Category Archives: History of Astronomy

THE MATHEMATICAL IEVVEL

Due to the impact of Isaac Newton and the mathematicians grouped around him, people often have a false impression of the role that England played in the history of the mathematical sciences during the Early Modern Period. As I have noted in the past, during the late medieval period and on down into the seventeenth century, England in fact lagged seriously behind continental Europe in the development of the mathematical sciences both on an institutional level, principally universities, and in terms of individual mathematical practitioners outside of the universities. Leading mathematical practitioners, working in England in the early sixteenth century, such as Thomas Gemini (1510–1562) and Nicolas Kratzer (1486/7–1550) were in fact immigrants, from the Netherlands and Germany respectively.

In the second half of the century the demand for mathematical practitioners in the fields of astrology, astronomy, navigation, cartography, surveying, and matters military was continually growing and England began to produce some home grown talent and take the mathematical disciplines more seriously, although the two universities, Oxford and Cambridge still remained aloof relying on enthusiastic informal teachers, such as Thomas Allen (1542–1632) rather than instituting proper chairs for the study and teaching of mathematics.

Outside of the universities ardent fans of the mathematical disciplines began to establish the so-called English school of mathematics, writing books in English, giving tuition, creating instruments, and carrying out mathematical tasks. Leading this group were the Welsh man, Robert Recorde (c. 1512–1558), who I shall return to in a later post, John Dee (1527–c. 1608), who I have dealt with in several post in the past, one of which outlines the English School, other important early members being, Dee’s friend Leonard Digges, and his son Thomas Digges (c. 1446–1595), who both deserve posts of their own, and Thomas Hood (1556–1620) the first officially appointed lecturer for mathematics in England.  I shall return to give all these worthy gentlemen, and others, the attention they deserve but today I shall outline the life and mathematical career of John Blagrave (d. 1611) a member of the landed gentry, who gained a strong reputation as a mathematical practitioner and in particular as a designer of mathematical instruments, the antiquary Anthony à Wood (1632–1695), author of Athenae Oxonienses. An Exact History of All the Writers and Bishops, who Have Had Their Education in the … University of Oxford from the Year 1500 to the End of the Year 1690, described him as “the flower of mathematicians of his age.”

John Blagrave was the second son of another John Blagrave of Bullmarsh, a district of Reading, and his wife Anne, the daughter of Sir Anthony Hungerford of Down-Ampney, an English soldier, sheriff, and courtier during the reign of Henry VIII, John junior was born into wealth in the town of Reading in Berkshire probably sometime in the 1560s. He was educated at Reading School, an old established grammar school, before going up to St John’s College Oxford, where he apparently acquired his love of mathematics. This raises the question as to whether he was another student, who benefitted from the tutoring skills of Thomas Allen (1542–1632). He left the university without graduating, not unusually for the sons of aristocrats and the gentry. He settled down in Southcot Lodge in Reading, an estate that he had inherited from his father and devoted himself to his mathematical studies and the design of mathematical instruments. He also worked as a surveyor and was amongst the first to draw estate maps to scale.

Harpsden a small parish near Henley-on-Thames Survey by John Blagrave 1589 Source

There are five known surviving works by Blagrave and one map, as opposed to a survey, of which the earliest his, The mathematical ievvel, from1585, which lends its name to the title of this post, is the most famous. The full title of this work is really quite extraordinary:

 THE MATHEMATICAL IEVVEL 

Shewing the making, and most excellent vse of a singuler Instrument So called: in that it performeth with wonderfull dexteritie, whatsoever is to be done, either by Quadrant, Ship, Circle, Cylinder, Ring, Dyall, Horoscope, Astrolabe, Sphere, Globe, or any such like heretofore deuised: yea or by most Tables commonly extant: and that generally to all places from Pole to Pole. 

The vse of which Ievvel, is so aboundant and ample, that it leadeth any man practising thereon, the direct pathway (from the first steppe to the last) through the whole Artes of Astronomy, Cosmography, Geography, Topography, Nauigation, Longitudes of Regions, Dyalling, Sphericall triangles, Setting figures, and briefely of whatsoeuer concerneth the Globe or Sphere: with great and incredible speede, plainenesse, facillitie, and pleasure:

The most part newly founde out by the Author, Compiled and published for the furtherance, aswell of Gentlemen and others desirous or Speculariue knowledge, and priuate practise: as also for the furnishing of such worthy mindes, Nauigators,and traueylers,that pretend long voyages or new discoueries: By John Blagave of Reading Gentleman and well willer to the Mathematickes; Who hath cut all the prints or pictures of the whole worke with his owne hands. 1585•

Dig the spelling!
Title Page Source Note the title page illustration is an  armillary sphere and not the Mathematical Jewel

Blagrave’s Mathematical Jewel is in fact a universal astrolabe, and by no means the first but probably the most extensively described. The astrolabe is indeed a multifunctional instrument, al-Sufi (903–983) describes over a thousand different uses for it, and Chaucer (c. 1340s–1400) in what is considered to be the first English language description of the astrolabe and its function, a pamphlet written for a child, describes at least forty different functions. However, the normal astrolabe has one drawback, the flat plates, called tympans of climata, that sit in the mater and are engraved with the stereographic projection of a portion of the celestial sphere are limited in their use to a fairly narrow band of latitude, meaning that if one wishes to use it at a different latitude you need a different climata. Most astrolabes have a set of plates each engraved on both side for a different band of latitude. This problem led to the invention of the universal astrolabe.

Full-page figure of the rete of Blagrave’s Jewel (Peterborough A.8.13) For more illustration from The Mathematical Jewel go here

The earliest known universal astrolabes are attributed to Abū Isḥāq Ibrāhīm ibn Yaḥyā al-Naqqāsh al-Zarqālī al-Tujibi (1029-1100), known simply as al-Zarqālī and in Latin as Arzachel, an Arabic astronomer, astrologer, and instrument maker from Al-Andalus, and another contemporary Arabic astronomer, instrument maker from Al-Andalus, Alī ibn Khalaf: Abū al‐Ḥasan ibn Aḥmar al‐Ṣaydalānī or simply Alī ibn Khalaf, about whom very little is known. In the Biographical Encyclopedia of Astronomers (Springer Reference, 2007, pp. 34-35) Roser Puig has this to say about the two Andalusian instrument makers: 

ʿAlī ibn Khalaf is the author of a treatise on the use of the lámina universal (universal plate) preserved only in a Spanish translation included in the Libros del Saber de Astronomía (III, 11–132), compiled by the Spanish King Alfonso X. To our knowledge, the Arabic original is lost. ʿAlī ibn Khalaf is also credited with the construction of a universal instrument called al‐asṭurlāb al‐maʾmūnī in the year 1071, dedicated to al‐Maʾmūn, ruler of Toledo. 

The universal plate and the ṣafīḥa (the plate) of Zarqalī (devised in 1048) are the first “universal instruments” (i.e., for all latitudes) developed in Andalus. Both are based on the stereographic meridian projection of each hemisphere, superimposing the projection of a half of the celestial sphere from the vernal point (and turning it) on to the projection of the other half from the autumnal point. However, their specific characteristics make them different instruments.

Al-Zarqālī’s universal astrolabe was known as the Azafea in Arabic and as the Saphaea in Europe.

A copy of al-Zarqālī’s astrolabe Source: Wikimedia Commons

Much closer to Blagrave’s time, Gemma Frisius (1508–1555) wrote about a universal astrolabe, published as the Medici ac Mathematici de astrolabio catholico liber quo latissime patientis instrumenti multiplex usus explicatur, in 1556. Better known than Frisius’ universal instrument was that of his one-time Spanish, student Juan de Rojas y Samiento (fl. 1540-1550) published in his Commentariorum in Astrolabium libri sex in 1551.

 

Although he never really left his home town of Reading and his work was in English, Blagrave, like the other members of the English School of Mathematics, was well aware of the developments in continental Europe and he quotes the work of leading European mathematical practitioners in his Mathematical Jewel, such as the Tübingen professor of mathematics, Johannes Stöffler (1452–1531), who wrote a highly influential volume on the construction of astrolabes, his Elucidatio fabricae ususque astrolabii originally published in 1513, which went through 16 editions up to 1620

or the works of Gemma Frisius, who was possibly the most influential mathematical practitioner of the sixteenth century. Blagrave’s Mathematical Jewel was based on Gemma Frisius astrolabio catholico.

Blagrave’s Mathematical Jewel was obviously popular because Joseph Moxon (1627–1691), England first specialist mathematical publisher, cartographer, instrument, and globe maker republished it under the title:

The catholique planisphaer which Mr. Blagrave calleth the mathematical jewel briefly and plainly discribed in five books : the first shewing the making of the instrument, the rest shewing the manifold vse of it, 1. for representing several projections of the sphere, 2. for resolving all problemes of the sphere, astronomical, astrological, and geographical, 4. for making all sorts of dials both without doors and within upon any walls, cielings, or floores, be they never so irregular, where-so-ever the direct or reflected beams of the sun may come : all which are to be done by this instrument with wonderous ease and delight : a treatise very usefull for marriners and for all ingenious men who love the arts mathematical / by John Palmer … ; hereunto is added a brief description of the cros-staf and a catalogue of eclipses observed by the same I.P.

Engraved frontispiece to John Palmer (ed.), ‘The Catholique Planispaer, which Mr Blagrave calleth the Mathematical Jewel’ (London, Joseph Moxon, 1658); woman, wearing necklace, bracelet, jewels in her hair, and a veil, and seated at a table, on which are a design of a mathematical sphere, a compass, and an open book; top left, portrait of John Blagrave, wearing a ruff; top right, portrait of John Palmer; top centre, an angel with trumpets.
Engraving David Loggan Source: British Museum

John Palmer (1612-1679), who was apparently rector of Ecton and archdeacon of Northampton, is variously described as the author or the editor of the volume, which was first published in 1658 and went through sixteen editions up to 1973.

Following The Mathematical Jewel, Blagrave published four further books on scientific instruments that we know of: 

Baculum Familliare, Catholicon sive Generale. A Booke of the making and use of a Staffe, newly invented by the Author, called the Familiar Staffe (London, 1590)

Astrolabium uranicum generale, a necessary and pleasaunt solace and recreation for navigators … compyled by John Blagrave (London, 1596)

An apollogie confirmation explanation and addition to the Vranicall astrolabe (London, 1597)

None of these survive in large numbers.

Blagrave also manufactured sundials and his fourth instrument book is about this: 

The art of dyalling in two parts (London, 1609)

Source

Here there are considerably more surviving copies and even a modern reprint by Theatrum Orbis Terrarum Ltd., Da Capo Press, Amsterdam, New York, 1968.

People who don’t think about it tend to regard books on dialling, that is the mathematics of the construction and installation of sundials, as somehow odd. However, in this day and age, when almost everybody walks around with a mobile phone in their pocket with a highly accurate digital clock, we tend to forget that, for most of human history, time was not so instantly accessible. In the Early Modern period, mechanical clocks were few and far between and mostly unreliable. For time, people relied on sundials, which were common and widespread. From the invention of printing with movable type around 1450 up to about 1700, books on dialling constituted the largest genre of mathematical books printed and published. Designing and constructing sundials was a central part of the profession of mathematical practitioners. 

As well as the books there is one extant map:

Noua orbis terrarum descriptio opti[c]e proiecta secundu[m]q[ue] peritissimos Anglie geographos multis ni [sic] locis castigatissima et preceteris ipsiq[ue] globo nauigationi faciliter applcanda [sic] per Ioannem Blagrauum gen[er]osum Readingensem mathesibus beneuolentem Beniamin Wright Anglus Londinensis cµlator anno Domini 1596 

This is described as:

Two engraved maps, the first terrestrial, the second celestial (“Astrolabium uranicum generale …”). Evidently intended to illustrate Blagrave’s book “Astrolabium uranicum generale” but are not found in any copy of the latter.
The original is in the Bodleian Library.

When he died in 1611, Blagrave was buried in the St Laurence Church in Reading with a suitably mathematical monument. 

Blagrave is depicted surrounded by allegorical mathematical figures, with five women each holding the five platonic solids and Blagrave (in the center) depicted holding a globe and a quadrant.
The monument was the work of the sculptor Gerard Christmas (1576–1634), who later in life was appointed carver to the navy. It is not known who produced the drawing of the monument. 
Modern reconstruction of the armillary sphere from the cover of The Mathematical Jewel created by David Harber a descendent of John Blagrave

Blagrave was a minor, but not insignificant, participant in the mathematical community in England in the late sixteenth century. His work displays the typical Renaissance active interest in the practical mathematical disciplines, astronomy, navigation, surveying, and dialling. He seems to have enjoyed a good reputation and his Mathematical Jewel appears to have found a wide readership.  

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Filed under Early Scientific Publishing, History of Astronomy, History of Cartography, History of Mathematics, History of Navigation, Renaissance Science

Beinecke Library Redux: From Bad to Worse!

On Monday I wrote a quick blogpost on the not insubstantial errors in the description of one of Galileo’s lunar washes posted on the Beinecke Library blog. I was somewhat pleasantly surprised when within a day the description had been heavily edited, removing all the sections that I had criticised, even if no acknowledgement was made that changes had taken place or why.  In my elation over this turn of events I failed to properly read what now stood under Galileo’s image. One of my readers, Todd Timberlake author of Finding Our Place in the Solar System: The Scientific Story of the Solar System, was more observant than I and correctly stated that the modified version was now, if possible worse than the original. So, what had curator Richard Clemens done now?

Above: Detail, p. 18. Galileo, Siderevu nvncivs, QB41 G33 1610, copy 2. 

Left us examine what can only be described as a disaster, the text now reads:

Our mini-exhibits end with the vitrine holding several copies of Galileo’s first printed images of the moon made with the benefit of the telescope.  He shows the shadow the earth casts on the moon and the moon’s rocky surface. [my emphasis] A photograph at the back of the vitrine was taken in 1968, before humans landed on the moon. It shows Earth as seen from the moon—the first time we saw our own planet from another astronomical body. This rough black and white image eerily resembles Galileo’s lunar landscape.

The only time the Earth’s shadow is visible on the Moon is during a lunar eclipse when the Earth comes between the Sun and the Moon thus blocking off the Sun’s light. Galileo did not make drawings of any telescopic observations of the Moon during a lunar eclipse. What we actually have is an image of the Moon at third quarter put together by Galileo from his observations. The light side on the left is the half of the Moon that is visible at third quarter, the dark side on right is the half not visible. The jagged line down the middle is the so-called lunar terminator: the division between the illuminated and dark hemispheres of the Moon.

Photo of the Moon at third quarter Source:

Without being snarky, I think that Mr Clemens would do well to consult somebody who knows what they are talking about before writing his descriptions.

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Filed under History of Astronomy, Myths of Science

Not with a bang but a whimper

Ethan Siegel is an astrophysicist, but he is better known as a highly successful science populariser, who even has his own Wikipedia page.  He first rose to fame as the author of the blog Starts With a Bang, which he launched in 2008. He expanded his brand, with the publication of popular books on physics. He expanded still further, making podcasts and writing posts under his brand name on MediumForbes, and Big Think. He is today one of the biggest names on the Internet in popularisation of physics. Here I’m going to look at his latest publication on Big ThinkBig Think is a multiplatform, multimedia Internet organisation who in their own words state: 

Our mission is to make you smater, faster.  At Big Think, we introduce you to the brightest minds and boldest ideas of our time, inviting viewers to explore new ways to work, live, and understand our ever-changing world. 

“Big Think challenges common sense assumptions and gives people permission to think in new ways.”

I’m sorry, but to my ears that sounds like those windy ads on the Internet that say, “Take our three-week course of our seminars once a week and you will be earning $100,000 a month within a year!”

So, what is the post of Dr Siegel on Big Think that has attracted the attention of The Renaissance Mathematicus and why? Our intrepid astrophysicist and physics populariser has decided to try his hand at history of science and has written a post about Johannes Kepler, Why Johannes Kepler is a scientist’s best role model. After all our author is a scientist and a successful science populariser, who has even won prestigious awards for his work, what could possibly go wrong, when he tries a bit of history of science? Unfortunately, as with other scientists and science populariser, who think they can do history of science, without investing serious time and effort in the discipline, almost everything.

Johannes Kepler unknown artist 1620

So why does Siegel think that the good Johannes should be every scientist’s role model? He tells us in his lede:

  • The annals of history are filled with scientists who had incredible, revolutionary ideas, sought out and found the evidence to support them, and initiated a scientific revolution. 
  • But much rarer is someone who has a brilliant idea, discovers that the evidence doesn’t quite fit, and instead of doggedly pursuing it, tosses it aside in favor of a newer, better, more successful idea. 
  • That’s exactly what separates Johannes Kepler from all of the other great scientists throughout history, and why, if we have to choose a scientific role model, we should admire him so thoroughly.

