Category Archives: Newton

The Jesuit Mirror Man

Although the theory that a curved mirror can focus an image was already known to Hero of Alexandria in antiquity and also discussed by Leonardo in his unpublished writings; as far as we know, the first person to attempt to construct a reflecting telescope was the Italian Jesuit Niccolò Zucchi.

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Niccolò Zucchi Source: Wikimedia Commons

Niccolò Zucchi, born in Parma 6 December 1586, was the fourth of eight children of the aristocrat Pierre Zucchi and his wife Francoise Giande Marie. He studied rhetoric in Piacenza and philosophy and theology in Parma, probably in Jesuit colleges. He entered the Jesuit order as a novice 28 October 1602, aged 16. Zucchi taught mathematics, rhetoric and theology at the Collegio Romano and was then appointed rector of the new Jesuit College in Ravenna by Cardinal Alessandro Orsini, who was also a patron of Galileo.

In 1623 he accompanied Orsini, the Papal legate, on a visit to the court of the Holy Roman Emperor Ferdinand II in Vienna. Here he met and got to know Johannes Kepler the Imperial Mathematicus. Kepler encouraged Zucchi’s interest in astronomy and the two corresponded after Zucchi’s return to Italy. Later when Kepler complained about his financial situation, Zucchi sent him a refracting telescope at the suggestion of Paul Guldin (1577–1643) a Swiss Jesuit mathematician, who also corresponded regularly with Kepler. Kepler mentions this gift in his Somnium. These correspondences between Kepler and leading Jesuit mathematicians illustrate very clearly how the scientific scholars in the early seventeenth century cooperated with each other across the religious divide, even at the height of the Counter Reformation.

Zucchi’s scientific interests extended beyond astronomy; he wrote and published two books on the philosophy of machines in 1646 and 1649. His unpublished Optica statica has not survived. He also wrote about magnetism, barometers, where he a good Thomist rejected the existence of a vacuum, and was the first to demonstrate that phosphors generate rather than store light.

Today, however Zucchi is best remember for his astronomy. He is credited with being the first, together with the Jesuit Daniello Bartoli (1608–1685), to observe the belts of Jupiter on 17 May 1630.  He reported observing spots on Mars in 1640. These observations were made with a regular Galilean refractor but it is his attempt to construct a reflecting telescope that is most fascinating.

In his Optica philosophia experimentis et ratione a fundamentis constituta published in 1652 he describes his attempt to create a reflecting telescope.

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Optica philosophia title page Source: Linder Hall Library

As I said at the beginning, and have described in greater detail here, the principle that one could create an image with a curved mirror had been known since antiquity. Zucchi tells us that he replaced the convex objective lens in a Galilean telescope with bronze curved mirror. He tried viewing the image with the eyepiece, a concave lens looking down the tube into the mirror. He had to tilt the tube so as not to obstruct the light with his head. He was very disappointed with the result as the image was just a blur, although as he said the mirror was, “ab experto et accuratissimo artifice eleboratum nactus.” Or in simple words, the mirror was very well made by an expert.

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Optica philosophia frontispiece

Zucchi had stumbled on a problem that was to bedevil all the early attempts to construct a reflecting telescope. Mirror that don’t distort the image are much harder to grind and polish than lenses. (The bending of light in a lens diminishes the effect of imperfections, whereas a mirror amplifies them). The first to solve this problem was Isaac Newton, proving that he was as skilled a craftsman as he was a great thinker. However, it would be more that fifty years before John Hadley could consistently repeat Newton’s initial success.

All the later reflecting telescope models had, as well as their primary mirrors, a secondary mirror at the focal point that reflected the image either to the side (a Newtonian), or back through the primary mirror (a Gregorian or a Cassegrain) to the eyepiece; the Zucchi remained the only single mirror telescope in the seventeenth century.

In the eighteenth century William Herschel initially built and used Newtonians but later he constructed two massive reflecting telescopes, first a twenty-foot and then a second forty-foot instrument.

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Herschel’s Grand Forty feet Reflecting Telescopes A hand-coloured illustration of William Herschel’s massive reflecting telescope with a focal length of forty feet, which was erected at his home in Slough. Completed in 1789, the telescope became a local tourist attraction and was even featured on Ordnance Survey maps. By 1840, however, it was no longer used and was dismantled, although part of it is now on display at the Royal Observatory, Greenwich. This image of the telescope was engraved for the Encyclopedia Londinensis in 1819 as part of its treatment of optics. Herschel’s Grand Forty feet Reflecting Telescopes Source: Wikimedia Commons

These like Zucchi’s instrument only had a primary mirror with Herschel viewing the image with a hand held eyepiece from the front of the tube. As we name telescopes after their initial inventors Herschel giant telescopes are Zucchis, although I very much doubt if he even knew of the existence of his Jesuit predecessor, who had died at the grand old age of eighty-three in 1670.

