ‘art of being truthful,’ and of the art of living.” (Encyclopedia Britannica, 1974, volume 12, page 396)
In Religion and Theology Mortimer J. Adler and Seymour Cain comment on three of Montaigne’s essays [I – XXXI on judging divine ordinances, I – LVI on prayers (their commenting separately on what he says in it about prayers and on what he says in it about the reading and the translation of the Bible), and II – XIX on liberty of conscience] and consider four questions about what he says in them. Here I’ll sketch Montaigne’s life, comment on the three essays guided by what Adler and Cain say about them, and pose the questions that Adler and Cain consider.

Michel de Montaigne

Montaigne was born Michel Eyquem on February 28, 1533, in the Château of Montaigne near Bordeaux. His father was a prosperous merchant and lord of the seigneury of Montaigne, and his mother was descended from a family of Spanish Jews that had recently converted to Catholicism. He was their third son, but by the death of his older brothers became heir to the estate.
Montaigne was brought up gently and until he was six was taught to speak only Latin. At that age he was sent to the Collège de Guyenne in Bordeaux. After seven disappointing years there, he studied law at Toulouse. In 1554 his father obtained a position for him in a new tax court in Bordeaux. In 1557 the court was abolished and its members were absorbed into one of the regional bodies that composed the Parlement of France, the king’s highest court of justice.
In 1565 Montaigne married Françoise de La Chassaigne, whose father was also a member of the the Parlement of Bordeaux. Although fond of women, he accepted marriage unenthusiastically as a social duty. However he lived on excellent terms with his wife and bestowed some pains on the education of their daughter, Léonore, the only one of six children to survive infancy.
In 1568 Montaigne’s father died, leaving him the lord of Montaigne. Two years later he sold his Parlement position, abandoned the name of Eyquem, and retired to his estate, intending to collect his ideas and write. While there (1571-1580) he wrote the first two books of the Essays, which were published in 1580 at Bordeaux.
The year after publishing the Essays Montaigne left the estate for extensive travel determined to find relief from internal disorders that had been troubling him. In 1581 while he was at La Villa in Italy, he learned that he had been elected mayor of Bordeaux. Returning there he served as mayor efficiently and was re-elected to a second term, which ended in 1585. He again retired to Montaigne but shortly after was driven from his estate by the plague.
Montaigne had begun revising the Essays almost immediately after their publication, perfecting their form and added new ones. While in Paris in 1588, he supervised the publication of the fifth edition of the Essays, the first to contain Book III. However he continued working on the Essays after returning to his estate, not writing any new books or chapters but adding numerous passages.
Sometime after returning to his estate in 1588, Montaigne was stricken with quinsy, which brought about a paralysis of the tongue. On the evening of September 13, 1592, he had his wife call together some of his neighbours so that he might bid them farewell. He requested mass to be said in his room and died while it was being said. He was 59.
The above is taken from the report which I made on the first selection of essays that I read from The Essays, https://opentheism.wordpress.com/2017/12/08/9-montaignes-the-essays/.

The Essays

On Judging Divine Ordinances
Montaigne classes as tellers of fables those who attribute reasons to God for the occurrence of our good and evil fortune, observing, “God, being pleased to show us, that the good have something else to hope for and the wicked something else to fear, than the fortunes or misfortunes of this world, manages and applies these according to His own occult will and pleasure, and deprives us of the means foolishly to make thereof their own profit. And those people abuse themselves who will pretend to dive into these mysteries by the strength of human reason.” (The Essays, in Great Books of the Western World, Encyclopedia Britannica, 1952, volume 25, page 98). Adler and Cain agree with Montaigne, commenting, “From the religious point of view, the best thing is to accept whatever happens as the will of God, without presuming to know the inscrutable divine purposes and meanings behind events” (Religion and Theology, in The Great Ideas Program, Encyclopedia Britannica, 1961, volume 4, page 146). I also agree with Montaigne, but I don’t agree with Adler and Cain that everything that happens is the will of God.

