Category Archives: Myths of Science

Christmas Trilogy 2016 Part 2: What a difference an engine makes

Charles Babbage is credited with having devised the first ever special-purpose mechanical computer as well as the first ever general-purpose mechanical computer. The first claim seems rather dubious in an age where there is general agreement that the Antikythera mechanism is some sort of analogue computer. However, Babbage did indeed conceive and design the Difference Engine, a special purpose mechanical computer, in the first half of the nineteenth century. But what is a Difference Engine and why “Difference”?

Both Babbage and John Herschel were deeply interested in mathematical tables – trigonometrical tables, logarithmic tables – when they were still students and Babbage started collecting as many different editions of such tables as he could find. His main object was to check them for mistakes. Such mathematical tables were essential for navigation and errors in the figures could lead to serious navigation error for the users. Today if I want to know the natural logarithm of a number, let’s take 23.483 for example, I just tip it into my pocket calculator, which cost me all of €18, and I instantly get an answer to nine decimal places, 3.156276755. In Babbage’s day one would have to look the answer up in a table each value of which had been arduously calculated by hand. The risk that those calculations contained errors was very high indeed.

Babbage reasoned that it should be possible to devise a machine that could carryout those arduous calculations free of error and if it included a printer, to print out the calculated answer avoiding printing errors as well. The result of this stream of thought was his Difference Engine but why Difference?

The London Science Museum's reconstruction of Difference Engine No. 2 Source: Wikimedia Commons

The London Science Museum’s reconstruction of Difference Engine No. 2
Source: Wikimedia Commons

Babbage needed to keep his machine as simple as possible, which meant that the simplest solution would be a machine that could calculate all the necessary tables with variations on one algorithm, where an algorithm is just a step-by-step recipe to solve a mathematical problem. However, he needed to calculate logarithms, sines, cosines and tangents, did such an algorithm exist. Yes it did and it had been discovered by Isaac Newton and known as the method of finite differences.

The method of finite differences describes a property shared by all polynomials. If it has been a while since you did any mathematics, polynomials are mathematical expressions of the type x2+5x-3 or 7x5-3x3+2x2-3x+6 or x2-2 etc, etc. If you tabulate the values of a given polynomial for x=0, x=1, x=2, x=3 and so on then subtract the first value from the second, the second from the third and so on you get a new column of numbers. Repeating the process with this column produces yet another column and so on. At some point in the process you end up with a column that is filled with a numerical constant. Confused? OK look at the table below!


x x3-3x2+6 xn+1-xn diff(1)n+1 –diff(1)n diff(2)n+1 – diff(2)n
0 6 -2 0 6
1 4 -2 6 6
2 2 4 12 6
3 6 16 18
4 22 34
5 56


As you can see this particular polynomial bottoms out, so to speak, with as constant of 6. If we now go back into the right hand column and enter a new 6 in the first free line then add this to its immediate left hand neighbour repeating this process across the table we arrive at the polynomial column with the next value for the polynomial. See below:


x x3-3x2+6 xn+1-xn diff(1)n+1 –diff(1)n diff(2)n+1 – diff(2)n
0 6 -2 0 6
1 4 -2 6 6
2 2 4 12 6
3 6 16 18 6
4 22 34
5 56


x x3-3x2+6 xn+1-xn diff(1)n+1 –diff(1)n diff(2)n+1 – diff(2)n
0 6 -2 0 6
1 4 -2 6 6
2 2 4 12 6
3 6 16 18 6
4 22 34 24
5 56


x x3-3x2+6 xn+1-xn diff(1)n+1 –diff(1)n diff(2)n+1 – diff(2)n
0 6 -2 0 6
1 4 -2 6 6
2 2 4 12 6
3 6 16 18 6
4 22 34 24
5 56 58


x x3-3x2+6 xn+1-xn diff(1)n+1 –diff(1)n diff(2)n+1 – diff(2)n
0 6 -2 0 6
1 4 -2 6 6
2 2 4 12 6
3 6 16 18 6
4 22 34 24
5 56 58
6 114

This means that if we set up our table and calculate enough values to determine the difference constant then we can by a process of simple addition calculate all further values of the polynomial. This is exactly what Babbage designed his difference engine to do.