He then delivers four examples of famous scientists, who could not admit they were wrong:

  • Albert Einstein could never accept quantum indeterminism as a fundamental property of nature.
  • Arthur Eddington could never accept quantum degeneracy as a source for holding white dwarfs up against gravitational collapse.
  • Newton could never accept the experiments that demonstrated the wave nature of light, including interference and diffraction.
  • And Fred Hoyle could never accept the Big Bang as the correct story of our cosmic origins, even nearly 40 years after the critical evidence, in the form of the Cosmic Microwave Background, was discovered.

I already have a couple of comments here. Niels Bohr is on record as saying that Einstein through his intelligent, astute, and penetrating criticisms of quantum theory that demanded answers contributed more to the development of that theory than almost anybody else. Not least Bell’s theorem, one of the key developments in quantum theory, was based on his analysis of the Einstein–Podolsky–Rosen paradox. Opposition to theories based on knowledge are important to the evolution of those theories. 

Newton did in fact reject a wave theory of light in favour of a particle theory. However, he was able with his theory to explain all the known optical phenomenon. Moreover, when Hooke rejected his theory of colour saying that it wouldn’t work in a wave theory, Newton developed a wave theory, that was more advanced than those of Hooke and Huygens, to show that his theory of colour did work in a wave theory. Lastly, as I love to point out, Einstein won the Nobel Prize for physics, not for relativity, but for demonstrating that light consists of particles, so Newton wasn’t so wrong after all.   

More generally, there is a famous quote from Max Planck about the development of new theories in science:

A new scientific truth does not generally triumph by persuading its opponents and getting them to admit their errors, but rather by its opponents gradually dying out and giving way to a new generation that is raised on it.

He then goes on to tell us why Kepler was a spectacular exception. First, we get a popular rundown of the observable phenomena of the cosmos and why that led to a geocentric model. On the whole OK but littered with small errors. For example, he tells us:

The Earth was big, and its diameter had been measured precisely [my emphasis] by Eratosthenes in the 3rd century B.C.E.

This is, unfortunately, typical of Siegel’s hyperbolic style. Depending on which value for the stadium one takes, Eratosthenes’ estimate of the size of the earth was relatively close to the real value but by no means precise. Also, in antiquity no one knew how correct it was and most people actually accepted other values.

We then get a description of the deferent/epicycle model for the planets and Siegel tells us that Ptolemy made the best, most successful model of the Solar system that incorporated epicycles. Nothing to criticise here but there follows immediately a small misstep, he writes:

Going all the way back to ancient times, there was some evidence — from Archimedes and Aristarchus, among others — that a Sun-centered model for planetary motion was considered. 

First off you really shouldn’t use an expression like “ancient times.” We know that both Archimedes and Aristarchus lived and worked in the third century BCE, so we can say that. The expression “there was some evidence from Archimedes and Aristarchus, among others” is a load of waffle, which doesn’t actually tell the reader anything. According to a couple of secondary sources Aristarchus of Samos devised a heliocentric system. We don’t have anything about it from Aristarchus himself. Archimedes is one of the secondary sources but not in a work on astronomy or cosmology. Archimedes wrote a work on calculating and expressing large numbers, The Sand Reckoner, in which he calculated the number of grains of sand needed to fill the cosmos. He used Aristarchus’ heliocentric model, which he only mentions in passing, because the heliocentric cosmos is considered to be larger the than the geocentric one.

Siegel now moves onto Copernicus and once again delivers up historical rubbish:

Copernicus was frustrated to discover that his model gave less successful predictions when compared against Ptolemy’s. The only way Copernicus could devise to equal Ptolemy’s successes, in fact, relied on employing the same ad hoc fix: by adding epicycles, or small circles, atop his planetary orbits!

As stated, this is rubbish. From the very beginning Copernicus used deferent/epicycle models for the planetary orbits. He didn’t add epicycles as an ad hoc solution because his model gave less successful predictions when compared against Ptolemy’s. In fact, Copernicus didn’t produce any planetary tables before he died in the year that his De revolutionibus was published, so he couldn’t know about the comparative predictive powers of his and Ptolemy’s system. When Erasmus Reinhold (1511–1553) did produce his Prutenic Tables (1551), the first ones based on Copernicus’ model, it turned out that in some cases the predictions were better than in tables based on Ptolemy and in some cases worse. This was because Copernicus used the same, in the meantime corrupted through frequent copying, basic data for his models as Ptolemy. This problem was recognised by Tycho Brahe, which is why he set up his massive astronomical observation programme, on the island of Hven, in order to provide new basic data. It is to Tycho that Siegel now turns.

Tycho Brahe, for example, constructed the best naked eye astronomy setup in history, measuring the planets as precisely as human vision allows: to within one arc-minute (1/60th of a degree) during every night that planets were visible towards the end of the 1500s. His assistant, Johannes Kepler, attempted to make a glorious, beautiful model that fit the data precisely.

This is Siegel’s introduction to Kepler’s Mysterium Cosmographicum published in 1596, four years before he even met Tycho and began to work with him! Siegel now gives a brief description of the model presented in the Mysterium Cosmographicumand follows it up with a pile of absolute garbage.

Maybe our astrophysicist author has slipped into a parallel universe because what he presents here is hyperbollocks, an assorted collection of made-up “facts” thrown together in a narrative that bears absolutely no relation to what really happened in history. As a Kepler fan when I read this and the following paragraphs eight days ago, I began banging my head against the wall and haven’t stopped since. No pain can blot out the stupidity presented here. 

Kepler formulated this model in the 1590s, and Brahe boasted that only his observations could put such a model to the test. But no matter how Kepler did his calculations, not only did disagreements with observation remain, but Ptolemy’s geocentric model still made superior predictions.

Tycho made no such boast, that is simply made up and in fact he was not in any way interested in Kepler’s model. Kepler wanted to work with Tycho to get access to his data to fine tune his model, Tycho wanted to employ Kepler to do the mathematics necessary to turn his data into models for the planets orbits in his own geo-heliocentric model. When Kepler arrived in Prague, Tycho refused him access to the data he wanted out of fear of being plagiarised. Instead, he set Kepler to write a paper proving that Ursus had plagiarised him. The resulting essay is brilliant, was however first published in the nineteenth century, and has been described by Cambridge historian of science, Nicholas Jardine as The Birth of History and Philosophy of Science (CUP, 2nd rev. ed. 1988). Following this he was given the task of determining the orbit of Mars using Tycho’s data, to which I will return in a minute. 

At this point in his life Kepler made no attempt to improve his geometrical model. The phrase, Ptolemy’s geocentric model still made superior predictions is quite simple mind boggling for anybody who knows what they are talking about. The geometric model that Kepler presents in his Mysterium Cosmographicum is his answer to the question, why are there exactly six planets? Kepler argues that his completely rational God, who is a geometer, designed his cosmos rationally and geometrically and there are exactly six planets because there are only five regular Platonic solids to fill the spaces between them. Not our idea of rational but Kepler was mighty pleased with his “discovery.” This model makes no predictions of any kind!

Now we get to the crux of Siegel’s whole argument, Kepler admitting he was wrong:

In the face of this, what do you think Kepler did?

  • Did he tweak his model, attempting to save it?
  • Did he distrust the critical observations, demanding new, superior ones?
  • Did he make additional postulates that could explain what was truly occurring, even if it was unseen, in the context of his model?

No. Kepler did none of these. Instead, he did something revolutionary: he put his own ideas and his own favored model aside, and looked at the data to see if there was a better explanation that could be derived from demanding that any model needed to agree with the full suite of observational data.

Kepler didn’t tweak his model, at this time, attempting to save it, he certainly didn’t mistrust Tycho’s data, and he didn’t at this time add any postulates. He did put his model aside but not to look at the data to see if there was a better explanation that could be derived from demanding that any model needed to agree with the full suite of observational data. He was too busy doing other thing, things that served other purposes. 

If only we could all be so brave, so brilliant, and at the same time, so humble before the Universe itself! Kepler calculated that ellipses, not circles, would better fit the data that Brahe had so painstakingly acquired. Although it defied his intuition, his common sense, and even his personal preferences for how he felt the Universe ought to have behaved — indeed, he thought that the Mysterium Cosmographicum was a divine epiphany that had revealed God’s geometrical plan for the Universe to him — Kepler was successfully able to abandon his notion of “circles and spheres” and instead used what seemed to him to be an imperfect solution: ellipses.

Here without explicitly naming it, Siegel is referencing Kepler’s work on the orbit of Mars that he published in his Astronomia Nova in 1609. It was during the many years of his “War with Mars”, his own description, that he finally discovered his first two laws of planetary motion: 1: Planetary orbits are ellipses with the Sun at one focus of the ellipse 2: A line from the Sun to the planet sweeps out equal areas in equal periods of time. For a good description of the route to the Astronomia Nova, I recommend James R. Voelkel’s excellent The Composition of Kepler’s Astronomia nova (Princeton University Press, 2001). 

Siegel apparently thinks that this refutes Kepler’s Mysterium Cosmographicum, it doesn’t. The Mysterium Cosmographicum doesn’t deal with the shape of orbits at all. His model has the Platonic solids filling the spaces between the spheres. In the Ptolemaic deferent/epicycle system the orbits are not simple circle because of the epicycle. Ptolemy in his Planetary Hypothesis embedded the deferent/epicycle in a sphere but the book that got lost and was only rediscovered in the 1960s in a single Arabic copy. However, Peuerbach (1423–1461) revived this model in his Theoricae Novae Planetarum (written in 1454, published by Regiomontanus in 1472), which is almost certainly based on a now lost copy of the Planetary Hypothesis, with illustrations. 

Peuerbach’s illustration of a sphere containing a deferent/epicycle Source: Wikimedia Commons

Copernicus’ heliocentric system, which also uses the deferent/epicycle models would suffer from the same problem and it is between these spheres that Kepler places his Platonic solids, irrespective of the orbit inside the sphere. The system would work equally well for elliptical orbits, so Kepler’s discovery of them had no effect on his Mysterium Cosmographicum

Siegel gives a table of Tycho’s Mars observations with the following caption:

Tycho Brahe conducted some of the best observations of Mars prior to the invention of the telescope, and Kepler’s work largely leveraged that data. Here, Brahe’s observations of Mars’s orbit, particularly during retrograde episodes, provided an exquisite confirmation of Kepler’s elliptical orbit theory. [my emphasis]

Kepler used Tycho’s Mars data to derive his first two laws, so they can’t be used by him as confirmation. In fact, at the beginning he didn’t actual confirm his theory, simple assuming it applied to all the planets. It wasn’t until his Epitome Astronomiae Copernicanae published in three volumes from 1618 to 1621, after he had discovered his third law and done a substantial amount of the work reducing Tycho’s observational data to planetary tables, the Rudolphine Tables published in 1627 and on which he had begun to work as Tycho was still alive, that he demonstrated all three laws for all the known planets.

I will now return to that third law and the Harmonice mundi (1619) in which it first appeared. Kepler had already suggested the possibility of fine tuning the Mysterium Cosmographicum model with the Pythagorean concept of a harmony of the spheres and this is what his magnus opus Harmonice mundi was. He had already conceived it in the late 1590s but because of other commitments didn’t actually get round to writing it until the second decade of the seventeenth century. 

Having created his harmony of the spheres, in 1621 Kepler published an expanded second edition of Mysterium Cosmographicum, half as long again as the first, detailing in footnotes the corrections and improvements he had achieved in the 25 years since its first publication, so far from abandoning his first theory to produce his elliptical orbits as Seigel claims, Kepler spent his whole life working to improve it.

What is truly bizarre is that Siegel appears to be aware of this fact. He writes:

It cannot be emphasized enough what an achievement this is for science. Yes, there are many reasons to be critical of Kepler. He continued to promote his Mysterium Cosmographicum even though it was clear ellipses fit the data better. He continued to mix astronomy with astrology, becoming the most famous astrologer of his time.

As already explained in detail, he didn’t just promote his Mysterium Cosmographicum, he worked very hard for many years to improve it. The statement, becoming the most famous astrologer of his time is another example of hyperbollocks. Kepler was a well-known astrologer in Southern Germany and Austria but the most famous astrologer of his time I hardly think so. I would also note that the modern astro-scientists disdain for astrology, as displayed here by Seigel, displays their ignorance of the history of their own discipline. Astrology was the driving force behind the developments in astronomy for its first three thousand years of its existence. 

Siegel, like many scientists, who think they can write history of science without doing the detailed research, has taken a set of half facts, embroidered them with stuff that he simply made up and created a nice fairy tale that has very little to do with real history of science. A fairy tale that will be swallowed by his large fan base, who will believe it and make life difficult for real historians of science. 

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I expect better of you Beinecke

The Beinecke Rare Book & Manuscript Library is the rare book library and literary archive of the Yale University Library. Yesterday their Twitter account posted a tweet entitled GalileoSiderius Nunc, which linked to a blog post from July 11, 2022, by Raymond Clemens, Curator, Early Books & Manuscripts. 

It featured one of Galileo’s famous washes of the Moon from his Sidereus Nuncius (1610) followed by a short text.

Above: Detail, p. 18. Galileo, Siderevu nvncivs, QB41 G33 1610, copy 2. 

Our mini-exhibits end with the vitrine holding several copies of Galileo’s first printed images of the moon, the first ever made with the benefit of the telescope. For the first time, most Europeans were shown the dark side of the moon. Galileo’s sketches also emphasize its barren and rocky nature—well known to us today, but something of a revelation in the sixteenth century, when most people thought of the moon as another planet, thus generating its own light. Galileo was the first person to accurately depict the moons of Jupiter (which he called “Medicean stars,” after his patron, the Florentine Medici family). A photograph at the back of the vitrine was taken in 1968, before humans landed on the moon. It shows Earth as seen from the moon—the first time we saw our own planet from another astronomical body. This rough black and white image eerily resembles Galileo’s lunar landscape.

It is a mere 152 words long, not much room for errors, one might think, but one would be wrong.

We start with the heading. The title of Galileo’s book is Sidereus Nuncius and there one really shouldn’t shorten Nuncius to Nunc, as this actually changes the meaning from message or messenger to now! Also, it is Sidereus not Siderius!

Addendum: A reader on Twitter, more observant than I, has pointed out, correctly, that 1609 and 1610 are in the seventeenth century and not the sixteenth century as stated by Clemens.

In the first line Clemens writes: Galileo’s first printed images of the moon, the first ever made with the benefit of the telescope. I shall be generous and assume that with this ambiguous phrase he means first ever printed images made with the benefit of the telescope. If, however, he meant first ever images made with the benefit of the telescope, then he would be wrong as that honour goes Thomas Harriot.

The real hammer comes in the next sentence, where he writes:

For the first time, most Europeans were shown the dark side of the moon.

The first time I read this, I did a double take, could a curator of the Beinecke really have written something that mind bogglingly stupid? By definition the dark side of the moon is the side of the moon that can never be seen from the earth. The first images of it were made, not by Galileo in 1609, after all how could he, but by the Soviet Luna 3 space probe in 1959, 350 years later. 

The problems don’t end here, he writes:

Galileo’s sketches also emphasize its barren and rocky nature—well known to us today, but something of a revelation in the sixteenth century, when most people thought of the moon as another planet, thus generating its own light.

In the geocentric system the moon was indeed regarded as one of the seven planets, but in the heliocentric system, which Galileo promoted, it had become a satellite of the earth and was no longer considered a planet. There was a long and complicated discussion throughout the history of astronomy as to whether the planets generated their own light or not. However, within Western astronomy there was a fairy clear consensus that the moon reflected sunlight rather than generating its own light. A brief sketch of the history of this knowledge starts with Anaxagoras (d. 428 BCE). The great Islamic polymath Ibn al-Haytham (965–1039) clearly promoted that the moon reflected sunlight. In the century before Galileo, Leonardo (1452–1519) in his moon studies clearly stated that the moon was illuminated by reflected sunlight. However, he never published. 

Maybe, Clemens is confusing this with the first recognition of the true cause of earth shine, the faint light reflected from the earth that makes the whole moon visible during the first crescent, a recognition that is often falsely attributed to Galileo. However, here the laurels go to Leonardo but who, as always, didn’t publish. The first published correct account was made by Michael Mästlin (1550–1631)

 Clemens’ next statement appears to me to be simply bizarre:

Galileo was the first person to accurately depict the moons of Jupiter (which he called “Medicean stars,” after his patron, the Florentine Medici family).

Galileo was the first to discover the moons of Jupiter, just one day ahead of Simon Marius, but to state that he accurately depicted them is somewhat more than an exaggeration. For Galileo and Marius, the moons of Jupiter were small points of light in the sky, the positions of which they recorded as ink dots on a piece of paper. To call this accurate depiction is a joke.

Somehow, I expect a higher standard of public information from the Beinecke Library, one of the world’s leading rare book depositories. 

Addendum 18:30 CEST: The post on the Beinecke blog that this post refers to has now been heavily edited. Everything I criticised has been either removed or corrected but without acknowledgement anywhere!

Renaissance Mathematicus 1 Beinecke Library 0!

