Sometimes the lights are shinning on me

Other times I can barely see

Lately it occurs to me

What a long strange trip it’s been


That we regard tenth or hundredth anniversaries as being special is actually just an accident of evolution. Because we have ten fingers, we based our most commonly used counting system on the number ten. If we had twelve fingers we would celebrate twelfth and one hundred and forty-fourth anniversaries instead; can’t see many people getting a telegram from the Queen on that system. If like the Simpsons we only had three fingers on each hand, we could make whoopee every six years with an extra big party every thirty-six years.


Today the Renaissance Mathematicus turns ten–time to blow up the balloons, hang out the bunting and bake a cake. I am in somewhat of a state of denial and disbelief that I have apparently managed to keep producing almost coherent scribblings on a fairly regular basis for all of ten years. As I have oft repeated in the past, when I started I wouldn’t have given this blog more than a ten per cent chance of surviving ten weeks let alone ten years. I also wouldn’t have seriously expected to gain more than ten readers. Instead of which we have the following, I think, mind boggling set of statistics for what is, after all, more than somewhat of a niche product in the grand scheme of all things Internet.

This is the 875th post on the Renaissance Mathematicus, there have been 1,318,488 views of those posts from 629,179 visitors, who have made 8.8 thousand comments. The Renaissance Mathematicus has 5,692 followers.

I’ve never counted but a rough guestimate is that in the last ten years I’ve written something north of half a million words! That 500,000! And I still claim I couldn’t write a book!

I don’t usually look at my blog statistics, as I see them as a sort of trap. Oh my god, so many readers, am I writing the right things to satisfy them? What, so few readers I must write something more popular/attractive/controversial or whatever to make my blog more attractive. No thanks! I just write what I want to write, ignore the statistics and if somebody reads what I write, fine. If not, also fine. In other words the only reason I trotted the statistics out today is because it’s my tenth boggiversary. If you want to see the statistics again come back in another ten years, assuming I’m still going or even still alive!

When I first started writing this blog I don’t really know what my aim/motivation/purpose was in writing it. I just felt that there were some things that I had collected in the back of my brain over the decades that I might possibly unload and a blog seemed like a good way to do so. Later I began to maybe regard the blog as a sort of substitute for the career I might have had, as a historian of science but for a number of complex reasons didn’t. I can’t say exactly when but somewhere down the line I realised that The Renaissance Mathematicus is not a substitute for anything, it’s me, it’s my calling, it’s what I do. In a different age I might have become a columnist or essayist in a newspaper or journal churning out weekly vignettes and reviews on a diverse range of history of science topics. It seems that is my strength and it’s what I feel comfortable with.

One of the things that became clear to me over the years is that I operate best just being me. I managed the history of science monthly blog carnival On Giants’ Shoulders for five years and complied and collated the online, weekly history of science journal Whewell’s Gazette for three years. These activities meant that I probably read more history of sciences blogs than anybody else in the whole Internet. There were and still are some very, very good history of science writers out there. I used to think I wish I could write as well as or express myself as cleverly as a whole lot of people that I regard as my superiors and betters. Somewhere down the line I stopped comparing, they do their thing I do mine. I now accept that I am who I am and other people do it differently.

In my teens I had already become a convinced atheist, something that has over the years never changed. I find it amusing when I write pieces defending or even praising a religious scientist and self-proclaimed radical atheists accuse me of being an apologist for the Church or Christianity in general, but I digress.  In my youth I was what in England during the religious wars in the seventeenth century was called a Seeker, someone, who doesn’t acknowledge any particular group but is looking for answers. You might say I was looking for a lebensphilosophie or a moral compass or the meaning of life or just somewhere to belong, I don’t really know myself.

I read quite a lot of Western philosophy, a lot of anthropology, a lot of Buddhist and Daoist literature, a lot of esoteric literature especially on the I Ching, the novels of Hermann Hesse, Ken Kessey and Robert Heinlein, and the LSD preachings of Timothy Leary amongst many other diverse things. I also took an awful lot of drugs. I was looking for something but I don’t think I ever truly knew what it was that I was seeking. For what it’s worth my personal lebensphilosophie is a bastard mixture of Buddhism, Daoism, the Ranters[1]and sex and drugs and rock’n’roll (in my case mostly West Coast rock especially the Grateful Dead). If I had a god it would be Shiva, the god of sex, drugs, rock’n’roll and death!

Amongst the things I read were the books of Carlos Castaneda supposedly about a Native Middle American shaman Don Juan, the first of which was The Teachings of Don Juan: A Yaqui Way of Knowledge. I say supposedly because although Castaneda claimed they were factual accounts, modern scholars think they are fiction. Sometimes when you read a sentence sticks in your mind and becomes part of your personal store of knowledge. For example, somewhere in his writings Leary wrote, based on his interpretation of Vedantic philosophy, “Life is a farce, death is a farce, suicide is the ultimate farce,” a phrase that has literally saved my live a couple of times during the worst periods of my mental illness. The part of Castaneda’s writings that has remained with me and I paraphrase: Don Juan said that there are many different paths through life, it doesn’t matter which path you choose as long as it’s a path with a heart. The Renaissance Mathematicus is my path with a heart, it took me a long time to find it, but it’s never too late.

What about the future? Above I casually mentioned the next ten years but who knows? I do know that I’m not planning on quitting yet. I have enough ideas for blog posts, in petto, to keep going for at least another ten weeks.

