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.


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]


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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Filed under Book Reviews, History of Astrology, History of Astronomy, History of Technology, Uncategorized

Imre and me – a turning point

Today is once again the anniversary of the day I started this blog nine years ago. Nine years‽ I have difficulty believing that I have really churned out blog posts on a regular basis, with only minor breaks, for nine years now. It has become something of a tradition that on my blog anniversary I post something autobiographical and I have decided this year to maintain that tradition and explain why, when asked, I always name Imre Lakatos’ Proof and Refutations not just as my favourite book but as the most important/influential book in my life.

As regular readers might have gathered my life has been anything but the normal career path one might expect from a white, middle class, British man born and raised in Northeast Essex. It has taken many twists and turns, detoured down one or other dark alleyway, gone off the rails once or twice and generally not taken the trajectory that my parents and school teachers might have hoped or expected it to take.

In 1970 I went to university in Cardiff to study archaeology but after one year I decided that archaeology was not what I wanted to do and dropped out. I however continued to live in Cardiff apart from some time I spent living in Belgium and but that’s another story. During this period of my life I earned my living doing a myriad of different things whilst I was supposedly trying to work out what it was that I actually wanted to do. As I’ve said on several occasions I became addicted to the history of mathematics at the age of sixteen and during this phase of my life I continued to teach myself both the history of maths and more generally the history of science.

In 1976 my life took another left turn when I moved to Malmö in Sweden.


Image of Malmö (Elbogen) in Scania, Southern Sweden from a German book (Civitates orbis terrarum, Vol. IV, by G. Braun & F. Hogenberg) .1580 Source: Wikimedia Commons

This was not my first attempt to move to Sweden there had been another abortive attempt a couple of years earlier but that is also another story. This time the move was not instituted by me but by my then partner K. K was a qualified nursery nurse and had applied for a job looking after the children of a pair of doctors in Malmö and her application had been successful. The couple agreed to my accompanying K on the condition that to pay my part of the rent of the flat (that went with the job) I would look after their garden until such time as I found work.

So after witnessing the rained out but brilliant Bob Marley open air in Cardiff football stadium in the summer of 76, we set of for a new life in Malmö. Not having employment my role was to do the cleaning, shopping, cooking and looking after the garden, all things I had been doing for years so no sweat. This left me with a lot of spare time and it wasn’t long before I discovered the Malmö public library. The Swedes are very pragmatic about languages; it is a country with a comparatively small population that lives from international trade so they start learning English in kindergarten. The result in that the public library has lots and lots of English books including a good section on the history and philosophy of mathematics and science, which soon became my happy hunting ground. Card catalogues sorted by subject are a great invention for finding new reading matter on the topic of your choice.

At that point in life I was purely a historian of mathematics with a bit of history of science on the side but in Malmö public library I discovered two books that would change that dramatically. The first was Stephan Körner’s The Philosophy of Mathematics–mathematics has a philosophy I didn’t know that–and the second was Karl Popper’s collection of papers, Conjectures and Refutations: The Growth of Scientific Knowledge. Both found their way back to our flat and were consumed with growing enthusiasm. From that point in my life I was no longer a historian of mathematics and science but had become that strange two-headed beast a historian and philosopher of mathematics and science.

Given the fundamental difference between empirical science and logically formal mathematics my next move might seem to some to be somewhat strange. However, I began to consider the question whether it would be possible to construct a Popperian philosophy of mathematics based on falsification. I gave this question much thought but made little progress. In 1977, for reasons I won’t expand upon here, we returned to the UK and Cardiff.

In Cardiff I continued to pursue my interest in both the histories and philosophies of mathematics and science. In those days I bought my books in a little bookshop in the Morgan Arcade in Cardiff.


Morgan Arcade Source: Wikimedia Commons

One day the owner, whose name I can’t remember but who knew my taste in books said, “I’ve got something here that should interest you” and handed me a copy of Imre Lakatos’ Proofs and Refutations: The Logic of Mathematical Discovery[1]. I now for the first time held in my hands a Popperian philosophy of mathematics or as Lakatos puts it a philosophy of mathematics based on the theories of George Pólya, Karl Popper and Georg Hegel, a strange combination.


This is still the copy that I bought on that fateful day in the small bookshop in the Morgan Arcade forty plus years ago

Lakatos was born Imre Lipschitz in Debrecen, Hungary in 1922. He studied mathematics, physics and philosophy graduating from the University of Debrecen in 1944. Following the German invasion in 1944 he formed a Marxist resistance group with his girlfriend and later wife. During the occupation he changed his Jewish name to Molnár to avoid persecution. After the War he changed it again to Lakatos in honour of his grandmother, who had died in Auschwitz. After the War he became a civil servant in the ministry of education and took a PhD from the University of Debrecen in 1948. He also studied as a post doc at the University of Moscow. Involved in political infighting he was imprisoned for revisionism from 1950 to 1953. One should point out that in the post War period Lakatos was a hard-line Stalinist and strong supporter of the communist government. His imprisonment however changed his political views and he began to oppose the government. Out of prison he returned to academic life and translated Georg Pólya’s How to Solve It[2] into Hungarian. When the Russians invaded in 1956, Lakatos fled to the UK via Vienna. He now took a second PhD at the University of Cambridge in 1961 under R.B. Braithwaite. In 1960 he was appointed to a position at the LSE where he remained until his comparatively early death at the age of 51 in 1974.


