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Maximilian and the Mathematici–astrology as political propaganda

For a long time most historians of science tried their best to ignore the history of astrology, basically sweeping it under the carpet where and when it poked its nose into their area of study. More recently this began to change with more and more historians acknowledging that astrology played a role in a large part of human history, although  most of them still treated it as some sort of largely irrelevant side issue that one could mention in passing, if necessary, and then safely ignore. However in large phases of European history astrology permeated all levels of society and was just as much a central factor of life as religion or politics. This was certainly very much the case in the Renaissance. A number of historians have begun to examine in depth the role that astrology played and present their findings in books and articles; one such book is Darin Hayton’s The Crown and the Cosmos: Astrology and the Politics of Maximilian I.[1]

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Maximilian I (1486–1519) was an Austrian Habsburg, who was King of the Romans (also known as King of the Germans) from 1486 and Holy Roman Emperor from 1508 until his death.

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Albrecht Dürer – Portrait of Maximilian I Source: Wikipedia Commons

Through marriage he became Duke of Burgundy and his son Philip the Handsome through his marriage to Joanna of Castile, arranged by Maximilian, established the Spanish Habsburg dynasty. As such Maximilian played a very important role in late medieval European history. Throughout his life Maximilian was involved in complex and protracted political and military campaigns and Hayton’s book illustrates in detail how Maximilian used astrology as political propaganda to further his aims in those multifarious campaigns.

Throughout his life Maximilian was associated with and actively promoted a significant number of well-known astrological mathematici, several of whom have over the years featured in various blog posts here. As Hayton explains, through his active promotion of the astrologers Maximilian wanted to present himself as a knowledgeable man of science, as erudite and educated. Maximilian’s close connection with astrology began with his birth, when his parents, the Holy Roman Emperor, Frederick III and Eleanor, infanta of Portugal, requested Regiomontanus to cast Maximilian’s natal horoscope. Regiomontanus was only twenty-three years old at the time. Regiomontanus’ teacher Peuerbach had been an astrological advisor to Frederick for some time and had cast Eleanor’s horoscope before the royal marriage.

In the early phase of his career Maximilian used the humanist scholars, Joseph Grünpeck (c. 1473–after 1530) (author of one of the first texts on the French Disease aka syphilis)

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Only known portrait of Joseph Grünpeck – artist unknown

and Sebastian Brant (1457–1521) (author of Das Narrenschiff (Ship of Fools))

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Sebastian Brant by Albrecht Dürer Source: Wikimedia Commons

to employ their poetical and astrological skills in helping him to create idealised works of autobiography presenting Maximilian as he whished to be viewed as a future Holy Roman Emperor. This was part of a much wider astrological propaganda campaign presenting Maximilian, as the ideal candidate for the position of power.

In a second element of his campaign Maximilian revitalised the University of Vienna, returning it to the high status it had when Georg Peuerbach (1423–1461) and Johannes Regiomontanus (1436–1476) represented the first Viennese School of Mathematics, as the heirs of Johannes von Gmunden (c. 1380–1442). A period, which had ended in 1561 when Peuerbach died and Regiomontanus left Vienna for Italy with Basilios Bessarion (c. 1400–­1472).

At the beginning of the sixteenth century Maximilian brought Conrad Celtis (1495–1508), the Arch-Humanist, from Ingolstadt to Vienna and established for him the Collegium poetarum et mathematicorum. Two professors for mathematics were installed Andreas Stiborius (c. 1464–1515) and Johannes Stabius (1450–1522), both also from Ingolstadt. Stabius was however soon promoted to court historian.

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Albrecht Dürer’s portrait of Johannes Stabius Source: Wikimedia Commons

The two also brought their favourite pupil with them, Georg Tannstetter (1482–1535), who would go on to make a long and successful career in Vienna.

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Georg Tannstetter Portrait ca. 1515, by Bernhard Strigel Source: Wikimedia Commons

Tannstetter would be succeeded by his own pupil Andreas Perlach (1490–1551). These men constitute the so-called second Viennese School of Mathematics.

