Category Archives: Book Reviews

History (of Science) Books by Women

Last weekend saw several major newspapers publishing their books of the year list. Unfortunately these displayed, in several aspects, a serious lack of balance. Science and history of science books came up more than somewhat short and in some categories the male dominance was glaring. The latter problem provoked the following tweet by historian and history book author Lucy Worsley:

8 of 9 of the ‘history books of the year’ in today’s Times, and 19 out of 21 of ditto in today’s Telegraph, are by men. I’m not impressed. Lucy Worsley

In reaction to this tweet a hash tag sprang into life, #HistoryBooksbyWomen, under which some just listed the names of female history book authors and others tweeted names and book titles. My discipline the history of science is blessed with many excellent female historians, authors of many first class books. This being the case I thought that I might cruise along my bookshelves and present here a lightly annotated list of some of those books by women that have enriched and informed my career as a historian of science.

I start with my #histsci soul sisterTM, Rebekah ‘Becky’ Higgitt, whose volume in the way the nineteenth century saw Isaac Newton, Recreating Isaac, I reviewed here.

Becky is also co-author of the beautiful Finding Longitude, which I reviewed here. (Her co-author Richard Dunn is a man but we won’t hold it against him).

Staying with Newton we have Sarah Dry telling us what happened to his manuscripts in The Newton Papers and Lesley Murdin Under Newton’s Shadow: Astronomical Practices in the Seventeenth Century.


In the world of navigation, cartography and geodesy we have Christine Garwood Flat Earth: The History of an Infamous Idea, Joyce E. Chaplin Round About the Earth: Circumnavigation from Magellan to Orbit, Silvia Sumira Globes: 400 Years of Exploration Navigation and Power and Rachel Hewitt Map of a Nation: A Biography of the Ordnance Survey.


Representing the Middle Ages we have two biographies Nancy Marie Brown The Abacus and the Cross: The Story of the Pope Who Brought the Light of Science to the Dark Ages and Louise Cochrane Adelard of Bath: The First English Scientist. For fans of automata there is E. R. Truitt’s delightful Medieval Robots: Mechanism, Magic, Nature, and Art.


In the early modern period and the emergence of modern science we have Pamela O. Long Artisan/Practitioners and the Rise of the New Science, Pamela H. Smith The Body of the Artisan, Paula Findlen Possessing Nature: Museums, Collecting, and Scientific Culture in Early Modern Italy, Deborah E. Harkness The Jewel House: Elizabethan London and the Scientific Revolution, Eileen Reeves Galileo’s Glassworks, Lisa Jardine Ingenious Pursuits: Building the Scientific Revolution, her Going Dutch: How England Plundered Holland’s Glory, her On a Grander Scale: The Outstanding Life and Tumultuous Times of Sir Christopher Wren, and her The Curious Life of Robert Hooke: The Man Who Measured London, Ulinka Rublack The Astronomer & the Witch: Johannes Kepler’s Fight for His Mother, Sachiko Kusukawa Picturing the Book of Nature: Image, Text, and Argument in Sixteenth-Century Human Anatomy and Medical Botany and Susan Dackerman ed. Prints and the Pursuit of Knowledge in the Early Modern Period Featuring essays by Susan Dackerman, Lorraine Daston, Katherine Park, Susanne Karr Schmidt and Claudia Swann.


Turning to the eighteenth century we have Patricia Fara A Entertainment for Angels: Electricity in the Enlightenment, Susannah Gibson Animal, Vegetable, Mineral? How eighteenth-century science disrupted the natural order and Jenny Uglow The Lunar Men: The Friends Who Made the Future.


No Renaissance Mathematicus book list would be complete without some esoteric history. We start with Monica Azzolini The Duke and the Stars: Astrology and Politics in Renaissance Milan that I reviewed here, Louise Hill Cuth English almanacs, astrology & popular medicine: 1550–1700, Tamsyn Barton Ancient Astrology, Pamela H. Smith The Business of Alchemy: Science and Culture in the Holy Roman Empire, Frances A. Yates The Rosicrucian Enlightenment and her Giordano Bruno and the Hermetic Tradition as well as Ingrid D. Rowland Giordano Bruno: Philosopher/Heretic. Somewhere between the stools Lorraine Daston & Katherine Park Wonders and the Order of Nature.


Mathematics are represented by Kim Plofker Mathematics in India and Serafina Cuomo Ancient mathematics. Astronomy and cosmology by M. R. Wright Cosmology in Antiquity, Kitty Ferguson Measuring the Universe and Jessica Ratcliff The Transit of Venus Enterprise in Victorian Britain.


We close with a potpourri of titles that don’t quite fit into any of the categories above. We start with two excellent books by Laura J. Snyder, her four-way biography of nineteenth-century Cambridge polymaths The Philosophical Breakfast Club: Four Remarkable Friends Who Transformed Science and Changed the World and her double seventeenth-century art and science biography Eye of the Beholder: Johannes Vermeer, Antoni van Leeuwenhoek, and the Reinvention of Seeing. Two further biographies are Brenda Maddox Rosalind Franklin: The Dark Lady of DNA and Dorothy Stein Ada: A Life and a Legacy. Patricia Fara gives us a general survey of science history in Science A Four Thousand Year History and a look at the role some women played in that history in Pandora’s Breeches: Women, Science & Power in the Enlightenment. Deborah Jaffé also looks at the role of women in science and technology in Ingenious Women: From Tincture of Saffron to Flying Machines. Last but by no means least we have Ingrid D. Rowland’s translation of Vitruvius: Ten Books of Architecture.