Above I mentioned my claim that I wouldn’t be able to write a book, good for sprints but not for marathons. In fact I’m currently contemplating writing not one but two books! Some time ago a reader of my blog who is a very successful science writer offered to help me find a publisher and an editor for a printed-paper version of the blog. I suggested the way I wanted it to be done and he said that the editor would decide how to present the blog in book form. In my life I have taken a lot of left turns and even more detours but I have always decided what to do with my life and have stood by my mistakes and by god I’ve made more than a few. The blog is my baby, it is one hundred per cent my own creation and if it is going to become a book then it will be my book and not that of some editor or other. I am seriously contemplating self-publishing, my concept is to do groups of posts on related subjects–history of cartography, early Dutch science, Renaissance Nürnberg, the Renaissance mathematicus, women in science, and so on–slightly rewritten for book form with a new general introduction for each section. Working title: “The Renaissance Mathematicus Garage Sale!” One of my readers, has successfully self-published and I’m hoping that he’ll give me some tips down the line. Another reader has already offered to help me set the final text for printing, he used to do this for a living, so maybe at some point I shall be running a GoFundMe to help launch the printed version of The Renaissance Mathematicus.

It should have become fairly obvious that the current series of posts, “The emergence of modern astronomy – a complex mosaic,” is actually the abstract/sketch/backbone for a potential book. When I finish the blog post series, if I like what I have, I will rewrite, refine, improve, expand the whole thing into a book and maybe try to find a publisher, maybe self-publish. All of this is of course future dreams but as Oscar Hammerstein II once wrote, “You’ve gotta have a dream. If you don’t have a dream, how you gonna have a dream come true?”

[1]If you don’t know who the Ranters were, they were a seventeenth century religious sect, who basically preached amoralism.


Filed under Autobiographical

The emergence of modern astronomy – a complex mosaic: Part XII

Although highly anticipated the expectation placed upon De revolutionibus and the reactions to it were highly diverse and covered a very wide spectrum from complete acceptance to total rejection with many variation in between. It would be impossible in a blog post series such as this one to deal with the multitude of single reactions that would require a fairly substantial book; in fact I have two such books sitting next to my computer at the moment–Pietro Daniel Omodeo, Copernicus in the Cultural Debates of the Renaissance: Reception, Legacy, Transformation (Brill, 2014) & Jerzy Dobrzycki ed., The Reception of Copernicus’ Heliocentric Theory (D Reidel, 1972)–which I recommend to anybody who wants an in depth, blow by blow account. What I intend to do here is sketch the basic trends of that reception.

Famously Robert Westman once claimed that only ten people in the whole world accepted Copernicus’ heliocentric hypothesis, including his cosmology, completely between its publication in 1553 and the year 1600. His list actually misses a couple of total accepters such as Gemma Frisius, who acknowledged his acceptance in his foreword to Johannes Stadius’ ephemerides, and the Englishman John Feild who made the same acknowledgement in his ephemerides. However, it does include three others who either dropped or appeared to drop their acceptance. Christoph Rothmann (born between 1550 & 1560 died probably after 1600) one of Wilhelm IV’s astronomers (of which more later), who had an extensive dispute with Tycho Brahe, who of course didn’t accept Copernicus’ cosmology, on the subject and in the end, and according to Tycho was converted to his point of view.  Diego de Zúñiga (1536–1597), a Spanish Augustinian hermit and academic, who wrote a defence of the heliocentric hypothesis in his In Job commentaria (1584) but later in life rejected Copernicus’ hypothesis as incompatible with Aristotelian philosophy, probably under religious pressure from his superiors. The most peculiar renegade was Copernicus’ first and initially strongest supporter, Rheticus. Having gone quiet on Copernicus and his hypothesis for some time after he moved to Kraków, in a correspondence with Pierre de la Ramée (1515-1572) he announced that he had erected a large gnomon in Kraków and was now practicing the true astronomy of the Egyptians, whatever that might be. Summa summarum, one can say without much contradiction that there were never more than about fifteen, and probably less, true Copernican in the world before 1600 or even before 1609/10 when the publications of Kepler and the invention of the telescope became game changers.

There were a few astronomers, who simply rejected Copernicus’ hypothesis without comment and some, who simply ignored it but they won’t interest us here because the evidence shows that the vast majority did react to it in some way or another. As already mentioned earlier Owen Gingerich carried out a survey of all known surviving copies of the 1st(Nürnberg 1543) and 2nd(Basel 1566) editions of De revolutionibus[1]and his analysis of the annotation and marginalia of the readers clearly shows that the majority took very little notice of the first cosmological part of the book but concentrated their reading instead on the technical parts of the book, the mathematical models and the data.

This rejection of the heliocentric aspect of Copernicus’ work was a simple and direct consequence of the fact that he could not provide any empirical evidence to support his claims that the Earth revolved on its own axis and that it orbited a stationary Sun. Both claims very clearly contradicted the evidence of one’s own senses, we still say the Sun rises and sets, and suggested consequences that Copernicus was unable to answer. If the Earth is rotating at approximately 1600 kilometres an hour at the equator, why doesn’t everything on the surface get blown off by the headwind? And if the Earth is orbiting the Sun, why can’t we detect stellar parallax? These are just two of the possible objections to which Copernicus could not provide scientific answers.

The answers, based on assumptions, which he did propose would prove with time and new developments in science to be fundamentally correct but at the time there were merely unsubstantiated assumptions. In answer to the first he suggested that everything on the Earth’s surface would be carried along with it in some sort of envelope. This turned out to be correct but Copernicus lacked the physics necessary to explain how this would function. In fact the history of physics of the seventeenth century, as we shall see, consisted to a large extent of developing the knowledge to provide this explanation. As far as stellar parallax was concerned, or rather the lack of it, Copernicus simply and correctly assumed that the stars were simply too far away for the parallax to be detected with the naked-eye. However, Copernicus and almost all of his contemporaries still believed in the sphere of the fixed stars and if this sphere was so far away that stellar parallax was undetectable then the distance between the orbit of Saturn and the sphere of the fixed stars would have to be inconceivably vast and thus not very acceptable. Simply put, why all of that empty space out there?