Having dealt with Maximilian’s use of astrology in his autobiographies and his political propaganda in the opening chapters, Hayton deals in successive chapters with the various aspects of astrology–teaching of the subject, astrological instruments, wall calendars and practica, ephemerides, prognostications–and how these were used by their producers to support and enable Maximilian’s political aims and ambitions. This is all down in substantive detail illustrating nicely how the work of the mathematici and their patron created a symbiosis serving the needs of both sides. In the chapter on Perlach and his ephemerides Hayton gives a very nice analysis of Perlach’s readers, based on the hand written marginalia found in the surviving copies of his texts.

It should be noted that this service of the Viennese mathematicians did not end with Maximilian’s death in 1519. Both Tannstetter and Perlach carried on producing their astrological publications in the political interest of the Habsburgs for Maximilian’s grandsons, Ferdinand Archduke of Austria (1503–1564) and Charles V (1500–1558) Holy Roman Emperor and Emperor of the Spanish Empire, Maximilian was predeceased by their father, his son Philip the Handsome.

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Ferdinand Archduke of Austria Portrait by Hans Bocksberger the Older Source: Wikimedia Commons

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Charles V by Juan Pantoja de la Cruz Source: Wikimedia Commons

The book is nicely illustrated with grey tone reproductions of the texts and their illustration from the various publications. There are extensive, informative endnotes, an equally extensive bibliography of primary and secondary sources and a useful index.

Hayton has written an important study on the political use of astrology by those in a centre of power during the Renaissance that can be profitably be read in tandem with Monica Azzolini’s The Duke and the Stars, which I reviewed some time ago. As Hayton says in his introduction historians of the period need to include the history of astrology in their studies and historians of astrology need to look more closely at the general historical picture. Hayton has excellently fulfilled his own demand.

 

 

 

[1]Darin Hayton, The Crown and the Cosmos: Astrology and the Politics of Maximilian I, University of Pittsburgh Press, Pittsburgh, 2015

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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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Filed under Book Reviews, History of Astronomy, History of Mathematics, Uncategorized

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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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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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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Exposing Galileo’s strawmanning

There is a widespread, highly erroneous, popular perception in the world, much loved by gnu atheists and supporters of scientism, that as soon as Petreius published Copernicus’s De Revolutionibus in 1543 the question as to which was the correct astronomical/cosmological system for the cosmos was as good as settled and that when Galileo published his Dialogo[1] everything was finally done and dusted and anybody who still persisted in opposing the acceptance of the heliocentric world view, did so purely on grounds of ignorant, anti-science, religious prejudice. Readers of this blog will know that I have expended a certain amount of energy and several thousand words over the years countering this totally mistaken interpretation of the history of astronomy in the early modern period and today I’m going to add even more words to the struggle.

Galileo is held up by his numerous acolytes as a man of great scientific virtue, who preached a gospel of empirical scientific truth in the face of the superstitious, faith based errors of his numerous detractors; he was a true martyr for science. The fact that Galileo was capable of scientific skulduggery does not occur to them, but not only was he capable of such, his work is littered with examples of it. One of his favourite tactics was not to present his opponents true views when criticising them but to create a strawman, claiming that this represents the views of his opponent and then to burn it down with his always-red-hot rhetorical flamethrower.

Towards the end of The First Day in the Dialogo, Galileo has Simplicio, the fall guy for geocentricity, introduce a “booklet of theses, which is full of novelties.” Salviati, who is the champion of heliocentricity and at the same time Galileo’s mouthpiece, ridicules this booklet as producing arguments full of “falsehoods and fallacies and contradictions” and as “thinking up, one by one, things that would be required to serve his purposes, instead of adjusting his purposes step by step to things as they are.” Galileo goes on to do a polemical hatchet job on what he claims are the main arguments in said “booklet of theses.” Amongst others he accuses the author of “setting himself up to refute another’s doctrine while remaining ignorant of the basic foundations upon which the whole structure are supported.”