This list is of course fairly random and somewhat arbitrary and is in no way comprehensive or exhaustive. All of the books that I have included are in my opinion good and quite a lot of them are excellent. They demonstrate that there is width, depth and variety in the writings produced by women in the history of science taken in its widest sense. Should any misogynistic male of the species turn up in the comments and claim that the above list is only so impressive, and I find it very impressive, because I, in some way, privilege or favour female historians then I must point out that I have many more history of science books by male authors than by female ones on my bookshelves.

If you wish to add your own favourite history of science books authored by women in the comments you are more than welcome.



Filed under Book Reviews, History of science, Ladies of Science

History of Science for Kids

I recently got an email from Chad Lillian with the following request:

I was wondering if you could recommend some books for me about mathematical and scientific history that would be interesting for my 10 year old son to read (or for me to read with him)?  I have looked through your book reviews, but am wondering if there are any books you haven’t reviewed on your blog, but would recommend?

Now I don’t have and never have had children and I also don’t teach children so I am basically the wrong person to answer this question. Can people recommend suitable, preferably myth free, books on the histories of mathematics and science for Chad? make your suggestions in the comments!


Filed under Book Reviews

Science contra Copernicus

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

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


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

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

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

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

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

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

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

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

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


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

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


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

Political correctness and the history of science

Anyone who regularly reads this blog will be already aware that the historian David Wootton has written a new book entitled The Invention of Science: A New History of The Scientific Revolution; in The Times (unfortunately behind a pay wall) Gerard DeGroot doesn’t so much review the book as perform a very nasty, vindictive hatchet job on it. DeGroot doesn’t just raise the spectre of eurocentrism in his critic he formally slaps Wootton in the face with it from the very opening paragraph of his review. This raises the question as to whether he is right to do so and whether Wootton is guilty as charged. Before I address these points I would like to briefly review what exactly eurocentrism with respect to the history of science is.

There used to be a brief standard sketch of the history of science, that probably arose some time in the Enlightenment but which owes much of its ethos to Renaissance historiography. This outline usually goes something like this. Science[1] was invented by the ancient Greeks. After the collapse of civilisation in the Dark Ages (a deliberate use of a discredited term here) science was rescued and conserved (but not changed or added to) by the Islamic Empire before being retrieved in the Renaissance by the Europeans, who then went on to create modern science in the Scientific Revolution. This piece of mythology reflected the triumphalist historiography of a colonialist Europe in the throws of dominating and exploiting large parts of the rest of the world.

During the twentieth century historians, many of them Europeans, dismantled this piece of fiction and began to explore and elucidate the histories of science of other cultures such as Egypt, Babylon, China, India and the Islamic Empire, creating in the process a much wider and infinitely more complex picture of the history of science, consisting of transfers of knowledge across space and time throughout the last approximately four thousand years. This newly acquired knowledge exposed anybody who still insisted on propagating part or all of the earlier fairy story to the charge of eurocentrism, a charge that when considering the whole of the history of science is more than justified.

Unfortunately, as I have commented in the past, this also led to an over zealous backlash on behalf of the previously wronged cultures particularly on the Internet. One only needs to state that X (a European) discovered/invented Y (some piece of science, technology, medicine, mathematics…) for some over assiduous commentator (almost always not a historian of science) to pop up saying, that’s not true Z (an Indian, Islamic, Chinese, or whatever scholar) discovered/invented Y long before X was even born. Occasionally these claims are correct but much more often they are inaccurate, exaggerated or just plain false. Any attempt to correct the informant leads inevitably to an accusation of eurocentrism. Eurocentrism has become a sort of universal weapon used indiscriminately whether it is applicable or not.

Wootton’s book deals not with a general universal history of science but as it very clearly states in its subtitle with the Scientific Revolution a historical episode that took place in Europe in the Early Modern Period. Whether one is, as a historian, a ‘revolutionary’ or a ‘gradualist’ there is no doubt that following its reintroduction into Europe during the High Middle Ages that which we call science, irrespective of its original sources, underwent a radical change that led to the emergence by, at the latest, the nineteenth century, science as we know it today. The major difference between Wootton and myself is that he thinks this process took place almost entirely within the seventeenth century whereas I see a timeframe stretching from the fourteenth century to at least the middle of the eighteenth.

Wootton is writing about a historical phenomenon that took place exclusively within Europe to accuse him of eurocentrism is to say the least perverse. If this were not a European phenomenon then the so-called Needham question would simply be nonsensical. Joseph Needham (1900-195) was the twentieth century’s greatest historian of Chinese science and instigator of the monumental, on going seven volume Science and Civilisation in China. The question that Needham posed runs as follows “Why did modern science, the mathematization of hypotheses about Nature, with all its implications for advanced technology, take its meteoric rise only in the West at the time of Galileo [but] had not developed in Chinese civilisation or Indian civilisation?” He could have equally well have posed the same question for the Islamic Empire. Many historians have tacked this question respective the three cultures and their answers are as diverse, as they are inconclusive. Some approach the question by trying to address the reasons for the decline of science and technology in China, India or the Islamic Empire whereas others try to isolate the factors that led to the Scientific Revolution in Europe. Although he doesn’t directly address the Needham question Wootton’s can be seen as an example of the latter.

