Category Archives: Newton

Chronology, history, or prophecy?

Bible chronology is a fascinating Early Modern intellectual phenomenon that combines science, history, and theology. Put simply, it is basically the attempt, assuming the Old Testament to be true and historically accurate, to develop the time frame of that history bringing into accord with what was known of the histories of the ancient cultures and calculate backwards to the point of God’s creation of the world. Although aware of its existence for a long time I paid it little heed because there were/are so many other things that interest me and occupy my time. This changed when the so-called gnu-atheists, whom I regard as smug ignoramuses, who give atheism a bad name, started to mock the Irish mathematician and theologian, James Ussher, Archbishop of Armagh, and Primate of All Ireland, on the “earth’s birthday”, 22 October, the date that Ussher calculated for the day of creation in his Bible chronology. A date well known amongst Protestants because it was enshrined in the Book of Common Prayer. I took up cudgels on Ussher’s behalf and wrote a blog post, In defence of the indefensible, pointing out that in the framework within which Ussher was working his calculations were in fact totally rational. In this post I wrote amongst other things:

Ussher was by no means the only prominent Bible chronologist of the 16th and 17thcenturies the most famous being the philologist and historian Joseph Justus Scaliger and of course Isaac Newton; others such as Johannes Kepler and Phillip Melanchthon also dabbled.

Now, it is well known that I am interested in everything that Isaac Newton indulged in during his long and unbelievably productive life, but that unbelievable productivity is exactly the problem. Newton wrote literally millions of words over a vast range of topics. If James Brown could crown himself, the hardest working man in show business, then Newton could crown himself the hardest working man in the history of science. Although I did write a brief post sketching Newton’s involvement in Bible chronology entitled, Newton was one too, the topic got put very definitely on the back burner.  I wrote another post on Bible chronology, about Joseph Justus Scaliger’s involvement, Counting the days, because his Julian Year Count, converted to the Julian Day Count became, in the nineteenth century, the universal dating system for astronomers.

Returning to Newton’s impossibly vast intellectual output, most people over the decades and centuries since his death concentrated on his mathematics, astronomy, and physics, actually by far the smallest part, whilst quietly ignoring the rest. There have been notable exceptions, which I’m not going to list here, but they were on the whole piecemeal. In more recent times the historian Rob Iliffe set up the Newton Project to systematically edit, comment upon, and make available Newtons vast inheritance, initially in Cambridge, and then somewhat ironically moving the whole to Oxford University, where it still current resides. There is a parallel Chymistry of Isaac Newton project at Indiana University. The Newton Project has been producing first class results and publishing first class material, such as Iliffe’s Priest of NatureThe Religious Worlds of Isaac Newton (OUP, 2019) for some time now and one of the most recent publications is Cornelius J Schilt, Isaac Newton and the Study of ChronologyProphecy, History, and Method (Amsterdam University Press, 2021), which could also be titled everything you ever wanted to know about Bible chronology in general and Isaac Newton’s involvement in it in particular. Yes, it really is that comprehensive!

The first thing to note is that this is a very serious piece of academic research and not in anyway a popular book. However, Schilt writes in a clear accessible style, so that anybody, who is interested, and is prepared to invest the effort can read the book with profit, even if they come to the topic as Bible chronology virgins, so to speak.

 A short introduction sets out the purpose of Schilt’s research, the problems that it entailed and a brief guide to the sections of the book. It closes with an unusually feature of the book. Instead of the usual massive bibliography at the end of the book, each section, and I will explain the sections shortly, closes with an, often extensive, bibliography for that section. The book is divided into four sections, each of which deals with a different aspect of Newton’s work and Schilt’s research into that work.

The first section is a comparatively short and concise, but highly informative, explanation of what exactly Bible chronology was in the Early Modern period. It illustrates how individual Bible chronologist approached the topic and what they hoped to achieve through their work. Having explained Bible chronology, Schilt closes the section with the question, Isaac Newton … Chronologist? Here Schilt discusses Newton’s two published chronology text, the first during his lifetime and heavily criticised and the second put together from his convolute of manuscripts by his acolytes after his death. Here Schilt touches upon, for the first time, the sheer volume of manuscripts and manuscript fragments on the topic, none of them noticeable finished, that Newton left behind in a total chaos, when he died, for historians to try and make some sort of sense out of. This section closes with an extremely extensive bibliography. If one just wished to read an introduction to Bible chronology and not Newton’s work in particular, then this section provides an excellent one. 

In the second section, Schilt introduces the reader to the mind of Isaac Newton and how it worked when he was producing his chronological work. We start with his library, the books he owned. The books that he read to inform himself about ancient history. Primary text by ancient authors for their historical content. Books by contemporary authors for information about which other ancient books he should read. Lists of books that he wished to acquire to further his knowledge. This is followed by Newton’s note taking habits. Here we run into major problems of which I was already aware from other areas of Newton’s work, mathematics, physics, astronomy. Newton was anything but organised in his note taking, using random sheets of paper, using the same sheet two-times years apart etc. etc. How Newton marked passages in books, not by underlining but by dogearing pages bending them over so far that the corner pointed to the passage in question.

The section closes out with a discussion of the fact Newton was an outsider, an independent scholar with no connections to others working in the same or related fields. Newton worked for himself not with others.

The second section makes very obvious that on a meta-level throughout the book we also get a very clear picture of how the researcher, Schilt, worked. He doesn’t just present the results of his research but outlines in detail how he extracted his results from the chaos that is both Newton’s papers and his approaches to his work over the years. This meta-level continues throughout the book and gives powerful insights into how to approach such a research task and carry it through to completion.

The third section takes the reader into the development history of Newton’s earliest chronological treatise, Theologiae gentilis origines philosophicae, known as Origines for short created literally over decades. This is simply not a working manuscript but an extensive collection of manuscripts, fragments, paragraphs, chapters, outlines. Schilt takes his reader through his analysis of what belongs where and why. Explaining his reasons for dating various pieces of writing and why he thinks over separately produced manuscripts belong to the Origines.

The reader gets presented with a master class in academic research detective work.

In the fourth and final section, Schilt does the same for the Chronology of Ancient Kingdoms Amended, as he did for Origines in section three. This is the manuscript on which Newton was working when he died, and which was edited and published by John Conduitt and Martin Folkes. Schilt also delivers a deep analysis as to why Newton was involved in chronological studies at all. Another master class in academic research detective work. As with the first two sections two and three both have their own bibliographies. 

I’m not going to go into any details of what Newton is trying the achieve with his chronological work, you’ll have to read the book for that, but his work is very different from that of the other Bible chronologists that the reader meets in section one. At the end of that first segment Schilt poses the question, is Newton a chronologist. His conclusion at the end of the fourth section is no he isn’t really. Newton’s chronology serves the higher purpose of helping him to analyse the Bible prophecies a central concern of his whole approach to religion. 

The book closes with “Some Concluding Remarks” which gives a one sentence summary of the book better then any I could create:

In this book, I have purposely presented the narrative of Newton’s chronological studies from the bottom up, as a quest in search of the real Chronology of Ancient Kingdoms Amended and the real Newton

This he does brilliantly. He goes on the point out that given the vast quantity of manuscript material that Newton left behind when he died and which became spread out all over the world when Newton’s papers were sold off in public auction in the 1930s, his work and the work in general of the Newton Project and the Chymistry of Isaac Newton project, has only become possible because of digitation of the material making it available to researchers.

The book is excellently presented, it closes with another general bibliography and an excellent index. Each of the four sections starts with a clear and informative short abstract explaining its contents. It has extensive footnotes, not the dreaded endnotes. There are illustrations that are just excerpts from manuscripts, which, however, are interesting as they often show Newton actively editing his work. There are also diagrammatical presentations of Schilt’s reconstructions of the order in which individual pieces of work were created and how various manuscripts fit together (see above).

I suspect Schilt’s book is compulsory reading for any serious student of the whole Newton, i.e., not just those interested in the maths and physics and also for scholars of Bible chronology. However, I think it can also be read by those more generally interested in Newton the man, a complex, puzzling and totally fascinating figure. Schilt has opened another window on that conundrum that is J M Keynes’ “the  last of the magicians” Woolsthorpe’s finest, Isaac Newton. 

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Filed under Book Reviews, Newton

STOMP, STOMP, STOMP … NEWTON DID WOT!

Oh dear! The HISTSCI_HULK has been woken from his post festive slumbers and is once again on the rampage. What has provoked this outbreak so early in the new year? He chanced to see a post, that one of my followers on Facebook had linked to, celebrating Newton’s new-style birthday on 4 January. As is well-known, we here at the Renaissance Mathematicus celebrate Newton’s old-style birthday, but that’s another story. 

The post is on a website called Wonders of Physics, is the work of an Indian physicist, Vedang Sati, and is titled:

10 Discoveries By Newton That Changed The World

I have reproduced the whole horror show below. Let us examine it.

Isaac Newton is one of the few names that will forever be enshrined in physics history and that too with a lot of glamour associated. Contributions of none other physicist match, his, well, Einstein’s, or not even his!? The following are Newton’s ten most well-known works that changed the world later on. 

A strong hagiographical vibe going down here, which doesn’t bode well.

Laws of motion

1. An object will remain at rest or move in a straight line unless acted upon by an external force.

2. F=ma.

3. For every action, there is an equal and opposite reaction. 

Newton’s three laws of motion, along with thermodynamics, stimulated the industrial revolution of the 18th and 19th centuries. Much of the society built today owes to these laws.

Remember these are supposedly the things that Newton discovered. His first law of motion, the law of inertia, was first formulated by Galileo, who, however, thought it only applied to circular motion. For linear motion it was first formulated by Isaac Beeckman and taken over from him by both René Descartes and Pierre Gassendi. Newton took it from Descartes. The second law, which was actually slightly different in the original form in which Newton used it, was taken from Christiaan Huygens. The third law was probably developed out of the studies of elastic and inelastic collision, which again originates by Descartes, who got much wrong which was corrected by both Huygens and Newton. Newton’s contribution was to combine them as axioms from which to deduce his mechanics, again probably inspired by Huygens. He tried out various combinations of a range of laws before settling on these three. Sati’s following statement is quite frankly bizarre, whilst not totally false. What about the Principia, where they occur, as the foundation of classical mechanics and perhaps more importantly celestial mechanics.

Binomial Theorem

Around 1665, Isaac Newton discovered the Binomial Theorem, a method to expand the powers of sum of two terms. He generalized the same in 1676. The binomial theorem is used in probability theory and in the computing sciences.

The binomial theorem has a very long history stretching back a couple of thousand years before Newton was born. The famous presentation of the binomial coefficients, known as Pascal’s Triangle, which we all learnt in school (didn’t we?), was known both to Indian and Chinese mathematicians in the Middle Ages. Newton contribution was to expand the binomial theorm to the so-called general form, valid for any rational exponent. 

Inverse square law

By using Kepler’s laws of planetary motion, Newton derived the inverse square law of gravity. This means that the force of gravity between two objects is inversely proportional to the square of the distance between their centers. This law is used to launch satellites into space.

I covered this so many times, it’s getting boring. Let’s just say the inverse square law of gravity was derived/hypothesized by quite a few people in the seventeenth century, of whom Newton was one. His achievement was to show that the inverse square law of gravity and Kepler’s third law of planetary motion are mathematically equivalent, which as the latter in derived empirically means that the former is true. Newton didn’t discover the inverse square law of gravity he proved it.

Newton’s cannon

Newton was a strong supporter of Copernican Heliocentrism. This was a thought experiment by Newton to illustrate orbit or revolution of moon around earth (and hence, earth around the Sun)

He imagined a very tall mountain at the top of the world on which a cannon is loaded. If too much gunpowder is used, then the cannon ball will fly into space. If too little is used, then the ball wouldn’t travel far. Just the right amount of powder will make the ball orbit the Earth. 