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Vision, Seeing Better, Seeing Further

In the normal blog post rotation, a book review should be due today. However, instead today’s post is a literature review, listing and describing books on the histories of the theories of vision, spectacles, and telescopes, with the latter coming first as they are the actual main theme of the review. I announced my intention to do this is response to a regular readers request, so long ago I’ve forgotten when, and I was recently reminded of that announcement when someone on Twitter asked me if one of the history of the telescope books, which I own is any good; it is as I will explain later.

The classical standard text on the early history of the telescope is Albert van Helden’s The Invention of the Telescope, which was first published as a paper in the Transactions of the American Philosophical Society in 1977 but has long been available as a monograph, the second edition appearing in 2008 to celebrate the 400thanniversary of the invention of the telescope. 

Van Helden presents and analyses all of the early literature related to the emergence of the telescope in the first decade of the seventeenth century, as well as earlier descriptions of instruments similar to the telescope that proceeded it His text contains full quotes from the original literature in their source languages followed by English translations. It is justifiably called a classic and is a must read for anybody seriously studying the history of the telescope.

Van Helden’s text includes the historical references to Zacharias Janssen (1585–before 1632), as one of the candidates for the invention of the telescope. In 2008, there was a big conference in Middelburg, in the Netherlands, where the telescope first emerged, to celebrate that 400th anniversary; I was there! In the conference proceedings, The origins of the telescope (edited by Albert van Helden, Sven Dupré, Rob van Gent, Huib Zuidervaart, and published by KNAW Press, Amsterdam, 2010) there is a paper by Huib J. Zuidervaart, The ‘true inventor’ of the telescopeA survey of 400 years of debatewhich clearly shows that Zacharias Janssen was not an inventor of the telescope.

The entire proceedings contain an amazing collection of papers on all possible aspects of the history of the telescope by an all star cast of the world’s best historians of optics. It is available as a printed book but is also available as an open access e-book online.

The two books I’ve described so far only really deal with the origins of the telescope; we now turn our attention to books that delve further into the history of the telescope. A classic that is substantially older than van Helden’s The Invention of the Telescope is Henry King’s The History of the Telescope, which was originally published by Charles Griffin & Co. Ltd. In 1955 and then republished by Dover in 1979. 

It opens with a short chapter on the beginning of astronomical observation that is followed by an even shorter chapter on the history of lenses and optics that ends with Lipperhey and his invention of the refracting telescope, with the rival claims of Metius and Jansen. There follows chapter for chapter a chronological history of telescopes and their user and uses beginning with Galileo and ending around 1950 with the construction of the Jodrell Bank radio telescope. Despite the fact that it is dated, it is well researched and well written and can still be read with profit.

More up to date is Fred Watson’s Stargazer the life and times of the Telescope (Da Capo Press, 2005).

As with King, Watson opens with the pre-telescopic era and the various reports of things that might have been telescope but probably weren’t prior to 1608 and Lipperhey.

He then takes his reader on an episodic journey through the history of the telescope down to the present day, ending with plans and discussion of a new generation of super telescopes. A well-researched and well written book, which I found a pleasure to read and highly informative. 

I managed an absolute classic in Middelburg in 2008. I got into a conversation with another participant at the conference and during the exchange started to talk about something from Watson’s book blithely unaware that my conversation partner was the man himself! Mildly embarrassing but also somewhat amusing.

For those readers, who are interested but don’t want to plough their way through a dense academic tome on the history of the telescope but would prefer something more digestible, I heartily recommend Richard Dunn’s The Telescope: A Short History (National Maritime Museum, 2009, Conway, 2011).

Dunn was then curator at the National Maritime Museum in Greenwich, which has its own excellent collection of telescopes, and is now Keeper of Technologies and Engineering at the Science Museum. The chapters of his book are more topic orientated rather than purely chronological. Beautifully illustrated, it is a comparatively light introduction to the history of the telescope, as I said ideal for those interested but not necessarily prepared to take a deep dive into the subject. This was the book I got asked about recently on Twitter. 

Of a somewhat different nature is Marvin Bolt’s Telescopes Though the Looking Glass (Adler Planetarium, 2009).

This is actually a catalogue of an exhibition that Bolt curated at the Adler upon his return from the 2008 conference in Middelburg. I will quote Bolt’s brief description of the exhibition in full because it captures the general concept of all of the history of the telescope texts:

The exhibition and catalogue address four themed zones. The first, the pretelescope zone, addresses ways in which people have looked at the sky and tried to make sense of it, using their surrounding landscapes or relatively simple tools to develop an understanding or model of the Universe. Zone two presents the invention of the telescope, the challenges it brought to the Earth-centered Universe, and the beautiful craftsmanship and ornamentation of some of the earliest surviving examples in the world. In zone three, the technical challenges of improving telescopes led to variations in design and materials; the telescopes also became popular devices with brand-name recognition. Zone four displays the culmination of the refracting telescope and the emergence of spectroscopy, leading to the marvels of modern telescopes: some see wavelengths beyond the optical realm, others detect invisible particles, a few compensate for atmospheric turbulence, while still others travel beyond the Earth’s atmosphere into space.

Each exhibit is illustrated with a description on the facing page. If you can find a copy, it’s a great introduction to the history of the telescope. 

The ‘if you can find a copy’, illustrates a major problem with this bibliography. Because they only have a limited appeal and target readership, many of the books I am describing are out of print and you have to hunt around to find second-hand copies. Several of mine were bought second-hand.

Galileo, of course, gets a whole telescope bibliography to himself. I’ll start with Eileen Reeves’ excellent Galileo’s Glassworks (Harvard University Press, 2008).

There was a significant gap between Galileo first hearing about the new invention from the Netherlands and the manufacture of his own first telescope. In her book Reeves argues convincingly that Galileo at first thought that the new instrument was somehow based on mirrors and spent substantial time and effort trying to work out how. Reeves backs this up with a detailed account of the history of (magical) mirrors that allowed their owners to see great distances.

The book also contains much information on the critical period before and during the early period of telescope manufacture. A fascinating, thoroughly researched, and beautifully book.

Galileo’s TelescopesA European Story (Harvard University Press, 2015) by Massimo Bucciantini, Michele Camerota, and Franco Giudice and translated by Catherine Bolton describes in great detail the spread of the influence of Galileo’s publications on his telescopic discoveries and the distribution of the instruments that he manufactured throughout Europe and the influence that he exercised thereby.

An important contribution to the literature on the early telescope and its influence, well researched and excellently presented.

The same phenomenon, Galileo’s telescopes and their influence, is treated from a different angle by Mario Biagioli in his Galileo’s Instruments of CreditTelescopes, Images, Secrecy (University of Chicago Press, 2007).

This can be read alone but is much better read as a sequel, which it was, to Biagioli’s Galileo CourtierThe Practice of Science in The Culture of Absolutism (University of Chicago Press, 1993). 

In the earlier book Biagioli basically presents Galileo as a social climber, who uses his scientific career to win status within the political climate of Northern and Middle Italy at the beginning of the seventeenth century. Hustling for status and favour, Biagioli argues, I think correctly, that Galileo’s downfall was largely a product of the mechanisms of absolutist politics. Having raised Galileo up as a favourite at his papal court, Maffeo Barberini, Pope Urban VIII, then cast him down as a demonstration of his absolute power during a period of political crisis. This treatment of court favourites was quite common in absolutist regimes throughout Europe.

In his second volume, Biagioli shows how Galileo, having become the telescope man throughout Europe, through the publication of his Sidereus Nuncius in 1610, manufactured telescopes together with his instrument maker, who usually gets left out of the story, and distributed them as favours throughout Europe.

However, he did not give them to other mathematicians and astronomers, who could have used them to confirm Galileo’s discoveries or made new ones of their own, but to powerful figures within the Catholic Church and political potentates, in order to raise his own social status. In his defence it should be pointed out Galileo was not alone in doing this. It was common practice for Renaissance mathematici to design and manufacture high class scientific instruments as gifts for potential aristocratic patrons.

Both of Biagioli’s books are excellent and highly recommended for anybody interested in Galileo, his telescopes, his telescopic discoveries, and his use of them within a socio-politic context rather than a scientific one.

Having looked briefly at the social, political, and cultural contexts of the telescope and Galileo’s use of the instrument and his discoveries, it should be obvious that the advent of the telescope and its impact was not just scientific. Two further books by Eileen Reeves investigate the impact of the new culture of visual awareness in two non-scientific areas.

Her Painting the HeavensArt and Science in the Age of Galileo (Princeton University Press, 1997) explores the impact that the new telescopic astronomical discoveries had on the work of a group of leading contemporary artists.

Her Evening NewsOptics, Astronomy, and Journalism in Early Modern Europe(University of Pennsylvania Press, 2014).

The weekly newssheets began to emerge in Early Modern Europe almost simultaneously with the invention of the telescope and the publication of Galileo’s Sidereus Nuncius. To quote the publishers blurb:

Early modern news writers and consumers often understood journalistic texts in terms of recent developments in optics and astronomy, Reeves demonstrates, even as many of the first discussions of telescopic phenomena such as planetary satellites, lunar craters, sunspots, and comets were conditioned by accounts of current events. She charts how the deployment of particular technologies of vision—the telescope and the camera obscura—were adapted to comply with evolving notions of objectivity, censorship, and civic awareness. Detailing the differences between various types of printed and manuscript news and the importance of regional, national, and religious distinctions, Evening News emphasizes the ways in which information moved between high and low genres and across geographical and confessional boundaries in the first decades of the seventeenth century.

Changing direction, the man who is credited with being the first to publicly present a working telescope Hans Lipperhey (c. 1570–1619) in Middelburg in 1608, was a professional spectacle maker. This is in no way surprising as spectacle makers were the artisans, who worked with lenses. This means if one wants to understand the invention of the telescope, one must also take a look at the history of spectacles. Above all one needs to answer the questions, how did spectacle come to be invented and given that spectacles first emerged in the late thirteenth century, why did it take more than two hundred years before somebody invented the telescope? 

There are two books that answer these questions in great detail of which the first is Rolf Willach’s magisterial Long Route to the Invention of the TelescopeA Life of Influence and Exile (American Philosophical Society, 2008), like van Helden’s The Invention of the Telescope, published in English both as a journal article in the society’s transactions and as a separate monograph.

It also appears in English in the volume The origins of the telescope described above. His essay was originally published in German in Der Meister und die FernrohreDas Wechselspiel zwischen Astronomie und Optik in der GeschichteFestschrift zum 85. Geburtstag von Rolf Riekher[1] herausgeben von Jürgen Hamel und Inge Keil, Acta Historica Astronomia Vol. 33, Verlag Harri Deutsch, 2007. 

For those of my readers who can read German this volume contains a large collection of excellent papers on the history of the telescope. A couple of them are even in English.

The number of different publications of Willach’s essay signify its ground-breaking status in the histories of spectacles and telescopes. Based on his very extensive empirical investigations he hypothesises that the invention of spectacles was made by monks working in medieval cloisters, cutting and polishing gemstones to decorate reliquaries, the containers for holy relics. At the other end of the two hundred years, he showed that the clue to constructing a successful telescope lay in stopping down the eyepiece lens with a mask. This is because early lenses were inaccurately ground, and the outer edges of the lens distorted the image. By masking off the outer edges, the image became comparatively sharp and usable. 

Equally impressive is Vincent Ilardi’s Renaissance Vision from Spectacles to Telescopes (Memoires of the American Philosophical Society, Band 259, 2007).

This is the definitive account of the Early Modern history of spectacles. Ilardi was a diplomatic historian, who studied a vast convolute of trade documents and correspondence in order to reconstruct the history of spectacles in the first two centuries of their existence. I have read this book twice but do not own a copy as it is prohibitively expensive, thank God for libraries. Iladi should have held a lecture in Middelburg in September 2008 but he was already dying of prostate cancer, which deprived the world of his excellence in January 2009. 

The histories of spectacles and telescopes are, of course, just integral parts of the much wider history of optics. Optics was originally the theory of vision, how do we see? How do our eyes perceive the world around us bringing information of everything within our field of vision into our brain for processing. 

The absolute classic, which outlines the various theories developed from the ancient Greeks down to Johannes Kepler at the beginning of the seventeenth century and the advent of the telescope is David C. Lindberg’s Theories of Vision from Al-Kindi to Kepler (University of Chicago Press, 1976).

Popular wisdom claims that the ancient Greeks believed that we see with a fire that the eyes emit to touch and illuminate the objects seen. This is in simplistic form the extramission theory of vision of Plato. Lindberg explains that this was only one of several extramission and intromission (rays entering the eyes) theories of vision held by different individuals and schools of philosophy in ancient Greece. He also presents the geometric opticians–Euclid, Ptolemaeus, Heron–who propagated a mathematical extramission theory. 

Moving on he shows how these theories were assimilated by Islamic scholars and how al-Kindi supported a Euclidian extramission theory but also developed his punctiform theory of reflection, which states that light is reflected from every point on an object in every direction. Enter al-Haytham, who produced a synthesis of an intromission theory, geometrical optics, and al-Kindi’s punctiform theory of reflection, which when translated into Latin in the thirteenth century became the so-called perspectivist theory, which led the field in Europe right down to Kepler. Lindberg sees Kepler as the last of the perspectivists. The book is a historical tour de force. If you are really interested, Lindberg has a long list of excellent academic papers investigating individual topics in medieval optics.

Even an absolute classic can be surpassed, and this has happened to Lindberg’s masterpiece. A. Mark Smith was a doctoral student of Lindberg’s and followed in his master’s footsteps becoming a brilliant historian of optics. His synthesis is From Sight to Light (University of Chicago Press, 2015).

His narrative follows that of Lindberg, but in greater detail and including many figure that Lindberg did not feature. The biggest difference come at the end, unlike Lindberg, he does not consider Kepler the last of the perspectivists but rather the first of a new direction in the optics. He argues his case very convincingly and I think he in probably correct.

If I were to recommend just one of the two, then it would have to be Smith and that despite the fact that the Lindberg was one of those turning point books in my own development. Of course, I think you should read both of them! Smith, like his mentor, has a very long list of papers and book on optics, all of which are recommended reading.

Both Lindberg and Smith stop at the beginning of the seventeenth century, although Smith has a short capital at the end sketching the further developments during the century. If you want to follow the story further then I recommend Oliver Darrigol’s A History of OpticsFrom Greek Antiquity to the Nineteenth Century (OUP, 2012).

Darrigol deals with the passage from the Greeks to Kepler in the first thirty-six pages of his books and devotes the rest to developing the story from there down to the end of the nineteenth century with Stoke, Poincare et al. 

As I noted above when talking about Galileo and his telescopic discoveries, the new possibilities revealed by the new instruments and the new theories of optics went well beyond the boundaries of science touching on other areas such as culture, politics and society. They literally changed people’s perceptions of the world in which they lived. I will briefly mention three books which deal with this, a by no means exhaustive list. 

The first one that I read was Svetlana Alpers’ The Art of DescribingDutch Art in the Seventeenth Century(University of Chicago Press, 1984).

As we have already seen with Eileen Revees’ Painting the HeavensArt and Science in the Age ofGalileo art visually reflected the new developments in optics. To quote a review of Alpers’ book: 

“The art historian after Erwin Panofsky and Ernst Gombrich is not only participating in an activity of great intellectual excitement; he is raising and exploring issues which lie very much at the centre of psychology, of the sciences and of history itself. Svetlana Alpers’s study of 17th-century Dutch painting is a splendid example of this excitement and of the centrality of art history among current disciples. Professor Alpers puts forward a vividly argued thesis. There is, she says, a truly fundamental dichotomy between the art of the Italian Renaissance and that of the Dutch masters. . . . Italian art is the primary expression of a ‘textual culture,’ this is to say of a culture which seeks emblematic, allegorical or philosophical meanings in a serious painting. Alberti, Vasari and the many other theoreticians of the Italian Renaissance teach us to ‘read’ a painting, and to read it in depth so as to elicit and construe its several levels of signification. The world of Dutch art, by the contrast, arises from and enacts a truly ‘visual culture.’ It serves and energises a system of values in which meaning is not ‘read’ but ‘seen,’ in which new knowledge is visually recorded.”—George Steiner, Sunday Times

My second book is Stuart Clark’s Vanities of the EyeVision in Early Modern European Culture (OUP, 2007).

Once again to quote the back cover blurb:

Vanities of the Eye investigates the cultural history of the senses in early modern Europe, a time in which the nature and reliability of human vision was the focus of much debate. In medicine, art theory, science, religion, and philosophy, sight came to be characterized as uncertain or paradoxical-mental images no longer resembled the external world. Was seeing really believing? Stuart Clark explores the controversial debates of the time-from the fantasies and hallucinations of melancholia, to the illusions of magic, art, demonic deceptions, and witchcraft. The truth and function of religious images and the authenticity of miracles and visions were also questioned with new vigor, affecting such contemporary works as Macbeth- a play deeply concerned with the dangers of visual illusion. Clark also contends that there was a close connection between these debates and the ways in which philosophers such as Descartes and Hobbes developed new theories on the relationship between the real and virtual. Original, highly accessible, and a major contribution to our understanding of European culture, Vanities of the Eye will be of great interest to a wide range of historians and anyone interested in the true nature of seeing.

