Category Archives: Myths of Science

Founders of science?

World-renowned wheelchair driver and astrophysicist, Stephen Hawking, recently held the first of this year’s BBC Reith Lectures. This prompted the following tweet from Roger Highfield, science writer and director of external affairs at the Science Museum Group:

If Hawking could time travel, he would like to meet Galileo – ‘founder of modern science’ and ‘a bit of a rebel’ #Reith

Philip Ball, science writer, responded:

Though certainly not, as Hawking claimed, “the first to challenge Aristotle”…

To which I added:

Also not the founder of modern science.

Tom Levenson, another science writer, contributed:

Probably kicked his dog and stiffed his waiter too.

Roger Highfield reacted to this exchange thus:


This moderately amusing, or not depending on you point of view, exchange on Twitter prompted Ángel Lamuño, Philosophy & Theology Follower of Bernard J. F. Lonergan SJ (self description), to pose the following question to me:

Who is (are) the founder(s) of modern science?

This whole rather trivial exchange contains several worrying aspects for historians of science, starting with Hawking’s original utterance. This is by no means the first time that Hawking has made such statements in public and in fact I quote one such in my take down of the founder of modern science and similar claims about Galileo – Extracting the stopper – that I wrote more than five years ago and which I’m not going to repeat here. The real problem is here that whatever Hawking’s merits as an astro-physicist he is not a historian of science and this is reflected in the naivety of his history of science comments that are almost invariably false. The problem is that Hawking because of his physical disability has become the most famous scientist in the world instantly recognised and admired whenever he appears in public. Whenever he makes a comment about the history of science then the majority of his audience, who don’t know better, immediately believe him because it’s ‘Stephen Hawking’! People believe Hawking because of who he is and not because his facts are correct, they aren’t. The irony of this situation is that what we have here is knowledge by authority, exactly the non-scientific epistemology that the scholastics supposedly practiced and which Galileo is said to have swept away, making him in Hawking’s words ‘the founder of modern science’.

Equally worrying is Ángel Lamuño’s question, [if Galileo isn’t the founder of modern science] “who is (are) the founder(s) of modern science?” This question is, in my opinion, based on a widespread misconception as to how science has evolved (developed, if you don’t like the word evolved). The misconception is supported in a vast number of texts, many of them written by highly respected historians of science but I think, in the meantime, rejected by a substantial part of the history of science community.

This misconception, or rather set of misconceptions, is that somehow major changes in the history of science are caused by one driving force in mainstream scientific thought and/or brought about by one heroic individual.

The traditional story that I grew up with was that the scientific revolution came about because science became quantified or mathematized when Neo-Platonism replaced Aristotelian scholasticism as the dominant philosophy in Europe. This is, however, not the Neo-Platonism of Plotinus of the third century CE but a Pythagorean Neo-Platonism. This theory was mainly propagated by philosophers. Mathematic historians however challenged this theory accepting that the scientific revolution was a mathematization of science but that this was brought about by an Archimedean renaissance beginning in the fourteenth century. Others have noted that the period also saw both a Euclidean and a Ptolemaic renaissance leading to increases in mathematical activity.

A different popular version of the story is that the scientific revolution was driven by the astronomical revolution brought about singlehandedly by Copernicus publishing his De revolutionibus in 1543. This is somewhat undermined by two facts. Firstly Copernicus’ work is only part of a general reform of astronomy carried out by a fairly large number of astronomers beginning with the first Viennese School of Mathematics in the fifteenth century. Secondly the so-called scientific revolution consists of far more than just astronomy.

There are theories that the astronomical revolution was driven by the renaissance in mathematical cartography sparked by the rediscovery of Ptolemaeus’ Geographia in 1406, alternatively by an attempt to put astrology on a solid empirical footing. At least one Arabic author has argued, with more than a little justification, that the astronomical revolution owes much more to the preceding Islamic astronomy than is usual credited. Another group of historians see the roots of the astronomical revolution in a shift in basic philosophy but not in a Neo-Platonic renaissance but in a Stoic one in the fifteenth and sixteenth centuries.

Another theory sees the scientific revolution being the rise in empirical experimental science, which has its roots in alchemy. An alternative explanation for this rise lies in the development of modern gunpowder based warfare and empirical studies of gunnery. Some see the rise of modern warfare as the driving force behind mathematical cartography, itself the driving force behind astronomical reform.

The above are some, but by no means all, of the theories that have been put forward to explain the emergence of modern science in the early modern period. So which one is the correct one? The answer is, all of them! The emergence of modern science was not caused by one single thing but by a whole range of activities, discoveries, renaissances as well as economic and socio-political developments. As historians we have a strong tendency to oversimplify, to want to find the ‘one’ cause for a given historical development, whereas in fact that development is almost inevitably the result of the interaction of a complex web of causes and it is often very difficult to weight the respective contributions of the individual causes. The mono-causal explanation only occurs if the researcher views the development from one standpoint whilst actively or passively ignoring all other possible standpoints. The same is true of the attribution of the titles ‘father of’ or ‘founder of’ to individuals. If you follow the link above to my earlier post about Galileo you will see how I show that he was only one of several, and sometimes many, making positive contributions to the fields in which he was active in the early seventeenth century and to raise him up on a pedestal is to deny due credit to the others and thus to falsify history. One can do the same with any of the other so-called ‘heroes’ of science, as I did fairly recently with exaggerated claims, contained in a book’s subtitle, for Johannes Kepler.

To repeat my central mantra as a historian of science, the evolution of science is driven by multiple complexly intertwined causes and is realised by the collective efforts of, often large, groups of researches and not by exceptional individuals. One day I hope that people will stop making the sort of statements that Stephen Hawking made, and which sparked off this post, but if I’m honest I’m not holding my breath whilst I wait.



Filed under Myths of Science

Christmas Trilogy 2015 Part 2: Understanding the Analytical Engine.