The ambivalence towards Copernicus magnum opus is nicely illustrated by the Welsh mathematicus Robert Recorde (c. 1512–1558) in his The Castle of Knowledge (1556) the first English text to refer to the Copernican hypothesis. On the subject of the possible motion of the Earth he wrote:

             But as for the quietness of the earth, I need not to spend any time in proving of it, since that opinion is so firmly fixed in most men’s heads, that they accompt it mere madness to bring the question in doubt. And therefore it is as much folly to travail to prove that which no man denieth, as it were with great study to dissuade that thing which no man doth covet, neither any man allow: or to blame that which no man praiseth, neither any man liketh.

Scholar: Yet sometimes it chanceth, that the opinion most generally received, is not most true

Master: And so do some man judge of this matter, for not only Eraclides [Heraclides] Ponticus, a great Philosopher, and two great clerks of Pythagoas school, Philolaus and Ecphantus, were of the contrary opinion, but also Nicias [Hicetas] Syracusius, and Aristarchus Samius, seem with strong arguments to approve it: but the reasons are too difficult for this first Introduction, and therefore I will omit them till another time. And so I will do the reasons that Ptolemy, Theon and others do allege, to prove the earth to be without motion: and the rather, because those reasons do not proceed so demonstrably, but they may be answered fully, of him that holds the contrary. I mean, concerning circular motion: marry, direct motion out of the centre of the world seemeth more easy to be confuted, and that by the same reasons, which were before alleged for proving the earth to be in the middle and centre of the world.

Scholar: I perceive it well: for as if the earth were always out of the centre of the world, those former absurdities would at all times appear: so if at any time the earth should move out of his place, those inconveniences would then appear.

Master: That is truly to be gathered: how be it, Copernicus, a man of great learning, of much experience, and of wonderful diligence in observation, hath renewed the opinion of Aristarchus Samius, and affirmeth that the earth not only moveth circularly about its centre, but also may be, yea and is, continually out of the precise centre of the world 38 hundred thousand miles: but because the understanding of that controversy dependeth of profounder knowledge than in this Introduction may be uttered conveniently, I will let it pass till some other time.

Scholar: Nay sir in good faith, I desire not to hear such vain fantasies, so far against common reason, and repugnant to the consent of all the multitude of Writers, and therefore let it pass for ever, and a day longer.

Master: You are too young to be a good judge in so great a matter: it passeth for your learning, and theirs also that are much better learned than you to improve [i.e. disprove] his supposition by good arguments, and therefore you were best to condemn nothing that you do not well understand but another time, as I said, I will so declare his supposition, that you shall not only wonder to hear it, but also peradventure be as earnest then to credit it, as you are now to condemn it.


In this exchange Recorde appears to both reject and praise Copernicus’ hypothesis. Unfortunately we will never know his true opinion as he died before he could write the advanced text that he promises his readers here. What, however, is very clear is that Recorde is very well informed about the history of both diurnal rotation and the heliocentric hypothesis.

Some of the readers, who only considered the mathematical parts of the book, simply took Copernicus’ models for the various planets and applied them to a geocentric system, hoping thereby to produce a better predictive model for the position of the planets. Other took this remodelling a step further and using Copernicus’ mathematical models revived the Capellan model, well-known and much loved in the Middle Ages; a geocentric system in which Mercury and Venus orbit the Sun, which in turn orbits the Earth.


Naboth’s representation of Martianus Capella’s geo-heliocentric astronomical model (1573) Source: Wikimedia Commons

Others took this thought one step further and developed, what is now known the Tychonic system, named after Tycho Brahe (1546–1601), although he was by no means the first or the only astronomer to publish this system in the second half of the sixteenth century, all claiming to have developed it independently. In this helio-geocentric system all of the planets except the Moon, orbit the Sun, which together with the Moon orbits the stationary Earth. Heliocentric, geocentric and helio-centric model based on Copernicus’ parameters and mathematical model can and have been shown to be mathematically equivalent with nothing to recommend one over the other, without further information.


The Tychonic System Source: Wikimedia Commons

One interesting but slightly confusing development was that some geocentric and helio-geocentric astronomers accepted the arguments for the Earth spinning on its own axis, diurnal rotation, whilst still rejecting the Earth orbiting the Sun. As I wrote here in an earlier blog post, this idea goes back at least to Heraclides Ponticus (c.390 BCE–c.310 BCE) and was adopted or discussed and rejected many times over the centuries down to Copernicus’ times. The argument in its favour is a purely physical one. It is much simpler for the comparatively small Earth to rotate than for the vastly larger and heavier sphere of the fixed stars. This acceptance of diurnal rotation would prove to be an important steeping stone to the complete acceptance of the heliocentric model in the seventeenth century.

On major group, who showed great interest in Copernicus’ mathematics and above all in the planetary tables and ephemerides that they delivered were the astrologers. This basically means all professional and half professional astronomers, as they were almost all practicing astrologers. As stated above Robert Westman once claimed that there were only ten Copernicans in the whole world between 1543 and 1600, a historian of astrology correctly pointed out that all ten were practicing astrologers. Like Regiomontanus in the previous century (see Part II of this series) they all thought that more accurate astronomical data would improve the quality of their astronomical prognoses. Not only did they avidly consult the ephemerides of Stadius and Feild but several of them such as the Italian mathematicus Giovanni Antonio Magini (1555–1617) unsatisfied with Stadius’ and Feild’s accuracy also calculated their own new ephemerides. In the end, however, the astrologers recognised that although the errors in Copernican tables were different to those in Ptolemaic ones they were not much more accurate as we will see in the next instalment.

