Category Archives: Newton

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

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

1024px-Johannes_Kepler_1610

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

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

kepler001

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

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

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

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

writing a few days later:

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

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

In modern terminology:

29791732_1734248579965791_6792966757406288833_n

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

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

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

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

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

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

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

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

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

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

third law001

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

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

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

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

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

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

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

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

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

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

[6] Newton, Principia, 1999 p. 467

[7] Newton, Principia, 1999 p. 468

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

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Filed under History of Astronomy, History of science, Newton, Renaissance Science, Uncategorized

Christmas Trilogy 2017 Part 1: Isaac the Imperator

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

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

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

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

Trinity College Great Court
Source: Wikimedia Commons

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

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

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

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

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

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

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

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

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

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

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

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

 

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

 

 

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Filed under History of Astronomy, History of Mathematics, History of Optics, History of Physics, History of science, Newton

Did Isaac leap or was he pushed?

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

Newton_-_1677.jpeg

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

 

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

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

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

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

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

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

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

Turning to the other two bold emphasised claims we have:

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

And:

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

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

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

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

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

The Institute of Arts and Ideas advertises itself as follows:

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

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

 

 

 

 

 

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Why doesn’t he just shut up?

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

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

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

“WHO’S THIS BLATHERING TYSON FOOL?”

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

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

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

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

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

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

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

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

On an excursion

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

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

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

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

Christmas Trilogy 2016 Part 1: Is Newtonian physics Newton’s physics?

Nature and nature’s laws lay hid in night;

God said “Let Newton be” and all was light.

Isaac Newton's Tomb in Westminster Abbey Photo: Klaus-Dieter Keller Source: Wikimedia Commons

Isaac Newton’s Tomb in Westminster Abbey
Photo: Klaus-Dieter Keller
Source: Wikimedia Commons

Alexander Pope’s epitaph sets the capstone on the myth of Newton’s achievements that had been under construction since the publication of the Principia in 1687. Newton had single-handedly delivered up the core of modern science – mechanics, astronomy/cosmology, optics with a side order of mathematics – all packed up and ready to go, just pay at the cash desk on your way out. We, of course, know (you do know don’t you?) that Pope’s claim is more than somewhat hyperbolic and that Newton’s achievements have, over the centuries since his death, been greatly exaggerated. But what about the mechanics? Surely that is something that Newton delivered up as a finished package in the Principia? We all learnt Newtonian physics at school, didn’t we, and that – the three laws of motion, the definition of force and the rest – is all straight out of the Principia, isn’t it? Newtonian physics is Newton’s physics, isn’t it? There is a rule in journalism/blogging that if the title of an article/post is in the form of a question then the answer is no. So Newtonian physics is not Newton’s physics, or is it? The answer is actually a qualified yes, Newtonian physics is Newton’s physics, but it’s very qualified.

Newton's own copy of his Principia, with hand-written corrections for the second edition Source: Wikimedia Commons

Newton’s own copy of his Principia, with hand-written corrections for the second edition
Source: Wikimedia Commons

The differences begin with the mathematics and this is important, after all Newton’s masterwork is The Mathematical Principles of Natural Philosophy with the emphasis very much on the mathematical. Newton wanted to differentiate his work, which he considered to be rigorously mathematical, from other versions of natural philosophy, in particular that of Descartes, which he saw as more speculatively philosophical. In this sense the Principia is a real change from much that went before and was rejected by some of a more philosophical and literary bent for exactly that reason. However Newton’s mathematics would prove a problem for any modern student learning Newtonian mechanics.