The Last of my three is Laura J Snyder’s Eye of the BeholderJohannes Vermeer, Antoni van Leeuwenhoek, and the Reinvention of Seeing (W. W. Norton, 2015):

Once again resorting to publisher’s blurb:

By the early 17th century the Scientific Revolution was well under way. Philosophers and scientists were throwing off the yoke of ancient authority to peer at nature and the cosmos through microscopes and telescopes. 

In October 1632, in the small town of Delft in the Dutch Republic, two geniuses were born who would bring about a seismic shift in the idea of what it meant to see the world. One was Johannes Vermeer, whose experiments with lenses and a camera obscura taught him how we see under different conditions of light and helped him create the most luminous works of art ever beheld. The other was Antoni van Leeuwenhoek, whose work with microscopes revealed a previously unimagined realm of minuscule creatures. 

By intertwining the biographies of these two men, Laura Snyder tells the story of a historical moment in both art and science that revolutionized how we see the world today.

I’m going to close this overlong literature review with two books that I don’t think you’ll be able to get hold of, but you might get lucky. Peter Louwman is a rich Dutchman, who has a very impressive automobile museum in De Haag. The museum also houses a massive historical collection of telescopes and binoculars.

For the 400th anniversary conference in Middelburg Louwman produced a wonderful annotated edition of the French newsletter reporting on the visit of the Ambassador of Siam to Den Haag in September 1608, which contains a description of Lipperhey’s demonstration of his telescope to the assembled delegates of the peace conference taking place there.

This special edition contains an explanatory introduction, a facsimile of the newsletter,

a French transcription, and an English as well as a Dutch translation.

First every report of a public demonstration of a telescope pp. 9-11

Every participant in the conference received a copy and I think it’s the best goody that I’ve every received at a conference. I think for a time it was on sale in the museum shop but that no longer appears to be the case.

Another Louwman publication is a wonderful catalogue of the Louwman Collection of Historic Telescopes, A Certain Instrument for Seeing Far by P.J.K. Louwman and H. J. Zuidervaart (2013), which definitely used to be sold by the museum, because I bought one, but no longer seems to be available.

One of hundreds of beautiful illustration in the book

I’m not trying to impress my readers with all the books that I’ve read on the history of optics and the telescopic but trying to make clear that if you truly want to understand that history, the road that led up to the invention of the telescope, its impact as a scientific instrument, and its impact outside of the direct field of science then you have to extend your scope and dig deep. 


[1] Rolf Riekher was a leading German optician and historian of optics, who bought me a cup of tea and a piece of cake on a sunny afternoon in Middelburg in 2008.

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History of science is global history

The simple statement that the history of science is global history is for me and, I assume, for every reasonably well-informed historian of science a rather trivial truism. So, I feel that James Poskett and the publishers Viking are presenting something of a strawman with the sensational claims for Poskett’s new book, HorizonsA Global History of Science[1]; claims that are made prominently by a series of pop science celebrities on the cover of the book. 

“Hugely Important,” Jim al-Khalili, really? 

“Revolutionary and revelatory,” Alice Roberts what’s so revolutionary about it?  

“This treasure trove of a book puts the case persuasively and compellingly that modern science did not develop solely in Europe,” Jim al-Khalili, I don’t know any sane historian of science, who would claim it did.

“Horizons is a remarkable book that challenges almost everything we know about science in the West. [Poskett brings to light an extraordinary array of material to change our thinking on virtually every great scientific breakthrough in the last 500 years… An explosive book that truly broadens our global scientific horizons, past and present.”] Jerry Brotton (The bit in square brackets is on the publisher’s website not on the book cover) I find this particularly fascinating as Brotton’s own The RenaissanceA Very Short Introduction (OUP, 2006) very much emphasises what is purportedly the main thesis of Horizons that science, in Brotton’s case the Renaissance, is not a purely Western or European phenomenon.

On June 22, Canadian historian Ted McCormick tweeted the following:

It’s not unusual for popular history to present as radical what has been scholarly consensus for a generation. If this bridges the gap between scholarship and public perception, then it is understandable. But what happens when the authors who do this are scholars who know better?

This is exactly what we have with Poskett’s book, he attempts to present in a popular format the actually stand amongst historian of science on the development of science over the last approximately five hundred years. I know Viking are only trying to drum up sales for the book, but I personally find it wrong that they use misleading hyperbole to do so. 

Having complained about the publisher’s pitch, let’s take a look at what Poskett is actually trying to sell to his readers and how he goes about doing so. Central to his message is that claims that science is a European invention/discovery[2] are false and that it is actually a global phenomenon. To back up his stand that such claims exist he reproduces a series of rather dated quotes making that claim. I would contend that very, very few historians of science actually believe that claim nowadays. He also proposes, what he sees as a new approach to the history of science of the last five hundred years, in that he divides the period into four epochs or eras, in which he sees science external factors during each era as the defining or driving force behind the scientific development in that era. Each is split into two central themes: Part One: Scientific Revolution, c. 1450–1700 1. New Worlds 2. Heaven and Earth, Part Two: Empire and Enlightenment, c. 1650–1800 3. Newton’s Slaves 4. Economy of Nature, Part Three:  Capitalism and Conflict, c. 1790–­1914 5. Struggle for Existence 6. Industrial Experiments, Part Four: Ideology and Aftermath, c. 1914–200 7. Faster Than Light 8. Genetic States.

I must sadly report that Part One, the area in which I claim a modicum of knowledge, is as appears recently oft to be the case strewn with factual errors and misleading statements and would have benefited from some basic fact checking.

New Worlds starts with a description of the palace of Emperor Moctezuma II and presents right away the first misleading claim. Poskett write:

Each morning he would take a walk around the royal botanical garden. Roses and vanilla flowers lined the paths, whilst hundreds of Aztec gardeners tended to rows of medicinal plants. Built in 1467, this Aztec botanical garden predated European examples by almost a century.[3]

Here Poskett is taking the university botanical gardens as his measure, the first of which was establish in Pisa in 1544, that is 77 years after Moctezuma’s Garden. However, there were herbal gardens, on which the university botanical gardens were modelled, in the European monasteries dating back to at least the ninth century. Matthaeus Silvaticus (c.1280–c. 1342) created a botanical garden at Salerno in 1334. Pope Nicholas V established a botanical garden in the Vatican in 1544. 

This is not as trivial as it might a first appear, as Poskett uses the discovery of South America to make a much bigger claim. First, he sets up a cardboard cut out image of the medieval university in the fifteenth century, he writes:

Surprisingly as it may sound today, the idea of making observations or preforming experiments was largely unknown to medieval thinkers. Instead, students at medieval universities in Europe spent their time reading, reciting, and discussing the works of Greek and Roman authors. This was a tradition known as scholasticism. Commonly read texts included Aristotle’s Physics, written in the fourth century BCE, and Pliny the Elder’s Natural History, written in the first century CE. The same approach was common to medicine. Studying medicine at medieval university in Europe involved almost no contact with actual human bodies. There was certainly no dissections or experiments on the working of particular organs. Instead, medieval medical students read and recited the works of the ancient Greek physician Galen. Why, then, sometime between 1500 and 1700, did European scholars turn away from investigating the natural world for themselves?[4]

His answer:

The answer has a lot to do with colonization of the New World alongside the accompanying appropriation of Aztec and Aztec and Inca knowledge, something that traditional histories of science fail to account for.[5]

Addressing European, medieval, medical education first, the practical turn to dissection began in the fourteenth century and by 1400 public dissections were part of the curriculum of nearly all European universities. The introduction of a practical materia medica education on a practical basis began towards the end of the fifteenth century. Both of these practical changes to an empirical approach to teaching medicine at the medieval university well before any possible influence from the New World. In general, the turn to empiricism in the European Renaissance took place before any such influence, which is not to say that that process was not accelerated by the discovery of a whole New World not covered by the authors of antiquity. However, it was not triggered by it, as Poskett would have us believe. 

Poskett’s next example to bolster his thesis is quite frankly bizarre. He tells the story of José de Acosta (c. 1539–1600), the Jesuit missionary who travelled and worked in South America and published his account of what he experienced, Natural and Moral History of the Indies in 1590. Poskett tells us: 

The young priest was anxious about the journey, not least because of what ancient authorities said about the equator. According to Aristotle, the world was divided into three climatic zones. The north and south poles were characterized by extreme cold and known as the ‘frigid zone’. Around the equator was the ‘torrid zone’, a region of burning dry heat. Finally, between the two extremes, at around the same latitudes as Europe, was the ‘temperate zone’. Crucially, Aristotle argued that life, particularly human life, could only be sustained in the ‘temperate zone’. Everywhere else was either too hot nor too cold.

Poskett pp. 17-18

Poskett goes on to quote Acosta:

I must confess I laughed and jeered at Aristotle’s meteorological theories and his philosophy, seeing that in the very place where, according to his rules, everything must be burning and on fire, I and all my companions were cold.

Poskett p. 18

Instead of commenting on Acosta’s ignorance or naivety, Aristotle’s myth of the ‘torrid zone’ had been busted decades earlier, at the very latest when Bartolomeu Dias (c. 1450–1500) had rounded the southern tip of Africa fifty-two years before Acosta was born and eight-two year before he travelled to Peru, Poskett sees this as some sort of great anti-Aristotelian revelation. He writes:

This was certainly a blow to classical authority. If Aristotle had been mistaken about the climate zones, what else might he have been wrong about?

Poskett p.18

This is all part of Poskett’s fake narrative that the breakdown of the scholastic system was first provoked by the contact with the new world. We have Poskett making this claim directly:

It was this commercial attitude towards the New World that really transformed the study of natural history. Merchants and doctors tended to place much greater emphasis on collecting and experimentation over classical authority.[6]

This transformation had begun in Europe well before any scholar set foot in the New World and was well established before any reports on the natural history of the New World had become known in Europe. The discovery of the New World accelerated the process but it in no way initiated it as Poskett would have his readers believe. Poskett once again paints a totally misleading picture a few pages on:

This new approach to natural history was also reflected in the increasing use of images. Whereas ancient texts on natural history tended not to be illustrated, the new natural histories of the sixteenth and seventeenth centuries were full of drawings and engravings, many of which were hand-coloured. This was partly a reaction to the novelty of what had been discovered. How else would those in Europe know what a vanilla plant or a hummingbird looked like?

Poskett pp.29-30

Firstly, both ancient and medieval natural history texts were illustrated, I refer Mr Proskett, for example, to the lavishly illustrated Vienna Dioscorides from 512 CE. Secondly, the introduction of heavily illustrated, printed herbals began in the sixteenth century before any illustrated natural history books or manuscripts from the New World had arrived in Europe. For example, Otto Brunfels’ Herbarium vivae eicones three volumes 1530-1536 or the second edition of Hieronymus Bock’s Neu Kreütterbuch in 1546 and finally the truly lavishly illustrated De Historia Stirpium Commentarii by Leonhard Fuchs published in 1542. The later inclusion of illustrations plants and animals from the New World in such books was the continuation of an already established tradition. 

Poskett moves on from natural history to cartography and produced what I can only call a train wreck. He tells us:

The basic problem, which was now more pressing [following the discovery of the New World], stemmed from the fact that the world is round, but a map is flat. What then was the best way to represent a three-dimensional space on a two-dimensional plane? Ptolemy had used what is known as a ‘conic’ projection, in which the world is divided into arcs radiating out from the north pole, rather like a fan. This worked well for depicting one hemisphere, but not both. It also made it difficult for navigators to follow compass bearings, as the lines spread outwards the further one got from the north pole. In the sixteenth century, European cartographers started experimenting with new projections. In 1569, the Flemish cartographer Gerardus Mercator produced an influential map he titled ‘New and More Complete Representation of the Terrestrial Globe Properly Adapted for Use in Navigation’. Mercator effectively stretched the earth at the poles and shrunk it in the middle. This allowed him to produce a map of the world in which the lines of latitude are always at right angles to one another. This was particularly useful for sailors, as it allowed them to follow compass bearings as straight lines.

Poskett p. 39

Where to begin? First off, the discovery of the New World is almost contemporaneous with the development of the printed terrestrial globe, Waldseemüller 1507 and more significantly Johannes Schöner 1515. So, it became fairly common in the sixteenth century to represent the three-dimensional world three-dimensionally as a globe. In fact, Mercator, the only Early Modern cartographer mentioned here, was in his time the premium globe maker in Europe. Secondly, in the fifteenth and sixteenth centuries mariners did not even attempt to use a Ptolemaic projection on the marine charts, instead they used portulan charts–which first emerged in the Mediterranean in the fourteenth century–to navigate in the Atlantic, and which used an equiangular or plane chart projection that ignores the curvature of the earth. Thirdly between the re-emergence of Ptolemy’s Geographia in 1406 and Mercator’s world map of 1569, Johannes Werner published Johannes Stabius’ cordiform projection in 1514, which can be used to depict two hemispheres and in fact Mercator used a pair of cordiform maps to do just that in his world map from 1538. In 1508, Francesco Rosselli published his oval projection, which can be used to display two hemispheres and was used by Abraham Ortelius for his world map from 1564. Fourthly, stereographic projection, known at least since the second century CE and used in astrolabes, can be used in pairs to depict two hemispheres, as was demonstrated by Mercator’s son Rumold in his version of his father’s world map in 1587. Fifthly, the Mercator projection if based on the equator, as it normally is, does not shrink the earth in the middle. Lastly, far from being influential, Mercator’s ‘New and More Complete Representation of the Terrestrial Globe Properly Adapted for Use in Navigation’, even in the improved version of Edward Wright from 1599 had very little influence on practical navigation in the first century after it first was published. 

After this abuse of the history of cartography Poskett introduces something, which is actually very interesting. He describes how the Spanish crown went about creating a map of their newly won territories in the New World. The authorities sent out questionnaires to each province asking the local governors or mayors to describe their province. Poskett notes quite correctly that a lot of the information gathered by this method came from the indigenous population. However, he once again displays his ignorance of the history of European cartography. He writes:

A questionnaire might seem like an obvious way to collect geographical information, but in the sixteenth century this idea was entirely novel. It represented a new way of doing geography, one that – like science more generally in this period – relied less and less on ancient Greek and Roman authority.

Poskett p. 41

It would appear that Poskett has never heard of Sebastian Münster and his Cosmographia, published in 1544, probably the biggest selling book of the sixteenth century. An atlas of the entire world it was compiled by Münster from the contributions from over one hundred scholars from all over Europe, who provided maps and texts on various topics for inclusion in what was effectively an encyclopaedia. Münster, who was not a political authority did not send out a questionnaire but appealed for contributions both in publications and with personal letters. Whilst not exactly the same, the methodology is very similar to that used later in 1577 by the Spanish authorities. 

In his conclusion to the section on the New World Poskett repeats his misleading summation of the development of science in the sixteenth century:

Prior to the sixteenth century, European scholars relied almost exclusively on ancient Greek and Roman authorities. For natural history they read Pliny for geography they read Ptolemy. However, following the colonization of the Americas, a new generation of thinkers started to place a greater emphasis on experience as the main source of scientific knowledge. They conducted experiments, collected specimens, and organised geographical surveys. This might seem an obvious way to do science to us today, but at the time it was a revelation. This new emphasis on experience was in part a response to the fact that the Americas were completely unknown to the ancients.

Poskett p. 44

Poskett’s claim simply ignores the fact that the turn to empirical science had already begun in the latter part of the fifteenth century and by the time Europeans began to investigate the Americas was well established, those investigators carrying the new methods with them rather than developing them in situ. 

Following on from the New World, Poskett takes us into the age of Renaissance astronomy serving up a well worn and well know story of non-European contributions to the Early Modern history of the discipline which has been well represented in basic texts for decades. Nothing ‘revolutionary and revelatory’ here, to quote Alice Roberts. However, despite the fact that everything he in presenting in this section is well documented he still manages to include some errors. To start with he attributes all of the mechanics of Ptolemy’s geocentric astronomy–deferent, eccentric, epicycle, equant–to Ptolemy, whereas in fact they were largely developed by other astronomers–Hipparchus, Apollonius–and merely taken over by Ptolemy.  

Next up we get the so-called twelfth century “scientific Renaissance” dealt with in one paragraph. Poskett tells us the Gerard of Cremona translated Ptolemy from Arabic into Latin in 1175, completely ignoring the fact that it was translated from Greek into Latin in Sicily at around the same time. This is a lead into the Humanist Renaissance, which Poskett presents with the totally outdated thesis that it was the result of the fall of Constantinople, which he rather confusingly calls Istanbul, in 1453, evoking images of Christians fleeing across the Adriatic with armfuls of books; the Humanist Renaissance had been in full swing for about a century by that point. 