[1]Owen Gingerich, An Annotated Census of Copernicus’ De Revolutionibus(Nuremberg, 1543 and Basel, 1566), Brill, Leiden, Boston, Köln, 2002


Filed under History of Astronomy, Renaissance Science, Uncategorized

The House of Wisdom is a Myth

When I first got really interested in the history of science, the history of science of the Islamic empires was not something dealt with in any detail in general works on the topic. If you wanted to get to know anything much about what happened in the various areas of the world dominated by Islamic culture in the period between the seventh and sixteenth centuries then you had to find and read specialist literature produced by experts such as Edward Kennedy. Although our knowledge of that history still needs to be improved, the basic history has now reached the popular market and people can inform themselves about major figures writing in Arabic on various areas of science between the demise of classical antiquity and the European Renaissance such as the mathematician Muḥammad ibn Mūsā al-Khwārizmī, the alchemist Abū Mūsā Jābir ibn Hayyān, the optician, Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham or the physician Abū Bakr Muhammad ibn Zakariyyā al-Rāzī. These and a handful of other ‘greats’ are not as well known as their later European counterparts but knowledge of them, usually under their popular names, so al-Khwarizmi, Jabir, al-Haytham and al-Razi, is these days quite widespread amongst well educated and well read people. There is even a flourishing popular book market for titles about Islamic science.

Amongst those non-professionals, who interest themselves for the topic, particularly well known is the so-called House of Wisdom, a reputed major centre for scientific translation and research in Baghdad under the Abbasid Caliphs. This reputed academic institution even provided the title for two of the biggest selling popular books on Islamic science Jim al-Khalili’s The House of Wisdom: How Arabic Science Saved Ancient Knowledge and Gave Us the Renaissance and Jonathan Lyons’ The House of Wisdom: How the Arabs Transformed Western Civilisation. Neither Jim al-Khalili nor Jonathan Lyons is a historian of science, let alone Islamic science; al-Khalili is a physicist and broadcaster and Lyons is a journalist and herein lies the rub. Real historians of Islamic science say that the House of Wisdom never existed, at least not in any form remotely resembling the institution presented by al-Khalili, Lyons and other popular sources including, unfortunately Wikipedia, where the article is largely based on Lyons’ pop book.

The picture painted by al-Khalili and Lyons, and to be fair they didn’t create it but copied it from other fantasts, is of a special academic research institution set up by the early Abbasid Caliphs, staffed with leading scientific scholars, who carried out a sponsored programme of translating Greek scientific texts, which they them analysed, commented and developed further. Here academic exchanges, discussions, conferences took place amongst the leading scientific scholars in the Abbasid Empire.

The reality looks very different.[1]To quote Gutas (page 54):

It is in this light that the very scanty reliable reports about the bayt al-hikmashould be evaluated. Much ink has been used unnecessarily on description of the bayt al-hikma, mostly in fanciful and sometimes wishful projections of modern institutions and research projects back into the eighth century. The fact is that we have exceedingly little historical [emphasis in original] information about the bayt al-hikma. This in tself would indicate that it was not something grandiose or significant, and hence a minimalist interpretation would fit the historical record better.

The bayt al-hikma, to give it its correct name, which doesn’t really translate as house of wisdom, was the palace archive and library or repository, a practice taken over by the Abbasid Caliphs from the earlier Sassanian rulers along with much other royal court procedure to make their reign more acceptable to their Persian subjects. The wisdom referred to in the translation refers to poetic accounts of Iranian history, warfare, and romance. The Abbasid Caliphs appear to have maintained this practice now translating Persian historical texts from Persian into Arabic. There is absolutely no evidence of Greek texts, scientific or otherwise, being translated in the bayt al-hikma.

Much is made of supposed leading Islamic scientific scholars working in the bayt al-hikmaby the al-Khalili’s, Lyons et al. In fact the first librarian under the Abbasids was a well-known Persian astrologer, again a Sassanian practice taken over by the Abbasids. Later al-Khwarizmi and Yahya ibn Abi Mansur both noted astronomers but equally noted astrologers served in the bayt al-hikmaunder the Abbasid Caliph al-Ma’mun.

We will give Gutas the final word on the subject (page 59):

The bayt al-hikmawas certainly also not an “academy” for teaching the “ancient” sciences as they were being translated; such a preposterous idea did not even occur to the authors of the spurious reports about the transmission of the teaching of these sciences that we do have. Finally it is not a “conference centre for the meeting of scholars even under al-Ma’mun’s sponsorship. Al-Ma’mun, of course (and all the early Abbasid caliphs), did host scholarly conferences or rather gatherings, but not in the library; such gauche social behaviour on the part of the caliph would have been inconceivable. Sessions (magalis) were held in the residences of the caliphs, when the caliphs were present, or in private residences otherwise, as the numerous descriptions of them that we have indicate.

As a final comment we have the quite extraordinary statement made by Jim al-Khalili on the BBC Radio 4 In Our Time discussion on Maths in the Early Islamic World:

In answer to Melvyn Braggs question, “What did they mean by the House of Wisdom and what sort of house was it? It is supposed to have lasted for 400 years, it is contested”

Jim al-Khalili: “It is contested and I’ll probably get into hot water with historians but let’s say what I think of it. There was certainly potentially something called the house of wisdom a bit like the Library of Alexandria many centuries earlier, which was a place where books were stored it may have also been a translation house. It was in Baghdad this was in the time of al-Ma’mun, it may have existed in some form or other in his father’s palace…”

Bragg: “Was it a research centre, was it a place where people went to be paid by the caliphs to get on with the work that you do in mathematics?”

Al-Khalili: “I believe it very well could have been…” He goes on spinning a fable, drawing parallels with the Library of Alexandria

History is not about what you choose to believe but is a fact-based discipline. Immediately after al-Khalili’s fairy story Peter Pormann, Professor of Classics & Graeco-Arabic Studies at the University of Manchester chimes in and pricks the bubble.

Pormann: “There’s the myth of the House of Wisdom as this research school, academy and so on and so forth, basically there is very little evidence…”

Listen for yourselves!

