Category Archives: History of Physics

Published on…

Today I have been mildly irritated by numerous tweets announcing the 5th July 1687, as the day on which Isaac Newton’s Principia was published, why? Partially because the claim is not strictly true and partially because it evokes a false set of images generated by the expression, published on, in the current age.

In the last couple of decades we have become used to images of hoards of teens dressed in fantasy costumes as witches queuing up in front of large bookstores before midnight to participate in the launch of the latest volume of a series of children’s books on a juvenile wizard and his adventures. These dates were the days on which the respective volumes were published and although the works of other authors do not enjoy quite the same level of turbulence, they do also have an official publication date, usually celebrated in some suitable way by author and publisher. Historically this has not always been the case.

In earlier times books, particularly ones of a scientific nature, tended to dribble out into public awareness over a vague period of time rather than to be published on a specific date. There were no organised launches, no publisher’s parties populated by the glitterati of the age and no official publication date. Such books were indeed published in the sense of being made available to the reading public but the process was much more of a slapdash affair than that which the term evokes today.

One reason for this drawn out process of release was the fact that in the early centuries of the printed book they were often not bound for sale by the publisher. Expensive works of science were sold as an unbound pile of printed sheets, allowing the purchaser to have his copy bound to match the other volumes in his library. This meant that there were not palettes of finished bound copies that could be shipped off to the booksellers. Rather a potential purchaser would order the book and its bindings and wait for it to be finished for delivery.

Naturally historians of science love to be able to nail the appearance of some game changing historical masterpiece to a specific date, however this is not always possible. In the case of Copernicus’ De revolutionibus, for example, we are fairly certain of the month in 1543 that Petreius started shipping finished copies of the work but there is no specific date of publication. With other equally famous works, such as Galileo’s Sidereus Nuncius, the historian uses the date of signing of the dedication as a substitute date of publication.

So what is with Newton’s Principia does it have an official date of publication and if not why are so many people announcing today to be the anniversary of its publication. Principia was originally printed written in manuscript in three separate volumes and Edmond Halley, who acted both as editor and publisher, had to struggle with the cantankerous author to get those volumes out of his rooms in Cambridge and into the printing shop. In fact due to the interference of Robert Hooke, demanding credit for the discovery of the law of gravity, Newton contemplated not delivering the third volume at all. Due to Halley’s skilful diplomacy this crisis was mastered and the final volume was delivered up by the author and put into print. July 5th 1687 is not the date of publication as it is understood today, but the date of a letter that Halley sent to Newton announcing that the task of putting his immortal masterpiece onto the printed page had finally been completed and that he was sending him twenty copies for his own disposition. I reproduce the text of Halley’s letter below.

 

Honoured Sr

I have at length brought you Book to an end, and hope it will please you. the last errata came just in time to be inserted. I will present from you the books you desire to the R. Society, Mr Boyle, Mr Pagit, Mr Flamsteed and if there be any elce in town that you design to gratifie that way; and I have sent you to bestow on your friends in the University 20 Copies, which I entreat you to accept.[1]

 

 

[1] Richard S. Westfall, Never at Rest: A Biography of Isaac Newton, Cambridge University Press, Cambridge etc., 1980, p. 468.

6 Comments

Filed under Early Scientific Publishing, History of Astronomy, History of Physics, Myths of Science, Newton

Niels & Me: Dysgraphia – A history of science footnote.

One of the symptoms that, I think most, sufferers from mental illness share is the feeling of being alone with their daemons. “I’m the only one who feels like this!” “Why have I alone been afflicted?” This feeling of isolation and of having been somehow singled out for punishment in itself causes mental distress and deepens the crisis. An important step along the road to recovery is the realisation that one is not alone, that there are others who suffer similarly, that one hasn’t been singled out. I can still remember very clearly the day when I became certain that I am an adult ADD sufferer and a lot of my symptoms, including several that I didn’t regard as part of my illness, fell into place, received a label and a possible path back to mental health. As I have already related in my previous post I had very similar feelings on discovering dysgraphia and realising that it was one of my central daemons. One of those revelations concerning dysgraphia actually has a close connection to my history of science obsession and as this is a history of science blog I would like to tell the story here.

As should be clear from the name of this blog my main interest as a historian of science lies with the mathematical sciences in the Early Modern Period, however I try not to be too narrow and get stuck in a historical cul-de-sac, only able to understand a very narrow field of science over a very short period of time. In order to maintain a broad overview of the history of science I buy and read general surveys of the histories of other disciplines in other periods. One such book that I own is Robert P. Crease and Charles C. Mann The Second Creation: Makers of the Revolution in Twentieth-Century Physics[1], which, if my memory serves me correctly, I bought on the recommendation of dog owner, physics blogger and popular science book author Chad Orzel; a recommendation that I would endorse. I vividly remember, shortly after I bought it, curling up in bed with the book for my half hour read before going to sleep and waking up rather than dosing off, as I read the revelatory words on the first pages of chapter two, The Man Who Talked. I’m now going quote some fairly large chunks of those pages:

Bohr’ working habits have become legendary among his successors, part of the lore of science along with Einstein’s flyaway hair and Rutherford’s remark that relativity was not meant to be understood by Anglo-Saxons. Bohr talked. [emphasis in original] He discovered his ideas in the act of enunciating them, shaping thoughts as they came out of his mouth. Friends, colleagues, graduate students, all had Bohr gently entice them into long walks in the countryside around Copenhagen, the heavy clouds scudding overhead as Bohr thrust his hands into his overcoat pockets and settled into an endless, hesitant, recondite, barely audible monologue. While he spoke, he watched his listeners’ reactions, eager to establish a bond in a shared effort to articulate. Whispered phrases would be pronounced, only to be adjusted as Bohr struggled to express exactly [emphasis in original] what he meant; words were puzzled over, repeated, then tossed aside, and he was always ready to add a qualification, to modify, a remark, to go back to the beginning, to start the explanation over again. Then flatteringly, he would abruptly thrust the subject on his listener – surely this cannot be all? what else is there? – his big, ponderous, heavy-lidded eyes intent on the response. Before it could come, however, Bohr would have started talking again, wrestling with the answer himself. He inspected the language with which an idea was expressed in the way a jeweller inspects an unfamiliar stone, slowly judging each facet by holding it before an intense light[2].

