The horror, the horror!

For those readers who might have wondered what The Renaissance Mathematicus looks and sounds like, you need wonder no more. There is now a video on Youtube in which I stumble and stutter my way through a very impromptu, not quite fifteen minute, lecture on the relationship between astronomy, astrology and medicine in the Early Modern Period. During which I indulge in a lot of arm waving and from time to time scratch my fleas. This video was filmed in the kitchen of the Remeis Observatory in Bamberg during a coffee break at the Astronomy in Franconia Conference last Monday, complete with the sounds of somebody loading the dishwasher.

The cameraman, who also puts some questions during this solo performance, was Chris Graney who requested my golden words for his students back in Louisville, the poor sods.

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Filed under Autobiographical, History of Astrology, History of Astronomy, History of medicine

Jesuit Day

Adam Richter (@AdamDRichter) of the Wallifaction Blog (he researches John Wallis) tells me that the Society of Jesus, known colloquially as the Jesuits, was officially recognised by Pope Paul III on 27th September 1540. He gives a short list of Jesuits who have contributed to the history of science over the centuries. Since this blog started I have attempted to draw my readers attention to those contributions by profiling individual Jesuits and their contributions and also on occasions defending them against their largely ignorant critics. I have decided to use this anniversary to feature those posts once again for those who came later to this blog and might not have discovered them yet.

My very first substantive post on this blog was about Christoph Clavius the Jesuit professor of mathematics at the Collegio Romano, the Jesuit university in Rome, who as an educational reformer introduced the mathematical sciences into the curricula of Catholic schools and universities in the Early Modern Period. I wrote about Clavius then because I was holding a lecture on him at The Remeis Observatory in Bamberg, his hometown, as part of the International Year of Astronomy. I shall be holding another lecture on Clavius in Nürnberg at the Nicolaus Copernicus Planetarium at 7:00 pm on 12 November 2014 as part of the “GestHirne über Franken – Leitfossilien fränkischer Astronomie“ series. If you’re in the area you’re welcome to come along and throw peanuts.

I wrote a more general rant on the Jesuits’ contributions to science in response to some ignorant Jesuit bashing from prominent philosopher and gnu atheist A. C. Grayling, which also links to a guest post I wrote on Evolving Thoughts criticising an earlier Grayling attack on them. This post also has a sequel.

One of Clavius’ star pupils was Matteo Ricci who I featured in this post.

A prominent Jesuit astronomer, later in the seventeenth-century, was Riccioli who put the names on the moon. I have also blogged about Chris Graney’s translation of Riccioli’s 126 arguments pro and contra heliocentricity. Chris, a friend and guest blogger on the Renaissance Mathematicus, has got a book coming out next year on The University of Notre Dame Press entitled Setting Aside All Authority: Giovanni Battista Riccioli and the Science against Copernicus in the Age of Galileo. It’s going to be a good one, so look out for it.

Riccioli’s partner in crime was another Jesuit, Francesco Maria Grimaldi, who features in this post on Refraction, refrangibility, diffraction or inflexion.

At the end of the seventeenth-century the Jesuit mathematician, Giovanni Girolamo Saccheri, without quite realising what he had achieved, came very close to discovering non-Euclidian geometry.

In the eighteenth-century a towering figure of European science was the Croatian Jesuit polymath, Ruđer Josip Bošković.

This is by no means all of the prominent Jesuit scientists in the Early Modern Period and I shall no doubt return to one or other of them in future posts.




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

If you’re going to pontificate about the history of science then at least get your facts right!

Recently, my attention was drawn to an article by Pascal-Emmanuel Gobry, on The Week website, telling the world what the real meaning of ‘science’ is (h/t Peter Broks @peterbroks). According to Mr Gobry science is the process through which we derive reliable predictive rules through controlled experimentation [his emphasis]. This definition is of course totally inadequate but I’m not going to try and correct it in what follows; I gave up trying to find a simple all encompassing definition of science, a hopeless endeavour, a long time ago. However Mr Gobry takes us on a whirlwind tour of the history of science that is to say the least bizarre not to mention horribly inaccurate and in almost all of its details false. It is this part of his article that I’m going to look at here. He writes:

A little history: The first proto-scientist was the Greek intellectual Aristotle, who wrote many manuals of his observations of the natural world and who also was the first person to propose a systematic epistemology, i.e., a philosophy of what science is and how people should go about it. Aristotle’s definition of science became famous in its Latin translation as: rerum cognoscere causas, or, “knowledge of the ultimate causes of things.” For this, you can often see in manuals Aristotle described as the Father of Science.