If you’ve been paying attention you might notice that the method of finite differences applies to polynomials and Babbage wished to calculate were logarithmic and trigonometrical functions. This is however not a serious problem, through the use of other bits of higher mathematics, which we don’t need to go into here, it is possible to represent both logarithmic and trigonometrical functions as polynomials. There are some problems involved with using the method of finite differences with these polynomials but these are surmountable and Babbage was a good enough mathematician to cope with these difficulties.

Babbage now had a concept and a plan to realise it, all he now needed was the finances to put his plan into action. This was not a problem. Great Britain was a world power with a large empire and the British Government was more than ready to cough up the readies for a scheme to provide reliable mathematical tables for navigation for the Royal Navy and Merchant Marine that serviced, controlled and defended that empire. In total over a period of about ten years the Government provided Babbage with about £17, 000, literally a fortune in the early nineteen hundreds. What did they get for their money, in the end nothing!

Why didn’t Babbage deliver the Difference Engine? There is a widespread myth that Babbage’s computer couldn’t be built with the technology available in the first half of the nineteenth century. This is simply not true, as I said a myth. Several modules of the Difference Engine were built and functioned perfectly. Babbage himself had one, which he would demonstrate at his scientific soirées, amongst other things to demonstrate his theory of miracles.

The Difference Engine model used by Babbage for his demonstrations of his miracle theory Source: Wikimedia Commons

The Difference Engine model used by Babbage for his demonstrations of his miracle theory
Source: Wikimedia Commons

Other Difference Engines modules were exhibited and demonstrated at the Great Exhibition in Crystal Palace. So why didn’t Babbage finish building the Difference Engine and deliver it up to the British Government? Babbage was not an easy man, argumentative and prone to bitter disputes. He became embroiled in one such dispute with Joseph Clement, the engineer who was actually building the Difference Engine, about ownership of and rights to the tools developed to construct the engine and various already constructed elements. Joseph Clement won the dispute and decamped together with said tools and elements. By now Babbage was consumed with a passion for his new computing vision, the general purpose Analytical Engine. He now abandoned the Difference Engine and tried to convince the government to instead finance the, in his opinion, far superior Analytical Engine. Having sunk a fortune into the Difference Engine and receiving nothing in return, the government, not surprisingly, demurred. The much hyped Ada Lovelace Memoire on the Analytical Engine was just one of Babbage’s attempts to advertise his scheme and attract financing.

However, the story of the Difference Engine didn’t end there. Using knowledge that he had won through his work on the Analytical Engine, Babbage produced plans for an improved, simplified Difference Engine 2 at the beginning of the 1850s.

Per Georg Schutz Source: Wikimedia Commons

Per Georg Schutz
Source: Wikimedia Commons

The Swedish engineer Per Georg Scheutz, who had already been designing and building mechanical calculators, began to manufacture difference engines based on Babbage’s plans for the Difference Engine 2 in 1855. He even sold one to the British Government.

Scheutz Difference Engine No. 2. (1859) Maschine im Science Museum, London Source: Wikimedia Commons

Scheutz Difference Engine No. 2. (1859) Maschine im Science Museum, London
Source: Wikimedia Commons


Filed under History of Computing, History of Mathematics, History of Technology, Myths of Science

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

Nature and nature’s laws lay hid in night;

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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





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


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

I wish a certain (tv) star would think before he tweets

On a couple of occasions I have blogged about the publically displayed history of science ignorance of mega-star science entertainer Neil deGrasse Tyson (NdGT). On Sunday I stumbled over one his tweets, which stridently proclaimed:


If you wished upon that first Star you saw tonight in twilight,

then it will not likely come true. You wished on planet Venus

Venus is always brighter than all other planets or stars as seen from Earth. The second brightest object on the image is Jupiter Source: Wikimedia Commons

Venus is always brighter than all other planets or stars as seen from Earth. The second brightest object on the image is Jupiter
Source: Wikimedia Commons

My first reaction was that this tweet was very mean spirited and to ask myself what NdGT’s intention was in tweeting it. Then as a historian of astronomy I replied to this tweet by pointing out that from antiquity up to the beginning of the eighteenth century all illuminated celestial bodies – stars, comets, planets – were referred to as stars and so one would still be wishing upon a star. Now NdGT has a trillion sycophants followers, so the last thing I expected was a response from the great man himself to my tweet. Imagine my surprise when I got just that:


The 7 “planetes” (Greek for “wanderer”) were distinct from stars:

Sun Moon Mercury Venus Mars Jupiter Saturn.


