Galileo was insufficiently woke?

We haven’t had a good Galileo rant here at the Renaissance Mathematicus for some time, but when you just begin to think that maybe people have stopped misusing the Tuscan natural philosopher for their own ends, up pops a new example and we’re off again.

My attention was drawn to today wonderful example by the following exchange on Twitter:

Seb Falk (@Seb_Falk): I’ve heard a lot of nonsense about Galileo, but persecuted by the Church for being insufficiently woke? That’s a new one on me.

Is there a Galileo-related law equivalent to Godwin’s Law? If not, Falk’s Law states that as a culture war continues, the probability that someone will invoke a mythologised account of the trial of Galileo in a specious defence of academic freedom approaches 1.

Dave Hitchcock (@Hitchcokian): Amazing. it shall definitely be known henceforth as Falk’s Law.

Seb Falk: I’m honoured – though I was just thinking that @rmathematicus has been calling this stuff out for so long we should call it Christie’s Law. Bloody history of science, always naming things after the wrong person

James Sumner (@JamesBSumner): Well, now, that’s perfectly consonant with Stigler’s law of eponymy

For those not aware of Stigler’s Law, it states that no scientific discovery is named after its original discoverer. Stigler’s law itself was in fact discovered by Robert K Merton and not Stephen Stigler.

So what was the piece about Galileo that provoked the creation of Falk’s Law?

Trevor Phillips (@MTREVORP) opens an article in the Times newspaper titled University bigots want to control minorities with the following:

Every scientist knows the Galileo story. When one of the greatest minds of the 17th (or any other) century concluded that, contrary to the Catholic Church’s teaching, the Earth was not the still centre of the universe but just one satellite of the sun he was for the high jump.

Subjected to six years at the hands of the Inquisition, character assassination and house arrest, he finally gave in and admitted his “wrongthink” but is reputed to have muttered under his breath “E pur si muove” – “Still, it moves”. The man whom Einstein called the father of modern science was said to be hurt most by the way his fellow philosophers abandoned him for fear of suffering the same fate.

I find it fascinating just how much a supposedly intelligent, educated, well informed writer can get wrong in just two very short paragraphs. We start with the opening sentence; experience has clearly shown that very few scientists know the actual Galileo story; most of them know one or other very mangled version of what might be termed the Galileo myth, which all have something in common, a factual, historical truth content on a par with an episode of Game of Thrones.

We then get the statutory hyperbollocks as soon as Galileo becomes the subject of discourse, “one of the greatest minds of the 17th (or any other) century.” This leads me to the thought, what if Galileo had not been hyped up to this larger than life, once in a century genius, would people be just as outraged if he had been mistreated by the Inquisition. Is it a worse crime if those in power mistreat a brilliant scientist, than if they mistreat Giuseppe, the guy who empties the trash cans? Not just here but in lots of things that I have read, I get the impression that is exactly what a very large number of people think. Are some lives really worth more than others? Their argument seems to be something along the lines of but Galileo changed the world, Giuseppe the trash can guy didn’t. What if the fact that Giuseppe was rotting in an Inquisition dungeon, instead of cleaning the streets led to an outbreak of cholera that wiped out half the population of the city? But I digress.

What follows is a significant misrepresentation of the facts that is dished every time somebody present their mythical version of the Galileo story and one that I have dealt with many times. It wasn’t just the Catholic Church’s teaching that we live in a geocentric cosmos but was the considered, majority opinion of informed astronomers based on the then available empirical evidence. Galileo was involved in a complex scientific debate on the astronomical and cosmological status of the solar system and was not this brilliant scientist taking on the ignorant, non-scientific, religious prejudices of the Catholic Church.  There are a couple of grammatical and lexigraphical anomalies in Phillips’ sentence that should have been picked up by a good sub-editor. If he is going to write Earth with a capital ‘E’ then he should also write sun with a capital ‘S’ and the earth is not a satellite of the sun it is a planet. Satellites orbit planets, planets orbit suns.

Subjected to six years at the hands of the Inquisition? Really? Galileo’s interrogation, trial and the passing of judgement by the Roman Inquisition lasted not quite four months, so I have literally no idea what Phillips is talking about here. I also have absolutely no idea what he means when he writes, “character assassination”, through out the whole affair he was treated with care and consideration and the respect due to him both because of his age and his reputation. Does one really need to repeat that Galileo was not tried for supporting the heliocentric hypothesis but for breaking an injunction from 1616 not to hold or teach the heliocentric theory as fact rather than, as a hypothesis? There was literally no question of “wrongthink”, Galileo was fully entitled to think what he liked about heliocentricity and even to express those thoughts verbally but he was not permitted to claim that heliocentricity was a proven fact. Just for the record, for the umpteenth time, it wasn’t. I find it almost funny that Phillips includes house arrest amongst the mistreatments before Galileo adjured. Having adjured he was, in fact, sentenced to imprisonment, which was immediately commuted to house arrest by the Pope, so after the fact not before.

Of course, having dished up a totally fictional account of Galileo’s dispute with the Church, Phillips doesn’t not spare us the “E pur si muove” – “Still, it moves” myth, in for a penny in for a pound. If we going to present fairy tales in place of historical accuracy then why not go the whole hog? We, natural, get that leading expert on the history of science, Albert Einstein, quoted on Galileo’s status in that history. Why ask a historian when you can ask Uncle Albert, the font of all wisdom? Another reminder, the expression ‘father of’ is a meaningless piece of crap.

Phillips’ last claim leaves me, once more, totally bewildered. “[Galileo] was said to be hurt most by the way his fellow philosophers abandoned him for fear of suffering the same fate.” There are two aspects to this claim. Firstly, the man, who is a serious candidate for the most egotistical and arrogant arsehole in the entire history of science and who spent a large part of his life actively insulting, denigrating and alienating ‘his fellow philosophers’ was hurt because they didn’t support him, really? Secondly, I have spent a life time reading about and studying Galileo and the historical context in which he lived and worked and I have never ever come across anybody claiming anything remotely like this claim made by Phillips. Put differently, Phillips is just making shit up to bolster the argument that he is going to present in his article. This is not history or journalism this is quite simply lying!

People used to refer to the Galileo Gambit, when somebody, almost always a crank, compared having his ‘fantastic ideas’ rejected to the Catholic Church’s persecution of Galileo. To this Bob Dylan delivered up the perfect retort:

He said, “They persecuted Jesus too.”

I said, “You’re not him.”

“I said you know, they refused Jesus, too. He said you’re not him.”

[Correct version of Dylan quote curtesy of Todd Timberlake]

Trevor Phillips delivers up a slightly different variation on the theme. He is using a totally mythical version of the Galileo story to beat people, who he disapproves of or disagrees with around the head. If he can’t make the points that he wishes to make without resorting to lies and deception in that he misuses an episode in the history of science then he should give up pretending to be a journalist.


Filed under Myths of Science, Uncategorized

Giambattista della Porta the most polymathic of all Renaissance polymaths?

Giambattista della Porta (1535(?)–1615) is well known to historians of Renaissance science but for the general public he remains a largely unknown figure. If he is known at all,  he is often written off as an occultist, because of the title of his most well known work Magia Naturalis. In fact in the late sixteenth and early seventeenth centuries he was a highly respected and influential member of the Italian Renaissance scientific community. Although he wrote and published profusely over a wide range of scientific and related topics he made no really major discoveries and produced no major inventions and unlike his contemporaries, Kepler and Galileo, who were both well acquainted with his work, he has been largely forgotten.


Giambattista della Porta Source: Wikimedia Commons

Giambattista Della Porta were born at Vico Equense, Near Naples, probably sometime in 1535 (he created the confusion about his birth date), the third of four sons of the nobleman Nardo Antonio dell Porta of whom three survived childhood.  His parental home resembled an intellectual salon where the boys were continually exposed to and educated by visiting philosophers, mathematicians, poets and musicians. Their education was completed by private tutors, who also taught the boys the attributes of a gentleman, dancing, riding, skilled performance in tournaments and games and how to dress well. Della Porta never attended university but enjoyed life as a well educated polymathic, gentleman of leisure. If he can be considered to have had a profession, then it is that of a dramatist, he wrote more than twenty theatrical works, but it is his extensive activities in the sciences that interest us here.

Already in 1558, at the age of 23, he published the fist version of his most well known work, the Magia Naturalis in four books, a sort of encyclopaedia of the Renaissance sciences. From the beginning it was a bestseller running to five editions in Latin within the first ten years with translations into Italian (1560), French (1565), Dutch (1566) and English (1658). A vastly expanded version in twenty books was published in 1589. This final version covers a wide range of topics:


Source: Wikimedia Commons

Book 1: Of the Causes of Wonderful Things Book 2: Of the Generation of Animals Book 3: Of the Production of New Plants Book 4: Of Increasing Household-Stuff Book 5: Of Changing Metals Book 6: Of Counterfeiting Glorious StonesBook 7: Of the Wonders of the Load-Stone Book 8: Of Physical Experiments Book 9: Of Beautifying Women Book 10: Of Distillation Book 11: Of Perfuming Book 12: Of Artificial Fires Book 13: Of Tempering Steel Book 14: Of CookeryBook 15: Of Fishing, Fowling, Hunting, etc. Book 16: Of Invisible Writing Book 17: Of Strange Glasses Book 18: Of Static Experiments Book 19: Of Pneumatic Experiment Book 20: Of the Chaos

The contents range from fairly banal parlour tricks, over engineering, experimental science, horticulture and husbandry to every day things. At the very beginning della Porta is very careful to explain what exactly he mean by the term natural magic:

There are two sorts of Magick; the one is infamous, and unhappy, because it has to do with foul Spirits and consists of incantations and wicked curiosity; and this is called Socery; an art which all learned and good men detest; neither is it able to yield an truth of reason or nature, but stands merely upon fancies and imaginations, such as vanish presently away, and leave nothing behind them; as Jamblicus writes in his book concerning the mysteries of the Egyptians. The other Magick is natural; which all excellent wise men do admit and embrace, and worship with great applause; neither is there any thing more highly esteemed, or better thought of, by men of learning. The most noble Philosophers that ever were, Pythagorus, Empedocles, Democritus, and Plato forsook their own countries, and lived abroad as exiles and banished men, rather than as strangers; and all to search out and to attain this knowledge; and when they came home again, this was the Science which they professed, and this they esteemed a profound mystery. They that have been most skillful in dark and hidden points of learning, do call this knowledge the very highest point, and the perfection’s of Natural Sciences; inasmuch that if they could find out or devise amongst all Natural Sciences, any one thing more excellent or more wonderful then another, that they would still call by the name of  Magick. Others have named it the practical part of natural Philosophy, which produces her effects by the mutual and fit application of one natural thing unto another.