Our student would use calculus in his study of the mechanics writing his work either in Leibniz’s dx/dy notation or the more modern F’(x) = f(x) notation of the French mathematician, Lagrange (1736–1813). He won’t be using the dot notation developed by Newton and against which Babbage, Peacock, Herschel and the Analytical Society campaigned so hard at the beginning of the nineteenth century. In fact if our student turns to the Principia, he won’t find Newton’s dot notation calculus there either, as I explained in an earlier post Newton didn’t use calculus when writing the Principia, but did all of his mathematics with Euclidian geometry. This makes the Principia difficult to read for the modern reader and at times impenetrable. It should also be noted that although both Leibniz and Newton, independently of each other, codified a system of calculus – they didn’t invent it – at the end of the seventeenth century, they didn’t produce a completed system. A lot of the calculus that our student will be using was developed in the eighteenth century by such mathematicians as Pierre Varignon (1654–1722) in France and various Bernoullis as well as Leonard Euler (1707­1783) in Switzerland. The concept of limits that are so important to our modern student’s calculus proofs was first introduced by Bernard Bolzano (1781–1848), Augustin-Louis Cauchy (1789–1857) and above all Karl Theodor Wilhelm Weierstrass (1815–1897) in the nineteenth century.

Turning from the mathematics to the physics itself, although the core of what we now know as Newtonian mechanics can be found in the Principia, what we actually use/ teach today is actually an eighteenth-century synthesis of Newton’s work with elements taken from the works of Descartes and Leibniz; something our Isaac would definitely not have been very happy about, as he nursed a strong aversion to both of them.

A notable example of this synthesis concerns the relationship between mass, velocity and energy and was brought about one of the very few women to be involved in these developments in the eighteenth century, Gabrielle-Émilie Le Tonnelier de Breteuil, Marquise du Châtelet, the French aristocrat, lover of Voltaire and translator of the first French edition of the Principia.

In the frontispiece to Voltaire's book on Newton's philosophy, du Châtelet appears as Voltaire's muse, reflecting Newton's heavenly insights down to Voltaire. Source: Wikimedia Commons

In the frontispiece to Voltaire’s book on Newton’s philosophy, du Châtelet appears as Voltaire’s muse, reflecting Newton’s heavenly insights down to Voltaire.
Source: Wikimedia Commons

One should remember that mechanics doesn’t begin with Newton; Simon Stevin, Galileo Galilei, Giovanni Alfonso Borelli, René Descartes, Christiaan Huygens and others all produced works on mechanics before Newton and a lot of their work flowed into the Principia. One of the problems of mechanics discussed in the seventeenth century was the physics of elastic and inelastic collisions, sounds horribly technical but it’s the physics of billiard and snooker for example, which Descartes famously got wrong. Part of the problem is the value of the energy[1] imparted upon impact by an object of mass m travelling at a velocity v upon impact.

Newton believed that the solution was simply mass times velocity, mv and belief is the right term his explanation being surprisingly non-mathematical and rather religious. Leibniz, however, thought that the solution was mass times velocity squared, again with very little scientific justification. The support for the two theories was divided largely along nationalist line, the Germans siding with Leibniz and the British with Newton and it was the French Newtonian Émilie du Châtelet who settled the dispute in favour of Leibniz. Drawing on experimental results produced by the Dutch Newtonian, Willem Jacob ‘s Gravesande (1688–1742), she was able to demonstrate the impact energy is indeed mv2.

Willem Jacob 's Gravesande (1688-1745) Portrait by Hendrik van Limborch (1681-1759) Source: Wikimedia Commons

Willem Jacob ‘s Gravesande (1688-1745) Portrait by Hendrik van Limborch (1681-1759)
Source: Wikimedia Commons

The purpose of this brief excurse into eighteenth-century physics is intended to show that contrary to Pope’s epitaph not even the great Isaac Newton can illuminate a whole branch of science in one sweep. He added a strong beam of light to many beacons already ignited by others throughout the seventeenth century but even he left many corners in the shadows for other researchers to find and illuminate in their turn.

 

 

 

 

[1] The use of the term energy here is of course anachronistic

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Filed under History of Physics, History of science, Myths of Science, Newton, Uncategorized

A spirited defence

After I had, in my last blog post, mauled his Scientific American essay in my usual uncouth Rambo style, Michael Barany responded with great elegance and courtesy in a spirited defence of his historical claims to which I now intend to add some comments, thus extending this exchange by a fourth part.

On early practical mathematicians Michael Barany acknowledges that their work is for the public good but argues correctly that that doesn’t then a “public good”. I acknowledge that there is a difference and accept his point however I have a sneaky feeling that something is only referred to as a “public good” when somebody in power is trying to put one over on the great unwashed.