If I were to be charitable to DeGroot it would appear that his main error lies in his interpretation of the word science as used by Wootton in his main title. It is clear that what Wootton intends is ‘modern science’ as used by Needham in the quote of his famous question above. DeGroot, I think disingenuously choses it to mean any form of scientific activity from anywhere and anytime in human history. We can see this conflict of interpretations in the following quotes from DeGroot:

…to assert that science was invented between certain dates in western European history automatically imposes a proprietary right – by defining science in a certain way it becomes, in essence, European.


A different intellectual climate existed in India, China and the Middle East, [in the Middle Ages] however. Outside Europe, minds were more open to progress and curiosity fired scientific enquiry. For instance great strides were made in pure and applied mathematics, optics, astronomy and medicine in the Middle East long before Columbus set sail [Wootton sees 1492 and Columbus’ first voyage as the starting point of the Scientific Revolution]. As early as the 10th century, brilliant scientists (not exclusively Muslim) were drawn to centres of learning in Baghdad, Balkh and Bukhara. These scholars considered Europe an intellectual backwater, yet hardly get a mention in this book. In other words, the so-called Scientific Revolution seems like a revolution only if we ignore what was happening outside Europe.

The first quote is a clear accusation of eurocentrism and the second is DeGroot’s attempt to justify his accusation. Nothing he writes in the second quote is wrong but also none of it has any real relevance to the book that David Wootton has written. Interesting is his attempt to deny that the Scientific Revolution ever took place. Whether you think that the very real change in the nature of science that took place in Europe in the Early Modern Period did so in the form of a revolution or more gradually over a longer timeframe to deny its very existence is to fly in the face of the historical facts. Whatever happened in the Islamic Empire between the eighth and twelfth centuries, the Golden Age of Islamic science, other than provided some of the foundations on which Kepler, Galileo, Newton et al built their new science, none of it had very much relevance to what took place in Europe in the seventeenth century.

This point is spelled out very clearly by A. Mark Smith in his recently published book, From Sight to Light, an essential volume for anybody interested in the history of optics. Smith’s book is a counter argument to David C. Lindberg’s Theories of Vision: From Al-Kindi to Kepler. Lindberg had argued that Kepler was, so to speak, the crowning glory of the European perspectivist tradition of optics that begins with the introduction of the work of Ibn al-Haytham into Europe in the thirteenth century. Following the same path, starting with ancient Greek optics, Smith, an expert on al-Haytham and Arabic optics, wants to show that Kepler is in fact a break with the perspectivist tradition and a new beginning in the theory of optics, a revolution if you will. Well aware that he might face charges of eurocentrism Smith devotes several pages of his introductions to explaining why such a charge would not be justified. He closes his explanation with the following paragraph:

The same holds for the evolution of modern optics over the sixteenth and seventeenth centuries. It may well be that certain key ideas, laws and concepts that contributed to that evolution were anticipated by Arabic or, for that matter, Indian, Chinese or Mesoamerican thinkers. And it is certainly the case that there was a lively cross-cultural marketplace of commodities and ideas between the Latin “West” and Arabic “East” throughout the Middle Ages and Renaissance. The fact remains, though, that it was in Europe that those ideas, laws, concepts were eventually assimilated, refined, channelled, and combined in such a way as to form the basis of what most of us today would characterize as modern optics. Any claim to the contrary strikes me as historically perverse. Furthermore, to contend that the evolution of modern optics over the sixteenth and seventeenth centuries happened in Europe is not to give Europe proprietary rights to that science or to accord Europe cultural exceptionalism or superiority for having developed it. I therefore strongly resist any charge of being trapped, whether wittingly or unwittingly, in some grand, master narrative or of engaging in hegemonic discourse.

If we substitute modern science for modern optics in Smith’s eloquent speech for the defence I think we can safely reject as baseless the accusations of eurocentrism that DeGroot makes against Wootton.


[1] Throughout this post I shall be using the word science as a collective noun for science, technology, medicine and mathematics to save time and effort whilst writing.


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

The growing pile – too many good books not enough time

One of the joys of having a moderately successful history of science blog and being omnipresent in cyberspace as a pedantic historian of science devoted to promoting the discipline is that generous professional writers send me copies of their books to peruse and hopefully review. Unfortunately the pile of such books keeps growing and the amount of time I have been able to devote to serious reading in the last months seems to shrink with every week. To relieve the pressure, and to convince the authors that their books have not been sold off on Amazon Market Place, I have decided to write this post at least giving a basic description of those wonderful tomes waiting for my attention so that readers of this blog can go out and buy them for themselves without having to wait for my reviews.