This thought experiment was in Newton’s De mundi systemate, a manuscript that was an originally more popular draft of what became the third book of the Principia. The rewritten and expanded published version was considerably more technical and mathematical. Of course, it has nothing to do with gunpowder, but with velocities and forces. Newton is asking when do the inertial force and the force of gravity balance out, leading to the projectile going into orbit. It has nothing to do directly with heliocentricity, as it would equally apply to a geocentric model, as indeed the Moon’s orbit around the Earth is. De mundi systemate was first published in Latin and in an English translation, entitled A Treatise of the System of the World posthumously in 1728, so fifty years after the Principia, making it at best an object of curiosity and not in any way world changing. 

Calculus

Newton invented the differential calculus when he was trying to figure out the problem of accelerating body. Whereas Leibniz is best-known for the creation of integral calculus. The calculus is at the foundation of higher level mathematics. Calculus is used in physics and engineering, such as to improve the architecture of buildings and bridges.

This really hurts. Newton and Leibniz both collated and codified systems of calculus that included both differential and integral calculus. Neither of them invented it. Both of them built on a two-thousand-year development of the discipline, which I have sketch in a blog post here. On the applications of calculus, I recommend Steven Strogatz’s “Infinite Powers”

Rainbow

Newton was the first to understand the formation of rainbow. He also figured out that white light was a combination of 7 colors. This he demonstrated by using a disc, which is painted in the colors, fixed on an axis. When rotated, the colors mix, leading to a whitish hue.

In the fourteenth century both the German Theodoric of Freiberg and the Persian Kamal al-Din al-Farsi gave correct theoretical explanations of the rainbow, independently of one another. They deliver an interesting example of multiple discovery, and that scientific discoveries can get lost and have to be made again. In the seventeenth century the correct explanation was rediscovered by Marco Antonio de Dominis, whose explanation of the secondary rainbow was not quite right. A fully correct explanation was then delivered by René Descartes. 

That white light is in fact a mixture of the colours of the spectrum was indeed a genuine Newton discovery, made with a long series of experiments using prisms and then demonstrated the same way. Newton’s paper on his experiments was his first significant publication and, although hotly contested, established his reputation. It was indeed Newton, who first named seven colours in the spectrum, there are in fact infinitely many, which had to do with his arcane theories on harmony. As far as can be ascertained the Newton Disc was first demonstrated by Pieter van Musschenbroek in 1762. 

Reflecting Telescope

In 1666, Newton imagined a telescope with mirrors which he finished making two years later in 1668. It has many advantages over refracting telescope such as clearer image, cheap cost, etc.

Once again, the reflecting telescope has a long and complicated history and Newton was by no means the first to try and construct one. However, he was the first to succeed in constructing one that worked. I have an article that explains that history here.

Law of cooling

His law states that the rate of heat loss in a body is proportional to the difference in the temperatures between the body and its surroundings. The more the difference, the sooner the cup of tea will cool down.

Whilst historically interesting, Newton’s law of cooling holds only for very small temperature differences. It didn’t change the world

Classification of cubics

Newton found 72 of the 78 “species” of cubic curves and categorized them into four types. In 1717, Scottish mathematician James Stirling proved that every cubic was one of these four types.

Of all the vast amount of mathematics that Newton produced, and mostly didn’t publish, to choose his classification of cubics as one of his 10 discoveries that changed the world is beyond bizarre. 

Alchemy

At that time, alchemy was the equivalent of chemistry. Newton was very interested in this field apart from his works in physics. He conducted many experiments in chemistry and made notes on creating a philosopher’s stone.

Newton could not succeed in this attempt but he did manage to invent many types of alloys including a purple copper alloy and a fusible alloy (Bi, Pb, Sn). The alloy has medical applications (radiotherapy).

Here we have a classic example of the Newton was really doing chemistry defence, although he does admit that Newton made notes on creating a philosopher’s stone. If one is going to call any of his alloys, world changing, then surely it should be speculum, an alloy of copper and tin with a dash of arsenic, which Newton created to make the mirror for his reflecting telescope, and which was used by others for this purpose for the next couple of centuries.

Of course, the whole concept of a greatest discovery hit list for any scientist is totally grotesque and can only lead to misconceptions about how science actually develops. However, if one is going to be stupid enough to produce one, then one should at least get one’s facts rights. Even worse is that things like the classification of the cubics or Newton’s Law of Cooling are anything but greatest discoveries and in no way “changed the world.” 

You might wonder why I take the trouble to criticise this website, but the author has nearly 190,000 followers on Facebook and he is by no means the only popular peddler of crap in place of real history of science on the Internet. I often get the feeling that I and my buddy the HISTSCI_HULK are a latter-day King Cnut trying to stem the tide of #histSTM bullshit. 

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Filed under History of science, Myths of Science, Newton

Christmas Trilogy 2021 Part 1: The evolving views of the Last of the Magicians

Some time back, it seemed that several times a year someone would post an article or a blog post on the Internet along the lines of, “Shock! Horror! Outrage! did you know that Isaac Newton was a practicing alchemist?” All the historians of science, who know their Newton, would shrug their shoulders, and quietly repeat, actually we have known about this for a long time. It is quite interesting to look at how the views of Newton the alchemist have changed over time, but first a little bit of general background on his alchemical activities.

There are two more or less popular takes from people who have never bothered to investigate the topic. There are those, who claim that Newton merely dabbled a bit in alchemy, so historian shouldn’t take it seriously. Others claim that Newton first took up alchemy in his dotage, after his scientific career was over, an old man’s foible. Both of these are fundamentally wrong. 

Newton was a dedicated student and practitioner of alchemy for thirty years from 1666 to 1696, massively reducing his engagement when he moved to London. He had a shed built in the gardens of Trinity College, which he used as his alchemical laboratory for six weeks before the start of winter and six weeks at the end of winter every year. 

Isaac Newton’s rooms. View of the rooms occupied by Sir Isaac Newton (1642-1727) at Trinity College, Cambridge. His rooms were on the first floor between the Great Gate and the Chapel. The small room projecting from the Chapel was probably his alchemical laboratory. Source:

This is of course the same period in which he did all of his ground-breaking work in mathematics, astronomy, physics, and optics. In these decades, he also did extensive work on theology and historical chronology. I sometimes get the impression that he never slept.

He accumulated a substantial library of books on alchemy, as well of hermeticism, at least 170 titles. There are quite literally reams of his writings on alchemy, a total of over one million words! He took notes on his readings and even copied out pages of some alchemical texts. Apparently, Newton seldom made annotations in the books that he owned but he heavily annotated two of his alchemical volumes, Eyraeneus Philaletha Cosmopolita, aka George Starkey’s Secrets Reveal’d and Lazarus Zetzner’s Theatrum chemicum.[1] 

Source: Wikimedia Commons

From his readings, Newton complied lexica of alchemical symbols and veiled terms in an attempt to decode the texts he was consuming. It is very obvious that Newton’s engagement was very serious and on a very large scale.

So, how did his contemporaries react to Newton’s alchemical activities? The straightforward answer is they didn’t because they didn’t know about them. Newton stuck to, what might be termed, the alchemists’ honour code that is only to communicate about his alchemical activities with other adepts and even then, in veiled terms. He even once rebuked Robert Boyle, a fellow practitioner, for publishing an article on alchemy.

When Newton died, his papers passed into the possession of his half-niece Catherine Barton and her husband John Conduitt. When they died the papers passed into the possession of their only daughter Catherine, who was born in 1721. In 1740, Catherine married John Wallop, Viscount Lymington, the eldest son of the Earl of Portsmouth. Catherine’s son John Wallop inherited the title from his grandfather in 1762. John Wallop senior had died in 1742. Newton’s papers, now in possession of the Portsmouth family were stored in a trunk and basically forgotten about for about for more than a century. 

In 1872, Isaac Newton Wallop[2], 5th Earl of Portsmouth donated Newton’s papers to Trinity College both his and Newton’s alma mater.

“Horseflesh”, the 5th Earl of Portsmouth, caricature by Spy in Vanity Fair, 1 July 1876. Source: Wikimedia Commons

A committee chaired by the astronomer John Couch Adams and the physicist George Stokes was set up to review the papers. In a process that lasted sixteen years, this committee only selected Newton’s mathematical and scientific papers rejecting the rest to protect the reputation of their scientific hero. The bulk of the papers were returned to the Portsmouth family. One could describe this action as, “if we ignore Newton’s alchemical, theological, and chronological activities, then we can pretend they never took place”. 

This committee’s behaviour was not the only negative reaction to Newton’s alchemical activities during the nineteenth century. In 1831, the Scottish physicist, David Brewster (1781–1868),

Inner picture of a cigar box from the early 1900s with a portrait of Brewster. Source: Wikimedia Commons

nowadays best known in popular culture as the inventor of the kaleidoscope,  published a hagiographical biography of his personal hero Isaac Newton, The Life of Sir Isaac Newton (J. Murry, 1831), as a reaction to the, as he saw it, denigrating biography written by the French astronomer, physicist, and mathematician, Jean-Baptiste Biot (1774–1862) and published in 1822. During the research for his biography, Brewster was mortified when he discovered that his hero had dabbled in alchemy, he wrote:

There is no problem of more difficult solution than that which relates to a belief in alchemy … by men of high character and lofty attainments.

He further argued that Newton was of “a peculiar bent of mind”, the same mind that was otherwise “of such a power and so nobly occupied with the abstraction of geometry.”

Brewster also refused to believe that Newton was a unitarian, stating that he was upright, orthodox, church-going Anglican. This led to a dispute with Augustus De Morgan (1806–1871, himself a unitarian, who vigorously defended Newton’s Unitarianism. Newton, in fact, devoted a lot of time and effort trying to prove that the Catholic Church had falsified the Bible to create the Trinitarian doctrine[3].

 In 1936, the Portsmouth family sold of the baulk of Newton’s papers by public auction. An act that brings tears to the eyes of every dedicated historian of science. Fortunately, the economist John Maynard Keynes (1883–1946), a true Cambridge man born so to speak, into the university, his father was a Cambridge lecturer, bought up a large chunk of Newton’s papers, also acquiring other papers from other buyers after the auction and donated them to King’s College Library.

Caricature of J M Keynes by David Low, 1934

He read through the documents that he had acquired and like Brewster was disappoint that his hero was a practicing alchemist and baptised him, in an essay, “the last of the magicians”, hence the title of this post. He also wrote “the last wonder child to whom the Magi could do sincere and appropriate homage.” Like Brewster he couldn’t understand why Newton would engage in something “wholly devoid of scientific value” and viewing Newton’s obsession as an aberration stated, “geniuses are very peculiar.”

In the late 1950s, two professional historians of science, Rupert Hall (1920–2009) and Marie Boas (1919–2009), began to examine the Portsmouth papers and came up with a, for professionals, peculiar reaction, in that they simply denied that Newton had practiced alchemy. For Hall and Boas, it was unthinkable that the scientist Newton would indulge in anything so unscientific as alchemy, what he was doing was legitimate chemistry and be merely consulted alchemical texts for their descriptions of laboratory methods. Well after all, nearly all the standard laboratory analytical practices in chemistry were devised/discovered/created/invented by alchemists. To be fair to Hall and Boas, Newton did in fact use the knowledge of chemical analysis that he had acquired through his alchemical activities to devise new, improved methods for assaying metals, when working at the Royal Mint. It was also Hall and Boas, who insisted that Newton’s “chemical activities” took place after he had effectively stopped producing real science and mathematics. The old man dabbling. I think the most charitable thing one can say about Hall and Boas’ efforts is, there are none so blind as those that will not see. 

The Big Bang in research into Newton’s alchemy can be dated to the publication of The Foundations of Newton’s Alchemyor the Hunting of the Green Lyon by Betty Jo Teeter Dobbs (1930–1994) in 1975 by CUP.

Here was a full-length monograph that dealt with Newton’s alchemy, as alchemy, in great depth and detail. No denial, no repulsion, just a highly readable but seriously academic analysis of the alchemical activities of the good Isaac, without value judgement. It was through this book that I first became aware of Newton the alchemist and the book also changed my attitude to the so-called occult sciences. Like most people of my generation, these were not science and so were not of interest to an apprentice historian of science. These days I spend at least as much time and effort defending the study of the occult science, as I do the “real” sciences. 