Barany thinks that the Liber Abbaci and per definition all the other abbacus books, only exist for a closed circle of insider and not for the general public. In fact abbacus books were used as textbooks in so-called abbacus schools, which were small private schools that taught the basics of arithmetic, algebra, geometry and bookkeeping open to all who could pay the fees demanded by the schoolteacher, who was very often the author of the abbacus book that he used for his teaching. It is true that the pupils were mostly the apprentices of tradesmen, builders and artists but they were at least in theory open to all and were not quite the closed shop that Michael Barany seems to be implying. In this context Michael Barany says that Recorde’s Pathway to Knowledge, a book on elementary Euclidean geometry, is eminently impractical. However elementary Euclidean geometry was part of the syllabus of all abbacus schools considered part of the necessary knowledge required by artist and builder/architect apprentices. In fact the first Italian vernacular translation of Euclid was made by Tartaglia, an abbacus schoolteacher.

Michael Barany makes some plausible but rather stretched argument to justify his couterpositioning of Recorde and Dee, which I don’t find totally convincing but slips into his argument the following gem. If you don’t like Dee as your English standard bearer for keeping mathematics close to one’s chest, try Thomas Harriot. Now I assume that this flippant comment was written tongue in cheek but just in case.

Michael Barany’s whole essay contrasts what he sees as two approaches to mathematics, those who see mathematics as a topic for everyone and those who view mathematics as a topic for an elitist clique. In the passage that I criticised in his original essay he presented Robert Recorde as an example of the former and John Dee as a representative of the latter. A contrast that he tries to defend in his reply, where this statement about Harriot turns up. Now his elitist argument is very much dependent on a clique or closed circle of trained experts or adepts who exchanged their arcane knowledge amongst themselves but not with outsiders. A good example of such behaviour in the history of science is alchemy and the alchemists. Harriot as an example of such behaviour is a complete flop. Thomas Harriot made significant discoveries in various fields of scientific endeavour, mathematics, dynamics, chemistry, optics, cartography and astronomy, however he never published any of his work and although he corresponded with other leading Renaissance scholars he also didn’t share his discoveries with these people. A good example of this is his correspondence with Kepler, where he discussed over several letters the problem of refraction but never once mentioned that he had already discovered what we now know as Snell’s Law. Harriot remained throughout his life a closed circle with exactly one member, not a very good example to illustrate Michael Barany’s thesis.

I claimed that there was no advance mathematics in Europe from late antiquity till the fifteenth century. Michael Barany counters this by saying: This cuts, for instance, the rich history of Islamic court mathematics out of the European history in which it emphatically belongs; it doesn’t cut it. Ignoring Islamic Andalusia, Islamic mathematics was developed outside of Europe and although it started to reappear in Europe during the twelfth and thirteen centuries during the translator period nobody within Europe was really capable of doing much with those advanced aspects of it before the fifteenth century, so I stand by my claim.

We now turn to Michael Barany’s defence of his original: In the seventeenth century’s Scientific Revolution, the new promoters of an experimental science that was (at least in principle) open to any observer were suspicious of mathematical arguments as inaccessible, tending to shut down diverse perspectives with a false sense of certainty. This he contrast with a, in his opinion, eighteenth century where mathematicians help sway over the scientific community. I basically implied that this claim was rubbish and I still stand by that to that, so what does Michael Barany produce in his defence.

In my original post I listed seven leading scholars of the seventeenth century who were mathematicians and whose very substantive contributions to the so-called scientific revolution was mathematical, on this Barany writes:

Thony pretends that naming some figures remembered today both for mathematics and for their contributions to the scientific revolution contradicts this well-established historical claim.

The, without any doubt, principle figures of the so-called scientific revolution are just some figures! Interesting? So what is Michael Barany’s well-established historical claim? We get offered the following:

Following Steven Shapin and many who have written since his classic 1988 article on Boyle’s relationship to mathematics, I chose to emphasize the conflicts between the experimental program associated with the scientific revolution and competing views on the role of mathematics in natural philosophy.