The Acolytes of the Holy Church of Saint Ada still persist in calling her a brilliant mathematician and the ‘first computer programmer’ despite the fact that both are provably wrong. In fact they have now moved into the realm of denialists, similar to evolution or climate denialists, in that they accuse people like myself who point to the historical facts of being male chauvinists who are trying to deny women their rights in the history of science! However the acolytes have gone a step further in the adulation of Lady King in that they now claim that she understood the Analytical Engine better than Babbage! Confronted by this patently ridiculous claim I’m not sure whether to laugh or cry. Babbage conceived, designed and attempted to construct parts of the Analytical Engine whereas Ada Lovelace merely wrote an essay about it based on her exchanges with Babbage on the subject, to suggest that she understood the machine better than its sole creator borders on the insane. I cannot be certain who first set this bizarre claim in the world as nearly all of those who repeat it give neither justification or source for their utterances but the most often quoted in this context is James Essinger and his biography of Ada, which appears to enjoy several different titles[1].

Trial model of a part of the Analytical Engine, built by Babbage, as displayed at the Science Museum (London). Source: Wikimedia Commons

Trial model of a part of the Analytical Engine, built by Babbage, as displayed at the Science Museum (London).
Source: Wikimedia Commons

Before going into detail it should be pointed out the Essinger’s book, which is popular rather then academic and thus lacks sources for many of his claims, suffers from two fundamental flaws. Like much pro Ada writing it doesn’t delve deep enough into the live and work of Charles Babbage. This type of writing tends to treat Babbage as an extra in the film of Ada’s life, whereas in reality in relation to the Analytical Engine it is Ada who is a minor character in Babbage’s life. Also Essinger writes about the translation of the Menabrea essay on the Analytical engine as if the appended notes were exclusively the product of Ada’s brain, whereas it is an established fact from the correspondence that they were very much a co-production between Babbage and Lovelace based on many exchanges both in personal conversations and in that correspondence. This means that in basing any argument on any idea contained in those notes the writer has the job of determining, which of the two would be the more probable source of that idea and not simply blindly attribute it to Ada. As we shall see Essinger’s failure to do this leads to a major flaw in his central argument that Ada understood the Analytical Engine better than Babbage.

Essinger’s approach is two pronged. On the one side he claims that Babbage didn’t understand the future potential of the machine that he, and he alone, conceived and created (on paper at least) and on the other he proposes on the basis of his interpretation of Note A of the essay that Ada, whom he assumes to be the originator of the thoughts this not contains, had a vision of the Analytical engine equivalent to modern computer science. As we shall see Essinger is mistaken on both counts.

Whilst offering absolutely no source for his claim, Essinger states time and again throughout his book that Babbage only every conceived of the Analytical Engine as a device for doing mathematics, a super number cruncher so to speak. If Essinger had taken the trouble to elucidate the origins of Babbage’s inspiration for the Analytical Engine he would know that he is seriously mistaken in his view, although in one sense he was right in thinking that Babbage concentrated on the mathematical aspects of the Engine but for reasons that Essinger doesn’t consider anywhere in his book.

Babbage lived in the middle of the Industrial Revolution and was fascinated by mechanisation and automation throughout his entire life. During the 1820s Babbage travelled throughout the British Isles visiting all sorts of industrial plant to study and analyse their uses of mechanisation and automation. In 1827 his wife, Georgiana, died and Babbage who had married against the opposition of his father out of love was grief stricken. Leaving Britain to escape the scene of his sorrow Babbage, by now having inherited his fathers fortune a rich man, spent many months touring the continent carrying out the same survey of the industrial advances in mechanisation and automation wherever his wanderings took him. It was on this journey that he first learnt of the automated Jacquard loom that would supply him with the idea of programming the Analytical Engine with punch cards. Returning to Britain Babbage now turned all those years of research into a book, On the Economy of Machinery and Manufactures published in 1832, that is a year before he met Ada Lovelace for the first time and ten years before Menabrea essay was written. The book was a massive success going through six editions in quick succession and influencing the work of Karl Marx and John Stuart Mill amongst others. It would be safe to say that in 1832 Babbage knew more about mechanisation and automation that almost anybody else on the entire planet and what it was capable of doing and which activities could be mechanised and/or automated. It was in this situation that Babbage decided to transfer his main interest from the Difference Engine to developing the concept of the Analytical Engine conceived from the very beginning as a general-purpose computer capable of carrying out everything that could be accomplished by such a machine, far more than just a super number cruncher.


What is true, however, is that Babbage did concentrate in his plans and drafts, and the Analytical Engine never got past the plans and drafts phase, on the mathematical aspects of the machine. This however does not mean that Babbage considered it purely as a mathematical machine. I am writing this post on a modern state of the art computer. I also use the same device to exchange views with my history of sciences peers on Twitter and Facebook, to post my outpourings, such as this one, on my Internet blog. I can telephone, with visual contact if I choose, with people all over the world using Skype. At the touch, or two, of a keyboard key I have access to dictionaries, encyclopaedias and all sorts of other reference tools and through various means I can exchange documents, photographs, sound files and videos with anybody who owns a similar device. I can listen to and watch all sorts of music recordings and videos and with easily accessible software even turn my computer into an unbelievably flexible musical instrument. Finally when I’m done for the day I can settle back and watch television on my large, high-resolution monitor screen. This is only a fraction of the tasks that my computer is capable of carrying out but they all have one thing in common, they can all only be accomplished if they are capable of being coded into an astoundingly banal logical language consisting only of ‘0s’ and ‘1s’. Of course between the activities I carry out on my monitor screen and the electrical circuits that are only capable of reading those ‘0s’ and ‘1s’ there are layer upon layer of so-called sub-routines and sub-sub-routines and sub-sub-sub…, you get the idea, translating an upper layer into a simpler logical form until we get all the way down to those ubiquitous ‘0s’ and ‘1s’. The language in which those ‘0s’ and ‘1s’ exist is a mathematical language, known as Boolean Algebra, and so in the final analysis my super smart ultra modern computer is nothing but a super number cruncher and only two numbers at that.

