Category Archives: History of Astronomy

Does the world really need another Galileo hagiography?

When it was first advertised several people drew my attention to Michael E. Hobart’s The Great Rift: Literacy, Numeracy, and the Religion-Science Divide[1]and it had hardly appeared when others began to ask what I thought about it and whether one should read it? I find it kind of flattering but also kind of scary that people want to know my opinion of a book before committing but even I can’t read a more than 500 page, intellectually dense book at the drop of the proverbial hat. Curiosity peaked piqued I acquired a copy, for a thick bound volume it’s actually quite reasonably priced, and took it with me to America, as my travel book. I will now give my considered opinion of Hobart’s tome and I’m afraid that it’s largely negative.

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Hobart’s title says nearly everything about his book and to make sure you know where he is going he spells it out in detail in an 18-page introductory chapter The Rift between Religion and Science, which he attributes to the fact that in the seventeenth century science ceased to be verbal and became numerical. If this should awaken any suspicions in your mind, yes his whole thesis is centred round Galileo’s infamous two books diatribe in Il Saggiatore. As far as I can see the only new thing that Hobart introduces in his book is that he clothes his central thesis in the jargon of information technology, something that I found irritating.

The next 34 pages are devoted to explaining that in antiquity the world was described both philosophically and theologically in words. Moving on, we get a 124-page section dealing with numbers and mathematics entitled, From the “Imagination Mathematical” to the Threshold of Analysis. Here Hobart argues that in antiquity and the Middle Ages numbers were thing numbers, i.e. they were only used in connection with concrete objects and never in an abstract sense simply as numbers for themselves. His presentation suffers from selective confirmation bias of his theory, when talking about the use of numbers in the Middle ages he only examines and quotes the philosophers, ignoring the mathematicians, who very obviously used numbers differently.

He moves on to the High Middle Ages and the Renaissance and outlines what he sees as the liberation of numbers from their thing status through the introduction of the Hindu-Arabic numbers through Leonardo Pisano, the invention of music notation, the introduction of linear perspective in art and the introduction of both Scaliger’s chronology and the Gregorian calendar. Here once again his presentation definitely suffers from selective confirmation bias. He sees both Scaliger and the Gregorian calendar as the first uses of a universal time measuring system for years. Nowhere in his accounts of using numbers or the recording of time in years does he deal with astronomy in antiquity and down to the Early Modern Period. Astronomers used the Babylonian number system, just as abstract as the Hindu-Arabic system, and the Egyptian solar calendar in exactly the same way as Scaliger’s chronology. He also ignores, except somewhere in a brief not much later, the earlier use of the Hindu-Arabic number system in computos.

Here it is worth mentioning a criticism of others that Hobart brings later. In a chapter entitled, Towards the Mathematization of Matter, he briefly discusses Peter Harrison on science and religion and David Wootton on the introduction of a new terminology in the seventeenth century. He goes on to say, “…both of these fine scholars overlook just how the mathematical abstractions born of the new information technology and modern numeracy supplied an alternative to literacy as a means for discerning patterns in nature.” Two things occur to me here, firstly the mathematization of science as the principle driving force behind the so-called scientific revolution is one of the oldest and most discussed explanation of the emergence of modern science, so Hobart is only really offering old wine in new bottles and not the great revolutionary idea that he thinks he has discovered. The second is that in his book, The Invention of Science, David Wootton has a 47-page section entitled The Mathematization of the World, dealing with the changes in the use and perception of mathematics in the Renaissance that is, in my opinion, superior to Hobart’s account.

The third and final part of Hobart’s book is titled Galileo and the Analytical Temper and is a straight up hagiography. This starts with a gushing account of Galileo’s proportional compass or sector, prominent on the book’s cover. In all of his account of how fantastic and significant this instrument is Hobart neglects an important part of its history. He lets the reader assume that this is a Galileo invention, which is far from true. Although in other places Hobart mentions Galileo’s patron and mentor Guidobaldo del Monte he makes no mention of the fact that Galileo’s instrument was a modification and development of any earlier instrument of del Monte’s, which in turn was a modification of an instrument designed and constructed by Fabrizio Mordente.

This sets the tone for Hobart’s Galileo. He invents the scientific method, really? Then we get told, “Then in a dazzling stroke he pointed it [the telescope] skyward. He was not the first to do so, but he was certainly the first to exploit the new telescope, using it to expand beyond normal eyesight and peer into the vastness of space.” No he wasn’t!  Hobart gives us a long discourse on Galileo’s atomism explaining in detail his theory of floating bodies but neglects to point out that Galileo was simply wrong. He is even more crass when discussing Galileo’s theory of the tides in his Dialogo. After a long discourse on how brilliantly-scientific Galileo’s analysis leading to his theory is Hobart calmly informs us, “Galileo’s theory, of course was subsequently proved wrong by Newton…”! Yes, he really did write that! Galileo’s theory of the tides was contradicted by the empirical facts before he even published it and is the biggest example of blind hubris in all of Galileo’s works.