The association of Magick with natural philosophy is continued in della Porta’s definition of the Magician:

This is what is required to instruct a Magician, both what he must know, and what he must observe; that being sufficiently instructed in every way, he may bring very strange and wonderful things to us. Seeing Magick, as we showed before, as a practical part of natural Philosophy, it behooves a Magician and one that aspires to the dignity of the profession, to be an exact and very perfect Philosopher.

Despite the very diverse nature of the Magia Naturalis it does contain elements of genuine experimental science. For example, it contains the first experimental disproof of the widely held medieval belief that garlic disables magnets. He also experimented with the cooling properties of dissolving nitre in water. As described here by Andrea Sella (@SellaTheChemist)

As well as the Magia Naturalis della Porta wrote and published a large number of monographs on a very wide range of topics. Cryptography was a popular topic in Renaissance Europe, the most famous book being Johannes Trithemius’ Poligraphia, della Porta published his De Furtivis Literarum Notis (1563), which contain innovative cryptographical ideas.


In 1586 he published a work on physiognomy De humana physiognomonia libri IIII,


From De humana physiognomonia, 1586 Source: Wikimedia Commons

which was still being referenced in the nineteenth century, two years later a book on phytonomy (the science of the origin and growth of plants), Phytognomonica, which contains the first observations on fungal spores.


Phytognomonica, 1588 Source: Wikimedia Commons

These two books confirm della Porta’s adherence to the Renaissance doctrine of signatures. This theory claimed that it was possible to determine the nature of things based on their external appearances.

This was by no means the limit to della Porta’s publishing activities. He also wrote an agricultural encyclopaedia, separate volumes on various fruit bearing trees, books on mathematics, astronomy, meteorology, military engineering, distillation and in 1589 a book on optics, his De refractione optics. We shall return to the latter.


This incredible literary outpouring was just part of his scientific activity, in about 1560 he founded an academic society, Accademia dei Segreti (Academia Secratorum Naturae), the Academy of the Secrets of Nature, which is considered to be the earliest scientific society. The academy met regularly in della Porta’s home and membership was open to all but to become a member one had to present a new secret of nature that one had discovered. We know what some of those new secrets were as della Porta included them in the twenty volume version of his Magia Naturalis. In 1578 della Porta was summoned to Rome and investigated by the Pope. We do not know the exact grounds for this summons but he was forced to shut down his academy on suspicion of sorcery. This is to a certain extent ironic because della Porta was very careful in all his writing to avoid controversial topics particularly religious ones.

Although it was shut down the Accademia dei Segreti, would later have a major influence on another, much more renowned, early scientific academy, Federico Cesi’s Accademia dei Lincei. Cesi was a huge admirer of della Porta and as a young man travelled to Naples to visit the older natural philosopher. On his return home he founded his own academy, whose name was inspired by a line from the preface of the Magia Naturalis:

… with lynx like eyes, examining those things which manifest themselves, so that having observed them, he may zealously use them.

In 1610 della Porta became the fifth member of the Accademia dei Lincei, one year before Galileo.

Another important aspect of Renaissance science was the establishment of private natural philosophical museums also known as Wunderkammer, or cabinets of curiosity. Della Porta had, as to be expected, a particular fine cabinet of curiosity that would influence others to create their own, the Jesuit Athanasius Kircher for example.


Fold-out engraving from Ferrante Imperato’s Dell’Historia Naturale (Naples 1599), the earliest illustration of a natural history cabinet Source: Wikimedia Commons

Della Porta made minor contribution to the advance of science and engineering over a wide range of disciplines but I first ran into della Porta in the context of the history of optics and it his association with this history that I want to look at in somewhat more detail. The early seventeenth century saw both a significant turn in the theory of optics and independently of that the invention of the telescope, an instrument that would go one to revolutionise astronomy, della Porta played a minor roll in both of these things.

The invention of the telescope, by Hans Lipperhey, first became public in September 1608 and the role it would play in the future of astronomy became explosively obvious when Galileo published his Sidereus Nuncius in March 1610. Already in August 1609 della Porta wrote a letter to Federico Cesi claiming to have invented the telescope, he wrote:

I have seen the secret use of the eyeglass and it’s a load of balls [coglionaria] in any case it is taken from book 9 of my De Refractione.[1]

Here della Porta’s memory is faulty, he is after all over seventy years old, what he is referring to is not in the De Refractione but rather in Chapter 10 of Book 17 of Magia Naturalis (1589). Here we find the following suggestive description:

Concave Lenticulars will make one see most clearly things that are afar off.  But Convexes, things near at hand.  So you may use them as your sight requires.  With a Concave Lenticulars you shall see small things afar off very clearly.  With a Convex Lenticular, things nearer to be greater, but more obscurely.  If you know how to fit them both together, you shall see both things afar off, and things near hand, both greater and clearly.  I have much helped some of my friends, who saw things afar off, weakly, and what was near, confusedly, that they might see all things clearly.  If you will, you may.

The lens combination that della Porta describes here is indeed that of the Dutch or Galilean telescope but as van Helden say, and I agree with him, he is here describing some form of spectacles but not a telescope. Kepler, however, who owned a copy of Magia Naturalis credits him with being the inventor of the telescope in his Dissertatio cum Nuncio Sidereo (Conversation with the Starry Messenger) (1610), where he wrote that a recent Dutch invention had been made public years earlier in Magia Naturalis. In 1641 Pierre Gassendi stated that the actual invention had been made by chance by Metius [Jacob Metius (after 1571–1628), who applied for a patent for a telescope two weeks later than Lipperhey] the idea for a similar one had been published years earlier by della Porta.

Later della Porta would graciously admit that his fellow Lynx, Galileo, had achieved much more with his telescope that he, della Porta, could have ever have hoped to do, whilst not abandoning his claim to having first conceived of the telescope.

Della Porta also played a small role in the history of the camera obscura, describing the improvement to the image obtained by placing convex lens into the pinhole, something probably first suggested by Gerolamo Cardano. He also suggested, this time as the first to do so, using a concave mirror to project the image onto a sheet of paper to facilitate drawing it. The popularity of the Magia Naturalis did much to spread knowledge of the camera obscura and its utility as a drawing instrument. Interestingly della Porta compared his camera obscura with the human eye but, unlike Kepler, failed to make the connection that the lens focuses the image on the retina. He continued to believe like everybody before him that the image in perceived in the lens itself.


First published picture of camera obscura in Gemma Frisius’ 1545 book De Radio Astronomica et Geometrica Source: Wikimedia Commons

Della Porta’s role in the turn in the theory of optics is less disputed but not so widely discussed.  Ancient Greek optics was almost exclusively about theories of vision and when taken up and developed in the Islamic Middle Ages this too remained the emphasis. Ibn al-Haytham in his work on optics showed that one could combine an intromission theory of vision with the geometric optics of Euclid, Hero and Ptolemaeus, who had all propagated an extramission theory of vision. This was a major development in the history of optics. In the thirteenth century Robert Grosseteste introduced optics as a central element in both his vision of science and his theology, which led to it being established as a mathematical discipline on the medieval university. Shortly after Roger Bacon, John Peckham and Witelo introduced al-Haytham’s theories on optics into the medieval European mainstream founding what became known as the perspectivist school of optics. Strangely there were no real further developments in the theory of optics down to the end of the sixteenth century when Johannes Kepler, almost singlehandedly, turned the study of optics from one of theories of vision to one of theories of light, thereby ending the reign of the perspectivists. I say almost singlehandedly but he did have two predecessors, who made minor contributions to this turn, Francesco Maurolico (1494–1575) and della Porta.

One major flaw in the perspectivist theory was its treatment of spherical convex lenses and spherical concave mirrors, which said that the images created by them appeared at a single focus point; this is a fallacy. This flaw was in the theory from its inception in the thirteenth century and remained unchecked and uncorrected all the way down to the end of the sixteenth century. The fact that the don’t create their images at a single focal point is, of course, the cause of spherical aberration, something that would plague the construction of telescopes and microscopes well into the eighteenth century. The man who corrected this error in optical theory was della Porta.  Using a mixture of experiments and analytical light ray tracing he came very close to the correct solution an important step towards Kepler’s light ray based theory of optics.


Della Porta’s ray tracing analysis of the reflection of a spherical concave mirror A. Mark Smith, “From Sight to Light: The Passage from Ancient to Modern Optics”, Chicago University Press, 2015 p. 349

Giambattista della Porta is an interesting example of a widespread phenomenon in the history of science. In his own times he was highly respected and regarded, throughout Europe, as a leading natural Philosopher. His books, translated into many languages, were bestsellers and that even long after his death. Johannes Kepler was a fan and Galileo disliked him because he saw him as a serious rival for the position of top dog natural philosopher, a position that Galileo very much desired for himself. However, today most people have never even heard of him and if then he is largely dismissed as a minor irrelevance or even, because of the title of his major work, as some sort of anti-science occultist. But if historians really want to understand what was going on in the scientific community of Europe in the Early Modern Period then they have to take figures like della Porta seriously and not just focus on the ‘big names’ such as Kepler and Galileo.













[1] Quoted from David Freedberg, The Eye of the Lynx: Galileo, His Friends and the Beginnings of Modern Natural History, University of Chicago Press, Chicago and London, 2002, ppb. p. 101 Albert van Helden in his The Invention of the Telescope, American Philosophical Society, Philadelphia, 1977, Reprint, 2008, translates the phrase with coglionaria as …”it’s a hoax” pp. 44-45

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Filed under History of Optics, History of science, Renaissance Science

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


Newton’s Principia is one of the most original and epoch making works in the history of science. There is absolutely nothing original in Newton’s Principia. These two seemingly contradictory judgements of Isaac Newton’s Philosophiæ Naturalis Principia Mathematica are slightly exaggerated versions of real judgements that have been made at various points in the past. The first was the general hagiographical view that was prevalent for much of the eighteenth, nineteenth and twentieth centuries. The second began to appear in the later part of the twentieth century as some historian of science thought that Newton, or better his reputation, needed to be cut down a bit in size. So, which, if either of them, is correct? The surprising answer is, in a way, both of them.


Isaac Newton’s Philosophiae Naturalis Principia Mathematica manuscript volume from which the first edition was printed. Written in the hand of Humphrey Newton, Isaac Newton’s assistant. Source: Royal Society Library via Wikimedia Commons

The Principia is a work of synthesis; it synthesises all of the developments in astronomy and physics that had taken place since the beginning of the fifteenth century. All of the elements that make up Newton’s work were, so to speak, laid out for him to integrate into the book. This is what is meant when we say that there is nothing original in the Principia, however the way that Newton integrated them and what he succeeded in creating was at the time unique and totally original. The Principia was truly a case of the whole being greater than the parts. Before we take a brief look at the contents of the Principia there are a couple of anomalies in its construction that need to be addressed.