Dobbs wrote several more books on Newton’s alchemy and how it fitted, in her opinion, into the rest of his activities, both scientific and theological. Important in the acceptance of her work was the active support that she and her theories received from Richard Westfall (1924–1996), author of the, up till now, best biography of Newton, Never at Rest CUP, 1980). As well as establishing beyond any reasonable doubt that Newton was a serious alchemist, Dobbs developed a theory based on her interpretation of the evidence that Newton had adopted the concept of action at a distance, against the prevailing mechanical philosophy leading to severe criticism from Leibniz and the Cartesians, from his alchemical research. This theory found a lot of general acceptance and up till recently, I too accepted it.

In 1988, Oxford University Press published a reader Let Newton Be! A new perspective on his life and works, with essays on all aspects of his work including his occult activities. Two of the essays Newton, matter, and magic by John Henry and The secret life of an alchemist by Jan Golinski accept and deal with Newton’s alchemy as a normal part of his intellectual makeup. Both accept Dobbs’ hypothesis that Newton’s concept of force derived from concepts of occult power.

In 2016, Cambridge University Press published the second edition of their Newton reader, The Cambridge Companion to Newton, which contains an essay from William R. Newman, one of a group of prominent historians of alchemy, who in recent years have completely rewritten the history of the topic. In his essay, A preliminary reassessment of Newton’s alchemy, Newman effectively demolishes the Dobbs theory showing that it doesn’t work. Instead, he proposes a new theory that Newton’s alchemical studies influenced his optic investigations in the late 1660s. 

Newman was working on an in-depth study and analysis of Newton’s alchemy, which appeared as a book in 2018, Newton the AlchemistScience, Enigma, and the Quest for Nature’s “Secret Fire” (Princeton University Press).

This will certainly prove to be the definitive account of Newton’s alchemy for the next years and my copy is somewhere near the top of my to read list, I hope to delve not to far in the future. 

Over the centuries the reactions to Newton the alchemist have gone from ignorance, we didn’t know he was one, to abhorrence and bewilderment, to if we ignore it it doesn’t exist, to acceptance and serious historical analysis.


[1] I owe this snippet of information to Cornelius J. Schilt’s excellent Isaac Newton and the Study of ChronologyProphecy, History, and Method (Amsterdam University Press, 2021) p. 96. The book is my current bedtime reading and a review will follow sometime next year.

[2] Yes, that really is his name!

[3] For an excellent analysis of the 19th century Newton biographies I heartily recommend Rebekah Higgitt’s Recreating NewtonNewtonian Biography and the Making of Nineteenth-Century History of Science (Pickering & Chatto, 207), which I reviewed here 

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Filed under History of Alchemy, Newton

Martin who?

Anna Marie Roos is one of those scholars, who make this historian of Early Modern science feel totally inadequate. Her depth and breadth of knowledge are awe inspiring and her attention to detail lets the reader know that what she is saying is with a probability bordering on certainty accurate and correct. Over the years she has churned out an imposing series of books covering a wide spectrum of the history of science in Britain during the Early Modern Period, each of them an impressive monument to her scholarship. Her latest addition to this series is a biography of Martin Folkes. I can already hear a significant number of readers of this blog muttering Martin who? Hence the title of this review. The fog lifts somewhat if one reads the full title of the volume, Martin Folkes (1690–1754)Newtonian, Antiquary, Connoisseur.[1]

Folkes is in fact a victim of a strange little hiccup in the popular history of science and also of the big names, big events approach to the discipline. The hiccup is the fact that the spotlight is shone very bright on the sixteenth and seventeenth centuries, the so-called scientific revolution, and on the nineteenth century, oft called the second scientific revolution, but the eighteenth century gets passed over with hardly a mention. Pass along folks nothing of interest to see here. This is, of course, not true a lot of important science was created in the eighteenth century, and this is one of the themes that Roos deals with, in her account of Folkes life, which encompassed the first half of the eighteenth century. 

On the problem of the big names, big events approach to the history of science, Folkes falls through the net because there are no theories, major discoveries or inventions that can be attributed to him. However, science does not just progress through the big events in fact most scientific progress comes from those, who, so to speak, dot the ‘I’s and cross the ‘T’s. What Thomas Kuhn in one of his most useful contributions called ‘normal science’. 

Martin Folkes was a mathematician, a Newtonian physicist, an antiquarian, a metrologist, a science administrator, an organiser, a science communicator, a science promotor, and a patron, and in all of these roles he made significant contributions to the progress of science not just in Britain but in the whole of Europe during the first half of the eighteenth century. Roos’ biography of this man with many hats brings all of these aspects of his personality and his activities vividly to light.

How did Martin Folkes become so significant and influential? One could say with more than somewhat justification that he was born with the proverbial silver spoon in his mouth. His family were wealthy, well connected, influential, landowning members of the London high society at the end of the seventeenth and beginning of the eighteenth centuries. He received an excellent private education receiving tuition in Latin, Greek, Hebrew and conversational French from the Huguenot refugee, James Cappel (1639–1722), and, perhaps more significantly, mathematics from another Huguenot refugee Abraham De Moivre (1667–1754), who was one of the leading mathematicians of the age and a member of the Newtonian inner circle. 

Folkes’ contact with De Moivre serves as an early introduction to what was probably Folkes’ greatest strength, he was, in modern parlance, a master networker. This aspect of Folkes’ life and personality is described in great detail throughout Roos’ narrative. Through De Moivre Folkes came into contact with De Moirve’s other private students a significant cross-section of the early eighteenth century scientific and social elite. Through De Moivre he also gained access to Newton and the Newtonians, becoming a life-long highly active Newtonian himself.

Through Newton, Folkes was elected to the Royal Society, the start of a career that would see him become president of that august organisation, as well as president of the equally august Society of Antiquities; he was the only man ever to hold both presidencies. Here we meet another aspect of Folkes personality that certainly played an important role in his networking activities, he was immensely clubbable. For those, who don’t know this somewhat archaic, wonderful English word, it means somebody that others like to have as members of their social clubs and groupings. It seems that if someone set up a new club or society for the intellectual and/or social elite in the first half of the eighteenth century then Folkes was member, oft a founding member, organiser, and driving force. 

Roos’ detailed description of the clubs, societies, and groups of which Folkes became an always-active member means that her biography is a historical guide to the social and cultural life of the social and intellectual upper echelons during Folkes lifetime. This not only includes the Royal Society and the Society of Antiquities, but also the then newly emerging English Freemasonry movement, in which Folkes played a leading role, the short lived but influential Egyptian Society, as well as various drinking and dinner clubs, in which members of the academic societies met more informally following sessions of those societies. Roos’ volume is also a guide to the eating and drinking habits of the well-heeled gentlemen of the period. 

Although very much a member of the English establishment, Folkes was anything but a Little Englander. He maintained active contact with natural philosophers, mathematicians, and other propagators of the new sciences throughout Europe. He encouraged foreigners to come to Britain, also to buy British scientific instruments, and to publish the results of their researchers in British journals. He also patronised and supported foreign scholars he thought worthy of promotion. 

Folkes extensive connections with the European mainland were also strengthened by his almost religious adherence to Newtonianism. Anybody who casts even a brief look at a modern English translation of Newton’s Principia quickly realises that it is not a work for the faint hearted or the ill prepared. The situation was not any different in the first half of the eighteenth century and Newton took no interest in popularising his work or making it available to the masses. Added to this was the fact that large parts of those in the know in Europe initially rejected much of Newton’s work on scientific and philosophical grounds, but also, with particular respect to his work in optics, because of their failure to reproduce many of his experiments. Various of Newton’s disciples jumped into the breach, left by the master’s silence, and presented popularisations of his major works, as books, lecture tours and demonstrations. Most notable, here, are another Huguenot refugee, John Theophilus Desaguliers (1683–1744) and the Dutchman, Willem ’s Gravesand (1688–1742). 

Folkes was also an eager missionary in the cause of Newtonianism. Folkes went on a grand tour of Europe between 1732 and 1735 preaching the gospel of Newton to learned societies and individual savants, in particular demonstrating those of Newton’s optical experiments that others had had difficulty replicating. During this tour Folkes made many friendships within the European intellectual milieu; friendships that he maintained through extensive correspondence when he returned to England.

One aspect of Roos’ biography that I found particularly interesting was her descriptions of Folkes’ activities as a metrologist. For those that don’t know this is not a typo for meteorologist, as my Word correction programme seemed to think, until I added metrologist to its dictionary. Metrology is the scientific study of measurement or as another dictionary defines it, the science of weights and measures; the study of units of measurements. Folkes interests was antiquarian, and he spent significant time and effort, on his grand tour, in trying to determine the correct length of a Roman foot. Why should I be interested in what seems, superficially at least, to be an arcane hobby on Folkes’ part? 

In reality there was nothing arcane about Folkes’ interest in metrology. The turn to quantitative, empirical, experimental science and the resultant mathematisation that we call the scientific revolution led to a widespread discussion within the scientific community on systems and units of measurement towards unification, standardisation, and accuracy in the seventeenth and eighteenth century. Historical investigations searching for supposed natural units of measurement were an integral part of that discussion. All of this peaked in the introduction of the metric system in France in 1799 and the Imperial system of measurement in the UK and British Empire in 1826. This important episode tends to get ignored in the mainstream history of science, so it was good that it gets handled here by Roos.

Oxford University Press have done Anna Marie Roos and Martin Folkes proud in the presentation of this biography. The front cover has a full colour portrait of the books subject and the book itself is extensively illustrated with grayscale and colour photos. The book is printed on bright white paper with an attractive typeface. Roos maintains her usual high scholarly standards, the book bursts at the seams with extensive, highly informative footnotes, which in turn reference a very extensive bibliography. All is rounded out by an equally extensive index.

All of the above is a mere sketch of all the context that Roos has packed into this model example of a biography of an eighteenth-century polymath, who definitely earns the attention that Roos has given to his life, work, and influence. This is an all-round, first-class piece of scholarship that not only introduces the reader to the little known but important figure of Martin Folkes, but because of the extensive contextual embedding provides a solid introduction to the social and cultural context in which science was practiced not only in England but throughout Europe in the first half of the eighteenth century. Highly recommended and not just for historians of science 


[1] Anna Marie Roos, Martin Folkes (1690–1754)Newtonian, Antiquary, Connoisseur, OUP, Oxford, 2021

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Filed under Book Reviews, History of science, Newton

Isaac goes to town

I appear to have become something of a fan of the Cambridge University historian of science, Patricia Fara. The first book of hers that I read, and that some years ago, was Newton: The Making of a Genius (Columbia University Press, 2002), an excellent deconstruction of the myths that grew up around England’s most lauded natural philosopher during the eighteenth and nineteenth centuries. I do not own this volume, but I do own her Pandora’s Breeches: Women, Science and Power in the Enlightenment (Pimlico, 2004), which delivers what the title promises. A detailed look at women, who contributed to enlightenment science and, who usually get ignored in mainstream history of science. I also own her An Entertainment for Angels: Electricity in the Enlightenment (Icon Books: 2002), a delightful romp through the first century of the scientific investigation of phenomenon of electricity. Also on my bookshelf is her ScienceA Four Thousand Year History (OUP, 2009), a fresh and provocative one volume overview of the history of science. To round out my Fara collection I also have her Sex, Botany & EmpireThe Story of Carl Linnaeus and Joseph Banks (Icon Books, 2003) on my to-read-pile; I mean who could resist a title like that from an author with a proven track record for excellent history of science narratives.

Patricia Fara’s latest publication returns to the subject of England’s most iconic natural philosopher, Isaac Newton, but deals not with his science but the last thirty years of his life after he had effectively abandoned the production of new science and mathematics for the life of a gentleman about town, Life after GravityIsaac Newton’s London Career[1].

Before I go into detail, this book maintains the high standards of historical research and literary excellence that Fara has consistently displayed over her previous publication. 

Anybody, who is reasonably acquainted with Newton’s biography will already know that he turned his back on Cambridge and academia in 1696, to move to London to become first Warden and then in 1699 Master of the Royal Mint. This move enabled him to become President of the Royal Society in 1704, an integral part of the socio-political power structure in the capitol during the next thirty years, and also to become immensely wealthy. It is to this part of Newton’s life that Fara turns her sharp and perceptive eye and which she analyses with her acerbic, historical scalpel.