Now I would never be so presumptuous to compare myself to Niels Bohr but this paragraph resonated with me on so many levels that I almost felt sick with excitement when I read it. With slight differences that is how I think, discover, formulate my ideas and my theories. In more recent years I sometimes feel really sorry for my listeners and try to throttle back the waterfall of words that pour out of my mouth; in earlier years I was not aware of my, basically anti-social, behaviour lost in that stream of consciousness word flow. However it was a paragraph two thirds of the way down the following page that made me sit bolt upright in bed.

As a schoolboy, Bohr’s worst subject had been Danish composition, and for the rest of his life he passed up no opportunity to avoid putting pen to paper. He dictated his entire doctoral dissertation to his mother, causing family rows when his father insisted that the budding Ph. D. should be forced to learn to write for himself; Bohr’s mother remained firm in her belief that the task was hopeless. It apparently was – most of Bohr’s later work and correspondence were dictated to his wife and a succession of secretaries and collaborators. Even with this assistance, it took him months to put together articles. Reading of his struggles, it is hard not to wonder if he was dyslexic[3]. [my emphasis]

I’m not a big fan of historical diagnosis by hearsay of illnesses that one or other famous figure from the past might have suffered. You could write an entire medical dictionary containing all the complaints that researchers have decided that the artist Van Gough suffered, according to their interpretation of the available facts. However my own personal situation leads me to the conclusion that Messrs. Crease and Mann are wrong and that Niels Bohr was not dyslexic but dysgraphic.

If you suffer from a disability that has caused you years of mental stress, then to discover that a famous historical figure suffered from the same ailment and despite this handicap was successful can be an incredible boost. Knowing that Bohr needed assistance to write his papers takes away some of the shame that I feel in having to ask people to check and correct the things that I write, as I said at the beginning, it’s knowing that you’re not alone.

 

 

 

[1] Robert P. Crease and Charles C. Mann,The Second Creation: Makers of the Revolution in Twentieth-Century Physics, Rutgers University Press, New Brunswick, New Jersey, Revised ed., 1996.

[2]Crease & Mann p. 20

[3]Crease & Mann p. 21

7 Comments

Filed under Autobiographical, History of Physics, History of science

Science grows on the fertilizer of disagreement

At the weekend German television presented me with all three episodes of Jim Al-Khalili’s documentary on the history of electricity, Shock and Awe: The Story of Electricity. On the whole I found it rather tedious largely because I don’t like my science or history of science served up by a star presenter who is the centre of the action rather than the science itself, a common situation with the documentaries of ‘he who shall not be named’-TPBoPS, and NdGT. It seems that we are supposed to learn whatever it is that the documentary nominally offers by zooming in on the thoughtful features of the presenter, viewing his skilfully lit profile or following him as he walks purposefully, thoughtfully, meaningfully or pensively through the landscape. What comes out is “The Brian/Neil/Jim Show” with added science on the side, which doesn’t really convince me, but maybe I’m just getting old.

However my criticism of the production style of modern television science programmes is not the real aim of this post, I’m much more interested in the core of the first episode of Al-Khalili’s documentary. The episode opened and closed with the story of Humphrey Davy constructing the, then, largest battery in the world in the cellars of the Royal Institution in order to make the first ever public demonstration of an arc lamp and thus to spark the developments that would eventually lead to electric lighting. Having started here the programme moved back in time to the electrical experiments of Francis Hauksbee at the Royal Society under the auspices of Isaac Newton. Al-Khalili then followed the development of electrical research through the eighteenth-century, presenting the work of the usual suspects, Steven Gray, Benjamin Franklin etc., until we arrived at the scientific dispute between the two great Italian physicists Luigi Galvani and Alessandro Volta that resulted in the invention of the Voltaic pile, the forerunner of the battery and the first producer of an consistent electrochemical current. All of this was OK and I have no real criticisms, although I was slightly irked by constant references to ‘Hauksbee’s’ generator when the instrument in question was an adaption suggested by Newton of an invention from Otto von Guericke, who didn’t get a single name check. What did irritate me and inspired this post was the framing of the Galvani-Volta dispute.

Al-Khalili, a gnu atheist of the milder variety, presented this as a conflict between irrational religious persuasion, Galvani, and rational scientific heuristic, Volta, culminating in a victory for science over religion. In choosing so to present this historical episode Al-Khalili, in my opinion, missed a much more important message in scientific methodology, which was in fact spelt out in the fairly detailed presentation of the successive stages of the dispute. Galvani made his famous discovery of twitching frog’s legs and after a series of further experiments published his theory of animal electricity. Volta was initially impressed by Galvani’s work and at first accepted his theory. Upon deeper thought he decided Galvani’s interpretation of the observed phenomena was wrong and conducted his own series of result to prove Galvani wrong and establish his own theory. Volta having published his refutation of Galvani’s theory, the latter not prepared to abandon his standpoint also carried out a series of new experiments to prove his opponent wrong and his own theory right. One of these experiments led Volta to the right explanation, within the knowledge framework of the period, and to the discovery of the Voltaic pile. What we see here is a very important part of scientific methodology, researchers holding conflicting theories spurring each other on to new discoveries and deeper knowledge of the field under examination. The heuristics of the two are almost irrelevant, what is important here is the disagreement as research motor. Also very nicely illustrated is discovery as an evolutionary process spread over time rather than the infamous eureka moment.