The problem with that is that it’s absolutely not true. Aristotelian “science” was a major setback for all of human civilization. For Aristotle, science started with empirical investigation and then used theoretical speculation to decide what things are caused by.

What we now know as the “scientific revolution” was a repudiation of Aristotle: science, not as knowledge of the ultimate causes of things but as the production of reliable predictive rules through controlled experimentation.

Galileo disproved Aristotle’s “demonstration” that heavier objects should fall faster than light ones by creating a subtle controlled experiment (contrary to legend, he did not simply drop two objects from the Tower of Pisa). What was so important about this Galileo Moment was not that Galileo was right and Aristotle wrong; what was so important was how Galileo proved Aristotle wrong: through experiment.

This method of doing science was then formalized by one of the greatest thinkers in history, Francis Bacon.

Where to start? We will follow the Red King’s advice to Alice, “Begin at the beginning,” the King said, very gravely, “and go on till you come to the end: then stop.”

Ignoring the fact that it is highly anachronistic to refer to anybody as a scientist, even if you qualify it with a proto-, before 1834, the very first sentence is definitively wrong. Sticking with Mr Gobry’s terminology Aristotle was by no means the first proto-scientists. In fact it would be immensely difficult to determine exactly who deserves this honour. Traditional legend or mythology attributes this title to Thales amongst the Greeks but ignores Babylonian, Indian and Chinese thinkers who might have a prior claim. Just staying within the realms of Greek thought Eudoxus and Empedocles, who both had a large influence on Aristotle, have as much right to be labelled proto-scientists and definitely lived earlier than him. Aristotle was also by no means the first person to propose a systematic epistemology. It would appear that Mr Gobry slept through most of his Greek philosophy classes, that’s if he ever took any, which reading what he wrote I somehow doubt.

We then get told that Aristotelian “science” was a major setback for all of human civilization. Now a lot of what Aristotle said and a lot of his methodology turned out in the long run to be wrong but that is true of almost all major figures in the history of science. Aristotle put forward ideas and concepts in a fairly systematic manner for people to accept or reject as they saw fit. He laid down a basis for rational discussion, a discussion that would, with time, propel science, that is our understanding of the world in which we live, forwards. I’m sorry Mr Gobry, but a Bronze Age thinker living on the fertile plains between the Tigris and the Euphrates is not coming to come up with the theory of Quantum Electro Dynamics whilst herding his goats; science doesn’t work like that. Somebody suggest an explanatory model that others criticise and improve, sometimes replacing it with a new model with greater explanatory power, breadth, depth or whatever. Aristotle’s models and methodologies were very good ones for the time in which he lived and for the knowledge basis available to him and without him or somebody like him, even if he were wrong, no science would have developed.

Gobry is right in saying that the traditional interpretation of the so-called scientific revolution consisted of a repudiation of Aristotelian philosophy, a point of view that has become somewhat more differentiated in more recent research, a complex problem that I don’t want to go into now. However he is wrong to suggest that Aristotle’s epistemology was replaced by reliable predictive rules through controlled experimentation. Science in the Early Modern Period still has a strong non-experimental metaphysical core. Kepler, for example, didn’t arrive at his three laws of planetary motion through experimentation but on deriving rules from empirical observations.

Gobry’s next claim would be hilarious if he didn’t mean it seriously. Galileo disproved Aristotle’s “demonstration” that heavier objects should fall faster than light ones by creating a subtle controlled experiment (contrary to legend, he did not simply drop two objects from the Tower of Pisa). Aristotle never demonstrated the fact that heavier objects fall faster than light ones; he observed it. In fact Mr Gobry could observe it for himself anytime he wants. He just needs to carry out the experiment. In the real world heavier objects do fall faster than light ones largely because of air resistance. What Aristotle describes is an informal form of Stokes’ Law, which describes motion in a viscous fluid, air being a viscous fluid. Aristotle wasn’t wrong he was just describing fall in the real world. What makes Gobry’s claim hilarious is that Galileo challenged this aspect of Aristotle’s theories of motion not with experimentation but with a legendary thought experiment. He couldn’t have disproved it with an experiment because he didn’t have the necessary vacuum chamber. Objects of differing weight only fall at the same rate in a vacuum. The experimentation to which Gobry is referring is Galileo’s use of an inclined plane to determine the laws of fall, a different thing altogether.