The first concerns the general methodological structure of the book. Medieval science was dominated, not exclusively, by the theories of Aristotle and Aristotelian methodology. The developments in astronomy, physics and mathematics that we have covered up to now in this series have seen a gradual but steady deconstruction of the Aristotelian structures and theories. In this situation it comes as a bit of surprise that the methodology of the Principia is classically Aristotelian. Aristotle stated that true episteme (Greek) or scientia (Latin), what we would term scientific knowledge, is achieved by setting out a set of first principles or axioms that are perceived as being true and not in need proof and then logically deducing new knowledge from them. Ironically the most famous example of this methodology is the Elements of Euclid, ironically because Aristotle regarded mathematics as not being real knowledge because it doesn’t deal with objects in the real world. This is the methodology that Newton uses in the Principia, setting out his three laws of motion as his basic principles, which we will come back to later, and not the modern methodologies of Francis Bacon or René Descartes, which were developed in the seventeenth century to replace Aristotle.

The second anomaly concerns the mathematics that Newton uses throughout the Principia. Ancient Greek mathematics in astronomy consisted of Euclidian geometry and trigonometry and this was also the mathematics used in the discipline in both the Islamic and European Middle Ages. The sixteenth and seventeenth centuries in Europe saw the development of analytical mathematics, first algebra and then infinitesimal calculus. In fact, Newton made major contributions to this development, in particular he, together with but independently of Gottfried William Leibniz, pulled together the developments in the infinitesimal calculus extended and codified them into a coherent system, although Newton unlike Leibniz had at this point not published his version of the calculus. The infinitesimal calculus was the perfect tool for doing the type of mathematics required in the Principia, which makes it all the more strange that Newton didn’t use it, using the much less suitable Euclidian geometry instead. This raises a very big question, why?

In the past numerous people have suggested, or even claimed as fact, that Newton first worked through the entire content of the Principia using the calculus and then to make it more acceptable to a traditional readership translated all of his results into the more conventional Euclidian geometry. There is only one problem with this theory. With have a vast convolute of Newton’s papers and whilst we have numerous drafts of various section of the Principia there is absolutely no evidence that he ever wrote it in any other mathematical form than the one it was published in. In reality, since developing his own work on the calculus Newton had lost faith in the philosophical underpinnings of the new analytical methods and turned back to what he saw as the preferable synthetic approach of the Greek Euclidian geometry. Interestingly, however, the mark of the great mathematician can be found in this retrograde step in that he translated some of the new analytical methods into a geometrical form for use in the Principia. Newton’s use of the seemingly archaic Euclidian geometry throughout the Principia makes it difficult to read for the modern reader educated in modern physics based on analysis.

When referencing Newton’s infamous, “If I have seen further it is by standing on the sholders [sic] of Giants”, originally written to Robert Hooke in a letter in 1676, with respect to the Principia people today tend to automatically think of Copernicus and Galileo but this is a misconception. You can often read that Newton completed the Copernican Revolution by describing the mechanism of Copernicus’ heliocentric system, however, neither Copernicus nor his system are mentioned anywhere in the Principia. Newton was a Keplerian, but that as we will see with reservations, and we should remember that in the first third of the seventeenth century the Copernican system and the Keplerian system were viewed as different, competing heliocentric models. Galileo gets just five very brief, all identical, references to the fact that he proved the parabola law of motion, otherwise he and his work doesn’t feature at all in the book. The real giants on whose shoulders the Principia was built are Kepler, obviously, Descartes, whose role we will discuss below, Huygens, who gets far to little credit in most accounts, John Flamsteed, Astronomer Royal, who supplied much of the empirical data for Book III, and possibly/probably Robert Hooke (see episode XXXIX).

We now turn to the contents of the book; I am, however, not going to give a detailed account of the contents. I Bernard Cohen’s A Guide to Newton’s Principia, which I recommend runs to 370-large-format-pages in the paperback edition and they is a whole library of literature covering aspects that Cohen doesn’t. What follows is merely an outline sketch with some comments.

As already stated the book consists of three books or volumes. In Book I Newton creates the mathematical science of dynamics that he requires for the rest of the book. Although elements of a science of dynamics existed before Newton a complete systematic treatment didn’t. This is the first of Newton’s achievement, effectively the creation of a new branch of physics. Having created his toolbox he then goes on to apply it in Book II to the motion of objects in fluids, at first glance a strange diversion in a book about astronomy, and in Book III to the cosmos. Book III is what people who have never actually read Principia assume it is about, Newton’s heliocentric model of the then known cosmos.

Mirroring The Elements of Euclid, following Edmond Halley’s dedicatory ode and Newton’s preface, Book I opens with a list of definitions of terms used. In his scholium to the definitions Newton states that he only defines those terms that are less familiar to the reader. He gives quantity of matter and quantity of motion as his first two definitions. His third and fourth definitions are rather puzzling as they are a slightly different formulation of his first law the principle of inertia. This is puzzling because his laws are dependent on the definitions. His fifth definition introduces the concept of centripetal force, a term coined by Newton in analogy to Huygens’ centrifugal force. In circular motion centrifugal is the tendency to fly outwards and centripetal in the force drawing to the centre. As examples of centripetal force Newton names magnetism and gravity. The last three definitions are the three different quantities of centripetal force: absolute, accelerative and motive. These are followed by a long scholium explicating in greater detail his definitions.

We now arrive at the Axioms, or The Laws of Motions:

1) Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed.

This is the principle of inertia that Newton had taken from Descartes, who in turn had taken it from Isaac Beeckman.

2) A change of motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.

Somewhat different from the modern formulation of F=ma, this principle has its origin in the work of Huygens although there is not a one to one correspondence.

3) To any action there is always an opposite and equal reaction, in other words, the actions of two bodies upon each other are always equal and always opposite in direction.

This law originates with Newton and its source is not absolutely clear. It seems to have been inspired by Newton’s examination of Descartes laws of inelastic collision but it might also have been inspired by a similar principle in alchemy of which Newton was an ardent disciple.

Most people are aware of the three laws of motion, the bedrock of Newton’s system, in their modern formulations and having learnt them, think that they are so simple and obvious that Newton just pulled them out of his hat, so to speak. This is far from being the case. Newton actually struggled for months to find the axioms that eventually found their way into the Principia. He tried numerous different combinations of different laws before finally distilling the three that he settled on.

Having set up his definitions and laws Newton now goes on to produce a systematic analysis of forces on and motion of objects in Book I. It is this tour de force that established Newton’s reputation as one of the greatest physicist of all time. However, what interests us is of course the law of gravity and its relationship to Kepler’s laws of planetary motion. The following is ‘plagiarised’ from my blog post on the 400th anniversary of Kepler’s third law.

In Book I of Principia, the mathematics and physics section, Newton first shows, in Proposition 11[1], that for a body revolving on an ellipse the law of the centripetal force tending towards a focus of the ellipse is inversely as the square of the distance: i.e. the law of gravity but Newton is not calling it that at this point. In Proposition 14[2] he then shows that, If several bodies revolve about a commo[3]n center and the centripetal force is inversely as the square of the distance of places from the center, I say that the principal latera recta of the orbits are as the squares of the areas which bodies describe in the same time by radii drawn to the center. And Proposition 15: Under the same supposition as in prop. 14, I say the square of the periodic times in ellipses are as the cubes of the major axes. Thus Newton shows that his law of gravity and Kepler’s third law are equivalent, although in this whole section where he deals mathematically with Kepler’s three laws of planetary motion he never once mentions Kepler by name. Newton would go one to claim the rights to laws one and two as he had, in his opinion, provided their first real proof. He acknowledges, however, Kepler’s claim to the third law.

Book II as already mentioned appears to go off a tangent in that it deals with motion in a fluid medium, as a result it tends to get ignored, although it is as much a tour de force as Book I. Why this detour? The answer can be found in the theories of René Descartes and Newton’s personal relationship to Descartes and his works in general. As a young man Newton undertook an extensive programme of self-study in mathematics and physics and there is no doubt that amongst the numerous sources that he consulted Descartes stand out as his initial primary influence. At the time Descartes was highly fashionable and Cambridge University was a centre for interest in Descartes philosophy. At some point in the future he then turned totally against Descartes in what could almost be describe as a sort of religious conversion and it is here that we can find the explanation for Book II.

Descartes was a strong supporter of the mechanical philosophy that he had learnt from Isaac Beeckman, something that he would later deny. Strangely, rather like Aristotle, objects could only be moved by some form of direct contact. Descartes also rejected the existence of a vacuum despite Torricelli’s and Pascal’s proof of its existence. In his Le Monde, written between 1629 and 1633 but only published posthumously in 1664 and later in his Principia philosophiae, published in 1644, Descartes suggested that the cosmos was filled with very, very fine particles or corpuscles and that the planets were swept around their orbits on vortexes in the corpuscles. Like any ‘religious’ convert, Newton set about demolishing Descartes theories. Firstly, the title of his volume is a play upon Descartes title, whereas Descartes work is purely philosophical speculation, Newton’s work is proved mathematically. The whole of Book II exists to show that Descartes’ vortex model, his cosmos full of corpuscles is a fluid, can’t and doesn’t work.

Book III, entitled The System of the World, is as already said that which people who haven’t actually read it think that the Principia is actually about, a description of the cosmos. In this book Newton applies the mathematical physics that he has developed in Book I to the available empirical data of the planets and satellites much of it supplied by the Astronomer Royal, John Flamsteed, who probably suffered doing this phase of the writing as Newton tended to be more than somewhat irascible when he needed something from somebody else for his work. We now get the astronomical crowning glory of Newton’ endeavours, an empirical proof of the law of gravity.

Having, in Book I, established the equivalence of the law of gravity and Kepler’s third law, in Book III of The PrincipiaThe System of the World Newton now uses the empirical proof of Kepler’s third law to establish the empirical truth of the law of gravity[4] Phenomena 1: The circumjovial planets, by radii drawn to the center of Jupiter, describe areas proportional to the times, and their periodic times—the fixed stars being et rest—are as 3/2 powers of their distances from that center. Phenomena 2: The circumsaturnian planets, by radii drawn to the center of Saturn, describe areas proportional to the times, and their periodic times—the fixed stars being et rest—are as 3/2 powers of their distances from that center. Phenomena 3: The orbits of the five primary planets—Mercury, Venus, Mars, Jupiter, and Saturn—encircle the sun. Phenomena 4: The periodic times of the five primary planets and of either the sun about the earth or the earth about the sun—the fixed stars being at rest—are as the 3/2 powers of their mean distances from the sun. “This proportion, which was found by Kepler, is accepted by everyone.”

Proposition 1: The forces by which the circumjovial planets are continually drawn away from rectilinear motions and are maintained in their respective orbits are directed to the center of Jupiter and are inversely as the squares of the distances of their places from that center. “The same is to be understood for the planets that are Saturn’s companions.” As proof he references the respective phenomena from Book I. Proposition 2: The forces by which the primary planets are continually drawn away from rectilinear motions and are maintained in their respective orbits are directed to the sun and are inversely as the squares of the distances of their places from its center. As proof he references the respective phenomenon from Book I.

