The Huygens Enigma

The seventeenth century produced a large number of excellent scientific researches and mathematicians in Europe, several of whom have been elevated to the status of giants of science or even gods of science by the writers of the popular history of science. Regular readers of this blog should be aware that I don’t believe in the gods of science, but even I am well aware that not all researches are equal and the contributions of some of them are much greater and more important than those of others, although the progress of science is dependent on the contributions of all the players in the science game. Keeping to the game analogy, one could describe them as playing in different leagues. One thing that has puzzled me for a number of years is what I regard as the Huygens enigma. There is no doubt in my mind whatsoever that the Dutch polymath Christiaan Huygens, who was born on the 14 April 1629, was a top premier league player but when those pop history of science writers list their gods they never include him, why not?

Christiaan Huygens by Caspar Netscher, Museum Hofwijck, Voorburg Source: Wikimedia Commons

Christiaan Huygens by Caspar Netscher, Museum Hofwijck, Voorburg
Source: Wikimedia Commons

Christiaan was the second son of Constantijn Huygens poet, composer, civil servant and diplomat and was thus born into the highest echelons of Dutch society. Sent to university to study law by his father Christiaan received a solid mathematical education from Frans van Schooten, one of the leading mathematicians in Europe and an expert on the new analytical mathematics of Descartes and Fermat. Already as a student Christiaan had contacts to top European intellectuals, including corresponding with Marine Mersenne, who confirmed his mathematical talent to his father. Later in his student life he also studied under the English mathematician John Pell.

Already at the age of twenty-five Christiaan dedicated himself to the scientific life, the family wealth sparing him the problem of having to earn a living. Whilst still a student he established himself as a respected mathematician with an international reputation and would later serve as one of Leibniz’s mathematics teachers. In his first publication at the age of twenty-two Huygens made an important contribution to the then relatively new discipline of probability. In physics Huygens originated what would become Newton’s second law of motion and in a century that saw the development of the concept of force it was Huygens’ work on centripetal force that led Christopher Wren and Isaac Newton to the derivation of the inverse square law of gravity. In fact in Book I of Principia, where Newton develops the physics that he goes on to use for his planetary theory in Book III, he only refers to centripetal force and never to the force of gravity. Huygens contribution to the Newtonian revolution in physics and astronomy was substantial and essential.

In astronomy Christiaan with his brother Constantijn ground their own lenses and constructed their own telescopes. He developed one of the early multiple lens eyepieces that improved astronomical observation immensely and which is still known as a Huygens eyepiece. He established his own reputation as an observational astronomer by discovering Titan the largest moon of Saturn. He also demonstrated that all the peculiar observations made over the years of Saturn since Galileo’s first observations in 1610 could be explained by assuming that Saturn had a system of rings, their appearance varying depending on where Saturn and the Earth were in their respective solar orbits at the time of observations. This discovery was made by theoretical analysis and not, as is often wrongly claimed, because he had a more powerful telescope.

In optics Huygens was, along with Robert Hooke, the co-creator of a wave theory of light, which he used to explain the phenomenon of double refraction in calcite crystals. Unfortunately Newton’s corpuscular theory of light initially won out over Huygens’ wave theory until Young and others confirmed Huygens’ theory in the nineteenth century.

Many people know Huygens best for his contributions to the history of clocks. He developed the first accurate pendulum clocks and was again along with Robert Hooke, who accused him of plagiarism, the developer of the balance spring watch. There were attempts to use his pendulum clocks to determine longitude but they proved not to be reliable enough under open sea conditions.

Huygens’ last book published posthumously, Cosmotheoros, is a speculation about the possibility of alien life in the cosmos.

Huygens made important contributions to many fields of science during the second half of the seventeenth century of which the above is but a brief and inadequate sketch and is the intellectual equal of any other seventeenth century researcher with the possible exceptions of Newton and Kepler but does not enjoy the historical reputation that he so obviously deserve, so why?

I personally think it is because there exists no philosophical system or magnum opus associated with his contributions to the development of science. He work is scattered over a series of relatively low-key publications and he offers no grand philosophical concept to pull his work together. Galileo had his Dialogo and his Discorsi, Descartes his Cartesian philosophy, Newton his Principia and his Opticks. It seems to be regarded as one of the gods of science it is not enough to be a top class premier league player who makes vital contributions across a wide spectrum of disciplines, one also has to have a literary symbol or philosophical methodology attached to ones name to be elevated into the history of science Olympus.