I have over the decades read a lot of Newton biographies, as well as papers and books that deal with specific aspects of his life and work, including aspects of the last thirty years of his life that he spent living in London, such as Tom Levenson’s excellent Money for NothingThe South Sea Bubble and the Invention of Modern Capitalism. Despite this, I learnt a lot of new things from Fara’s excellent small volume.

Fara’s book is actually two interlinked narratives; the contextual biography of Newton’s years in London is interwoven with an analysis of William Hogarth’s 1732 painting, The Indian Emperor. Or the Conquest of Mexico. As performed in the year 1731 in Mr Conduitt’s, Master of the Mint, before the Duke of Cumberland etc. Act 4, Scene 4.

This painting by Hogarth shows a performance of a heroic drama, written by John Dryden (1631–1700) and first performed in 1665, being performed by a group of children in the drawing room of the town house of John Conduitt (1688–1737), the husband of Newton’s niece and one time housekeeper, Catherine Barton; Conduitt was also Newton’s successor as Master of the Mint. This picture depicts several of the main characters of the book’s biographical narrative, including Newton as a bust mounted on the wall. It also reflects some of the main themes of the books such as imperialism. The interweaving of the descriptions of the painting and the various episodes of Newton’s life in London is a very powerful literary device and is representative for the fact that Fara’s book is deeply contextual and not just a simple listing of Newton’s activities during those last thirty years of his life.

The book is divided into three sections, the first of which deals mainly with Newton’s various residences in London and his general domestic life, within the context of early eighteenth-century London. The second section turns the reader’s attention to Newton’s reign at the Royal Society and the reign of the first Hanoverian King, George I, and his family and court with whom Newton was intimately involved. The final section takes the reader to the Royal Mint and also turns the spotlight on English imperialism.

I’m not going to go into much detail, for that you’ll have to read the book and I heartily recommend that you do so, but I want to draw attention to two prominent aspects of the book that I found particularly good.

The first is, surprising perhaps in a Newton biography, a good dose of feminist historiography. As one would expect from the author of Pandora’s Breeches and more recently A LAB of ONE’S OWNScience and Suffrage in the First World War(OUP, 2018)–I love the indirect Virginia Woolf reference–Fara pays detailed attention to the women in her narrative. 

In her description of life in the Tower of London, where the Mint was situated and where Newton initially lived when he moved to London, she introduces the reader to Elizabeth Tollet (1694-1754). Tollet, a poet and translator, was the handicapped daughter of George Tollet a Royal Navy, who lived with her father in the Tower. Unusually for the time, she was highly educated, Fara uses her diaries to describe life in the Tower and also features some of her poems that dealt with Newtonian natural philosophical themes and her elegy, On the Death of Sir Isaac Newton (1727).

Fara also paints a very sympathetic portrait of Queen Anne (1665–1714), who ruled over Britain for slightly more that the first decade of the eighteenth century. She has often been much maligned by her biographers and Fara presents her in a more favourable light. Newton niece and sometime housekeeper, Catherine Barton (1679–1739), naturally, features large and in this context Fara discusses an interesting aspect of male chauvinism from the period, of which I was previously unaware. The habit of older gentlemen having sexual relations with much younger, often closely related, women sometimes within a marital relationship, sometimes not. She details the case of Robert Hooke (1635–1703), who slept with his niece Grace. She speculates, whether Voltaire’s claim that Newton got his job at the Mint, because Charles Montagu (1661–1715) had slept with Catherine Barton is true or not. If he had, she would have been a teenager at the time.

The section on the Hanoverian court concentrates on Caroline of Ansbach (1683–1737), George I daughter-in-law, a fascinating woman, who enjoyed intellectual relations with both Leibniz and Newton. Effectively abandoning the former for the latter, when she moved, with the court, from Hanover to London. Fara’s book is worth the purchase price alone, for her presentation of the women surrounding Newton during his London residency.

The second aspect of the book that I would like to emphasise is Fara’s treatment of British imperialism and the associated exploitation and racism during the first third of the eighteenth century. Recently, there have been major debates about various aspects of these themes. In the general actually debate on racism, historians have pointed out that the modern concept of racism is a product of the eighteenth century. Others have opposed this saying that one should instead emphasise the eighteenth century as the century of the Enlightenment, quoting Newtonian physics and astronomy as one of its great contributions, apparent unsullied by associations with Empire and slavery. Coming from a different direction the debate on the restoration of art works stolen by the colonial powers, Britain leading the pack, has cast another strong spotlight on this period and its evils.

Fara tackles the themes head on. She goes into detail about how the gold that Newton minted in large quantities, the major source of his own private wealth, came from British exploitation of Africa. She also goes into quite a lot of detail concerning the joint stock companies, set up to further Britain’s imperial aims, to establish and exploit its colonies and their active involvement in the slave trade. As well as profiting from the African gold that he minted for the British government, Newton also profited from his extensive investments in the East India Company and initially from his investments in the South Sea Company, both of which were involved in the slave trade. He, of course, famously also lost heavily in the collapse of the South Sea Company’s share price. Fara successfully removes the clean white vest that many attempt to award Newton in this context.

Fara’s book is much more that a portrait of Newton’s final three decades, it is also a wide ranging and illuminating portrait of London in the first third of the eighteenth century, its social life, its economics, its politics, and its imperialism. This is not just the London of Newton, but also of Swift, Defoe, Pope, and many others. Everything is carefully and accurately researched and presented for the reader in an attractive, easy to read, narrative form. The book has endnotes, which are just references to the very extensive bibliography. There is also as very good index.

The book is illustrated with a block of colour illustration, which are repeated in black and white at the relevant points in the text, and here I must make my only negative comment on Fara’s otherwise excellent book. The quality of the reproduction of colour prints is at best mediocre and, in my copy at least the black and white prints are so dark as to render them next to useless. Something went wrong somewhere.

As should be clear, if you have read your way through all of this review,  I think this is an excellent book and I can’t recommend it enough. If I had a five-star system of valuation, I would be tempted to give Fara’s volume six, with perhaps half a star taken off for the poor quality of the illustrations, for which, of course, the author is not responsible. In my opinion it is a must read for anybody interested in Newton and his life but also for those more generally interested in the Augustan Age. If you one of those general interested in reading, well written, accessible, entertaining, and informative history books then you can add Fara’s tome to your reading list without reservations.


[1] Patricia Fara, Life after GravityIsaac Newton’s London Career, OUP, Oxford, 2021

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Filed under Book Reviews, History of science, Newton

The emergence of modern astronomy – a complex mosaic: Part LII

This is a concluding summary to my The emergence of modern astronomy – a complex mosaic blog post series. It is an attempt to produce an outline sketch of the path that we have followed over the last two years. There are, at the appropriate points, links to the original posts for those, who wish to examine a given point in more detail. I thank all the readers, who have made the journey with me and in particular all those who have posted helpful comments and corrections. Constructive comments and especially corrections are always very welcome. For those who have developed a taste for a continuous history of science narrative served up in easily digestible slices at regular intervals, a new series will start today in two weeks if all goes according to plan!

There is a sort of standard popular description of the so-called astronomical revolution that took place in the Early Modern period that goes something liker this. The Ptolemaic geocentric model of the cosmos ruled unchallenged for 1400 years until Nicolas Copernicus published his trailblazing De revolutionibus in 1453, introducing the concept of the heliocentric cosmos. Following some initial resistance, Kepler with his three laws of planetary motion and Galileo with his revelatory telescopic discoveries proved the existence of heliocentricity. Isaac Newton with his law of gravity in his Principia in 1687 provided the physical mechanism for a heliocentric cosmos and astronomy became modern. What I have tried to do in this series is to show that this version of the story is almost totally mythical and that in fact the transition from a geocentric to a heliocentric model of the cosmos was a long drawn out, complex process that took many stages and involved many people and their ideas, some right, some only half right and some even totally false, but all of which contributed in some way to that transition.

The whole process started at least one hundred and fifty years before Copernicus published his magnum opus, when at the beginning of the fifteenth century it was generally acknowledged that astronomy needed to be improved, renewed and reformed. Copernicus’ heliocentric hypothesis was just one contribution, albeit a highly significant one, to that reform process. This reform process was largely triggered by the reintroduction of mathematical cartography into Europe with the translation into Latin of Ptolemaeus’ Geōgraphikḕ Hyphḗgēsis by Jacopo d’Angelo (c. 1360 – 1411) in 1406. A reliable and accurate astronomy was needed to determine longitude and latitude. Other driving forces behind the need for renewal and reform were astrology, principally in the form of astro-medicine, a widened interest in surveying driven by changes in land ownership and navigation as the Europeans began to widen and expand their trading routes and to explore the world outside of Europe.

2880px-1660_celestial_map_illustrating_Claudius_Ptolemy's_model_of_the_Universe

The Ptolemaic Cosmos: Andreas Cellarius, Harmonia Macrocosmica 1660 Source: Wikimedia Commons

At the beginning of the fifteenth century the predominant system was an uneasy marriage of Aristotelian cosmology and Ptolemaic astronomy, uneasy because they contradicted each other to a large extent. Given the need for renewal and reform there were lively debates about almost all aspects of the cosmology and astronomy throughout the fifteenth and sixteenth centuries, many aspects of the discussions had their roots deep in the European and Islamic Middle Ages, which shows that the 1400 years of unchallenged Ptolemaic geocentricity is a myth, although an underlying general acceptance of geocentricity was the norm.

A major influence on this programme of renewal was the invention of moving type book printing in the middle of the fifteenth century, which made important texts in accurate editions more readily available to interested scholars. The programme for renewal also drove a change in the teaching of mathematics and astronomy on the fifteenth century European universities. 

One debate that was new was on the nature and status of comets, a debate that starts with Toscanelli in the early fifteenth century, was taken up by Peuerbach and Regiomontanus in the middle of the century, was revived in the early sixteenth century in a Europe wide debate between Apian, Schöner, Fine, Cardano, Fracastoro and Copernicus, leading to the decisive claims in the 1570s by Tycho Brahe, Michael Mästlin, and Thaddaeus Hagecius ab Hayek that comets were celestial object above the Moon’s orbit and thus Aristotle’s claim that they were a sub-lunar meteorological phenomenon was false. Supralunar comets also demolished the Aristotelian celestial, crystalline spheres. These claims were acknowledged and accepted by the leading European Ptolemaic astronomer, Christoph Clavius, as were the claims that the 1572 nova was supralunar. Both occurrences shredded the Aristotelian cosmological concept that the heaven were immutable and unchanging.

The comet debate continued with significant impact in 1618, the 1660s, the 1680s and especially in the combined efforts of Isaac Newton and Edmund Halley, reaching a culmination in the latter’s correct prediction that the comet of 1682 would return in 1758. A major confirmation of the law of gravity.

During those early debates it was not just single objects, such as comets, that were discussed but whole astronomical systems were touted as alternatives to the Ptolemaic model. There was an active revival of the Eudoxian-Aristotelian homocentric astronomy, already proposed in the Middle Ages, because the Ptolemaic system, of deferents, epicycles and equant points, was seen to violate the so-called Platonic axioms of circular orbits and uniform circular motion. Another much discussed proposal was the possibility of diurnal rotation, a discussion that had its roots in antiquity. Also, on the table as a possibility was the Capellan system with Mercury and Venus orbiting the Sun in a geocentric system rather than the Earth.