In the 1st edition of Principia Newton referenced the solar system itself and the moons of Jupiter as system that could be shown empirically to Kepler’s third law and added the moons of Saturn in the 3rd edition.

Book III in the first edition closes with Newton’s study of the comet of 1680/81 and his proof that its flight path was also determined by the inverse square law of gravity showing that this law was truly a law of universal gravity.

I have gone into far more detain describing Newton’s Principia than any other work I have looked out in this series because all the various streams run together. Here we have Copernicus’s initial concept of a heliocentric cosmos, Kepler’s improved elliptical version of a heliocentric cosmos with it three laws of planetary motion and all of the physics that was developed over a period of more than one hundred and fifty years woven together in one complete synthesis. Newton had produced the driving force of the heliocentric cosmos and shown that it resulted in Kepler’s elliptical system. One might consider that the story we have been telling was now complete and that we have reached an endpoint. In fact, in many popular version of the emergence of modern astronomy, usually termed the astronomical revolution, they do just that. It starts with Copernicus’ De revolutionibus and end with Newton’s Principia but as we shall see this was not the case. There still remained many problems to solve and we will begin to look at them in the next segment of our story.

[1]  Isaac Newton, The PrincipiaMathematical Principles of Natural Philosophy, A New Translation by I: Bernard Cohen and Anne Whitman assisted by Julia Budenz, Preceded by A Guide to Newton’s Principia, by I. Bernard Cohen, University of California Press, Berkley, Los Angeles, London, 1999 p. 462

[2] Newton, Principia, 1999 p. 467

[3] Newton, Principia, 1999 p. 468

[4] Newton, Principia, 1999 pp. 797–802



Filed under History of Astronomy, History of Mathematics, History of Physics, Newton

Chilli 19.02.2006–27.07.2020

The sweetest little lady in the world has left us. Somewhat more than a year ago I explained how Chilli came into my life. Yesterday she left it taking my heart with her as she went. In recent months she had begun to display the symptoms of dementia. They were unmistakable but still fairly mild, so I thought we would still have some time together.


On Friday morning, on the way home from our early walk in the woods she had some sort of brain malfunction that seems to have blown some fuses in her head. She took off like a rocket and I had no idea where she had gone. She ran wild through the area for nearly one and a half hours, till I could finally catch her with the help of a very generous lady dog owner. She was in total panic and didn’t recognise me and attacked and bit me. She is normally the most passive and friendliest dog in the world. I managed to get her on a lead and she immediately calmed down and we walked home. Once there she fell into her bed and didn’t leave it again the whole day except when I took her briefly outside to pee.

Things did not really improve on Saturday; she was confused, disorientated and apathetic. By Sunday it was clear that the little lady, who had brought me so much joy over the last fifteen or so months was suffering without hope of recovery and that I would have to release here from her distress. On Monday afternoon the vet helped her on her way out the vale of suffering and now she is no more. My flat seems suddenly very empty.

Chilli as puppy005

Chilli as a puppy taken from her vaccination pass Added 29/08/2020


Filed under Autobiographical

Our medieval technological inheritance.

“Positively medieval” has become a universal put down for everything considered backward, ignorant, dirty, primitive, bigoted, intolerant or just simply stupid in our times. This is based on a false historical perspective that paints the Middle Ages as all of these things and worse. This image of the Middle Ages has its roots in the Renaissance, when Renaissance scholars saw themselves as the heirs of all that was good, noble and splendid in antiquity and the period between the fall of the Roman Empire and their own times as a sort of unspeakable black pit of ignorance and iniquity. Unfortunately, this completely false picture of the Middle Ages has been extensively propagated in popular literature, film and television.

Particularly in the film and television branch, a film or series set in the Middle Ages immediately calls for unwashed peasants herding their even filthier swine through the mire in a village consisting of thatch roofed wooden hovels, in order to create the ‘correct medieval atmosphere’. Add a couple of overweight, ignorant, debauching clerics and a pox marked whore and you have your genuine medieval ambient. You can’t expect to see anything vaguely related to science or technology in such presentations.

Academic medieval historians and historians of science and technology have been fighting an uphill battle against these popular images for many decades now but their efforts rarely reach the general lay public against the flow of the latest bestselling medieval bodice rippers or TV medieval murder mystery. What is needed, is as many semi-popular books on the various aspects of medieval history as possible. Whereby with semi-popular I mean, written for the general lay reader but with its historical facts correct. One such new volume is John Farrell’s The Clock and the Camshaft: And Other Medieval Inventions We Still Can’t Live Without.[1]


Farrell’s book is a stimulating excursion through the history of technological developments and innovation in the High Middle Ages that played a significant role in shaping the modern world.  Some of those technologies are genuine medieval discoveries and developments, whilst others are ones that either survived or where reintroduced from antiquity. Some even coming from outside of Europe. In each case Farrell describes in careful detail the origins of the technology in question and if known the process of transition into European medieval culture.

The book opens with agricultural innovations, the deep plough, the horse collar and horse shoes, which made it possible to use horses as draught animals instead of or along side oxen, and new crop rotation systems. Farrell explains why they became necessary and how they increased food production leading indirectly to population growth.

Next up we have that most important of commodities power and the transition from the hand milling of grain to the introduction of first watermills and then windmills into medieval culture. Here Farrell points out that our current knowledge would suggest that the more complex vertical water mill preceded the simpler horizontal water mill putting a lie to the common precept that simple technology always precedes more complex technology. At various points Farrell also addresses the question as to whether technological change drives social and culture change or the latter the former.


Having introduced the power generators, we now have the technological innovations necessary to adapt the raw power to various industrial tasks, the crank and the camshaft. This is fascinating history and the range of uses to which mills were then adapted using these two ingenious but comparatively simple power take offs was very extensive and enriching for medieval society. One of those, in this case an innovation from outside of Europe, was the paper mill for the production of that no longer to imagine our society without, paper. This would of course in turn lead to that truly society-changing technology, the printed book at the end of the Middle Ages.


Along side paper perhaps the greatest medieval innovation was the mechanical clock. At first just a thing of wonder in the towers of some of Europe’s most striking clerical buildings the mechanical clock with its ability to regulate the hours of the day in a way that no other time keeper had up till then gradually came to change the basic rhythms of human society.

Talking of spectacular clerical buildings the Middle Ages are of course the age of the great European cathedrals. Roman architecture was block buildings with thick, massive stonewalls, very few windows and domed roofs. The art of building in stone was one of the things that virtually disappeared in the Early Middle Ages in Europe. It came back initially in an extended phase of castle building. Inspired by the return of the stonemason, medieval, European, Christian society began the era of building their massive monuments to their God, the medieval cathedrals. Introducing architectural innovation like the pointed arch, the flying buttress and the rib vaulted roof they build large, open buildings flooded with light that soared up to the heavens in honour of their God. Buildings that are still a source of wonder today.


In this context it is important to note that Farrell clearly explicates the role played by the Catholic Church in the medieval technological innovations, both the good and the bad. Viewed with hindsight the cathedrals can be definitely booked for the good but the bad? During the period when the watermills were introduced into Europe and they replaced the small hand mills that the people had previously used to produce their flour, local Church authorities gained control of the mills, a community could only afford one mill, and forced the people to bring their grain to the Church’s mill at a price of course. Then even went to the extent of banning the use of hand mills.

People often talk of the Renaissance and mean a period of time from the middle of the fifteenth century to about the beginning of the seventeenth century. However, for historians of science there was a much earlier Renaissance when scholars travelled to the boundaries between Christian Europe and the Islamic Empire in the twelfth and thirteenth centuries in order to reclaim the knowledge that the Muslims had translated, embellished and extended in the eight and ninth centuries from Greek sources. This knowledge enriched medieval science and technology in many areas, a fact that justifies its acquisition here in a book on technology.

Another great medieval invention that still plays a major role in our society, alongside the introduction of paper and the mechanical clock are spectacles and any account of medieval technological invention must include their emergence in the late thirteenth century. Spectacles are something that initially emerged from Christian culture, from the scriptoria of the monasteries but spread fairly rapidly throughout medieval society. The invention of eyeglasses would eventually lead to the invention of the telescope and microscope in the early seventeenth century.

Another abstract change, like the translation movement during that first scientific Renaissance, was the creation of the legal concept of the corporation. This innovation led to the emergence of the medieval universities, corporations of students and/or their teachers. There is a direct line connecting the universities that the Church set up in some of the European town in the High Middle Ages to the modern universities throughout the world. This was a medieval innovation that truly helped to shape our modern world.

Farrell’s final chapter in titled The Inventions of Discovery and deals both with the medieval innovations in shipbuilding and the technology of the scientific instruments, such as astrolabe and magnetic compass that made it possible for Europeans to venture out onto the world’s oceans as the Middle Ages came to a close. For many people Columbus’ voyage to the Americas in 1492 represents the beginning of the modern era but as Farrell reminds us all of the technology that made his voyage possible was medieval.

All of the above is a mere sketch of the topics covered by Farrell in his excellent book, which manages to pack an incredible amount of fascinating information into what is a fairly slim volume. Farrell has a light touch and leads his reader on a voyage of discovery through the captivating world of medieval technology. The book is beautifully illustrated by especially commissioned black and white line drawing by Ryan Birmingham. There are endnotes simply listing the sources of the material in main text and an extensive bibliography of those sources. The book also has, what I hope, is a comprehensive index.[2]

Farrell’s book is a good, readable guide to the world of medieval technology aimed at the lay reader but could also be read with profit by scholars of the histories of science and technology and as an ebook or a paperback is easily affordable for those with a small book buying budget.

So remember, next time you settle down with the latest medieval pot boiler with its cast of filthy peasants, debauched clerics and pox marked whores that the paper that it’s printed on and the reading glasses you are wearing both emerged in Europe in the Middle Ages.

[1] John W. Farrell, The Clock and the Camshaft: And Other Medieval Inventions We Still Can’t Live Without, Prometheus Books, 2020.

[2] Disclosure: I was heavily involved in the production of this book, as a research assistant, although I had nothing to do with either the conception or the actual writing of the book that is all entirely John Farrell’s own work. However, I did compile the index and I truly hope it will prove useful to the readers.


Filed under Book Reviews, History of science, History of Technology, Mediaeval Science

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

The event that would eventually lead to Isaac Newton writing and publishing his magnum opus, the Philosophiæ Naturalis Principia Mathematica (the Mathematical Principles of Natural Philosophy), took place in a London coffee house.