The ones I’ve started:

Physics, History and God: Tom McLeish – Faith & Wisdom in Science

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Tom McLeish is a professor for modern physics, a historian of medieval science and a devote Christian who has written a challenging contribution to the science and religion debate. As a life-long atheist I am trying to be very careful not to let my personal prejudices influence me whilst reading McLeish’s stimulating book. And very stimulating it is. At the moment I am stalled in the central chapter of the book A Theology of Science but what I have read up till now, more than half of the book, has convinced me that there is much to be got from McLeish’s well argued and extremely well written book. I will report back when I finally finish it.

Problem solving the scientific way: Chad Orzel – Eureka! Discovering Your Inner Scientist

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After two books on teaching physics to dogs, fellow blogger, physicist and popular science writer Chad Orzel has turned his hand to the philosophy of science. However the reader need not fear complex arguments about Kuhn, Popper et al written in words that require constant recourse to a dictionary, Orzel’s book is a delightful romp through the way that scientists in real life solve problems. At the moment I’m stalled about a quarter of the way through because there are ‘more important’ things that I have to read but I shall definitely come back and finish this one because it’s not only informative but a pleasure to read.

DNA the whole story: Matthew CobbLife’s Greatest Secret

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Based on having read the first half this is a superb book. Cobb writes informatively, wittily, entertainingly and with an obviously deep grasp of his material. Up till now I have learned such things as the real story of Rosalind Franklin and Photograph 51, so very different to the myths, and all about Oswald Avery, who I’d never heard of before but whose contribution to the DNA story was mega significant. Don’t wait for my review buy, borrow or as Abbie Hoffman said, steal this book and read it! I promise you that you won’t regret it.

Science contra Copernicus: Christopher M. Graney Setting Aside All Authority: Giovanni Battista Riccioli and the Science against Copernicus in the Age of Galileo

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I’ve actually finished this one and the review should appear here shortly. I’ll just say for now that it’s going to be a five star review with extra fairy dust

The ones I haven’t started yet:

Twentieth-Century Physics: Paul Halpern – Einstein’s Dice and Schrödinger’s Cat

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Paul Halpern is an excellent science writer and the subject is one that really interests me so I’m really looking forward to finding the time for this one. I’m certain that it will live up to its excellent reviews.

Renaissance Technology: Paul Engle – Conciatore: The Life and Times of 17th Century Glassmaker Antonio Neri

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I don’t have to read this one to know that it is first class history of science and technology. I have been following Paul Engle’s truly excellent blog on the book (and if you don’t already follow it you should!) for a long time and I know that this book is destined to become a classic.

Optics and Art: Laura J. Snyder – Eye of the Beholder: Johannes Vermeer, Antoni van Leeuwenhoek and the Reinvention of Seeing

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I was really pleased when Laura Snyder sent me a copy of this book not only because the subject interests me very much indeed, but because if it’s only half as well researched and written as her last book The Philosophical Breakfast Club then it’ll still be twice as good as most other semi-popular history of science books on the market. However I’m convinced it’ll be just as good as the last one and a real pleasure to read as well as being highly educational.

Last but by no means least the latest addition to the pile that arrived just hours ago in the post.

A revisionist view of the scientific revolution: David Wootton – The Invention of Science: A New History of The Scientific Revolution

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David Wootton’s just published new tome, all 770 pages of it, is really burning a hole in my conscience. I would love to drop all my other commitments and dive straight into this challenging book. I know, and David Wootton knows, that he is defending a hypothesis that I, in principle, reject, the real existence of the Scientific Revolution. His personal dedication reads “For Thony in amicable disagreement. Respectfully…” This book has received glowing reviews from both Andrea Wulf and Philip Ball, two science writers whom I regard very highly so I am more than curious if David Woottton can convince me to, at least, modify my views on the so-called Scientific Revolution. I found his last history of science book Galileo: Watcher of the Skies, in which he challenged the orthodox view that Galileo was a devote Catholic, stimulating, challenging and convincing. So I think that I am again in for an interesting intellectual ride through the Early Modern Period in the hands of a master historian. We will see and I will report back when the ride is over.


Filed under Book Reviews

To Explain the Weinberg: The discovery of a Nobel Laureate’s view of the history of science

In my dim and distant youth, I was an ardent fan of twentieth-century physics and consumed a large quantity of popular books and articles (mostly New Scientist and Scientific American) on the subject as well as graduating to some high-grade serious history of science on both relativity and quantum physics. One of the books I read was The First Three Minutes: A Modern View of the Origin of the Universe by theoretical physicist and Nobel Laureate Steven Weinberg. This book impressed me very much, as it did the reviewers at the time, and I came away with a deep respect for Steven Weinberg as a science writer. Now in his eighties Weinberg is still highly active and this year he published his own history of science, To Explain the World: The Discovery of Modern Science. This book proved to be highly contentious because of Weinberg’s avowed presentist approach to writing history of science and its appearance generated a lot of debate some of which I collected in one edition of Whewell’s Gazette (scroll down to book reviews). This situation led me to the thought that I should read and review Weinberg’s tome for myself, a thought that for various reasons didn’t really appeal. However rescue was at hand. Chris Graney, Renaissance Mathematicus friend and more than welcome guest blogger, has taken on the task, read, analysed and reviewed To Explain the World and it is with great pleasure and some relief (I won’t have to read it after all) that I present his thoughts on Weinberg’s book to the eager readers of the Renaissance Mathematicus.