What we have here is an argument by authority, that of Steven Shapin, whose work and the conclusions that he draws are by no means undisputed, and one name Robert Boyle! Curiously a few days before I read this, science writer, John Gribbin, commentated on Facebook that Robert Hooke had to work out Boyle’s Law because Boyle was lousy at mathematics, might this explain his aversion to it? However Michael Barany does offer us a second argument:

But to take just his most famous example, Newton’s prestige in the Royal Society is generally seen today to have had at least as much to do with his Opticks and his other non-mathematical pursuits as with his calculus, which contemporaries almost uniformly found impenetrable.

Really? I seem to remember that twenty years before he published his Opticks, Old Isaac wrote another somewhat significant tome entitled Philosophiæ Naturalis Principia Mathematica [my emphasis], which was published by the Royal Society. It was this volume of mathematical physics that established Newton’s reputation, not only with the fellows of the Royal Society, but with the entire scientific community of Europe, even with those who rejected Newton’s central concept of gravity as action at a distance. This book led to Newton being elected President of the Royal Society, in 1704, the same year as the Opticks was published. The Opticks certainly enhanced Newton’s reputation but he was already considered almost universally by then to be the greatest living natural philosopher.

Is the Opticks truly non-mathematical? Well, actually no! When it was published it was the culmination of two thousand years of geometrical optics, a mathematical discipline that begins with Euclid, Hero and Ptolemaeus in antiquity and was developed by various Islamic scholars in the Middle Ages, most notably Ibn al-Haytham. One of the first mathematical sciences to re-enter Europe in the High Middle Ages it was propagated by Robert Grosseteste, Roger Bacon, John Peckham and Witelo. In the seventeenth-century it was one of the mainstream disciplines contributing to the so-called scientific revolution developed by Thomas Harriot, Johannes Kepler, Willebrord van Roijen Snell, Christoph Scheiner, René Descartes, Pierre Fermat, Christiaan Huygens, Robert Hooke, James Gregory and others. Newton built on and developed the work of all these people and published his results in his Opticks in 1706. Yes, some of his results are based on experiments but that does not make the results non-mathematical and if you bother to read the book you will find more than a smidgen of geometry there in.

In my opinion trying to recruit Newton as an example of non-mathematical experimental science is an act of desperation.

To be fair to Michael Barany the division between those who favoured non-mathematical experimental science and the mathematician really did exist in the seventeenth century, however it was largely confined to England and most prominently in the Royal Society. This is the conflict between the Baconians and the Newtonians that I have blogged about on several occasions in the past. Boyle, Hooke and Flamsteed, for example, were all Baconians who, following Francis Bacon, were not particularly fond of mathematical proofs. This conflict has an interesting history within the Royal Society, which led to disadvantages for the development of the mathematical sciences in England in the eighteenth century.

When the Royal Society was initially founded some mathematician did not become members because of the dominance of the Baconians and that despite the fact that the first President, William Brouncker, was a mathematician. Later under Newton’s presidency the mathematicians gained the ascendency, but first in 1712 after an eight-year guerrilla conflict between Newton and Hans Sloane, a Baconian and the society’s secretary. Following Newton’s death in 1727 (ns) the Baconians regained power and the result was that, whereas on the continent the mathematical sciences flourished and evolved throughout the eighteenth century, in England they withered and died, leading to a new power struggle in the nineteenth century featuring such figures as Charles Babbage and John Herschel.

To claim as Michael Barany does that this conflict within the English scientific community meant that mathematics played an inferior role in the seventeenth century is a bridge too far and contradicts the available historical facts. Yes, the mathematization of nature was not the only game in town and interestingly non-mathematical experimental science was not the only alternative. In fact the seventeenth century was a wonderful cuddle-muddle of conflicting meta-physical views on the sciences. However whatever Steven Shapin might or might not claim the seventeenth century was a very mathematical century and mathematics was the principle driving force behind the so-called scientific revolution. As a footnote I would point out that many of the leading experimental natural philosophers of the seventeenth century, such as Galileo, Pascal, Stevin and Newton, were mathematicians who interpreted and presented their results mathematically.

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Filed under History of Mathematics, History of science, Newton