Title page of ‘Principia’, first edition (1687). Source: Wikimedia Commons

This is not quite as strange as it might at first appear, shortly after their first appearance in England around 1650 coffee houses became the favourite meeting places of the English scientific intelligentsia, the astronomers, mathematicians and natural philosophers. Here, these savants would meet up to exchange ideas, discuss the latest scientific theories and pose challenges to each other. These institutions also earned the appellation Penny Universities, as some of those savants, such as William Whiston, Francis Hauksbee and Abraham de Moivre, bettered their incomes by holding lectures or demonstrating experiments to willing audiences, who paid the price of a cup of coffee, a penny, for their intellectual entertainment. Later, after he had become Europe’s most famous living natural philosopher, Isaac Newton would come to hold court in a coffee shop, surrounded by his acolytes, the original Newtonians, distributing words of wisdom and handing round his unpublished manuscripts for scrutiny. However, all that still lay in the future.

One day in January 1684 Christopher Wren, Robert Hooke and Edmond Halley were discussing the actual astronomical theories over a cup of coffee. Wren, today better known as one of England most famous architects, was a leading mathematician and astronomers, who had served both as Gresham and Savilian professor of astronomy. Newton would name him along with John Wallis and William Oughtred as one of the three leading English mathematicians of the seventeenth century.


Wren, portrait c.1690 by John Closterman Source: Wikimedia Commons

Hooke was at the time considered to be the country’s leading experimental natural philosopher and Halley enjoyed an excellent reputation as a mathematician and astronomer.

NPG 4393; Edmond Halley by Richard Phillips

Portrait by Richard Phillips, before 1722 Source: Wikimedia Commons

The topic of discussion was Kepler’s elliptical, heliocentric astronomy and an inverse, squared law of gravity. All three men had arrived separately and independently at an inverse, squared law of gravity probably derived from Huygens’ formula for centrifugal force. Wren posed the question to the other two, whether they could demonstrate that such a law would lead to Kepler’s elliptical planetary orbits.

Hooke asserted that he already had such a demonstration but he would first reveal it to the others after they had admitted that they couldn’t solve the problem. Wren was sceptical of Hooke’s claim and offered a prize of a book worth forty shillings to the first to produce such a demonstration.  Hooke maintained his claim but didn’t deliver. It is worth noting that Hooke never did deliver such a demonstration. Halley, as already said no mean mathematician, tried and failed to solve the problem.

In August 1684 Halley was visiting Cambridge and went to see Newton in his chambers in Trinity College, who, as we know, he had met in 1682.


Trinity College Cambridge, David Loggan’s print of 1690 Source: Wikimedia Commons

According the Newton’s account as told to Abraham DeMoivre, Halley asked Newton, “what he thought the Curve would be that would be described by the Planets supposing the force of attraction towards the Sun to be reciprocal to the square of the distance from it. Sir Isaac replied immediately that it would be an Ellipse…” Here was Newton claiming to know the answer to Wren’s question. Halley asked Newton how he knew it and he replied, “I have calculated it…” Newton acted out the charade of looking for the supposed solution but couldn’t find it. However he promised Halley that he would send him the solution.

In November Edward Paget, a fellow of Trinity College, brought Halley a nine page thesis entitled De motu corporum in gyrum (On the Motion of Bodies in an Orbit).


Page of the De motu corporum in gyrum

When Halley read Newton’s little booklet he was immediately aware that he held something truly epoch making in the history of astronomy and physics in his hand. Newton had delivered up a mathematical proof that an elliptical orbit would be produced by an inverse square force situated at one of the foci of the ellipse, thus combining the inverse square law of gravity with Kepler’s first law. He went on to also derive Kepler’s second and third laws as well as laying down the beginnings of a mathematical theory of dynamics. Halley reported details of this extraordinary work to the Royal Society on 10 December 1684:

Mr Halley gave an account, that he had lately seen Mr. Newton at Cambridge, who had shewed him a curious treatise, De motu: which, upon Mr. Halley’s desire, was he said promised to be sent to the Society to be entered upon their register.

Mr. Halley was desired to put Mr. Newton in mind of his promise for securing his invention to himself till such time as he could be at leisure to publish it. Mr. Paget was desired to join with Mr. Halley.

The interest in and the demand to read Newton’s new production was very high but the author decided to improve and rewrite his first offering, triggering one of the most extraordinary episodes in his life.

Although he was Lucasian Professor and would turn forty-two on 25 December 1684, Newton remained a largely unknown figure in the intellectual world of the late seventeenth century. Following the minor debacle that resulted from the publication of his work in optics in the 1670s he had withdrawn into his shell, living in isolation within the walls of Cambridge University. He carried out his duties as Lucasian Professor but had almost no students to speak of and definitely no disciples. Thanks to the word of mouth propaganda of people like his predecessor as Lucasian Professor, Isaac Barrow, and above all the assiduous mathematics groupie, John Collins, it was rumoured that a mathematical monster slumbered in his chambers in Trinity College but he had done nothing to justify this bruited reputation. His chambers were littered with numerous unfinished scientific manuscripts, mostly mathematical but also natural philosophical and an even larger number of alchemical and theological manuscripts but none of them was in a fit state to publish and Newton showed no indication of putting them into a suitable state. Things now changed, Newton had found his vocation and his muse and the next two and a half years of his life were dedicated to creating the work that would make him into a history of science legend, the reworking of De motu into his Principia.

Over those two and a half years Newton turned his nine-page booklet into a major three-volume work of science. The modern English translation by I B Cohen runs to just over 560 large format pages, although this contains all the additions and alterations made in the second and third editions, so the original would have been somewhat shorter. Halley took over the editorship of the work, copyediting it and seeing it through the press. In 1685 the Royal Society had voted to take over the costs of printing and publishing Newton’s masterpiece, so everything seemed to be going smoothly and then disaster struck twice, firstly in the form of Robert Hooke and secondly in the form of a financial problem.

Hooke never slow to claim his priority in any matter of scientific discovery or invention stated that he alone had first discovered the inverse square law of gravity and that this fact should, indeed must, be acknowledged in full in the preface to Newton’s book. Halley, realising at once the potential danger of the situation, was the first to write to Newton outlining Hooke’s claim to priority, stating it, of course, as diplomatically as possible. Halley’s diplomacy did not work, Newton went ballistic. At first his reaction was comparatively mild, merely pointing out that he had had the inverse square law well before his exchanges with Hook in 1679 and had, in fact, discussed the matter with Wren in 1677, go ask him, Newton said. Then with more time to think about the matter and building up a head of steam, Newton wrote a new letter to Halley tearing into Hooke and his claim like a rabid dog. All of this ended with Newton declaring that he would no longer write volume three of his work. Halley didn’t know this at the time but this was in fact, as we shall see, the most important part of the entire work in which Newton presented his mathematical model of a Keplerian cosmos held together by the law of gravity. Halley remained calm and used all of his diplomatic skills to coax, flatter, persuade and cajole the prickly mathematician into delivering the book as finished. In the end Newton acquiesced and delivered but acknowledgements to Hooke were keep to a minimum and offered at the lowest level of civility.

The financial problem was of a completely different nature. In 1685 the Royal Society had taken over the cost of printing and publishing the deceased Francis Willughby’s Historia piscium as edited by John Ray.

This was an expensive project due to the large number plates that the book contained and the book was, at the time, a flop. This meant when it came time to print and publish Newton’s work the Royal Society was effectively bankrupt. One should note here that the popular ridicule poured out over Willughby’s volume, it having almost prevented Newton’s masterpiece appearing, is not justified. Historia piscium is an important volume in the history of zoology. Halley once again jumped into the breach and took over the costs of printing the volumes; on the 5 July 1687 Halley could write to Newton to inform him that the printing of his Philosophiæ Naturalis Principia Mathematica had been completed.









Filed under Early Scientific Publishing, History of Astronomy, History of Mathematics, History of science, Newton

Oh really, might as well pack up and go home then.

The New Statesman recently had a review of Catherine Fletcher’s new book on the history of the Italian Renaissance, The Beauty and the Terror,[1] written by Rowan Williams under the title, Breaking the Renaissance myth.  For those, who might not know Rowan Williams is an ex Archbishop of Canterbury, who although ordained served as an academic rather than as a priest: However, he is/was a theologian and not a historian and very definitely not a historian of science.

Fletcher’s book is largely about what we might term the dark side of the Italian Renaissance and this is reflected in the title of Williams’ review.


I had no problems with the general tenor of what he had to say until I stumbled across the following two paragraphs in the middle of his review:

If we demythologise the Renaissance a little, we may learn to do more justice to what preceded it. Professor Fletcher has a brief discussion of scientific advances in the mid 16th century, especially in anatomy, navigational skills and botany – the latter two spurred on by the fresh stimulus of colonial travel and discovery. But the fact that this treatment is relatively brief and relates to a period rather later than the “high Renaissance” should give us pause if we are inclined to think of this as an epoch of spectacular scientific progress.

Many scholars have pointed out that the 15th and early 16th centuries are a rather stagnant period in many areas of natural science compared with some parts of the Middle Ages, when astronomy, mechanics and logic made substantial advances. The great 16th-century exception, Copernicus’s treatise of 1543 on the circulation of planets around the sun, was not a dramatic and total rejection of earlier astronomical method based on new scientific evidence, but a refinement designed to clear up the mathematics of charting the heavenly bodies. It was received with interest and some enthusiasm at the time, but was clearly not seen as a radical departure from the principles of Aristotle. Only with slightly later figures like Tycho Brahe (1546-1601) and Johannes Kepler (1571-1630) did actual observation of the heavens play a decisive part in the argument.

As somebody, who generally describes himself as a historian of Renaissance science I was, to say the least, more than somewhat discombobulated by the good Reverend Williams’ claims about my chosen discipline and I thought I might take a couple of minutes to examine them.

I’ll start with what Williams describes as Professor Fletcher’s brief discussion of scientific advances in the mid 16th century, especially in anatomy, navigational skills and botany. This is indeed extremely brief. The main text of the book is 350 pages long and there is a just-15-pages long chapter entitled, Art, Science and Reform of which only three pages deal with the scientific topics mentioned by Williams. This is principally a book of political history and the comment here have almost a throw away quality, something mentioned in passing. The anatomy mentioned is, of course, Vesalius’ De fabrica, which together with all the new developments in medicine, mainly in the North Italian universities, constitutes one of the largest revolutions in the entire history of medicine.  Fletcher does not discuss advances in the science of navigation, which were in fact very extensive in the 15th and 16th centuries, but the ‘navigations’ another term for the voyages of exploration and discovery undertaken in those centuries and their influence on developments back in Italy, as recorded by authors such as Giovanni Battista  Ramusio and Richard Hakluyt.

The botany refers to the establishment of botanical gardens at the universities of Padua and Pisa and the publications of herbaria (herbals) aimed at correcting such works as Pliny’s Natural History, as Vesalius had corrected Galen in medicine. What she doesn’t mention is that both the botanical gardens and the herbals were also part of the medical revolution, the scientific investigation of healing herbs being one of their central functions.