Hobart’s Galileo bias is also displayed in his treatment of Galileo’s conflicts with the Catholic Church and Catholic scientists. After a very good presentation of Galileo’s excellent proof, in his dispute with Scheiner, that the sunspots are on the surface of the sun and not satellites orbiting it. Hobart writes in an endnote, “A committed Aristotelian, Scheiner continued to advance fierce polemics against Galileo, but even he eventually accepted Galileo’s analysis.” In fact Scheiner accepted Galileo’s analysis fairly rapidly and went on to write the definitive work on sunspots. Hobart somehow neglects to mention that Galileo falsely accused Scheiner of plagiarism in his Il Saggiatore and then presented some of Scheiner’s results as his own in his Dialogo. Describing the dispute in 1615/16 Hobart quoting Bellarmino’s Foscarini letter, “I say that if there were a true demonstration that the sun is at the centre of the world and the earth in the third heaven, and that the sun does not circle the earth but the earth circles the sun, then one would have to proceed with great care in explaining the Scriptures that appear contrary, and say rather that we do not understand them, than that what is demonstrated is false”, goes on to say without justification that Bellarmino would not have accepted a scientific proof but only an Aristotelian one. This is, to put it mildly, pure crap. The behaviour of the Jesuit astronomers throughout the seventeenth century proves Hobart clearly wrong.

I’m not even going to bother with Hobart’s presentation of the circumstances surrounding the trial, it suffices to say that it doesn’t really confirm with the known facts.

I also have problems with Hobart’s central thesis, “The Great Rift.” At times he talks about it as if it was some sort of explosive event, as his title would suggest then admits on more than one occasion that it was a very long drawn out gradual process. Although he mentions it in asides he never really addresses the fact that long after Galileo many leading scientists were deeply religious and saw their scientific work as revealing God’s handy work; scientists such as Kepler and Newton who were just as analytical and even more mathematical than Galileo.

Throughout the book I kept getting the feeling that Hobart is simply out of touch with much of the more recent research in the history of science although he has obviously invested an incredible amount of work in his book, which boasts 144-pages of very extensive endnotes quoting a library full of literature. Yes, the mathematization of science played a significant role in the evolution of science. Yes, science and religion have been drifting slowly apart since the Early Modern Period but I don’t think that the mathematization of science is the all-encompassing reason for that separation that Hobart is trying to sell here. No, Galileo did not singlehandedly create modern science as Hobart seem to want us to believe, he was, as I pointed out in a somewhat notorious post several years ago, merely one amongst a crowd of researchers and scholars involved in that process at the end of the sixteenth and the beginning of the seventeenth centuries. Does Hobart’s book bring anything new to the table? No, I don’t think it does. Should one read it? That is up to the individual but if I had known what was in it before I read it, I wouldn’t have bothered.

 

 

 

[1]Michael E. Hobart, The Great Rift: Literacy, Numeracy, and the Religion-Science Divide, Harvard University Press, Cambridge & London, 2018

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Sobel’s five books

 

Five Books is an Internet website that invites an expert to discuss in interview format five books that they recommend in a given discipline or academic area. Somebody recently drew my attention to a Five Books interview with pop science writer Dava Sobel asking my opinion of her chosen five books. Although I actually own all of the books that she recommends I have serious problems with her choices that start with the title of interview, The best books on The Early History of Astronomy recommended by Dava Sobel.

I remain a sceptic about a lot of the claims made by archeoastronomers concerning supposed astronomical alignments of various archaeological features but I am quite happy to admit that Stonehenge, for example, does have such an alignment, which would place early astronomy at least as early as the third millennium BCE. Maybe astronomy and not archaeoastronomy was meant it which case we would be in the second millennium BCE with the Babylonians. Perhaps Ms Sobel thinks astronomy doesn’t really start until we reach the ancient Greeks meaning about five hundred BCE. But wait, all five of her books are about astronomy in the sixteenth and seventeenth centuries CE! This is not by any definition the early history of astronomy. What is in fact meant is the early history of the Copernican heliocentric theory.

We now turn to the books themselves. I should point out before I start that I actually own and have read all five of the books that Sobel has chosen, so my criticisms are well informed.

First up we have Owen Gingerich’s The Book Nobody Read. This is not actually a book on the history of astronomy. During his years of research into the history of astronomy Gingerich carried out a census of the existing copies of the first and second editions of Copernicus’ De revolutionibus, which I also own. The Book Nobody Read is a collection of personal anecdotes about episodes involved in the creation of that census. Sobel also repeats a major error that Gingerich made in choosing his title.