We now arrive at Gobry’s biggest error, and one that produced snorts of indignation from my friend Pete Langman (@elegantfowl), a Bacon expert. Gobry tells us that Galileo proved Aristotle wrong: through experiment. This method of doing science was then formalized by one of the greatest thinkers in history, Francis Bacon. Galileo’s methodology of science was basically the hypothetical deductive methodology that most people regard as the methodology of science today. Bacon however propagated an inductive methodology that consists of accumulating empirical data until a critical mass is reached and the theories, somehow, crystallise out by themselves. (Apologies to all real philosophers and epistemologists for these too short and highly inadequate descriptions!) These two epistemologies stood in stark contrast to each other and have even been considered contradictory. In reality, I think, scientific methodology consists of elements of both methodologies along with other things. However the main point is that Bacon did not formalise Galileo’s methodology but produced a completely different one of his own.

Apparently Mr Gobry also slept through his Early Modern Period philosophy classes.




Filed under History of science, Myths of Science

Childhood, war games and becoming a historian.

This week’s A Point of View on BBC Radio 4 The Horror of War by Renaissance historian Lisa Jardine was truly excellent and well worth ten minutes of your time. From the starting point of having visited a war exhibition she discussed how museums sometimes/often sanitize war when presenting it attractively pre-packaged for the viewing public. Turning to the anything but attractive reality of war she ended her short piece with a very personal anecdote from the bringing up of her own children. She told how her five-year-old son came home from primary school wishing to be bought a khaki shirt. It transpired that a group of kids in his class had started to play war games, re-enacting the Second World War. I was slightly surprised that the initiator or this activity was a recently arrived German boy because one of the things that struck me when I moved to Germany more than thirty years ago is that German children, unlike myself and my friends in my childhood, don’t play war games; a legacy of the German guilt for the Second World War and everything that happened in Germany during the Nazi period. In fact many of my German friends who had spent time in Britain told me how shocked they had been by the war stories in English children’s comics. How Lisa dealt with her own qualms about her son’s wish to play war games I will leave you to find out for yourselves, I want to talk about my own childhood, the war games I played and how it led to me becoming a historian.

I grew up I the 1950s in the shadow of the Second World War; although I don’t remember it the bottled milk on which I was fed was still rationed. From about the age of four to about the age of eleven me and my best friend Pete (and yes grammar fascists I know that is grammatically wrong!) played war games; it was one of our principle activities.

We were Royal Marine Commandoes parachuting behind enemy lines in France to rescue some imagined imprisoned spy, we were Viking warriors slashing and pillaging our way through some imagined coastal settlement or sailing the high seas in our dragon boat, we were Roman legionaries battling the wild Pictish hoards to regain the Eagle of the Ninth (slightly ironic as my father was a lowland Scot!), we were members of the French Foreign Legion besieged by marauding Arabs, you name it if there was a war in history we fought in it.

We had a large storage cupboard, without doors in a loft above a stables on whose top shelf we sat back to back whilst flying our Lancaster bomber; Pete was the pilot and I was by turns the tail-gunner and the bomb aimer. We had an old coalbunker in the yard that was by turns our tank or Panzerkampfwagen (we knew all the right terminology), or our submarine. I had a real periscope that I had built myself with the help of my mother. We were always in the workshop building the accoutrements of war. We carved swords out of fence palings and made shields of every imaginable shape and form out of plywood. We built wooden Sten submachine guns and Bren light machine guns. We fashioned bows and arrows out of hazel wood saplings and constructed lethal crossbows. When we played inside we glued together vast fleets of warships and airplanes, as well as squadrons of tanks from Airfix plastic kits.