 

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Filed under History of Astronomy, History of Optics, History of science, History of Technology, Newton, Renaissance Science

A Newtonian Refugee

Erlangen, the Franconian university town, where I (almost) live and where I went to university is known in German as ‘Die Hugenottenstadt’, in English the Huguenot town. This name reflects the religious conflicts within Europe in the 17thcentury. The Huguenots were Calvinists living in a strongly and predominantly Catholic France. Much persecuted their suffering reached a low point in 1572 with the St Bartholomew’s Day massacre, which started in the night of 23-24 August. It is not know how many Huguenots were murdered, estimates vary between five and thirty thousand. Amongst the more prominent victims was Pierre de la Ramée the highly influential Humanist logician and educationalist. The ascent of Henry IV to the French Throne saw an easing of the situation for the Huguenots, when he issued the Edict of Nantes confirming Catholicism as the state religion but giving Protestants equal rights with the Catholics. However the seventeenth century saw much tension and conflict between the two communities. In 1643 Louis XIV gained the throne and began systematic persecution of the Huguenots. In 1685 he issued the Edict of Fontainebleau revoking the Edict of Nantes and declaring Protestantism illegal. This led to a mass exodus of Huguenots out of France into other European countries.

Franconia had suffered intensely like the rest of Middle Europe during the Thirty Years War (1618-1648) in which somewhere between one third and two thirds of the population of this area died, most of them through famine and disease. The Margrave of Brandenburg-Bayreuth, Christian Ernst invited Huguenot refugees to come to Erlangen to replace the depleted inhabitants. The first six Huguenots reached Erlangen on 17 May 1686 and about fifteen hundred more followed in waves. Due to the comparatively large numbers the Margrave decided to establish a new town south of the old town of Erlangen and so “Die Hugenottenstadt” came into being.

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The earliest known plan of New Erlangen (1686) Attributed to Johann Moritz Richter Source: Wikimedia Commons

In 1698 one thousand Huguenots and three hundred and seventeen Germans lived in Erlangen. Many of the Huguenot refugees also fled to Protestant England establish settlements in many towns such as Canterbury, Norwich and London.

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Town plan of Erlangen 1721 Johann Christoph Homann Source: Wikimedia Commons

In the early eighteenth century Isaac Newton, now well established in London at the Royal Mint, would hold court in the London coffee houses surrounded by a group of enthusiastic mathematical scholars, the first Newtonian, eager to absorb the wisdom of Europe’s most famous mathematician and to read the unpublished mathematical manuscripts than he passed around for their enlightenment. One of those coffee house acolytes was the Huguenot refugee, Abraham de Moivre (1667–1754).

abraham-de-moivre

Abraham de Moivre artist unknown

Abraham de Moivre the son of a surgeon was born in Vitry-le-François on 26 May 1667. Although a Huguenot, he was initially educated at the Christian Brothers’ Catholic school. At the age of eleven he moved to Protestant Academy at Sedan, where he studied Greek. As a result of the increasing religious tension the Protestant Academy was suppressed in 1682 and de Moivre moved to Saumur to study logic. By this time he was teaching himself mathematics using amongst others Jean Prestet’s Elémens desmathématiquesand Christiaan Huygens’ De Rationciniis in Ludo Aleae, a small book on games of chance. In 1684 he moved to Paris to study physics and received for the first time formal teaching in mathematics from Jacques Ozanam a respected and successful journeyman mathematician.

Although it is not known for sure why de Moivre left France it is a reasonable assumption that it was Edict of Fontainebleau that motivated this move. Accounts vary as to when he arrived in London with some saying he was already there in 1686, others that he first arrived a year later, whilst a different account has him imprisoned in France in 1688. Suffering the fate of many a refugee de Moivre was unable to find employment and was forced to learn his living as a private maths tutor and through holding lectures on mathematics in the London coffee houses, the so-called Penny Universities.

Shortly after his arrival in England, de Moivre first encountered Newton’s Principia, which impressed him greatly. Due to the pressure of having to earn a living he had very little time to study, so according to his own account he tore pages out of the book and studied them whilst walking between his tutoring appointments. In the 1690s he had already become friends with Edmund Halley and acquainted with Newton himself. In 1695 Halley communicated de Moivre’s first paper Methods of Fluxions to the Royal Society of which he was elected a member in 1697.

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Edmund Halley portrait by Thomas Murray Source: Wikipedia Commons

In 1710 de Moivre, now an established member of Newton’s inner circle, was appointed to the Royal Society Commission set up to determine whether Newton or Leibniz should be considered the inventor of the calculus. Not surprisingly this Commission found in favour of Newton, the Society’s President.

De Moivre produced papers in many areas of mathematics but he is best remembered for his contributions to probability theory. He published the first edition of The Doctrine of Chances: A method of calculating the probabilities of events in playin 1718 (175 pages).

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Title page of he Doctrine of Chances: A method of calculating the probabilities of events in playin 1718

An earlier Latin version of his thesis was published in the Philosophical Transactionsof the Royal Society in 1711. Although there were earlier works on probability, most notably Cardano’s Liber de ludo aleae(published posthumously 1663), Huygens’De Rationciniis in Ludo Aleaeand the correspondence on the subject between Pascal and Fermat, De Moivre’s book along with Jacob Bernoulli’s Ars Conjectandi(published posthumously in 1713) laid the foundations of modern mathematical probability theory. There were new expanded editions of The Doctrine of Chance sin 1738 (258 pages) and posthumously in 1756 (348 pages).

