Category Archives: History of Physics

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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.


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


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.


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.



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.


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]


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.



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.


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

A mind bogglingly stupid statement!

In an interview with the Sydney Morning Herald the British “poster boy of pop science”TM made the following series of statements:

“When you’ve got difficult economic times, you see governments saying, ‘Well, maybe we should cut back on this kind of blue-sky stuff.’ It’s just drivel. Imagine if that had happened in 1799 when the Royal Institute [sic] was being set up. Then, in the worst-case scenario, you don’t get electricity.” [my emphasis]

Let us take a brief look at a list of some of the prominent names associated with the evolution of the science of electricity between 1600 and 1900. This list is of course by no means exhaustive:

William Gilbert, Otto von Guericke, Robert Boyle, Stephen Gray, Francis Hauksbee, John Desaguliers, C. F. du Fay, Abbé Nollet, Pieter van Musschenbroek, Benjamin Franklin, Charles-Augustin de Coulomb, Luigi Galvani, Alessandro Volta, Hans Christian Ørsted, André-Marie Ampère, Michael Faraday, Georg Simon Ohm, James Clerk Maxwell, Galileo Ferraris, Oliver Heaviside, Charles Parsons, Joseph Swan, Thomas Edison, Nikola Tesla, Ernst Werner von Siemens and William Thomson.

Your quiz question for today, which of the men in this list were not involved with the Royal Institution?

Now some of you might accuse me of just being nasty to the “poster boy of pop science”TM, as he was obviously referring to Michael Faraday who did work for the Royal Institution from 1813 (unlike any of the others) and who is normally credited with having invented the electric generator or more accurately discovered the principle of electromagnetic induction on which the generator is based. So is the “poster boy of pop science”TM right after all?

Well, the question is, as always, given the general developments in electrical research at the beginning of the 1830s, might it not be possible that someone else would have discovered this principle and thus we would have had electricity with or without Faraday? Are we going to replace one dubious hypothetical with another one? Well, actually no! We just have to take a somewhat closer look at the history of electricity to discover that is exactly what happened.

Both the Italian Francesco Zantedeschi and the American Joseph Henry discovered the principle of electromagnetic induction before Faraday. Zantedeschi published his discovery, which however went unnoticed, while Henry first published when he realised that he had been beaten to the punch by Faraday. If this wasn’t enough to show that we would have had electricity if Faraday and the Royal Institution had never existed the Hungarian inventor Ányos István Jedlik actually invented a generator, superior to Faraday’s, several years before Faraday made his legendary discovery.

As I’ve said on several occasions in the past statements in the history of science and technology along the lines of if it hadn’t been for X we wouldn’t have Y are almost inevitably wrong and are on close inspection likely to leave their utterer looking pretty stupid.


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

5 Brilliant Mathematicians – 4 Crappy Commentaries

I still tend to call myself a historian of mathematics although my historical interests have long since expanded to include a much wider field of science and technology, in fact I have recently been considering just calling myself a historian to avoid being pushed into a ghetto by those who don’t take the history of science seriously. Whatever, I have never lost my initial love for the history of mathematics and will automatically follow any link offering some of the same. So it was that I arrived on the Mother Nature Network and a blog post titled 5 brilliant mathematicians and their impact on the modern world. The author, Shea Gunther, had actually chosen 5 brilliant mathematicians with Isaac Newton, Carl Gauss, John von Neumann, Alan Turing and Benoit Mandelbrot and had even managed to avoid the temptation of calling them ‘the greatest’ or something similar. However a closer examination of his commentaries on his chosen subjects reveals some pretty dodgy not to say down right crappy claims, which I shall now correct in my usual restrained style.

He starts of fairly well on Newton with the following:

There aren’t many subjects that Newton didn’t have a huge impact in — he was one of the inventors of calculus, built the first reflecting telescope and helped establish the field of classical mechanics with his seminal work, “Philosophiæ Naturalis Principia Mathematica.” He was the first to decompose white light into its constituent colors and gave us, the three laws of motion, now known as Newton’s laws.

But then blows it completely with his closing paragraph:

We would live in a very different world had Sir Isaac Newton not been born. Other scientists would probably have worked out most of his ideas eventually, but there is no telling how long it would have taken and how far behind we might have fallen from our current technological trajectory.