Slam -Bam! A killer etymological put down or at least I assume that was what NdGT thought he had achieved. Unfortunately he had just ridden himself deeper into the mire. If we actually consult an etymological dictionary on the origins of the term planet we discover the following:

Planet (n): late Old English planete, from Old French planete (Modern French planète), from Late Latin planeta, from Greek planetes, from (asteres) planetai “wandering (stars),” from planasthai “to wander…

Oh dear, planet doesn’t mean wanderer in the original Greek; it means wandering star! The Greeks did indeed differentiate between fixed stars, our stars, wandering stars, the seven planets and hairy stars (I’ve always liked that one) the comets, but, and this is the decisive point, they are all stars, as I stated in the first place. Whether NdGT’s etymological error was out of ignorance or a result of deliberate quote mining I can’t say.

NdGT might have saved himself some embarrassment if he had paused for a moment to consider the etymology of astronomy, the mother discipline of his own profession, astrophysics. Astronomy is also derived from ancient Greek, as was astrology and as I pointed out in another post the two terms were, from their origin up till the late seventeenth century, synonyms. Let’s just check out those etymologies shall we.

Astronomy (n): c. 1200, from Old French astrenomie, from Latin astronomia, from Greek astronomia, literally “star arrangement,” from astron “star”

Astrology (n): late 14c., from Latin astrologia “astronomy, the science of the heavenly bodies,” from Greek astrologia “telling of the stars,” from astron “star”

So astrologia, which is the older of the two terms, means the science of the heavenly bodies, which of course includes the planets. Astronmia naturally includes the planets too, as stars.

What evidence can I bring forth that this was still the case in the Early Modern Period? I have no lesser witness than that well-known Elizabethan playwright and poet Will Shakespeare. In his tragedy Romeo and Juliet he refers to the fact that their doom has been predetermined by their astrological fate. Now an astrological horoscope determines the position of the planets along the elliptic, the apparent path of the sun around the earth, so astrology is very much planetary. So how does the good bard describe the astrological doom of his two young lovers?

From forth the fatal loins of these two foes,

A pair of star-cross’d lovers take their life

Note Romeo and Juliet are star-crossed, although it is the planets that determine their fate. In fact the expression ones fate is written in the stars is still very much used today in the English language.

I do have a last sad note for NdGT concerning his original tweet. Most people probably associate the expression ‘to wish upon a star’ with the pop song When You Wish Upon a Star originally from the Walt Disney film Pinocchio from 1940, which has been covered by many, many artists. However the tradition is much older and in fact goes back at least to the ancient Romans. The tradition says that if you make a wish when you see the first star of the evening then that wish will come true. Now the first star of the evening is ‘the evening star’ also known as the planet Venus and in fact the tradition derives from the Roman worship of Venus their goddess of love, so if you did make a wish upon seeing Venus, as NdGT claimed in his original tweet, then you would be doing exactly the right thing to have your wish come true. You are just offering up a prayer to the divine Venus.

The Birth of Venus, by Sandro Botticelli c. 1485–1486 Source: Wikimedia Commons

The Birth of Venus, by Sandro Botticelli c. 1485–1486
Source: Wikimedia Commons

The saddest aspect of this brief collision on Twitter is just how many of NdGT’s sycophants followers retweeted and/or liked his etymology of the term planet tweet thinking he had brilliantly seen of the bothersome history of astronomy troll. I wouldn’t mind him spouting history of science crap if he was some brain damaged loony with 15 followers on Twitter but unfortunately he is the most well-known and influential English language science communicator in the world and his false utterances mislead and misinform a lot of trusting people.





Filed under History of Astronomy, Myths of Science

Not a theology student

On the 10 August 1591 (os) (according to Max Caspar, 11 August according to Owen Gingerich!) Johannes Kepler graduated MA at the University of Tübingen. This is a verified undisputed historical fact, however nearly all secondary sources go on to state that he then went on to study theology, his studies being interrupted, shortly before completion, when he was appointed school teacher and district mathematicus in Graz. A post he took up on 11 April 1594. The part about the theology studies is however not true. This myth was created by historians and it would be interesting to trace who first put it out in the world and it is also interesting that nobody bothered to check this claim against the sources until Charlotte Methuen published her Kepler’s Tübingen: Stimulus to a Theological Mathematics in 1998.