De Moivre is most well known for the so-called De Moivre’s formula, which he first

(cos θ + i sin θ)n = cos n θ + i sin n θ

published in a paper in 1722 but which follows from a formula he published in 1707. In his Miscellanea Analytica from 1730 he published what is now falsely known as Stirling’s formula, although de Moivre credits James Stirling (1692–1770) with having improved his original version.

Although a well known mathematician, with a Europa wide reputation, producing much original mathematics de Moivre, the refugee (he became a naturalised British citizen in 1705), never succeeded in obtaining a university appointment and remained a private tutor all of his life, dying in poverty on 27 November 1754. It is claimed that he accurately predicted the date of his own death.

 

 

 

 

 

 

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400 Years of The Third Law–An overlooked and neglected revolution in astronomy

Four hundred years ago today Johannes Kepler rediscovered his most important contribution to the evolution of astronomy, his third law of planetary motion.

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Portrait of Johannes Kepler 1610 by unknown artist. Source: Wikimedia Commons

He had originally discovered it two months earlier on 8 March but due to a calculation error rejected it. On 15 May he found it again and this time recognised that it was correct. He immediately added it to his Harmonices Mundi:

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For when the true distances between the spheres were found, through the observations of Brahe, by continuous toil for a very long time, at last, at last, the genuine proportion of the periodic times to the proportion of the spheres –

Only at long last did she look back at him as she lay motionless,

But she look back and after a long time she came [Vergil, Eclogue I, 27 and 29.]

And if you want the exact moment in time, it was conceived mentally on the 8th of March in this year one thousand six hundred and eighteen, but submitted to calculation in an unlucky way, and therefore rejected as false, and finally returning on the 15th of May and adopting a new line of attack, stormed the darkness of my mind. So strong was the support from the combination of my labor of seventeen years on the observations of Brahe and the present study, which conspired together, that at first I believed I was dreaming, and assuming my conclusion among my basic premises. But it is absolutely exact that proportion between the periodic times of any two planets is precisely the sesquialterate[1] proportion of their mean distances, that is of the actual spheres, though with this in mind, that the arithmetic mean between the two diameters of the elliptical orbit is a little less than the longer diameter. Thus if one takes one third of the proportion from the period, for example, of the Earth, which is one year, and the same from the period of Saturn, thirty years, that is, the cube roots, and one double that proportion, by squaring the roots, he has in the resulting numbers the exactly correct proportion of the mean distances of the Earth and Saturn from the Sun.[2]

writing a few days later:

Now, because eighteen months ago the first dawn, three months ago the broad daylight, but a very few days ago the full sun of a most remarkable spectacle has risen, nothing holds me back. Indeed, I give myself up to a sacred frenzy.

He finished the book on 27 May although the printing would take a year.

In modern terminology:

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The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit: i.e. for two planets with P = orbital period and R = semi-major axis P12/P22=R13/R23

Kepler’s third law is probably the most important discovery on the way to the establishment of a heliocentric astronomy but its importance was initially overlooked and its implications were somehow neglected until Isaac Newton displayed its significance in his Principia Mathematica, published in 1687 sixty-eight years after the third law first appeared in print.

What the third law gives us is a direct mathematical relationship between the size of the orbits of the planets and their duration, which only works in a heliocentric system. In fact as we will see later it’s actually equivalent to the law of gravity. There is nothing comparable for either a full geocentric system or for a geo-heliocentric Tychonic or semi-Tychonic system. It should have hit the early seventeenth-century astronomical community like a bomb but it didn’t, which raises the question why it didn’t.

The main answer lies in Kepler’s own writings. Although he viewed its discovery as the crowning glory of his work on the Harmonices Mundi Kepler didn’t give it any prominence in that work. The Harmonices Mundi is a vast sprawling book explicating Kepler’s version of the Pythagorean theory of the harmony of the spheres in five books. After four introductory books covering plane geometry, music theory and astrology Kepler gets down to harmonic planetary theory in the fifth and final book. Book V, 109 pages in the English translations, contains lots of musical relationships between various aspects of the planetary orbits, with the third law presented as just one amongst the many with no particular emphasis. The third law was buried in what is now regarded as a load of unscientific dross. Or as Carola Baumgardt puts it, somewhat more positively,  in her Johannes Kepler life and letters (Philosophical Library, 1951, p. 124):

Kepler’s aspirations, however, go even much higher than those of modern scientific astronomy. As he tried to do in his “Mysterium Cosmographicum” he coupled in his “Harmonice Mundi” the precise mathematical results of his investigations with an enormous wealth of metaphysical, poetical, religious and even historical speculations. 

Although most of Kepler’s contemporaries would have viewed his theories with more sympathy than his modern critics the chances of anybody recognising the significance of the harmony law for heliocentric astronomical theory were fairly minimal.

The third law reappeared in 1620 in the second part of Kepler’s Epitome Astronomiae Copernicanae, a textbook of heliocentric astronomy written in the form of a question and answer dialogue between a student and a teacher.

How is the ratio of the periodic times, which you have assigned to the mobile bodies, related to the aforesaid ratio of the spheres wherein, those bodies are borne?