Following the introduction of Georg of Trebizond and his translation of the Almagest from Greek, not the first as already noted above as Poskett seems to imply, up next is a very mangled account of the connections between Bessarion, Regiomontanus, and Peuerbach and Bessarion’s request that Peuerbach produce a new translation of the Almagest from the Greek because of the deficiencies in Trebizond’s translation. Poskett completely misses the fact that Peuerbach couldn’t read Greek and the Epitome, the Peuerbach-Regiomontanus Almagest, started as a compendium of his extensive knowledge of the existing Latin translations. Poskett then sends Regiomontanus off the Italy for ten years collecting manuscripts to improve his translation. In fact, Regiomontanus only spent four years in Italy in the service of Bessarion collecting manuscripts for Bessarion’s library, whilst also making copies for himself, and learning Greek to finish the Epitome.

Poskett correctly points out that the Epitome was an improved, modernised version of the Almagest drawing on Greek, Latin and Arabic sources. Poskett now claims that Regiomontanus introduced an innovation borrowed from the Islamic astronomer, Ali Qushji, that deferent and epicycles could be replaced by the eccentric. Poskett supports this argument by the fact that Regiomontanus uses Ali Qushji diagram to illustrate this possibility. The argument is not original to Poskett but is taken from the work of historian of astronomy, F. Jamil Ragip. Like Ragip, Poskett now argues thus:

In short, Ali Qushji argued that the motion of all the planets could be modelled simply by imagining that the centre of their orbits was at a point other than the Earth. Neither he nor Regiomontanus went as far as to suggest this point might in fact be the Sun. By dispensing with Ptolemy’s notion of the epicycle, Ali Qushji opened the door for a much more radical version of the structure of the cosmos.[7]

This is Ragip theory of what motivated Copernicus to adopt a heliocentric model of the cosmos. The question of Copernicus’s motivation remains open and there are numerous theories. This theory, as presented, however, has several problems. That the planetary models can be presented either with the deferent-epicycle model or the eccentric model goes back to Apollonius and is actually included in the Almagest by Ptolemy as Apollonius’ theorem (Almagest, Book XII, first two paragraphs), so this is neither an innovation from Ali Qushji nor from Regiomontanus. In Copernicus’ work the Sun is not actually at the centre of the planetary orbits but slightly offset, as has been pointed out his system is not actually heliocentric but more accurately heliostatic. Lastly, Copernicus in his heliostatic system continues to use the deferent-epicycle model to describe planetary orbits.

Poskett is presenting Ragip’s disputed theory to bolster his presentation of Copernicus’ dependency on Arabic sources, somewhat unnecessary as no historian of astronomy would dispute that dependency. Poskett continues along this line, when introducing Copernicus and De revolutionibus. After a highly inaccurate half paragraph biography of Copernicus–for example he has the good Nicolaus appointed canon of Frombork Cathedral after he had finished his studies in Italy, whereas he was actually appointed before he began his studies, he introduces us to De revolutionibus. He emphasis the wide range of international sources on which the book is based, and then presents Ragip’s high speculative hypothesis, for which there is very little supporting evidence, as fact:

Copernicus suggested that all these problems could be solved if we imagined the Sun was at the centre of the universe. In making this move he was directly inspired by the Epitome of the Almagest. Regiomontanus, drawing on Ali Qushji, had shown it was possible to imagine that the centre of all the orbits of the planets was somewhere other than the Earth. Copernicus took the final step, arguing that that this point was in fact the Sun.[8]

We simply do not know what inspired Copernicus to adopt a heliocentric model and to present a speculative hypothesis, one of a number, as the factual answer to this problem in a popular book is in my opinion irresponsible and not something a historian should be doing. 

Poskett now follows on with the next misleading statement. Having, a couple of pages earlier, introduced the Persian astronomer Nasir al-Din al-Tusi and the so-called Tusi couple, a mathematical device that allows linear motion to be reproduced geometrically with circles, Poskett now turns to Copernicus’ use of the Tusi couple. He writes:

The diagram in On the Revolution of the Heavenly Spheres shows the Tusi couple in action. Copernicus used this idea to solve exactly the same problem as al-Tusi. He wanted a way to generate an oscillating circular movement without sacrificing a commitment to uniform circular motion. He used the Tusi couple to model planetary motion around the Sun rather than the Earth. This mathematical tool, invented in thirteenth-century Persia, found its way into the most important work in the history of European astronomy. Without it, Copernicus would not have been able to place the Sun at the centre of the universe.[9] [my emphasis]

As my alter-ego the HISTSCI_HULK would say the emphasised sentence is pure and utter bullshit!

The bizarre claims continue, Poskett writes:

The publication of On the Revolution of the Heavenly Spheres in 1543 has long been considered the starting point for the scientific revolution. However, what is less often recognised is that Nicolaus Copernicus was in fact building on a much longer Islamic tradition.[10]

When I first read the second sentence here, I had a truly WTF! moment. There was a time in the past when it was claimed that the Islamic astronomers merely conserved ancient Greek astronomy, adding nothing new to it before passing it on to the Europeans in the High Middle Ages. However, this myth was exploded long ago. All the general histories of astronomy, the histories of Early Modern and Renaissance astronomy, and the histories of Copernicus, his De revolutionibus and its reception that I have on my bookshelf emphasise quite clearly and in detail the influence that Islamic astronomy had on the development of astronomy in Europe in the Middle Ages, the Renaissance, and the Early Modern period. Either Poskett is ignorant of the true facts, which I don’t believe, or he is presenting a false picture to support his own incorrect thesis.

Having botched European Renaissance astronomy, Poskett turns his attention to the Ottoman Empire and the Istanbul observatory of Taqi al-Din with a couple of pages that are OK, but he does indulge in a bit of hype when talking about al-Din’s use of a clock in an observatory, whilst quietly ignoring Jost Bürgi’s far more advanced clocks used in the observatories of Wilhelm IV of Hessen-Kassel and Tycho Brahe contemporaneously. 

This is followed by a brief section on astronomy in North Africa in the same period, which is basically an extension of Islamic astronomy with a bit of local colouration. Travelling around the globe we land in China and, of course, the Jesuits. Nothing really to complain about here but Poskett does allow himself another clangour on the subject of calendar reform. Having correctly discussed the Chinese obsession with calendar reform and the Jesuit missionaries’ involvement in it in the seventeenth century Poskett add an aside about the Gregorian Calendar reform in Europe. He writes:

The problem was not unique to China. In 1582, Pope Gregory XIII had asked the Jesuits to help reform the Christian Calendar back in Europe. As both leading astronomers and Catholic servants, the Jesuits proved an ideal group to undertake such a task. Christoph Clavius, Ricci’s tutor at the Roman College [Ricci had featured prominently in the section on the Jesuits in China], led the reforms. He integrated the latest mathematical methods alongside data taken from Copernicus’s astronomical tables. The result was the Gregorian calendar, still in use today throughout many parts of the world.[11]

I have no idea what source Poskett used for this brief account, but he has managed to get almost everything wrong that one can get wrong. The process of calendar reform didn’t start in 1582, that’s the year in which the finished calendar reform was announced in the papal bull Inter gravissimas. The whole process had begun many years before when the Vatican issued two appeals for suggestion on how to reform the Julian calendar which was now ten days out of sync with the solar year. Eventually, the suggestion of the physician Luigi Lilio was adopted for consideration and a committee was set up to do just that. We don’t actually know how long the committee deliberated but it was at least ten years. We also don’t know, who sat in that committee over those years; we only know the nine members who signed the final report. Clavius was not the leader of the reform, in fact he was the least important member of the committee, the leader being naturally a cardinal. You can read all of the details in this earlier blog post. At the time there were not a lot of Jesuit astronomers, that development came later and data from Copernicus’ astronomical tables were not used for the reform. Just for those who don’t want to read my blog post, Clavius only became associated with the reform after the fact, when he was commissioned by the pope to defend it against its numerous detractors.  I do feel that a bit of fact checking might prevent Poskett and Viking from filling the world with false information about what is after all a major historical event. 

The section Heaven and Earth closes with an account of Jai Singh’s observatories in India in the eighteenth century, the spectacular instruments of the Jantar Mantar observatory in Jaipur still stand today. 

Readers of this review need not worry that I’m going to go on at such length about the other three quarters of Poskett’s book. I’m not for two reasons. Firstly, he appears to be on territory where he knows his way around better than in the Early Modern period, which was dealt with in the first quarter Secondly, my knowledge of the periods and sciences he now deals with are severely limited so I might not necessarily have seen any errors. 

There are however a couple more train wrecks before we reach the end and the biggest one of all comes at the beginning of the second quarter in the section titled Newton’s Slaves. I’ll start with a series of partial quote, then analyse them:

(a) Where did Newton get this idea [theory of gravity] from? Contrary to popular belief, Newton did not make his great discovery after an apple fell on his head. Instead in a key passage in the Principia, Newton cited the experiments of a French astronomer named Jean Richer. In 1672, Richer had travelled to the French colony of Cayenne in South America. The voyage was sponsored by King Louis XIV through the Royal Academy of Science in Paris.

[…]

(b) Once in Cayenne, Richer made a series of astronomical observations, focusing on the movements of the planets and cataloguing stars close to the equator.

[…]

(c) Whilst in Cayenne, Richer also undertook a number of experiments with a pendulum clock.

[…]

(d) In particular, a pendulum with a length of just one metre makes a complete swing, left to right, every second. This became known as a ‘seconds pendulum’…

[…]

(e) In Cayenne, Richer noticed that his carefully calibrated pendulum was running slow, taking longer than a second to complete each swing.

[…]

(f) [On a second voyage] Richer found that, on both Gorée and Guadeloupe, he needed to shorten the pendulum by about four millimetres to keep it running on time.

[…]

(g) What could explain this variation?

[…]

(h) Newton, however, quickly realised the implications the implications of what Richer had observed. Writing in the Principia, Newton argued that the force of gravity varied across the surface of the planet. 

[…]

(i) This was a radical suggestion, one which seemed to go against common sense. But Newton did the calculations and showed how his equations for the gravitational force matched exactly Richer’s results from Cayenne and Gorée. Gravity really was weaker nearer the equator.

[…]

(j) All this implied a second, even more controversial, conclusion. If gravity was variable, then the Earth could not be a perfect sphere. Instead, Newton argued, the Earth must be a ‘spheroid’, flattened at the poles rather like a pumpkin. 

[…]

(k) Today, it is easy to see the Principia as a scientific masterpiece, the validity of which nobody could deny. But at the time, Newton’s ideas were incredibly controversial.

[…]

(l) Many preferred the mechanical philosophy of the French mathematician René Descartes. Writing in his Principles of Philosophy (1644), Descartes denied the possibility of any kind of invisible force like gravity, instead arguing that force was only transferred through direct contact. Descartes also suggested that, according to his own theory of matter, the Earth should be stretched the other way, elongated like an egg rather than squashed like a pumpkin.

[…]

(m) These differences were not simply a case of national rivalry or scientific ignorance. When Newton published the Principia in 1687, his theories were in fact incomplete. Two major problems remained to be solved. First, there were the aforementioned conflicting reports of the shape of the Earth. And if Newton was wrong about the shape of the Earth, then he was wrong about gravity.[12]

To begin at the beginning: (a) The suggestion or implication that Newton got the idea of the theory of gravity from Richer’s second pendulum experiments is quite simply grotesque. The concept of a force holding the solar system together and propelling the planets in their orbits evolved throughout the seventeenth century beginning with Kepler. The inverse square law of gravity was first hypothesised by Ismaël Boulliau, although he didn’t believe it existed. Newton made his first attempt to show that the force causing an object to fall to the Earth, an apple for example, and the force that held the Moon in its orbit and prevented it shooting off at a tangent as the law of inertia required, before Richer even went to Cayenne.

(c)–(g) It is probable that Richer didn’t make the discovery of the difference in length between a second pendulum in Northern Europe and the equatorial region, this had already ben observed earlier. What he did was to carry out systematic experiments to determine the size of the difference.

(l) Descartes did not suggest, according to his own theory of matter, that the Earth was an elongated spheroid. In fact, using Descartes theories Huygens arrived at the same shape for the Earth as Newton. This suggestion was first made by Jean-Dominique Cassini and his son Jacques long after Descartes death. Their reasoning was based on the difference in the length of one degree of latitude as measured by Willebrord Snel in The Netherlands in 1615 and by Jean Picard in France in 1670. 

This is all a prelude for the main train wreck, which I will now elucidate. In the middle of the eighteenth century, to solve the dispute on the shape of the Earth, Huygens & Newton vs the Cassinis, the French Academy of Science organised two expeditions, one to Lapland and one to Peru in order to determine as accurately as possible the length of one degree of latitude at each location. Re-enter Poskett, who almost completely ignoring the Lapland expedition, now gives his account of the French expedition to Peru. He tells us:

The basic technique for conducting a survey [triangulation] of this kind had been pioneered in France in the seventeenth century. To begin the team needed to construct what was known as a ‘baseline’. This was a perfectly straight trench, only a few inches deep, but at least a couple of miles long.[13]

Triangulation was not first pioneered in France in the seventeenth century. First described in print in the sixteenth century by Gemma Frisius, it was pioneered in the sixteenth century by Mercator when he surveyed the Duchy of Lorraine, and also used by Tycho Brahe to map his island of Hven. To determine the length of one degree of latitude it was pioneered, as already stated, by Willebrord Snell. However, although wrong this is not what most disturbed me about this quote. One of my major interests is the history of triangulation and its use in surveying the Earth and determining its shape and I have never come across any reference to digging a trench to lay out a baseline. Clearing the undergrowth and levelling the surface, yes, but a trench? Uncertain, I consulted the book that Poskett references for this section of his book, Larrie D Ferreiro’s Measure of the EarthThe Enlightenment Expedition that Reshaped the World (Basic Books, 2011), which I have on my bookshelf. Mr Ferreiro make no mention of a baseline trench. Still uncertain and not wishing to do Poskett wrong I consulter Professor Matthew Edney, a leading expert on the history of surveying by triangulation, his answer:

This is the first I’ve heard of digging a trench for a baseline. It makes little sense. The key is to have a flat surface (flat within the tolerance dictated by the quality of the instruments being used, which wasn’t great before 1770). Natural forces (erosion) and human forces (road building) can construct a sufficiently level surface; digging a trench would only increase irregularities.[14]

The problems don’t end here, Poskett writes:

La Condamine did not build the baseline himself. The backbreaking work of digging a seven-mile trench was left to the local Peruvian Indians.[15]

This is contradicted by Ferreiro who write:

Just as the three men completed the alignment for the baseline, the rest of the expedition arrived on the scene, in time for the most difficult phase of the operation. In order to create a baseline, an absolutely straight path, seven miles long and just eighteen inches wide, had to be dug into, ripped up from, and scraped out of the landscape. For the scientists, who had been accustomed to a largely sedentary life back in Europe, this would involve eight days of back breaking labour and struggling for breath in the rarefied air. “We worked at felling trees,” Bouguer explained in his letter to Bignon, “breaking through walls and filling in ravines to align [a baseline] of more than two leagues.” They employed several Indians to help transport equipment, though Bouguer felt it necessary that someone “keep an eye on them.”[16]

Poskett includes this whole story of the Peruvian Indians not digging a non-existent baseline trench because he wants to draw a parallel between the baseline and the Nazca Lines, a group of geoglyphs made in the soil of the Nazca desert in southern Peru that were created between 500 BCE and 500 CE. He writes:

The Peruvian Indians who built the baseline must have believed that La Condamine wanted to construct his own ritual line much like the earlier Inca rulers.[17]

Also:

Intriguingly some are simply long straight lines. They carry on for miles, dead straight, crossing hills and valleys. Whilst their exact function is still unclear, many historians now believe they were used to align astronomical observations, exactly as La Condamine intended with his baseline.[18]

The Nazca lines are of course pre-Inca. The ‘many historians’ is a bit of a giveaway, which historians? Who? Even if the straight Nazca lines are astronomically aligned, they by no means serve the same function as La Condamine’s triangulation baseline, which is terrestrial not celestial.  

To be fair to Poskett, without turning the baseline into a trench and without having the Indians dig it, Ferreiro draws the same parallel but without the astronomical component: 

For their part, the Indians were also observing the scientists, but to them “all was confusion” regarding the scientists’ motives for this arduous work. The long straight baseline the had scratched out of the ground certainly resembled the sacred linear pathways that Peruvian cultures since long before the Incas, had been constructing.[19]

Poskett’s conclusion to this section, in my opinion, contains a piece of pure bullshit.

By January 1742, the results were in. La Condamine calculated that the distance between Quito and Cuenca was exactly 344,856 metres. From observations made of the stars at both ends of the survey, La Condamine also found that the difference in latitude between Quit and Cuenca was a little over three degrees. Dividing the two, La Condamine concluded that the length of a degree of latitude at the equator was 110,613 metres. This was over 1,000 metres less than the result found by the Lapland expedition, which had recently returned to Paris. The French, unwittingly relying on Indigenous Andean science [my emphasis] had discovered the true shape of the Earth. It was an ‘oblate spheroid’, squashed at the poles and bulging at the equator. Newton was right.[20]

Sorry, but just because Poskett thinks that a triangulation survey baseline looks like an ancient, straight line, Peruvian geoglyph doesn’t in anyway make the French triangulation survey in anyway dependent on Indigenous Andean science. As I said, pure bullshit. 