2880px-Andreas_Cellarius_-_Planisphaerium_Copernicanum_Sive_Systema_Universi_Totius_Creati_Ex_Hypothesi_Copernicana_In_Plano_Exhibitum

The Copernican Cosmos: Andreas Cellarius, Harmonia Macrocosmica 1660 Source: Wikimedia Commons

Early in the sixteenth century, Copernicus entered these debates, as one who questioned the Ptolemaic system because of its breaches of the Platonic axioms, in particular the equant point, which he wished to ban. Quite how he arrived at his radical solution, replace geocentricity with heliocentricity we don’t know but it certainly stirred up those debates, without actually dominating them. The reception of Copernicus’ heliocentric hypothesis was complex. Some simply rejected it, as he offered no real proof for it. A small number had embraced and accepted it by the turn of the century. A larger number treated it as an instrumentalist theory and hoped that his models would deliver more accurate planetary tables and ephemerides, which they duly created. Their hopes were dashed, as the Copernican tables, based on the same ancient and corrupt data, proved just as inaccurate as the already existing Ptolemaic ones. Of interests is the fact that it generated a serious competitor, as various astronomers produced geo-heliocentric systems, extensions of the Capellan model, in which the planets orbit the Sun, which together with the Moon orbits the Earth. Such so-called Tychonic or semi-Tychonic systems, named after their most well-known propagator, incorporated all the acknowledged advantages of the Copernican model, without the problem of a moving Earth, although some of the proposed models did have diurnal rotation.

2880px-1660_chart_illustrating_Danish_astronomer_Tycho_Brahe's_model_of_the_universe

The Tychonic Cosmos: Andreas Cellarius, Harmonia Macrocosmica 1660 Source: Wikimedia Commons

The problem of inaccurate planetary tables and ephemerides was already well known in the Middle Ages and regarded as a major problem. The production of such tables was seen as the primary function of astronomy since antiquity and they were essential to all the applied areas mentioned earlier that were the driving forces behind the need for renewal and reform. Already in the fifteenth century, Regiomontanus had set out an ambitious programme of astronomical observation to provide a new data base for such tables. Unfortunately, he died before he even really got started. In the second half of the sixteenth century both Wilhelm IV Landgrave of Hessen-Kassel and Tycho Brahe took up the challenge and set up ambitious observation programmes that would eventually deliver the desired new, more accurate astronomical data.

At the end of the first decade of the seventeenth century, Kepler’s Astronomia Nova, with his first two planetary laws (derived from Tycho’s new accurate data), and the invention of the telescope and Galileo’s Sidereus Nuncius with his telescopic discoveries are, in the standard mythology, presented as significant game changing events in favour of heliocentricity. They were indeed significant but did not have the impact on the system debate that is usually attributed them. Kepler’s initial publication fell largely on deaf ears and only later became relevant. On Galileo’s telescopic observations, firstly he was only one of a group of astronomers, who in the period 1610 to 1613 each independently made those discoveries, (Thomas Harriot and William Lower, Simon Marius, Johannes Fabricius, Odo van Maelcote and Giovanni Paolo Lembo, and Christoph Scheiner) but what did they show or prove? The lunar features were another nail in the coffin of the Aristotelian concept of celestial perfection, as were the sunspots. The moons of Jupiter disproved the homocentric hypothesis. Most significant discovery was the of the phases of Venus, which showed that a pure geocentric model was impossible, but they were conform with various geo-heliocentric models.

1613 did not show any clarity on the way to finding the true model of the cosmos but rather saw a plethora of models competing for attention. There were still convinced supporters of a Ptolemaic model, both with and without diurnal rotation, despite the phases of Venus. Various Tychonic and semi-Tychonic models, once again both with and without diurnal rotation. Copernicus’ heliocentric model with its Ptolemaic deferents and epicycles and lastly Kepler’s heliocentric system with its elliptical orbits, which was regarded as a competitor to Copernicus’ system. Over the next twenty years the fog cleared substantially and following Kepler’s publication of his third law, his Epitome Astronomiae Copernicanae, which despite its title is a textbook on his elliptical system and the Rudolphine Tables, again based on Tycho’s data, which delivered the much desired accurate tables for the astrologers, navigators, surveyors and cartographers, and also of Longomontanus’ Astronomia Danica (1622) with his own tables derived from Tycho’s data presenting an updated Tychonic system with diurnal rotation, there were only two systems left in contention.

Around 1630, we now have two major world systems but not the already refuted geocentric system of Ptolemaeus and the largely forgotten Copernican system as presented in Galileo’s Dialogo but Kepler’s elliptical heliocentricity and a Tychonic system, usually with diurnal rotation. It is interesting that diurnal rotation became accepted well before full heliocentricity, although there was no actually empirical evidence for it. In terms of acceptance the Tychonic system had its nose well ahead of Kepler because of the lack of any empirical evidence for movement of the Earth.

Although there was still not a general acceptance of the heliocentric hypothesis during the seventeenth century the widespread discussion of it in continued in the published astronomical literature, which helped to spread knowledge of it and to some extent popularise it. This discussion also spread into and even dominated the newly emerging field of proto-sciencefiction.

Galileo’s Dialogo was hopelessly outdated and contributed little to nothing to the real debate on the astronomical system. However, his Discorsi made a very significant and important contribution to a closely related topic that of the evolution of modern physics. The mainstream medieval Aristotelian-Ptolemaic cosmological- astronomical model came as a complete package together with Aristotle’s theories of celestial and terrestrial motion. His cosmological model also contained a sort of friction drive rotating the spheres from the outer celestial sphere, driven by the unmoved mover (for Christians their God), down to the lunar sphere. With the gradual demolition of Aristotelian cosmology, a new physics must be developed to replace the Aristotelian theories.

Once again challenges to the Aristotelian physics had already begun in the Middle Ages, in the sixth century CE with the work of John Philoponus and the impetus theory, was extended by Islamic astronomers and then European ones in the High Middle Ages. In the fourteenth century the so-called Oxford Calculatores derived the mean speed theorem, the core of the laws of fall and this work was developed and disseminated by the so-called Paris Physicists. In the sixteenth century various mathematicians, most notably Tartaglia and Benedetti developed the theories of motion and fall further. As did in the early seventeenth century the work of Simon Stevin and Isaac Beeckman. These developments reached a temporary high point in Galileo’s Discorsi. Not only was a new terrestrial physics necessary but also importantly for astronomy a new celestial physics had to be developed. The first person to attempt this was Kepler, who replaced the early concept of animation for the planets with the concept of a force, hypothesising some sort of magnetic force emanating from the Sun driving the planets around their orbits. Giovanni Alfonso Borelli also proposed a system of forces as the source of planetary motion.

Throughout the seventeenth century various natural philosophers worked on and made contributions to defining and clarifying the basic terms that make up the science of dynamics: force, speed, velocity, acceleration, etc. as well as developing other areas of physics, Amongst them were Simon Stevin, Isaac Beeckman, Borelli, Descartes, Pascal, Riccioli and Christiaan Huygens. Their efforts were brought together and synthesised by Isaac Newton in his Principia with its three laws of motion, the law of gravity and Kepler’s three laws of planetary motion, which laid the foundations of modern physics.

In astronomy telescopic observations continued to add new details to the knowledge of the solar system. It was discovered that the planets have diurnal rotation, and the periods of their diurnal rotations were determined. This was a strong indication the Earth would also have diurnal rotation. Huygens figured out the rings of Saturn and discovered Titan its largest moon. Cassini discovered four further moons of Saturn. It was already known that the four moons of Jupiter obeyed Kepler’s third law and it would later be determined that the then known five moons of Saturn also did so. Strong confirming evidence for a Keplerian model.

Cassini showed by use of a heliometer that either the orbit of the Sun around the Earth or the Earth around the Sun was definitively an ellipse but could not determine which orbited which. There was still no real empirical evidence to distinguish between Kepler’s elliptical heliocentric model and a Tychonic geo-heliocentric one, but a new proof of Kepler’s disputed second law and an Occam’s razor argument led to the general acceptance of the Keplerian model around 1660-1670, although there was still no empirical evidence for either the Earth’s orbit around the Sun or for diurnal rotation. Newton’s Principia, with its inverse square law of gravity provided the physical mechanism for what should now best be called the Keplerian-Newtonian heliocentric cosmos.

Even at this juncture with a very widespread general acceptance of this Keplerian-Newtonian heliocentric cosmos there were still a number of open questions that needed to be answered. There were challenges to Newton’s work, which, for example, couldn’t at that point fully explain the erratic orbit of the Moon around the Earth. This problem had been solved by the middle of the eighteenth century. The mechanical philosophers on the European continent were anything but happy with Newton’s gravity, an attractive force that operates at a distance. What exactly is it and how does it function? Questions that even Newton couldn’t really answer. Leibniz also questioned Newton’s insistence that time and space were absolute, that there exists a nil point in the system from which all measurement of these parameters are taken. Leibniz preferred a relative model.

There was of course also the very major problem of the lack of any form of empirical evidence for the Earth’s movement. Going back to Copernicus nobody had in the intervening one hundred and fifty years succeeded in detecting a stellar parallax that would confirm that the Earth does indeed orbit the Sun. This proof was finally delivered in 1725 by Samuel Molyneux and James Bradley, who first observed, not stellar parallax but stellar aberration. An indirect proof of diurnal rotation was provided in the middle of the eighteenth century, when the natural philosophers of the French Scientific Academy correctly determined the shape of the Earth, as an oblate spheroid, flattened at the pols and with an equatorial bulge, confirming the hypothetical model proposed by Newton and Huygens based on the assumption of a rotating Earth.

Another outstanding problem that had existed since antiquity was determining the dimensions of the known cosmos. The first obvious method to fulfil this task was the use of parallax, but whilst it was already possible in antiquity to determine the distance of the Moon reasonably accurately using parallax, down to the eighteenth century it proved totally impossible to detect the parallax of any other celestial body and thus its distance from the Earth. Ptolemaeus’ geocentric model had dimensions cobbled together from its data on the crystalline spheres. One of the advantages of the heliocentric model is that it gives automatically relative distances for the planets from the sun and each other. This means that one only needs to determine a single actually distance correctly and all the others are automatically given. Efforts concentrated on determining the distance between the Earth and the Sun, the astronomical unit, without any real success; most efforts producing figures that were much too small.

Developing a suggestion of James Gregory, Edmond Halley explained how a transit of Venus could be used to determine solar parallax and thus the true size of the astronomical unit. In the 1760s two transits of Venus gave the world the opportunity to put Halley’s theory into practice and whilst various problems reduced the accuracy of the measurements, a reasonable approximation for the Sun’s distance from the Earth was obtained for the very first time and with it the actually dimensions of the planetary part of the then known solar system. What still remained completely in the dark was the distance of the stars from the Earth. In the 1830s, three astronomers–Thomas Henderson, Friedrich Wilhelm Bessel and Friedrich Georg Wilhelm von Struve–all independently succeeded in detecting and measuring a stellar parallax thus completing the search for the dimensions of the known cosmos and supplying a second confirmation, after stellar aberration, for the Earth’s orbiting the Sun.

In 1851, Léon Foucault, exploiting the Coriolis effect first hypothesised by Riccioli in the seventeenth century, finally gave a direct empirical demonstration of diurnal rotation using a simple pendulum, three centuries after Copernicus published his heliocentric hypothesis. Ironically this demonstration was within the grasp of Galileo, who experiment with pendulums and who so desperately wanted to be the man who proved the reality of the heliocentric model, but he never realised the possibility. His last student, Vincenzo Viviani, actually recorded the Coriolis effect on a pendulum but didn’t realise what it was and dismissed it as an experimental error.

From the middle of the eighteenth century, at the latest, the Keplerian-Newtonian heliocentric model had become accepted as the real description of the known cosmos. Newton was thought not just to have produced a real description of the cosmos but the have uncovered the final scientific truth. This was confirmed on several occasions. Firstly, Herschel’s freshly discovered new planet Uranus in 1781 fitted Newton’s theories without problem, as did the series of asteroids discovered in the early nineteenth century. Even more spectacular was the discovery of Neptune in 1846 based on observed perturbations from the path of Uranus calculated with Newton’s theory, a clear confirmation of the theory of gravity. Philosophers, such as Immanuel Kant, no longer questioned whether Newton had discovered the true picture of the cosmos but how it had been possible for him to do so.