Babbage, a brilliant mathematician, was well aware that he could only programme his Engine to carry out tasks that could be reduced over a series of steps to a mathematical language and this is the reason he concentrated on the mathematical aspects of his machine but this by no means meant that he only conceived of it only carrying out mathematical tasks, as we will see when addressing Essinger’s second prong.

Essinger quotes the following passage from Note A of the Malebrea translation:

In studying the action of the Analytical Engine, we find that the peculiar and independent nature of the considerations which in all mathematical analysis belong to operations, as distinguished from the objects operated upon and from the results of the operations performed upon those objects, is very strikingly defined and separated.

It is well to draw attention to this point, not only because its full appreciation is essential to the attainment of any very just and adequate general comprehension of the powers and mode of action of the Analytical Engine, but also because it is one which is perhaps too little kept in view in the study of mathematical science in general. It is, however, impossible to confound it with other considerations, either when we trace the manner in which that engine attains its results, or when we prepare the data for its attainment of those results. It were much to be desired, that when mathematical processes pass through the human brain instead of through the medium of inanimate mechanism, it were equally a necessity of things that the reasonings connected with operations should hold the same just place as a clear and well-defined branch of the subject of analysis, a fundamental but yet independent ingredient in the science, which they must do in studying the engine. The confusion, the difficulties, the contradictions which, in consequence of a want of accurate distinctions in this particular, have up to even a recent period encumbered mathematics in all those branches involving the consideration of negative and impossible quantities, will at once occur to the reader who is at all versed in this science, and would alone suffice to justify dwelling somewhat on the point, in connexion with any subject so peculiarly fitted to give forcible illustration of it as the Analytical Engine.

Attributing its contents to Ada he makes the following comment, “What Ada is emphasising here is the clear distinction between data and data processing: a distinction we tend to take for granted today, but which – like so much of her thinking about computers –was in her own day not only revolutionary but truly visionary”. What is being described here is indeed new in Ada’s day but is a well known development in mathematics know at the time as the Calculus of Operations, a branch of mathematics developed in the first half of the nineteenth century, which differentiates between operators and operations, and in which Babbage worked and to which he made contributions. If the ideas contained in this passage are indeed visionary then the vision is Babbage’s being channelled by Ada and not originating with her. The words might be Ada’s but the thoughts they express are clearly Babbage’s.

Essinger now quotes the next part of the Note:

It may be desirable to explain, that by the word operation, we mean any process which alters the mutual relation of two or more things, be this relation of what kind it may. This is the most general definition, and would include all subjects in the universe. In abstract mathematics, of course operations alter those particular relations which are involved in the considerations of number and space, and the results of operations are those peculiar results which correspond to the nature of the subjects of operation. But the science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value; just as logic has its own peculiar truth and value, independently of the subjects to which we may apply its reasonings and processes.

Essinger now reaches maximum bullshit level, “Ada is seeking to do nothing less than invent the science of computing and separate it from the science of mathematics. What she calls ‘the science of operations’ is indeed in effect computing”. As I have already explained what she calls the ‘science of operations’ is in fact the calculus of operation a new but well developed branch of mathematics of which Babbage was fully cognisant. If anybody is inventing the science of computing it is once again Babbage and not Ada.

Essinger now takes up the case further along in Note A:

The distinctive characteristic of the Analytical Engine, […]is the introduction into it of the principle which Jacquard devised for regulating, by means of punched cards, the most complicated patterns in the fabrication of brocaded stuffs… […]The bounds of arithmetic [emphasis in original] were however outstepped the moment the idea of applying the cards had occurred; and the Analytical Engine does not occupy common ground with mere “calculating machines.” It holds a position wholly its own; and the considerations it suggests are most interesting in their nature. In enabling mechanism to combine together general [emphasis in original] symbols in successions of unlimited variety and extent, a uniting link is established between the operations of matter and the abstract mental processes of the most abstract [emphasis in original] branch of mathematical science. [Ellipsis in quote by Essinger]

Essinger introduces this quote with the following: “In a terse passage she explains (perhaps better than Babbage ever could, who as designer saw many trees but perhaps no longer the forest itself) the essential relationship between the Analytical Engine and the Jacquard loom and how it is different from the earlier invention”. After the quote he then writes: “In perhaps one of the most visionary sentences written during the nineteenth century [he sure doesn’t hold back on the hyperbole], she lays out what these cards shall be capable of doing by way of programming the machine”

First off, if you put back the bits Essinger removed from this passage it is anything but terse, in fact it’s rather verbose. Is Essinger really trying to tell us that Babbage was not aware of what he was doing when he conceived of programming his Engine with punch cards? Unfortunately for Essinger Babbage himself tells us that this is not the case, writing in his notebook on 10 July 1836, that is 8 years before the original French version of the Malebrea essay was published, he has the following to say:

This day I had for the first time a general but very indistinct conception of the possibility of making the engine work out algebraic developments – I mean without any reference to the value of the letters. My notion is that as the cards (Jacquards) of the calc. engine direct a series of operations and the recommence with the first…[2]

Here we have in Babbage’s own words the germ of the idea contained in the Ada quote, an idea that would naturally mature over the intervening nine years before Ada wrote her piece, so I have problems whatsoever in again attributing the thoughts contained here to Babbage.