In To Explain the World: The Discovery of Modern Science, author Steven Weinberg covers science history from the Milesians of ancient times to the Standard Model of today. His emphasis is on physics and astronomy, and he includes thirty-five ‘Technical Notes’ for the mathematically advanced reader that explain the physics and mathematics of things such as ellipses, refraction, and centripetal acceleration. His treatment of science’s history is not just a re-hashing of stock stories: he gives attention to Tycho Brahe; he does not lionize Galileo. He tries to show what he thinks science is and is not. The average Joe or Jane who has a casual interest in science and history and wants an overview by a prominent scientist should read the book. He or she will learn quite a few things, most of them not wrong.

However, the Renaissance Mathematicus is about neither casual interest in the history of science, nor history in which most things are not wrong, nor deference to prominent authors. And so, having generally recommended this book, I have two big specific criticisms of it: one regards facts; and the other regards philosophizing.


Weinberg makes factual errors. For example, in Chapter 10 on Medieval Europe, he discusses how the French cleric Jean Buridan rejected the Aristotelian idea that all motion requires a mover and introduced the idea that objects remain in motion once set in motion. Buridan called this impetus. Weinberg mischaracterizes impetus, saying that it was a foreshadowing of the modern idea of momentum, not momentum itself. “He [Buridan] never identified the impetus carried by a body as its mass times its velocity,” writes Weinberg (p. 133), “which is how momentum is defined in Newtonian physics.”

This is not correct. Buridan wrote regarding impetus that a moving body is impressed with —

…a certain impetus or a certain motive force of the moving body, in the direction toward which the mover was moving the moving body, either up or down, or laterally, or circularly. And by the amount the [mover] moves that moving body more swiftly, by the same amount it will impress in it a stronger impetus… by the amount more there is of matter, by that amount can the body receive more of that impetus and more intensely.

Thus Buridan plainly says that impetus is proportional to mass and proportional to velocity. That is mass-times-velocity momentum. He differs from modern momentum only in that he does not separate angular momentum, moment of inertia, etc. He uses momentum to explain the motion of bouncing balls, vibrating strings, and falling bodies in a manner consistent with Newtonian physics. He says that in the absence of resistive forces that will corrupt momentum, an object will continue in motion forever.

The Buridan quote above is from Edward Grant’s Source Book in Medieval Science p. 276-277. Weinberg cites the Source Book twice in that chapter, but not regarding Buridan. Regarding Buridan he cites the Dictionary of Scientific Biography.

Buridan is not the only instance of Weinberg getting things wrong. He says a number of weird things about the appearance of stars, mostly because he insists on discussing the stars in modern terms of brightness, rather than of size as they were traditionally viewed. He tries to explain the term magnitude (p. 88), never drawing the connection to size. This creates problems in a number of places, most notably when he wonders how Copernicus could speak of the Sun, Moon, planets, and stars all being seen to be circular in shape — “how could [Copernicus] know anything about the shape of the stars?” Weinberg asks (p. 155; I wonder how he thought Copernicus might know anything about the shape of the planets?). The answer is found by looking at the sky with good eyes. Then one sees that Copernicus (like Ptolemy and Tycho and many others) was right and that all these bodies do appear round to the eye. They appear as little round dots — the more prominent ones look like larger round dots, the less prominent like smaller round dots. Thus the term magnitude — size — and thus Copernicus’s comments.

There are other examples of, if not errors, at least odd phrasing:

  • Weinberg tries (p. 58) to distinguish a gnomon (“simply a vertical pole, placed in a level patch of ground open to the Sun’s rays”) from a sundial (“different from a gnomon; its pole is parallel to the Earth’s axis rather than to the vertical direction, so that its shadow at a given hour is in the same direction every day. This makes a sundial more useful as a clock, but useless as a calendar.”). But all shadows fall in the same direction at a given hour, and so both the vertical pole and the sundial pole can be used to keep time; and all shadows vary in length with the seasons, and so both can be used to mark the time of year.
  • He cites Newton as noting that “the observed phases of the five planets other than Earth show that they revolve around the Sun [p. 237]”, but Jupiter and Saturn show no observable phases, and Mars only shows a gibbous phase consistent with it having a certain position relative to Sun and Earth. Only the phases of Venus and Mercury prove their motions around the Sun. Newton did talk about phases of all five planets (in his Phenomena), but Weinberg’s phrasing is odd.
  • He says the Inquisition gave a public formal order censoring Copernican books (p. 184), but according to Maurice Finocchiaro, the historian who translated and published the relevant documents, the Inquisition took no formal action; it was the Congregation for the Index (which Weinberg does mention elsewhere) that issued the censoring order.
  • Weinberg states that Kepler made a case for heliocentrism “based on mathematical simplicity and coherence, not on its better agreement with observations [p. 172]”, but Kepler seems to indicate otherwise. “It behoves us,” Kepler wrote, “to whom by divine benevolence such a very careful observer as Tycho Brahe has been given, in whose observations an error of 8′ of Ptolemy’s computation could be disclosed, to recognize this boon of God with thankful mind and use it by exerting ourselves in working out the true form of celestial motions….”