Library of the London School of Economics and Political Science – Professor Imre Lakatos, c1960s Source: Wikimedia Commons

The book that I had acquired is a large part of Lakatos’ 1961 PhD thesis, published in book form posthumously[3], and extends Popper’s philosophy of logical discovery into the realm of mathematics. In his seminal work The Logic of Scientific Discovery, (which I had read shortly after discovering his Conjectures and Refutations) Karl Popper moved the discussion in the philosophy of science from justification to discovery. Most previous work in the philosophy of science had been devoted to attempting to justify the truth of accepted scientific theories; Popper’s work was concerned on a formal level at how we arrive at those theories. The same situation existed in the philosophy of mathematics. Philosophers of mathematics were concerned with the logical justification of proven mathematical theorems. Lakatos turned his attention instead to the historical evolution of mathematical theorem.

Proofs and Refutations is written in the form of a Socratic dialogue, although the discussion has more than two participants. A teacher and his class, the students all have Greek letters for names, who are trying to determine the relationship between the number of vertices, edges and faces in polyhedra, V-E+F = 2; a formula now known as the Euler characteristic or Euler’s Gem[4]. The discussion in the class follows and mirrors the evolution in spacial geometry that led to the discovery of this formula. Lakatos giving references to the historical origins of each step in the footnotes. The discussion takes the reader down many byways and cul de sacs and on many detours and around many corners where strange things are waiting to surprise the unwary reader.

The book is thoroughly researched and brilliantly written: erudite and witty, informative on a very high level but a delight to read. I don’t think I can express in words the effect that reading this book had on me. It inspired me to reach out to new heights in my intellectual endeavours, although I knew from the very beginning that I could never possibly reach the level on which Lakatos resided. Before reading Proofs and Refutations, history of mathematics had been a passionate hobby for me; afterwards it became the central aim in my life. I applied to go back to university in Cardiff to study philosophy, having already matriculated six years earlier to study archaeology this meant a one to one interview with a head of department. I completely blew the interview; I always do!

In 1980 I moved to Germany and in 1981 I applied to go to university in Erlangen to study mathematics, which I was able to do after having spent a year learning German. I wanted to choose philosophy as my subsidiary, which meant an interview with a professor. The man I met was Christian Thiel, a historian of logic and mathematics although I didn’t know that at the time, who was just starting his first year as professor, although he had earlier studied in Erlangen. We clicked immediately and although he no longer remembers on that day we discussed the theories of Imre Lakatos. As I documented here Christian Thiel became my mentor and is indirectly more than somewhat responsible for this blog

I have read a lot of books in my life and I continue to do so, although now much more slowly than in the past, but no book has ever had the same impact on me as Proofs and Refutations did the first time I read it. This is why I always name it when asked questions like, what was the most important book you have read or what is your all time favourite book.


[1] Imre Lakatos, Proofs and Refutations: The Logic of Mathematical Discovery, eds. John Worrall and Elie Zahar, CUP, Cambridge etc., 1976

[2] How to Solve It is a wonderful little volume describing methods for solving mathematical problems; its methodology can also be used for a much wider range of problems and not just mathematical ones.

[3] Part of the thesis had been published as a series of four papers paper under the title Proofs and Refutations in The British Journal for the Philosophy of Science, 14 1963-64. The main part of the book is an expanded version of those original papers.

[4] I recommend David S. Richeson, Euler’s Gem, University Press Group Ltd., Reprint 2012

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History of astronomy – reading the classics

Most non-specialists get their knowledge of the history of astronomy from general surveys of the subject or from even more general surveys of the history of science. The information contained in these on Ptolemaeus, Copernicus and the other boys in the history of astronomy band is often from secondary if not tertiary or even quaternary sources and as a result also often inaccurate if not completely false. The solution to this problem is of course to read the originals but not all of us are blessed with the linguistic abilities necessary to tackle second century Greek or Early Modern Latin, to say nothing of Galileo’s seventeenth century Tuscan. However, the current scholar interested in the classical texts from the history of astronomy is blessed with modern, annotated English translations of these and in this post I want to briefly present these and some secondary literature to assist in understanding them.

We start with the mother load lode, Ptolemaeus’ Mathēmatikē Syntaxis more commonly known by its Arabic name, the Almagest.