P.S. If you like most English speakers think that his name is pronounced something like Hoi-gens then you are wrong, it being Dutch is nothing like that as you can hear in this splendid Youtube video!

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

Well no, actually he didn’t.

Ethan Siegel has written a reply to my AEON Galileo opinion piece on his Forbes blog. Ethan makes his opinion very clear in the title of his post, Galileo Didn’t Invent Astronomy, But He DID Invent Mechanical Physics! My response is also contained in my title above and no, Galileo did not invent mechanical physics. For a change we’ll start with something positive about Galileo, his inclined plane experiments to determine the laws of fall, the description of which form the bulk of Ethan’s post, are in fact one of the truly great pieces of experimental physics and are what makes Galileo justifiably famous. However the rest of Ethan’s post leaves much to be desired.

Ethan starts off by describing the legendary Leaning Tower of Pisa experiment, in which Galileo supposedly dropped two ball of unequal weight of the tower and measured how long they took to fall. The major problem with this is that Galileo almost certainly never did carry out this experiment, however both John Philoponus in the sixth century CE and Simon Stevin in 1586 did so, well before Galileo considered the subject. The laws of fall were also investigated theoretically by the so-called Oxford Calculatores, who developed the mean speed theory, the foundation of the laws of fall, and the Paris Physicists, who represented the results graphically, both in the fourteenth century CE. Galileo knew of the work of John Philoponus, the Oxford Calculatores and the Paris Physicists, even using the same graph to represent the laws of fall in his Two New Sciences, as Oresme had used four hundred years earlier. In the sixteenth centuries the Italian mathematician Tartaglia investigated the path of projectiles, publishing the results in his Nova Scientia, his work was partially validated, partially refuted by Galileo. His landsman Benedetti anticipated most of Galileo’s results on the laws of fall. With the exception of Stevin’s work Galileo knew of all this work and built his own researches on it thus rather challenging Ethan’s claim that Galileo invented mechanical physics.

Galileo’s central achievement was to provide empirical proof of the laws of fall with his ingenious ramp experiments but even here there are problems. Galileo’s results are simply too good, not displaying the expected experimental deviations, leading Alexander Koyré, the first great historian of Galileo’s work, to conclude that Galileo never did the experiments at all. The modern consensus is that he did indeed do the experiments but probably massaged his results, a common practice. The second problem is that any set of empirical results requires confirmation by other independent researchers. Mersenne, a great supporter and propagator of Galileo’s physics, complains of the difficulties of reproducing Galileo’s experimental results and it was first Riccioli, who finally succeeded in doing so, publishing the results in 1651.

A small complaint is Ethan’s claim that Galileo’s work on the laws of fall “was the culmination of a lifetime of work”. In fact although Galileo first published his Two New Sciences in 1638 his work on mechanics was carried out early in his life and completed well before he made his telescopic discoveries.

The real problem with Ethan’s post is what follows the quote above, he writes:

…and the equations of motion derived from Newton’s laws are essentially a reformulation of the results of Galileo. Newton indeed stood on the shoulders of giants when he developed the laws of gravitation and mechanics, but the biggest titan of all in the field before him was Galileo, completely independent of what he contributed to astronomy.

This is quite simply wrong. After stating his first two laws of motion in the Principia Newton writes:

The principles I have set forth are accepted by mathematicians and confirmed by experiments of many kinds. By means of the first two laws and the first two corollaries Galileo found that the decent of heavy bodies is the squared ratio of the time that the motion of projectiles occurs in a parabola, as experiment confirms, except insofar as these motion are somewhat retarded by the resistance of the air.

As Bernard Cohen points out, in the introduction to his translation of the Principia from which I have taken the quote, this is wrong because, Galileo certainly did not know Newton’s first law. As to the second law, Galileo would not have known the part about change in momentum in the Newtonian sense, since this concept depends on the concept of mass which was invented by Newton and first made public in the Principia.