The next section deals with the reliance of European navigators of interaction with indigenous navigators throughout the eighteenth century and is OK. This is followed by the history of eighteenth-century natural history outside of Europe and is also OK. 

At the beginning of the third quarter, we again run into a significant problem. The chapter Struggle for Existence open with the story of Étienne Geoffroy Saint-Hilaire, a natural historian, who having taken part in Napoleon’s Egypt expedition, compared mummified ancient Egyptian ibises with contemporary ones in order to detect traces of evolutions but because the time span was too short, he found nothing. His work was published in France 1818, but Poskett argues that his earliest work was published in Egyptian at the start of the century and so, “In order to understand the history of evolution, we therefore need to begin with Geoffroy and the French army in North Africa.” I’m not a historian of evolution but really? Ignoring all the claims for evolutionary thought in earlier history, Poskett completely blends out the evolutionary theories of Pierre Louis Maupertuis (1751), James Burnett, Lord Monboddo, (between 1767 and 1792) and above all Darwin’s grandfather Erasmus, who published his theory of evolution in his Zoonomia (1794–1796). So why do we need to begin with Étienne Geoffroy Saint-Hilaire?

Having dealt briefly with Charles Darwin, Poskett takes us on a tour of the contributions to evolutionary theory made in Russia, Japan, and China in the nineteenth century, whilst ignoring the European contributions. 

Up next in Industrial Experiments Poskett takes us on a tour of the contributions to the physical sciences outside of Europe in the nineteenth century. Here we have one brief WTF statement. Poskett writes:

Since the early nineteenth century, scientists had known that the magnetic field of the Earth varies across the planet. This means that the direction of the north pole (‘true north’) and the direction that the compass needle points (‘magnetic north’) are not necessarily identical, depending on where you are.[21]

Magnetic declination, to give the technical name, had been known and documented since before the seventeenth century, having been first measured accurately for Rome by Georg Hartmann in 1510, it was even known that it varies over time for a given location. Edmund Halley even mapped the magnetic declination of the Atlantic Ocean at the end of the seventeenth century in the hope that it would provide a solution to the longitude problem. 

In the final quarter we move into the twentieth century. The first half deals with modern physics up till WWII, and the second with genetic research following WWII, in each case documenting the contribution from outside of Europe. Faster than Light, the modern physics section, move through Revolutionary Russia, China, Japan, and India; here Poskett connects the individual contributions to the various revolutionary political movements in these countries. Genetic States moves from the US, setting the background, through Mexico, India, China, and Israel.  I have two minor quibbles about what is presented in these two sections.

Firstly, in both sections, instead of a chronological narrative of the science under discussion we have a series of biographical essays of the figures in the different countries who made the contribution, which, of course, also outlines their individual contributions. I have no objections to this, but something became obvious to me reading through this collection of biographies. They all have the same muster. X was born in Y, became interested in topic Z, began their studies at some comparatively local institute of higher education, and then went off to Heidelberg/Berlin/Paris/London/Cambridge/Edinburg… to study with some famous European authority, and acquire a PhD. Then off to a different European or US university to research, or teach or both, before to returning home to a professorship in their mother country. This does seem to suggest that opposed to Poskett’s central thesis of the global development of science, a central and dominant role for Europe.  

My second quibble concerns only the genetics section. One of Poskett’s central theses is that science in a given epoch is driven by an external to the science cultural, social, or political factor. For this section he claims that the external driving force was the Cold War. Reading through this section my impression was that every time he evoked the Cold War he could just have easily written ‘post Second World War’ or even ‘second half of the twentieth century’ and it would have made absolutely no difference to his narrative. In my opinion he fails to actually connect the Cold War to the scientific developments he is describing.

The book closes with a look into the future and what Poskett thinks will be the force driving science there. Not surprisingly he chooses AI and being a sceptic what all such attempts at crystal ball gazing are concerned I won’t comment here.

The book has very extensive end notes, which are largely references to a vast array of primary and mostly secondary literature, which confirms what I said at the beginning that Poskett in merely presenting in semi-popular form the current stand in the history of science of the last half millennium. There is no separate bibliography, which is a pain if you didn’t look to see something the first time it was end noted, as in subsequent notes it just becomes Smith, 2003, sending you off on an oft hopeless search for that all important first mention in the notes. There are occasional grey scale illustrations and two blocks, one of thirteen and one of sixteen, colour plates. There is also an extensive index.

So, after all the negative comments, what do I really think about James Poskett, highly praised volume. I find the concept excellent, and the intention is to be applauded. A general popular overview of the development of the sciences since the Renaissance is an important contribution to the history of science book market. Poskett’s book has much to recommend it, and I personally learnt a lot reading it. However, as a notorious history of science pedant, I cannot ignore or excuse the errors than I have outlined in my review, some of which are in my opinion far from minor. The various sections of the book should have been fact checked by other historians, expert in the topic of the section, and this has very obviously not been done. It is to be hoped that this will take place before a second edition is published. 

Would I recommend it? Perhaps surprisingly, yes. James Poskett is a good writer and there is much to be gained from reading this book but, of course, with the caveat that it also contains things that are simply wrong. 


[1] James Poskett, Horizons: A Global History of Science, Viking, 2022 

[2] Take your pick according to your personal philosophy of science.

[3] Poskett p. 11

[4] Poskett p. 16

[5] Poskett 16

[6] Poskett p. 23

[7] Poskett p. 59

[8] Poskett p. 61

[9] Poskett p. 62

[10] Poskett p. 62

[11] Poskett p. 84

[12] Poskett pp. 101-104

[13] Poskett p. 107

[14] Edney private correspondence 27.07.2022

[15] Poskett p. 108

[16] Ferreiro p. 107

[17] Poskett p. 111

[18] Poskett p. 110

[19] Ferreiro p. 107

[20] Poskett pp. 111-112

[21] Poskett p. 251

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Filed under Book Reviews, Early Scientific Publishing, History of Astronomy, History of botany, History of Cartography, History of Geodesy, History of Islamic Science, History of Navigation, Natural history, Renaissance Science

The Wizard Earl’s mathematici 

In my recent post on the Oxford mathematician and astrologer Thomas Allen, I mentioned his association with Henry Percy, 9th Earl of Northumberland, who because of his strong interest in the sciences was known as the Wizard Earl.

HENRY PERCY, 9TH EARL OF NORTHUMBERLAND (1564-1632) by Sir Anthony Van Dyck (1599-1641). The ‘Wizard Earl’ was painted posthumously as a philosopher, hung in Square Room at Petworth. This is NT owned. via Wikimedia Commons

As already explained there Percy actively supported four mathematici, or to use the English term mathematical practitioners, Thomas Harriot (c. 1560–1621), Robert Hues (1553–1632), Walter Warner (1563–1643), and Nathaniel Torporley (1564–1632). Today, I’m going to take a closer look at them.

Thomas Harriot is, of course, the most well-known of the four; I have already written a post about him in the past, so I will only brief account of the salient point here.

Portrait often claimed to be Thomas Harriot (1602), which hangs in Oriel College, Oxford. Source: Wikimedia Commons

He graduatied from Oxford in 1580 and entered the service of Sir Walter Raleigh (1552–1618) in 1583. At Raleigh’s instigation he set up a school to teach Raleigh’s marine captains the newest methods of navigation and cartography, writing a manual on mathematical navigation, which contained the correct mathematical method for the construction of the Mercator projection. This manual was never published but we can assume he used it in his teaching. He was also directly involved in Raleigh’s voyages to establish the colony of Roanoke Island.

Sir Walter Ralegh in 1588 artist unknown. Source: Wikimedia Commons

In 1590, he left Raleigh’s service and became a pensioner of Henry Percy, with a very generous pension, the title to some land in the North of England, and a house on Percy’s estate, Syon House, in Middlesex.[1] Here, Harriot lived out his years as a research scientist with no obligations.

Syon House Attributed to Robert Griffier

After Harriot, the most significant of the Wizard Earl’s mathematici was Robert Hues. Like Harriot, Hues attended St Mary’s Hall in Oxford, graduating a couple of years ahead of him in 1578. Being interested in geography and mathematics, he was one of those who studied navigation under Harriot in the school set up by Raleigh, having been introduced to Raleigh by Richard Hakluyt (1553–1616), another student of Thomas Allen and a big promoter of English colonisation of North America.  

Hakluyt depicted in stained glass in the west window of the south transept of Bristol Cathedral – Charles Eamer Kempe, c. 1905. Source: Wikimedia Commons

Hues went on to become an experienced mariner. During a trip to Newfoundland, he came to doubt the published values for magnetic declination, the difference between magnetic north and true north, which varies from place to place.

In 1586, he joined with Thomas Cavendish (1560–1592), a privateer and another graduate of the Harriot school of navigation, who set out to raid Spanish shipping and undertake a circumnavigation of the globe, leaving Plymouth with three ships on 21 July. After the usual collection of adventures, they returned to Plymouth with just one ship on 9 September 1588, as the third ever ship to complete the circumnavigation after Magellan and Drake. Like Drake, Cavendish was knighted by Queen Elizabeth for his endeavours.

Thomas Cavendish An engraving from Henry Holland’s Herōologia Anglica (1620). Animum fortuna sequatur is Latin for “May fortune follow courage.” Source: Wikimedia Commons

Hues undertook astronomical observations throughout the journey and determined the latitudes of the places they visited. In 1589, he served with the mathematicus Edward Wright (1561–1615), who like Harriot worked out the correct mathematical method for the construction of the Mercator projection, but unlike Harriot published it in his Certaine Errors in Navigation in 1599.

Source: Wikimedia Commons

In August 1591, he set out once again with Cavendish on another attempted circumnavigation, also accompanied by the navigator John Davis (c. 1550–1605), another associate of Raleigh’s, known for his attempts to discover the North-West passage and his discovery of the Falkland Islands.

Miniature engraved portrait of navigator John Davis (c. 1550-1605), detail from the title page of Samuel Purchas’s Hakluytus Posthumus or Purchas his Pilgrimes (1624). Source: Wikimedia Commons

Cavendish died on route in 1592 and Hues returned to England with Davis in 1683. On this voyage Hues continued his astronomical observations in the South Atlantic and made determinations of compass declinations at various latitudes and the equator. 

Back in England, Hues published the results of his astronomical and navigational research in his Tractatus de globis et eorum usu (Treatise on Globes and Their Use, 1594), which was dedicated to Raleigh.

The book was a guide to the use of the terrestrial and celestial globes that Emery Molyneux (died 1598) had published in 1592 or 1593.

Molyneux CEltial Globe Middle Temple Library
A terrestrial globe by Emery Molyneux (d.1598-1599) is dated 1592 and is the earliest such English globe in existence. It is weighted with sand and made from layers of paper with a surface coat of plaster engraved with elaborate cartouches, fanciful sea-monsters and other nautical decoration by the Fleming Jodocus Hondius (1563-1611). There is a wooden horizon circle and brass meridian rings.

Molyneux belong to the same circle of mariners and mathematici, counting Hues, Wright, Cavendish, Davis, Raleigh, and Francis Drake (c. 1540–1596) amongst his acquaintances. In fact, he took part in Drake’s circumnavigation 1577–1580. These were the first globes made in England apparently at the suggestion of John Davis to his patron the wealthy London merchant William Sanderson (?1548–1638), who financed the construction of Molyneux’s globes to the tune of £1,000. Sanderson had sponsored Davis’ voyages and for a time was Raleigh’s financial manager. He named his first three sons Raleigh, Cavendish, and Drake.

Molyneux’s terrestrial globe was his own work incorporating information from his mariner friends and with the assistance of Edward Wright in plotting the coast lines. The circumnavigations of Drake and Cavendish were marked on the globe in red and blue line respectively. His celestial globe was a copy of the 1571 globe of Gerard Mercator (1512–1594), which itself was based on the 1537 globe of Gemma Frisius (1508–1555), on which Mercator had served his apprenticeship as globe maker. Molyneux’s globes were engraved by Jodocus Hondius (1563–1612), who lived in London between 1584 and 1593, and who would upon his return to the Netherlands would found one of the two biggest cartographical publishing houses of the seventeenth century.

Hues’ Tractatus de globis et eorum usu was one of four publications on the use of the globes. Molyneux wrote one himself, The Globes Celestial and Terrestrial Set Forth in Plano, published by Sanderson in 1592, of which none have survived. The London public lecturer on mathematics Thomas Hood published his The Vse of Both the Globes, Celestiall and Terrestriall in 1592, and finally Thomas Blundeville (c. 1522–c. 1606) in his Exercises containing six treatises including Cosmography, Astronomy, Geography and Navigation in 1594.

Hues’ Tractatus de globis has five sections the first of which deals with a basic description of and use of Molyneux’s globes. The second is concerned with matters celestial, plants, stars, and constellations. The third describes the lands, and seas displayed on the terrestrial globe, the circumference of the earth and degrees of a great circle. Part four contains the meat of the book and explains how mariners can use the globes to determine the sun’s position, latitude, course and distance, amplitudes and azimuths, and time and declination. The final section is a treatise, inspired by Harriot’s work on rhumb lines, on the use of the nautical triangle for dead reckoning. Difference of latitude and departure (or longitude) are two legs of a right triangle, the distance travelled is the hypotenuse, and the angle between difference of latitude and distance is the course. If any two elements are known, the other two can be determined by plotting or calculation using trigonometry.

The book was a success going through numerous editions in various languages. The original in Latin in 1593, Dutch in 1597, an enlarged and corrected Latin edition in 1611, Dutch again in 1613, enlarged once again in Latin in 1617, French in 1618, another Dutch edition in 1622, Latin again in 1627, English in 1638, Latin in 1659, another English edition also in 1659, and finally the third enlarged Latin edition reprinted in 1663. There were others.

The title page of Robert Hues (1634) Tractatvs de Globis Coelesti et Terrestri eorvmqve vsv in the collection of the Biblioteca Nacional de Portugal via Wikimedia Commons

Hues continued his acquaintance with Raleigh in the 1590s and was one of the executors of Raleigh’s will. He became a servant of Thomas Grey, 15th Baron Gray de Wilton (died 1614) and when Grey was imprisoned in the Tower of London for his involvement in a Catholic plot against James I & VI in 1604, Hues was granted permission to visit and even to stay with him in the Tower. From 1605 to 1621, Northumberland was also incarcerated in the Tower because of his family’s involvement in the Gunpowder Plot. Following Grey’s death Hues transferred his Tower visits to Northumberland, who paid him a yearly pension of £40 until his death in 1632.

He withdrew to Oxford University and tutored Henry Percy’s oldest son Algernon, the future 10th Earl of Northumberland, in mathematics when he matriculated at Christ’s Church in 1617.

Algernon Percy, 10th Earl of Northumberland, as Lord High Admiral of England, by Anthony van Dyck. Source: Wikimedia Commons

In 1622-23 he would also tutor the younger son Henry.

Oil painting on canvas, Henry Percy, Baron Percy of Alnwick (1605-1659) by Anthony Van Dyck Source: Wikimedia Commons

During this period, he probably visited both Petworth and Syon, Northumberland’s southern estates. He in known to have had discussion with Walter Warner on reflection. He remained in Oxford discussing mathematics with like minded fellows until his death.

Compared to the nautical adventures of Harriot and Hues, both Warner and Torporley led quiet lives. Walter Warner was born in Leicestershire and educated at Merton College Oxford graduating BA in 1579, the year between Hues and Harriot. According to John Aubrey in his Brief Lives, Warner was born with only one hand. It is almost certain that Hues, Warner, and Harriot met each other attending the mathematics lectures of Thomas Allen at Oxford. Originally a protégé of Robert Dudley, 1st Earl of Leicester, (1532–1588), he entered Northumberland’s household as a gentleman servitor in 1590 and became a pensioner in 1617. Although a servant, Warner dined with the family and was treated as a companion by the Earl. In Syon house, he was responsible for purchasing the Earl’s books, Northumberland had one of the largest libraries in England, and scientific instruments. He accompanied the Earl on his military mission to the Netherlands in 1600-01, acting as his confidential courier.       

Like Harriot, Warner was a true polymath, researching and writing on a very wide range of topics–logic, psychology, animal locomotion, atomism, time and space, the nature of heat and light, bullion and exchange, hydrostatics, chemistry, and the circulation of the blood, which he claimed to have discovered before William Harvey. However, like Harriot he published almost nothing, although, like Harriot, he was well-known in scholarly circles. Some of his work on optics was published posthumously by Marin Mersenne (1588–1648) in his Universæ geometriæ (1646).

Source: Google Books

It seems that following Harriot’s death Warner left Syon house, living in Charing Cross and at Cranbourne Lodge in Windsor the home of Sir Thomas Aylesbury, 1st Baronet (!576–1657), who had also been a student of Thomas Allen, and who had served both as Surveyor of the Navy and Master of the Mint. Aylesbury became Warner’s patron.