Almost all the errors/oddities that I have pointed out here could have been fixed with relatively little effort, and without substantially changing the book. I have read complaints from historians concerning Weinberg writing about history as a non-historian, and in particular writing as a scientist who judges the past by his own standards as a scientist of today (see Steven Shapin’s review in the Wall Street Journal; there was an editorial about this in Physics in Perspective). In my opinion, Weinberg is clear about his approach, often stating “I think this” or “I don’t think that”. An example is found in his discussion of Descartes, where he both praises Descartes (“This was Descartes at his best as a scientist [p. 209]”) and criticizes him (“The writings of Descartes on scientific method have attracted much attention among philosophers, but I don’t think they have had much positive influence on the practice of scientific research…. [p. 213]”). I have no complaint with what Weinberg is doing. His position is clear. The reader can consider accordingly. But Weinberg is obligated to get the historical facts right.


Weinberg peppers To Explain the World with comments related to philosophy and religion, some of which are problematic. For instance, at one point Weinberg writes “whatever the final laws of nature may be, there is no reason to suppose that they are designed to make physicists happy [p. 165]”. But then later we find, “We learn how to do science, not by making rules about how to do science, but from the experience of doing science, driven by desire for the pleasure we get when our methods succeed in explaining something [p. 214].” And so apparently science exists because indeed the laws of nature are designed to make physicists happy — a sentiment Weinberg repeats elsewhere (p. 248, 255).

Weinberg also writes, “Modern science is impersonal…; it has no sense of purpose; and it offers no hope for certainty…. We learn not to worry about purpose…. We learn to abandon the search for certainty [p. 254-255]”. But then later we find, “…the Standard Model provides a remarkably unified view of all types of matter and force (except for gravitation) that we encounter in our laboratories, in a set of equations that can fit on a single sheet of paper. We can be certain that the Standard Model will appear as at least an approximate feature of any better future theory [p. 264].” And so apparently there is hope for certainty after all.

Such contradictions arise because Weinberg juxtaposes an insistence on purposelessness with an insistence that science is purposeful and inevitable because it uncovers a beautiful (i.e. makes physicists happy) reality, or at least it approaches that reality over time (p. 252, 254, 268). He describes the Standard Model (p. 264-265) as impersonal, lacking element of purpose, not being deduced from mathematics or philosophical preconceptions, and not following straightforwardly from observation of nature, yet he then states that it is a product of guesswork and aesthetic judgment, validated by its successes. Is there nothing personal, purposeful, and philosophically preconceived in aesthetic judgment? In closing the last chapter Weinberg writes, “Still, we have come a long way on this path, and are not yet at its end…. It is toward a more fundamental physical theory that the wide-ranging scientific principles we discover have been, and are being, reduced [p. 268]”. Is there nothing personal, purposeful, and hope-filled about being on a path, moving toward some fundamental end but not yet being there? The point here is not to argue for purpose in science or for a nature designed to make physicists happy, but to illustrate the contradictions in Weinberg’s philosophical musings.

Unfortunately, where Weinberg is more consistent in his philosophizing is on religion, and there he does a disservice to science. To Explain the World is not especially hard on religion as these things go, but Weinberg does insert comments that seem religion-unfriendly, and entirely disposable. There is a comment about the Copernican “demotion of earth” (p. 156) being a problem for all religions; a comment about the works of Descartes being placed on the Index of books forbidden to Roman Catholics (p. 213); a comment about how even if Galileo had been mistaken it would still have been wrong for the church to sentence him to imprisonment and deny his right to publish, just as it was wrong to burn Giordano Bruno for being a heretic (p. 187-188).

Each of these are isolated remarks that do not tie in with the rest of the text, and each can be debated. Kepler thought the Copernican system actually elevated Earth’s position up from the sump of the universe. As for the church being wrong about censorship and treatment of Galileo, well, Weinberg is clear on judging the past by the standards of today, and no, we do not do such things today. But he is selecting what to judge. It was also wrong to execute people for who-knows-what crime and to stick their heads on pikes by the dozen on the town bridge for everyone and their toddler to see, as was done at the time, and we do not do such things today. Yes, some church people in the seventeenth century behaved like ogres. But at that time a lot of other people behaved like ogres in many ways, too. To insert comments about these ogres but not those ogres is to select your data points, and, as judged by the standards of the modern scientist, that is poor practice.


Impaled heads on the south gate of London Bridge, 

from Claes Visscher’s Panorama of London in 1616.

This selecting of data points extends more deeply than just throwaway comments. Weinberg’s discussion of figures such as Kepler, Boyle, and Newton omits just how large religion loomed in their thinking. The Kepler discussion is the most egregious example of this (Weinberg does include some references to religion regarding Boyle and Newton). Kepler was an astronomer who wrote about how he originally wanted to be a theologian but how he was able to glorify God through astronomy; who saw the Holy Trinity reflected in the Copernican universe, with the Sun representing God the Father and thus properly placed at the focus of elliptical orbits; whose Mysterium Cosmographicum (which Weinberg discusses) was an effort to uncover the mathematical rationale God used in building the solar system. But none of this is in To Explain the World. Weinberg portrays Kepler as simply a Platonist who applied to historical accidents an interest in mathematical oddities (p. 163-164). Perhaps most annoying is the following Kepler quote, which Weinberg includes (p. 179) to illustrate how Kepler challenged opponents of Copernicus:

Advice for Idiots. But whoever is too stupid to understand astronomical science, or too weak to believe Copernicus without affecting his faith, I would advise him that, having dismissed astronomical studies, and having damned whatever philosophical opinions he pleases, he mind his own business and betake himself home to scratch in his own dirt patch, abandoning this wandering about the world.