Johannes Kepler Source: Wikimedia Commons

Johannes Kepler
Source: Wikimedia Commons

One reason for the lack of control is because the version with the theology studies seems so plausible. At medieval universities all student started their studies with the seven liberal arts graduating BA, in Kepler’s case in 1588 having matriculated two years earlier. Those, who stayed on at the university now intensified those studies graduating MA, essentially a teaching qualification. Those, who now wished to continue in academia had, in the normal run of events, the choice between taken a doctorate in law, medicine or theology. We know that Kepler was initially very disappointed with his appointment as a school teacher for mathematics because he would have preferred to become a Protestant pastor, so it would seem logical that because he stayed on at the university after graduating MA he must have studied theology. However appearances can be, and in this case are, deceptive. The problem is that Tübingen, or at least the Tübinger Stift in which Kepler studied was not a conventional medieval university.

A major problem that the Lutheran Protestant Church faced following the Reformation was finding enough pastors to run their churches and enough schoolteachers for their schools. In areas that converted to Protestantism the churches naturally had Catholic priest many of whom were not prepared or willing to convert and the education system, including both schools and universities, was firmly in the hands of the Catholic Church. This meant that the Lutheran Church had to build its own education system from scratch. This was the task taken on by Phillip Melanchthon, whom Luther called his Preceptor Germania – Germany’s schoolteacher – a task that he mastered brilliantly.

The state of Baden-Württemberg, one of the largest and most important early Protestant states gasped here the initiative, setting up a state sponsored school and university system to educate future Protestant schoolteachers and pastors. The Tübinger Stift was established in 1536 for exactly this purpose. The Dukes of Württemberg also provided stipends for gifted children of less wealthy families to enable them to attend the Stift. Kepler was the recipient of such a stipend.

Tübinger Still (left and University (right) Source: Kepler-Gesellschaft e.V.

Tübinger Still (left) and University (right)
Source: Kepler-Gesellschaft e.V.

All the students did a general course of studies, which upon completion with an MA qualified them to become either a schoolteacher or a pastor depending on the positions required to be filled, when they graduated. Allocation was also to some extent conditioned by the abilities of the individual student. Upon completion of their MAs student remained at the university receiving instruction in the various practical aspects of their future careers, teaching practice, basic theology for sermons and so forth until a suitable vacancy became available. Only a very, very small percentage of these students formally matriculated for a doctorate in theology, an unnecessary qualification for a simple pastor. Most Catholic priest of the period also did not possess a doctorate in theology. Kepler was not one of those who chose to do a doctorate in theology but was simply a participant in the general career preparation course for schoolteachers and pastor; a course for which there were no formal final exams or qualifications.

Kepler had been in this career holding pattern, so to speak, for not quite three years when the Evangelical Church authorities in Graz asked the University in Tübingen to recommend a new mathematics teacher for their school. After due consideration the university chose Kepler, who had displayed a high aptitude for mathematics, for the position. After some hesitation Kepler accepted the posting. He could have refused but it would not have placed him as a stipendiary in a very good position with the authorities. He was also free to leave the system and return to civil life but this would have meant having to reimburse his stipend.

It was clear from the beginning of his studies that he could, or would, be appointed either a schoolteacher or a pastor but the young Johannes had set his heart on serving his God as a pastor and was thus initially deeply disappointed by his appointment. The turning point came in Graz when he realised, in a moment of revelation, that he could best serve his God, a geometrical creator, by revealing the mathematical wonders of that creation. And so he dedicated his life to being God’s geometer, a task that he fulfilled with some distinction.