A imaginary portrait of Ptolemaeus from 1564 Source: Wikimedia Commons

This is by no means the earliest astronomical text in the European tradition but much of what we know about ancient Greek astronomy we only know through references by Ptolemaeus. He is of course preceded by the Babylonians and the ancient Egyptians but neither of these traditions has a comparable text to Mathēmatikē Syntaxis. Also Ptolemaeus stands patron for a tradition in astronomical observation, calculation and recording that remained largely unchanged for fifteen hundred years down to the work of the first Astronomer Royal, John Flamsteed. The methods were over the centuries refined but remained fundamentally the same. Even the invention of the telescope did not initially change much in the methodology of astronomy to be found in Ptolemaeus’ Great Treatise, a title for the work that is the origin of the Arabic name.

There is an excellent, annotated, English translation of Ptolemy’s Almagest by G.J. Toomer.[1] Even with Toomer’s excellent guidance the Almagest is not an easy text for non-specialists to comprehend so readers might find the following secondary literature useful. We start with Olaf Pedersen’s A Survey of the Almagest.[2] Pedersen (1920–1997) was one of the best historians of astronomy for antiquity and the Middle Ages and his opinions are always well founded. I would also recommend Liba Taub’s Ptolemy’s Universe: The Natural Philosophical and Ethical Foundations of Ptolemy’s Astronomy[3] for some solid background to Ptolemaeus’ work.

We now take a major jump of fourteen hundred years to CopernicusDe revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres), published in Nürnberg in 1543 by Johannes Petreius.

Copernicus followed the layout of Ptolemaeus’ Almagest and viewed his own volume as a modern version of the Ptolemaeus’ work, so to speak. There are several English translations but the one that I would recommend is quasi the official one. In 1973, the 500th anniversary of Copernicus’ birth, The Polish Academy of Sciences started a project to produce a uniform edition of Copernicus’ extant works. As well as publishing the Latin originals they published a set of authorised translations in the main modern European languages, the English translation is Edward Rosen’s On the Revolutions.[4] For various reasons I’m not a big fan of Rosen but as a historian he really knows his Copernicus and his commentaries are very good. A useful but specialist addition to understanding De revolutionibus is Swerdlow’s and Neugebauer’s Mathematical astronomy in Copernicus’ De revolutionibus,[5] which is justifiably regarded as a classic in the history of astronomy.

Next up is my personal favourite astronomer Johannes Kepler and here we have not just one but four books that we have to consider.


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

We start with Kepler’s first ever publication the Mysterium Cosmographicum (1596). This book with its theory that the planets in their spheres are separated by the five Platonic solids appears totally bizarre to us today. However, if you want to understand Kepler’s astronomical thoughts then you should start here because its divine geometry remained Kepler’s leitmotif for all of his astronomical work. He published a second edition in 1621 following the publication of his magnum opus the Harmonice Mundi. There is an English translation of the second edition, Mysterium CosmographicumThe Secret of the Universe,[6] which is unfortunate no longer in print.


Kepler’s Platonic solid model of the Solar system from Mysterium Cosmographicum (1596) Source: Wikimedia Commons


From the point of view of modern astronomy, much more important is Kepler’s Astronomia nova, which contains his first two laws of planetary motion and the story of how he arrived at them. There is an excellent annotated English translation of this book from William Donahue.[7] I would also recommend James Voelkel’s The Composition of Kepler’s Astronomia nova potential readers,[8] which explains the strange narrative structure of Kepler’s book and why he employed it. Donahue has also published a short introduction to the Astronomia nova for students.[9]

Kepler regarded his Harmonice Mundi as his astronomical magnum opus. A big sprawling book it covers a wide range of topics that I sketched in a blog post here. It is of course most famous for containing his third law of planetary motion. There is an excellent, annotated English translation by E.J. Aiton, A.M. Duncan and J.V. Field.[10]

Our fourth astronomical book from Kepler book is his Epitome Astronomiae Copernicanae published in three sections 1618, 1620 and 1621. Unfortunately only a part of this book (Books VI & V of seven) is available in English translation.[11]

The counterpart to Kepler is of course Galileo Galilei and he has been much better served by his translators.


Galileo Galilei. Portrait by Leoni Source: Wikimedia Commons

We start with the book that established his reputation the Sidereus Nuncius. Here we have an excellent annotated translation by Albert van Helden.[12] Galileo is of course famously erudite and highly readable and so one doesn’t initially need any secondary literature to understand him. However, the reader is warned that Galileo is anything but honest in published works and one should check with the vast secondary Galileo literature before taking anything he say as true, in particular about supposed rivals. His infamous Dialogo has long been available in a standard English translation by Stillman Drake.[13]

For our final classic we spring to the end of the seventeenth century and Isaac Newton’s Principia.


This a copy of a painting by Sir Godfrey Kneller (1689). Source: Wikimedia Commons

The best English translation can be acquired in one volume with the best introduction to the text by one of its translators I. Bernard Cohen.[14] The two, guide and Principia, are available as separated volumes if you prefer. For those who find Newton heavy going despite Cohen’s assistance there is Chandrasekhar’s Newton’s Principia for the common reader.[15] Also recommended is The Cambridge Companion to Newton.[16]

I own most of the books that I have listed here but I won’t claim to have read them from cover to cover. (I have read the Harmonice Mundi from cover to cover!) However when reading about the history of astronomy I find it useful and informative to check what a particular scholar actually said rather than what somebody else thinks they said.