Five Books: And that is why the 20th century author and journalist Arthur Koestler dismissed it as “the book that nobody read”, which is something that Owen Gingerich is at pains to correct with this book.

Sobel: Yes, he is referring to Koestler’s comment with his title. This was the insult hurled at Copernicus’s book because it is so long and mathematical.

During his census Gingerich recorded the annotations in all of the copies of De revolutionibus that he examined showing that people in the sixteenth and seventeenth centuries did indeed read the book. However, Koestler’s comment was not addressed at those original readers but at the wanna be historians in the nineteenth century during the Copernicus renaissance (Copernicus effectively disappeared out of the history of astronomy in the early seventeenth century and only returned with Kant’s “Copernican Turn” in the late eighteenth century leading to the concept of the Copernican revolution), who claimed that De revolutionibus was mathematically simpler than the prevailing geocentric model, as Koestler showed this was not the case prompting him to make his famous quip about “the book nobody read.”

Next up we have Robert Westman’s The Copernican Question. Now I’m a Westman fan, who has learnt much over the years reading almost every thing that he has written. However, The Copernican Question is a complex, highly disputed book that I would not recommend for somebody new to the subject.

Sobel’s third choice is Galileo’s Sidereus Nuncius, once again not a book that I would recommend for a beginner. To understand Sidereus Nuncius you really need to understand it in the context in which it was written. There are also several comments made by Sobel that are to say the least dubious.

Sobel: This is a thrilling book. It is the moment that astronomy became an observational science.

Astronomy has always been an observational science!

Sobel: Until Galileo’s time, the most that anyone could know about a planet was where it was.

You could also determine its orbit, its speed and its apparent relative distance from the earth.

Sobel: With his telescope Galileo was able to determine the composition of the moon.

Galileo could determine that the moon was not smooth but was mountainous like the earth, which is not quite the same as determining its composition. We had to wait for the Apollo Programme for that.

Five Books: How did he manage to get hold of the telescope?

Sobel: He had heard of such a thing being invented as a novelty and so he figured out how to build one. And although at first he considered it a military tool, which was passed to the navy in Italy to keep watch on the horizon for enemy ships, he very soon realised he could turn it skywards. So he made these amazing discoveries and published them.

The telescope was not invented as a novelty; its inventor, Lipperhey, offered it to the States General in the Dutch Republic as a military tool. There was of course no navy in Italy; in fact there was in that sense no Italy. Galileo offered his telescope to the Venetian Senate, in fact to be able to observe ships approaching the port earlier than with the naked eye, both for trade and military purposes.

Number four is Stillman Drake’s Galileo at Work. On the face of it an excellent choice but however one with a slight blemish, Drake is a straight up Galileo groupie, which makes his descriptions and judgements somewhat less than objective. Here once again we find a more than somewhat strange claim by Sobel

Five Books: And the church didn’t have an issue with what he was doing?

Sobel: Not at that point. The minute he started agreeing out loud with Copernicus and writing about it in Italian and not Latin then he became more controversial. The Sidereal Messenger is written in Latin but soon after that he switched to Italian and that is when it became an issue. His controversial views were investigated by the Roman Inquisition which concluded that his ideas could only be supported as a possibility and not an established fact, and he spent the rest of his life under house arrest.

Galileo’s choice of Italian as the language in which he wrote his Dialogo had little or nothing to do with his trial and eventual condemnation by the Inquisition.

Sobel’s final choice is more than somewhat bizarre, Arthur Koestler’s The Sleepwalkers.

Five Books: Lastly, you have chosen The Sleepwalkers by Arthur Koestler, which is an overview of that period, though he is not quite so complimentary about Copernicus and Galileo as the other authors you have chosen.

 Sobel: Arthur Koestler was a journalist with an interest in science. He really got fascinated by this subject. So this book traces the early history of astronomy because he too found it fascinating. Unfortunately, as you say, he didn’t like Copernicus, or Galileo for that matter. The only one he seems to really have liked was Kepler. So one reads his book sceptically. But it is a book that was widely read and it had a tremendous influence on people. Even though it came out in the 1950s you still meet people who will talk about that book. And for many it was the book that got them interested in astronomy. I read it years ago as well and it has stayed with me.

Now, Sleepwalkers is without doubt one of the five most influential books in my development as a historian of science and I still have my much thumbed copy bought when I was still comparatively young, but it is severely dated and I would certainly not recommend it today as an introductory text on the history of astronomy. Koestler’s book started out as the first full length English biography of Kepler and this is why Kepler takes the central position in his book. On Koestler’s treatment of Copernicus and Galileo we get the following:

Five Books: Why do you think he was so scathing of Copernicus and Galileo?