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However, appearances were deceptive, and cracks were perceptible in the Keplerian-Newtonian heliocentric model. Firstly, Leibniz’s criticism of Newton’s insistence on absolute time and space rather than a relative model would turn out to have been very perceptive. Secondly, Newton’s theory of gravity couldn’t account for the observed perihelion precession of the planet Mercury. Thirdly in the 1860s, based on the experimental work of Michael Faraday, James Maxwell produced a theory of electromagnetism, which was not compatible with Newtonian physics. Throughout the rest of the century various scientists including Hendrik Lorentz, Georg Fitzgerald, Oliver Heaviside, Henri Poincaré, Albert Michelson and Edward Morley tried to find a resolution to the disparities between the Newton’s and Maxwell’s theories. Their efforts finally lead to Albert Einstein’s Special Theory of Relativity and then on to his General theory of Relativity, which could explain the perihelion precession of the planet Mercury. The completion of the one model, the Keplerian-Newtonian heliocentric one marked the beginnings of the route to a new system that would come to replace it.

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Christmas Trilogy 2020 Part 1: Where did all that money come from Isaac?

If you have read my review of Thomas Levenson’s excellent Money for Nothing, then you know that when the South Sea Bubble burst in 1621 Isaac Newton lost £25,000 and despite these loses, when he died eight years later his estate was estimated to be worth about the same sum. By today’s standards £25,000, whilst a tidy sum, is not actually a lot of money. However, in the early seventeenth century £25,000 was the equivalent of as much as £3 million pounds today. This, of course, raises the question as to how a poor farm boy from Lincolnshire, who had to work his way through college, who then became a professor of mathematics, not the best paid job at the end of the seventeenth century, succeeded in becoming, by anybody’s standards, a very wealthy man.

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Portrait of Newton at 46 by Godfrey Kneller, 1689 Source: Wikimedia Commons

Starting at the beginning, Isaac wasn’t actually a poor farm boy. It is true that when he went up to Cambridge in 1661, he entered Trinity College as a subsizar, which meant he had to pay his way by working as a valet for other students, but the facts deceive. His father, also called Isaac, was a wealthy yeoman farmer and the owner of Woolsthorpe Manor in Woolsthorpe-by-Colsterworth.

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Woolsthorpe Manor Source: Wikimedia Commons

Isaac senior died before his only son was born leaving Isaac’s mother, Hannah Ayscough a wealthy woman. Hannah could have paid for her son’s tuition with ease and there is some discussion, as to why she chose not to do so. The standard account is that she was simple mean and miserly. However, I personally think, that there is another reason. The Newtons were of puritan stock and I think that the decision to make Isaac earn his tuition was a moral one. At the beginning of the seventeenth century Jeremiah Horrocks, who also came from a well-off puritan family, also had to pay his university tuition by working as a servant. In 1664, Isaac won a scholarship and in 1667 he was appointed a minor fellow of Trinity and a year later a major fellow, which meant that he was now financially independent but by no means well-off. However, the fact that as fellow he received free board and lodging meant that he could afford to live comfortably.

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Trinity College Cambridge: David Loggan’s print of 1690 showing Nevile’s Great Court (foreground) and Nevile’s Court with the then-new Wren Library (background) – New Court had yet to be built. Source: Wikimedia Commons

The minor fellowship received a stipend of £2 p.a. with a livery allowance of £1 6s 8d per annum. In the Oxbridge college system, the fellows are the share holders of the college and receive a yearly dividend, as a minor fellow Newton received a dividend of £10 p.a. As a major fellow his stipend was £2 13s 4d p.a. plus £1 13s 4d for livery and a yearly dividend of £25. As a major fellow his total income was about £60 a year of which about £20 t0 £25 was his board and lodging. By modern standards this might not seem a lot, but it is approximately double the yearly income of a skilled craftsman at the time, with a fellow free to do whatever he liked with his time.

In 1669, Newton’s financial situation improved once again when Isaac Barrow resigned the Lucasian chair of mathematics to take on the study of divinity and was appointed Master of Trinity College and Newton was appointed as his successor to the Lucasian chair. This position carried with it a salary of £100 p.a., which is equivalent to £10,000 p.a. at todays prices. He also retained the income from his fellowship. I love the fact that on the National Archive historical converter I’m using, they point out that £100 was worth 24 cows. I have visions of Newton grazing his herd of milk cows on the lawns of Trinity College.

Newton’s steadily increasing wealth received a very major boost ten years later in 1679, when his mother, Hannah, died and he inherited the Newton family estates. These generated an income of about £600 p.a. Newton was by any standards now a wealthy man, although this income would not have enabled him to generate saving of £50,000 by the 1720s. In fact, Newton did not hoard his money but spent freely, stocking up his extensive library and equipping the alchemy laboratory that he set up in the gardens of Trinity College.

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Hannah Newton-Smith born Ayscough Source

Contrary to the popular myths that Newton living in isolation, totally immersed in his studies was completely unworldly, Newton, although an absentee manager of the family estate mastered the task skilfully and also took good care of the needs of his extended family.

It was normal practice for fellows to increase their incomes through preferment in the Anglican Church, stipends often being awarded in absentia, with a minor cleric undertaking the actuall duties. Although all fellows were required to take holy orders, Newton, because of his unorthodox beliefs, had received a special dispensation from the King upon his appointment to the Lucasian Chair, so this route was not open to him.

Towards the end of the century, Newton tired of Cambridge and now, following the publication of his Principia, universally acknowledge as Europe’s leading natural philosopher, he began looking for some form of public post with a sinecure or pension to match his social status. In 1696, he achieved his aim, when his one-time student and mentor in the Whig Party, Charles Montagu, offered him the post of Warden of the Royal Mint in London. Newton accepted the post without hesitation. The warden’s income was £400 p.a. a large step up from the Lucasian £100, which, however, together with his fellowship he initially retained.

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Portrait of Charles Montagu by Godfrey Kneller

The job of warden was a sinecure and Newton could have simply played the man about town and left the actually work to assistants. However, that was not Newton’s style and he took over the day-to-day management of the mint. One anomaly, that Newton became aware of straight away, was that although the warden was the boss, the master, who was actually responsible for minting the coinage, received a salary of £500 p.a., so more than the warden, plus a payment for every pound weight of copper, silver or gold that he minted. Newton immediately petitioned for equal pay with the master, but this was denied. However, when the incumbent master died in 1699, Newton had himself appointed as his successor. This was the only time in the history of the Royal Mint that a warden became the master.

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In 1701, Newton finally resigned from the Lucasian chair and his Trinity fellowship. In that year his income from the mint was £3,500, we have now arrived at the source of that vast later wealth. Although it tended to go up and down like a yo-yo, Newton’s average income over the twenty-six years that he was master was about £1,650 p.a. One should not forget that he also had the £600 p.a. from his estates in Lincolnshire.

Newton was a good financial manager and through his work as advisor to the treasury he also had close contacts to all the leading finance experts in London. By nature, a cautious man, he usually invested his wealth wisely in the flourishing joint stock companies operating in London. He owed sizable stocks in both the Bank of England, set up by his mentor Charles Montagu, and the highly profitable East India Company both of which generated further income for him. However, even Newton couldn’t resist the allure of the spectacularly rising value of the South Sea Company and he invested heavily. Interestingly, he sold out once, making a tidy profit but as the value continued to rise and rise, he couldn’t resist and reinvested heavily taking that famous £25,000 hit.

There was however one occasion when Newton actually turned down the chance to improve his financially situation. Around 1713, during a period of Tory rule, the party wanted to secure the various political sinecures for their own supporters but knew that due to his, in the meantime, massive social status to remove Newton from the Royal Mint would be a political disaster, so the sent Jonathan Swift to offer him a bribe. If he would freely resign, as master of the mint, the government would bestow a lifetime pension of £2,000 p.a. upon him. Newton must have loved his work, or maybe he just wanted to annoy the Tories, he was after all a Whig, because he declined this incredibly generous offer.

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Astrology in the age of Newton

My Annus Mythologicus blog post was recently retweeted on Twitter in response to an inane tweet from Richard Dawkins and somebody questioned the reference in it that Newton was inspired to take up mathematics upon reading a book on astrology. This was not a nasty attack but a genuine statement on interest from somebody who had difficulty believing a man, who has been called the greatest mathematician ever, should have had anything to do with an astrology book. There is a sort of naïve belief that it is impossible for the people in the age of Newton, which is touted as the birth of the age of modern science and rationalism, could have had anything to do with the so-called occult sciences. This belief led many people, who should have known better, to try and sweep Newton’s very active engagement with alchemy under the carpet. During Newton’s lifetime astrology lost its status as a university discipline but was still all pervasive and permeated all aspects and levels of society. In what follows I will sketch some of the details of the role of astrology in the age of Newton.

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Newton – 1677 Source: Wikimedia Commons

The Renaissance/Early Modern Period could with justification be called the golden age of astrology in Europe. This period was actually coming to an end during Newton’s lifetime, but astrology had by no means totally disappeared. That golden age began roughly with the beginning of the fifteenth century. During the first half of the century the humanist universities of Northern Italy and Poland created the first regular, dedicated chairs for mathematics and astronomy, which were in fact chairs for astrology, created to teach astrology to medical students. Teaching astrology to medical students was one of the principle obligations of the professors for mathematics at these universities and continued to be so well down into the seventeenth century. This trend continued with the creation of the first such chair in Germany, at the University of Ingolstadt, in the early 1470s. Astrological medicine, or iatromathematics to it is formal name was just one branch of astrology that flourished in this period.

Medical astrology was along with astrological meteorology considered to be a form of natural astrology and even those, who rejected natal astrology, for example, accepted the validity of natural astrology. Opposed to natural astrology was judicial astrology collective term for a group of other forms of astrology. Natal astrology, or genethliacal astrology, is the classic birth horoscope astrology that everybody thinks of, when they first hear the term astrology.  Other forms of judicial horoscope astrology are mundane astrology concerns the fate of nations etc., horary astrology answers question by casting a horoscope when the question is presented, and electional astrology, which is used to determine the most appropriate or auspicious time to carry out a planned action.

All these forms of astrology were widespread and considered valid by the vast majority during the fifteenth and sixteenth centuries. Astrology was firmly established in the fabric of European society and almost all of the active astronomers were also active astrologers right down to those astronomers, who were responsible for the so-called astronomical revolution. Georg Peuerbach, Regiomontanus, Tycho Brahe, Johannes Kepler and Galileo Galilei were all practicing astrologers and in fact owed much of the patronage that they received to their role as astrologer rather to that of astronomer, although the terms were interchangeable in this period. The terms Astrologus, Astronomus and Mathematicus were all synonym and all had astrologer in the modern sense as their principle meaning. Following the invention of moving type printing in about 1450, by far and away, the largest number of printed articles were astrological ephemera, almanacs, prognostica, and writing and single sheet wall calendars. A trend that continued all the way down to the eighteenth century.

During the fifteenth and sixteenth century efforts to give astrology a solid empirical footing were central to the activities of the astronomer-astrologers. Starting with Regiomontanus several astronomers believed that the inaccuracies in astrological forecasting were due to inaccuracies in the astronomy on which it was based. The reform of astronomy, for exactly this reason, was a principle motivation for the research programmes of Regiomontanus, Tycho Brahe and Wilhelm IV, Landgrave of Hessen-Kassel. Another approach was through astro-meteorology, with astronomer keeping weather diaries in which they noted the horoscope for the day and the actual weather on that day. They were looking for correlations, which they failed to find, but the practice led to the beginnings of modern weather forecasting. Notable weather diarists were Tycho Brahe and Johannes Werner. There were also attempts to find genuine correlations between birth charts and biographies of prominent people. Such biographical horoscope collections existed in manuscript before the invention of movable type printing. One of the largest, still extant, such manuscript collections is that of Erasmus Reinhold, a professor of mathematics at Wittenberg. The first such printed collection was that of Gerolamo Cardano, Libelli duo: De Supplemento Almanach; De Restitutione temporum et motuum coelestium; Item Geniturae LXVII insignes casibus et fortuna, cum expositione, printed and published by Johannes Petreius, specialist for astrological literature, in Nürnberg in 1543; the same year as he published Copernicus’ De revolutionibus.