Now look at Kepler’s words in a larger context:

So everything the psalmodist said of the world relates to living things. He tells nothing that is not generally acknowledged, because his purpose was to praise things that are known, not to seek out the unknown. It was his wish to invite men to consider the benefits accruing to them from each of these works of the six days.

I, too, implore my reader, when he departs from the temple and enters astronomical studies, not to forget the divine goodness conferred upon men, to the consideration of which the psalmodist chiefly invites. I hope that, with me, he will praise and celebrate the Creator’s wisdom and greatness, which I unfold for him in the more perspicacious explanation of the world’s form, the investigation of causes, and the detection of errors of vision. Let him not only extol the Creator’s divine beneficence in His concern for the well-being of all living things, expressed in the firmness and stability of the Earth, but also acknowledge His wisdom expressed in its motion, at once so well hidden and so admirable.

But whoever is too stupid to understand astronomical science, or too weak to believe Copernicus without affecting his faith, I would advise him that, having dismissed astronomical studies and having damned whatever philosophical opinions he pleases, he mind his own business and betake himself home to scratch in his own dirt patch, abandoning this wandering about the world. He should raise his eyes (his only means of vision) to this visible heaven and with his whole heart burst forth in giving thanks and praising God the Creator. He can be sure that he worships God no less than the astronomer, to whom God has granted the more penetrating vision of the mind’s eye, and an ability and desire to celebrate his God above those things he has discovered.

To talk about Kepler as a Platonist while leaving out this aspect of Kepler is to select the data points. (Note — “Advice to Idiots” is a marginal note in Kepler’s book, not part of the text itself.)

My real job is to be a community college professor — to, ahem, Bring Science to The Community — and I absolutely hate the sort of thing Weinberg is doing. Not only is selecting the data not in the spirit of science, it does a disservice to science in general, and makes my job harder in particular. Why? Because Weinberg is in the USA (Texas, specifically), and here in the USA (especially Texas) we have many flare-ups over religion, science, school textbooks, and the like. See the March issue of National Geographic, whose cover story is “The War on Science” for a recap. I experience this issue directly with a number of my students. Weinberg, by choosing to highlight books on the Index or the troubles of Galileo, while being silent on the deep religious motivations of people like Kepler, skews the story of science in such a way as to add fuel to those flare-ups, when he could instead help to cool them down (he is not alone in this regard). Kepler is obviously a possible point of connection between “science people” and “religion people”. It is in science’s interest to emphasize such points of connection, as science is not winning in “The War on Science”. We need what allies (or at least non-enemies) we can get. Science needs prominent writers like Weinberg to talk up Kepler’s religion just as much as they talk up the Inquisition. Weinberg’s philosophy comments and selecting the data points on religion is a missed opportunity for science.

Read it — but with eyes open

The problems with facts and philosophizing are significant in To Explain the World, but they will not prevent its readers from learning a good deal about science and its long history. Indeed, the amount of history touched upon is at times itself a drawback. Chapter 9 on Arab scientists is a particular example of this. Here Weinberg introduces one scientist after another — in two pages of text (p. 110-111) we meet, and leave, Omar Khayyam, Ibn Sahl, Jabir ibn Hayyan, al-Kindi, al-Razi, and Ibn Sina. But, most readers probably know nothing about any of these scientists, and after finishing the book they will know something. And, the problems with facts and philosophizing will not prevent readers from picking up some technical details on physics and mathematics — although those readers should be aware that Weinberg occasionally includes mathematical material that many readers will not follow. For example, his discussion of the derivative, which includes invoking the idea that squares and cubes of small terms can be neglected (p. 223), will likely be useless to readers not already familiar with that material. The readers can just wade through and continue on, knowing they will likely learn something about the derivative no matter what. The problem regarding technical material is not aided by the absence of any illustrations in the main text, where they are often needed — where Weinberg describes Kepler’s nesting of Platonic solids, for instance (p. 162).

The problems with Weinberg’s book will not prevent readers from learning a good deal about science and its history, and will not prevent them from getting a scientist’s perspective on this subject. Read To Explain the World. Just keep your eyes open for its problems.


Filed under Book Reviews

Teaching the Revolution.

Anthony Millevolte is professor for chemistry at the University of Wisconsin Colleges where he also teaches the history of science courses. When he was teaching an introductory course on the so-called Copernican or Astronomical Revolution he realised that there was no suitable modern textbook available for such a course so he decided to write one: The Copernican Revolution: Putting the Earth into Motion.[1] His resolve to do so was strengthened when he realised that some people wee still teaching such courses using Thomas Kuhn’s The Copernican Revolution from 1957. He writes, “As well written as it is, the obviously unavoidable weakness of Kuhn’s text is that it doesn’t reflect over a half century of active scholarship in this field”[2]. Being somewhat less diplomatic than Millevolte I would add that Kuhn’s book was flawed in some aspects in 1957 and those flaws haven’t improved in the almost sixty years since.