This is the type of hagiographical claim that fans of great scientists tend to make who have no real idea of the context in which their hero worked. Let’s examine step by step each of the achievements of Newton listed here and see if the claim made in this final paragraph actually holds up.

Ignoring the problems inherent in the claim that Newton invented calculus, which I’ve discussed here, the author acknowledges that Newton was only co-inventor together with Leibniz and although Newton almost certainly developed his system first it was Leibniz who published first and it was his system that spread throughout Europe and eventually the world so no changes here if Isaac had not been born.

Newton did indeed construct the first functioning reflecting telescope but as I explained here it was by no means the first. It would also be fifty years before John Hadley succeeded in repeating Newton’s feat and finally making the commercial production of reflecting telescopes viable. However Hadley also succeeded in making working models of James Gregory’s reflecting telescope, which actually predated Newton’s and it was the Gregorian that, principally in the hands of James Short, became the dominant model in the eighteenth century. Although to be fair one should mention that William Herschel made his discoveries with Newtonians. Once again our author’s claim fails to hold water.

Sticking with optics for the moment it is a little know and even less acknowledge fact that the Bohemian physicus and mathematician Jan Marek Marci (1595 – 1667) actually decomposed white light into its constituent colours before Newton. Remaining for a time with optics, James Gregory, Francesco Maria Grimaldi, Christian Huygens and Robert Hooke were all on a level with Newton although none of them wrote such an influential book as Newton’s Optics on the subject. Now this was not all positive. Due to the influence won through the Principia, The Optics became all dominant preventing the introduction of the wave theory of light developed by Huygens and Hooke and even slowing down its acceptance in the nineteenth century when proposed by Fresnel and Young. If Newton hadn’t been born optics might even have developed and advance more quickly than it did.

This just leaves the field of classical mechanics Newton real scientific monument. Now, as I’ve pointed out several times before the three laws of motion were all borrowed by Newton from others and the inverse square law of gravity was general public property in the second half of the seventeenth century. Newton’s true genius lay in his mathematical combination of the various elements to create a whole. Now the question is how quickly might this synthesis come about had Newton never lived. Both Huygens and Leibniz had made substantial contribution to mechanics contemporaneously with Newton and the succeeding generation of French and Swiss-German mathematicians created a synthesis of Newton’s, Leibniz’s and Huygens’ work and it is this that is what we know as the field of classical mechanics. Without Newton’s undoubtedly massive contribution this synthesis might have taken a little longer to come into being but I don’t think the delay would have radically changed the world in which we live.

Like almost all great scientists Newton’s discoveries were of their time and he was only a fraction ahead of and sometimes even behind his rivals. His non-existence would probably not have had that much impact on the development of history.

Moving on to Gauss we will have other problems. Our author again makes a good start:

Isaac Newton is a hard act to follow, but if anyone can pull it off, it’s Carl Gauss. If Newton is considered the greatest scientist of all time, Gauss could easily be called the greatest mathematician ever.

Very hyperbolic and hagiographic but if anybody could be called the greatest mathematician ever then Gauss would be a serious candidate. However in the next paragraph we go off the rails. The paragraph starts OK:

Carl Friedrich Gauss was born to a poor family in Germany in 1777 and quickly showed himself to be a brilliant mathematician. He published “Arithmetical Investigations,” a foundational textbook that laid out the tenets of number theory (the study of whole numbers).

So far so good but then our author demonstrates his lack of knowledge of the subject on a grand scale:

Without number theory, you could kiss computers goodbye. Computers operate, on a the most basic level, using just two digits — 1 and 0

Here we have gone over to the binary number system, with which Gauss book on number theory has nothing to do, what so ever. In modern European mathematics the binary number system was first investigated in depth by Gottfried Leibniz in 1679 more than one hundred years before Gauss wrote his Disquisitiones Arithmeticae, which as already stated has nothing on the subject. The use of the binary number system in computing is an application of the two valued symbolic logic of George Boole the 1 and 0 standing for true and false in programing and on and off in circuit design. All of which has nothing to do with Gauss. Gauss made so many epochal contributions to mathematics, physics, cartography, surveying and god knows what else so why credit him with something he didn’t do?