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

Getting Kepler wrong

In recent times a bit of philosophy of science bun fight took place on the Intertubes. It started off in the New York Times with an opinion piece by James Blachowicz entitled, There is no Scientific Method. The title is actually a misnomer, as what Blachowicz actually argues is that the problem solving procedure usually called the scientific method is not unique to science. I’m not going to discuss it here but it is hardly an original theory, in fact I’ve argued something very similar myself in the past. I will, however, say that I don’t think that Blachowicz argues his case very well. Above all I think that his final three paragraphs in which he explains why, if the method is not exclusive to science, science is different to other form of knowledge are pretty crappy and largely wrong. Someone who also disparages those final three paragraphs in physics blogger Chad Orzel, who has written a pretty nifty book about the scientific method himself.[1] Chad wrote a post on his Uncertain Principles blog entitled, Why Physicists Disparage Philosophers, In Three Paragraphs, which if your read or have already read Blachowicz’s opinion piece you should definitely also read.

Chad was not the only physicist who weighed in on Blachowicz’s opinion piece with Ethan Siegel posting on his Forbes blog, Starts with a Bang, a rejoinder entitled Yes, New York Times, There Is a Scientific Method. In his piece Blachowicz illustrates his interpretation of the use of the scientific method in actual science with a brief discussion of Kepler’s search for the shape of the orbit of Mars using Tycho Brahe’s observational data as extensively described by Kepler in his Astronomia Nova in 1609. Here are the actual paragraphs from Blachowicz:

Now compare this with a scientific example: Johannes Kepler’s discovery that the orbit of Mars is an ellipse.

In this case, the actual meaning of courage (what a definition is designed to define) corresponds with the actual observations that Kepler sought to explain — that is, the data regarding the orbit of Mars. In the case of definition, we compare the literal meaning of a proposed definition with the actual meaning we want to define. In Kepler’s case, he needed to compare the predicted observations from a proposed explanatory hypothesis with the actual observations he wanted to explain.

 Early on, Kepler determined that the orbit of Mars was not a circle (the default perfect shape of the planetary spheres, an idea inherited from the Greeks). There is a very simple equation for a circle, but the first noncircular shape Kepler entertained as a replacement was an oval. Despite our use of the word “oval” as sometimes synonymous with ellipse, Kepler understood it as egg-shaped (in the asymmetrical chicken-egg way). Maybe he thought the orbit had to be lopsided (rather than symmetrical) because he knew the Sun was not at the center of the oval. Unfortunately, there is no simple equation for such an oval (although there is one for an ellipse).

When a scientist tests a hypothesis and finds that its predictions do not quite match available observations, there is always the option of forcing the hypothesis to fit the data. One can resort to curve-fitting, in which a hypothesis is patched together from different independent pieces, each piece more or less fitting a different part of the data. A tailor for whom fit is everything and style is nothing can make me a suit that will fit like a glove — but as a patchwork with odd random seams everywhere, it will also not look very much like a suit.

The lesson is that it is not just the observed facts that drive a scientist’s theorizing. A scientist would, presumably, no more be caught in a patchwork hypothesis than in a patchwork suit. Science education, however, has persistently relied more on empirical fit as its trump card, perhaps partly to separate science from those dangerous seat-of-the-pants theorizings (including philosophy) that pretend to find their way apart from such evidence.

Kepler could have hammered out a patchwork equation that would have represented the oval orbit of Mars. It would have fit the facts better than the earlier circle hypothesis. But it would have failed to meet the second criterion that all such explanation requires: that it be simple, with a single explanatory principle devoid of tacked-on ad hoc exceptions, analogous to the case of courage as acting in the face of great fear, except for running away, tying one’s shoelace and yelling profanities.

 It is here that Ethan launches his attack accusing Blachowicz of not having dug deep enough and of misrepresenting what Kepler actually did. After posting a picture of Kepler’s wonderful 3D model of his Platonic cosmos:


Ethan posted the following:

Kepler’s original model, above, was the Mysterium Cosmographicum, where he detailed his outstandingly creative theory for what determined the planetary orbits. In 1596, he published the idea that there were a series of invisible Platonic solids, with the planetary orbits residing on the inscribed and circumscribed spheres. This model would predict their orbits, their relative distances, and — if it were right — would match the outstanding data taken by Tycho Brahe over many decades.