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During the first half of the seventeenth century the failures to find empirical evidence for astrology, a change in the philosophy underpinning science, astrology was justified with Aristotelian metaphysics, and changes in the ruling methodologies of mainstream medicine led to a decline in the academic status of astrology. Although a few universities continued teaching astrology for medical students into the eighteenth century, astrology as a university discipline largely ceased to exist by 1660. However, astrology was still very much woven into the fabric of European society.

Newton was born in 1642, which meant he grew up during the Civil War and the Interregnum. Astrology was used by both sides as propaganda during Civil War. Most famously William Lilly (1602–1681) publishing powerful pamphlets on behalf of the parliamentary side.

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Portrait of Lilly, aged 45, now housed in the Ashmolean Museum at Oxford Source: Wikimedia Commons

This caused him major problem following the restitution. Lilly’s Christian Astrology (1647) was a highly influential book in the genre. Lilly was friends with many important figures of the age including Elias Ashmole (1617–1692) an antiquary who gave his name to the Ashmolean Museum of Art and Archaeology in Oxford, which was founded on his collection of books, manuscripts many objects. Ashmole was a passionate astrologer and a founding member of the London Society of Astrologers, which included many prominent intellectuals and existed from 1649 to 1658 and was briefly revived in 1682 by the astronomer, astrologer, printer and globemaker Joseph Moxon (1627–1691).

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Joseph Moxon. Line engraving by F. H. van Hove, 1692. Source: Wikimedia Commons

Moxon successfully sold Ptolemaic globes in the last quarter of the seventeenth century, which were intended for astrologers not astronomers. Moxon’s Ptolemaic globes reflect an actual fashion in astrological praxis that could be described as back to the roots. In the middle of the seventeenth century many astrologers decide that astrology wasn’t working, as it should, because the methodology used had drifted to far from that described by Ptolemaeus in his Tetrabiblos. This movement was led by the Italian P. Placido de Titis (1603 – 1668) whose Physiomathematica sive coelestis philosophia published in 1650 with an improved 2nd edition, 1675.

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Alongside Moxon another English supporter of this back to the roots movement was John Partridge (1644–c. 1714), who published the first ever English translation of Ptolemaeus’ Tetrabiblos in 1704. Partridge was one of the most well-known astrologers of the age until he got skewered by Jonathan Swift in his infamous Isaac Bickerstaff letters beginning in 1708.

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John Partridge. Line engraving by R. White, 1682 Credit: Wellcome Library, London. Wellcome Images Source: Wikimedia Commons http://wellcomeimages.org John Partridge. Line engraving by R. White, 1682, after himself. 1682 By: Robert WhitePublished: – Copyrighted work available under Creative Commons Attribution only licence CC BY 4.0 http://creativecommons.org/licenses/by/4.0/

We always talk about the big names in the histories of astronomy and mathematics, but it is often more insignificant practitioners, who teach the next generation. In this Newton’s education in astronomy followed the norm and he learnt his astronomy from the books of Vincent Wing (1619–1668) Astronomia Britannica (1669)

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Author portrait of Vincent Wing engraved by T. Cross (Frontispiece to the “Astronomia Britannica” of 1669) Source: Wikimedia Commons

and Thomas Streete (1621–1689) Astronomia Carolina, a new theorie of Coelestial Motions (1661).

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They were the two leading astronomers in England during Newton’s youth and were both practicing astrologers. The two men were rivals and wrote polemics criticising the errors in the others work. Streete was friends with several other astronomers such as Flamsteed, who also used the Astronomia Carolina as his textbook, or Halley together with whom Streete made observation. Streete was Keplerian and it’s Kepler’s astronomy that he presents in his Astronomia Carolina , although he rejected Kepler’s second law and presented the theories of Boulliau and Ward instead. It is very probable that reading Streete was Newton’s introduction to Kepler’s theories.

Flamsteed, as already said, like Newton, a student of Steete, actually cast an electional horoscope for the laying of the foundation stone of the Royal Observatory in 1675 although he didn’t actually believe in astrology but was maintaining a well-established tradition.

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Another example of this sort of half belief can be found in the attitude of Newton and Halley to comets. The two of them did far more than anybody else to establish comets as real celestial bodies affected by the same physical laws as all other celestial bodies and not some sort of message from the heavens. However, whilst neither of them believed in the truth of astrology both retained a belief that comets were indeed harbingers of doom.

As I said at the beginning Newton grew up and lived all of his life in a culture permeated with a belief in astrology. At the end of the seventeenth century astrological ephemera–almanacs, prognostica, etc.–were still a mass market phenomenon.

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Zodiac man in EPB/61971/A: Goldsmith, 1679. An almanack for the year of our Lord God, 1679 (London: Printed by Mary Clark, for the Company of Stationers, 1679), leaf B2 recto. Image credit: Elma Brenner. Source:

A large annual fair such as Sturbridge in 1663, the largest annual fair in Europe, would have had a large selection of astrological literature on offer for the visitors; a public many of whose yearly almanac was the only printed book that they bought and read.

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It is perfectly reasonable that a twenty-one year old Newton, just entering his second year at Cambridge university, stumbled across an astrological publication that awakened his mathematical curiosity as reported separately by both John Conduitt and Abraham DeMoirvre, in their memoirs based on conversations with Newton.

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The emergence of modern astronomy – a complex mosaic: Part XLIV

Whilst the European community mathematicians and physicist, i.e. those who could comprehend and understand it, were more than prepared to acknowledge Newton’s Principia as a mathematical masterpiece, many of them could not accept some of the very basic premises on which it was built. Following its publication the Baconians, the Cartesians and Leibniz were not slow in expressing their fundamental rejection of various philosophical aspects of Newton’s magnum opus.  

Francis Bacon had proposed a new scientific methodology earlier in the seventeenth century to replace the Aristotelian methodology.

Sir Francis Bacon, c. 1618

You will come across claims that Newton’s work was applied Baconianism but nothing could be further from the truth. Bacon rejected the concept of generating theories to explain a group of phenomena. In his opinion the natural philosopher should collect facts or empirical data and when they had acquired a large enough collections then the explanatory theories would crystallise out of the data. Bacon was also not a fan of the use of mathematics in natural philosophy. Because of this he actually rejected both the theories of Copernicus and Gilbert.

Newton, of course did the opposite he set up a hypothesis to explain a given set of seemingly related phenomena, deduced logical consequences of the hypothesis, tested the deduced conclusions against empirical facts and if the conclusions survive the testing the hypothesis becomes a theory. This difference in methodologies was bound to lead to a clash and it did. The initial clash took place between Newton and Flamsteed, who was a convinced Baconian. Flamsteed regarded Newton’s demands for his lunar data to test his lunar theory as a misuse of his data collecting. 

Source: Wikimedia Commons

The conflict took place on a wider level within the Royal Society, which was set up as a Baconian institution and rejected Newton’s type of mathematical theorising. When Newton became President of the Royal Society in 1704 there was a conflict between himself and his supporters on the one side and the Baconians on the other, under the leadership of Hans Sloane the Society’s secretary. At that time the real power in Royal Society lay with the secretary and not the president. It was first in 1712 when Sloane resigned as secretary that the Royal Society became truly Newtonian. This situation did not last long, when Newton died, Sloane became president and the Royal Society became fundamentally Baconian till well into the nineteenth century. 

Hans Sloane by Stephen Slaughter Source: Wikimedia Commons

This situation certainly contributed to the circumstances that whereas on the continent the mathematicians and physicists developed the theories of Newton, Leibnitz and Huygens in the eighteenth century creating out of them the physics that we now know as Newtonian, in England these developments were neglected and very little advance was made on the work that Newton had created. By the nineteenth century the UK lagged well behind the continent in both mathematics and physics.

The problem between Newton and the Cartesians was of a completely different nature. Most people don’t notice that Newton never actually defines what force is. If you ask somebody, what is force, they will probably answer mass time acceleration but this just tells you how to determine the strength of a given force not what it is. Newton tells the readers how force works and how to determine the strength of a force but not what a force actually is; this is OK because nobody else does either. The problems start with the force of gravity. 

Frans Hals – Portrait of René Descartes Source: Wikimedia Commons

The Cartesians like Aristotle assume that for a force to act or work there must be actual physical contact. They of course solve Aristotle’s problem of projectile motion, if I remove the throwing hand or bowstring, why does the rock or arrow keep moving the physical contact having ceased? The solution is the principle of inertia, Newton’s first law of motion. This basically says that it is the motion that is natural and it requires a force to stop it air resistance, friction or crashing into a stationary object. In order to explain planetary motion Descartes rejected the existence of a vacuum and hypothesised a dense, fine particle medium, which fills space and his planets are carried around their orbits on vortices in this medium, so physical contact. Newton demolished this theory in Book II of his Principia and replaces it with his force of gravity, which unfortunately operates on the principle of action at a distance; this was anathema for both the Cartesians and for Leibniz. 

What is this thing called gravity that can exercise force on objects without physical contact? Newton, in fact, disliked the concept of action at a distance just as much as his opponents, so he dodged the question. His tactic is already enshrined in the title of his masterpiece, the Mathematical Principles of Natural Philosophy. In the draft preface to the Principia Newton stated that natural philosophy must “begin from phenomena and admit no principles of things, no causes, no explanations, except those which are established through phenomena.” The aim of the Principia is “to deal only with those things which relate to natural philosophy”, which should not “be founded…on metaphysical opinions.” What Newton is telling his readers here is that he will present a mathematical description of the phenomena but he won’t make any metaphysical speculations as to their causes. His work is an operative or instrumentalist account of the phenomena and not a philosophical one like Descartes’.  

The Cartesians simply couldn’t accept Newton’s action at a distance gravity. Christiaan Huygens, the most significant living Cartesian natural philosopher, who was an enthusiastic fan of the Principia said quite openly that he simply could not accept a force that operated without physical contact and he was by no means alone in his rejection of this aspect of Newton’s theory. The general accusation was that he had introduced occult forces into natural philosophy, where occult means hidden.

Christiaan Huygens. Cut from the engraving following the painting of Caspar Netscher by G. Edelinck between 1684 and 1687. Source: Wikimedia Commons

Answering his critics in the General Scholium added to the second edition of the Principia in 1713 and modified in the third edition of 1726, Newton wrote:

Thus far I have explained the phenomena of the heavens and of our sea by the force of gravity, but I have not assigned a cause to gravity.

[…]

I have not been able to deduce from phenomena the reasons for these properties of gravity, and I do not feign hypotheses; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this experimental philosophy, propositions are deduced from the phenomena and are made general by induction. The impenetrability, mobility, and impetus of bodies, and the laws of motion and the law of gravity have been found by this method. And it is enough that gravity really exists and acts according to the laws that we have set forth and is sufficient to explain all the motions of the heavenly bodies and of our sea.

Newton never did explain the cause of gravity but having introduced the concept of a pervasive aethereal medium in the Queries in Book III of his Opticks he asks if the attraction of the aether particles could be the cause of gravity. The Queries are presented as speculation for future research.

Both the Baconian objections to Newton’s methodology and the Cartesian objections to action at a distance were never disposed of by Newton but with time and the successes of Newton’s theory, for example the return of Comet Halley, the objections faded into the background and the Principia became the accepted dominant theory of the cosmos.

Leibniz shared the Cartesian objection to action at a distance but also had objections of his own.

Engraving of Gottfried Wilhelm Leibniz Source: Wikimedia Commons

In 1715 Leibniz wrote a letter to Caroline of Ansbach the wife of George Prince of Wales, the future George III, in which he criticised Newtonian physics as detrimental to natural theology. The letter was answered on Newton’s behalf by Samuel Clarke (1675–1729) a leading Anglican cleric and a Newtonian, who had translated the Opticks into Latin. There developed a correspondence between the two men about Newton’s work, which ended with Leibniz’s death in 1716. The content of the correspondence was predominantly theological but Leibniz raised and challenged one very serious point in the Principia, Newton’s concept of absolute time and space.

In the Scholium to the definitions at the beginning of Book I of Principia Newton wrote: 

1. Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly and by another name is called duration. 

Relative, apparent, and common time […] is commonly used instead of true time.

2. Absolute space, of its own nature without reference to anything external, always remains homogeneous and immovable. Relative space is any moveable or dimension of the absolute space…

Newton is saying that space and time have a separate existence and all objects exists within them.