A large part of our lives was devoted to the pursuit of war but it wasn’t just practical, there was a strong and surprisingly deep theoretical side to our endeavours. We wished our war games to be as authentic as possible and so we devoted a large part of our time to studying war history. Whilst still at primary school I could detail every model of tank (Panzerkampfwagen) produced in Germany during the 1930s and 40s, including who had designed them, which company had built them etc. etc. I knew the ranks of all the members of a Roman legion, how many men constituted a cohort, a legion, where which legions were deployed and so on, and so on. Aided by my historian father, I had books on such things as Lancelot de Mole’s tank and the construction of Samurai armour. I was a war history junkie, but more importantly I was a practicing historian. I served my first apprenticeship as a historian whilst still at primary school learning, in detail, about all of the ways humanity had dreamt up to kill itself off.

By the time I was fifteen I had become the totally convinced pacifist I remain today but my passion for history had grown and would soon turn first to the history of mathematics and then later to the more general history of science but that passion has its roots very firmly in those childhood years where, in my imagination, I slaughtered thousands and, it should be pointed out, died a thousand spectacular deaths. Being able to act out an Oscar worthy death was an essential part of our war games.

I never had children and being old, set in my ways as a single and, as my contribution to contraception, sterilised I never will have, so I can’t say how I would react to a child of mine wishing to play war games. I can only wish that my reaction would have been as wonderful as that of Lisa Jardine.



Filed under Autobiographical

The naming of America – Redux

This is a brief addenda to my previous naming of America post, as my copy of Peter Macdonald’s Cabot & The Naming of America: Dawn of Arrival, Newfoundland, June 1497 has finally arrived; remaindered, it cost all of £0.01! (p&p £4!).

As I suspected the book is self-published by the author, always a bad sign for a history book, and it lives down to expectations. Macdonald’s arguments in favour of the Ap Meric (Amerike) theories are even worse than those of Rodney Broome and are centred on a straightforward lie. On the second, unnumbered, page Macdonald writes:

In 1507 a cartographer by the name of Waldseemuller [sic] (meaning the miller from the forest sea [it’s actually wood lake]) produced a map in which he attributed the name of the place he had heard called America to Amerigo Vespucci. People assumed that he had got his facts right and that from this slender beginning grew the legend. However, it is more than probable that the miller man gave the credit to the wrong person. It is far more likely that the great continent was named after Richard Amerike, the King’s Customs Officer for Bristol in 1497, as will become evident in this book, and that Herr Waldseemuller’s was a shot in the dark that hit the wrong target.

As is very clear from the passages from the Cosmographiae Introductio, that I quoted in my previous post, Ringmann, its author, states that he and Waldseemüller had not attributed the name of the place he had heard called America to Amerigo Vespucci but believing Vespucci to be the discoverer of the new territories and coined the name themselves in his honour. Macdonald repeats this deliberate lie again on page 35:

In 1507 a young geographer who lived in Freiburg [St Dié actually], Martin Waldseemuller by name, drew a map of the new continent and gave it the name ‘America’. Because he knew that Amerigo Vespucci had accompanied Hojeda he assumed the name America, by which the place was beginning to be known, referred to him.

Naturally, Macdonald doesn’t quote a single occurrence of the name ‘America’ before it was coined by Ringmann and Waldseemüller in 1507.

An impression of Macdonald’s abilities as a historian can be gained from the following introductory paragraph on page 3. A warning to all serious medieval historians you might feel offended by Macdonald’s description of the late fifteenth-century. On the other hand you might fall about laughing.

It is difficult, today, to imagine just how ignorant people were five hundred years ago; they knew nothing about almost everything. They had no idea how their bodies worked – no idea why they breathed, urinated, defecated or felt hungry, felt sick or had a temperature – and many made no connection between the sexual act and childbirth. They knew nothing of geography – indeed most people didn’t know or care what went on on the other side of the horizon – and they thought the world was flat [my emphasis]. Nearly everyone was illiterate, even kings; only a few of the clergy knew how to read and write.