This painting by William Dobson probably represents Sir Thomas Aylesbury, 1st Baronet. 
Source: Wikimedia Commons

Aylesbury had inherited Harriot’s papers and encouraged Warner in the work of editing them for publication (of which more later), together with the young mathematician John Pell (1611–1685), asking Northumberland for financial assistance in the endeavour.

Northumberland died in 1632 and Algernon Percy the 10th Earl discontinued Warner’s pension. In 1635, Warner tried to win the patronage of Sir Charles Cavendish and his brother William Cavendish, enthusiastic supporters of the new scientific developments, in particular Keplerian astronomy. Charles Cavendish’s wife was the notorious female philosopher, Margaret Cavendish. Warner sent Cavendish a tract on the construction of telescopes and lenses for which he was rewarded with £20. However, Thomas Hobbes, another member of the Cavendish circle, managed to get Warner expelled from Cavendish’s patronage. Despite Aylesbury’s support Warner died in poverty. 

Nathaniel Torporley was born in Shropshire of unknow parentage and educated at Shrewsbury Grammar Scholl before matriculating at Christ Church Oxford in 1581. He graduated BA in 1584 and then travelled to France where he served as amanuensis to the French mathematician François Viète (1540–1603).

François Viète Source: Wikimedia Commons

He is thought to have supplied Harriot with a copy of Viète’s Isagoge, making Harriot the first English mathematician to have read it.

Source

Torporley returned to Oxford in 1587 or 1588 and graduated MA from Brasenose College in 1591. 

He entered holy orders and was appointed rector of Salwarpe in Worcestershire, a living he retained until 1622. From 1611 he was also rector of Liddington in Wiltshire. His interest in mathematics, astronomy and astrology attracted the attention of Northumberland and he probably received a pension from him but there is only evidence of one payment in 1627. He was investigated in 1605, shortly before the Gunpowder Plot for having cast a nativity of the king. At some point he published a pamphlet, under the name Poulterey, attacking Viète. In 1632, he died at Sion College, on London Wall and in a will written in the year of his death he left all of his books, papers, and scientific instrument to the Sion College library.

Although his papers in the Sion College library contain several unpublished mathematical texts, still extant today, he only published one book his Diclides Coelometricae; seu Valuae Astronomicae universales, omnia artis totius munera Psephophoretica in sat modicis Finibus Duarum Tabularum methodo Nova, generali et facillima continentes, (containing a preface, Directionis accuratae consummata Doctrina, Astrologis hactenus plurimum desiderata and the Tabula praemissilis ad Declinationes et coeli meditations) in London in 1602.

Source

This is a book on how to calculate astrological directions, a method for determining the time of major incidents in the life of a subject including their point of death, which was a very popular astrological method in the Renaissance. This requires spherical trigonometry, and the book is interesting for containing new simplified methods of solving right spherical triangles of any sort, methods that are normally attributed to John Napier (1550–1617) in a later publication. The book is, however, extremely cryptic and obscure, and almost unreadable. Despite this the surviving copies would suggest that it was widely distributed in Europe.

Our three mathematici came together as executors of Harriot’s will. Hues was charged with pricing Harriot’s books and other items for sale to the Bodleian Library. Hues and Torporley were charged with assisting Warner with the publication of Harriot’s mathematical manuscripts, a task that the three of them managed to bungle. In the end they only managed to publish one single book, Harriot’s algebra Artis Analyticae Praxis in 1631 and this text they castrated.

Source

Harriot’s manuscript was the most advanced text on the topic written at the time and included full solutions of algebraic equations including negative and complex solutions. Either Warner et al did not understand Harriot’s work or they got cold feet in the face of his revolutionary new methods, whichever, they removed all of the innovative parts of the book making it basically irrelevant and depriving Harriot of the glory that was due to him.

For myself the main lesson to be learned from taking a closer look at the lives of this group of mathematici is that it shows that those interested in mathematics, astronomy, cartography, and navigation in England the late sixteenth and early seventeenth centuries were intricately linked in a complex network of relationships, which contains hubs one of which was initially Harriot and Raleigh and then later Harriot and Northumberland. 


[1] For those who don’t know, Middlesex was a small English county bordering London, in the South-West corner of Essex, squeezed between Hertfordshire to the north and Surry in the South, which now no longer exists having been largely absorbed into Greater London. 

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Filed under Early Scientific Publishing, History of Astrology, History of Astronomy, History of Cartography, History of Mathematics, History of Navigation, History of Optics, History of science, Renaissance Science

Astrology, data, and statistics

Is western astrology a big data science, or even the very first big data science? Data scientist Alexander Boxer thinks it is and has written a book to back up his claim, A Scheme of HeavenThe History of Astrology and The Search for Our Destiny in Data.[1] 

His justification for having written this book is interesting:

Over two thousand years ago, astrologers became the first to stumble upon the powerful storytelling possibilities inherent in numerical data, possibilities that become all the more persuasive when presented graphically in a chart or figure. Although it took a while for the rest of the world to catch on, the art of weaving a story out of numbers of figures, often a specific course of action, is used everywhere today, from financial forecasts to dieting advice to weather models.

And yet numbers still mislead, figures still mislead, figures still deceive, and predictions still fail–sometimes spectacularly so–even those that rely on exceptionally sophisticated mathematics. So, are the techniques being used today to parse and package quantitative information any more effective that what was devised by astrologers millennia ago?

            In order to make that assessment, it’s first necessary to have a basic understanding of what astrology is and how it works. But that sort of understanding–one that’s at least adequate to resolve some seemingly straightforward technical questions–is surprisingly hard to come by for such a long-lived and influential craft. Being frustrated in my own search for a simple yet competent overview of astrology, I decided I might just as well write one myself. This, curious reader, is the book you now hold in your hands.

Boxer is actually correct “a simple yet competent overview of astrology” doesn’t, as far as I know, exist, so has he succeeded in providing one? My answer is a qualified “yes, no, maybe, probably not!” Large parts of Boxer’s book are excellent, other parts are OK, some parts I found simply baffling, and one of his central claims is simply wrong. The biggest problem with the book, as far as I’m concerned, is that it tries to be too many different things in far too few pages. It wants to be a history of astrology from its beginnings down to the present days, at the same time being a data scientist’s, statistical analysis of fundamental aspects of astrology, as well as presenting a quasi-philosophy of science meta-analysis of some central themes of astrology, and that all whilst attempting to achieve to authors declared central aim of providing “a simple yet competent overview of [western][2] astrology.” All of this in just 263 pages of an octavo book with a medium typeface. He also largely leaves out any serious attempt to present the interpretation of a horoscope, which is actually the essence of astrology.

The excellent bits of Boxer’s book are almost all confined to the technical and mathematical aspects of casting a horoscope and to the data scientist’s statistical analysis of various aspects of astrology. There is for example a competently presented, entire chapter devoted to the nuts and bolts of mathematical astronomy, without which it is impossible to actually cast a horoscope. However, this illustrates one, in my opinion serious error in the book. In the opening chapter Boxer presents a brief greatest hits tour of what he labels the obscure beginnings of astrology. I’ve read accounts of the material he presents here that are longer than his entire book, to which I’ll return in a minute, but that is not what concerns me at the moment. Here he presents for the second time (the first one in in the introduction) one of the excellent illustrations that occur throughout the book. This is a horoscope presented on the mater and tympan of an astrolabe without the rete but with the ecliptic. Also presented are all of the relevant astronomical data, time, in various formats, celestial coordinates in all three variants, geographical coordinates and so forth. See below:

However, there is absolutely no explanation of what is being presented here. Now, I’ve spent a number of years studying this stuff, so I know roughly what I’m looking at, although I need to look up which celestial coordinate system is which, for example. A naïve reader coming to this book to learn about astrology would have no idea what they are looking at and nowhere in the book do they get this diagram explained carefully step for step. The knowledge required is contained in the book, scattered around in various sections and chapters but with no linking references to the diagrams. The celestial coordinates are, for example, explained in the chapter on mathematical astronomy, whereas the astrolabe only gets explained in dribs and drabs about one hundred pages later in the book. The Julian Day Count, one of the methods listed on the diagram to denote the time of the horoscope only gets explained on pages 225-226! The information needed to understand what is in fact an excellent diagram is scattered throughout the book like a scavenger hunt without rules or clues.

Remaining by the topic, the book is liberally illustrated with diagrams and tables to explain themes under discussion, and these are excellently done both from a pedagogical and a graphical viewpoint and this is one of the great strengths of the book. There is not a conventional bibliography but at the end of the book there is an annotated collection of source material for each section of the book. There is also a competent index. 

Following up on the all too brief sketch of the origins of western astrology and the more comprehensive introduction to the basics of astronomy, Boxer now dives into what is without doubt one of the greatest error in the book, he fell in love with Marcus Menilius’ Astronomica. After briefly dismissing our knowledge of astronomy in the last five centuries BCE, a serious error because we actually know far more that Boxer is prepared to admit. However, if he did acknowledge it, he would have to abandon his love affair with Manilius. Boxer correctly explains that although the Roman took over large parts of Alexander’s Hellenistic Empire, they were initially reluctant to adopt the Hellenistic astrology. He illustrates this with the fact that there are absolutely no astrological discussions of Julius Caesar’s assassination in 44 BCE. Enter Marcus Manilius and his Astronomica stage left. 

A brief explanation, the Astronomica is a Latin didactic poem dating to the early first century CE, which happens to be the earliest surviving, relatively complete account of western astrology.  About its probable author Marcus Manilius, we know next to nothing. 

Boxer goes complexly overboard about the Astronomica. He writes:

The Astronomica is a fascinating work in its own right, but it takes on a special significance when we recognise that this poem is, essentially, astrology’s grand unveiling on the historical stage. And like Minerva issuing from Jupiter’s skull fully grown and clad in armour, the Astronomica presents an astrology emerging from obscurity remarkably complete and fully formed. Even today, two thousand years later, there is hardly any astrological idea, no matter how sophisticated or complex, which can’t trace its debut to Manilius’s poem.

If the Astronomica is “astrology’s grand unveiling on the historical stage” then it must have got lousy reviews from the critics. Not one single author in antiquity is known to have quoted the Astronomica. There are a grand total of about thirty existing medieval manuscripts of the work none of them older than the ninth century CE. It does not feature in any other medieval literature and appears to have been largely ignored in the Middle Ages. It was (re)discovered in c. 1416 by the zealous Renaissance Humanist manuscript hunter, Poggio Bracciolini (1380–1459) and only really emerged on the European literary and scientific stage when the editio princeps was published by Regiomontanus (1436–1476) in Nürnberg in 1473. 

In his love affair with the Astronomica, Boxer seems to think that modern horoscope astrology is somehow a Roman invention. Later in the book when taking about Arabic astrology he describes Masha’allah’s theory of astrological historical cycles as the “most significant addition to astrology since Roman times.” Manilius is in fact merely describing an existing system that was created by the Hellenistic Greeks between the fifth and first centuries BCE, something that Boxer acknowledges elsewhere in his book, when he goes overboard about the wonders of ancient Alexandria.

As for the guff about “astrology emerging from obscurity remarkably complete and fully formed” and “there is hardly any astrological idea, no matter how sophisticated or complex, which can’t trace its debut to Manilius’s poem,” as already stated Manilius is reporting on an existing system not creating it. More importantly as the modern commentators point out you wouldn’t be able to cast a horoscope having read it and it contains nothing on planetary influence in astrology, the very heart of the discipline.  In fact, although they adopted astrology and used it widely until the decline of the Empire, in the sixth century, the Romans actually contributed next to nothing to the history of astrology.

However, the chapter ends with an example of Boxer’s biggest strength the data based statistical analysis of various aspect of astrology. He starts here with the personality traits that Manlius attributes to those born under a particular sun sign, setting them out in a handy table first. Using the data of different professional groups, he introduces the reader to the concept of statistical significance and shows that the astrological divisions into personality types doesn’t hold water.

Next up we have Ptolemy the most significant author in the whole of the history of western astrology. He gives an adequate sketch of Ptolemy’s contributions to astronomy, geography and astrology and shows that they are actually three aspects of one intellectual project. In his brief discussion of map projection, he makes not an error, but a misleading statement. Introducing Ptolemy’s Planisphere and the stereographic projection the key to the astrolabe he writes:

For the basic idea of a stereographic projection, imagine looking down on a globe from above its North Pole [my emphasis], and then squashing in into the equator. The visual effect ends up looking like a scoop of ice cream that’s melted onto a warm plate from the bottom out. Because there’s no limit to how far outward these maps spread, it’s customary to extend them only as far as the Tropic of Capricorn.

The following pages contain stereographic projections of the celestial sphere, the terrestrial sphere and four tympans from astrolabes taken for different latitudes. Boxer’s error is that these are taken from the South Pole as projection point. Almost all astrolabes are for the Northern Hemisphere and are projections from the South Pole, there are only a handful of Southern Hemisphere astrolabes with the North Pole as projection point. 

Boxer also makes an error in his etymology of the Name Almagest for Ptolemy’s Mathēmatikē Syntaxis. Almagest comes from the Arabic al-majistī, which in turn comes from the Greek megiste all of which mean the greatest. Boxer justifies this as follows:

The Almagest was the greatest of all ancient treatises on astronomy, just as Ptolemy was the greatest of ancient astronomers.

In fact, all of this derives from the alternative Greek name of the Mathēmatikē SyntaxisHē Megalē Syntaxis meaning The Great Treatise as opposed to a smaller work by Ptolemy on astronomy known as The Small Treatise. In other words, the Almagest is the big book on astronomy as opposed to the small book on astronomy.

Boxer has a rather negative opinion of Ptolemy’s Apotelesmatika commonly called the Tetrabiblos in Greek, or Quadripartitum in Latin, meaning four books, his big book on astrology. He finds it dry, technical, and uninspiring, unlike the Astronomica. After introducing Ptolemy’s astrological geography Boxer once again applies his statistical analysis to Ptolemy’s claims on the geographical acceptance of homosexuality comparing it with the modern data on the topic.

Boxer’s next target is the only substantial collection of actual horoscopes from antiquity, by the second century Hellenistic astrologer, Vettius Valens’ Anthologies. We move from the theoretical, Ptolemy, to the practical, Valens. Here Boxer once again reverts to his role as data scientist and gives an interesting seminar on the theme of “how unique is a horoscope? Along the way he sings a brief eulogy for ancient Alexandria as a centre for the mathematical sciences including of course astrology. He also makes a brief excursion into the philosophy of science evoking the falsifiability criterion of Karl Popper and the separation of science and pseudoscience, a couple of pages that are far too brief for what is a very complex discussion and could have been happily edited out. His work, however, on codifying the basics of a horoscope according to Valens and examining the uniqueness of the result is stimulating and a high point of the book.

Next, Boxer moves onto medieval Arabic astrology but doesn’t really. He starts, as do many authors on this topic, with the horoscopes cast to determine the right time to found the city of Baghdad and having given a brief but largely correct account of why the Abbasid caliphs adopted astrology, and the parallel transmission of astrology into Europe in the High Middle Ages, he then passes rapidly to Masha’allah’s theory of historical cycles based on the conjunctions of Jupiter and Saturn and that’s it! Arabic astrology is a massive topic and given its powerful influence on astrology as its practiced today deserves much more attention in any book claiming to provide a “simple yet competent overview of astrology.” Once again, the chapters strength lies in Boxer’s statistics-based analysis of Masha’allah’s theory, which drifts off into the theories of encryption. One thing that did piss me off was in a discussion of the use of symbols he writes:

By necessity, then, efficacy of this magic will hinge upon the fitness of these symbols to their task: Nowhere is this more evident than in mathematics. (If you don’t believe me, try adding the Roman numerals CXXXIX and DCXXIII together; or, even worse, the Greek numerals 𝛒𝛌𝛉 and 𝛘𝛋𝛄.)

This is pure bullshit! Assuming that you are cognisant with the numeral systems and the values of the symbols than these additions are no more difficult than carrying out the same sums using Hindu-Arabic numerals. Division and multiplication are, at least at first glance, more difficult but there are algorithms for both numerical systems that also make those operations as easy as the algorithms for Hindu-Arabic numerals. The major point, however, is that nobody bothered; arithmetical calculations were carried out using an abacus and the numerals were only used to write down the results. 

Having very inadequately dealt with Arabic astrology, Boxer now turns to Guido Bonatti (died around 1300). Before he gets to him, we get a brief section on the transmission from Arabic into Latin where Boxer manages to conflate and confuse two periods of translation in Toledo, one of the major centres for that work. In the twelfth century translators such as Gerard of Cremona translated the major Greek scientific works from Arabic into Latin often with the help of Jewish intermediaries. Later in the thirteenth century Alfonso X of Castille set up a school of translators in Toledo translating Hebrew and Arabic texts into Latin and Castilian, establishing Castilian as a language of learning.  Boxer goes off into an unfounded speculation about texts being translated from Greek into Syriac into Arabic into Hebrew into Castilian (here Boxer incorrectly uses the term Spanish, a language that didn’t exist at the time) into Latin, with all the resulting errors. This paragraph should have been thrown out by a good editor. We then get a couple of paragraphs of waffle about the medieval universities that appears to exist purely to point out that Abelard and Héloïse named their son astrolabe. These should have been replaced with a sensible account of the medieval universities or thrown out by the same good editor. 