The inspiration produced from watching Al-Khalili’s story of the invention of the battery chimes in very nicely with another post I was planning on writing. In a recent blog post, Joe Hanson of “it’s OKAY to be SMART” wrote about Galileo and the first telescopic observations of sunspots at the beginning of the seventeenth-century. The post is OK as far as it goes, even managing to give credit to Thomas Harriot and Johannes Fabricius, however it contains one truly terrible sentence that caused my heckles to rise. Hanson wrote:

Although Galileo’s published sunspot work was the most important of its day, on account of the “that’s no moon” smackdown it delivered to the Jesuit scientific community, G-dub was not the first to observe the solar speckles.

Here we have another crass example of modern anti-religious sentiment of a science writer getting in the way of sensible history of science. What we are talking about here is not the Jesuit scientific community but the single Jesuit physicist and astronomer Christoph Scheiner, who famously became embroiled in a dispute on the nature of sunspots with Galileo. Once again we also have an excellent example of scientific disagreement driving the progress of scientific research. Scheiner and Galileo discovered sunspots with their telescopes independently of each other at about the same time and it was Scheiner who first published the results of his discoveries together with an erroneous theory as to the nature of sunspots. Galileo had at this point not written up his own observations, let alone developed a theory to explain them. Spurred on by Scheiner’s publication he now proceeded to do so, challenging Scheiner’s claim that the sunspots where orbiting the sun and stating instead that they were on the solar surface. An exchange of views developed with each of the adversaries making new observations and calculations to support their own theories. Galileo was not only able to demonstrate that sunspots were on the surface of the sun but also to prove that the sun was rotating on its axis, as already hypothesised by Johannes Kepler. Scheiner, an excellent astronomer and mathematician, accepted Galileo’s proofs and graciously acknowledge defeat. However whereas Galileo now effectively gave up his solar observations Scheiner developed new sophisticated observation equipment and carried out an extensive programme of solar research in which he discovered amongst other things that the sun’s axis is tilted with respect to the ecliptic. Here again we have two first class researchers propelling each other to new important discoveries because of conflicting views on how to interpret observed phenomena.

My third example of disagreement as a driving force in scientific discovery is not one that I’ve met recently but one whose misrepresentation has annoyed me for many years, it concerns Albert Einstein and quantum mechanics. I have lost count of the number of times that I’ve read some ignorant know-it-all mocking Einstein for having rejected quantum mechanics. That Einstein vehemently rejected the so-called Copenhagen interpretation of quantum mechanics is a matter of record but his motivation for doing so and the result of that rejection is often crassly misrepresented by those eager to score one over the great Albert. Quantum mechanics as initial presented by Niels Bohr, Erwin Schrödinger, Werner Heisenberg et. al. contradicted Einstein fundamental determinist metaphysical concept of physics. It was not that he didn’t understand it, after all he had made several significant contributions to its evolution, but he didn’t believe it was a correct interpretation of the real physical world. Einstein being Einstein he didn’t just sit in the corner and sulk but actively searched for weak points in the new theory trying to demonstrate its incorrectness. There developed a to and fro between Einstein and Bohr, with the former picking holes in the theory and the latter closing them up again. Bohr is on record as saying that Einstein through his informed criticism probably contributed more to the development of the new theory than any other single physicist. The high point of Einstein’s campaign against quantum mechanics was the so-called EPR (Einstein-Podolsky-Rosen) paradox, a thought experiment, which sought to show that quantum mechanics as it stood would lead to unacceptable or even impossible consequences. On the basis of EPR the Irish physicist John Bell developed a testable theorem, which when tested showed quantum mechanics to be basically correct and Einstein wrong, a major step forward in the establishment of quantum physics. Although proved wrong in the end Einstein’s criticism of and disagreement with quantum mechanics contributed immensely to the theories evolution.

The story time popular presentations of the history of science very often presents the progress of science as a series of eureka moments achieved by solitary geniuses, their results then being gratefully accepted by the worshiping scientific community. Critics who refuse to acknowledge the truth of the new discoveries are dismissed as pitiful fools who failed to understand. In reality new theories almost always come into being in an intellectual conflict and are tested, improved and advanced by that conflict, the end result being the product of several conflicting minds and opinions struggling with the phenomena to be explained over, often substantial, periods of time and are not the product of a flash of inspiration by one single genius. As the title says, science grows on the fertilizer of disagreement.

17 Comments

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

What Isaac actually asked the apple.

Yesterday on my twitter stream people were retweeting the following quote:

“Millions saw the apple fall, but Newton asked why.” —Bernard Baruch

For those who don’t know, Bernard Baruch was an American financier and presidential advisor. I can only assume that those who retweeted it did so because they believe that it is in some way significant. As a historian of science I find it is significant because it is fundamentally wrong in two different ways and because it perpetuates a false understanding of Newton’s apple story. For the purposes of this post I shall ignore the historical debate about the truth or falsity of the apple story, an interesting discussion of which you can read here in the comments, and just assume that it is true. I should however point out that in the story, as told by Newton to at least two different people, he was not hit on the head by the apple and he did not in a blinding flash of inspiration discover the inverse square law of gravity. Both of these commonly held beliefs are myths created in the centuries after Newton’s death.