Millevolte’s book is exactly what he set out to write an introductory textbook for college students on the developments in European astronomy in the sixteenth and early seventeenth centuries centred on the period between Copernicus and Galileo. Having above referred to the so-called Copernican Revolution I should point out that Millevolte doesn’t believe in a revolution either, as he explains in the final chapter of the book, An Epilogue, but uses the term in his title because it “reflects a long-standing historical convention – not because it accurately summarizes a series of events that unfolded over many centuries”[3].

The first three chapters could be summarized as setting the scene, giving a quick survey of European astronomy prior to the Renaissance. Consisting of only eight-two pages they don’t offer much depth but however cover all of the salient points clearly and accurately. All the chapters of the book have excellent endnotes and these contain references to the extensive bibliography helping any reader who wishes to pursue any given topic further.

The fourth chapter is devoted to Renaissance astronomy and Copernicus and contains one of the few minor criticisms that I have of the book. In his biographical sketch of Copernicus Millevolte makes some errors only significant to a pedant like me, which however could profitably corrected in a second edition. Otherwise this like all the other chapters in the book is clearly presented and the history of science is as far as it goes correct.

In his introduction Millevolte says that in the process of writing he realised why nobody had written such an up to date textbook. He writes, “It turns out that the experts disagree on a good many of the central elements of the story – so much so that it is sometimes challenging to identify an acceptable narrative”[4]. On this point I agree with him so one should bear this in mind when considering any criticism that I might make here. Despite this problem throughout the book Millevolte had managed to produce a clear, coherent narrative suitable for beginners. On those points that are contentious he includes clearly written, extensive endnotes, which list alternative viewpoints, thus managing very successfully to have his cake and eat it, too.

Having set the astronomical revolution in motion Millevolte produces one chapter each on Tycho Brahe and Kepler and three on Galileo. Here I would complain that the balance is false as Kepler contributed far more to the astronomical revolution than Galileo. However the traditional narrative always favours Galileo over Kepler and as this is a college textbook Millevolte stays within the tradition. He does however redress the balance somewhat in the final chapter where he attributes equal weight to Kepler and Galileo in establishing heliocentricity. I still think this gives too much credit to Galileo but it is it is better than the standard mythology that gives almost all the credit to Galileo and almost none to Kepler.

In his chapters on Galileo Millevolte also tend to emphasise positive aspects of Galileo’s activities oft by simply omitting the negative. For example whilst discussing the dispute between Galileo and Orazio Grassi concerning comets, that led to Galileo writing Il Saggiatore, whilst conceding that Galileo’s attacks on Grassi were, to say the least, immoderate Millevolte neglects to mention that on the question of whether the comets were sub- or supralunar Grassi was in the right and Galileo very much in the wrong.

The same subject turns up in the discussion of the third day in the Dialogo, which is devoted amongst other things to the novas and that they were supralunar. Millevolte claims that Galileo devoted space to this theme because “there remained many Aristotelians who refused to believe the novas were located beyond the sphere of the moon”[5]. This may well have been but the Jesuit, who were without doubt the leading geocentric astronomers, had already accepted the supralunar status of the novas in the sixteenth century. Galileo is here flogging the proverbial dead horse. Again not mentioned by Millevolte, who in general fails to make the important distinction between Aristotelian cosmology and Ptolemaic and/or Tychonic astronomy; a distinction that played a central and significant role in the gradual acceptance of heliocentricity. Geocentric astronomers were prepared to abandon Aristotelian cosmology when the evidence showed it to be wrong but not to give up geocentric astronomy without clear evidence against it and for heliocentricity.

Concerning day four of the Dialogo, Millevolte fails to mention that Galileo’s much favoured theory of the tides was in fact refuted by the empirical facts.

All of the above points whilst, in my opinion important, are for an introductory text not absolutely essential and should not be thought to lead to a negative assessment of Millevolte’s book.

The closing chapter of the book delivers a brief but very clear assessment of the further progress towards heliocentricity up to and including Isaac Newton. As already mentioned the book has an extensive bibliography and the endnotes to each chapter deal skilfully with many of the historically contentious points in the story. I personally would have welcomed an index. The book is attractively illustrated with black and white pictures and diagrams.

Taken as a whole Millevolte has fulfilled his original resolve extremely well and what we have here is a first class up to date textbook on one of the most important episodes in the history of astronomy. I would heartily recommend this book to anyone who wishes to read an introductory text on the subject to inform and educate themselves and especially to anyone wishing to teach an introductory course on the subject to college students or even to the upper classes/grades of grammar schools, high schools etc. Currently priced at circa $17 US on most students should be able to afford a copy.


[1] Anthony Millevolte, The Copernican Revolution: Putting the Earth into Motion, Tuscobia Press, 2014.

[2] Millevolte, p. iv

[3] Millevolte, p. 294

[4] Millevolte, p. v

[5] Millevolte, p. 270


Filed under Book Reviews, History of Astronomy, Uncategorized