Moving on to John von Neumann we again have a case of credit being given where credit is not due but to be fair to our author, this time he is probably not to blame for this misattribution.  Our author ends his von Neumann description as follows:

Before his death in 1957, von Neumann made important discoveries in set theory, geometry, quantum mechanics, game theory, statistics, computer science and was a vital member of the Manhattan Project.

This paragraph is fine and if Shea Gunther had chosen to feature von Neumann’s invention of game theory or three valued quantum logic I would have said fine, praised the writer for his knowledge and moved on without comment. However instead our author dishes up one of the biggest myths in the history of the computer.

he went on to design the architecture underlying nearly every single computer built on the planet today. Right now, whatever device or computer that you are reading this on, be it phone or computer, is cycling through a series of basic steps billions of times over each second; steps that allow it to do things like render Internet articles and play videos and music, steps that were first thought up by John von Neumann.

Now any standard computer is called a von Neumann machine in terms of its architecture because of a paper that von Neumann published in 1945, First Draft of a Report on the EDVAC. This paper described the architecture of the EDVAC one of the earliest stored memory computers but von Neumann was not responsible for the design, the team led by Eckert and Mauchly were. Von Neumann had merely described and analysed the architecture. His publication caused massive problems for the design team because the information now being in the public realm it meant that they were no longer able to patent their innovations. Also von Neumann’s name as author on the report meant that people, including our author, falsely believed that he had designed the EDVAC. Of historical interest is the fact that Charles Babbage’s Analytical Engine in the nineteenth century already possessed von Neumann architecture!

Unsurprisingly we walk straight into another couple of history of the computer myths when we turn to Alan Turing.  We start with the Enigma story:

During World War II, Turing bent his brain to the problem of breaking Nazi crypto-code and was the one to finally unravel messages protected by the infamous Enigma machine.

There were various versions of the Enigma machine and various codes used by different branches of the German armed forces. The Polish Cipher Bureau were the first to break an Enigma code in 1932. Various other forms of the Enigma codes were broken by various teams at Bletchley Park without Turing. Turing was responsible for cracking the German Naval Enigma. The statement above denies credit to the Polish Cipher Bureau and the other 9000 workers in Bletchley Park for their contributions to encoding Enigma.

Besides helping to stop Nazi Germany from achieving world domination, Alan Turing was instrumental in the development of the modern day computer. His design for a so-called “Turing machine” remains central to how computers operate today.

I’ve lost count of how many times that I’ve seen variations on the claim in the above paragraph in the last eighteen months or so, all equally incorrect. What such comments demonstrate is that their authors actually have no idea what a Turing machine is or how it relates to computer design.

In 1936 Alan Turing, a mathematician, published a paper entitled On Computable Numbers, with an Application to the Entscheidungsproblem. This was in fact one of four contemporaneous solutions offered to a problem in meta-mathematics first broached by David Hilbert, the Entscheidungsproblem. The other solutions, which needn’t concern us here, apart from the fact that Post’s solution is strongly similar to Turing’s, were from Kurt Gödel, Alonso Church and Emil Post. Entscheidung is the German for decision and the Entscheidungsproblem asks if for a given axiomatic system whether it is also possible with the help of an algorithm to decide if a given statement in that axiom system is true or false. The straightforward answer that all four men arrived at by different strategies is that it isn’t. There will always be undecidable statements within any sufficiently complex axiomatic system.

Turing’s solution to the Entscheidungsproblem is simple, elegant and ingenious. He hypothesised a very simple machine that was capable of reading a potentially infinite tape and following instruction encoded on that tape. Instruction that moved the tape either right or left or simply stopped the whole process. Through this analogy Turing was able to show that within an axiomatic system some problems would never be Entscheidbar or in English decidable. What Turing’s work does is, on a very abstract level, to delineate the maximum computability of any automated calculating system. Only much later, in the 1950s, after the invention of electronic computers a process in which Turing also played a role did it occur to people to describe the computational abilities of real computers with the expression ‘Turing machine’.  A Turing machine is not a design for a computer it is term used to described the capabilities of a computer.