I’m not going to go on analysing Essinger’s Ada hagiography for almost all of the things that he attributes to Ada it is not difficult to find its origins in Babbage’s work thus reinforcing the claim in an earlier post that Ada is being used here as Babbage’s mouth piece. Not so much the originator as the parrot. I will however close with one last quote from Note A and Essinger’s comment to demonstrate that his grasp of the history of science in the nineteenth century is apparently almost non-existent. Without really introducing it Essinger quotes the following sentence:

Those who view mathematical science, not merely as a vast body of abstract and immutable truths, whose intrinsic beauty, symmetry and logical completeness, when regarded in their connexion together as a whole, entitle them to a prominent place in the interest of all profound and logical minds, but as possessing a yet deeper interest for the human race, when it is remembered that this science constitutes the language through which alone we can adequately express the great facts of the natural world, and those unceasing changes of mutual relationship which, visibly or invisibly, consciously or unconsciously to our immediate physical perceptions, are interminably going on in the agencies of the creation we live amidst: those who thus think on mathematical truth as the instrument through which the weak mind of man can most effectually read his Creator’s works, will regard with especial interest all that can tend to facilitate the translation of its principles into explicit practical forms.

Essinger wonderingly comments on this sentence, “This 158-word sentence is very likely one of the longest sentences in the history of science, but it is also one of the most intriguing. Ada succeeds in this one sentence in linking mathematics, science, religion and philosophy.” Any competent historian of science would immediately recognise this as a rather flowery expression of the basic tenets of natural theology, a philosophy that flourished in the first half of the nineteenth century. This statement could have been made by a very large number of natural philosophers starting with Isaac Newton and going up to and beyond William Whewell and Charles Babbage, for example in the dispute that I outlined on this day last year. What this example clearly illustrates is that Essinger is in no way a real historian who researches and understands his sources but one who thinks he can read the text of Note A and interpret it on the basis of his lack of knowledge rather than on his procession of it.

[1] The copy I read was James Essinger, A Female Genius: how Ada Lovelace, Lord Byron’s daughter started the computer age, London 2015

[2] Babbage notebook quote taken from Dorothy Stein, Ada: A Life and a Legacy, MIT Press, Cambridge Massachusetts &London, 1985 p.102


Filed under History of Computing, Myths of Science

Mensis or menstruation?

I recently stumbled upon this rather charming rant by Anglo-Danish comedian, writer, broadcaster and feminist Sandi Toksvig.

Women's Calendar


Now I’m a very big fan of Ms Toksvig and was very sad when she retired as presenter of BBC Radio 4’s excellent News Quiz, so I don’t want to give the impression that I’m trying to put her down, but if she had know a little bit more about the early history of the calendar then she might not have jumped to the conclusion that this supposed bone calendar must have been made by a woman.

Before I start to explain why Ms Toksvig might be mistaken in her assumption that this purported primitive calendar came from the hands of a woman I would like to waste a few words on all such artefacts. There are a number of bone and stone objects of great antiquity bearing some number of scratches, incisions, notches, indentations or other forms of apparent marking and someone almost always comes along and declares them to be purposely created mathematical artefacts with one or other function. I must say that being highly sceptical by nature I treat all such claims with more than a modicum of wariness. Even assuming that the markings were made by a human hand might they not have been made in an idle moment by a Neolithic teenager trying out his newly acquired flint knife or in the case of our incised bone by an early musician making himself scraper to accompany the evening camp fire sing-a-long? What I’m am saying is that there are often multiple possible explanations for the existence of such marked artefacts and regarding them as signs of some sort of mathematical activity is only one of those possibilities.

However, back to Ms Toksvig and her revelation. She is of course assuming that the twenty-eight incisions are the result of a women counting off the days between her periods, the menstrual cycle being roughly twenty-eight days for most women. Now if Ms Toksvig had taken her thoughts a little further she might have realised that the word menstruation derives from the Latin word for month, which is mensis: a month being originally a lunar month which, depending on how you measure it, has approximately twenty-eight days. In fact much human thought has been expended over the centuries over the fact that a lunar month and the menstrual circle have the same length.

What we have here with this incised bone could well be not a menstrual record, as Ms Toksvig seems to assume, but a mensis record or part of a lunar calendar. This supposition is lent credence by the fact that, with the very notable exception of the ancient Egyptian calendar, all early cultures and civilisations had lunar and not solar calendars including the ancient Romans before Gaius Julius Caesar borrowed the Egyptian solar calendar, the forerunner of our own Gregorian one.

Assuming that the archaeologist or anthropologist who decided that said bone was a primitive calendar was right and it is not the idle whittling of some bored stone-age teenager, we of course still have no idea whether it was the work of a man or a woman.


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

A misleading book title that creates the wrong impression

A new biography of Johannes Kepler has just appeared and although I haven’t even seen it yet, let alone read it, it brings out the HistSci Hulk side of my personality. What really annoys me on David Love’s book, Kepler and the Universe[1], is the title or rather the subtitle, How One Man Revolutionised Astronomy. Now, I for one have for many years conducted a private campaign to persuade people not to claim that we live in a Copernican Cosmos, a standard cliché, but that we live in a Keplerian Cosmos, because it was the very different elliptical system of Kepler that helped heliocentricity to its breakthrough and not the system of Copernicus. However Love’s subtitle immediately evokes the spectre of the lone genius and for all his undoubted brilliance Kepler was not a lone genius and especially not in terms of his cosmology/astronomy.

A 1610 portrait of Johannes Kepler by an unknown artist Source: Wikipedia Commons

A 1610 portrait of Johannes Kepler by an unknown artist
Source: Wikipedia Commons

Even a cursory examination of Kepler’s road to his system will immediately reveal his intellectual debts and his co-conspirators, both willing and unwilling. First off is naturally Copernicus himself. Kepler did not conceive a heliocentric system from scratch but was, on his own admission a glowing admirer or even acolyte of the Ermländer scholar. This admiration is one of the principle reasons that we don’t truly acknowledge Kepler’s achievement but tend to dismiss it as having just dotted the ‘Is’ and crossed the ‘Ts’ in Copernicus’ system, a demonstrably false judgement. Kepler, of course, didn’t help the situation when he titled the most simple and readable version of his system, and the one that together with the Rudolphine Tables had the most influence, the Epitome Astronomiae Copernicanae. Not a smart move! Whatever, we are already at two men who revolutionised astronomy.