The ration of the times is not equal to the ratio of the spheres, but greater than it, and in the primary planets exactly the ratio of the 3/2th powers. That is to say, if you take the cube roots of the 30 years of Saturn and the 12 years of Jupiter and square them, the true ration of the spheres of Saturn and Jupiter will exist in those squares. This is the case even if you compare spheres that are not next to each other. For example, Saturn takes 30 years; the Earth takes one year. The cube root of 30 is approximately 3.11. But the cube root of 1 is 1. The squares of these roots are 9.672 and 1. Therefore the sphere of Saturn is to the sphere of the Earth as 9.672 is to 1,000. And a more accurate number will be produced, if you take the times more accurately.[3]

Here the third law is not buried in a heap of irrelevance but it is not emphasised in the way it should be. If Kepler had presented the third law as a table of the values of the orbit radiuses and the orbital times and their mathematical relationship, as below[4], or as a graph maybe people would have recognised its significance. However he never did and so it was a long time before the full impact of the third law was felt in astronomical community.

third law001

The real revelation of the significance of the third law came first with Newton’s Principia Mathematica. By the time Newton wrote his great work the empirical truth of Kepler’s third law had been accepted and Newton uses this to establish the empirical truth of the law of gravity.

In Book I of Principia, the mathematics and physics section, Newton first shows, in Proposition 11[5], that for a body revolving on an ellipse the law of the centripetal force tending towards a focus of the ellipse is inversely as the square of the distance: i.e. the law of gravity but Newton is not calling it that at this point. In Proposition 14[6] he then shows that, If several bodies revolve about a common center and the centripetal force is inversely as the square of the distance of places from the center, I say that the principal latera recta of the orbits are as the squares of the areas which bodies describe in the same time by radii drawn to the center. And Proposition 15[7]: Under the same supposition as in prop. 14, I say the square of the periodic times in ellipses are as the cubes of the major axes. Thus Newton shows that his law of gravity and Kepler’s third law are equivalent, although in this whole section where he deals mathematically with Kepler’s three laws of planetary motion he never once mentions Kepler by name.

Having established the equivalence, in Book III of The Principia: The System of the World Newton now uses the empirical proof of Kepler’s third law to establish the empirical truth of the law of gravity[8]. Phenomena 1: The circumjovial planets, by radii drawn to the center of Jupiter, describe areas proportional to the times, and their periodic times—the fixed stars being et rest—are as 3/2 powers of their distances from that center. Phenomena 2: The circumsaturnian planets, by radii drawn to the center of Saturn, describe areas proportional to the times, and their periodic times—the fixed stars being et rest—are as 3/2 powers of their distances from that center. Phenomena 3: The orbits of the five primary planets—Mercury, Venus, Mars, Jupiter, and Saturn—encircle the sun. Phenomena 4: The periodic times of the five primary planets and of either the sun about the earth or the earth about the sun—the fixed stars being at rest—are as the 3/2 powers of their mean distances from the sun. “This proportion, which was found by Kepler, is accepted by everyone.”

Proposition 1: The forces by which the circumjovial planets are continually drawn away from rectilinear motions and are maintained in their respective orbits are directed to the center of Jupiter and are inversely as the squares of the distances of their places from that center. “The same is to be understood for the planets that are Saturn’s companions.” As proof he references the respective phenomena from Book I. Proposition 2: The forces by which the primary planets are continually drawn away from rectilinear motions and are maintained in their respective orbits are directed to the sun and are inversely as the squares of the distances of their places from its center. As proof he references the respective phenomenon from Book I:

One of the ironies of the history of astronomy is that the general acceptance of a heliocentric system by the time Newton wrote his Principia was largely as a consequence of Kepler’s Tabulae Rudolphinae the accuracy of which convinced people of the correctness of Kepler’s heliocentric system and not the much more important third taw of planetary motion.

[1] Sesquialterate means one and a half times or 3/2

[2] The Harmony of the World by Johannes Kepler, Translated into English with an Introduction and Notes by E.J. Aiton, A.M. Duncan & J.V. Field, Memoirs of the American Philosophical Society Held at Philadelphia for Promoting Useful Knowledge, Volume 209, 1997 pp. 411-412

[3] Johannes Kepler, Epitome of Copernican Astronomy & Harmonies of the World, Translated by Charles Glenn Wallis, Prometheus Books, New York, 1995 p. 48

[4] Table taken from C.M. Linton, From Eudoxus to Einstein: A History of Mathematical Astronomy, CUP, Cambridge etc., 2004 p. 198

[5] Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy, A New Translation by I: Bernard Cohen and Anne Whitman assisted by Julia Budenz, Preceded by A Guide to Newton’s Principia, by I. Bernard Cohen, University of California Press, Berkley, Los Angeles, London, 1999 p. 462

[6] Newton, Principia, 1999 p. 467

[7] Newton, Principia, 1999 p. 468

[8] Newton, Principia, 1999 pp. 797–802

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Christmas Trilogy 2017 Part 1: Isaac the Imperator

Isaac Newton came from a fairly humble although not poor background. His father was a yeoman farmer in Lincolnshire, who unfortunately died before he was born. A yeoman farmer owned his own land and in fact the Newton’s were the occupants of the manor house of Woolsthorpe-by-Colsterworth.