I hear Galileo’s fans protesting that Newton’s first law is the law of inertia, which was discovered by Galileo, so he did know it. However Galileo’s version of the law of inertia is flawed, as he believes natural unforced motion to be circular and not linear. In fact Newton takes his first law from Descartes who in turn took it from Isaac Beeckman. Newton’s Principia, or at least his investigation leading up to it, are in fact heavily indebted to the work of Descartes rather than that of Galileo and Descartes in turn owes his greatest debts in physics to the works of Beeckman and Stevin and not Galileo.

An interesting consequence of Newton’s false attribution to Galileo in the quote above is that it shows that Newton had almost certainly never read Galileo’s masterpiece and only knew of it through hearsay. Galileo’s laws of fall are only minimally present in the Principia and then only mentioned in passing as asides, whereas the parabola law occurs quite frequently whenever Newton is resolving forces in orbits but then only as Galileo has shown.

One small irony remains in Ethan’s post. He loves to plaster his efforts with lots of pictures and diagrams and videos. This post does the same and includes a standard physics textbook diagram showing the force vectors of a heavy body sliding down an inclined plane. You can search Galileo’s work in vain for a similar diagram but you will find an almost identical one in the work of Simon Stevin, who worked on physical mechanics independently of and earlier than Galileo. Galileo made some very important contributions to the development of mechanical physics but he certainly didn’t invent the discipline.

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

A bit on the side

Galileo by Justus Sustermans/Wikipedia

Galileo by Justus Sustermans/Wikipedia

For those of my readers who don’t follow me on Twitter or Facebook I have indulged in my favourite pastime, slagging of Galileo Galilei, but this time in an opinion piece in the online science journal AEON. If you’ve already read my old Galileo post Extracting the stopper, this is just a shorter punchier version of the same. If not or if you want to read the updated sexy version then mosey on over to AEON and read Galileo’s reputation is more hyperbole than truth.

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The Reformation, Astrology, and Mathematics in Schools and Universities.

It is one of the ironies of the medieval universities that mathematics played almost no role in undergraduate education. It is ironical because the curriculum was nominally based on the seven liberal arts of which the mathematical sciences – arithmetic, geometry, music and astronomy – formed one half, the quadrivium. Although the quadrivium was officially a large part of the curriculum in reality the four mathematical disciplines were paid little attention and hardly taught at all. This only began to change in the fifteenth century with the rise of astro-medicine or iatromathematics, to give it its formal name. With the rise of this astrology-based medicine the humanist universities of Northern Italy and Kraków introduced chairs of mathematics to teach astrology to their students of medicine. This of course entailed first teaching mathematics and then astronomy in order to be able to do astrology and thus mathematics gained a first foothold in the European universities. Ingolstadt became the first German university to introduce a chair for mathematics, also for teaching astrology to medical students, in the 1470s. It became an important centre for seeding new chairs at other universities with its graduates. Stabius and Stiborius going from there to Vienna with Celtis, for example. However there was no systematic introduction of mathematics into the university curriculum as of yet, this would first come as a result of the Reformation and the educational reforms of Philip Melanchthon.

Melanchthon in 1526: engraving by Albrecht Dürer Translation of Latin caption: «Dürer was able to draw Philip’s face, but the learned hand could not paint his spirit». Source: Wikimedia Commons

Melanchthon in 1526: engraving by Albrecht Dürer Translation of Latin caption: «Dürer was able to draw Philip’s face, but the learned hand could not paint his spirit».
Source: Wikimedia Commons

Melanchthon was born Philip Schwartzerdt in Bretten near Karlsruhe on 16 February 1497. A great nephew of Johann Reuchlin a leading humanist scholar Philip changed his name to Melanchthon, a literal Greek translation of his German name, which means black earth, at Reuchlin’s suggestion. Melanchthon was a child prodigy who would grow up to be Germany’s greatest humanist scholar. He studied at Heidelberg University where he was denied his master degree in 1512 on account of his youth. He transferred to Tübingen where he came under the influence of Johannes Stöffler, one of those Ingolstadt graduates, a leading and highly influential mathematician/astrologer.

Johannes Stöffler Source Wikimedia Commons

Johannes Stöffler
Source Wikimedia Commons

The cosmograph Sebastian Münster was another of Stöffler’s famous pupils. Stöffler also has a great influence on several of the Nürnberger mathematician-astronomers, especial Johannes Schöner and Georg Hartmann. Under Stöffler’s influence Melanchthon became a passionate supporter of astrology.