The “booklet of theses”, which Galileo doesn’t name, is in fact the splendidly titled:

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English translation of the Latin title page Source: Notre Dame Press

Now most of the acolytes who fervently praise Galileo as the great defender of science against superstition probably have no idea who Johann Georg Locher was but they might well have heard of Christoph Scheiner, who was famously embroiled in a dispute with Galileo over the nature of sunspots and who first observed them with a telescope. In fact the authorship of the Mathematical Disquisitions has often falsely attributed to Scheiner and Galileo’s demolition of it seen as an extension of that dispute and it’s sequel in the pages of his Il Saggiatore.

Whereas Galileo’s Dialogo has been available to the general reader in a good English translation by Stillman Drake since 1953, anybody who wished to consult Locher’s Mathematical Disquisitions in order to check the veracity or lack thereof of Galileo’s account would have had to hunt down a 17th century Latin original in the rare books room of a specialist library. The playing field has now been levelled with the publication of an excellent modern English translation of Locher’s booklet by Renaissance Mathematicus friend, commentator and occasional guest contributor Chris Graney[2].

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Graney’s translation (Christopher M. Graney, Mathematical Disquisitions: The Booklet of Theses Immortalised by Galileo, University of Notre Dame Press, Notre Dame, Indiana, 2017)  presents a more than somewhat different picture of Locher’s views on astronomy to that served up by Galileo in the Dialogo and in fact gives us a very clear picture of the definitely rational arguments presented by the opponents to heliocentricity in the early part of the seventeenth century. The translation contains an excellent explanatory introduction by Graney, extensive endnotes explaining various technical aspects of Locher’s text and also some of the specific translation decisions of difficult terms. (I should point out that another Renaissance Mathematicus friend, Darin Hayton acted as translation consultant on this volume). There is an extensive bibliography of the works consulted for the explanatory notes and an excellent index.

The book is very nicely presented by Notre Dame Press, with fine reproductions of Locher’s wonderful original illustrations.

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Locher’s illustration to his discussion of diurnal rotation p. 32

Graney’s translation provides a great addition to his previous Setting Aside All Authority, which I reviewed here. Graney is doing sterling work in adjusting the very distorted view of the astronomical system discussion in the first half of the seventeenth century and anybody, who is seriously interested in learning the true facts of that discussion, should definitely read his latest contribution.

 

 

 

[1] By a strange cosmic coincidence the first printed copy of the Dialogo was presented to the dedicatee Ferdinando II d’Medici, Grand Duke of Tuscany 386 years ago today on 22 February 1632.

[2] At the end of my review of Setting Aside All Authority I wrote the following, which applies equally to this review; in this case I provided one of the cover blurbs for Chris’ latest book.

Disclosure; Chris Graney is not only a colleague, but he and his wife, Christina, are also personal friends of mine. Beyond that, Chris has written, at my request, several guest blogs here at the Renaissance Mathematicus, all of which were based on his research for the book. Even more relevant I was, purely by accident I hasten to add, one of those responsible for sending Chris off on the historical trail that led to him writing this book; a fact that is acknowledged on page xiv of the introduction. All of this, of course, disqualifies me as an impartial reviewer of this book but I’m going to review it anyway. Anybody who knows me, knows that I don’t pull punches and when the subject is history of science I don’t do favours for friends. If I thought Chris’ book was not up to par I might refrain from reviewing it and explain to him privately why. If I thought the book was truly bad I would warn him privately and still write a negative review to keep people from wasting their time with it. However, thankfully, none of this is the case, so I could with a clear conscience write the positive review you are reading. If you don’t trust my impartiality, fair enough, read somebody else’s review.

Addendum: The orthography of the neologism in the title was change—23,02,18— following a straw pole on Twitter

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Filed under Book Reviews, Early Scientific Publishing, History of Astronomy, History of Mathematics, Myths of Science, Renaissance Science

Juggling information

One of the parlour games played by intellectuals and academic, as well as those who like to think of themselves as such, is which famous historical figures would you invite to a cocktail or dinner party and why. One premise for the game being, which historical figure or figures would you most like to meet and converse with. As a historian of mostly Early Modern science I am a bit wary of this question, as many of the people I study or have studied in depth have very unpleasant sides to their characters, as I have commented in the past in more than one blog post. However in my other guise, as a historian of formal or mathematical logic and the history of the computer there is actually one figure, who I would have been more than pleased to have met and that is the mathematician and engineer, Claude Shannon.