Woolsthorpe Manor, Woolsthorpe-by-Colsterworth, Lincolnshire, England. This house was the birthplace and the family home of Isaac Newton.
Source: Wikimedia Commons

Destined to become a farmer until he displayed little aptitude for life on the land, his mother was persuaded by the local grammar school master to let him complete his education and he was duly dispatched off to Cambridge University in 1661. Although anything but poor, when Newton inherited the family estates they generated an income of £600 per annum, at a time when the Astronomer Royal received an income of £100 per annum, his mother enrolled him at Cambridge as a subsizar, that is a student who earned his tuition by working as a servant. I personally think this reflects the family’s puritan background rather than any meanness on the mother’s part.

In 1664 Newton received a scholarship at Trinity and in 1667 he became a fellow of the college. In 1669 he was appointed Lucasian professor of mathematics. Cambridge was in those days a small market town and a bit of a backwater. The university did not enjoy a good reputation and the Lucasian professorship even less of one. Newton lived in chambers in Trinity College and it was certainly anything but a life of luxury.

Trinity College Great Court
Source: Wikimedia Commons

There is an amusing anecdote about David Hilbert writing to the authorities of Trinity at the beginning of the twentieth century to complain about the fact that Godfrey Hardy, whom he regarded as one of the greatest living mathematicians, was living in what he regarded as a squalid room without running water or adequate heating. What Hilbert didn’t realise was that Hardy would never give up this room because it was the one that Newton had inhabited.

Newton remained an obscure and withdrawn Cambridge don until he presented the Royal Society with his reflecting telescope and published his first paper on optics in 1672. Although it established his reputation, Newton was anything but happy about the negative reactions to his work and withdrew even further into his shell. He only re-emerged in 1687 and then with a real bombshell his Philosophiæ Naturalis Principia Mathematica, which effectively established him overnight as Europe’s leading natural philosopher, even if several of his major competitors rejected his gravitational hypothesis of action at a distance.

Having gained fame as a natural philosopher Newton, seemingly having tired of the provinces, began to crave more worldly recognition and started to petition his friends to help him find some sort of appropriate position in London. His lobbying efforts were rewarded in 1696 when his friend and ex-student, Charles Montagu, 1st Earl of Halifax, had him appointed to the political sinecure, Warden of the Mint.

Newton was no longer a mere university professor but occupant of one of the most important political sinecures in London. He was also a close friend of Charles Montagu one of the most influential political figures in England. By the time Montagu fell from grace Newton was so well established that it had little effect on his own standing. Although Montagu’s political opponents tried to bribe him to give up his, now, Mastership of the Mint he remained steadfast and his fame was such that there was nothing they could do to remove him from office. They wanted to give the post to one of their own. Newton ruled the Mint with an iron hand like a despot and it was not only here that the humble Lincolnshire farm lad had given way to man of a completely different nature.

As a scholar, Newton held court in the fashionable London coffee houses, surrounded by his acolytes, for whom the term Newtonians was originally minted, handing out unpublished manuscripts to the favoured few for their perusal and edification. Here he was king of the roost and all of London’s intellectual society knew it.

He became President of the Royal Society in 1703 and here with time his new personality came to the fore. When he became president the society had for many years been served by absentee presidents, office holders in name only, and the power in the society lay not with the president but with the secretary. When Newton was elected president, Hans Sloane was secretary and had already been so for ten years and he was not about to give up his power to Newton. There then followed a power struggle, mostly behind closed doors, until Newton succeeded in gaining power in about 1610 1710, Sloane, defeated resigned from office in 1613 1713 but got his revenge by being elected president on Newton’s death. Now Newton let himself be almost literally enthroned as ruler of the Royal Society.

Isaac Newton’s portrait as Royal Society President Charles Jervas 1717
Source: Royal Society

The president of the society sat at table on a raised platform and on 20 January 1711 the following Order of the Council was made and read to the members at the next meeting.

That no Body Sit at the Table but the President at the head and the two Secretaries towards the lower end one on the one Side and the other Except Some very Honoured Stranger, at the discretion of the President.

When the society was first given its royal charter in 1660, although Charles II gave them no money he did give them an old royal mace as a symbol of their royal status. Newton established the custom that the mace was only displayed on the table when the president was in the chair. When Sloane became president his first act was to decree that the mace was to be displayed at all meetings, whether the president was present or not. Newton ruled over the meetings with the same iron hand with which he ruled over the Mint. Meeting were conducted solemnly with no chit chat or other disturbances as William Stukeley put it:

Indeed his presence created a natural awe in the assembly; they appear’d truly as a venerable consessus Naturae Consliariorum without any levity or indecorum.

Perhaps Newton’s view of himself in his London years in best reflected in his private habitat. Having lived the life of a bachelor scholar in college chambers for twenty odd years he now obtained a town house in London. He installed his niece Catherine Barton, who became a famous society beauty, as his housekeeper and lived the life of a London gentleman, albeit a fairly quiet one. However his personal furnishings seem to me to speak volumes about how he now viewed himself. When he died an inventory of his personal possessions was made for the purpose of valuation, as part of his testament. On the whole his household goods were ordinary enough with one notable exception. He possessed crimson draperies, a crimson mohair bed with crimson curtains, crimson hangings, a crimson settee. Crimson was the only colour mentioned in the inventory. He lived in an atmosphere of crimson. Crimson is of course the colour of emperors, of kings, of potentates and of cardinals. Did the good Isaac see himself as an imperator in his later life?