But beginning in the early 1600s, when Kepler had access to the full suite of Brahe’s data, he found that it didn’t match his model. His other efforts at models, including oval-shaped orbits, failed as well. The thing is, Kepler didn’t just say, “oh well, it didn’t match,” to some arbitrary degree of precision. He had the previous best scientific model — Ptolemy’s geocentric model with epicycles, equants and deferents — to compare it to. In science, if you want your new idea to supersede the old model, it has to prove itself to be superior through experiments and observations. That’s what makes it science. And that’s why the ellipses succeeded, because they gave better, more accurate prediction than all the models that came before, including Ptolemy’s, Copernicus’, Brahe’s and even Kepler’s own earlier models.

Unfortunately Ethan has hoisted himself with his own petard. He has not dug deep enough and what he presents here is presentist interpretation of what Kepler actually thought and did over a period of around thirty years. I will explain.

At the various stages of Kepler’s development that Ethan sketches Kepler is dealing with and providing answers for different non-exclusive question, which don’t replace each other sequentially.

At the beginning Kepler was looking for an answer to the question, why there are only six planets? In the Copernican system the seven planets of the Greek’s had been reduced to six as the Earth and the Sun exchanged places and the Moon became the Earth’s satellite (a word that Kepler would coin later with reference to the newly discovered moons of Jupiter). This metaphysical question seems rather strange to us today but it fitted into Kepler’s metaphysics. Kepler was deeply religious and his God was a rational, logical creator of a mathematical (read geometrical) cosmos. Kepler’s cosmos was also finite, so there were and could only be six planets. He was later mortified when Galileo announced the discovery of four new celestial bodies and infinitely relieved when there turned out to be satellites and not planets. Kepler’s answer to his question was the model shown above with the spheres of the six planets inscribing and circumscribing the five regular Platonic solids. There are, and can only be, only five regular Platonic solids therefore there can only be six planets, Q.E.D. Using the available data on the size of the planetary orbits Kepler turned his vision into a mathematical model of the cosmos and discovered that it fit roughly but not accurately enough. His passion for precision and accuracy was a major driving force throughout Kepler’s scientific career. Kepler was aware that Tycho had been collecting new more accurate astronomical data for thirty years and this was one of his major reasons for wanting to work with Tycho in Prague; the other reason was that Kepler, as a Protestant who refused to convert to Catholicism, was being expelled from Graz and desperately needed a new job.

In Prague Tycho, who thought he had been plagiarised by Ursus, was not prepared to hand over his precious data to a comparative stranger and instead gave Kepler a couple of commissions. The first was to write an account of Tycho’s dispute with Ursus, which Kepler did producing a classic in the history and philosophy of science, which unfortunately was not published at the time. Kepler second task was to determine the orbit of Mars based on Tycho’s observational data. At this time, this had nothing to do with his previous work in the Mysterium Cosmographicum. Famously, what Kepler thought would be a simple mathematical exercise taking a couple of weeks turned into a six year battle to tame the god of war, published in all its gory detail in his Astronomia nova in 1609. Having at some point abandoned the traditional circular orbits Kepler hit upon his oval, meaning egg shaped rather than elliptical, orbit and calculated it using Tycho’s data. His calculations displayed eight arc minutes of error in places, that’s eight sixtieths of one degree, a level of accuracy way above anything that either Ptolemaeus or Copernicus had ever produced. He had superseded the old model easily to quote Ethan, however eight arc minutes of error was an affront to Kepler’s love of accuracy and in his opinion an insult to Tycho’s observational accuracy, so it was back to the drawing board. In his further efforts Kepler finally discovered his first two laws of planetary motion and his elliptical orbits[2]. This set of answers were however to a different set of questions to those in the Mysterium Cosmographicum and in no way were considered to replace them.