Our quote above implies that of all the millions of people who saw apples, or any other objects for that matter, fall, Newton was the first or even perhaps the only one to ask why. This is of course complete and utter rubbish people have been asking why objects fall probably ever since the hominoid brain became capable of some sort of primitive thought. In the western world the answer to this question that was most widely accepted in the centuries before Newton was born was the one supplied by Aristotle. Aristotle thought that objects fall because it was in their nature to do so. They had a longing, desire, instinct or whatever you choose to call it to return to their natural resting place the earth. This is of course an animistic theory of matter attributing as it does some sort of spirit to matter to fulfil a desire.

Aristotle’s answer stems from his theory of the elements of matter that he inherited from Empedocles. According to this theory all matter on the earth consisted of varying mixtures of four elements: earth, water, fire and air. In an ideal world they would be totally separated, a sphere of earth enclosed in a sphere of water, enclosed in a sphere of air, which in turn was enclosed in a sphere of fire. Outside of the sphere of fire the heavens consisted of a fifth pure element, aether or as it became known in Latin the quintessence. In our world objects consist of mixtures of the four elements, which given the chance strive to return to their natural position in the scheme of things. Heavy objects, consisting as they do largely of earth and water, strive downwards towards the earth light objects such as smoke or fire strive upwards.

To understand what Isaac did ask the apple we have to take a brief look at the two thousand years between Aristotle and Newton.

Ignoring for a moment the Stoics, nobody really challenged the Aristotelian elemental theory, which is metaphysical in nature but over the centuries they did challenge his physical theory of movement. Before moving on we should point out that Aristotle said that vertical, upwards or downwards, movement on the earth was natural and all other movement was unnatural or violent, whereas in the heavens circular movement was natural.

Already in the sixth century CE John Philoponus began to question and criticise Aristotle’s physical laws of motion. An attitude that was taken up and extended by the Islamic scholars in the Middle Ages. Following the lead of their Islamic colleagues the so-called Paris physicists of the fourteenth century developed the impulse theory, which said that when an object was thrown the thrower imparted an impulse to the object which carried it through the air gradually being exhausted, until when spent the object fell to the ground. Slightly earlier their Oxford colleagues, the Calculatores of Merton College had in fact discovered Galileo’s mathematical law of fall: The two theories together providing a quasi-mathematical explanation of movement, at least here on the earth.

You might be wondering what all of this has to do with Isaac and his apple but you should have a little patience we will arrive in Grantham in due course.

In the sixteenth century various mathematicians such as Tartaglia and Benedetti extended the mathematical investigation of movement, the latter anticipating Galileo in almost all of his famous discoveries. At the beginning of the seventeenth century Simon Stevin and Galileo deepened these studies once more the latter developing very elegant experiments to demonstrate and confirm the laws of fall, which were later in the century confirmed by Riccioli. Meanwhile their contemporary Kepler was the first to replace the Aristotelian animistic concept of movement with one driven by a non-living force, even if it was not very clear what force is. During the seventeenth century others such as Beeckman, Descartes, Borelli and Huygens further developed Kepler’s concept of force, meanwhile banning Aristotle’s moving spirits out of their mechanistical philosophy. Galileo, Beeckman and Descartes replaced the medieval impulse theory with the theory of inertia, which says that objects in a vacuum will either remain at rest or continue to travel in a straight line unless acted upon by a force. Galileo, who still hung on the Greek concept of perfect circular motion, had problems with the straight-line bit but Beeckman and Descartes straightened him out. The theory of inertia was to become Newton’s first law of motion.

We have now finally arrived at that idyllic summer afternoon in Grantham in 1666, as the young Isaac Newton, home from university to avoid the plague, whilst lying in his mother’s garden contemplating the universe, as one does, chanced to see an apple falling from a tree. Newton didn’t ask why it fell, but set off on a much more interesting, complicated and fruitful line of speculation. Newton’s line of thought went something like this. If Descartes is right with his theory of inertia, in those days young Isaac was still a fan of the Gallic philosopher, then there must be some force pulling the moon down towards the earth and preventing it shooting off in a straight line at a tangent to its orbit. What if, he thought, the force that holds the moon in its orbit and the force that cause the apple to fall to the ground were one and the same? This frighteningly simple thought is the germ out of which Newton’s theory of universal gravity and his masterpiece the Principia grew. That growth taking several years and a lot of very hard work. No instant discoveries here.

Being somewhat of a mathematical genius, young Isaac did a quick back of an envelope calculation and see here his theory didn’t fit! They weren’t the same force at all! What had gone wrong? In fact there was nothing wrong with Newton’s theory at all but the figure that he had for the size of the earth was inaccurate enough to throw his calculations. As a side note, although the expression back of an envelope calculation is just a turn of phrase in Newton’s case it was often very near the truth. In Newton’s papers there are mathematical calculations scribbled on shopping lists, in the margins of letters, in fact on any and every available scrap of paper that happened to be in the moment at hand.

Newton didn’t forget his idea and later when he repeated those calculations with the brand new accurate figures for the size of the earth supplied by Picard he could indeed show that the chain of thought inspired by that tumbling apple had indeed been correct.

 

11 Comments

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

Getting the measure of the earth.