A couple of more general histories of astronomy that I would recommend for the wanna be historian of the subject as starting points and to provide a more general background into which to place the classics that I’ve listed above are John North’s Cosmos,[17] the Cambridge Illustrated History of Astronomy,[18] Linton’s From Eudoxus to Einstein,[19] and Crowe’s Theories of the World.[20]

By the time you’ve worked your way through that lot you can start your own history of astronomy blog – happy reading!

[1] Ptolemy’s Almagest, Translated and Annotated by G.J. Toomer, with a foreword by Owen Gingerich, Princeton University Press, Princeton, New Jersey, 1998

[2] Olaf Pedersen, A Survey of the Almagest, Odense University Press, 1974.

[3] Liba Taub, Ptolemy’s Universe: The Natural Philosophical and Ethical Foundations of Ptolemy’s Astronomy, Open Court Publishing Company, Chicago, 1993

[4] Nicolas Copernicus Complete Works, On the Revolutions, translation and commentary by Edward Rosen, The Johns Hopkins University Press, Baltimore & London, 1978

[5] Swerdlow, N.M., O. Neugebauer: Mathematical astronomy in Copernicus’ De revolutionibus, Springer, New York, 1984

[6] Johannes Kepler, Mysterium CosmographicumThe Secret of the Universe, (Facsimile of 2nd ed., 1621, and English translation on facing pages) translated by A.M. Duncan, introduction and commentary by E.J. Aiton, preface by I: Bernard Cohen, Abaris Books, New York, 1981

[7] Johannes Kepler, Astronomia Nova (New Revised Edition), translated by William H. Donahue, Green Lion Press, Santa Fe, 2015

[8] James Voelkel, The Composition of Kepler’s Astronomia nova, Princeton University Press, Princeton, 2001

[9] Selections from Kepler’s Astronomia Nova, A science Classics Module for Humanities Studies, Selected, translated, and annotated by William H. Donahue, Green Cat Books, Santa Fe, 2008

[10] 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

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

[12] Galileo Galilei, Sidereus Nuncius or The Sidereal Messenger, Translated with introduction, conclusion, and notes by Albert Van Helden, University of Chicago Press, Chicago and London, 1989

[13] Galileo, Dialogue Concerning the Two Chief World Systems, Translated with revised notes by Stillman Drake, University of California Press, Berkley, Los Angeles, London, 1967

[14] 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.

[15] Subramanyan Chandrasekhar, Newton’s Principia for the Common Reader, Clarendon Press, Oxford, 1995

[16] The Cambridge Companion to Newton, 2nd edition, ed. Robert Iliffe and George E. Smith, Cambridge University Press, Cambridge, 2016

[17] John North, Cosmos: An Illustrated History of Astronomy and Cosmology, University of Chicago Press, Chicago & London, 2008

[18] The Cambridge Illustrated History of Astronomy, ed. Michael Hoskin, Cambridge University Press, Cambridge, 1997

[19] C.M. Linton, From Eudoxus to Einstein: A History of Mathematical Astronomy, CUP, Cambridge etc., 2004

[20] Michael J. Crowe, Theories of the World: From Antiquity to the Copernican Revolution, Dover Publication Ltd., New York, 2001


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Getting Hooke wrong!

I actually have a finished blog post lined up for this week but somebody on twitter linked to a website called ThoughtCo. and the post, Robert Hooke Biography (1635 – 1703), which I skim read. A couple of the statements about microscopes and telescopes brought out my inner Hist_Sci HulkTM and I couldn’t resist, so you are getting a bonus blog post to make up for the lack of one last week.

ThoughtCo. tells us that:

 He invented the compound microscope and Gregorian compound telescope.


Hooke’s microscope, from an engraving in Micrographia. Source: Wikimedia Commons

Now, long time readers of this blog will perhaps remember that I wrote a post celebrating Hooke’s Micrographia in which I outlined the history of the microscope in the seventeenth century. The very first microscopes that appeared in the second decade of the seventeenth century, more than twenty years before Hooke was born, were compound microscope and we don’t actually know who should be credited for its invention. I suggested that several people, like Galileo, accidentally looked through a Dutch or Galilean telescope the wrong way, noticed the diminution and went on from there to develop purpose built microscopes. We do know that the Keplerian microscope, two convex lenses, was invented by Cornelis Drebbel in 1621.

As far as the Gregorian (compound) telescope (I’m not sure what the word compound is doing in there) the name of the inventor might just possibly be deducible from the name of the telescope. It was of course not Hooke but James Gregory who first thought out this piece of optical hardware. Hooke apparently earns the honours for having constructed the first working model of a Gregorian telescope, something that its inventor had failed to do.