Throughout his life Kepler remained convinced that his Platonic model just required fine-tuning, which he meant quite literally. Already in the Mysterium Cosmographicum he muses about the Pythagorean music of the spheres and his magnum opus, the Harmonices Mundi published in 1619, is a truly amazing conglomeration of plane and spherical geometry, music theory, astrology and astronomy containing many gems but most famous for his third law of planetary motion, the harmonic law. Throughout all of this work the Platonic solids model of the Mysterium Cosmographicum remained Kepler’s vision of the cosmos and in 1621 he published a revised and extended version of his first book confirming his belief in it. It is this combination of, from our point of view, weird Renaissance heuristics, Platonic solids, harmony of the spheres, combined with the high level highly accurate modern science that it generated, the laws of planetary motion etc., that led Arthur Koestler to title his biography of Kepler, The Watershed. He saw Kepler as straddling the watershed between the Middle Ages and the Early Modern Period with one foot planted firmly in the past and the other striding determinedly into the future. The inherently contradictory duality is what leads presentists such as Ethan to misunderstand and misrepresent Kepler. He didn’t replace his metaphysical Platonic solids model of the cosmos with his mathematical elliptical model of the planetary orbits but considered them as equal parts of his whole astronomical/cosmological vision. We do not have Ethan’s Whig march of progress of one model replacing another but rather a Renaissance concept of the cosmos that can only be considered on its own terms and simply doesn’t make sense if we try to interpret it from our own modern perspective.

Since I started writing this post there have been two further contributions to the debate that inspired it. On the bigthink Jag Bhalla interviews Rebecca Newberger Goldstein on the topic under the title, What’s Behind A Science vs. Philosophy Fight?

On The Multidisciplinarian, William Storage, in his The Myth of Scientific Method, takes apart Ethan’s (mis)use of Galileo in his contribution. This one is highly recommended


[1] Chad Orzel, Eureka! Discover Your Inner Scientist, Basic Books, New York, 2014

[2] As I’ve said more than once in the past the best account of Kepler’s Astronomia nova is James R. Voelkel, The Composition of Kepler’s Astronomia nova, Princeton University Press, 2001


Filed under History of Astronomy, Myths of Science

A Rant Roundup!

Last week saw Steve King a Member of the US House of Representatives make a really stupid white supremacist statement on television, which the media caught up with and went to town on. I don’t intend to discuss his stupidity here as there are two good blog posts from Sarah Bond on Forbes and Rebecca Onion on Slate that deal with different aspects of it much better than I could. However, I would like to comment briefly on the coverage and comments on the VOX website. Under the title US Rep. Steve King preaches literal white supremacy on national television VOX reported on the incident and included a list of non-white, non-Western achievements, which include the following claim:

Egyptians helped bring paper and ink pens to Western civilizations

Now if you are going to criticise somebody’s undeniable ignorance then it helps if you are not ignorant yourself. The Egyptians gave us papyrus and not paper, as in actually explained in the link provided by VOX to the word paper. Paper as they should have known came to Europe from China via the Islamic Empire in the thirteenth century CE. Now papyrus and paper are both made of plant fibres but their fabrication processes and their physical properties are substantially different, which is why we now write on paper and not papyrus.

 Another major Internet so-called news website that allowed itself a bit of #histsci related stupidity last week was BUZZFEED with an article with the click bait title, 17 Maps That Will Change The Way You Look At The World Forever. This article illustrates the cartographical distortions produced by the Mercator projection the further that you move away from the equator. In itself this is not a bad demonstration of a fact that everybody should be aware of but BUZZFEED rather spoiled its article with the introduction, which reads:

Historically it’s been very hard to represent a 3D planet on a 2D map. The Mercator Projection was created as a way around this

Yes it is very hard to represent a 3D spherical planet on a 2D map and not just historically (a 3D cube planet would not be a problem) and numerous solutions to this problem had been developed long before Mercator came along, three alone from Ptolemaeus in the second century CE. All of them have their advantages and disadvantages. However, and this is a very important point, the Mercator projection was not developed initially to solve this very general cartographical problem. The Mercator projection was originally developed to solve the much more specific problem of how to represent a constant compass bearing as a straight line on a 2D map.

The 1569 Mercator map of the world based on the Mercator projection Source: Wikimedia Commons

The 1569 Mercator map of the world based on the Mercator projection
Source: Wikimedia Commons

For this very specific function the size distortions that the Mercator projection produces are completely irrelevant. The problems come about because this projection, conceived as an aid to marine navigation, is misused for general geographical and political maps of the world. This cannot be repeated oft enough in the extremely tedious debate about the so-called shortcomings of the Mercator projection.


Gerald Mercator Source: Wikimedia Commos

Gerald Mercator
Source: Wikimedia Commons


Yesterday was the ninety-sixth anniversary of the birth of Rosalind Franklin brilliant x-ray crystallographer and physical chemist.