It is generally accepted that the Pythagoreans in the sixth century BCE were the first to recognise and accept that the earth is a sphere. It is also a historical fact that since Aristotle in the fourth century BCE nobody of any significance in the western world has doubted this fact. Of course recognising and accepting that the earth is a sphere immediately prompts other questions, one of the first being just how big a sphere is it? Now if I want to find the circumference of a cricket ball (American readers please read that as a baseball ball) I whip out my handy tape measure loop it around the ball and read of the resulting answer, between 224mm and 229mm (circa 230mm for American readers). In theory I could take an extremely long tape measure and following a meridian (that is a great circle around the globe through the north and south poles) loop it around the globe reading off the answer as before, 40,007.86 km (radius) 6356.8km according to Wikipedia. However it doesn’t require much imagination to realise the impracticality of this suggestion; another method needs to be found.

Famously, the earliest known scientific measurement of the polar circumference was carried out by Eratosthenes in the third century BCE. Eratosthenes measured the elevation of the sun at midday on the summer solstice in one of two cities that he thought to be on the same meridian knowing that the sun was directly overhead at the other.  Knowing the distance between the cities it is a relative simple trigonometrical calculation to determine the polar circumference. Don’t you love it when mathematicians say that a calculation is simple!  He achieved an answer of 250 000 stadia but as there were various stadia in use in the ancient world at this time and we don’t know to which stadia he was referring we don’t actually know how accurate his measure was.

Other astronomers in antiquity used the more common method of measuring a given distance on a meridian, determining the latitude of the ends and again using a fairly simple trigonometrical calculation determining the polar circumference. This method proved to be highly inaccurate because of the difficulties of accurately measuring a suitably long, straight north south section of a meridian. The errors incurred leading to large variations in the final circumference determined.

In the eleventh century CE the Persian scholar al-Biruni developed a new method of determining the earth’s circumference. He first measured the height of a suitable mountain, using another of those simple trigonometrical calculations, then climbing the mountain measuring the angle of dip of the horizon. These measurements were followed by, you’ve guessed it, yet another simple trigonometrical calculation to determine the circumference. Various sources credit al-Biruni with an incredibly accurate result from his measurements, which is to be seriously doubted. For various reasons it is almost impossible to accurately determine the angle of dip and the method whilst theoretically interesting is in practice next to useless.

In the Renaissance Gemma Frisius’ invention of triangulation in 1533 provided a new method of accurately measuring a suitably long north south section of a meridian. The first to apply this method to determine the length of one degree of meridian arc was the Dutch mathematician Willibrord Snel, as described in his Eratosthenes Batavus (The Dutch Eratosthenes) published in 1617. He measured a chain of triangles between Alkmaar and Bergen op Zoom and determined one degree of meridian arc to be 107.395km about 4km shorter than the actual value. Snel’s measurement initially had little impact but it inspired one that was to become highly significant.

The meridian arc measurement inspired by Snel was carried out by the French astronomer Jean-Félix Picard who was born the son of a bookseller, also called Jean, in La Flèche on 21st July 1620.  As is unfortunately all too often the case for mathematicians in the Early Modern Period we know very little about Picard’s background or childhood but we do know that he went to school at the Jesuit College in La Flèche where he benefited from the Clavius mathematical programme as did other La Flèche students such as Descartes, Mersenne and Gassendi. Picard left La Flèche around 1644 and moved to Paris where he became a student of Gassendi then professor for mathematics at the Collège Royal. Whether he was ever formally Gassendi’s student is not known but he certainly assisted in his astronomical observations in the 1640s. In 1648 Picard left Paris for health reasons but in 1655 he returned as Gassendi’s successor at the Collège Royal; an appointment based purely on his reputation, as he had published nothing at this point in his life.

Jean Picard (artist unknown)

Jean Picard (artist unknown)

In 1665 Jean-Baptist Colbert became finance minister of France and began to pursue an aggressive science policy.

Colbert 1666 Philippe de Champaigne

Colbert 1666 Philippe de Champaigne

He established the Académie des sciences in 1666 modelled on its English counterpart the Royal Society but unlike Charles who gave his scientists no financial support Colbert supplied his academicians, of whom Picard was one, with generous salaries. It was also Colbert who motivated his academicians to produce a new, modern, accurate map of France and this was when Picard became a geodesist and cartographer.

Following the methods laid down by Snel Picard made the first measurement of what is now the legendary Paris meridian, which would a hundred years later in extended form become the basis of the metre and thus the metric system. He first measured an eleven-kilometre base line south of Paris between Villejuif and Juvisy across what is now Orly airport using standardised wooden measuring rods.

Southern end of Picard's baseline

Southern end of Picard’s baseline

 

Northern end of Picard's baseline

Northern end of Picard’s baseline

The straight path that he created became the Avenue de Paris in Villejuif and later the Route National 7 through Orly to Juvisy. From this baseline Picard triangulated northwards through Paris and a little further south. For his triangulation Picard used a theodolite whose sighting telescope was fitted with cross hair. The first ever use of such an instrument. Picard determined one degree of meridian arc to be 110.46 km making the polar radius 6328.9 km.

Picard's triangulation and his instruments

Picard’s triangulation and his instruments

Whilst Picard was out in the field measuring triangles Colbert was hiring Giovanni Domenico Cassini away from Bologna to work in the newly constructed Paris Observatory in what was probably to most expensive scientific transfer deal in the seventeenth century.

Giovanni Cassini (artist unknown)

Giovanni Cassini (artist unknown)

Following the success of Picard’s meridian triangulation he set about using the skills he had developed to map the coastline of France together with Cassini and Philippe de La Hire. The results of their endeavours greatly reduced the presumed size of France provoking Louise XIV’s famous quip that he had lost more territory to the cartographers than he had ever lost to his enemies.