On Prayers
Montaigne encourages the use of the Lord’s Prayer and discourages our praying while our souls are impure and our praying for God’s help in our endeavours without considering whether what we want is just. Regarding the former, he notes that the Lord’s Prayer was the only prayer that he used regularly. Regarding the latter, he observes, “He who calls God to his assistance whilst in a course of vice, does as if a cut purse should call a magistrate to help him, or like those who introduce the name of God to the attestation of a lie” (The Essays, page 156). In agreeing with Mointaigne, Adler and Cain emphasize that prayer is a spiritual matter, concluding, “It is our whole life that attests to our devotion, repentance, at-one-ness with God. God finds the sacrifice of a contrite heart more pleasing than a stockyard full of burnt offerings or other outward show” (Religion and Theology, page 147). I also agree with Montaigne (and with Adler and Cain).
Midway in the essay, Montaigne comments on the increasing availability of the Bible. He criticizes the casual reading of it and affirms that only select people should study it and write about religion, observing, “A pure and simple ignorance and wholly depending upon the exposition of qualified persons, was far more learned and salutary than this vain and verbal knowledge [of ordinary people from translations into their own language], which has only proved the nurse of temerity and presumption” (The Essays, page 154). Adler and Cain observe that Montaigne was just supporting the policy of the Roman Catholic Church of his day and further on (in the questions about the reading; see below) consider whether ordinary believers can understand the Bible.

On Liberty of Conscience
Montaigne opens this essay by observing that in the current religious civil war good intentions resulted in vicious effects. He devotes most of the essay to a consideration of the noble qualities of Julian the Apostate, the Roman Emperor who renounced the Christian faith and tried to restore paganism. On the topic, he points out that although Julian allowed freedom of religion to inflame dissension between Christians with different beliefs so that they wouldn’t unite against him and paganism, the princes of Montaigne’s day allowed it to lessen dissension and thus to encourage peace, concluding, “I think that it is better for the honour of the devotion of our kings, that not having been able to do what they would [establish that the religion of country must follow that of its ruler, according to Adler and Cain], they have made a show of being willing to do what they could” (The Essays, page 326). Besides summarizing the essay, Adler and Cain observe regarding its focus on Julian, “Montaigne sees Julian as the prime example of the Christian tendency to approve all emperors who were pro-Christian and to condemn completely all emperors who were anti-Christian. Montaigne demonstrates that it is possible to give a perceptive and honest account of a man whom he considers ‘wrong throughout’ in religious matters” (Religion and Theology, page 149). I agree with them.

Questions about the Reading

1. Is religion, for Montaigne, a purely spiritual matter, without relation to the everyday, empirical world?
2. Does prayer have any effect?
3. How does Montaigne regard the social effect of religion?
4. Can ordinary believers understand the Bible?

12. Newton’s Mathematical Principles of Natural Philosophy

“Occasionally in the history of thought there occurs a moment when some man or some book shatters preceding tradition by a great leap. Such a moment certainly occurred with the publication of Newton’s Mathematical Principles” (Mortimer J. Adler and Peter Wolff, Foundations of Science and Mathematics, Encyclopedia Britannica, 1960, page 161). I’ve just finished reading the passages in that work assigned for reading in Foundations of Science and Mathematics, Reading Plan 3 of Encyclopedia Britannica’s The Great Ideas Program.
In the Reading Plan Mortimer J. Adler and Peter Wolff (I) quote tributes paid to Sir Isaac Newton by the astronomer Edmund Halley and the poet Alexander Pope; (II) summarize Newton’s accomplishments; (III) discuss the characteristics of Newton’s method; (IV) discuss some of the characteristic concepts of Newton’s physics; and (V) pose and discuss three questions. Here I’ll sketch Newton’s life, outline the passages in Mathematical Principles of Natural Philosophy assigned for reading in Foundations of Science and Mathematics, and pose the questions asked in V.