In his correspondence with Clarke, Leibniz rejected Newton’s use of absolute time and space, proposing instead a relational time and space; that is space and time are a system of relations that exists between objects. 

 In his third letter to Clarke he wrote:

As for my own opinion, I have said more than once, that I hold space to be something merely relative, as time is, that I hold it to be an order of coexistences, as time is an order of successions.

Leibniz died before any real conclusion was reached in this debate and it was generally thought at the time that Newton had the better arguments in his side but as we now know it was actually Leibniz who was closer to how we view time and space than Newton. 

Newton effectively saw off his philosophical critics and the Principia became the accepted, at least mathematical, model of the then known cosmos. However, there was still the not insubstantial empirical problem that no proof of any form of terrestrial motion had been found up to the beginning of the seventeenth century.

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The emergence of modern astronomy – a complex mosaic: Part XLIII

The Moon is the Earth’s nearest celestial neighbour and the most prominent object in the night sky. People have been tracking, observing and recording the movements of the Moon for thousands of years, so one could assume that calculating its orbit around the Earth should be a reasonable simple matter, however in reality it is anything but.

The problem can be found in the law of gravity itself, which states that any two bodies mutually attract each other. However, that attraction is not restricted to just those two bodies but all bodies attract each other simultaneously. Given the relative masses of somebody standing next to you and the Earth, when calculating the pull of gravity on you, we can, in our calculation, neglect the pull exercised by the mass of your neighbour. With planets, however, it is more difficult to ignore multiple sources of gravitational force. We briefly touched on the gravitational effect of Jupiter and Saturn, both comparatively large masses, on the flight paths of comets, so called perturbation. In fact when calculating the Earth orbit around the Sun then the effects of those giant planets, whilst relatively small, are in fact detectable.

With the Moon the problem is greatly exacerbated. The gravitation attraction between the Earth and the Moon is the primary force that has to be considered but the not inconsiderable gravitational attraction between the Sun and the Moon also plays an anything but insignificant role. The result is that the Moon’s orbit around the Sun Earth is not the smooth ellipse of Kepler’s planetary laws that it would be if the two bodies existed in isolation but a weird, apparently highly irregular, dance through the heavens as the Moon is pulled hither and thither between the Earth and the Sun.

Kepler in fact did not try to apply his laws of planetary motion to the Moon simply leaving it out of his considerations. The first person to apply the Keplerian elliptical astronomy to the Moon was Jeremiah Horrocks (1618–1641), an early-convinced Keplerian, who was also the first person to observe a transit of Venus having recalculated Kepler’s Rudolphine Tables in order to predict to correct date of the occurrence. Horrocks produced a theory of the Moon based on Kepler’s work, which was far and away the best approximation to the Moon’s orbit that had been produced up till that time but was still highly deficient. This was the model that Newton began his work with as he tried to make the Moon’s orbit fit into his grand gravitational theory, as defined by his three laws of motion, Kepler’s three laws of planetary motion and the inverse square law of gravity; this would turn into something of a nightmare for Newton and cause a massive rift between Newton and John Flamsteed the Astronomer Royal.

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Portrait of Newton at 46 by Godfrey Kneller, 1689 Source: Wikimedia Commons

What Newton was faced with was attempting to solve the three-body problem, that is a general solution for the mutual gravitational attraction of three bodies in space. What Newton did not and could not know was that the general analytical solution simple doesn’t exist, the proof of this lay in the distant future. The best one can hope for are partial local solutions based on approximations and this was the approach that Newton set out to use. The deviations of the Moon, perturbations, from the smooth elliptical orbit that it would have if only it and the Earth were involved are not as irregular as they at first appear but follow a complex pattern; Newton set out to pick them off one by one. In order to do so he need the most accurate data available, which meant new measurement made during new observations by John Flamsteed the Astronomer Royal.

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Source: Wikimedia Commons

For Newton solving the lunar orbit was the most pressing problem in his life and he imperiously demanded that Flamsteed supply him with the data that he required to make his calculations. For Flamsteed the important task in his life, as an observational astronomer, was to complete a new star catalogue on a level of observational accuracy hitherto unknown. The principle interests of the two men were thus largely incompatible. Newton demanded that Flamsteed use his time to supply him with his lunar data and Flamsteed desired to use his time to work on his star catalogue, although to be fair he did supply Newton, if somewhat grudgingly with the desired data. As Newton became more and more frustrated by the problems he was trying to solve the tone of his missives to Flamsteed in Greenwich became more and more imperious and Flamsteed got more and more frustrated at being treated like a lackey by the Lucasian Professor. The relations between the two degenerated rapidly.

The situation was exacerbated by the presence of Edmond Halley in the mix, as Newton’s chief supporter. Halley had started his illustrious career as a protégée of Flamsteed’s when he, still an undergraduate, sailed to the island of Saint Helena to make a rapid survey of the southern night skies for English navigators. The men enjoyed good relations often observing together and with Halley even deputising for Flamsteed at Greenwich when he was indisposed. However something happened around 1686 and Flamsteed began to reject Halley. It reached a point where Flamsteed, who was deeply religious with a puritan streak, disparaged Halley as a drunkard and a heathen. He stopped referring him by name calling him instead Reymers, a reference to the astronomer Nicolaus Reimers Ursus (1551–1600). Flamsteed was a glowing fan of Tycho Brahe and he believed Tycho’s accusation that Ursus plagiarised Tycho’s system. So Reymers was in his opinion a highly insulting label.

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Portrait of Edmond Halley painted around 1687 by Thomas Murray (Royal Society, London) Source: Wikimedia Commons

Newton only succeeded in resolving about half of the irregularities in the Moon’s orbit and blamed his failure on Flamsteed. This led to one of the most bizarre episodes in the history of astronomy. In 1704 Newton was elected President of the Royal Society and one of his first acts was to call Flamsteed to account. He demanded to know what Flamsteed had achieved in the twenty-nine years that he had been Astronomer Royal and when he intended to make the results of his researches public. Flamsteed was also aware of the fact that he had nothing to show for nearly thirty years of labours and was negotiating with Prince George of Denmark, Queen Anne’s consort, to get him to sponsor the publication of his star catalogue. Independently of Flamsteed, Newton was also negotiating with Prince George for the same reason and as he was now Europe’s most famous scientist he won this round. George agreed to finance the publication, and was, as a reward, elected a member of the Royal Society.

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Prince George of Denmark and Norway, Duke of Cumberland Portrait by Michael Dahl c. 1705 Source: Wikimedia Commons

Newton set up a committee, at the Royal Society, to supervise the work with himself as chairman and the Savilian Professors of Mathematics and Astronomy, David Gregory and Edmond Halley, both of whom Flamsteed regarded as his enemies, Francis Robartes an MP and teller at the Exchequer and Dr John Arbuthnotmathematician, satirist and physician extraordinary to Queen Anne. Although Arbuthnot, a Tory, was of opposing political views to Newton, a Whig, he was a close friend and confidant. Flamsteed was not offered a place on this committee, which was decidedly stacked against him.

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David Gregory Source: Wikimedia Commons

Flamsteed’s view on what he wanted published and how it was to be organised and Newton’s views on the topic were at odds from the very beginning. Flamsteed saw his star catalogue as the centrepiece of a multi-volume publication, whereas all that really interested Newton was his data on the planetary and Moon orbits, with which he hoped to rectify his deficient lunar theory. What ensued was a guerrilla war of attrition with Flamsteed sniping at the referees and Newton and the referees squashing nearly all of Flamsteed wishes and proposals. At one point Newton even had Flamsteed ejected from the Royal Society for non-payment of his membership fees, although he was by no means the only member in arrears. Progress was painfully slow and at times virtually non-existent till it finally ground completely to a halt with the death of Prince George in 1708.

George’s death led to a two-year ceasefire in which Newton and Flamsteed did not communicate but Flamsteed took the time to work on the version of his star catalogue that he wanted to see published. Then in 1710 John Arbuthnot appeared at the council of the Royal society with a royal warrant from Queen Anne appointing the president of the society and anybody the council chose to deputise ‘constant Visitors’ to the Royal Observatory at Greenwich. ‘Visitor’ here means supervisor in the legal sense. Flamsteed’s goose was well and truly cooked. He was now officially answerable to Newton. Instead of waiting for Flamsteed to finish his star catalogue the Royal Society produced and published one in the form that Newton wanted and edited by Edmond Halley, the man Flamsteed regarded as his greatest enemy. It appeared in 1712. In 1713 Newton published the second edition of his Principia with its still defective lunar theory but with Flamsteed name eliminated as far as possible.

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John Arbuthnot Portrait by Godfrey Kneller Source: Wikimedia Commons

The farce did not end here. In 1714 Queen Anne died and the Visitor warrant thus lost its validity. The Tory government fell and the Whigs regained power. Newton’s political sponsor, Charles Montagu, 1st Earl of Halifax, died in 1715 leaving him without a voice in the new government. Flamsteed, however, was friends with the Lord Chamberlain, Lord Boulton. On 30 November 1715 Boulton signed a warrant ordering Newton and co to hand over the remaining 300 copies of their ‘pirate’ catalogue to Flamsteed.  After some procrastination and some more insults aimed at Flamsteed they finally complied on 28 March 1716. Flamsteed “made a Sacrifice of them to Heavenly truth”, that is he burnt them. Flamsteed had in the mean time published his star catalogue at his own expense and devoted the rest of his life to preparing the rest of his life’s work for publication. He died in 1719 but his widow, Margaret, and two of his former assistants, Joseph Crosthwait and Abraham Sharp, edited and published his Historia coelestis britannia in three volumes in 1725; it is rightly regarded as a classic in the history of celestial observation. Margaret also took her revenge on Halley, who succeeded Flamsteed as Astronomer Royal. Flamsteed had paid for the instruments in the observatory at Greenwich out of his own pocket, so she stripped the building bare leaving Halley with an empty observatory without instruments. For once in his life Newton lost a confrontation with a scientific colleague, of which there were quite a few, game, set and match

The bitter and in the end unseemly dispute between Newton and Flamsteed did nothing to help Newton with his lunar theory problem and to bring his description of the Moon’s orbit into line with the law of gravity. In the end this discrepancy in the Principia remained beyond Newton’s death. Mathematicians and astronomers in the eighteen century were well aware of this unsightly defect in Newton’s work and in the 1740s Leonhard Euler (1707­–1783), Alexis Clairaut (1713–1765) and Jean d’Alembert (1717–1783) all took up the problem and tried to solve it, in competition with each other.  For a time all three of them thought that they would have to replace the inverse square law of gravity, thinking that the problem lay there. Clairaut even went so far as to announce to the Paris Academy on 15 November 1747 that the law of gravity was false, to the joy of the Cartesian astronomers. Having then found a way of calculating the lunar irregularities using approximations and confirming the inverse square law, Clairaut had to retract his own announcement. Although they had not found a solution to the three-body problem the three mathematicians had succeeded in bringing the orbit of the Moon into line with the law of gravity. The first complete, consistent presentation of a Newtonian theory of the cosmos was presented by Pierre-Simon Laplace in his Traité de mécanique céleste, 5 Vol., Paris 1798–1825.

Mathematicians and astronomers were still not happy with the lack of a general solution to the three-body problem, so in 1887 Oscar II, the King of Sweden, advised by Gösta Mittag-Leffler offered a prize for the solution of the more general n-body problem.

Given a system of arbitrarily many mass points that attract each according to Newton’s law, under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series converge uniformly.

Nobody succeeded in solving the challenge but Henri Poincaré’s attempt to find a solution although not successful, contained enough promising leads that he was awarded the prize. As stated a solution to the problem was found for three bodies by Karl F Sundman in 1912 and generalised for more than three bodies by Quidong Wang in the 1990s.

The whole episode of Newton’s failed attempt to find a lunar theory consonant with his theory of gravitation demonstrates that even the greatest of mathematicians can’t solve everything. It also demonstrates that the greatest of mathematicians can behave like small children having a temper tantrum if they don’t get their own way.

 

 

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Filed under History of Astrology, History of Mathematics, History of Physics, Newton