 Sobel: It is hard to say. He found Copernicus dull, and I admit that his book On the Revolution makes dull reading for a person who is not capable of understanding the maths. But Copernicus is far from dull.

Both Copernicus and Galileo acolytes detest Koestler’s book for his portrayals of their heroes. He didn’t find Copernicus dull he labels him “The Timid Canon “ because he thought that Copernicus lacked the courage of his convictions as far as his heliocentric theory was concerned. This is a hard but not unfair judgement of Copernicus’s behaviour. As far as Galileo is concerned, Koestler is one of the earliest authors to attack and demolish the Galileo hagiography, in particular with reference to his problems with the Church.

I wrote this blog post because one of my followers on Twitter asked my opinion of Sobel’s list. As I said at the beginning I own all of these five books and think all of them are in some sense good, however as a recommendation for somebody to learn about the early phase of heliocentricity in the Early Modern Period I find it a not particularly appropriate collection.

This of course immediately raises the question what I would recommend for this purpose. I hate this question. I have acquired my knowledge of the subject over the years by reading umpteen books and even more academic papers and filtering out the reliable facts and information from this vast collection of material. The moment I recommend a book I start to qualify my recommendation but you must also read this paper and chapter 10 in that book and you really need to look at… On the whole I would recommend people to start with John North’s Cosmos: An Illustrated History of Astronomy and Cosmology and if they want to discover more to proceed with North’s bibliographical recommendations.

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Some good Copernican mythbusting

For those who haven’t already seen it Tim O’Neill, Renaissance Mathematicus friend and guest blogger, has posted a superb essay on his excellent blog, History for Atheists, on the myths surrounding the dissemination, publication and reception of Copernicus’ heliocentric theory, The Great Myths 6: Copernicus’ Deathbed Publication. Regular readers of the Renaissance Mathematicus won’t learn anything new but it is an excellent summary of the known historical facts and well worth a read. As with this blog the comments are also well worth reading.

The earliest mention of Copernicus’ theory – Matthew of Miechów’s 1514 catalogue

Go on over and give Tim a boost!

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A multi-functional book for a multi-functional instrument

Probably the most talked about astronomical instrument in recent years is the so-called Antikythera Mechanism, several corroded chunks of bronze gear work found in the sea of the coast of the Greek island of Antikythera at the end of the nineteenth century.

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The Antikythera mechanism (Fragment A – front); visible is the largest gear in the mechanism, approximately 140 millimetres (5.5 in) in diameter Source: Wikimedia Commons

Historian of ancient astronomy, Alexander Jones, who was a member of one of the teams investigating and interpreting the mechanism, has now written a book about it, A Portable Cosmos.[1]

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I say that he has written a book but in fact it is really several books in one. The first two chapters deal with the story of the original discovery and recovery of the mechanism. They also sketch the history of the succession of investigations and interpretations of the mechanism that have taken place between its discovery and the present. The longest section of the book deals with a detailed description of the external aspects of the mechanism, its dials, scales and pointers. The penultimate chapter is an examination of the physical aspects of the mechanism, its gears and gear shafts. The final chapter, an afterword, is titled The Meaning of the Mechanism. For me, the most fascinating element of the book is that Jones in his explanations of the functions of the dials and pointers delivers up a comprehensive introduction to the histories of astronomy, astrology and cosmology of ancient Babylon and Greece, in fact I would rate it as the best such introduction that I have ever read.

Despite his very obviously high level command of the material Jones does not baffle with science but writes in a light and very accessible style and I for one found the book highly readable. Of interest is the fact that because large parts of the mechanism are missing and what is there is highly damaged there is not a general agreement under the experts, who have worked on the mechanism, about how to interpret the function or purpose of numerous aspects of it. Jones doesn’t just express his own well-informed and well-reasoned explanations but draws his readers’ attention to alternative suggestions and interpretations, explaining why he prefers his own chosen one. Having said this archaeoastronomer Doris Vickers, who recommended the book to me suggested also consulting the official Greek Antikythera Mechanism Research Project website, which has more information and other viewpoints to those of Jones.

The book has a very useful glossary of technical terms, endnotes (regular readers already know my views on endnotes contra footnotes), a comprehensive bibliography so you can read up on those interpretations that deviate from Jones’ and a good index.

To quote a cliché, if you only read one book on the Antikythera Mechanism, then it really should be this one. It kept me occupied and entertained during my recent four days in hospital and proved to be an excellent companion for that period and I would whole heartedly recommended for happier circumstances as well.

