A little learning is a dangerous thing

“A little learning is a dangerous thing

Drink deep, or taste not the Pierian spring: 

There shallow draughts intoxicate the brain,

And drinking largely sobers us again. 

Fired at first sight with what the muse imparts,

In fearless youth we tempt the heights of arts 

While from the bounded level of our mind 

Short views we take nor see the lengths behind 

But more advanced behold with strange surprise,

New distant scenes of endless science rise!”

In a recent New Yorker essay Adam Gopnik delivered up his view of Galileo Galilei. The essay is long and meandering and I don’t intend to do a complete analysis but there is one central point of Gopnik’s that I do wish to discuss. He gets off to a lousy start by calling Galileo “The founder of modern science”. I’ve already dealt with this elsewhere and don’t intend to repeat myself here. However Gopnik returns to the theme towards the end of his essay with proof! He begins with the following:

Contemporary historians of science have a tendency to deprecate the originality of the so-called scientific revolution, and to stress, instead, its continuities with medieval astrology and alchemy. And they have a point. It wasn’t that one day people were doing astrology in Europe and then there was this revolution and everyone started doing astronomy. Newton practiced alchemy; Galileo drew up all those horoscopes. But if you can’t tell the difference in tone and temperament between Galileo’s sound and that of what went before, then you can’t tell the difference between chalk and cheese.

Those historians of science can make their claims but Gopnik, a literary critic/humourist/art critic [please choose the appellation for Gopnik that best fits your prejudices or lack of them: see comments] knows better! He has read a book!

The difference is apparent if you compare what astrologers actually did and what the new astronomers were doing. “The Arch-Conjuror of England” (Yale), Glyn Parry’s entertaining new biography of Galileo’s contemporary the English magician and astrologer John Dee, shows that Dee was, in his own odd way, an honest man and a true intellectual. He races from Prague to Paris, holding conferences with other astrologers and publishing papers, consulting with allies and insulting rivals. He wasn’t a fraud. His life has all the look and sound of a fully respectable intellectual activity, rather like, one feels uneasily, the life of a string theorist today.

Now I have read the same book and although that book is excellent it, in my opinion, suffers from a major deficiency that I actually discussed on twitter a while back with Ted Hand (@t3dy) a historian of alchemy. However before we turn to Parry’s book and its deficiency let us see how Gopnik uses it to justify his belief in Galileo’s modernity.

The look and the sound of science . . . but it does have a funny smell. Dee doesn’t once ask himself, “Is any of this real or is it all just bullshit?” If it works, sort of, and you draw up a chart that looks cool, it counts. Galileo never stopped asking himself that question, even when it wasn’t bullshit but sounded as though it might well be. That’s why he went wrong on the tides; the-moon-does-it-at-a-distance explanation sounds too much like the assertion of magic. The temperament is not all-seeing and curious; it is, instead, irritable and impatient with the usual stories.

So there we have it. Galileo may have been a practicing astrologer but he was also a questioning scientist whereas his near contemporary John Dee was just a gullible pseudo-scientist. Case closed. Galileo is different. He is the founder of modern science as claimed. Gopnik 1 historians of science 0.

Unfortunately for Gopnik reading one book on Dee, no matter how good, isn’t enough. He has fallen head first into the error illustrated by the famous quote from Alexander Pope with which this post is headed, “a little learning is a dangerous thing”. If instead he had drunk deep of the springs of Dee scholarship he would not have so confidently labelled Dee chalk to Galileo’s cheese.

What is Parry’s deficiency and why is Gopnik wrong?

To understand the problem we have to look at how John Dee’s image has changed over the centuries. In the 16th century Dee was a highly respected member of the European scientific community highly involved in mathematics, astronomy, astrology, alchemy, cartography, navigation and history. By the middle of the 17th century his star was fading fast and he was largely forgotten then Meric Casaubon published the so-called Angel Diaries, Dee’s supposed conversations with angels through the medium Edward Kelly. Through this publication of previously unknown material Dee became the archetypal Renaissance magus in the popular imagination, a dabbler in magic probably in league with the devil.