I find Bragg’s choice of words, repeated by al-Khalili, “it is contested” highly provocative and extremely contentious. It is not contested; there is absolutely no evidence to support the House of Wisdom myth as presented by Lyons, al-Khalili et al. What we have here is another glaring example of unqualified pop historians propagating a myth and blatantly ignoring the historical facts, which they find boring.

[1]The facts in the following are taken from Dimitri Gutas, Greek Thought, Arabic Culture: The Graeco-Arabic Translation Movement in Baghdad and Early Abbasid Society (2nd–4th/8th–10th centuries), Routledge, Oxford, ppb. 1998 pp. 53-60 and Lutz Richter-Bernburg, Potemkin in Baghdad: The Abbasid “House of Wisdom” as Constructed by 1001 inventions In Sonja Brentjes–Taner Edis­–Lutz Richter-Bernburg eds., 1001 Distortions: How (Not) to Narrate History of Science, Medicine, and Technology in Non-Western Science, Biblioteca Academica Orientalistik, Band 25, Ergon Verlag, Würzburg, 2016 pp. 121-129


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

The emergence of modern astronomy – a complex mosaic: Part XI

Despite the high level of anticipation De revolutionibus cannot be in anyway described as hitting the streets running; it was more a case of dribbling out very slowly into the public awareness. There are several reasons for this. Today there is a well-oiled machine, which goes into operations when an important new book is published. Book reviews and adverts in the relevant journals and newspapers, books delivered in advance to bookshops all over the country, radio and television interviews with the author and so on.

Absolutely none of this apparatus existed in anyway in the fifteenth century. There were no journals or newspapers, where reviews and adverts could be published. Information about a new publication was distributed over the academic grapevine by mail; the grapevine was quite efficient with scholars communicating with each other throughout Europe but the mail system wasn’t. Letters often took months and quite often never arrived at all. There were no bookstores, as we know them today and no book distribution network. Petreius had a stall on the local market place but he probably would not have sold many copies of De revolutionibus in Nürnberg itself.


A 19th century painting of the Nürnberg market place

In this context it is interesting that the town library doesn’t own a copy of the 1st edition. For other sales, other than by mail, Petreius would have transported copies of the book packed into barrels to the annual fairs in Leipzig and Frankfurt, where, as well as private customers, other printer publishers would buy copies of the book to take back to their home towns to supplement their own production for their local customers. The Leipzig fair took place at Easter and in autumn, the Frankfurt fair only in autumn. Easter 1543 was in April so the distribution of De revolutionibus only really began in the autumn of that year.


Frankfurt Book Fair 1500

The next factors that slowed the reception of De revolutionibus were the price and the content. As a large book with a complex mathematical content with lots of tables and diagrams, De revolutionibus was a very expensive book putting it outside of the financial range of students or anybody without a substantial income or private fortune. A first edition bought by the astrologer Valentin Engelhart (1516-1562) in 1545 cost 1 florin = 12 groschen. A students university matriculation fees at this time cost between 6 and 10 groschens. It is indicative that Kepler could only afford to acquire a second hand copy. Owen Gingerich speculates that the high cost of the book is the reason for the comparatively high survival of copies, Gingerich estimates about fifty per cent. It was very expensive so people took good care of it. The high price and the complex contents very much limited potential sales.


De Revolutionibus woodcut of the heliocentric cosmos Source: Latin Wikisource

In terms of content this was a major, heavy duty, large-scale mathematical text and not in anyway something for the casual reader, no mater how well read. Copernicus’ Mathemata mathematicis scribuntur was meant very seriously. This suggests that the potential circle of purchasers was fairly strictly limited to the comparatively small group of mathematical astronomers, who would be capable of reading and understanding Copernicus’ masterpiece. Given his record in the field of mathematical and astronomical/astrological publishing Petreius naturally already had a group of customers to whom he could offer his latest coup in this genre, otherwise he probably would not have published De revolutionibus. However, even if he could get this very specialist book to its specialist group of readers, they would require a comparatively long time to read, work through and digest its complex contents. The earliest known published reaction to De revolutionibus was Gemma FrisiusDe radio astronomico et geometrico a booklet of a multipurpose astronomical and geometrical instrument published in 1545 two years after Copernicus’ volume.

Here at this comparatively early point Frisius, who knew of Copernicus’ hypothesis through the Narratio Prima and and had been invited by Dantiscus, Prince-Bishop of Frombork, one of his patrons, to come to Frombork and work with Copernicus, displays a very cautious attitude towards the new heliocentric astronomy although he is very critical towards Ptolemaeus’ work.


Johannes Dantiscus Source: Wikimedia Commons

Given that the main purpose of astronomy was, at this time, still to provide astronomical data for astrology, navigation and cartography many of those potentially interested in the new astronomy were waiting for new planetary tables and ephemerides before passing judgement. The earliest planetary tables, the Tabulae prutenicae (Prutenic Tables) based on De revolutionibus, but not exclusively, were produced by the professor for the higher mathematics (music and astronomy) at Wittenberg Erasmus Reinhold (1511–1553) and first published in 1551.


Source: Wikimedia Commons

These tables were financed by Albrecht I, Duke of Prussia hence the name Prutenic i.e. Prussia.


Albrecht, Duke of Prussia portrait by Lucas Cranach the elder Source: Wikimedia Commons

Interestingly Reinhold was not a supporter of heliocentricity. Ephemerides based on the Prutenic Tables were produced in the Netherlands by Johannes Stadius (1527–1579) a pupil of Gemma Frisius in 1554 with an introductory letter by his old teacher.


Johannes Stadius Source: Wikimedia Commons

A second set of ephemerides, also based on the Prutenic Tables, were produced in England by John Feild (c. 1525–1587), a pupil of John Dee (1527–1608) in 1557. Dee was another pupil of Gemma Frisius, so this might be a case of the academic grapevine in operation. These tables and ephemerides played an important roll in spreading awareness of the new heliocentric hypothesis.