Filed under Myths of Science, Renaissance Science

Another one bites the dust

This is a sort of footnote to my last post in which I criticised science writer Tim Radford for propagating myths about the reception of heliocentricity in the sixteenth-century. Now a second truly legendary astronomer and science writer, John Gribbin, has turned up in the comments and shown that he also lives in the nineteenth-century, as far as history of science is concerned, when John William Draper and Andrew Dickson White created the myth of an eternal war between science and religion and presented Giordano Bruno and Galileo Galilei, alongside lesser lights such as Michael Servetus and Marco-Antonio de Dominis, as the scientific victims of Christian persecution.

Rushing in where angels fear to tread Gribbin sought to defend Radford’s honour with the following comment:

As a card-carrying pedant, I would point out that Tim says “ideas like that”, not “that idea”. Which makes Bruno relevant, whether you like it or not.

Now I appreciate Mr Gribbin’s attempt to help his friend and colleague but in doing so he has only displayed his own ignorance of the material. There was a very good reason why I ended my last post with the following tongue in cheek warning:

P.S. If anybody mentions either Giordano Bruno or Galileo Galilei in the comments I will personally hunt them down and beat them to death with a rolled up copy of The Guardian.

No modern historian of science, knowledgeable of the history of astronomy in the Early Modern Period, would follow Draper and White in viewing Bruno as a martyr of science. This is a myth that has been thoroughly debunked and which is, these days, usually only dug up by historically ignorant gnu atheists and others of that ilk, as a weapon with which to beat the Catholic Church around the head. As John Gribbin has walked straight into the trap we will just briefly examine why the Church committed Giordano Bruno to the flames.

A Dominican monk, Bruno came under suspicion of heresy and fled his Southern Italian monastery in 1576. He spent the next sixteen years wandering around Europe blowing his own trumpet, generally annoying people and pissing off the authorities, both civil and religious, wherever he went. Returning to Italy he landed, not unsurprisingly in the clutches of the Roman Inquisition. He was held prisoner and interrogated for seven years before being tried for heresy, found guilty, and executed by burning at the stake in 1600. The proceedings of his trial have disappeared so it is not known what exactly he was found guilty of but summary was discovered in 1940 and a list of the charges against him is known:

  • holding opinions contrary to the Catholic faith and speaking against it and its ministers;
  • holding opinions contrary to the Catholic faith about the Trinity, divinity of Christ and Incarnation;
  • holding opinions contrary to the Catholic faith pertaining to Jesus as Christ;
  • holding opinions contrary to the Catholic faith regarding the virginity of Mary, mother of Jesus;
  • holding opinions contrary to the Catholic faith about both Transubstantiation and Mass;
  • claiming the existence of a plurality of worlds and their eternity;
  • believing in metempsychosis and in the transmigration of the human soul into brutes;
  • dealing in magics and divination.

Now this list is not hidden away somewhere, I just borrowed it from the Wikipedia Bruno article, so Mr Gribbin could have consulted it himself. He would of course pounce on the sixth item on the list gleefully crying I told you so, but let us examine if he should be so sure of being right.

Given the fact that Bruno was accused of breaching almost every single central doctrine of the Catholic Church did this one point of highly speculative cosmology really play such a central role in his conviction and subsequent execution, I hardly think so. In fact I don’t think it played much of a role at all compared to his denying the divinity of Christ and the virgin birth. However there is more.

Bruno’s claiming the existence of a plurality of worlds and their eternity has little or nothing to do with Copernicus’ heliocentric theory the original statement for which Tim Radford claimed one could be condemned to the stake. Copernicus proposed a finite sun centred cosmos, Bruno speculated about an infinite universe filled with homogenously distributed infinite sun each with their own populated planets and no centre. The two proposals don’t have an awful lot in common. Copernicus expressly refused to enter the discussion as to whether the cosmos was finite or infinite, and never speculated about other inhabited planets. He, as a good Catholic cleric, would definitely have rejected an eternal universe as this contradicted the Creation. What about the two leading Copernican of Bruno’s own times? Kepler explicitly rejected Bruno’s infinite universe and infinite suns and in doing so brought the earliest known argument against Olbers’ paradox. Galileo simply ignored him. I think it is safe to say that the cosmological statements that were included in Bruno’s indictment were not ideas like Copernicus’ heliocentric theory, as claimed by Gribbin.