To be quite open and honest I don’t know enough about Benoit Mandelbrot and fractals to be able to say whether our author at least got that one right, so I’m going to cut him some slack and assume that he did. If he didn’t I hope somebody who knows more about the subject that I will provide the necessary corrections in the comments.

All of the errors listed above are errors that could have been easily avoided if the author of the article had cared in anyway about historical accuracy and truth. However as is all to often the case in the history of science or in this case mathematics people are prepared to dish up a collection of half baked myths, misconceptions and not to put too fine a point on it crap and think they are performing some sort of public service in doing so. Sometimes I despair.



Filed under History of Computing, History of Logic, History of Mathematics, History of Optics, History of Physics, History of science, Myths of Science, Newton

Isaac Newton: The Last Lone Genius?

The Friday before last, with much advanced publicity, the BBC broadcast a new documentary film biography of Isaac Newton with the title The Last Magician. This phrase is part of a famous quote by John Maynard Keynes, “not the first scientist but the last magician”, describing his feeling upon reading the Newtonian alchemical manuscripts that he acquired at the auction of the Portsmouth family Newton papers in 1936.  This of course together with the advanced advertising for the programme signalled that we were due for a fresh dose of “did you know that Newton was a secret alchemist?” A phenomenon that Rebekah “Becky” Higgitt has blogged on informatively in the past.

Based on quotes from Newton’s own writings and correspondence as well of those of his contemporaries the programme was in its basics factually correct. As usual for BBC historical documentaries it was well-produced and excellently filmed and thus pleasant to watch. The basic structure was the direct quotes being spoken by actors in costume and commented upon by five more or less experts. These were the historians of science Rob Iliffe head of the Newton Papers editing project and a genuine Newton expert, Patricia Fara author of an excellent book on the changing image of Newton down the centuries and Lisa Jardine expert on Renaissance history of science, as well as popular science writer James Gleick author of a competent popular Newton biography and astrophysicist turned novelist Stuart Clark.

Given all of these preconditions it should have been an excellent hours entertainment for a historian of science like myself, unfortunately it turned out to be a major disappointment for two reasons. The programme deliberately created two principle impressions that were and are fundamentally wrong.

The first of these turned up in the pre-programme publicity but also featured prominently fairly early in the documentary in what seems at first glance to be a fairly harmless statement:

By the age of 21, he had rejected 2,000 years of scientific orthodoxy

This brief phrase contains two claims one implicit and one explicit. The implicit claim is how wonderful Newton was to take such a bold step when he was only 21 years old. Anyone who has spent anytime at all looking at the history of mathematics knows that mathematicians tend to be very precocious. Pascal wrote the paper that gained him entry to the top flight of seventeenth century mathematics at the age of sixteen. In the nineteenth century the teenage William Rowan Hamilton was trotted out in public like a circus pony to display his brilliance. The stories are legion and there is absolutely nothing unusual in Newton intellectual development it’s par for the course for a highly talented mathematician.

As Becky put it very succinctly in a tweet what they are actually saying here is that there had been no science since Aristotle, which is of course complete rubbish. The scientific orthodoxy of the day, which was by the way on the verge of disappearing, of which more shortly, came into being in the thirteenth century when Albertus Magnus and his pupil Thomas Aquinas created a synthesis of Catholic theology and Aristotle’s philosophy with the addition of Ptolemaic geocentric astronomy. This synthesis is known as Scholastic or Aristotelian physics or natural philosophy. However as Edward Grant, one of the leading experts on medieval science, points out Aristotelian philosophy is not Aristotle’s philosophy. It is also important to note that Aristotelian philosophy was never carved in stone but in fact changed and developed continuously over the next four hundred years. Examples of major changes are the work of the Oxford Calculatores and the Paris Physicists in the fourteenth century. The Aristotelian physics of the fifteenth century is a very different beast to that of the thirteenth century. The geocentric astronomy produced in the middle of the fifteenth century by Peuerbach and Regiomontanus differed substantially from that of the first Ptolemaic translations of the twelfth century.