James Gregory artist unknown Source: Wikimedia Commons

Further on in the article ThoughtCo. informs us that:

In 1665, Hooke used his primitive compound microscope to examine the structure in a slice of cork. He was able to see the honeycomb structure of cell walls from the plant matter, which was the only remaining tissue since the cells were dead. He coined the word “cell” to describe the tiny compartments he saw. This was a significant discovery because prior to this, no one knew organisms consisted of cells. Hooke’s microscope offered a magnification of about 50x. The compound microscope opened up a whole new world to scientists and marked the beginning of the study of cell biology.

Hooke did indeed apply the word cell to the walled in empty spaces that he observed in a slice of cork because as he said they reminded him of monk’s cells in a monastery. To claim that he or anybody else deduced from this that organisms consisted of cells is a step too far. All Hooke showed was that a slice of cork has empty cell like structures; the study of cell biology didn’t take off until the nineteenth century long after Hooke gave the organic cell its name.


Schem. XI – Of the Schematisme or Texture of Cork, and of the Cells and Pores of some other such frothy Bodies. Source: National Library of Wales via Wikimedia Commons

The same paragraph continues as follows:

 In 1670, Anton van Leeuwenhoek, a Dutch biologist, first examined living cells using a compound microscope adapted from Hooke’s design.

Anton van Leeuwenhoek was a draper and amateur microscopist, calling him a biologist is not only incorrect but also misleading.


Portrait of Anthonie van Leeuwenhoek (1632-1723) by Jan Verkolje Source: Wikimedia Commons

Whatever else van Leeuwenhoek examined it is also incorrect and again somewhat misleading to say that he examined living cells. His main discoveries were bacteria and spermatozoa. The real hammer here is in the claims about van Leeuwenhoek’s choice of optical instrument. He definitely did not use a “compound microscope adapted from Hooke’s design.” Van Leeuwenhoek is famous for the fact that he made all of his ground-breaking discoveries uses high powered single lens microscopes that he designed and constructed himself. In fact when the Royal Society began to publish his discoveries in their Philosophical Transactions, it was Hooke who constructed single lens microscopes based on van Leeuwenhoek’s design.


A replica of a microscope by van Leeuwenhoek Source: Wikimedia Commons

ThoughCo. Writes the following about itself:

ThoughtCo, a Dotdash brand, is an education website that launched in March of 2017. Dotdash is a trusted media company that has been in operation since 1997 and is part of the IAC family of websites.

We take pride in the content that we create for our readers and strive to make our articles trustworthy and reliable.

They obviously don’t strive very hard or very successfully.



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My #histSTM Internet family

I came late to computers, no teenage Commodores or Ataris for me, which is slightly ironic as I was well versed in the history of computing and computers long before I owned one. I first launched myself into the murky waters of the Internet about twelve years ago. It was not long before I discovered that there were people on the Internet, who shared my love and fascination for the history and philosophy of mathematics and science. Almost exactly nine years ago I then launched this blog, see the blogiversary post next week, and officially joined the #histSTM Internet community. Over the years I have tried to hold to writing at least one substantive blog post a week, as a matter of self-imposed writing discipline. This is with the background thought that if I skip a week then I’ll probably skip two and finally, because of lack of inertia, grind to a halt. Knowing that I have a couple of loyal and regular readers I imagine that some of them might even have expectations and not wishing to disappoint them, when I know for some reason that I can’t post in the coming week or weeks, I usually announce the fact.

This was the case last week, as at very short notice I was ordered back into hospital for a second operation. The response to that short announcement on Twitter and Facebook was both mind-blowing and humbling. Over the years I have become an integral part of the large Internet #histSTM community and that community rose up to the occasion with friendliness and warmth on an extremely high level. Their kind words and well-wishes sustained and supported me through the hours and days in my hospital bed and left me feeling good despite everything.

I can’t really express in words the gratitude that I feel towards all the historians, philosophers, curators, scientists and just plain good people, who sent me their positive thoughts and wishes at this low point in my life. I’ll just say from the bottom of my heart that you are all wonderful and I love every single one of you. Thank you!



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Taking some time off!


Just spent a very tiring and frustrating day undergoing test and filling in forms in order to be admitted to hospital tomorrow morning at 6:30am! This means there will no blog post this week and possible not next week either, we’ll have to see.

To fill in the time you could read Karl Galle’s excellent Copernicus guest post if you have already done so, or my guest post on Forbidden Histories on astronomy & astrology.

In the mean time I wish all my readers a good time and promise that I will be back in the not too distant future.


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Publish and Perish

As I announced yesterday I am playing away this week with a tasty post on astrology and astronomy on the excellent Forbidden Histories blog site. However the substitute bank here at The Renaissance Mathematicus is filled with the finest from the fine. This week stepping up to the plate is mega historian of Early Modern science and Renaissance Mathematicus friend, Karl Galle, brought to you all the way from the sunny streets of Cairo (we are truly international here).