On Reuchlin’s recommendation Melanchthon became professor of Greek at Luther’s University of Wittenberg at the age of twenty-one and thus a central figure in the Reformation. One of the major problems faced by the reformers was the fact that the education system was totally in the hands of the Catholic Church, which meant that they had to start from scratch and create their own school and university system; this task was taken on by Melanchthon, who became Luther’s Preceptor Germania, Germany’s Schoolmaster.

Because of his own personal passion for astrology Melanchthon introduced mathematics into the curriculum of all the Lutheran schools and universities. He invented a new type of school on a level between the old Church Latin schools and the universities that were devised to prepare their pupils for a university education. The very first of these was the Eigidien Oberschule in Nürnberg, which opened in 1526 with Johannes Schöner, as its first professor for mathematics.

Johannes_Schoner_Astronomer_01

These type of school created by Melanchthon would become the Gymnasium, still today the highest level secondary schools in the German education system.

In Wittenberg he appointed Johannes Volmar (1480-1536) professor for the higher mathematic, music and astronomy, and Jakob Milich (1501- 1559) professor for the lower mathematic, arithmetic and geometry, in 1525. Their most famous students were Erasmus Reinhold, who followed Volmar on the chair for higher mathematics when he died in 1536, and Georg Joachim Rheticus, who followed Milich on the chair for lower mathematics, in the same year when Milich became professor for medicine. Schöner, Reinhold and Rheticus were not the only mathematicians supported by Melanchthon, who played an important role in the dissemination of the heliocentric astronomy. Although following Melanchthon’s lead these Protestant mathematicians treated the heliocentric hypothesis in a purely instrumentalist manner, i.e. it is not true but is mathematically useful, they taught it in their university courses alongside the geocentric astronomy.

As a result of Melanchthon’s passion for astrology the Lutheran Protestant schools and universities of Europe all had departments for the study of mathematics headed by qualified professors. The Catholic schools and universities would have to wait until the end of the sixteenth century before Christoph Clavius did the same for them, although his motivation was not astrology. Sadly Anglican England lagged well behind the continent with Oxford first appointing professors for geometry and astronomy in the 1620s at the bequest of Henry Savile, who had had to go abroad to receive his own mathematical education. Cambridge only followed suit with the establishment of the Lucasian Chair in 1663, whose first occupant was Isaac Barrow followed by that other Isaac, Newton. In 1705 John Arbuthnot could still complain in an essay that there was not one single school in England that taught mathematics.

 

 

 

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Filed under History of Astrology, History of Astronomy, History of Mathematics, History of science, Renaissance Science, University History

Retraction of a Retraction – Turns out I wasn’t wrong after all!

Yesterday I deleted a post about Caroline Herschel, the Google doodle that had been posted for her birthday and the type of telescope that she had used to make he comet discoveries only hours after I had posted it. I went on to claim that I was mistaken in my claims and to apologies widely on the Internet to anybody I might have misled. In the cold grey light of dawn I realised that I had indeed made an error, however not in my original post but in retracting it. How this came about can be attributed to one or more of the following:

1) Extreme tiredness

2) Mental and physical confusion brought about by my first day of remedial orthopaedic treatment

3) A brain fart

4) Early signs of dementia

5) Congenital stupidity

6) An inability to read

7) Late repercussion of my substantial drug abuse in my misspent youth

8) Aliens!

9) Add your own reason!

In my post I had said that the Google Doodle was wrong because it displayed Caroline Herschel with a ‘normal’ refractor, i.e. with lenses, telescope whereas the Herschel used reflectors, i.e. telescopes with mirror, which they designed and constructed themselves. So far, so good. Then in the comments Tony Angel drew my attention to an interesting article about Caroline Herschel and her comet hunting. I hastily, and here is where the problems begin, skimmed the article and read the following quote from Caroline:

I found I was to be trained for an assistant-astronomer, and by way of encouragement a telescope adapted for ‘sweeping,’ consisting of a tube with two glasses, such as was commonly used as a ‘finder,’ was given to me.

 I read “a tube with two glasses” as being the description of a refractor with two lenses, thought ‘Oh FUCK!’ and in a state of confused panic deleted my post.