The last sentence of the first paragraph and the first of the second paragraph are a bit of a stunner. You know that I have a tendency to call myself a historian of Renaissance science and Williams is saying that I’m a historian of a bit of a damp squib. I’m used to people, who should know better, making rude and highly inaccurate statements about the history of medieval science, but to have somebody praise the vitality of medieval science, whilst at the same time putting the boot into Renaissance science is I think a first, at least as far as I’m concerned. This raises all sorts of problems, not least because the division between medieval science and Renaissance science is totally artificial and there is in reality continuity in European scientific activity that goes through from the translation movement in the twelfth century to at least the middle of the sixteenth century. Also I think to claim that medieval science made “substantial advances in astronomy, mechanics and logic” is a bit strong, as they were more involved in a game of catch up with antiquity and medieval Islam. On the other hand if you do try to identify a specifically Renaissance science, you first have to decide when it begins and when it ends. My own period definition of Renaissance science starts at the beginning of the fifteenth century and ends with the Thirty Years War. Kepler for all of his modernity is philosophically much more a Renaissance philosopher than a modern one, as is also Tycho. Galileo is more transitional but still has at least one foot in the Middle Ages.

Let us take stock and make an inventory of all the scientific activities that were developed and/or advanced in the period between 1400 and 1600. Regular readers will already have encountered much of what follows in various posts here over the years but it might prove of interest to see it laid out, if only in outline, all in one place.

We start with the first Latin translation of Ptolemaeus’ Geographia from the Greek by Jacobus Angelus in Florence in 1406. This is of course Renaissance culture in pure form, the translation from Greek into Latin of a major text from antiquity, above all because it was a text that had never been translated out of Arabic in the original translation movement. This text kicked off mathematical cartography in Renaissance Europe and with it revitalised astronomy, which was needed to determine latitude and longitude coordinates for this new form of cartography. The Ptolemaic world map, which very soon followed the translation both in manuscript and in print, was a totally new perception of the world in comparison to the medieval mappa mundi.

Harley 7182 ff.58v-59

A mid-15th century Florentine map of the world based on Jacobus Angelus’s 1406 Latin translation of Maximus Planudes’s late-13th century rediscovered Greek manuscripts of Ptolemy’s 2nd-century Geography. Ptolemy’s 1st (modified conic) projection. Credited to Francesco di Antonio del Chierico – Ptolemy’s Geography (Harleian MS 7182, ff 58–59) Source: Wikimedia Commons

The new cartography spread northwards throughout Europe helping to trigger the First Viennese School of Mathematics. Here Gmunden, Peuerbach and Regiomontanus modernised Ptolemaic astronomy, integrating the newly developing trigonometry and many Arabic developments into Peurbach’s Theoricae Novae Plaetarum (1473) and the Peuerbach & Regiomontanus Epitoma in Almagestum Ptolemae (1496), which became the new textbooks for astronomy for the next one hundred plus years and were also the books Copernicus used to learn his astronomy.


Title page Epitoma in Almagestum Ptolemae Source: Wikimedia Commons

The Second Viennese School of Mathematics with Johannes Stabius, Andreas Stiborius, Georg Tannstetter and Peter Apian pushed the advances in cartography and astronomy further.


Apian’s copy of the Waldseemüller world map, naming the new fourth continent America Source: Wikimedia Commons

The Viennese mathematici stood in close contact with their colleagues in Nürnberg, where Johannes Schöner and Johannes Werner also made substantial contributions to theses advances. Schöner in particular was heavily involved in the activities that led to the publication of Copernicus’ De revolutionibus in Nürnberg in 1543. It was Schöner, who also kicked off the production of printed terrestrial and celestial globe pairs,


Celestial globe by Johann Schöner, c.1534 Source: Museum of the History of Science, Oxford

which was picked up by Gemma Frisius, who taught astronomy, cartography and mathematics to Gerhard Mercator, who in turn would go on to revolutionise both cartography and globe making triggering the golden age of both disciplines in the Netherlands in the seventeenth century.


Abraham Ortelius, who produced and published the first modern atlas, was also a member of the Frisius-Mercator circle along with numerous other important cartographical innovators.


Frisius, of course, introduced triangulation an important new tool in cartography, surveying and geodesy. New surveying instruments, such as the plane table, were also developed to carry out surveying using triangulation.

The early modern cartographers were not just simple mapmakers, their publications also contained much geographical information, much of it new, as well as historical, anthropological and ethnographical information about the areas mapped.

Another member of this European wide group of mathematici, Pedro Nunes, in Portugal was the discovery of the fact that a course of constant compass bearing on the globe is not part of a great circle but a loxodrome, a spiral.


Image of Portuguese mathematician Pedro Nunes in Panorama magazine (1843); Lisbon, Portugal. Source: Wikimedia Commons

This knowledge lies at the centre of the so-called Mercator map projection. Turning to navigation, the Portuguese and later Spanish explorations out into the Atlantic led to major developments such as the determination of latitude and the development of new instruments for this purpose such as the backstaff and the marine astrolabe. At the end of our period in 1600 to be exact, William Gilbert published his De Magnete, as well as being the definitive text up to that time on magnets and magnetism, it was also an important text on empirical, experimental science. Although published at the end of our period it relied on earlier work on magnetism and the magnet by such researchers as Robert Norman.

Coming back to astronomy, Copernicus’ De revolutionibus didn’t, as often presented, appear out of thin air but was part of a general movement to modernise astronomy and above all to make it more accurate that begins with Peuerbach and Regiomontanus and gains a lot of momentum in the sixteenth century particularly in the Europa wide debate in the 1530s, in which Copernicus also took an active part. I will address here Williams’ mindboggling statement about De revolutionibus:

The great 16th-century exception, Copernicus’s treatise of 1543 on the circulation of planets around the sun, was not a dramatic and total rejection of earlier astronomical method based on new scientific evidence, but a refinement designed to clear up the mathematics of charting the heavenly bodies. It was received with interest and some enthusiasm at the time, but was clearly not seen as a radical departure from the principles of Aristotle. [my emphasis]

As almost always we are dealing with someone whose knowledge of Renaissance cosmology and astronomy is obviously very minimal. The Peuerbachian geocentric system of the cosmos with which Copernicus was working was not Aristotelian astronomy but an uneasy mash up of Aristotelian cosmology and Ptolemaic astronomy. In fact there was a major attempt to return to Aristotelian homocentric astronomy, launched by Fracastoro amongst other, during those debates in the 1530s. Whilst, in a mathematical sense, Copernicus’ heliocentric astronomy didn’t stray far from Ptolemaic astronomy with its deferents and epicycles, but without its, for Copernicus, offensive equant points, it deviated radically from Aristotle’s cosmology and physics. Fundamental to Aristotelian cosmology is the fact that the Earth is immobile at the centre of the cosmos, to place the Sun there instead and the Earth in orbit around the Sun is a very a radical departure from the principles of Aristotle. Fundamental to Aristotelian physics is that the cosmos in divide into supralunar and sublunar areas. Above the Moon’s orbit natural motion is uniform and circular below it natural motion is perpendicular to the Earth’s surface. Upwards for fire and air, downwards for earth and water. Giving the Earth three additional motions–diurnal rotation, annual orbit around the Sun and a circulating of the poles– was a very radical departure from the principles of Aristotle.

Moving on from the mathematical sciences–astronomy, cartography, navigation, and surveying–to mathematics itself, the Renaissance saw a massive development in trigonometry and its applications. All four of the named mathematical sciences make extensive use of trigonometry. Regiomontanus wrote the first complete account of the six basic trigonometrical functions in Europe, this had been done much earlier in Arabic science, which also presented trigonometry as a separate mathematical discipline and not just a subsidiary of astronomy; this was published by Schöner in 1533.

Rheticus published an expanded version of the trigonometry section of De revolutionibus as a separate work before De revolutionibus itself was published. The historian of mathematics, Grattan-Guinness, calls the Renaissance the age of trigonometry. We also have the transition of algebra from being merely commercial arithmetic to becoming a central mathematical discipline during the sixteenth century. This new analytical mathematics lay at the core of the so-called scientific revolution in the seventeenth century.

The fifteenth and sixteenth centuries also saw a renaissance in the mathematics and physics of Archimedes, in which Regiomontanus, once again, played a significant role. This renaissance peaked in 1544 when Thomas Venatorius published a bilingual, Greek and Latin, edition of the Works of Archimedes in Basel.


Archimedes, Opera omnia, Basel, 1544,

Galileo, who is often (falsely) called the founder of modern physics, explicitly took the work of Archimedes rather than that of Aristotle as reference point for his own work.

In the so-called natural sciences the Middle Ages were dominated by the Naturalis Historia of Gaius Plinius Secundus, or Pliny as he is know in English. This work is an encyclopaedia of everything that Pliny considered related to nature, astronomy, meteorology, geography, ethnography, anthropology, physiology, zoology, botany including agriculture and horticulture, pharmacology, magic, water, mining and mineralogy.  The work lacks originality and depth and is a ragbag of other sources thrown together under one concept, natural history; a term that we still use today. The Renaissance, especially after the invention of moving type book printing in the middle of the fifteenth century, saw the separating out and development of the individual disciplines as we known them today.

Vannoccio Biringuccio in his De la pirotechnia (1540) and Georgius Agricola in his De re metalica (1556) modernised and established metallurgy as an independent discipline. Agricola’s work together with his De natura fossilium also contributed substantially to the founding of geology and mineralogy as separate disciplines.


Zoology found its independence in the works of Ulisse Aldrovandi, who also contributed substantially to the foundations of geology, a word that he coined, and Conrad Gesner, who also published a fossil book. Aldrovandi was one of those who established a botanical garden and wrote and published a herbal. In zoology, some of the anatomists, who followed in the wake of Vesalius in the second half of sixteenth century, also instituted comparative anatomy, dissecting animal as well as human corpses.


Albrecht Dürer’s Rhinoceros from Conrad Gesner’s History Animalium

Herbals had already existed in the Middle Ages but following the invention of the printed book they took on a whole new dimension. The sixteenth century became the age of the great herbals of Otto Brunfels, Leonhart Fuchs, Hieronymus Bock, Rembert Dodoens, Carolus Clusius, Pietro Andrea Mattioli, Propero Alpino and others. Botanical gardens and herbariums, collections of dried plant specimens, were also established all over Europe and not just in university towns. Both the herbals and the botanical gardens served two purposes, on the one hand the study of botany and on the other the study of pharmacology. The authors of the herbals and the keepers of the botanical gardens and herbariums exchanged seeds, plants and dried specimens with their colleagues throughout Europe and even further afield. Researchers in the newly discovered lands (newly discovered for Europeans that is) sending specimens home from all over the world.


Leonhart Fuch’s Herbal

Williams emphasises that the little bit of scientific activity that he acknowledges took place during the Renaissance did so outside of the “high Renaissance”:

But the fact that this treatment is relatively brief and relates to a period rather later than the “high Renaissance” should give us pause if we are inclined to think of this as an epoch of spectacular scientific progress.