Whereas with a modern publication reception will probably be judged in terms of months or even weeks for a popular book and a few years for a serious academic title; looking at De revolutionibus to judge its reception we really need to cover the sixty plus years following its publication up to the invention of the telescope, the next major game changer in astronomy.

There is a popular misconception that that reception can be quantified in terms of those for and those against the heliocentric hypothesis. This is very much not the case. As I tried to make clear at the beginning of this series the sixteenth century was very much characterised by very lively debates on various aspects of astronomy–the nature, status and significance of comet, a lively revival of the Aristotelian homocentric spheres model of the cosmos and a growing dissatisfaction with the quality of the available astronomical data. There were small smouldering fires of debate everywhere within the European astronomical community, Copernicus’ De revolutionibus turned them into a raging bush fire; the reactions to its publication were multifaceted and the suggested changes it provoked were wide-ranging and highly diverse. It would be more than a hundred years before the smoke cleared and a general consensus could be found within the astronomical community.







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Filed under Early Scientific Publishing, History of Astrology, History of Astronomy, Renaissance Science

Unsound History of the Sound of Space

Those readers, who have been around for a number of years, will know that from time to time the Renaissance Mathematicus has hosted guest posts. One thing that we are very proud of is the very high standard of the authors, who have delivered up, at our invitation, those literary #histSTM highpoints. We only host the best! Todays guest post continues this tradition with a real star of the world of science, science writing and #histSTM, Tom McLeish FRS. Tom was Professor of Physics at Durham University, where he was one of the initiators and chief investigators of the on going Ordered Universe international research project: Interdisciplinary Readings of Medieval Science: Robert Grosseteste (c.1170–1253).


!4th Century portrait of Robert Grosseteste, Bishop of Lincoln Source: Wikimedia Commons

Tom is now Professor of Natural Philosophy in the Department of Physics at the University of York (I think he’s doing a slow tour of the beautiful cathedral cities of England). His most recent, in fact very recent, publication is a book that you all should read The Poetry and Music of Science: Comparing Creativity in Science and Art (OUP, 2019).

Recently he tweeted some truly horrendous #histSTM errors in a BBC publication, I’ll let him explain further, and I immediately thought that would be something for the HIST_SCI HULKTMbut then thought it would be nice if Tom wrote a guest post about it himself. I asked, he said yes and so I give you the HIST_SCI HULK’s mild mannered, but very erudite cousin Tom McLeish.

For some years now I have been treating myself to the weekly delight and lifelong education in the history of science that is Thony Christie’s ‘Renaissance Mathematicus’ blog. To be invited to write a guest instalment is therefore a great surprise and joy. But I’ll rapidly wrap up my imposter syndrome in a few tight twists of context before getting on with the main task of joining the host author in calling out bad and sloppy history of science – and calling for getting it right – for both writers and readers of this blog know that getting history right matters.

As much as I look forward to the weekly arrival of the R-mathematicus email alert, I also anticipate the annual publication of the BBC Proms guide. Science and music are equal passions for me, and as far as I am concerned, music doesn’t get more exciting than the best classical music festival in the world – the London Promenade series of summer concerts at the Royal Albert Hall. Although the science I do professionally turns around the physics of soft materials and biophysics, astronomy was my childhood gateway to the study of nature, and is still my own amateur scientific passion. So when I discovered that a chosen theme of this year’s Prom concerts was space, responding to the 50thanniversary of the first human moon landing, I became understandably excited. Sure enough, the usually well-researched and written Proms Guide contained a promising article by Neil Brand, The Sound of Space.

The first page takes the reader on a musical pathway through the scores for science fiction films – an area of expertise for Brand, and a good read. But his thesis that the cosmos and music have been linked for centuries requires some history of science. This is where, as is sadly so often the case, the source-checking (frankly even encyclopaedia checking) runs out. A first indication that trouble is afoot appears in the categorisation of Cicero’s Dream of Scipioas a ‘philosophical treatise’. This marvellous dream-discourse is just the closing portion of the 6thbook of Cicero’s De res publica– the whole work really a political treatise, though highly expansive. It is very significant for the imaginative tradition of viewing the Earth from Space, as I have noted elsewhere , but does indeed mention the ‘music of the spheres’, the author’s point. So we read on for now.


The Universe, the Earth in the centre, surrounded by the seven planets within the zodiacal signs Images from a 12th-century manuscript of Macrobius’ Commentarii in Somnium Scipionis Source: Copenhagen, Det Kongelige Bibliotek, ms. NKS 218 4° via Wikimedia Commons

Enter Johannes Kepler (1571-1630), one of my personal Renaissance/Early-Modern astronomical heroes. I ceaselessly find it impressive that Kepler was able to deduce the three propositions concerning planetary motion that we now refer to as ‘Kepler’s Laws’, including the discovery of the elliptical orbit of Mars (and the other planets) from naked eye observations. He could not have done this, however, without the equally heroic contribution of Danish astronomer Tycho Brahe, who improved the accuracy of stellar positional measurements over his predecessors by two orders of magnitude – and this without a telescope. It was Tycho’s observations that enabled Kepler to deduce the elliptical planetary motion, work begun around 1601 but first published in his Astronomia Nova of 1609. Given that the first telescopic astronomical observations were not made until Thomas Harriot and then Galileo Galilei turned their primitive telescopes skyward in 1609, it is strange that Brand is able to assure us that Kepler used ‘observation through early telescope lenses’ to establish his laws of motion.

A decade’s error may perhaps be forgivable (though not the silence on Tycho Brahe), but errors of, several centuries and more stretches all generosity on my part. For Brand then attempts to link Kepler casually to the adoption of music within the ‘quadrivium’ of mathematical subjects taught in medieval universities.