[1] Alexander Jones, A Portable Cosmos: Revealing the Antikythera Mechanism, Scientific Wonder of the Ancient World, OUP, Oxford, 2007

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

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

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

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

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

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

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

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

writing a few days later:

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

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

In modern terminology:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[6] Newton, Principia, 1999 p. 467

[7] Newton, Principia, 1999 p. 468

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

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Who cares about facts? – Make up your own, it’s much more fun!

Math Horizons is a magazine published by Taylor & Francis for the Mathematical Association of America aimed at undergraduates interested in mathematics: It publishes expository articles about “beautiful mathematics” as well as articles about the culture of mathematics covering mathematical people, institutions, humor, games, cartoons, and book reviews. (Description taken from Wikipedia, which attributes it to the Math Horizons instructions for authors January 3 2009). Apparently, however, authors are not expected to adhere to historical facts, they can, it seems, make up any old crap.

The latest edition of Math Horizons (Volume 25, Issue 3, February 2018) contains an article by a Stephen Luecking entitled Albrecht Dürer’s Celestial Geometry. As I am currently, for other reasons, refreshing my knowledge of Albrecht the mathematician I thought, oh that looks interesting I must read that. I wish I hadn’t.

Luecking’s sub-title seems innocent enough: Renaissance artist Albrecht Dürer designed a specialty compass for astronomical drawings, but when you read the article you discover that Luecking says an awful lot more and most of it is hogwash. What does he have to say?

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Albrecht Dürer Self-Portrait 1500 Source: Wikimedia Commons

Albrecht Dürer (1471–1528), noted Renaissance printer and painter, twice left his native Germany for sojourns to Italy, once from 1494 to 1495 and again from 1505 to 1507. During those years his wide-ranging intellect absorbed the culture and thinking of noted artists and mathematicians. Perhaps the most important
 outcome of these journeys was his
introduction to scientific methods. 
His embrace of these methods
 went on to condition his thinking 
for the rest of his life. 


So far so good. However what Dürer absorbed on those journeys to Italy was not scientific methods but linear perspective, the mathematical method, developed in Northern Italy in the fifteenth century, to enable artists to represent three dimensional reality realistically in a two dimensional picture. Dürer played a significant role in distributing these mathematical techniques in Europe north of the Alps. His obsession with mathematics in art led to him developing the theory that the secret of beauty lay in mathematical proportion to which de devoted a large part of the rest of his life. He published the results of his endeavours in his four-volume book on human proportions, Vier Bücher von Menschlicher Proportion, in the year of his death, 1528.

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Title page of Vier Bücher von menschlicher Proportion showing the monogram signature of artist Source: Wikimedia Commons

If Dürer wanted to learn scientific methods, by which, as we will see Luecking means astronomy, he could and probably did learn them at home in Nürnberg. Dürer was part of the humanist circle of Willibald Pirckheimer, he close friend and patron.

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Engraving of Willibald Pirckheimer at 53 by Albrecht Dürer, 1524. We live by the spirit. The rest belongs to death. Source: Wikimedia Commons

Franconian houses are built around a courtyard; Dürer was born in the rear building of the Pirckheimer house on the market square in Nürnberg. Although his parents bought their own house a few years later Albrecht and Willibald remained close friends and possibly even lovers all of their lives. Pirckheimer was a big supporter of the mathematical sciences—astronomy, mathematics, cartography and astrology—and his circle included, amongst others, Johannes Stabius, Johannes Werner, Erhard Etzlaub, Georg Hartmann, Konrad Heinfogel and Johannes Schöner all of whom were either astronomers, mathematicians, cartographers, instrument makers or globe makers some of them all five and all of them friends of Dürer.

Next up Luecking tells us:

One notable
consequence was Dürer’s abandonment of astrological subject
matter—a big seller for a printer
and publisher such as himself—in favor of astronomy.

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Albrecht Dürer Syphilis 1496 Syphilis was believed to have an astrological cause Source: Wikimedia Commons

Luecking offers no evidence or references for this claim, so I could offer none in saying that it is total rubbish, which it is. However I will give one example that shows that Albrecht Dürer was still interested in astrology in 1517. Lorenz Beheim (1457–1521) was a humanist, astrologer, physician and alchemist, who was a canon of the foundation of the St Stephan Church in Bamberg, he was a close friend of both Pirckheimer and Dürer and corresponded regularly with Pirckheimer. In a letter from 8 December 1517 he informed Pirckheimer that Johannes Schöner was coming to Nürnberg with printed celestial globes that could be used for astrology, which if his wished could be acquired by him and Albrecht Dürer. He would not have passed on the information if he thought that they wouldn’t be interested. Beheim also cast horoscopes for both Pirckheimer and Dürer.