In fact, if I had read a few lines further I would have seen the following:

Table 1. The Parameters of Caroline’s two alt-azimuth

                 Newtonian reflecting sweepers.

 And on the following page there is even a diagram of the two telescopes with a caption that clearly states that they are Newtonian reflectors. So now being once again of sound mind and body I shall restore my post with a little bit of added information i.e. the illustration of Caroline’s reflector telescopes.

 

 

 

 

 

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I WAS WRONG!

I have deleted my previous  post on the Caroline Herschel Google Doodle because I was wrong! I will explain tomorrow.

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It’s the wrong telescope.

I know I announced a blogging hiatus yesterday, but I have some time evenings and I simply couldn’t ignore this.

Caroline Herschel Source: Wikimedia Commons

Caroline Herschel
Source: Wikimedia Commons

 

Today is Caroline Herschel’s birthday and Google have celebrated it with a doodle, which is cool and an overdue acknowledgement of a great lady astronomer. If you don’t already know who Caroline Herschel is then you should read the two Guardian articles by Stuart Clark and Becky Higgitt. Google’s doodle is all well and good but I have a complaint, it’s the wrong telescope.

The Google doodle for Caroline Herschel’s 266th birthday. Photograph: google

The Google doodle for Caroline Herschel’s 266th birthday. Photograph: google

If you look at the picture Caroline is standing behind a mounted telescope and in the animated version of the doodle she bends down to look through the telescope as a comet flies passed overhead. This is to acknowledge the fact that she is most well known for the eight comets that she discovered. So what’s my problem? The telescope displayed in the doodle is a refractor that is a telescope with lenses at the front, the objective, and at the back, the eyepiece or ocular. The problem is that the Herschels, that is Caroline and her brother William, used reflectors; that is telescopes that have a mirror and not a lens as objective and then a lens or lenses as the eyepiece to observe the image created by the mirror. To be precise they used Newtonian reflectors that they built themselves. That they used Newtonians was rather unusual at the time because most other professional, or serious amateur like the Herschels, astronomers used Gregorian reflector telescopes, which are of a different design. The Gregorian is actually superior but the Newton is simpler to construct and this is almost certainly the reason that William stuck with Newtonians.

Replica of a Herschel Newtonian Refractor. Herschel Museum Bath Source: Wikimedia Commons

Replica of a Herschel Newtonian Reflector. Herschel Museum Bath
Source: Wikimedia Commons

Added: 17 March 2016

If you go to the article Caroline Lucretia Herschel – comet huntress (h/t Tony Angel)on the second page you can see sketches of the comet-sweeper Newtonian reflectors that William built for Caroline, which are not quite as elegant or impressive as the telescope pictured above but which served their purpose admirably.

The fact that the doodle shows a refractor and not a reflector is, viewed historically, not a trivial matter. In the eighteenth century the reflectors were capable of resolving much weaker light sources than the contemporary refractors and were thus superior for the type of deep space celestial mapping that William Herschel pioneered and which he taught to his younger sister. To show Caroline using a refractor and not a Herschel Newtonian reflector is a complete historical misrepresentation and totally misleading.

Now Google might argue that your average Google doodle viewer would probably not recognise a Herschel Newtonian reflector as a telescope and therefore they put a simple refractor in the picture as a generic telescope that people would recognise as such. All well and good but I can best explain my aversion by a simple analogy.

Lewis Hamilton is the current world Formula One racing champion. I want you to imagine the following. Next season Hamilton wins his fourth world championship and Google celebrate the occasion with one of their doodles, unlikely but you never know. So we get a cartoon of the well know figure of Lewis Hamilton in a Formula One racing car but he is not driving a Mercedes, the team for which he drives and has won two of his three titles up till now, but a Ferrari because that is the generic racing car that most people see in their minds eye when they think of racing cars. The Lewis Hamilton fans would probably launch a crusade against the Google head quarters in Mountain View and hang the offending doodler from a lamppost.

As far as I’m concerned in the history of science details matter a lot and the fact that the Herschels used Newtonian reflectors is not a triviality but an important factor in the astronomical achievements for which they are justifiably renowned. It should also be pointed out that this renown led to William becoming one of the commercially most successful telescope constructors in the eighteenth century because other astronomers wanted to own one of those telescopes, which had made the discoveries of William and Caroline possible.

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