It is elementary educational history that the structure of the ‘Liberal Arts’, for which the quadrivium formed the second year of study, was conceived by the time the late Roman commentator Macrobius wrote about them (interestingly in a lengthy commentary on the Dream of Scipio, see above!) around 430 AD. There is strong corroboration for this early adoption two centuries later from Isidore of Seville in his compendious Etymologies. Music remained a mathematical art from late antiquity, through the cathedral schools and early universities of the high middle ages to Kepler’s own time.

Brand’s final science-history sin is an even stranger one. For in the next section he introduces us to William Herschel, a Hanoverian, who emigrated to England in 1757. Herschel is a fascinating figure, most famous for his discovery of the first new planet since antiquity – Uranus, in 1781.


William Herschel 1785 portrait by Lemuel Francis Abbott Source: Wikimedia Commons

But in an astonishingly dense sweep of double confusion, Brand tells us that Herschel managed this feat ‘through careful calculation with superb new and enormously large optical telescopes.’ The discovery was actually made by observing the tiny greenish disk of Uranus move over several nights against the background of stars, and through a relatively small reflecting telescope[1]. Herschel’s massive 40’ reflector was not operational before 1789, and no more than a twinkle in its designer’s eye in 1781. Brand’s other confusion is, of course, with the discovery of Neptune. This was indeed effected by calculation (simultaneously by Le Verrier in France and Adams in England), following perturbations noticed in the orbit of Uranus. Le Verrier’s theoretical predictions of the whereabouts of the planet that accounted for Uranus’ wanderings lead to the 1846 observational discovery of Neptune in Berlin by Johan Galle.

The reason that the mangling of Herschel’s history is strange, especially in a BBC Proms Guide, is that he was first a musician, not an astronomer. Composer, singer and oboist, his first position in England was as director of the military band in Durham. His later moves to Birmingham and then Bath were also to musical posts, and only in the last did his astronomical interests begin to dominate. His famous sister Carolyn accompanied him, also as a singer, and in parallel career development became an astronomer in her own right, discovering several comets, and recording their observations meticulously. But in the musical phase of his career, William himself composed 24 symphonies and three remarkable oboe concertos among other pieces. It is perhaps the greatest pity of all that, in a year dedicated to music and astronomy, none has found a place at any of the 2019 Prom performances, where they might have embodied a beautiful and historical sound of space.

[1]If you are ever in the area, the Herschel Museum of Astronomy  in Bath, situated in Herschel’s old place of residence, is a delight and you can go out into the back garden where he made his discovery of Uranus.


Filed under History of Astronomy, Myths of Science

The emergence of modern astronomy – a complex mosaic: Part X

The publication in the spring of 1543 Copernicus’ De revolutionibus orbium coelestium (On the Revolutions of the Heavenly Spheres) had been widely advertised in advance by his own Commentariolus, distributed in manuscript from about 1510 and Rheticus’ De libris revolutionum Copernici narratio prima (1stedition Danzig 1540 and 2ndedition Basel 1541), so there was a certain level of anticipation to finally be able to view the mathematical models on which Copernicus had based his heliocentric hypothesis. The interest was particularly great as this was the first major, extensive work of mathematical astronomy since Ptolemaeus’ Syntaxis Mathematiké was published in the middle of the second century CE. The inaccuracy of the tables and ephemerides based on Ptolemaeus’ work had been grounds for concern amongst astronomers and astrologers for several centuries by the time Copernicus’ magnum opus appeared. So what did the eager reader get for his money when he finally got De revolutionibus in his hands?

De revolutionibus is closely modelled on Ptolemaeus’ Syntaxis Mathematiké or more accurately, as is clear from internal textual evidence, Peuerbach’s and Regiomontanus’ Epytoma in almagesti Ptolemei, which together with Peuerbach’s Theoricarum novarum planetarum had been the book from which Copernicus had learnt his astronomy. However unlike the Syntaxis Mathematiké and the Epytoma, which both have thirteen books, De revolutionibus only has six books.

These six books are preceded by a title page and three separate documents. As well as the title, the title page contains the following message, which almost certainly stems from the publisher, Johannes Petreius, rather than from Copernicus:


Source: Wikimedia Commons

Diligent reader, in this work, which has just been created and published, you have the motion of the fixed stars and planets, as these motions have been reconstituted on the basis of ancient as well as recent observations, and have been moreover been embellished by new and marvellous hypotheses. You also have most convenient tables, from which you will be able to compute those motions with the utmost ease for any time whatever. Therefor buy, read, enjoy.[1]


This is followed by the motto, in Greek, that supposedly graced the gates of Plato’s Academy:

Let no one untrained in geometry enter here

The first opening document is the Ad lectorum added by Andreas Osiander that I dealt with in Part IX. The second is a letter that Copernicus received from Nicolas Schönberg, Cardinal of Capua, in 1536 urging him to make his new cosmology public. Publishing this display of support by a leading Church official, Schönberg was secretary to the pope, was obviously intended to deflect any potential theological objections to his work. This is very obviously also the intention of the third document, the book’s preface, a dedication to His Holiness, Pope Paul III. In this preface Copernicus defends and justifies his heterodox cosmological hypothesis. The strongest statement coming shortly before the conclusion:

Perhaps there will be babblers who claim to be judges of astronomy although completely ignorant of the subject and, badly distorting some passages of Scripture to their purpose, will dare to find fault with my undertaking and censure it. I disregard them even to the extent of despising their criticism as unfounded. For it is not unknown that Lactantius, otherwise an illustrious writer but hardly an astronomer, speaks quite childishly about the earth’s shape, when he mocks those who declared that the earth has the form of a globe. Hence scholars need not be surprised if any such person will likewise ridicule me. Astronomy is written for astronomers.

(The Latin text of the final phrase is Mathemata mathematicis scribuntur, which is often translated as mathematics is written for mathematicians, but I think Rosen is right to translate it as astronomy and astronomers because in the Renaissance the terms mathematicus, astronomicus and astrologus are actually synonyms.)