The expression “high Renaissance” is a highly dubious and rather meaningless historical concept, as it just basically means the short period when Leonardo, Raphael and Michelangelo were active, but is William’s implied claim that this period invoked no scientific progress really true?

The books on zoology and botany listed above were spectacularly illustrated, large format volumes and can even be viewed as the first printed coffee table books. What is interesting here is that they reflected and contributed to the development in fine art now labelled Naturalism. Many of the illustrators of those early coffee table books trained in the studios of the high Renaissance artists. Similarly the illustrations in the anatomical, medical works. This development lies at the heart of the so-called high Renaissance and alongside the realistic depiction of the natural world this included as a central element the development and use of linear perspective. Linear perspective is in fact a branch of applied or practical mathematics that developed in the Renaissance out of the medieval theories of optics. It developed further in the seventeenth century into projective geometry. The high Renaissance was not quite as devoid of scientific progress as Williams would have us believe.

Medicine also saw many new developments alongside the Vesalian revolution in anatomy. Many new drugs both botanical and mineral were sent back to Europe and investigated for their efficacy by those at home. With Paracelsus a whole new direction is medicine was established which grew and expanded following his death in 1541.


Paracelsus Source: Wikimedia Commons

This was a medicine based on alchemy and mineral rather than plant based medicines. The Paracelsian alchemy played a significant role in the transition from alchemy to modern chemistry and helped to establish the modern science of pharmacology. The first university chairs for chemistry at the beginning of the seventeenth century were chairs for Paracelsian medicine.

The sixteenth century also saw a restructuring of the medical industry in general with the physicians gaining prominence over the apothecaries, midwives and herbalist, creating a medical hierarchy that persists, with modifications, to the present day.

The above is merely a sketch of the scientific activity during the Renaissance and is by no means exhaustive. There are certainly other activities that I haven’t listed and even ones that I’m not aware of yet. However, I think I have outlined enough to show that the 15th and early 16th centuries are anything but a rather stagnant period in many areas of natural science compared with some parts of the Middle Ages. In fact those two centuries were rich in scientific developments and advances more than equal to anything produced in the earlier part of the Middle Ages. I would, however, once again emphasise that I think dividing the period between the twelfth and seventeenth centuries into Middle Ages and Renaissance with relation to the history of science is artificial and unproductive and we should look more at the continuities and less at the divisions.


[1] Catherine Fletcher, The Beauty and the Terror, The Bodley Head, London, 2020, As it is a book largely about political history I probably won’t be reviewing it here.


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

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

One of the most often repeated false statements in the history of science is that Isaac Newton discovered gravity. Of course he didn’t discovery it, it’s all around us. You can observe gravity every time you drop something. Making the claim more precise, by saying Newton discovered the law of gravity, doesn’t really improve the situation much. What Newton did do was he proved the law of gravity and made the fairly rational assumption based on the available evidence that this law applies universally to all bodies in the cosmos. An assumption that is not written in stone and has been questioned in the present time for the general theory of relativity, the theory that replaced the Newtonian theory of universal gravity and of which the Newtonian theory of gravity is a very good approximation for local cases. However we don’t want to take the path to modern theories of cosmology and dark matter but want to stay firmly in the seventeenth century with Newton.

We can start with a brief survey of theories of gravity before Newton. Originally gravity was the Latin term applied to Aristotle’s explanation of why, when dropped, things fall to the ground. Aristotle thought that objects did so through a form of vital attraction, returning to their natural home, consisting predominantly of the elements earth and water. Fire and air rise up. This only applied to the Earth, as things beyond the Moon were made of a fifth element, aether, the quintessence, for which the natural form of motion was uniform circular motion.

This neat model wouldn’t work, however for Copernicus’ heliocentric model, which disrupted the division between the sublunar and supralunar worlds. To get around this problem Copernicus suggested that each planet had its own gravity, like the Earth. So we have terrestrial gravity, Saturnian gravity, Venusian gravity etc. This led Alexander von Humboldt, in the 19th century, to claim that Copernicus should be honoured as the true originator of the universal theory of gravity, although it is by no means clear that Copernicus thought that he planetary gravities were all one and the same phenomenon.

The whole concept became even more questionable when the early telescopic astronomers, above all Galileo, showed that the Moon was definitely Earth like and by analogy probably the other planets too. At the end of a long line of natural philosophers stretching back to John Philoponus in the sixth century CE, Galileo also showed that gravity, whatever it might actually be, was apparently not a vitalist attraction but a force subject to mathematical laws, even if he did get the value for the acceleration due to gravity ‘g’ wrong and although he didn’t possess a clear concept of force.. Throughout the seventeenth century other natural philosophers, took up the trail and experimented with pendulums and dropped objects. A pendulum is of course an object, whose fall is controlled. Most notable were the Jesuit, natural philosopher Giovanni Battista Riccioli (1598–1671) and the Dutch natural philosopher Christiaan Huygens (1629–1695). Riccioli conducted a whole series of experiments, dropping objects inside a high tower, making a direct confirmation of the laws of fall. Both Riccioli and Huygens, who independently of each other corrected Galileo’s false value for ‘g’, experimented extensively with pendulums in particular determining the length of the one-second pendulum, i.e. a pendulum whose swing in exactly one second. As we will see later, the second pendulum played a central roll in an indirect proof of diurnal rotation. Huygens, of course, built the first functioning pendulum clock.

Turning to England, it was not Isaac Newton, who in the 1670s and 80s turned his attention to gravity but Robert Hooke (1635–1703), who was Curator of Experiments for the newly founded Royal Society. Like Riccioli and Huygens Hooke experimented extensively with dropping objects and pendulums to try and determine the nature of gravity. However his experiments were not really as successful as his continental colleagues. However, he did develop the idea that it was the force of gravity that controlled the orbits of the planets and, having accepted that comets were real solid objects and not optical phenomena, also the flight paths of comets. Although largely speculative at this point Hooke presented a theory of universal gravity, whilst Newton was still largely confused on the subject. Hooke turned to Newton in a letter with his theory in order to ask his opinion, an act that was to lead to a very heated priority dispute.

Before we handle that correspondence we need to go back to the beginnings of the 1670s and an earlier bitter dispute between the two.  In 1672 Newton announced his arrival on the European natural philosophy scene with his first publication, a letter in the Philosophical Transactions of the Royal Society (1671/72), A New Theory of Light and Colours, which described the experimental programme that he had carried out to demonstrate that white light actually consisted of the colours of the spectrum.


Newton’s original letter. Source: Royal Society

This brilliant piece of experimental optics did not receive the universal praise that, reading it today, we might have expected, in fact it was heavily criticised and attacked. Some critics were unable to reproduce Newton’s experimental results, probably because their prisms were of too poor quality. However, others, Hooke to the fore, criticised the content. Hooke and Huygens, the two current leaders in the field of optics both criticised Newton for interpreting his results within the framework of a particle theory of light, because they both propagated a wave theory of light. Newton actually wrote a paper that showed that his conclusions were just as valid under a wave theory of light, which, however, he didn’t publish. The harshest criticism came from Hooke alone, who dismissed the whole paper stating that he had already discovered anything of worth that it might contain . This did not make Newton very happy, who following this barrage of criticism announced his intention to resign from the Royal Society, to which he had only recently been elected.  Henry Oldenburg (c. 1619–1677), secretary of the Royal Society, offered to waive Newton’s membership fees if he would stay. Newton stayed but had little or nothing more to do with the society till after Hooke’s death in 1703. Newton did, however, write a very extensive paper on all of his optical work, which remained unpublished until 1704, when it formed a major part of his Opticks.

By  1679 tempers had cooled and Robert Hooke, now secretary of the Royal Society, wrote to Isaac Newton to enquire if he would be interested in reopening his dialogue with the Royal Society. In the same letter he asked Newton’s opinion on his own hypothesis that planetary motions are compounded of a tangential motion and “an attractive motion towards the centrall body…” Hooke is here referencing his Attempt to Prove the Motion of the Earth from Observations (1674, republished 1679),


which contains the following fascinating paragraph:

This depends on three Suppositions. First, That all Coelestial Bodies whatsoever, have an attractive or gravitating power towards their own Centers, whereby they attract not only their own parts, and keep them from flying from the, as we observe the earth to do, [here Hooke is obviously channelling Copernicus] but that they do also attract all other Coelestial Bodies that are within the sphere of their activity … The second supposition is this, That all bodies whatsoever that are put into a direct and simple motion, will so continue to move forward in a streight line, till they are by some other effectual power deflected and bent into a Motion, describing a Circle, Ellipsis, or some other more compounded Curve Line. [the principle of inertia, as propounded by Descartes] The third supposition is, That these attractive powers are so much the more powerful in operating, by how much nearer the body wrought upon is to there own Centers. Now what these several degrees are I have not yet experimentally verified…

Whether or not this is truly a universal theory of gravity is a much-debated topic, but if not, it comes very close and was moving much more in that direction than anything Newton had produced at the time. As we shall see later this was to cause not a little trouble between the two rather prickly men.

Newton declined the offer of a regular exchange of ideas, claiming that he was moving away from (natural) philosophy to other areas of study. He also denied having read Hooke’s paper but referred to something else in it in a later letter to Flamsteed. However, in his reply he suggested an experiment to determine the existence of diurnal rotation involving the usually dropping of objects from high towers. Unfortunately for Newton, he made a fairly serious error in his descripting of the flight path of the falling object, which Hooke picked up on and pointed out to him, if unusually politely, in his reply. Newton of course took umbrage and ended the exchange but he did not forget it.

In our next episode we will deal with the events leading up to the writing and publication of Newton’s great masterpiece, Philosophiæ Naturalis Principia Mathematica (1687), which include the repercussions of this brief exchange between Hooke and its author.




Filed under History of Astronomy, History of Mathematics, History of Optics, History of Physics, Renaissance Science

We just don’t know!

Matthew Cobb is one of those people that you can’t help but admire but also secretly hate just a little bit for being so awesome. He is professor for zoology at the University of Manchester with a sizable teaching load that he apparently masters with consummate skill. He’s a scientific researcher, who researches the sense of smell of fruit fly maggots; I kid you not!  He’s also an attentive and loving family father but he still finds time and energy to write brilliant history of science books, three to date. His first, The Egg and Sperm Race, describes the search for the secret of human reproduction in the seventeenth and eighteenth centuries and is one of my favourite history of science books, on the period. His second, Life’s Greatest Secret is a monster, both in scope and detail, description of the hunt to decipher the structure and function of DNA that along the way demolishes a whole boatload of modern #histSTM myths. The most recent, and the subject of this review, is The Idea of the Brain: A History. Actually I don’t really need to review it, on the cover there is a quote from Adam Rutherford, who is also a brilliant science communicator, This is a masterpiece. Agreed, end of review!