This remained the public persona of Dee right up to the beginning of the twentieth century and he became a notorious trans-continental figure turning up as the essence of sorcery in several works of fiction. In the twentieth century, however, historians began to investigate and re-assess the real historical John Dee and the role that he played in European Renaissance culture. What emerged was a very different figure from the archetypal Renaissance magus. The last forty or fifty years has seen the publication of many academic papers and a series of monographs containing biographical studies of Dee, illustrating various aspects of his highly complex character. Glyn Parry’s The Arch Conjuror of England: John Dee is the latest such biography to be published.

Parry’s book, which is excellent and highly recommended for those interested in the subject, is a well researched and minutely documented study of the role played by alchemy and magic in the European royal courts of the sixteenth century, in particular the court of Elizabeth I of England, structured around the life story of John Dee. This is not the first such study but follows in the tradition of R. J. W. Evan’s excellent Rudolph II and his World: A study in intellectual history, 1576–1612 and Bruce T. Moran’s equally excellent The Alchemical World of the German Court: Occult Philosophy and Chemical Medicine in the Circle of Moritz of Hessen (1572–1632) both of which also feature John Dee, albeit in a less central role, who was active on both courts. Both books are regarded as classics and standard works on the role of the occult in Renaissance culture and Parry’s book is a more than worthy companion but there is a minor and important difference. Both Evan’s and Moran’s books were marketed as academic books written for specialists and although Parry’s volume is equally academic his publishers have seized upon Dee’s public popularity and marketed it as a popular book. They have also, and this is the crucial point, marketed it as a biography. This marketing strategy has led Gopnik to the belief that having read Parry’s book he now knows all about John Dee but unfortunately he is highly mistaken.

Parry actually only deals with one aspect of Dee’s multi-faceted nature, his activities as a magus almost completely ignoring Dee the mathematicus and it is here that Gopnik walks straight into a trap of his own making. If instead of just reading Parry’s book he had done some basic research on Dee he would have discovered that Dee and Galileo are by no means so far apart as he would like to think.

Several times in his book Parry alludes to the fact that mathematics plays a very central role in Dee’s whole philosophy but never bothers to elucidate what or why, concentrating instead on Dee’s occult activities leading Gopnik to a totally false picture of Dee the mathematical scientist. Early in his book Parry explains that after graduating from Cambridge Dee paid two visits to the University of Leuven, in the Spanish Netherlands, one short and one substantially longer to study under Gemma Frisius and Gerard Mercator. Parry discusses the astrology that Dee studied under the two Netherlanders but makes no mention of the mathematics. In fact Frisius was one of the leading teachers of the cutting edge mathematical sciences of the age and Dee came back to Britain with the best mathematical education available anywhere in the world at the time. He introduced into Britain, which lagged far behind the rest of Europe in the development of the mathematical sciences, the newest procedures in mathematics, astronomy, cartography and navigation as well as bringing with him the newest terrestrial and celestial globes and astronomical instruments from the workshops of Frisius and Mercator. On his early journeys through Europe Dee also got to know and to learn from other leading European mathematical practitioners such as Pedro Nunes in Portugal and Federico Commandino in Italy.

In his house in Mortlake Dee set up a research centre for the mathematical sciences, which contained the largest private scientific library in Europe, including at least two copies of Copernicus’ De revolutionibus, where other interested scholars could and did come to learn and discuss the latest in mathematical knowledge. Dee’s foster son Thomas Digges wrote and published one of the first works on Copernican astronomy in English, which contained the first published partial translation of De revolutionibus into the vernacular. Another acolyte of Dee’s John Feild (sic) published, at Dee’s urging, the first ephemeris based on Copernicus’ work. Dee himself wrote the extensive preface to Henry Billingsley’s English translation of The Elements of Euclid. This preface is an important early work on the philosophy of mathematics. Dee corresponded on mathematical topics with many of the leading mathematicians and astronomers in Europe including a correspondence with Tycho Brahe on the problems of determining the parallax of moving celestial bodies, i.e. comets, a topic at the cutting edge of contemporary astronomical research. Dee was also a close friend and colleague of Thomas Harriot the greatest of English Renaissance mathematicians whose scientific discoveries easily rivalled those of Galileo but because he never published anything remained unknown and unacknowledged.