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Gores for Johannes Schöner’s Celestial Globe 1517  Source: Hans Gaab, Die Sterne Über Nürnberg: Albrecht Dürer und seine Himmelskarten von 1515, Nürnberger Astronomische Gesellschaft, Michael Imhof Verlag, 2015 p. 115

 

Next up Luecking starts, as he means to go on, with pure poppycock. All of the above Nürnberger mathematician, who all played significant roles in Dürer’s life, were of course practicing astrologers.

Astronomy was not to be a casual interest. Just before his second trip to Italy, Dürer published De scientia motus orbis, a cosmological treatise by the Persian Jewish astronomer Masha’Allah ibn Atharī (ca. 740–815 CE). Since Masha’Allah wrote the treatise for laymen and included ample illustrations, it was a good choice for introducing Europeans to Arabic astronomy.

The claim that Dürer published Masha’Allah’s De scientia motus orbis is so mind bogglingly wrong anybody with any knowledge of the subject would immediately stop reading the article, as it is obviously a complete waste of time and effort. The book was actually edited and published by Johannes Stabius and printed by Weissenburger in Nürnberg in 1504.

The woodcut illustrations came from the workshop of Albrecht Dürer, but probably not from Dürer himself. There were traditionally attributed to Hans Süß von Kulmbach (1480–1522), one of Dürer’s assistants, who went on to become a successful painter in his own right, but modern research has shown that Süß didn’t move to Nürnberg until 1505, a year after the book was published.

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Hans Süß portrait  Source: Wikimedia Commons

Although Luecking wants Masha’Allah to be an astronomer he was in fact a very famous astrologer, who amongst other things cast the horoscope for the founding of Bagdad. De scientia motus orbis is indeed a book on Aristotelian cosmology and physics but it includes his theory that there are ten heavenly spheres not eight as claimed by Aristotle. His extra heavenly spheres play a significant role in his astrological theories. It is very common practice for astrologers, starting with Ptolemaeus, to publish their astronomy and astrology in separate books but they are seen as complimentary volumes. From their beginnings in ancient Babylon down to the middle of the seventeenth century astronomy and astrology were always seen as two sides of the same coin.

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Title page De scientia motus orbis Although this woodcut is usually titled The Astronomer I personally think the figure looks more like an astrologer Source: Wikimedia Commons

In 1509 Dürer purchased the entire library of Regiomontanus (1436–1476 CE) from the estate of Nuremberg businessman Bernhard Walther. Regiomontanus was Europe’s leading astronomer,
a noted mathematician, and a designer of astronomical instruments. Walther had sponsored Regiomontanus’s residency in Nuremberg between 1471 and 1475. Part of Walther’s largesse was to provide a print shop from which Regiomontanus published the world’s first scientific texts ever printed.

Regiomontanus was of course first and foremost an astrologer and most of those first scientific texts that he published in Nürnberg were astrological texts. Walther did not sponsor Regiomontanus’ residency in Nürnberg but was his colleague and student in his endeavours in the city. An analysis of Walther’s astronomical observation activities in Nürnberg after Regiomontanus’ death show that he too was an astrologer rather than an astronomer. When Regiomontanus came to Nürnberg he brought a very large number of manuscripts with him, intending to edit and publish them. When he died these passed into Walther’s possession, who added new books and manuscripts to the collection. The story of what happened to this scientific treasure when Walther died in 1504 is long and very complicated. In fact Dürer bought not “the entire library” but a mere ten manuscripts not when he bought Walther’s house, the famous Albrecht Dürer House, in 1509 but first in 1522.

In 1515, Dürer and Austrian cartographer and mathematician Johannes Stabius produced the first map of the world portraying the earth as a sphere.

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Johannes Statius portrait by Albrecht Dürer Source: Wikimedia Commons

The Stabius-Dürer world map was not “the first map of the world portraying the earth as a sphere”. The earliest know printed world map portraying the earth as a sphere is a woodcut in a Buchlein über die Kunst Corsmographia, (Booklet about the Art of Cosmographia) published in Nürnberg in about 1490. There are others that predate the Stabius-Dürer map most notably on the title page of Waldseemüller’s Die Welt Kugel (The Earth Sphere) published in Straßburg in 1509.

There are no surviving copies of the Stabius-Dürer world map from the sixteenth century so we don’t actually know what it was produced for. The woodblocks survived and were rediscovered in the 18th century.

It is however dedicated to both the Emperor Maximilian, Stabius’s employer who granted the printing licence, and Cardinal Matthäus Lang, so it might well have been commissioned by the latter. Lang commissioned the account of Magellan’s circumnavigation on which Schöner based his world map of that circumnavigation.