Map showing both old and new French coastlines

Map showing both old and new French coastlines

Picard now began preparations for the accurate mapping of France but died before the project could begin. Cassini took up the reins and the mapping of France became a Cassini family project stretching over four generations.

Picard’s determination of the size of the earth would go on to play a significant role in the history of physics. In 1666 when the young Isaac Newton first got an inkling of the concept of a universal gravity he asked himself if the force that causes an object to fall to the ground (that infamous apple) is the same force that prevents the moon from shooting off at a tangent to its orbit, which it should do according to the law of inertia. Young Newton did a quick calculation on the back of an envelope and determined that it wasn’t.  As we now know they are of course the same force so what went wrong with the young Isaac’s calculations? The size of the earth that he had used in his calculation had been wrong. In the 1680s when Newton returned to the subject and redid his calculation he now took Picard’s value and discovered that his original assumption had indeed been correct. In his Principia Newton uses Picard’s value with acknowledgement.

The difference between Picard’s value for one degree of meridian arc and that determined by Snel led Cassini and his son to hypothesise that the earth is a prolate spheroid (lemon shaped) whereas Newton and Huygens had hypothesised that it is an oblate spheroid (orange shaped) a dispute that I’ve blogged about in the past.

CASSINIS'_ELLIPSOID;_HUYGEN'S_THEORETICAL_ELLIPSOID

Picard made other important contributions to astronomy and physics and it’s a little bit sad that that today when people hear or read the name Jean Picard they think of a character in a TV science fiction series and not a seventeenth century French astronomer.

[The photos showing the monuments marking the ends of Picard's baseline are taken from Paul Murdin, Full Meridian of Glory: Perilous Adventures in the Competition to Measure the Earth, Copernicus Books, 2009]

10 Comments

Filed under History of Astronomy, History of Cartography, History of Physics, History of science, Uncategorized

“If he had lived, we might have known something”

The title of this post is Newton’s rather surprising comment on hearing of the early death of the Cambridge mathematician Roger Cotes at the age of 33 in 1716. I say rather surprising, as Newton was not known for paying compliments to his mathematical colleagues, rather the opposite. Newton’s compliment is a good measure of the extraordinary mathematical talents of his deceased associate.

Cotes the son of rector from Burbage in Leicestershire born 10th July 1682 is a good subject for this blog for at least three different reasons. Firstly he is like many of the mathematicians portrayed here relatively obscure although he made a couple of significant contributions to the history of science. Secondly one of those contributions, which I’ll explain below, is a good demonstration that Newton was not a ‘lone’ genius, as he is all too often presented. Lastly he just scraped past the fate of Thomas Harriot, of being forgotten, having published almost nothing during his all too brief life, he had the luck that his mathematical papers were edited and published shortly after his death by his cousin Robert Smith thus ensuring that he wasn’t forgotten, at least by the mathematical community.

Cotes was recognised as a mathematical prodigy before he was twelve years old. He was taken under the wing of his uncle, Robert Smith’s father, and sent to St Paul’s School in London from whence he proceeded to Trinity College Cambridge, Newton’s college, in 1699. Newton whilst still nominally Lucasian Professor had already departed for London and the Royal Mint. Cotes graduated BA in 1702. Was elected minor fellow in 1705 and major fellow in 1706 the same year he graduated MA. His mathematical talent was recognised on all sides and in the same year he was nominated, as the first Plumian Professor of Astronomy and Natural Philosophy, still not 23 years old. However he was only elected to this position on 16th October 1707. It should be noted that the newly created Plumian Chair was only the second chair for the mathematical sciences in Cambridge following the creation of the Lucasian Chair in 1663. In comparison, for example, Krakow University in Poland, the first humanist university outside of Northern Italy, already had two dedicated chairs for the mathematical sciences in the middle of the sixteenth century. This illustrates how much England was lagging behind the continent in its promotion of the mathematical sciences in the Early Modern Period.

Cotes election to the Plumian chair was supported by Richard Bentley, Master of Trinity, and by William Whiston, in the meantime Newton’s successor as Lucasian professor, who claimed to be “a child to Mr Cotes” in mathematics but was opposed by John Flamsteed, the Astronomer Royal, who wanted his former assistant John Witty to be appointed. In the end Flamsteed would be proven right, as Cotes was shown to be a more than somewhat mediocre astronomer.

Cotes’ principle claim to fame is closely connected to Newton and his magnum opus the Principia. Newton gave the task of publishing a second edition of his masterpiece to Richard Bentley, who now took on the role filled by Edmond Halley with the first edition. Now Bentley who was a child prodigy, a brilliant linguist and a groundbreaking philologist was anything but a mathematician and he delegated the task of correcting the Principia to his protégé, Cotes in 1709. Newton by now an old man and no longer particularly interested in mathematical physics had intended that the second edition should basically be a reprint of the first with a few minor cosmetic corrections. Cotes was of a different opinion and succeeded in waking the older man’s pride and convincing him to undertake a complete and thorough revision of the complete work. This task would occupy Cotes for the next four years. As well as completely reworking important aspects of Books II and III this revision produced two highly significant documents in the history of science, Newton’s General Scholium at the end of Book III, a general conclusion missing from the first edition, and Cotes’ own preface to the book. Cotes’ preface starts with a comparison of the scientific methodologies of Aristotle, the supporters of the mechanical philosophy, where here Descartes and Leibniz are meant but not named, and Newton. He of course come down in favour of Newton’s approach and then proceeds to that which Newton has always avoided a discussion of the nature of gravity introducing into the debate, for the first time, the concept of action at a distance and gravity as a property of all bodies. The second edition of Principia can be regarded as the definitive edition and is very much a Newton Cotes co-production.