 

All the quotes in this post are taken from Richard S, Westfall’s excellent Newton biography Never at Rest.

 

 

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Did Isaac leap or was he pushed?

In 2016 2017 it would not be too much to expect a professor of philosophy at an American university to have a working knowledge of the evolution of science in the seventeenth century, particularly given that said evolution had a massive impact on the historical evolution of philosophy. One might excuse a freshly baked adjunct professor at a small liberal arts college, in his first year, if they were not au fait with the minutiae of the history of seventeenth-century astronomy but one would expect better from an established and acknowledged expert. Andrew Janiak is just that, an established and acknowledged expert. Creed C. Black Professor of Philosophy and Chair of Department at Duke University; according to Wikipedia, “Duke is consistently included among the best universities in the world by numerous university rankings”. Janiak is also an acknowledge expert on Isaac Newton and author of Isaac Newton in the Blackwell Great Minds series, so one is all the more dumbfounded to read the following in his article entitled Newton’s Leap on the Institute of Arts and Ideas: Philosophy for our times website:

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Isaac Newton 1677 after Peter Lely Source: Wikimedia Commons Comment from CJ Schilt (a Newton expert) on Facebook: On another note, that picture is probably not Newton, despite what Finegold thinks.

 

But wait a minute: what could be more amazing than a young man discovering a fundamental force of nature while sitting under a tree? For starters, we have to recognize how foreign Newton’s ultimate idea about gravity was to philosophers, astronomers and mathematicians in the era of the Scientific Revolution. Newton provided an answer to a question that hadn’t even been asked yet. The problem with understanding the distant past is that we take our twenty-first century ideas and attitudes for granted. We think, for example, that the following is obvious: if the planets, like the Earth and Jupiter, regularly orbit the Sun, there must be something that causes them to follow their orbits. After all, if nothing caused them to orbit the Sun, they would fly off into deep space. [my emphasis]That seems so obvious to us, it’s hard to imagine that for centuries, the world’s leading thinkers, from Aristotle to Ptolemy and onwards, did not have that idea at all. Instead, for many generations, leading philosophers and mathematicians thought this: the circle is a perfect mathematical form, and the planetary orbits are circular, so they are ever-lasting aspects of the natural world. To them, the orbits were so perfect that nothing caused them to occur. They simply were. [my emphasis] The question of what caused the planetary orbits was not even on the table for astronomers in those days. [my emphasis] Down on earth, apples fell from trees throughout history just as they do now. But philosophers and mathematicians didn’t have any reason to think that whatever causes apples to fall to the ground might somehow be connected to anything going on in the heavens. After all, the heavens were thought to be the home of everlasting motions, of perfect circles, and were therefore nothing like the constantly changing, messy world down below, where worms eat through apples as they rot on the ground.

So what is wrong with this piece of #histSTM prose? Let us start with the second of my bold emphasised segments:

Instead, for many generations, leading philosophers and mathematicians thought this: the circle is a perfect mathematical form, and the planetary orbits are circular, so they are ever-lasting aspects of the natural world. To them, the orbits were so perfect that nothing caused them to occur. They simply were.

Whilst it is true that, following Empedocles, Western culture adopted the so-called Platonic axioms, which stated that celestial motion was uniform and circular, it is not true that they claimed this motion to be without cause. Aristotle, whose system became dominant for a time in the Middle Ages, hypothesised a system of nested crystalline spheres, which working from the outside to the centre drove each other through direct contact; a system that probably would not have worked due to friction. His outer-most sphere was moved by the unmoved mover, who remained unnamed, making the theory very attractive for Christian theologians in the High Middle Ages, who simple called the unmoved mover God. Interestingly the expression love makes the world go round originates in the Aristotelian belief that that driving force was love. In the Middle Ages we also find the beliefs that each of the heavenly bodies has a soul, which propels it through space or alternatively an angel pushing it around its orbit.

All of this is all well and good but of course doesn’t have any real relevance for Newton because by the time he came on the scene the Platonic axioms were well and truly dead, killed off by one Johannes Kepler. You might have heard of him? Kepler published the first two of his planetary laws, number one: that the planetary orbits are ellipses and that the sun is at one focus of the ellipse and number two: that a line connecting the sun to the planet sweeps out equal areas in equal time periods in 1609, that’s thirty-three years before Newton was born. Somewhat later Cassini proved with the support of his teachers, Riccioli and Grimaldi, using a heliometer they had constructed in the San Petronio Basilica in Bologna, that the earth’s orbit around the sun or the sun’s around the earth, (the method couldn’t decide which) was definitely elliptical.