Afterward, Stabius proposed continuing their collaboration by publishing a star map—the first such map published in Europe. Their work relied heavily on data assembled by Regiomontanus, plus refinements from Walther.

It will probably not surprise you to discover that this was not “the first such map published in Europe. It’s the first printed one but there are earlier manuscript ones, two of which from 1435 in Vienna and 1503 in Nürnberg probably served as models for the Stabius–Dürer–Heinfogel one. Their work did not rely “heavily on data assembled by Regiomontanus, plus refinements from Walther” but was based on Ptolemaeus’ star catalogue from the Almagest. There is a historical problem in that there was not printed copy of that star catalogue available at the time so they probably work from one or more manuscripts and we don’t know which one(s). The star map contains the same dedications to Maximilian and Lang as the world map so one again might have been a commission from Lang, Stabius acting as the commissioning agent. Stabius and Lang studied together at the University of Ingolstadt.

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Stabs-Dürer-Heinfogel Star Map Northern Hemisphere Source: Ian Ridpath’s Star Tales

For more details on the star maps go here

The star map required imprinting the three- dimensional dome of the heavens onto a two- dimensional surface without extreme distortions, a task that fell to Stabius. He used a stereographic projection. In this method, rays originate at the pole in the opposite hemisphere, pass through a given point in the hemisphere, and yield a point on a circular surface.

You will note that I have included the name of Konrad Heinfogel to the producers of the map and it was actually he, and not Stabius, who was responsible for the projection of the map and the location of the individual stars. In fact in this project Johannes Stabius as commissioning agent was project leader, Konrad Heinfogel was the astronomical expert and Albrecht Dürer was the graphic artist hired to draw the illustration. Does one really have to point out that in the sixteenth century star maps were as much, if not more, for astrologers than for astronomers.

Luecking now goes off on an excurse about the history of stereographic projection, which ends with the following paragraph.

As the son of a goldsmith, Dürer’s exposure to stereographic projection would have been by way of the many astrolabes being fabricated in Nuremburg, then Europe’s major center for instrument makers. As the 16th century moved on, the market grew for such scientific objects as astrology slipped into astronomy. Handcrafted brass instruments, however, were affordable only to the wealthy, whereas printed items like the Dürer-Stabius maps reached a wider market.

Nürnberg was indeed the major European centre for the manufacture of scientific instruments during Dürer’s lifetime but scientific instrument makers and goldsmiths are two distinct professional groups, so Luecking’s argument falls rather flat, although of course Dürer would have well acquainted with the astrolabes made by his mathematical friends. Astrolabes are of course both astrological and astronomical instruments and astrology did not slip into astronomy during the 16th century. In fact the 16th century is regarded by historians as the golden age of astrology.

There now follows another excurse on the epicycle-deferent model of planetary orbits as a lead up to the articles thrilling conclusion.

In his 1525 book Die Messerung (On Measurement), Dürer presents an instrument of his own design used to draw these and other more general curves. This compass for drawing circles upon circles consisted of four telescoping arms and calibrated dials. An arm attached to the first dial could rotate in a full circle, a second arm fixed to another dial mounted on the end of this first arm could rotate around the end of the first arm, and so on.

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Dürer’s four arm compass

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Underweysung der Messung mit dem Zirkel und Richtscheyt Title Page

The title of Dürer’ 1525 book is actually Underweysung der Messung mit dem Zirckel und Richtscheyt (Instructions for Measuring with Compass and Straightedge). It is a basic introduction to geometry and its applications, which Dürer wrote when he realised that his Vier Bücher von Menschlicher Proportion was too advanced for the artist apprentices that he thought should read it. The idea was first read and digest the Underweysung then read the Vier Bücher von Menschlicher Proportion.

Luecking tells us that:

As a trained metalsmith, Dürer possessed the expertise to craft this complex tool. Precision calibration and adjustable arms allowed its user to plot an endless number of curves by setting the length of each telescoping arm and determining the rate at which the arms turned. This, in effect, constituted manual programming by setting the parameters of each curve plotted.

As a teenager Dürer did indeed serve an apprenticeship under his father as a goldsmith, but immediately on completing that apprenticeship he undertook a second apprenticeship as a painter with Michael Wolgemut from 1486 to 1490 and dedicated his life to painting and fine art printing. Luecking has already correctly stated that Nürnberg was the major European centre for scientific instrument making and Dürer almost certainly got one of those instrument makers to produce his multi-armed compass. Luecking describes the use to which Dürer put this instrument in drawing complex geometrical curves. He then goes on to claim that Dürer might actually have constructed it to draw the looping planetary orbits produced by the epicycle-deferent model. There is absolutely no evidence for this in the Underweysung and Luecking’s speculation is simple pulled out of thin air.