His English language preface to Billingley’s Euclid was not a one off but is symbolic for one of Dee’s most important contribution that of co-founder of the so-called English school of mathematics. As already mention in the second half of the sixteenth century England lagged behind the rest of Europe in the mathematical sciences. The first person to undertake series efforts to correct this deficit was Robert Recorde who wrote and published a series of textbooks in English covering the mathematical sciences including Copernican astronomy. After Recorde’s death Dee brought out several revised and expanded editions of those textbooks. The two of them started a tradition of English mathematics that stretched through the second half of the sixteenth century all the way through the seventeenth century up to Newton, which encompasses such important figures as William Oughtred, Seth Ward, John Wallis, Christopher Wren and even Newton himself.

Far from being the naïve magician that Gopnik imagines him to have been John Dee was acknowledged and recognised as one of the leading European mathematical practitioners in the third quarter of the sixteenth century. Whose mathematical heritage echoed all the way through the seventeenth century and the creation of modern science.

Contrary to the commonly held myth Galileo did not invent modern mathematical science but built his research on a solid foundation a Renaissance mathematical advances that goes back all the way to Georg Peuerbach and Regiomontanus in the middle of the fifteenth century. One of the Renaissance mini-giants on whose shoulders Galileo and his contemporaries constructed their contributions to the evolution of modern science was John Dee. Far from being the contrast obsolescent model to Galileo’s shiny new show room model as Gopnik would have us believe John Dee, in his own way, contributed as much to the creation of modern science as Galileo himself.


Filed under Book Reviews, History of Astrology, History of Astronomy, History of Cartography, History of science, Myths of Science, Renaissance Science

19 responses to “A little learning is a dangerous thing

  1. Michael Weiss

    The other problem with Gopnik’s comment is that he completely ignores Galileo’s dependence on the medieval tradition for his physics. This is pretty old stuff in HOS; doesn’t Heilbron say anything about it in his bio?

    Whatever the technical problems with Galileo’s theory of tides, his worst sin was rejecting the notion that there could be another explanation for them. In short, he failed to ask, “Is my theory real or is it bullshit?”

  2. Kia Penso

    I take exception to your characterization of Gopnik as a literary critic. We are a downtrodden, forgotten people, our voices unheard, unheeded. We just keep climbing one after another of those Alps upon Alps, taking the deep sips of Pierian Spring Water from our camel packs, minding our own business. We no longer even complain of the world’s indifference to our silent labors. What have we done that Gopnik should be tossed in amongst us? We do have standards, you know. Gopnik is a humorist. Of course he is conspicuously not funny, which seems to make lots of people think he must be serious. I believe I may safely speak for all literary critics when I disavow any responsibility for this misunderstanding, which might have been prevented had someone thought to ask us.

    • I apologies if I have inadvertently caused offence in calling Gopnik a literature critic but he has fulfilled this function for the New Yorker as well as that of art critic and humourist. I will make suitable alterations to my text.

      • Michael Weiss

        I think the rambling essay is pretty much the New Yorker “house style”. Sometimes it works, sometimes it doesn’t.

  3. Sean Carroll’s book on general relativity identifies the separate treatment of orthogonal vectors as Galileo’s idea. Do you agree with that?


    • Michael Weiss

      Depends on how you view things. On the one hand, Jordanus de Nemore (13th C., exact dates unknown) was doing something that “in modern terms may be viewed” as decomposing a force vector into components (note scare-quotes; see Moody and Clagett, The Medieval Science of Weights). On the other hand, vector analysis in the modern sense came much later. Even talking about force in connection with Galileo calls for scare-quotes.