Part of the San Petronio Basilica heliometer.
The meridian line sundial inscribed on the floor at the San Petronio Basilica in Bologna, Emilia Romagna, northern Italy. An image of the Sun produced by a pinhole gnomon in the churches vaults 66.8 meters (219 ft) away fills this 168×64 cm oval at noon on the winter solstice.
Source Wikimedia Commons

By the time Newton became interested in astronomy it was accepted by all that the planetary orbits were Keplerian ellipses and not circles. Kepler’s first and third laws were accepted almost immediately being based on observation and solid mathematics but law two remained contentious until about 1670, when it was newly derived by Nicholas Mercator. The dispute over alternatives to Kepler’s second law between Ismaël Boulliau and Seth Ward was almost certainly Newton’s introduction to Kepler’s theories.

Turning to the other two bold emphasised claims we have:

 Newton provided an answer to a question that hadn’t even been asked yet. The problem with understanding the distant past is that we take our twenty-first century ideas and attitudes for granted. We think, for example, that the following is obvious: if the planets, like the Earth and Jupiter, regularly orbit the Sun, there must be something that causes them to follow their orbits. After all, if nothing caused them to orbit the Sun, they would fly off into deep space.

And:

The question of what caused the planetary orbits was not even on the table for astronomers in those days.

I’m afraid that Herr Kepler would disagree rather strongly with these claims. Not only had he asked this question he had also supplied a fairly ingenious and complex answer to it. Also quite famously his teacher Michael Maestlin rebuked him quite strongly for having done so. Kepler is usually credited with being the first to reject vitalist explanations of planetary motion by souls, spirits or angels (anima) and suggest instead a non-vitalist force (vir). His theory, based on the magnetic theories of Gilbert, was some sort of magnetic attraction emanating from the sun that weakened the further out it got. Kepler’s work started a debate that wound its way through the seventeenth century.

Ismaël Boulliau, a Keplerian, in his Astronomia philolaica from 1645 discussed Kepler’s theory of planetary force, which he rejected but added that if it did exist it would be an inverse-square law in analogy to Kepler’s law of the propagation of light. Newton was well aware of Boulliau’s suggestion of an inverse-square law. In 1666 Giovanni Alfonso Borelli, a disciple of Galileo, published his Theoricae Mediceorum planetarum ex causis physicis deductae in which he suggested that planetary motion was the result of three forces.

Famously in 1684 in a London coffee house Christopher Wren posed the question to Robert Hooke and Edmond Halley, if the force driving the planets was an inverse-square force would the orbits be Keplerian ellipses, offering a book token as prize to the first one to solve the problem. This, as is well known, led to Halley asking Newton who answered in the positive and wrote his Principia to prove it; in the Principia Newton shows that he is fully aware of both Kepler’s and Borelli’s work on the subject. What Newton deliberately left out of the Principia is that in an earlier exchange it had in fact been Hooke who first posited a universal force of gravity.

As this all too brief survey of the history shows, far from Newton providing an answer to a question that hadn’t been asked yet, he was, so to speak, a Johnny-come-lately to a debate that when he added his contribution was already eighty years old.

The Institute of Arts and Ideas advertises itself as follows:

So the IAI seeks to challenge the notion that our present accepted wisdom is the truth. It aims to uncover the flaws and limitations in our current thinking in search of alternative and better ways to hold the world.

Personally I don’t see how having a leading philosopher of science propagating the lone genius myth by spouting crap about the history of science fulfils that aim.

 

 

 

 

 

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Filed under History of Astronomy, History of science, Myths of Science, Newton

Why doesn’t he just shut up?

Neil deGrasse Tyson (NdGT), probably the most influential science communicator in the world, spends a lot of time spouting out the message that learning science allows you to better detect bullshit, charlatans, fake news etc. etc. However it apparently doesn’t enable you to detect bullshit in the history of science, at least judging by NdGT’s own record on the subject. Not for the first time, I was tempted recently to throw my computer through the window upon witnessing NdGT pontificating on the history of science.

On a recent video recorded for Big Think, and also available on Youtube and already viewed by 2.6 million sycophants, he answers the question “Who’s the greatest physicist in history?” His answer appears under the title My Man, Sir Isaac Newton. Thoughtfully, Big Think have provided a transcription of NdGT’s blathering that I reproduce below for your delectation before I perform a Hist_Sci Hulk autopsy upon it.

Question: Who’s the greatest physicist in history?DeGrasse Tyson:    Isaac Newton.  I mean, just look… You read his writings.  Hair stands up… I don’t have hair there but if I did, it would stand up on the back of my neck.  You read his writings, the man was connected to the universe in ways that I never seen another human being connected.  It’s kind of spooky actually.  He discovers the laws of optics, figured out that white light is composed of colors.  That’s kind of freaky right there.  You take your colors of the rainbow, put them back together, you have white light again.  That freaked out the artist of the day.  How does that work?  Red, orange, yellow, green, blue, violet gives you white.  The laws of optics.  He discovers the laws of motion and the universal law of gravitation.  Then, a friend of his says, “Well, why do these orbits of the planets… Why are they in a shape of an ellipse, sort of flattened circle?  Why aren’t… some other shape?”  He said, you know, “I can’t… I don’t know.  I’ll get back to you.”  So he goes… goes home, comes back couple of months later, “Here’s why.  They’re actually conic sections, sections of a cone that you cut.”  And… And he said, “Well, how did find this out?  How did you determine this?”  “Well, I had to invent integral and differential calculus to determine this.”  Then, he turned 26.  Then, he turned 26.  We got people slogging through calculus in college just to learn what it is that Isaac Newtown invented on a dare, practically.  So that’s my man, Isaac Newton. 