Added to all this change and development the first seeds of what would become modern science began to poke their slender stems out of the substrate of scientific innovation around the beginning of the fifteenth century. By 1661 when Newton went up to university Keplerian heliocentric astronomy had become the new orthodoxy and Aristotelian physics was being pushed out by the new physics developed by mathematicians such as Tartaglia and Benedetti in the sixteenth century and Stevin, Galileo, Borelli, Descartes, Pascal, Huygens and others in the seventeenth. One should bear in mind that the Leopoldina, the Accademia del Cimento, the Royal Society and the Acadédemie des Sciences all institutions dedicated to the propagation and development of the new science were founded in 1652, 1657, 1660 and 1666 respectively. The young Newton did not like some Carrollian hero draw his Vorpal Blade to slay the Jabberwock of ancient Greek science but like any bright young academic would do jumped on the band wagon of modern science that was speeding full speed ahead into the future.

We now turn to what I see as the most serious failing of the documentary expressed in the question posed in the title of this post. For the best part of an hour the documentary banged on about Newton’s solitude, his isolation his lone path to the secrets of nature. We were presented with the ultimate lone genius of the history of science. It went so far that the only other contemporary researchers mentioned by name were Descartes in passing and Hooke purely in a negative light. The way that the programme was structured created a totally false impression of Newton’s scientific endeavours.

We actually know very little about Newton’s time as a student though it is safe to say that he was more the type to curl up in front of the fire with a good book on a Friday evening than to go to the latest rave at which ever student hostelry was in that term. As a fellow we know that he communicated and worked together with other scholars such as Isaac Barrow so to talk of total solitude as the documentary did is wrong. After he emerged from obscurity at the beginning of the 1670s with his reflecting telescope and his famous paper on the phenomenon of colours he was in no way isolated. Even if Cambridge was somewhat off the beaten track in those days Newton corresponded with other scholars in Britain and also abroad as can easily be seen in his voluminous correspondence as edited by Turnbull. He was also often visited by other mathematical scholars such as Halley or John Collins. When he left Cambridge to go to London he became positively gregarious. Maintaining a town house with his niece Catherine Barton, a renowned social beauty, as his housekeeper where he received and entertained visitors. At the Royal Mint, which he attended daily, he was surrounded by a large staff. After 1703 he presided over the weekly meetings of the Royal Society and on other evenings surrounded by his acolytes he held court in one or other of the then fashionable London coffee bars.

More important for me was the totally false impression created by the documentary of Newton’s mathematical and scientific work. Anyone being introduced to Newton for the first time would come away with the impression that he revolutionised mathematics, physics and astronomy in a superhuman solo endeavour completely isolated from the rest of the late seventeenth century intellectual world.

We got presented with Newton in 1666 creating a completely new branch of mathematics, he only actually started it then and it took a number of years to develop. At no point was any other mathematician mentioned. The fact that Newton either, directly or indirectly, knew of and built on the previous work in this field of Kepler, Cavalieri, Fermat, Pascal, Descartes, van Schooten, Barrow and others was quietly swept under the carpet. Even worse no mention what so ever of Leibniz who independently developed the same mathematics almost at the same time from the same sources. This of course led eventually to the most notorious priority dispute in the history of science involving many of the leading mathematicians of Europe.

The same thing occurred with the presentation of his work in optics, no mention of Kepler, Schiener, Descartes, Grimaldi, Gregory, Hooke, Huygens or anybody for that matter. Isaac apparently did it all alone in isolation.

This form of presentation continued with his greatest work the Principia. We got each of the famous laws of motion presented individually but no hint of the fact that the first was taken from Beeckman by way of Descartes, the second from Huygens and the third from his readings in alchemy. We were told that he derived the law of gravity from his three laws but no mention was made of the fact that the concept of the law of gravity was common, much discussed intellectual property in academic circles at the time. No mention of the contributions made to the substance of the Principia by the work of Kepler, Galileo, Cassini, Halley and above all Flamsteed. We had the strange spectacle of Hooke famous accusation of Newton having stolen his law of gravity and plagiarised him delivered in a passionate speech to the Royal Society in 1660 but no mention what so ever that Hooke’s accusation had more than a little substance. Hooke and Newton had corresponded on the subject in the early 1680s and Hooke had already formulated a concept of universal gravity before Newton. This correspondence was with certainty one of the spurs that led Newton to write the Principia although Hook’s claims as to the extent of his contribution are wildly exaggerated.