    • Michael Weiss is quite correct that one can find something that in modern terms could be viewed as decomposing a force vector in the works of Jordanus de Nemore. One can also find it much more clearly in the works of Simon Stevin predating similar efforts in the works of Galileo. Stevin even has very clearly what we now call the parallelogram of forces but all of this has to be prefaced with a very, very big but.

      None of these writers had anything approaching a clear concept of force or any concept of force, as we understand it, for that matter. The concept of force evolved very slowly in the 17th century with Kepler generally credited as being the first to even suggest such a thing. Even Newton actively avoids actually saying what force is and please don’t say force is mass times acceleration! That is how the force acting on a body is calculated it is not however a definition of force.

      The second important point is that none of these people is using vectors. That what they are doing came in the 19th century to be recognised with hindsight as a primitive form of vector analysis but at the time none of them had anything remotely resembling our vector concept.

      • Michael Weiss

        It’s curious that even today it’s unclear what force “really is”. Enough so that the Nobelist Frank Wilczek wrote three articles musing about it, “Whence the Force of F=ma?”, in Physics Today (2004-2005). He begins the first one:
        When I was a student, the subject that gave me the most trouble was classical mechanics. That always struck me as peculiar, because I had no trouble learning more advanced subjects, which were supposed to be harder. Now I think I’ve Figured it out. It was a case of culture shock. …
        Newton’s second law of motion, F = ma, is the soul of classical mechanics. Like other souls, it is insubstantial. The right−hand side is the product of two terms with profound meanings. … The left−hand side, on the other hand, has no independent meaning.

      • Thony C

        Ask any physicist ,”What is force?” and he will answer “F = Ma” without giving any thought to what he is actually saying.

      • Michael Weiss

        That’s probably a residue of positivism, which lead to an emphasis on operational definitions. Also of the success of this viewpoint with relativity and quantum mechanics. (The connection breaks down under closer scrutiny, but it certainly influenced both Einstein and Heisenberg.)

        I think your “any” is a bit of an exaggeration, as witness Wilczek’s essays. Maybe it’s true if you exclude Nobel prize-winners and mathematical physicists 😉

        Finally, perhaps you can help me with a related point. I know from Clagett that different Latin words were used by the Schoolmen where we would say ‘force’; I think he mentions ‘potentia’, ‘virtus’, ‘vis’, ‘fortitudo’, and perhaps also ‘inclinatio’, ‘impulsus’, and ‘impetus’. Alas, I have no Latin. Do you know if Kepler and Newton were more consistent in their terminology?

      • Michael Weiss


  4. Jeb

    History aside even from simply literary perspective, I could not read it. Epic editorial fail by the looks of things?

    An issue not unknown in the Academic world where error can be in a few notable cases more of a collective (more serious) editorial fail as much as individual error.

  5. Jeb

    “simply literary perspective”
    Oops. Sorry in advance Kai. I don’t actually think of history as being much different from English lit. sense was you would not have to be an expert in.. ….to note

  6. Personally, I love the way he fails to realise what went before. He notes of Galileo writing the following, in 1632:
    “Therefore, Simplicius, come either with arguments and demonstrations,” Salviati declares, in Thomas Salusbury’s fine Jacobean translation, in words that remain the slogan of science, “and bring us no more Texts and authorities, for our disputes are about the Sensible World, and not one of Paper.”

    Good old Francis Bacon had been saying that for years such as in the Parasceve of 1620:

    ‘In the first place, no more of antiquities, citations and differing opinions of authorities, or of squabbles and controversies, and, in short, everything philological […] In addition I demand that everything to do with natural phenomena, be they bodies or virtues, should (as far as possible) be set down, counted, weighed, measured and defined. For we are after work not speculations, and, indeed, a good marriage of Physics and Mathematices begets Practice.’

    Just thought I’d add that …

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