“WHO’S THIS BLATHERING TYSON FOOL?”

Let us examine the actual history of science content of this stream of consciousness bullshit. We get told, “He discovers the laws of optic…!” Now Isaac Newton is indeed a very important figure in the history of physical optics but he by no means discovered the laws of optics. By the time he started doing his work in optics he stood at the end of a two thousand year long chain of researchers, starting with Euclid in the fourth century BCE, all of whom had been uncovering the laws of optics. This chain includes Ptolemaeus, Hero of Alexandria, al-Kindi, Ibn al-Haytham, Ibn Sahl, Robert Grosseteste, Roger Bacon, John Pecham, Witelo, Kamal al-Din al-Farisi, Theodoric of Freiberg, Francesco Maurolico, Giovanni Battista Della Porta, Friedrich Risner, Johannes Kepler, Thomas Harriot, Marco Antonio de Dominis, Willebrord Snellius, René Descartes, Christiaan Huygens, Francesco Maria Grimaldi, Robert Hooke, James Gregory and quite a few lesser known figures, much of whose work Newton was well acquainted with. Here we have an example of a generalisation that is so wrong it borders on the moronic.

What comes next is on safer ground, “…figured out that white light is composed of colors…” Newton did in fact, in a series of groundbreaking experiment, do exactly that. However NdGT, like almost everybody else is apparently not aware that Newton was by no means the first to make this discovery. The Bohemian Jesuit scholar Jan Marek (or Marcus) Marci (1595–1667) actually made this discovery earlier than Newton but firstly his explanation of the phenomenon was confused and largely wrong and secondly almost nobody knew of his work so the laurels go, probably correctly, to Newton.

NdGT’s next statement is for a physicist quite simply mindboggling he says, “That freaked out the artist of the day.  How does that work?  Red, orange, yellow, green, blue, violet gives you white.” Apparently NdGT is not aware of the fact that the rules for mixing coloured light and those for mixing pigments are different. I got taught this in primary school; NdGT appears never to have learnt it.

Up next are Newton’s contributions to mechanics, “He discovers the laws of motion and the universal law of gravitation.  Then, a friend of his says, “Well, why do these orbits of the planets… Why are they in a shape of an ellipse, sort of flattened circle?  Why aren’t… some other shape?”  He said, you know, “I can’t… I don’t know.  I’ll get back to you.”  So he goes… goes home, comes back couple of months later, “Here’s why.  They’re actually conic sections, sections of a cone that you cut.””

Where to begin? First off Newton did not discover either the laws of motion or the law of gravity. He borrowed all of them from others; his crowing achievement lay not in discovering them but in the way that he combined them. The questioning friend was of course Edmond Halley in what is one of the most famous and well document episodes in the history of physics, so why can’t NdGT get it right? What Halley actually asked was, assuming an inverse squared law of attraction what would be the shape of aa planetary orbit? This goes back to a question posed earlier by Christopher Wren in a discussion with Halley and Robert Hooke, “would an inverse squared law of attraction lead to Kepler’s laws of planetary motion?” Halley could not solve the problem so took the opportunity to ask Newton, at that time an acquaintance rather than a friend, who supposedly answered Halley’s question spontaneously with, “an ellipse.” Halley then asked how he knew it and Newton supposedly answered, “I have calculated it.” Newton being unable to find his claimed calculation sent Halley away and after some time supplied him with the nine-page manuscript De motu corporum in gyrum, which in massively expanded form would become Newton’s Principia.

NdGT blithely ignoring the, as I’ve said, well documented historical facts now continues his #histsigh fairy story, “And he said, “Well, how did find this out?  How did you determine this?”  “Well, I had to invent integral and differential calculus to determine this.”” This is complete an utter bullshit! This is in no way what Newton did and as such he also never claimed to have done it. In fact one of the most perplexing facts in Newton’s biography is that although he was a co-discoverer/co-inventor of the calculus (we’ll ignore for the moment the fact that even this is not strictly true, read the story here) there is no evidence that he used calculus to write Principia.

NdGT now drops his biggest historical clangour! He says, “Then, he turned 26.  Then, he turned 26.  We got people slogging through calculus in college just to learn what it is that Isaac Newtown invented on a dare, practically.  So that’s my man, Isaac Newton.” Newton was twenty-six going on twenty seven when he carried out the optics research that led to his theory of colours in 1666-67 but the episode with Halley concerning the shape of planetary orbits took place in 1682 when he was forty years old and he first delivered up De motu corporum in gyrum two years later in 1684. NdGT might, as an astro-physicist, be an expert on a telescope but he shouldn’t telescope time when talking about historical events.

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Filed under History of Optics, History of science, Myths of Science, Newton

On an excursion

If you wish to read the latest words of wisdom, this time on the conception and invention of the reflecting telescope, then you will have to take an excursion to AEON magazine, where you can peruse:

How many great minds does it take to invent a telescope?

Isaac Newton’s reflecting telescope of 1671. Photo ©The Royal Society, London

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Filed under History of Astronomy, History of Optics, History of Technology, Newton