Nicolaus Copernicus 1580 portrait (artist unknown) in the Old Town City Hall, Toruń Source: Wikimedia Commons

Nicolaus Copernicus 1580 portrait (artist unknown) in the Old Town City Hall, Toruń
Source: Wikimedia Commons

Kepler did not discover Copernicus himself but was introduced to him by his teacher Michael Maestlin at the University of Tübingen. Usually Maestlin gets mentioned in passing as Kepler’s teacher and then forgotten but he played a very important role in Kepler’s early development. In reality Maestlin was himself one of the leading European astronomers and mathematicians in the latter part of the sixteenth century, as well as being by all accounts an excellent teacher. He was also one of the very few supporters of both Copernican astronomy and cosmology. This meant that he gave Kepler probably the best foundation in the mathematical sciences that he could have found anywhere at the time, as well as awakening his interest in Copernican thought. It was also Maestlin who decided Kepler would be better off becoming a teacher of mathematics and district mathematician rather than training for the priesthood; a decision that Kepler only accepted very, very reluctantly. Even after he had left Tübingen Maestlin continued to support the young Kepler, although he would withdraw from him in later years. Maestlin edited, corrected and polished Kepler’s, so important, first publication, the Mysterium Cosmographicum. In fact Maestlin’s contributions to the finished book were so great he might even be considered a co-author. Some people think that in later life Kepler abandoned the, for us, rather bizarre Renaissance hypothesis of the Cosmographicum, but he remained true to his initial flash of inspiration till the very end, regarding all of his later work as just refinements of that first big idea. Maestlin’s contribution to the Keplerian system was very substantial. And then there were three.

Michael Maestlin Source: Wikimedia Commons

Michael Maestlin
Source: Wikimedia Commons

Tycho! Without Tycho Brahe there would be no Keplerian System. Tycho and Kepler are the Siamese twins of elliptical astronomy joined at the astronomical data. Without Tycho’s data Kepler could never have built his system. This duality is recognised in many history of astronomy texts with the two, so different, giants of Renaissance astronomy being handled together. The popular history of science writer, Kitty Ferguson even wrote a dual biography, Tycho and Kepler, The Unlikely Partnership that Forever Changed our Understanding of the Heavens[2], a title that of course contradicts Love’s One Man. Her original title was The Nobleman and His Housedog, with the rest as a subtitle, but it seems to have been dropped in later editions of the book. The ‘housedog’ is a reference to Kepler characterising himself as such in the horoscope he wrote when he was twenty-five years old.

Portrait of Tycho Brahe (1596) Skokloster Castle Source: Wikimedia Commons

Portrait of Tycho Brahe (1596) Skokloster Castle
Source: Wikimedia Commons

Tycho invited Kepler to come and work with him in Prague when the Counter Reformation made him jobless and homeless. Tycho welcomed him back when Kepler went off in a huff at their first meeting. It was Tycho who assigned him the task of calculating the orbit of Mars that would lead him to discover his first two laws of planetary motion. It has been said that Tycho’s data had just the right level of accuracy to enable Kepler to determine his elliptical orbits. Any less accurate and the slight eccentricities would not have been discernable. Any more accurate and the irregularities in the orbits, thus made visible, would have made the discovery of the elliptical form almost impossible. It has also been said that of all the planets for which Tycho had observation data Mars was the one with the most easily discernable elliptical orbit. Serendipity seems to have also played a role in the discovery of Kepler’s system. The high quality of Tycho’s data also led Kepler to reject an earlier non-elliptical solution for the orbit of Mars, which another astronomer would probably have accepted, with the argument that it was not mathematically accurate enough to do honour to Tycho’s so carefully acquired observational data.

Tycho was anything but a one-man show and his observatory on the island of Hven has quite correctly been described as a research institute. A substantial number of astronomer, mathematicians and instrument maker came and went both on Hven and later in Prague over the almost thirty years that Tycho took to accumulate his data. The number of people who deserve a share in the cake that was Kepler’s system now reaches a point where it become silly to count them individually.

Our list even includes royalty. Rudolph II, Holly Roman Emperor, was the man, who, at Tycho’s request, gave Kepler a position at court, even if he was more than somewhat lax at paying his salary, official to calculate the Rudolphine Tables, a task that would plague Kepler for almost thirty years but would in the end lead to the acceptance of his system by other astronomers. Rudolph also appointed Kepler as Tycho’s successor, as Imperial Mathematicus, after the latter’s untimely death, thus giving him the chance to continue his analysis of Tycho’s data. Rudolph could just as easily have sacked him and sent him on his way. Tycho’s heirs did not assist Kepler in his struggle to maintain access to that all important data, which belonged to them and not the Emperor, causing him much heartache before they finally allowed him to use Tycho’s inheritance. After he had usurped his brother, Rudolph, in 1612, Matthias allowed Kepler to keep his official position and title as Imperial Mathematicus, although sending him away from court, a fact that certainly assisted Kepler in his work. Being Imperial Mathematicus gave him social status and clout.

Rudolph II portrait by Joseph Heinz the Elder Source: Wikimedia Commons

Rudolph II portrait by Joseph Heinz the Elder
Source: Wikimedia Commons

Kepler described his long and weary struggles with the orbit of Mars as a battle, but he did not fight this battle alone. In a long and fascinating correspondence with the astronomer, David Fabricius, Kepler tried out his ideas and results with a convinced supporter of Tycho’s system. Kepler would present his ideas and David Fabricius subjected them to high level and very knowledgeable criticism. Through this procedure Kepler honed, refined and polished his theories to perfection before he submitted them to public gaze in his Astronomia Nova, Knowing that they would now withstand high-level professional criticism. David Fabricius, who never met Kepler, nevertheless took a highly active role in the shaping of the Keplerian system[3].