Cotes’ posthumously published mathematical papers contain a lot of very high class but also highly technical mathematics to which I’m not going to subject my readers. However there is one of his results that I think should be better known, as the credit for it goes to another. In fact a possible alternative title for this post would have been, “It’s not Euler’s Formula it’s Cotes’”.

It comes up fairly often that mathematicians and mathematical scientists are asked what their favourite theorem or formula is. Almost invariably the winner of such poles polls is what is known technically as Euler’s Identity

e + 1 = 0

 

Now this is just one result with x = π of Euler’s Formular:

cosx  + isinx = eix

Where i is the square root of -1, e is Euler’s Number the base of natural logarithms and x is an angle measured in radians. This formula can also be expressed as a natural logarithm thus:

ln[cosx + isinx] = ix

and it is in this form that it can be found in Cotes’ posthumous mathematical papers.

As one mathematics’ author expresses it:

This identity can be seen as an expression of the correspondence between circular and hyperbolic measures, between exponential and trigonometric measures, and between orthogonal and polar measures, not to mention between real and complex measures, all of which seemed to be within Cotes’ grasp.

Put simply, for the non-mathematical readers, this formula is one of the most important fundamental relationships in analysis.

Cotes died unexpectedly on 5th June 1716 of a, “Fever attended with a violent Diarrhoea and constant Delirium”. Despite his important contributions to Newton’s Principia Cotes is largely forgotten even by mathematicians and their ilk so the next time somebody waxes lyrical about Euler’s Formula you can gentle point out to them that it should actually be called Cotes’ Formula.

 

7 Comments

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

He didn’t publish and so he perished (historically).

On 2nd July 1621 Thomas Harriot died of cancer of the nose in London. As he had learnt to smoke from the Indians, in what would later become Virginia, he is possibly the first recorded death caused by smoking. This would naturally give him a small footnote in the history of science but he deserves much, much more than a footnote.

Readers of this blog should by now be well aware that I think that expressions such as ‘the greatest’ should be banned forever out of the history of science. If people, as they do, ponder who was the greatest scientist in the seventeenth century (ignoring the anachronistic use of the term scientist for the moment) they invariably discuss the respective merits of Kepler, Galileo, Descartes and Newton just possibly adding Huygens to the mix. I personally think that Thomas Harriot is a serious candidate for such a discussion. Now I can already hear one or the other of my readers thinking, if Harriot is so important for the history of seventeenth century science how come I’ve never even heard of him? The answer is quite simple; although the good Thomas made starting contributions to many branches of knowledge in the early years of the seventeenth century he published almost nothing, thus depriving himself of the fame and historical recognition that went to others. As the title of this post says, he didn’t publish and so he perished.

Little is known about Harriot’s origins other than the fact that he was born in Oxfordshire around 1560 and entered Oxford University in 1577; graduating in 1580 whence he is thought to have moved to London. In 1583 he entered the service of Sir Walter Raleigh, who had been his contemporary at Oxford. He seems to have been a promising mathematician at university as is confirmed by his friendship there with Thomas Allen (1542 – 1632) and Richard Hakluyt (c.1552 – 1616) both acknowledged as leading mathematical practitioners of the age. Harriot served as house mathematicus to Raleigh, teaching his master mariners the then comparatively knew arts of mathematical navigation and cartography for their expeditions, as well as helping to design his ships and serving as his accountant. During his instruction Harriot wrote a manual on mathematical navigation, which included the correct mathematical method for the construction of the Mercator projection but this manual like nearly all of his scientific work was to remain unpublished. However Harriot’s work was not just theoretical he possibly sailed on Raleigh’s 1584 exploratory voyage to Roanoke Island fore the coast of North America and definitely took part in the 1585 – 1586 attempt to establish a colony on Roanoke. This second voyage gives Harriot the distinction of being the first natural philosopher/natural historian/mathematician of North America. During his time in the failed colony Harriot carried out cartographical surveys, studied the flora and fauna and made an anthropological study of the natives even starting to learn the Algonquian language; inventing a phonetic alphabet to record it and writing a grammar of the language.

The attempt to establish a colony ended in disaster and the colonists, including Harriot had to be rescued by Francis Drake, on his way back from harassing the Spanish in Middle America, Raleigh having sailed back to England to fetch more supplies and settlers. This adventure was to provide Harriot’s one and only publication during his lifetime entitled A Brief and True Report of the New Found Land of Virginia; an advertising pamphlet published in 1588 designed to help Raleigh find new sponsors for a renewed attempt at establishing a colony. This pamphlet, the first English language publication on North America, was reprinted in Latin in a collection of literature about the America’s published in Frankfurt and became known throughout Europe.

Back in England Harriot became involved in another scheme of Raleigh’s to establish a colony in Ireland, serving for a number of years as his surveyor and general factotum. In the 1590s he left Raleigh’s service and became a pensioner of Henry Percy, Duke of Northumberland. Percy gave Harriot a very generous pension as well as title to some land in the North of England and a house on his estate of Syon House near London. It appears that Percy required nothing in return from Harriot and had given him what amounted to an extremely generous research grant for life, allowing him to become what we would now call a research scientist. Quite why Percy should choose to take this course of action with Harriot is not known, other than his own interest in the sciences. It was during his time in Percy’s service that Harriot did most of the scientific work that should by rights have made him famous.