Sir Isaac Newton

Isaac Newton was born on Christmas Day, 1642, in the English town of Woolsthorpe. His father, a farmer, died a few months before his birth. In 1645 his mother remarried and left him with his maternal grandmother at Woolsthorpe. In 1656 his stepfather died and his mother returned to Woolsthrope to take care of the farm. She took Isaac out of school and brought him home so that he could prepare himself to manage the farm. However before long she realized that he wasn’t suited for farm life and sent him back to school. In 1661 he entered Trinity College in Cambridge University, and he graduated in 1665.
Newton wanted to stay on at the university to continue his studies but it was closed because of the Black Plague and he returned to Woolsthorne. In the eighteen months that he was there, he conducted experiments in optics and chemistry and continued his mathematical speculations. During the time he hit upon a new mathematical tool, now called calculus; began working out the law of attraction between all objects in the universe, the law of gravitation; and experimented with light, succeeding in showing that a beam of sunlight is made up of bands of colour from red to violet which he called the spectrum.
After the plague ended Newton returned to Cambridge and continued working on light and colour. This work led to the discovery of the reflecting telescope. In recognition of his work in mathematics and optics (the science of light), he was appointed professor of mathematics at Trinity College in 1669. Although he experimented mainly with optics, his mind always returned to the problem of gravitation. Finally he completed the mathematics of the laws of gravitation Using this law, in 1682 he proved mathematically a law of planetary motion that had been figured out by the astronomer Johannes Kepler in the early 1660’s. Encouraged by friends, in 1685 he plunged into the task of writing a book explaining his work on planetary motion, gravitation, and other matters. The book, The Mathematical Principles of Natural Philosophy, appeared in 1687 and “is not only Newton’s masterpiece but also the fundamental work for the whole of modern science” (“Newton, Sir Isaac,” Encyclopedia Britannica, Encyclopedia Britannica, 1974, volume 13, page 19).
In 1696 Newton was appointed Warden of the Mint and, although he didn’t resign his Cambridge appointments until 1701, he moved to London and from then on centred his life there. He was made Master of the Mint in 1699, became president of the Royal Society in 1703, and was knighted in 1705. When he died in 1727 (March 20), he was buried in Westminster Abbey, among the great men of England. A statue of him stands today in the hall of Trinity College, Cambridge University.

Mathematical Principles of Natural Philosophy

DEFINITIONS
[Newton defines the quantity of matter, the quantity of motion, the vis insita or inertia of matter, an impressed force, a centripetal force, the absolute quantity of a centripetal force, and the accelerative quantity of a centripetal force; and he distinguishes between absolute and relative time, absolute and relative space, absolute and relative place, and absolute and relative motion.]

AXIOMS OR LAWS OF MOTION
LAW I. Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed on it.
LAW II. The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.
LAW III. To every action there is always an equal reaction: or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.
[Newton also gives six corollaries to the three laws of motion and a scholium, but I didn’t work through them.]

RULES OF REASONING IN PHILOSOPHY
RULE I. We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.
RULE II. Therefore to the same natural effects we must, as far as possible, assign the same causes.
RULE III. The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiences, are tio be esteemed the universal qualities of all bodies whatsoever.
RULE IV. In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may either may be made more accurate, or liable to exceptions.
[Adler and Wolff call these the rules of simplicity, consilience, empiricism, and induction. They observe that Rules 1 and 2 are so closely related that they might almost have been combined into one rule and that Rules 3 and 4 also belong closely together with Rule 4 just reaffirming Rule 3.]

GENERAL SCHOLIUM
[Newton summarizes the motions of the sun, planets, moons, and comets.] This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being.… 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. [Newton considers the attributes of this God.]
Hitherto we have explained the phenomena of the heavens and of our sea by the power of gravity…but hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypothesis. [Adler and Wolff maintain that Newton does make hypotheses in the sense of tentative formulations to be explored mathematically and verified or disproved by experiment but agree that he doesn’t make them in the sense of fictional explanations such as nature’s abhorring a vacuum.]

Questions about the Reading

1. How does Newton describe his method of reasoning? [see RULES OF REASONING IN PHILOSOPHY above.]
2. Does Newton continue the “Keplerian revolution”?
3. How does Newton distinguish between absolute and relative motion?