You want a bit more detail before you commit your shekels and purchase a copy? OK! What Cobb presents us with is a history of the various attempts by researchers to understand the brain and its functions, which of course also includes such concrete things as the nervous system and abstract ones as thought, memory, consciousness, all of those things that we think make us human. The book is divided into three sections past, present and future. The first deals with those attempts to explain the brain offered up roughly from the seventeenth century up to about 1950. The second deals with approximately the last 70 years, which saw a major change in the tools available to the researchers and in the final section Cobb offers us his opinions on where the research might go from here; a brief survey that he admits is highly speculative.

Astute readers of this review might wonder why Cobb’s book only gets going in the seventeenth century, when humans of some sort or another have been around for a couple of million years, their brains also. This gets explained in the first chapter, which at first glance is confusingly entitled Heart and not Brain! Whilst reading this introductory chapter I found myself humming old pop songs by Cilla Black and Bonnie Tyler, the lyrics of which contain the answer to my question. Anyone Who had a Heart, and Total Eclipse of the Heart reflect a belief that existed for most of humanity’s existence. It was believed that the heart was the seat of emotions, thoughts, consciousness etc. and not the brain. As those pop songs nicely illustrate, much of our everyday speech still reflects that belief. ‘He thought with his heart and not his head’ ‘If you weren’t so hard hearted’ and many, many more. It was first in the seventeenth century that the attention of the natural philosophers turned from the heart to the brain to try and solve the conundrums thrown up by thoughts about thinking. Here the developing empirical approach to science in general kicked in as nicely illustrated by the book’s motto supplied by Nicolaus Steno (1638–1686) in his On the Brain (1669), which also supplies the leitmotif for the whole book:

The brain being indeed a machine, we must not hope to find its artifice through other ways than those which are used to find artifice in other machines. It thus remains to do what we would do for any other machine; I mean to dismantle it piece by piece and to consider what these can do separately and together.

I did briefly muse on the fact that Steno, a truly fascinating figure, also played a leading role in Cobb’s first book, The Egg and Sperm Race, but I digress.

It is well known that the brain is a glibbery, grey mass that you can’t really take apart, let alone put back together again. The best you can do is cut it up into slices, which I’m sure some early investigators did, but without high power microscopes that is not going to tell you an awful lot. All you can really do is fry the slices in breadcrumbs and eat them with a good sauce. What the early brain researchers did do was to set up analogies to other scientific systems and technologies and hypothesize that the brain functions in the same or a similar way. Then try to find some way to test your hypothesis. Cobb takes us through a whole series of these analogy models of the brain and shows clearly how they all failed. What is interesting is that the models were almost always based on the newest scientific theories or technological development within each generation. Hey we’ve got this wonderful new whatsit, I bet the brain functions like that too. This first section of the book is a fascinating journey through a couple of centuries of science and technology and failed and abandoned models of the brain. However not all was lost or totally wrong. This process produced, for example, the valid information that the nervous system and with it the brain are somehow powered by electricity.

Following WWII Cobb takes us into what he terms the present of brain research. Here a whole lot of new investigatory possibilities begin to be developed, computer tomography scans for examples. But of course the analogy game doesn’t stop and we what is probably the most widespread and well-known analogy of all, the brain is a computer, which harks back to earlier technological analogies, the telegraph network and the telephone exchange.


Cobb devotes quite a lot of space to showing the efforts invested in the computer analogy and why in the end those efforts also all failed. Within the present section of his book Cobb lays out the whole battery of modern neurological research and the immense effort that has been invested in the last circa seventy years to try and understand the brain, the nervous system and related questions about the nature of memory, consciousness etc.

The strongest impression that I took away from this section was the complexity of the task. Before I read this book my thoughts about the brain were related to the saying, if the brain was simple enough that we could understand it, we wouldn’t be intelligent enough to do so. I sort of knew that the brain was mind bogglingly complex, but having read Cobb’s book I now know that mind bogglingly complex doesn’t come anywhere near describing just how complex it is. One aspect that was new to me is that some researchers, who have accepted the complexity problem (paradox?), have stopped trying to understand the human brain and are trying their luck with smaller less complex brains, in fact the smallest and simplest that they can find. Remember Cobb’s research on the sense of smell of fruit fly maggots? What is the summa summarum of all these efforts? How does the brain really function? The answer that emerges at the end of Cobb’s book is, we just don’t know!

Having stunned us with the science and its inability to answer fundamental questions about the brain the book now takes us into the future, where do we go from here? There are probably as many answers to this question as there are people currently researching the brain or hoping to do so in the future. Cobb takes us through some of the, perhaps, more hopeful approaches but admits that there in no real clean line for the researchers of the future to follow.

The book is beautifully presented the English edition has a wonderful cover and stunning end papers, black and white line illustrations throughout the text and a section of photos in the middle. There is an extensive bibliography and endnotes that are mainly simple bibliographical references. It is rounded off with a good index.

The astute reader, and this blog only has astute readers, will have noticed that this review is strong on general waffle but low on detail; this is intentional. Matthew Cobb is an excellent writer and a highly skilled storyteller. Each chapter of the book is presented as a scientific adventure story with much humour and enough bad jokes and snide comments to keep any reader happy. I found that the individual chapters made for good bedtime stories. To have gone into more detail would have been the equivalent of revealing the murderer in an Agatha Christie novel and I really don’t want to spoil the fun you the readers are going to have following Professor Cobb down the winding and contorted paths of the historical attempts to understand what is perhaps the most complex object on the planet, the human brain. The final page is I think the best final page that I have ever read in a history of science book.

I can only repeat what I said at the beginning, quoting Adam Rutherford, This is a masterpiece, so get hold of a copy and read it, you won’t regret it.





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

At the end of the last section Isaac Newton was still a student, who had embarked on a six-year period of intensive study teaching himself the modern analytical mathematics, the basics of mechanics and optics.In 1666 during the phase when he was learning mechanics, principally from the works of Descartes and where like Huygens he corrected Descartes theories of elastic collision and Galileo’s false value for g, the acceleration due to gravity, he had his legendary flash on inspiration, possibly inspired by the equally legendary falling apple, in which he asked himself if the force that causes an object to fall to the ground is the same as the force that prevents the Moon from flying off at a tangent, as the law of inertia, acquired from Descartes, said it should. Newton made a back of an envelope calculation, which gave an interesting correlation but was somewhat inaccurate due to inaccurate input data. Newton dropped the line of enquiry and didn’t take it up again for almost twenty years. However, one aspect of his calculation was very important for the future. In order to calculate the force holding the Moon he plugged Kepler’s third law into Huygens’ formula for centripetal force, which led to the inverse square law of gravity.

In 1669, on the recommendation of Isaac Barrow the retiring incumbent, Newton was appointed Lucasian Professor of Mathematics at Cambridge University.The appointment was not as impressive as it appears today and Newton remained still largely under the radar, although the mathematics fan John Collins (1625–1683) had circulated some of his mathematical manuscripts awaking the world to his immense mathematical talent. This changed in the early 1670s when he presented the world with his reflecting telescope, the first functioning one, and published his first paper on the nature of white light. A new leading natural philosopher had arrived on the European stage.

In 1680 and 1681 two new great comets lit up the skies and once again the astronomers all turned their attentions into trying to determine their flight paths. The 1680 comet was discovered by the German astronomer Gottfried Kirch (1639–1710) from Coburg, who lived from writing and publishing almanacs, on 4 November.


The Comet C/1680 V1 as seen over Nürnberg just south of Coburg with Georg Christoph Eimart’s observatory in the foreground Source

It was the first ever comet to be discovered by telescope, that is before it became visible to the naked eye. It remained visible until 7 December when it disappeared. The comet of 1681 first appeared on 20 December. One astronomer, John Flamsteed (1646–1719), who had been appointed Astronomer Royal for the new Royal Observatory at Greenwich in 1675, had the bright idea that these were not two separate comets but one single comet on its way to and from the sun (modern designation C/1680 V1). Unsure of his assumption Flamsteed turned to Isaac Newton to ask his opinion. Flamsteed did not know Newton personally so the contact, by letter, was initially through a mutual acquaintance at Cambridge.


Historical picture of the first comet ever discovered using telescope,  the Great Comet of 1680 (C/1680 V1), as painted by Lieve Verschuier: Source

Flamsteed’s hypothesis was that the comet turned in front of the Sun upon reaching it; he, echoing Johannes Kepler, suggested that the comet was attracted to the Sun magnetically and then through a change in polarity as it neared the Sun repulsed. In two letters in February 1881 Newton dismantled Flamsteed’s hypothesis, concentrating on his magnetic argument but also not accepting that the two comets were actually just one. Newton had applied the inverse square law of gravity to a theoretical system consisting of a single planet and the Sun, a year earlier, but did not apparently consider applying it to the comet at this point in time. However, in a draft of his second letter to Flamsteed, which he never sent, he did sketch a dynamic system of the comet circling behind the Sun but in terms of magnetic attraction.


John Flamsteed by Godfrey Kneller, 1702 Source. Wikimedia Commons

Later in the year Newton received new observational data on the comet from an old school acquaintance, Arthur Storer (c. 1648–1686) an amateur astronomer, who had emigrated to Maryland in 1679. He also later sent Newton data on the 1682 comet (Comet Halley), which he was amongst the first to observe in North America and which was named after him there for some time. Edmond Halley (1656–1741), an excellent astronomer and mathematician, who observed the comet of 1680/81, whilst travelling in France, also believed, like Flamsteed, that the two comets were one. In 1682 he came to Cambridge to visit Newton and the two of them discussed the comets.


Source: Wikimedia Commons

Newton observed the comet of 1682 and at some point after 1680 he systematically collected together data on all recorded comets and decided that comets did indeed obey the inverse square law of gravity just like planets, their paths being oval if they returned and hyperbola if not. This was possibly the point where Newton’s thoughts on gravity became a universal theory of gravity. Comets and their flight paths would go on to play a significant role in the Principia. Newton apparently didn’t think to inform Flamsteed of his change of mind and acknowledge that Flamsteed had been right, at least in principle, until 1685.


The orbit of the comet of 1680, fit to a parabola, as shown in Isaac Newton’s Principia Source: Wikimedia Commons

Newton and Flamsteed were not the only people to reconsider the flight paths of comets in the early 1680s and Newton was not the only person to think that the inverse square law of gravity applied to them, Newton’s rival Robert Hooke also did so. Robert Hooke had been investigating the effects of gravity for many years and had discovered the inverse square law for himself and became convinced of a universal gravity. He thought that the flight paths of comets, like planets, were determined by gravity and that the inverse square law also applied to them. However, unlike Newton he didn’t do the mathematics. This mutual independent discovery of universal gravity would lead to renewed conflict between the two natural philosophers, who had already crossed swords over the nature of light.




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