To summarise for those at the back who haven’t been paying attention. Dürer did not absorb scientific methods in Italy. He did not abandon astrology for astronomy. He didn’t publish Masha’Allah’s De scientia motus orbis, Johannes Stabius did. Dürer only bought ten of Regiomontanus’ manuscripts and not his entire library. The Stabius-Dürer world map was not “the first map of the world portraying the earth as a sphere”. The Stabius–Dürer–Heinfogel star charts were the first star-charts printed in Europe but by no means the first ones published. Star charts are as much astrological, as they are astronomical. Astrology did not slip into astronomy in the 16th century, which was rather the golden age of astrology. There is absolutely no evidence that Dürer’s multi-arm compass, as illustrated in his geometry book the Underweysung, was ever conceived for drawing the looping orbits of epicycle-deferent planetary models, let alone used for this purpose.

It comes as no surprise that Stephen Luecking is not a historian of mathematics or art for that matter. He is the aged (83), retired chairman of the art department of DePaul University in Chicago.

Whenever I come across an article as terrible as this one published by a leading scientific publisher in a journal from a major mathematical organisation such as the MAA I cringe. I ask myself if the commissioning editor even bothered to read the article; it was certainly not put out to peer review, as any knowledgeable Dürer expert would have projected it in an elegant geometrical curve into his trashcan. Above all I worry about the innocent undergraduates who are subjected to this absolute crap.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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

Conversations in a sixteenth century prison cell

Science writer Michael Brooks has thought up a delightful conceit for his latest book.* The narrative takes place in a sixteenth century prison cell in Bologna in the form of a conversation between a twenty-first century quantum physicist (the author) and a Renaissance polymath. What makes this conversation particularly spicy is that the Renaissance polymath is physician, biologist, chemist, mathematician, astronomer, astrologer, philosopher, inventor, writer, auto-biographer, gambler and scoundrel Girolamo Cardano, although Brooks calls him by the English translation of his name Jerome. In case anybody is wondering why I listed autobiographer separately after writer, it is because Jerome was a pioneer in the field writing what is probably the first autobiography by a mathematician/astronomer/etc. in the Early Modern Period.

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Portrait of Cardano on display at the School of Mathematics and Statistics, University of St Andrews. Source: Wikimedia Commons

So what do our unlikely pair talk about? We gets fragments of conversation about Jerome’s current situation; a broken old man rotting away the end of his more than extraordinary life in a prison cell with very little chance of reprieve. This leads to the visitor from the future, relating episodes out of that extraordinary life. The visitor also picks up some of Jerome’s seemingly more strange beliefs and relates them to some of the equally, seemingly strange phenomena of quantum mechanics. But why should anyone link the misadventures of an, albeit brilliant, Renaissance miscreant to quantum mechanics. Because our author sees Jerome the mathematician, and he was a brilliant one, as the great-great-great-great-great-great-great-great-great-great-great-great-great grandfather of quantum mechanics!

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As most people know quantum mechanics is largely non-deterministic in the conventional sense and relies heavily on probability theory for its results. Jerome wrote the first mathematical tome on probability theory, a field he entered because of his professional gambling activities. He even included a section about how to cheat at cards. I said he was a scoundrel. The other thing turns up in his Ars Magna (printed and published by Johannes Petreius the publisher of Copernicus’ De revolutionibus in Nürnberg and often called, by maths historians, the first modern maths book); he was the first person to calculate with so-called imaginary numbers. That’s numbers using ‘i’ the square root of minus one. Jerome didn’t call it ‘i’ or the numbers imaginary, in fact he didn’t like them very much but realised one could use them when determining the roots of cubic equation, so, holding his nose, that is exactly what he did. Like probability theory ‘i’ plays a very major role in quantum mechanics.

What Michael Brooks offers up for his readers is a mixture of history of Renaissance science together with an explanation of many of the weird phenomena and explanations of those phenomena in quantum mechanics. A heady brew but it works; in fact it works wonderfully.

This is not really a history of science book or a modern physics science communications volume but it’s a bit of both served up as science entertainment for the science interested reader, lay or professional. Michael Brooks has a light touch, spiced with some irony and a twinkle in his eyes and he has produced a fine piece of science writing in a pocket-sized book just right for that long train journey, that boring intercontinental flight or for the week in hospital that this reviewer used to read it. If this was a five star reviewing system I would be tempted to give it six.

*  Michael Brooks, The Quantum Astrologer’s Handbook, Scribe, Melbourne & London, 2017

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Filed under Book Reviews, Early Scientific Publishing, History of Astrology, History of Astronomy, History of Physics, Renaissance Science, Uncategorized