 Some time ago I realised that although I specialise in the history of Renaissance astronomy, I have up till now written no substantive biographical post about Nicolaus Copernicus. Now potted biography posts are one of my specialities and I have written them about almost everyone of significance in the Renaissance astronomy crew but not of the good old Nicky. Whilst I was pondering how I could best correct this omission, It occurred to me that my #histsci buddy Karl is currently engaged in researching and writing a modern biography of the Cannon of Frombork Cathedral. Knowing no shame, I immediately contacted Karl and suggested that he could take on the task in hand as a Renaissance Mathematicus guest blogger. With enough arm-twisting and the promise of an undisclosed number of free beers next time he is in Nürnberg he graciously agreed to write an authoritative blog post on Warmia’s most famous son. Read and enjoy!


 On May 24, 1543, Nicholas Copernicus achieved every writer’s great dream of finally holding in his hands a published copy of the book he had worked on for most of his life. Having done so, he then died that same day. Sadly, he was probably unconscious when the book was placed in his hands, as we learn from the only surviving account of his death in a letter from his best friend, Bishop Tiedemann Giese, to his only student, Georg Rheticus.

I’d like to thank Thony very much for inviting me to commemorate this year’s 475th anniversary of Copernicus’s death and the publication of his book De revolutionibus orbium coelestium (“On the Revolutions of the Heavenly Spheres”) with a guest post. While I won’t attempt to match Thony’s polymathic virtuosity on all things Mathematicus related, I thought I would try and channel a bit of the blog’s myth-busting spirit by using this opportunity to look at a few of the stories traditionally told in connection with Copernicus’s remarkable idea that the Earth, formerly assumed to be resting naturally at the center of the cosmos, is in fact both rotating on its axis and moving at high speed around the sun.


Figure 1: Copernicus’s manuscript diagram of the cosmos, showing the Sun at the center and the Earth and Moon in sphere #5, from the digitized autograph copy at the Jagiellonian University Library in Cracow.

Myth #1: Debates over the Copernican theory are central to understanding Copernicus’s own life and work.

It should be an obvious point given the timing of Copernicus’s death, but virtually the entire debate over the heliocentric theory took place posthumously and without further participation by the theory’s original author. The most famous episodes occurred more than half a century later. While many writers did discuss Copernicus’s mathematical models – usually with high praise – in the early years after De revolutionibus appeared, the next really detailed defense of the heliocentric theory didn’t appear in print until 1596 with Johannes Kepler’s Mysterium Cosmographicum. The Catholic Church only declared heliocentrism theologically heretical and suspended Copernicus’s book “until corrected” in 1616 (with a list of corrections approved in 1620), and Galileo’s trial for advocating the heliocentric theory took place in 1633.

All of these and many other less well-remembered episodes are fantastically interesting in their own right. For understanding the so-called Copernican revolution, however, they are the historiographical equivalent of studying the Bolshevik movement for insight into the composition of the Communist Manifesto. They provide useful lessons about the transformation and application of radical new ideas but are often profoundly misleading in regard to those ideas’ original contexts.

Kepler’s education and worldview were shaped by Protestant university reforms that had barely begun when Copernicus died, and Galileo’s trial took place under Counter-Reformation pressures dramatically different from the political and theological environment of 1543. This is before one even discusses the invention of the telescope, the huge observational programs of Tycho Brahe and others, and the extraordinary proliferation of mathematical texts and practitioners in the century after De revolutionibus, all of which were profoundly new developments from the time in which Copernicus lived and worked (1473-1543).


Figure 2: Statue of at the base of Frombork’s cathedral hill, where Copernicus lived for most of his professional life (author photograph).

Myth #2: We don’t know very much about Copernicus’s life.

One reason why historians have often spent more time examining posthumous debates over the heliocentric theory rather than Copernicus’s own era is the assumption that we don’t have much information about his life, and this is at least a moderately defensible point. Kepler, Galileo, and other canonical giants like Darwin all enjoyed the good fortune of having not just voluminous correspondence networks but great fame while they were still alive. When they died, the bulk of their manuscripts were gathered and preserved well enough to eventually become happy hunting grounds for generations of historians. By contrast, Copernicus’s posthumous renown arrived much later and after a good share of his books and personal papers had likely been dispersed. The Giese-Rheticus letter providing the date of Copernicus’s death was one of a few surviving manuscripts that were found and published by the Cracow professor Jan Brożek after he made a pilgrimage to Warmia in 1618 in search of information about Copernicus.

Nevertheless, when people say we know little about Copernicus’s life, what they really mean is we have few documents pertaining to his life as an astronomer, and therein lies one of the key differences between Copernicus and his successors. Brahe, Brożek, Galileo, Kepler, and other notable contemporaries like Christoph Clavius and Michael Maestlin occupied a diverse range of positions across universities, courts, and church institutions. What they all had in common, however, was an ability to earn a living working on subjects related to astronomy or mathematics for most of their professional careers and to have a large and technically accomplished peer group while they did so.