Rosalind Franklin (25 July 1920 – 16 April 1958) Source: Wikimedia Commons

Rosalind Franklin (25 July 1920 – 16 April 1958)
Source: Wikimedia Commons

This is certainly a #histSTM anniversary that should be widely acknowledged, as indeed it was, but unfortunately nearly all the people acknowledging it did so by repeating or linking to the same old factually and historically false myths about her role in the discovery of the structure of DNA. Yes, she did play a very central role in that discovery, but it was her publically available data on the physical measurements of the DNA structure that Francis Crick used to complete his and Watson’s model and not the legendary ‘Photo 51’.

Photo 51, showing x-ray diffraction pattern of DNA Source: Wikimedia Commons

Photo 51, showing x-ray diffraction pattern of DNA
Source: Wikimedia Commons

On Photo 51 itself, this was made by Raymond Gosling and not by Franklin.

Professor Raymond Gosling in 2003 "DNA at King's - the continuing story: 50th anniversary of the discovery of the structure of DNA" Source Wikimedia Commons: Image seen on Kings College website and permission sought from public relations office. Image not their copyright but that of Professor Gosling himself who in email stated: Re the photo. Feel free to use it. My wife took it so it does not need any acknowledgements! Kind regards, Ray Gosling

Professor Raymond Gosling in 2003 “DNA at King’s – the continuing story: 50th anniversary of the discovery of the structure of DNA”
Source Wikimedia Commons: Image seen on Kings College website and permission sought from public relations office. Image not their copyright but that of Professor Gosling himself who in email stated: Re the photo. Feel free to use it. My wife took it so it does not need any acknowledgements! Kind regards, Ray Gosling

Gosling had been Franklin’s doctoral student for a time but because she was due to leave the King’s College laboratory he had reverted to Maurice Wilkins as his supervisor when Wilkins showed James Watson the infamous photo. As Gosling’s doctoral supervisor Wilkins was fully entitled to show the photo to Watson, whether his actions were wise or ethically correct when he did so is another question. However it is a myth that Watson’s seeing Photo 51 led to the discovery of the structure of DNA, a myth unfortunately set in the world by Watson himself.

Yes Franklin certainly deserves to be acknowledged as one of those who made substantial contributions to the discovery of the structure of DNA. No, Watson and Crick did not steal the discovery of the structure of DNA from Franklin. No, Franklin did not take Photo 51 Gosling did, and no Photo 51 was not crucial to the discovery of the structure of DNA. And finally for those who refuse to pay attention, the Noble prize for the discovery of the structure of DNA was awarded in 1962; Rosalind Franklin died in 1958 and so could not, according to the rules for Noble prizes, be considered for the award.

One final plea, stop referring to Rosalind Franklin as unsung! This might have been true in 1965 or even in 1985 but it is certainly in no way true today.

For the accurate historical details on the discovery of the structure of DNA read Matthew Cobb’s excellent Life’s Greatest Secret.



Filed under Myths of Science

If you are going to blazon out history of science ‘facts’ at least get them right

Today’s Torygraph has a short video entitled 10 Remarkable Facts about rainbows, at 57 seconds it displays the following text:

Until the 17th Century, no one had

the faintest idea what a rainbow

was, how it got there or what it was

made of…

This is, of course, simply not true. In the 14th century the Persian scholar Kamal al-Din Hasan ibn Ali ibn Hasan al-Farisi (1267–1319) gave the correct scientific explanation of the rainbow in his Tanqih al-Manazir (The Revision of the Optics). Almost contemporaneously the German scholar Theodoric of Freiberg (c. 1250–c. 1310) gave the same correct explanation in his De iride et radialibus impressionibus (On the Rainbow and the impressions created by irradiance). The two scholars arrived at their conclusion independently of each other but both of them did experiments involving the study of light rays passing through glass spheres full of water and both scholars were influenced by the optical theories of Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham. Unfortunately both explanations disappeared and it was in fact first in the 17th Century that the Croatian scholar Marco de Antonio Dominis (1560–1624) once again gave an almost correct explanation of the rainbow in his Tractatus de radiis visus et lucis in vitris, perspectivis et iride.

De Dominis' explanation of the rainbow Source: Wikimedia Commons

De Dominis’ explanation of the rainbow
Source: Wikimedia Commons


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