Monument for David and Johann Fabricius in the Graveyard of Osteel

Monument for David and Johann Fabricius in the Graveyard of Osteel

Even after Kepler’s death the active participation of others in shaping his astronomical system did not cease. Jeremiah Horrocks corrected and extended the calculations of the Rudolphine Tables, enabling him to predict and observe a transit of Venus, an important stepping-stone in the acceptance of the elliptical astronomy. Horrocks also determined that the moon’s orbit was a Keplerian ellipse, something that Kepler had not done.


Stained glass roundel memorial in Much Hoole Church to Jeremiah Horrocks making the first observation and recording of a transit of Venus in 1639. The Latin reads "Ecce gratissimum spectaculum et tot votorum materiem": "oh, most grateful spectacle, the realization of so many ardent desires". It is taken from Horrocks's report of the transit

Stained glass roundel memorial in Much Hoole Church to Jeremiah Horrocks making the first observation and recording of a transit of Venus in 1639. The Latin reads “Ecce gratissimum spectaculum et tot votorum materiem”: “oh, most grateful spectacle, the realization of so many ardent desires”. It is taken from Horrocks’s report of the transit

Cassini, together with Riccioli and Grimaldi, using a heliometer determined that either the orbit of the sun around the earth or the earth around the sun, the method can’t determine which is true, is an ellipse another important empirical stepping-stone on the road to final acceptance for the system.

Giovanni Cassini Source: Wikimedia Commons

Giovanni Cassini
Source: Wikimedia Commons

Nicholas Mercator produced a new mathematical derivation of Kepler’s second law around 1670. Kepler’s own derivation was, as he himself admitted, more than a little suspect, viewed mathematically. The first and third laws had been accepted by the astronomical community fairly easily but the second law was a major bone of contention. Mercator’s new derivation basically laid the dispute to rest.

Cassini in his new role as director of the Paris observatory showed empirically that the satellite systems of both Jupiter and Saturn also obeyed Kepler’s third law extending it effectively to all orbitary systems and not just the planets of the solar system.

Lastly Newton derived Kepler’s first and second laws from his axiomatic system of dynamics giving them the true status of laws of physics. This led Newton to claim that the third law was Kepler’s but the first two were his because he, as opposed to Kepler, had really proved them

As we can see the list of people involved in revolutionising astronomy in the seventeenth century in that they replaced all the geocentric systems with a Keplerian elliptical system is by no means restricted to ‘one man’ as claimed in the subtitle to David Love’s book but is quite extensive and very diverse. There are no lone geniuses; science is a collective, collaborative enterprise.





[1] David Love, Kepler and the Universe: How One Man Revolutionized Astronomy, Prometheus Books, 2015

[2] Kitty Ferguson, Tycho and Kepler, The Unlikely Partnership that Forever Changed our Understanding of the Heavens, Walker Books, 2002

[3] For a wonderful description of this correspondence and how it contributed to the genesis of Astronmia Nova see James Voelkel’s excellent, The Composition of Kepler’s Astronomia nova, Princeton University Press, 2001


Filed under History of Astronomy, Myths of Science, Uncategorized

The Renaissance Mathematicus “Live & Uming”

Those of you with nothing better to do can listen to a podcast of the Renaissance Mathematicus (that’s me folks!) searching for words, desperately trying to remember names, uming & ahing, thinking on his feet (I was actually sitting down the whole time) and generally stumbling his way through an eighty minute spontaneous, unrehearsed, live interview with Scott Gosnell of Bottle Rocket Science on such scintillated topics, as why the Pope got his knickers in a twist over Galileo or that notorious seventeenth century religious fanatic Isaac Newton. In fact the same boring load of old codswallop that you can read at you leisure here on this blog. As I say if you have nothing more exciting to do, such as watching paint dry or listening to the grass grow, then go listen.

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

The Phlogiston Theory – Wonderfully wrong but fantastically fruitful

There is a type of supporter of gnu atheism and/or scientism who takes a very black and white attitude to the definition of science and also to the history of science. For these people, and there are surprisingly many of them, theories are either right, and thus scientific, and help the progress of science or wrong, and thus not scientific, and hinder that progress. Of course from the point of view of the historian this attitude or stand point is one than can only be regarded with incredulity, as our gnu atheist proponent of scientism dismisses geocentrism, the phlogiston theory and Lamarckism as false and thus to be dumped in the trash can of history whilst acclaiming Copernicus, Lavoisier and Darwin as gods of science who led as out the valley of ignorance into the sunshine of rational thought.

I have addressed this situation before on more than one occasion but as a historian of science I think that it’s a lesson that needs to be repeated at regular intervals. Because it is the American Chemical Society’s “National Chemistry Week 2015” I shall be re-examining the Phlogiston Theory whose creator Georg Ernst Stahl was born on 22 October 1659 in Ansbach, which is in Middle Franconia just down the road from where I live.

Stahl had a fairly conventional career, studying medicine at Jena University from 1679 to 1684. 1687 he became court physician to the Duke of Sachen-Weimar and in 1694 he was appointed professor of medicine at the newly founded University of Halle, where he remained until 1715 when he became personal physician to Friedrich Wilhelm I, King of Prussia. Stahl like most chemists in the Early Modern Period was a professional physician, chemistry only existing within the academic context as a sub-discipline of medicine.

To understand the phlogiston theory we need to go back and take a brief look at the development of the theory of matter since the ancient Greeks. Empedocles introduced the famous four-element theory, Earth, Water, Air and Fire, in the fifth century BCE and this remained the basic theory in Europe until the Early Modern Period. In the ninth century CE Abu Mūsā Jābir ibn Hayyān added Sulphur and Mercury to the four-elements as principles, rather than substances, to explain the characteristics of the seven metals. In the sixteenth century CE, Paracelsus took over al- Jābir’s Sulphur and Mercury adding Salt as his tria prima to explain the characteristics of all matter. In the seventeenth century, when Paracelsus’ influence was at its height, many alchemists/chemists adopted a five-element theory – Earth, Water, Sulphur, Mercury and Salt – dropping air and fire. Robert Boyle, in his The Sceptical Chymist (1661), threw out both the Greek four-element theory and Paracelsus’ tria prima, groping towards a more modern concept of element. We now arrive at the origins of the phlogiston theory.