Isaac Newton did not live and work in an intellectual vacuum as was very strongly implied either deliberately or accidently through bad scripting by this documentary. He was part of a strong multi-faceted scientific community who supplied both the scaffolding and a significant part of substance of Newton’s life work in mathematics, physics and astronomy. He was in no way a lone genius but a highly significant cog in a large intellectual endeavour.

There was a time some decades back when some historians of science went so far as to decry the Principia as purely a work of synthesis with only a very small original contribution from Newton. This view was shown to be exaggerated and invalid and has been dropped but the opposite point of view implied by this documentary of the Principia as being alone the work of Newton’s genius is even more false.

Before I close there are a couple of small points from the film that I think should be mentioned. As is all too often the case we had the tired old statement that after Newton became President of the Royal Society he produced no more original scientific work. This was as always made without explicit comment but with a strong implicit negative aura. Dear people, when Isaac Newton became President of the Royal Society in 1703 he was already sixty years old. He had written and published two of the most important major scientific works in the history of mankind, his Principia and his Optics, as well as vast quantities of, largely unpublished, absolutely world-class mathematics, which he did however circulate in manuscript amongst his acolytes. What more did you expect him to do (FFS)?

I noted four major scientific/historical errors during the film, a fairly low quota; there may have been others. We of course get introduced to Newton’s reflecting telescope, the invention that first made him known to the world at large, but then we get informed that this instrument played a major role in marine navigation in the eighteenth century. Now whilst it is true that the reflecting telescope, mostly Gregorian’s and not Newtonian’s, had become the instrument of choice for astronomers by the middle of the eighteenth century they were for several good reasons not used for navigation on ships. Firstly reflecting telescopes whilst in principle smaller than refracting ones don’t telescope and so are more massive and cumbersome than the classical marine telescope. Secondly until the nineteenth century reflecting telescopes had metal mirrors made of so-called speculum metal an alloy that unfortunately was very susceptible to corrosion necessitating regular re-polishing. The salt-water atmosphere of sea voyages would have been very adverse for such mirrors requiring almost daily re-polishing and thus completely impractical.

The next error I spotted was a real howler. A voice over informed the viewer that, “for centuries light was considered the purest form of energy in the universe.” Really? Although etymologically derived from an ancient Greek word the physics concept of energy was first appeared in the nineteenth century, as did the recognition that light is a form of energy. Nuff said.

Moving along the historical time scale in the opposite direction voice over informed us the Newton’s Principia made possible the accurate prediction of comets and eclipses. Now the former is indeed true although the credit should properly go to Halley who first showed that some comets were periodical and obeyed Newton’s law of gravity. The latter is however again a real history of science howler. The Babylonians could accurately predict lunar eclipses in about the fifth century BCE and the ability to accurately predict solar eclipses was also developed in antiquity. No need to wait for Newton.

My final error is the one that as a historian of science causes me the most concern. Whilst discussing Newton’s alchemy voice over stated correctly Newton’s alchemical belief that light and matter are both products of some as yet undiscovered primal alchemical substance. The claim was immediately made that Newton had anticipated Einstein’s famous E = MC2! This claim being, to my surprise, repeated by Rob Iliffe an excellent historian of science. Now I’m not a big fan of the Kuhn/Feyerabend principle of the incommensurability of scientific theories. This says that one can’t compare scientific theories because the definitions of the concepts that they contain differ and are thus not comparable. Newton’s concept of force is not Maxwell’s concept of force for example. However I think that here we have a genuine case of incommensurability. The metaphysical concepts behind Newton’s alchemical theory and the metaphysical concepts behind Einstein’ theory of relativity are in no way comparable. It is not even comparing apples with oranges; it’s comparing apples with bicycles!

On the whole I think what was superficially a very good and certainly an excellently produced documentary failed miserably as a piece of history of science for the reasons that I have outlined above. Maybe I’m being too harsh but on the whole I don’t think so. For me the very strong emphasis of the biography of Newton as some sort of lone genius whether intended or an accidental product of ill considered scripting made this documentary next to worthless as a contribution to popular history of science.




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