Gribbin’s claim also suffers from another problem. The reason why Bruno’s cosmological speculations were included in his indictment was very clearly theological and not scientific. As already mentioned if, as Bruno claimed, the universe were eternal then there could be no Creation, highly heretical. In fact this was one of the central reasons why the Catholic Church rejected the Greek philosophy of Atomism. Secondly if there were infinite populated worlds there would be serious problems with the doctrine of salvation through Jesus. If he was the only Son of God did he visit all of the infinite populated planets, simultaneously, one after the other? Or were there infinite Jesuses? Did he only save the earth? Then what about the other planets? A really tangled mess for the Catholic theologians! As with Galileo in 1615 if Bruno had had anything remotely like proof for his cosmology he might have had something he could argue with but he didn’t, all he had was pure unscientific, unsubstantiated speculation. As I sated in earlier posts Bruno’s cosmological speculations were anything but scientific and anything but accurate. As far as we know the universe is finite and not infinite, it had a starting point and will almost certainly have an end. There are neither infinite stars (suns) nor infinite planets and those that there are, are not distributed homogenously. To stylise Bruno as a scientific martyr, as Draper/White did in the nineteenth-century and as John Gribbin apparently still wants to do, boarders on the grotesque.







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

I expected better of Tim Radford

Tim Radford is a science writer who works for The Guardian newspaper. In fact many people consider him the best British science writer of the current crop, not without a certain amount of justification. Because of this I was, as a historian of science, more than disappointed by the opening paragraph of his latest post on the science section of the Guardian’s website, a book review: “The Copernicus Complex by Caleb Scharf review – a cosmic quest”. Radford opens his review with three sentences of which the third caused me to groan inwardly and bang my head in resignation on my computer keyboard.

The Copernican principle changed everything. It was not formulated by Copernicus, who in 1543 proposed only that the Earth was not the centre of the universe, and that the motion of the Earth around the sun could explain the irregularities in the heavens. At the time, ideas like that could get people condemned to the stake. [my emphasis]

I ask myself how much longer historians of science are going to have to keep repeating that this statement is complete and utter rubbish before science writers like Tim Radford finally take their hands off their ears and the blinkers from their eyes and actually accept that it is wrong. No Mr Radford, an astronomer or cosmologist in the sixteenth-century suggesting that we live in a heliocentric cosmos rather than a geocentric one was not in danger of being condemned to the stake and yes there is solid historical evidence, which apparently you choose to ignore in favour of your fantasies, to prove this. Let us briefly review that evidence for those, like Tim Radford, who have obviously not been paying attention.

Already in the fifteenth- century Nicholas Cusanus openly discussed various aspects of the heliocentric hypothesis in his works, presenting them in a favourable light. Was he condemned to the stake for his audacity? No he was treated as an honoured Church scholar and appointed cardinal.

Let us move on to the subject of Radford’s highly inaccurate statement, Copernicus, like Cusanus a cleric and a member of the Church establishment, how did the Church react to his provocative heliocentric claims? In 1533 the papal secretary, Johann Albrecht Widmannstetter held a lecture on Copernicus’ theories to Pope Clemens VII and assembled company in the papal gardens. We assume this was based on Copernicus’ Commentariolus, the manuscript pamphlet of his ideas written around 1510, as De revolutionibus wasn’t published until 1543. Was he condemned to the stake for his rashness? No, Clemens found much favour in his lecture and awarded him a valuable present for his troubles. Two years later Widmannstetter became secretary to Cardinal Nikolaus von Schönberg, an archbishop and papal legate, who had been present at that lecture. In 1536 Schönberg wrote a letter to Copernicus urging him to make his theories public and even offering to pay the costs of having his manuscript copied. Not a lot of condemning to the stake going on there. Copernicus had Schönberg’s letter printed in the front of De revolutionibus.

Dear Tim Radford I am sure that as a topflight science writer you check the scientific facts in the articles that you write very carefully to ensure that you are not misleading your many readers. May I humbly request that in future you pay the same attention to the historical facts that you publish so as not to serve up your readers with pure unadulterated historical hogwash?

P.S. If anybody mentions either Giordano Bruno or Galileo Galilei in the comments I will personally hunt them down and beat them to death with a rolled up copy of The Guardian.




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