The German Johann Joachim Becher (1635–1682), a physician and alchemist, was a big fan of Boyle and his theories and even travelled to London to learn at the feet of the master. Like Boyle he rejected both the Greek four-element theory and Paracelsus’ tria prima, in his Physica Subterranea (1667) replacing them with a two-element theory Earth and Water with Air present just as a mixing agent for the two. However he basically reintroduced Paracelsus’ tria prima in the form of three different types of Earth.

  • terra fluida or mercurial Earth giving material the characteristics, fluidity, fineness, fugacity, metallic appearance
  • terra pinguis or fatty Earth giving material the characteristics oily, sulphurous and flammable
  • terra lapidea glassy Earth, giving material the characteristic fusibility

Stahl took up Becher’s scheme of elements concentrating on his terra pinguis, making it his central substance and renaming it phlogiston. In his theory all substances, which are flammable contain phlogiston, which is given up when they burn, the combustion ceasing when the phlogiston is exhausted. The classic demonstration of this was the combustion of mercury, which turns to ash, in Stahl’s terminology (mercuric oxide in ours). If this ash is reheated with charcoal the phlogiston is restored (according to Stahl) and with it the mercury. (In our view the charcoal removes the oxygen restoring the mercury). In a complex series of experiment Stahl turned sulphuric acid into sulphur and back again, explaining the changes once again through the removal and return of phlogiston. Through extension Stahl, an excellent experimental chemist, was able to explain, what we now know as the redox reactions and the acid-base reactions, with his phlogiston theory based on experiment and empirical observation. Stahl’s phlogiston theory was thus the first empirically based ‘scientific’ explanation of a large part of the foundations of chemistry. It is a classic example of what Thomas Kuhn called a paradigm and Imre Lakatos a scientific research programme.

Viewed with hindsight the phlogiston theory is gloriously, wonderfully and absolutely wrong in all of its aspects thus leading to the scorn with which it is viewed by our gnu atheist proponent of scientism, however they are wrong to do so. I prefer Lakatos’ scientific research programme to Kuhn’s paradigm exactly because it describes the success of the phlogiston theory much better. For Lakatos it’s irrelevant whether a theory is right or wrong, what matters are its heuristics. A scientific research programme that produces new facts and phenomena that fit within the descriptive scope of the programme has a positive heuristic. One that produces new facts and phenomena that don’t fit has a negative heuristic. Scientific research programmes have both positive and negative heuristics simultaneously throughout their existences, so long as the positive heuristic outweighs the negative one the programme continues to be accepted. This was exactly the case with the phlogiston theory.

Most European eighteenth-century chemist accepted and worked within the framework of the phlogiston theory and produced a great deal of new important chemical knowledge. Most notable in this sense are the, mostly British, so-called pneumatic chemists. Working within the phlogiston theory Joseph Black (1728–1799), professor for medicine in Edinburgh, isolated and identified carbon dioxide whilst his doctoral student Daniel Rutherford (1749–1819) isolated and identified nitrogen. The Swede Carl Wilhelm Scheele (1742–1786) produced, identified and studied oxygen for which he doesn’t get the credit because although he was first, he delayed in publishing his results and was beaten to the punch by Joseph Priestley (1733–1804), who had independently also discovered oxygen labelling it erroneously dephlogisticated air. Priestley by far and away the greatest of the pneumatic chemists isolated and identified at least eight other gases as well as laying the foundations for the discovery of photosynthesis, perhaps his greatest achievement.

Henry Cavendish (1731–1810) isolated and identified hydrogen, which he thought for a time might actually be phlogiston, before going on to make the most important discovery within the framework of the phlogiston theory, the structure of water. By a series of careful experiments Cavendish was able to demonstrate that water was not an element but a compound consisting of two measures of phlogiston (hydrogen) with one of dephlogisticated air (oxygen). With the same level of precision he also demonstrated that normal air consists of four parts of nitrogen to one of oxygen or better said not quite. He constantly found something he couldn’t identify present in one one-hundredth and twentieth of the volume of nitrogen. In the nineteenth century this would finally be identified as the gas argon.

All of these discoveries are to be counted to the positive heuristic of the phlogiston theory. What weighed heavily on the negative side is the fact that as the accuracy of measurement increased in the eighteenth century it was discovered that the ashes, of mercury for example, left behind on burning were heavier than the original substance being burnt. This was troubling as combustion was supposed to be the release of phlogiston. Some supporters of the theory even suggested negative phlogiston to explain this anomaly. This suggestion, which never caught on, gets particularly mocked today, something I find somewhat strange in an age that has had to accept anti-matter and is now being asked to accept dark matter and dark energy to explain known anomalies in current theories.

Ironically it was the discoveries of oxygen and the composition of water that gave Lavoisier the necessary building blocks to dismantle the phlogiston theory and build his own competing theory, which would in the end prove successful and commit the phlogiston theory to the scrap heap of the history of chemistry. However one should never forget that it was exactly this theory that delivered him the tools he needed to do so. As I wrote in my sub-title even a theory that is wonderfully wrong can be fantastically fruitful and should be treated with respect when viewed with hindsight.