With his “astronomy is written for astronomers” Copernicus a stridently telling potential readers I will only accept criticism from people who know what they are talking about. Copernicus citing Lactantius, as an ignorant critic has a certain historical irony. Lactantius a notorious flatearther had been almost entirely forgotten and committed to the trashcan of history but was brought back into circulation by Copernicus’ citation.

The first eleven chapters of Book I give a general overview of Copernicus’ heliocentric hypothesis and present his cosmology. Here Copernicus makes very clear his strict adherence to the ancient Greek axiom that the motion of celestial bodies is uniform circular motion, which would prove to be the biggest drawback of his entire system and eventually lead to its downfall. Chapter twelve deals with the maths of cords of circles, chapter thirteen the trigonometry of plain triangles and chapter fourteen spherical trigonometry. These chapters constitute the section of the book that Rheticus had published in advance in Copernicus’ name De lateribus et angulis triangulorum (On the Sides and Angles of Triangles), which appeared in 1542.


Book II of De revolutionibus deals with the principles of spherical astronomy and closes with a catalogue of the fixed stars, which is largely Ptolemaeus’ star catalogue. Book III is devoted to the Sun, Book IV to the moon and Books V & VI deal with the motion of the planets in a heliocentric system.

De revolutionibus is a weighty, mathematical tome running to 330 large format pages in Edward Rosen’s English translation and definitely not for the casual reader or the faint of heart. Some historians have claimed that it was a bad seller and compare its publication figures with Christoph Clavius’ commentary on the Sphere of Sacrobosco, In Sphaeram Ioannis de Sacro Bosco commentaries, which went through numerous editions in the late sixteenth and early seventeenth centuries. This is an unfair comparison. Clavius’ volume is a university textbook on the basics of geocentric astronomy written for undergraduates. De revolutionibus is an advanced mathematical text written, as Copernicus said, for working astronomers. There were only a fairly small number of scholars in Europe in the second half of the sixteenth century, who possessed the necessary knowledge and level of mathematical skill to read and understand it. In the sixteenth century there were only two editions, the first in Nürnberg in 1543 and the second unchanged edition in Basel in 1566 published by Petreius’ cousin Heinric Petri. Each edition has been estimated to have been around five hundred copies.


Title page, 2nd edition, Basel, Officina Henricpetrina, 1566 Source: Wikimedia Commons

Owen Gingerich carried out a detailed survey over many years of all the known surviving copies of both the first and second editions and it is clear that every notable mathematician/astronomer in Europe in the second half of the sixteenth century possessed a copy of De revolutionibus. Gingerich also surveyed the marginalia in all the surviving copies and one general result was that nearly all the readers ignored the first, heliocentric cosmological Book, confining themselves to the mathematical models in the other five books. We will be looking somewhat more closely at the reception history of Copernicus’ magnum opus in the next part of this series.


[1]All English quotes from De revolutionibus are taken from On the Revolutions, translated and commentary by Edward Rosen, Johns Hopkins University Press, Baltimore and London, ppb. 1992


Filed under History of Astronomy, Renaissance Science

Hagiography without context – how not to celebrate a historical figure

This is not so much a blog post as a brief comment. Today marks the five hundredth anniversary of the death of the Renaissance artist-engineer Leonardo da Vinci. This of course has led to a massive bun fight in the form celebrations not just today but throughout the entire year–exhibitions, articles, blog posts, etc., etc. The one thing that has been missing in almost all of the articles, posts, broadcasts and so on that I have come across up till now has been context. We get told that Leonardo was unique, a genius, one of a kind, a visionary, an amazing polymath, a man of the future and all of the verbal hyperbole that you can think of but in almost all cases there is absolutely no context presented for his life and work.


Francesco Melzi – Portrait of Leonardo Source: Wikimedia Commons

As I said above, and also in an earlier blog post, Leonardo was a Renaissance artist-engineer and his whole life and the wide spread of activities are actually characteristic for the carrier profile of a typical artist-engineer. He was not as unique in that sense as these hagiographic portraits without context present him. He is one of a crowd, a man of his times not some sort of freak or anomaly beamed back from the future into the fifteenth century. There are plenty of other polymath Renaissance artist-engineers, who were his predecessors and role models, as well as his contemporaries. To quote Leonardo da Vinci: The Man Behind the Myth on Google Arts & Culture, one of the better articles:

The way that Renaissance knowledge brought together many different disciplines and studies cannot be applied to modern times. In the Renaissance, Leonardo was one of many polymaths – perhaps the best, together with humanists like Filippo Brunelleschi, Leon Battista Alberti and Francesco di Giorgio Martini. 

Saying this does not diminish his stature. Whilst one of many Leonardo was primus inter pars, a man whose undeniably immense talents let him delve deeper, develop further and express better than any other of the Renaissance artist-engineers. However, if you really wish to understand and appreciate Leonard you can only really do so if you view him embedded in the historical context in which he lived and worked.

A good example of this is the notorious Vitruvian Man drawing by Leonardo, which at least two sources that I have read in the last few days claimed originated with Leonardo.


In fact, as I demonstrated in an earlier post, Vitruvian Man was an iconic image of the Renaissance artist-engineer milieu well before Leonardo produced his version of it. However, his version is superior to all the others.

An exception to the hagiographic posturing being presented on Leonardo is today’s essay on Thinking 3D about Leonardo’s anatomical drawings by Monica Azzolini, Leonardo Inside Out, which embeds his efforts in the medical history of the time. Do yourself a favour and read how to do it properly. Also readable is the Max Planck Institute for the History of Science essay Leonardo da Vinci’s Intellectual Cosmos: Exhibitions with Museo Galileo and Staatsbibliothek zu Berlin, which features a reconstruction of Leonardo’s library and so his rich and diverse sources.


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Filed under Myths of Science, Renaissance Science