Harriot was already, by necessity, a working astronomer during his time as Raleigh’s mathematicus but that his knowledge was wider and deeper than that required for cartography and navigation is obvious from a comment in one of his manuscripts. He complains about the inaccuracies of the Alfonsine Tables based on Ptolemaeus’ Syntaxis Mathematiké and then goes on to state that the Prutenic Tables based on Copernicus’ De revolutionibus are, in the specific case under consideration, even worse. However he’s sure the situation will improve in the future because of the work being carried out by Wilhelm IV and his astronomers in Kassel and Tycho Brahe in Hven. Harriot was obviously well connected and well informed as this before either group had published any of their results.

Now freed of obligations by Percy’s generosity Harriot took up serious astronomical research. In 1607 he and his pupil Sir William Lower (1570 – 1615) made accurate observations of Comet Halley. This led Lower to become the first to suggest in 1610 after they had both read Kepler’s Astronomia Nova that the paths of comets orbits, a hot topic of discussion in the astronomical community of the times, were Keplerian ellipses. Harriot and Lower are considered to be the earliest Keplerian astronomers, accepting Kepler’s theories almost immediately on publication. In 1609 Harriot became probably the first practicing astronomer to make systematic observations of the heavens with the new Dutch instrument invented in the previous year, the telescope. On 26 July 1609 he made a sketch of the moon using a telescope with a magnification of 6. This was several weeks before Galileo first turned a telescope towards the heavens. It should in fairness be pointed out that, unlike Galileo, Harriot did not recognise the three dimensionality of the moons surface. However after seeing a copy of Sidereus Nuncius he drew maps of the moon that were much more complete and accurate than those of his Tuscan rival. He also made the first systematic telescopic study of sunspots, which had he published would have spared Scheiner and Galileo their dispute over which of them had first observed sunspots. Harriot constructed very good telescopes and together with Lower, using one of Harriot’s instruments, continued a programme of observation. Harriot observing in London and Lower in Wales; the two of them comparing there their results in a correspondence parts of which still exist. Harriot also observed the phases of Venus independently of Galileo. Had he published his astronomical work his impact would have been at least as great as that of the Tuscan mathematicus.

It should not be thought that being set up as he was by a rich benefactor that life was just plain sailing for Harriot. In 1603 Raleigh, with whom he was still in close contact, was imprisoned in the Tower of London for treason. He was tried, found guilty and sentenced to death. The sentence was commuted to imprisonment and he remained in the Tower until 1616. In 1605 he was joined in the Tower by Harriot’s new patron, Henry Percy, together with Harriot himself. Percy had been arrested on suspicion because his second cousin, Thomas Percy, who was also the manager of his Syon estate, was one of the principals in the Gunpowder Plot. Harriot it seems was arrested simply because of his connections to Henry Percy and was released without charge within a couple of months. Percy was also never charged, although he was fined a fortune for his cousin’s involvement and remained imprisoned in the Tower until 1621. Percy was an immensely rich man and rented Martin Tower where he set up home even installing a bowling alley. Over the years Harriot regularly visited his two patrons in their stately prison where the three of them discussed scientific problems even conducting some experiments. This was certainly one of the most peculiar scientific societies ever.

Like most astronomers of the time Harriot was also very interested in physical optics because of the role that atmospheric refraction plays in astronomical observations. Harriot discovered the sine law of refraction twenty years before Willebrord Snel after whom the law is usually named. Although Harriot corresponded with Kepler on this very subject, after he had discovered the law, he never revealed his discovery again missing the chance to enter the history of science hall of fame.

Like his contemporaries Galileo and Stevin Harriot was very interested in dynamics and although he failed to abandon the Aristotelian concept that heavier bodies fall faster than lighter ones, his analysis of projectiles in flight is more advanced than Galileo’s. Harriot separately analysed the vertical and horizontal components of the projectiles’ flight and came very close to inventing vector analysis. One historian of science places Harriot’s achievements in dynamics between those of Galileo and Newton but once again he failed to publish.

Harriot’s greatest achievement was probably his algebra book, which was without doubt the most advanced work on the subject produced in the first half of the sixteenth century. It was superior to Viète’s work on the subject although there are some questions as to how much exchange took place between the two men’s efforts, as Nathaniel Torporley an associate of Harriot’s who would become one of his mathematical executors had earlier been Viète’s amanuensis. Harriot gave a complete analysis of the solution of simple algebraic equations that was well in advance of anything previously published. His algebra book was the only one of his works other than his Virginia pamphlet that was actually published if only posthumously. Unfortunately his mathematical executors Torporley and Walter Warner did not understand his innovations and removed them before publication. Even in its castrated form the book was very impressive. The real nature of his work in algebra was obviously known to his near contemporaries leading to John Wallis accusing Descartes of having plagiarised Harriot in his Géométrie. An accusation that probably had more to do with Wallis’ dislike of the French than any real intellectual theft, although Harriot’s work is certainly on a level with the Frenchman’s.

Mathematician, cartographer, navigator, anthropologist, linguist, astronomer, optical physicist, natural philosopher Thomas Harriot was a polymath of astounding breadth and in almost all that he attempted of significant depth. However, for reasons that are still not clear today he chose to publish next to nothing of a life’s work devoted to science. Had he published he would without doubt now be considered a member of the pantheon of gods of the so-called scientific revolution but because he chose not to he suffered the fate of all academics who don’t publish, he perished.

22 Comments

Filed under History of Astronomy, History of Cartography, History of Mathematics, History of Optics, History of Physics, History of science, Renaissance Science