A young Claude Shannon
Source: Wikimedia Commons

For those who might not know who Claude Shannon was, he was a man who made two very major contributions to the development of the computers on which I am typing this post and on which you are reading it. The first was when he at the age of twenty-one, in what has been described as the most important master’s thesis written in the twentieth century, combined Boolean algebra with electric circuit design thus rationalising the whole process and simplifying the design of complex circuitry beyond measure. The second was sixteen years later when he in his A Mathematical Theory of Communication, building, it should be added, on the work of others, basically laid the foundations of our so-called information age. His work laid out how to transmit digital signals through circuitry without loss of information. He is regarded as the über-guru of information theory, to quote Wikipedia:

 Information theory studies the quantification, storage, and communication of information. It was originally proposed by Claude E. Shannon in 1948 to find fundamental limits on signal processing and communication operations such as data compression, in a landmark paper entitled “A Mathematical Theory of Communication”.

Given that the period we live in is called both the computer age and the information age, it is somewhat surprising that the first full-length biography of Shannon, A Mind at Play,[1] only appeared this year. Having somewhat foolishly said that I would hold a public lecture in November on Vannevar Bush, who was Shannon’s master’s thesis supervisor, and Shannon, I have been reading Soni’s and Goodman’s Shannon biography, which I have to say I enjoyed immensely.

 

This is a full length, full width biography that covers both the live of the human being as well as the intellectual achievements of the engineer-mathematician. Shannon couldn’t decide which to study as an undergraduate so he did a double BSc in both engineering and mathematics. This dual course of studies is what led to that extraordinary master’s thesis. Having studied Boolean algebra in his maths courses Shannon realised that he could apply it to rationalise and simplify electrical switching when working, as a postgrad, on the switching circuits for Bush’s analogue computer, the differential analyser. It’s one of those things that seems obvious with hindsight but required the right ‘prepared mind’, Shannon’s, to realise it in the first place. It is a mark of his character that he shrugged off any genius on his part in conceiving the idea, claiming that he had just been lucky.

Shannon’s other great contribution, his treatise on communication and information transmission, came out of his work at Bell Labs as a cryptanalyst during World War II. The analysis of language that he developed in order to break down codes led him to a more general consideration of the transmission of information with languages out of which he then laid down the foundations of his theories on communication and information.

Soni’s and Goodman’s and volume deals well with the algebraic calculus for circuit design and I came away with a much clearer picture of a subject about which I already knew quite a lot. However I found myself working really hard on their explanation of Shannon’s information theory but this is largely because it is not the easiest subject in the world to understand.

The rest of the book contains much of interest about the man and his work and I came away with the impression of a fascinating, very deep thinking, modest man who also possessed a, for me, very personable sense of humour. One aspect that appealed to me was that Shannon was a unicyclist and a juggler, who also loved toys, hence the title of my review. As I said at the beginning Claude Shannon is a man I would have liked to have met for a long chat over a cup of tea.

An elder Claude Shannon
Source: Wikimedia Commons

On the whole I found the biography well written and light to read, except for the technical details of Shannon information theory, and it contains a fairly large collection of black and white photos detailing all of Shannon’s life. As far as the notes are concerned we have the worst of all possible solutions, hanging endnotes; that is endnotes, with page numbers, to which there is no link or reference in the text. There is an extensive and comprehensive bibliography as well as a good index. This is a biography that I would whole-heartedly recommend to anybody who might be interested in the man or his area of work or both.

 

 

[1] Jimmy Soni & Rob Goodman, A Mind at Play: How Claude Shannon Invented the Information Age, Simon & Shuster, New York etc., 2017

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Filed under Book Reviews, History of Computing, History of Logic, History of Technology