By contrast, as far as we know Copernicus never earned a single schilling specifically for his work in astronomy. His professional rank was as a canon serving the prince-bishopric of Warmia, and the largest portion of his surviving papers thus derive from administrative work for the church or correspondence with regional political figures. Surveying these materials, one gets the impression of a skilled but unpretentious professional who was frequently relied on to handle some of the chapter’s most challenging tasks. If you needed a contentious land dispute settled, a sensitive diplomatic communiqué drafted, or a castle’s defenses organized during a siege by invading Teutonic Knights, Copernicus was the guy who would get it done and probably not ask for a promotion when it was all over. While these documents therefore tell us almost nothing about his astronomy, they do hint at a rather rich and interesting life.


Figure 3: Remains of the castle at Olsztyn, where Copernicus organized the defenses during an invasion by the Teutonic Knights (author photograph).

Myth #3: We should still think of Copernicus as a professional astronomer.

Astronomy was unquestionably Copernicus’s main intellectual passion and the subject to which he devoted the bulk of his private study. Even when he was called on for scholarly rather than administrative tasks, however, it was probably not what his colleagues most valued. The oldest manuscript evidence of interest in his mathematical pursuits is a set of letters in 1510 from a spy who was attempting to steal one of Copernicus’s maps on behalf of the Teutonic Knights during a period of tense territorial negotiations in the years before their armies invaded and overran most of Warmia. (The fact that this spy later became Copernicus’s boss and effectively a head of state despite being a paid agent of a hostile foreign power is only one of the remarkable stories that virtually every Copernican biographer ignores simply because it doesn’t relate to astronomy.) This particular map doesn’t survive, but other non-espionage correspondence confirms that Copernicus’s map-making abilities were called on throughout his life for political and also economic purposes like delineating fishing rights.

Sometime around 1514, Copernicus wrote a now lost commentary on calendar reform, and in 1517 he finished a first draft of a treatise on currency reform that was later revised and submitted to Polish and Prussian authorities in late 1525 or early 1526. Throughout his career in Warmia he was also in demand as a personal physician to successive bishops and other patients. The point is not that any of these other responsibilities or pursuits eclipsed (so to speak) his interest in astronomy, but that if we are going to speak in anachronistic terms, it makes at least as much sense to think of Copernicus professionally not as an astronomer but as a government functionary who occasionally wore the hat of technical specialist or senior policy advisor, all while pursuing a longstanding intellectual hobby that was only indirectly relevant to his career.

Significantly, this is very much what most of his peer group looked like as well. To list only a few examples, a rare surviving letter that mentions Copernicus’s astronomical work is one from 1535 that accompanied a set of his planetary tables. The recipient of the tables, Sigismund von Herberstein, was a life-long Habsburg diplomat who published a lengthy geography and ethnography of Russia near the end of his life based on his travels to that country. The sender of the tables, Bernard Wapowski, is best remembered as a cartographer and therefore closer to Copernicus in having mathematical interests, but he served the Polish crown for most of his life and left behind a long unpublished manuscript on Polish history. Johannes Albrecht Widmanstetter, who discussed Copernicus’s theory in the Vatican gardens in 1533, spent much of his career as a papal secretary before publishing his magnum opus, a dictionary of the Syriac language, shortly before he died.

One could multiply these cases many times to illustrate how common it was for late medieval figures to produce major scholarly works while following varied careers as public officials or church leaders rather than solely university-based teachers. Even Albert de Brudzewo – frequently cited as a likely influence on Copernicus’s early astronomical studies – left his teaching post at Cracow University in order to take up a position with the Jagiellonian Grand Duke Alexander in Vilnius. The fact that Widmanstetter was invited by Pope Clement VII to explain Copernicus’s ideas, and then rewarded with a costly manuscript for doing so, also points toward one of the most persistent misperceptions about how the heliocentric theory was received during its earliest years.

Myth #4: Church leaders were unanimously horrified and opposed to Copernicus’s theory as soon as it appeared.

The 1543 letter between Rheticus and Bishop Giese also includes details about the only actual controversy that publication of Copernicus’s book sparked immediately, namely that both Giese and Rheticus were furious about an anonymous preface Andreas Osiander had attached to the work. The background behind this preface and the complaint that Giese made to the Nuremberg city council are a fascinating story of their own, but let’s pause for a moment just to consider the nature of the participants. You have on one side a Catholic bishop allying himself with a former professor from Wittenberg university (literally the birthplace of the Protestant Reformation) in a conflict with the copy editor of De revolutionibus (Osiander), a firebrand Protestant minister who had previously been reprimanded by Nuremberg’s council after publishing a pamphlet declaring the pope to be the anti-Christ. All of this was over a book that was dedicated to the pope, written by a Catholic church official, only came into existence because Wittenberg allowed one of their professors to take extended faculty leave to help bring it out, and was solicited and issued by one of the era’s greatest printers, a man renowned for publishing not just scientific but Protestant theological and musical works. One can argue all you like about the nature of Osiander’s preface, but short of throwing in a laudatory poem by Ulrich Zwingli or a posthumous endorsement by Jan Huss, it’s hard to imagine how Copernicus’s book could have featured a broader array of church figures who might have disagreed over certain aspects of the book’s merits but had very little problem supporting its appearance.