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

Science contra Copernicus

One of the most persistent and pernicious myths in the history of astronomy is that Galileo, with his telescopic observations, proved the validity of the Copernican heliocentric hypothesis and thus all opposition to it from that point on was purely based on ignorance and blind religious prejudice. Strangely, this version of the story is particularly popular amongst gnu atheists. I say strangely because these are just the people who pride themselves on only believing the facts and basing all their judgements on the evidence. Even Galileo knew that the evidence produced by his telescopic observations only disproved some aspects of Aristotelian cosmology and full scale Ptolemaic astronomy but other Tychonic and semi-Tychonic geocentric models still fit the available facts. A well as this the evidence was still a long way from proving the existence of a heliocentric model and many physical aspects spoke strongly against a moving earth. Put another way, the scientific debate on geocentrism versus heliocentrism was still wide open with geocentrism still in the most favourable position.

Apart from the inconclusiveness of the telescopic observations and the problems of the physics of a moving earth there were other astronomical arguments against heliocentricity at the time that remain largely unknown today. Christopher M. Graney[1] has done the history of astronomy community a big service in uncovering those arguments and presenting them in his new book Setting Aside All Authority: Giovanni Battista Riccioli and the Science against Copernicus in the Age of Galileo[2].


We’ll start with the general summary, as I’ve already stated in an earlier post this is an excellent five star plus book and if you have any interest in this critical period of transition in the history of astronomy then it is quite simply an obligatory text that you must read. So if you follow my advice, what are you getting for your money?

In 1651 the Jesuit astronomer Giovanni Battista Riccioli published his Almagestum Novum or New Almagest , which contains a list of 126 arguments concerning the motion of the earth, i.e. the heliocentric hypothesis, 49 for and 77 against and it is this list that provides the intellectual scaffolding for Graney’s book. Interestingly in discussion on seventeenth-century astronomy Riccioli’s book, and its list, has largely been dismissed or ignored in the past. The prevailing attitudes in the past seem to have been either it’s a book by a Jesuit so it must be religious and thus uninteresting or, as was taught to me, it’s a historical account of pre-Galilean astronomy and thus uninteresting. In fact before Graney and his wife undertook the work this list had never even been translated into English. As to the first objections only a few of Riccioli’s arguments are based on religion and as Graney points out Riccioli does not consider them to be very important compared with the scientific arguments. As to the second argument Riccioli’s account is anything but historical but reflects the real debate over heliocentrism that was taking place in the middle of the seventeenth century.

The strongest scientific argument contra Copernicus, which occupies pride of place in Graney’s book, is the so-called star size argument, which in fact predates both Galileo and the telescope and was first posited by Tycho Brahe. Based on his determination of the visible diameter of a star, Tycho calculated that for the stars to be far enough away so as to display no visible parallax, as required by a Copernican model with a moving earth, then they must be in reality unimaginably gigantic. A single star would have the same diameter as Saturn’s orbit around the sun. These dimensions for the stars didn’t just appear to Tycho to be completely irrational and so unacceptable. In a Tychonic cosmos, however, with its much smaller dimensions the stars would have a much more rational size. Should anyone think that this argument was not taken seriously, much later in the seventeenth century Christiaan Huygens considered the star size problem to be Tycho’s principle argument against Copernicus.

Many, more modern, historians dismissed the star size problem through the mistaken belief that the telescope had solved the problem by showing that stars are mere points of light and Tycho’s determined star diameters were merely an illusion caused by atmospheric refractions. In fact the opposite was true, early telescopes as used by Galileo and Simon Marius, amongst others, showed the stars to have solid disc shaped bodies like the planets and thus confirming Tycho’s calculations. Marius used this fact to argue scientifically for a Tychonic cosmos whilst Galileo tried to dodge the issue. We now know that what those early telescopic astronomers saw was not the bodies of stars but Airy discs an optical artefact caused by diffraction and the narrow aperture of the telescope and so the whole star size argument is in fact bogus. However it was first Edmond Halley at the beginning of the eighteenth century who surmised that these observed discs were in fact not real.

Graney details the whole history of the star size argument from Tycho down to Huygens revealing some interesting aspect along the way. For example the early Copernicans answered Tycho’s objections not with scientific arguments but with religious ones, along the lines of that’s the way God planned it!

Although the star size argument was the strongest scientific argument contra Copernicus it was by no means the only one and Graney gives detailed coverage of the whole range offering arguments and counter arguments, as presented by the participants in the seventeenth-century debate. Of interest particular here is Riccioli’s anticipation of the so-called Coriolis effect, which he failed to detect experimental thus rejecting a moving earth. Far from being a decided issue since 1610 when Galileo published his Sidereus Nuncius heliocentricity remained a scientifically disputed hypothesis for most of the seventeenth century.

Graney’s book is excellently written and clear and easy to understand even for the non-physicists and astronomers. He explains clearly and simply the, sometimes complex, physical and mathematical arguments and it is clear from his writing style that he must be a very good college teacher. The book is well illustrated, has an extensive bibliography and a useful index.

As a bonus the book contains two appendixes. The first is a translation (together with the original Latin text) and technical discussion of Francesco Ingoli’s 1616 Essay to Galileo, a never published but highly important document in the on going discussion on heliocentricity; Ingoli a Catholic cleric argued in favour of the Tychonic system. The second appendix is a translation (together with the original Latin text) and technical discussion of Riccioli’s Reports Regarding His Experiments with Falling Bodies. These experiments are of historical interest as they demonstrate Riccioli’s abilities, as a physicist, as he delivered the first empirical confirmation of Galileo’s laws of fall.

Graney’s book is a first class addition to the literature on the history of astronomy in the seventeenth century and an absolute must read for anyone claiming serious interest in the topic. If you don’t believe me read what Peter Barker, Dennis Danielson and Owen Gingerich, all first class historians of Early Modern astronomy, have to say on the back cover of the book.


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

[2] Christopher M. Graney, Setting Aside All Authority: Giovanni Battista Riccioli and the Science against Copernicus in the Age of Galileo, University of Notre Dame Press; Notre Dame Indiana, 2015


Filed under Book Reviews, History of Astronomy, Myths of Science