This is not to say there weren’t a few early rumblings of concern. Martin Luther is reputed to have made disparaging verbal remarks before De revolutionibus appeared about how certain people wanted to seem clever and turn astronomy upside down. However, this only counts as sharp criticism in Luther’s world if you’ve never read any of his published texts on Jews, Turks, papists, or pretty much anyone else he considered truly theologically dangerous. In Italy during the late 1540s, at least a couple of Dominican writers previewed some of the Catholic church’s later objections to Copernicus on the grounds of illogical physics and contradictions with scriptural passages, but these criticisms seem to have gained little traction at the time. As for Copernicus, other correspondence suggests that when he wrote of his fears that some people might mock his ideas, he was referencing not simply church authorities so much as “Peripatetics,” or Aristotelian philosophers whom he correctly feared might point out among other things that he hadn’t really answered all questions that would arise from the physics of a moving Earth.

The challenge of rewriting terrestrial physics to account for complex motions and then connect with the movements of the heavens would in fact occupy natural philosophers for the next century and a half. During that same period, much of Europe would tear itself apart in increasingly apocalyptic wars inflamed by religious tensions, and the potential grounds for heresy would expand to occupy philosophical domains including astronomy that had only occasionally been considered dangerous territory in centuries past. The condemnation of Galileo and the censorship of De revolutionibus were two consequences of this expanded politicization of knowledge, but this is not something that would have necessarily been predicted when Copernicus’s book first appeared in 1543. Ironically Nuremberg’s council seems to have been entirely unconcerned with the subject matter of heliocentrism, but they did investigate and censor another book that came out that same year because the Vatican’s Copernicus expert Widmanstetter wanted to publish a selection of Latin excerpts from the Qur’an. (See my comment above about episodes that are entirely ignored by Copernican biographers because anything that doesn’t explicitly mention astronomy is considered too boring to write about.)


Figure 4: Modern memorial to Copernicus in Frombork cathedral; his coffin is below the glass tile at the base (author photograph).

The afterlife of Copernicus

Copernicus died as a liked and well-respected figure to his colleagues, but not yet an unusually famous or controversial thinker among other scholars. As a new generation of astronomers worked through the lengthy text of De revolutionibus and began trying to fit its models to more accurate observations of the heavens, however, they also increasingly acclaimed Copernicus, hailing him repeatedly as “another Ptolemy” in recognition of his great mathematical abilities despite the fact that the heliocentric theory threatened to overturn Ptolemy’s old geocentric cosmos. A memorial plaque was belatedly erected in 1581 at Frombork cathedral, and Brożek copied out its text during his visit there in 1618. The exact location of Copernicus’s burial site was nevertheless forgotten until recent years when a research team located a set of remains and ingeniously matched them to Copernicus through genetic comparison with hairs found inside one of Copernicus’s former books now at Uppsala University. (Lesson to librarians – protect your rare books, but don’t clean them too well!) He was reburied beneath a tasteful modern monument in 2010, and I had the good fortune of visiting the site last fall.

One might justifiably ask why I’ve spent so much time harping about Copernicus’s era and social context rather than going into more detail about his astronomy and mathematics. There are indeed numerous interesting things to say on the latter subject, from the ongoing debates over exactly how Copernicus arrived at the heliocentric theory to the very tangible advantages his theory offered even during an era when astronomical observations were not yet precise enough to prove the empirical advantages of his individual planetary models over comparable models derived from Ptolemy.

As much as I enjoy the details of Copernicus’s astronomy, though, I think there’s a point at which exclusively focusing on the mathematics of De revolutionibus risks becoming the late medieval equivalent of writing a micro-history of free-return trajectories as if it’s the only subject worth talking about in regard to the US-Soviet space race. To say there are other topics worth discussing is not an either-or declaration of how to do history but a simple recognition that we need to understand more realistically how new knowledge takes shape and what transformations happen when it’s applied. Especially now, it’s worth resisting the regular incorporation of figures like Copernicus and Galileo into broader societal myths about how progress only happens when a tiny number of under-appreciated geniuses, working in isolation and free of interference from Big Government, acquire their wisdom through flashes of insight that spring fully formed like Athena from the head of Zeus, after which it only remains for the rest of us to appreciate their greatness rather than numbering among the benighted peasants and medieval reactionaries if we ask too many questions. If there is a lesson to be culled from the life of Copernicus and the period that followed, perhaps it is instead that understanding the cosmos is difficult, but sometimes even a few mild-mannered professionals who work well with their colleagues might get there in the end.

Karl Galle (@GalleKarl) is working on a new biography of Nicholas Copernicus that he hopes will be completed in less time than it took to write De revolutionibus. You can browse more photos from his Copernicus-related travels here.



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