We then get an account of the twelfth and thirteenth centuries war between the Guelphs and Ghibellines in Northern Italy largely to introduce Guido Bonatti, who was a Guelph astrologer and author of the Liber Astronomiae, which Boxer tells us, hyperbolically, is the most influential astrology book of the Middle Ages. Here Boxer makes two major errors. Firstly, he presents judicial astrology, which he defines as follows:

The basic premise of judicial astrology is that you ask the stars a question–a question about pretty much anything–and the stars then reveal a judgement or, in Latin, iudicium. The astrologer’s job is to interpret these judgements on your behalf. So far, so good. The odd thing about judicial astrology, however, was that for many questions, and especially the broad category of yes-or-no questions, the astrologer would determine the stars’ judgement based on their positions in the sky at the moment your question was asked.

What Boxer is actually describing is horary astrology, just one of the four branches of judicial astrology, the other three are natal astrology, mundane astrology, and elective astrology; Boxer goes on later to discuss elective astrology. Judicial astrology was opposed to natural astrology, which meant astrometeorology and astromedicine, or to give it its proper name iatromathematics, neither of which Boxer deals with, in any depth, just giving a two-line nod to astromedicine. 

Having described horary astrology, albeit under the wrong label, Boxer goes off on a rant how ridiculous it is/was. Then come two more misleading statements, he writes:

Yet however ho-hum this fatalistic outlook may have been during astrology’s early days in Stoic Rome, to deny the existence of free will was a decidedly and damnably heretical opinion in medieval Christian Europe.

[…]

As was obvious to Dante. Petrarch, and many others, astrology–and especially judicial astrology–was fundamentally incompatible with Christian doctrine. 

First off, Stoic Rome was not astrology’s early days, by that time Hellenistic astrology had been around for about four to five hundred years. Yes, Hellenistic astrology was totally deterministic and did in fact clash with the Church doctrine of free will in the beginnings of the High Middle Ages. However, Albertus Magnus and Thomas Aquinas, who laid the foundations of Church doctrine down to the present day, redefined astrology in their writings in the thirteenth century, as acceptable but non-deterministic thus removing the doctrinal clash. In terms of the impact of their work for the acceptance of astrology not just in the Middle Ages, surely it is far more influential than Bonatti’s Liber Astronomiae.

In the passage that I left out of the quote above Boxer writes, amongst other things:

Well, that’s the sort of thinking that could get you burnt at the stake in you insisted on making a fuss about it. The astrologer Cecco d’Ascoli was condemned by the Inquisition on precisely these grounds and burnt at the stake in Florence on September 16, 1327. [i.e., for practicing deterministic astrology]

This is simply not true! In 1324, Cecco d’Ascoli was admonished by the Church and punished for his commentary on the Sphere of John de Sacrobosco, nothing whatsoever to do with astrology. To avoid his punishment he fled from Bologna, where he was professor for astrology, to Florence. Here, he was condemned for trying to determine the nativity of Christ by reading his horoscope, and as a repeat offender was burnt by the Inquisition. Even under the non-deterministic interpretation of judicial astrology from Albertus Magnus and Thomas Aquinas, casting the horoscope of Christ was considered unacceptable. 

Next, Boxer introduces the Houses of Heaven and claims that, “these are astrology’s system of local coordinates the astrological analog to the modern-day quantities azimuth an elevation.” Sorry but this statement is garbage the houses are not a coordinate system, they are divisions of the ecliptic plane. Boxer introduces them here because they play a central role in Bonatti’s horary astrology. Once again Boxer the data scientist comes to the fore with the question whether it would be possible to construct an algorithm to automatically answer questions posed in horary astrology. As usually one of the best parts of the book.

Traditionally, one of the major disputes amongst astrologers in the question how exactly to determine the boundaries of the houses and Boxer now turns his attention to the various solutions presenting nine different solutions that have been used at some time in the history of astrology. 

One system that was very popular in the Renaissance and Early Modern Period was devised by Regiomontanus (1436–1476), which Boxer looks at in somewhat more detail. He starts with a very brief rather hagiographical biographical sketch, which includes the following claim:

By the time he was twenty-six, Regiomontanus had finished a complete reworking Ptolemy’s Almagest using all the newest trigonometrical methods. 

The Epitome of the Almagest was commissioned from Georg von Peuerbach, Regiomontanus’ teacher, and later colleague, by Cardinal Basilios Bessarion in 1460. Peuerbach had only completed six of the thirteen books by 1461 when he died. On his death bed he commissioned Regiomontanus to complete the work. Regiomontanus went off to Italy with Bessarion, basically as his librarian, and spent the next four years travelling through Italy collecting and copying manuscripts for Bessarion’s library. During this time, he probably completed the Epitome. Meaning he was twenty-nine. Although he might have finished it during the next two years, when we don’t know where he was or what he was doing. He intended to publish the finished book when he set up his publishing house in Nürnberg in 1471 but still hadn’t by the time he died in 1476. It was first published by Johannes Hamman in Venice in 1496

Further on Boxer writes:

Thus, when a certain archbishop in Hungary demanded an improved system for determining the Houses of Heaven–in particular one that would be more faithful to the vague instructions given by Ptolemy in his Tetrabiblos–there was only one person to ask.

            Regiomontanus accepted the challenge. In a brash and masterly treatise, he surveyed the existing methods of House division, dismissed them all as inadequate, introduced an entire new method, and provided tables for computing their boundaries at any latitude to the nearest minute of arc.

A nice story but unfortunately not exactly true. The title of the book that Regiomontanus wrote at the request, not demand, of János Vitéz Archbishop of Esztergom, for whom he had been working as a librarian since 1467 was his Tabulae directionum profectionumque. The purpose and content of the book is revealed in the title, this is not a book about the determination of the Houses, which are only secondary product of the book but about calculating directions, also called prorogratio or progression from the original Greek aphesis. A method to determine major events in the life of a horoscope subject including their death, described by Ptolemy in the Tetrabiblos, which was very popular in Renaissance astrology. 

This error by Boxer is rather bizarre because he describes the method of aphesis, albeit wrongly, whilst dealing with Manilius earlier in his book. Here he writes:

…a procedure … entailed identifying two key points on a birth horoscope: the “starter” and “destroyer.” As time elapsed from the moment of birth, the destroyer revolved along with the heavens towards the starters original position, all the while shooting evil rays at it. When the destroyer finally reached the starter, it was game over: death. The number of hours and minutes it took for the destroyer to reach the starter was then converted to the number of years and months the individual was expected to live.

A very colourful description but actually fundamentally wrong. First the astrologer has to determine the starter on the ecliptic, which is often the moment of birth but not necessarily. Then various destroyers are identified signalling major events in the life of the subjects not just their death, also on the ecliptic. Both points, started and destroyer are projected using spherical trigonometry onto the celestial equator and the number of degrees between the projected points is the time in years. Regiomontanus’ Tabulae directionum provide the mathematical apparatus to carry out this not particularly simple mathematical process. 

Which system of Houses division is still disputed amongst astrologers and Boxer possesses the impertinence to suggest they should use a particular system because he finds it mathematically the most elegant. 

The chapter closes with a short discourse on time, unequal hours, and equinoctial hours, which serves two functions to introduce the index or rule on the astrolabe which makes possible the conversion between unequal and equal hours. Boxer then states:

That the development of the mechanical clock occurred precisely when the most intricate astrological algorithms were in vogue is a historical synchronicity too striking to ignore.

[…]

In fact, the technological crossover between astrology and clock design was significant.

Here he is referring back to an earlier statement on the previous page:

This is why the earliest mechanical clocks of which the one in Prague’s old town square is the most magnificent example had astrolabe-style faces.

Source: Wikimedia Commons

Unfortunately for Boxer’s enthusiasm David S Landes, a leading historian of the clock, argues convincingly that the simple mechanical clock with a “normal” clock face preceded the astrolabe-style clock faces.

The next chapter opens with Tycho Brahe and the nova of 1572. Here once again Boxer choses to distort history for dramatic effect. He writes:

Yet, by all accounts, Tycho wanted nothing to do with Denmark’s administration, its wars, its politics, or its pageantry.

            For a nobleman like Tycho, the purpose of a university education was not to obtain a degree–that would have been unthinkably déclassé–but merely to pick up a little worldly polish of the sort that might prove serviceable in war and diplomacy. In this respect, Tycho’s education backfired spectacularly. He returned from Germany utterly captivated by the latest advances in alchemy, astronomy, and astrology.

Boxer carries on in this manner presenting Tycho as a rebel kicking against the pricks. What he neglects to mention is that although Tycho’s decision to become a professional astronomer was somewhat unorthodox, in all his endeavours Tycho received strong support from his maternal uncle Peder Oxe. Oxe was a university graduate, and a strong supporter of Paracelsian alchemical medicine, who just happened to be the Danish finance minister and Steward of the Realm, de facto prime minister, and politically by far the most powerful man in the whole of Denmark. 

Boxer closes his short section on Tycho with another piece of purple prose:

Tycho’s supernova is of tremendous historical importance because it was the first detailed observation which the old cosmological framework simply could not explain away. Something was rotten in the state of astronomy indeed. Tycho’s new star was a small crack in what had been considered a pristine crystalline firmament. There would be others–so many, in fact, that the entire system would soon collapse and shatter. It wasn’t just the heavens which had proven themselves mutable. A revolution was underway, and science, philosophy astronomy–and astrology–would never be the same.

The immutability of the heavens had been discussed and disputed by astronomers throughout Europe with respect to comets (sub– or supralunar?) since Paolo dal Pozzo Toscanelli (1397–1482) viewed them as supralunar based on his observations of the comet of 1456. The observations and reports of the 1572 supernova by many European astronomers only increased an ongoing debate. A debate that was only one part of a general trend to reform astronomy, which started around 1400 and in which everything was up for discussion. The period also saw a revival of Stoic philosophy and cosmology contra Aristotelian philosophy and cosmology. The supernova of 1572 was not the dramatic turning point that Boxer paints it as.

Boxer now delivers, what I regard as the absolute low point of the book, in that he presents the hairbrained theory of Peter Usher that Shakespeare’s Hamlet is “an elaborate astronomical analogy.” He does however backpedal and state, “I enjoy reading this quite a bit, even if I don’t find it very persuasive.” So, why include it at all?

We then move on to a very rapid sketch of the so-called astronomical revolution with the usual Copernicus=>Tycho/Kepler=>Galileo=>Newton cliché. Boxer now allows himself a real humdinger:

            Clearly Tycho’s commitment to a geocentric cosmos ran much deeper than astronomical arguments alone. IN fact, so central was the Earth’s fixity to Tycho’s philosophy that he proposed a compromise cosmology, one in which Mercury, Venus, Mars, Jupiter, and Saturn orbited the Sun, as in the Copernican system, but the Sun and Moon orbited the Earth as in the Ptolemaic system. It sounds ungainly, and Tycho may have been the only person who ever thought otherwise… [my emphasis].

Tycho may have been the only person? A handful of astronomers all independently came up with the so-called Tychonic geo-heliocentric system around the same time, as an alternative to the Copernican system, leading Tycho to accuse others of plagiarism. From about 1620 till about 1660 the majority of European astronomers thought a Tychonic model with diurnal rotation was the most probable system for the known universe.

Boxer finally gets back on course with the next section where he investigates the use of the words, astronomy, astrology, and mathematics to describe either astronomy or astrology as we know them. A very well-done section. This is followed by a section on the Gregorian calendar reform and why it was necessary, relatively good except for a false claim about Copernicus. He writes:

Copernicus cited the prospect of a more accurate calendar as one reason why he hoped (quite wrongly) that his new, Sun-centered theory of the universe might be well received by the Church.

I have no idea where Boxer found this but it’s simply not true. Copernicus’s only connection with the calendar reform was when he was approached around 1520, like many other European astronomers, to contribute to the calendar reform, he declined, stating that one first needed to accurately determine the length of the year. The chapter closes with a brief account of Kepler’s attitude and contributions to astrology, which falsely claims that he rejected astrology at the end of his life. He didn’t, he rejected traditional horoscope astrology most of his life, although he earned money with it, but believed till the end in his own system of celestial influence.

The final section of the book deals with modern forms of astrology. We have the Madame Blavatsky’s Theosophical Society and her creation of spiritual astrology. The creation of the popular twelve-paragraph newspaper horoscope and finally the creation of psychological astrology, first by the theosophist Alan Leo and developed further by psychoanalyst Carl Jung. Here Boxer delivers, what I regard as the biggest error in his entire book. He writes:

Yet the converse opinion–that every good astrologer must also be a good psychoanalyst–is pretty much the default amongst modern astrologers and their clients alike. For the professional astrologer, this represents a tremendous job promotion. A classical astrologer was, first and foremost, a human calculator, one whose most important qualification was his ability to solve long and tedious mathematical equations. [My emphasis]

Here Boxer, the mathematician, shows that he has literally not understood the difference between casting a horoscope and interpreting a horoscope. In fact, in his book he never really addresses the interpretation of horoscopes, which is the real work of a classical astrology. From the few hints that Boxer gives when discussing horary astrology (which he falsely labels judicial astrology) and elective astrology, he appears to think that you just plug in the planetary positions and the horoscopic spits out the interpretation algorithmically. Nothing could be further from the truth. 

Ptolemy writes at the beginning of the Tetrabiblos, I paraphrase, the science of the stars has two aspects, the first deals with the positions of the stars [our astronomy, his Almagest] and is precise, the second deals with their influence [our astrology, his Tetrabiblos], which is not precise. The first involves casting horoscopes and is mathematical, the second with their interpretations and is not mathematical.

If an astrologer, let us say in the sixteenth century the golden age of astrology, casts a full birth horoscope with planetary positions, houses, aspects, lunar nodes (which Boxer doesn’t deal with as being unnecessarily confusing, directions (explained wrongly by Boxer), lots of fortune (which he doesn’t even mention), etc. You have a very complex collection of material that has to be weighed up very carefully against each other. It is highly unlikely that any two professional astrologers would give the same interpretation, each arguing for their interpretation and explaining why the other interpretation is wrong. Very much of this art of interpretation is based on simplel psychology. A court astrologer, who is basically a political advisor, is going to include many psychological, political, and social factors into the interpretation that he delivers up for employer. 

I recently copyedited the translation of a chapter from a thirteenth century Arabic treatise on astrology that dealt with the interaction of the lunar nodes with the houses when practicing elective astrology. The complexity of the interpretive factors that have to be taking into consideration is mindboggling, so please don’t claim that “a classical astrologer was, first and foremost, a human calculator,” it simply isn’t true. 

If you have read this far you might come to the conclusion that my opinion of Boxer’s book is entirely negative, it isn’t. I think there is an excellent, interesting, and important book struggling to get out of a pool of confusion. Boxer’s strength is that of the data scientist and statistician and his sympathetic to astrology statistical analyses of various aspect of astrology are excellent and very much worth reading for anybody interested in the topic. His book cannot be considered a history of western astrology as he simply leaves much too much out. In fact, it is clear that those things he chooses to include are those that give him the possibility to apply his statistical analysis. Is it a “competent overview of astrology”? No, he leaves too much out, for example any competent overview of astrology must include the lunar nodes and their function in astrology and makes too many errors in his presentations of both the history of astrology and astronomy. Most importantly astrology is about the interpretation of horoscopes, a topic that he does his best to avoid.


[1] Alexander Boxer, A Scheme of HeavenThe History of Astrology and The Search for Our Destiny in Data

[2] Although he constantly refers to astrology rather than western astrology, he does state that his book doesn’t deal with other forms of astrology such as Indian or Chinese. 

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Filed under Book Reviews, History of Astrology, History of Astronomy

Is he  Moonstruck? 

Definition of moonstruck: affected by or as if by the moon: such as: mentally unbalanced

There was a total lunar eclipse on Monday 16 May. This celestial event was, of course, widely announced in advance on social media, with experts giving start and end times as well as duration. They also give detailed explanation of why, how, and when lunar eclipses take place. This meant that worldwide literally millions of people were happily, even excitedly, looking forward, weather permitting, to observing it. So, TV celebrity and aging popinjay Neil deGrasse Tyson decided to dump on all of these people when he tweeted to his 14.6 million followers the following tweet on 16 May:

Lunar eclipses are so un-spectacular that if nobody told you what was happening to the Moon you’d probably not notice at all. Just sayin’.

Ignoring, for a second, the glaring, factual inaccuracy contained in this tweet, it has to be a very serious candidate for the most mean-spirited tweet of the year if not of the decade. One has to seriously ask, why did he do this? Has he become such a desperate, attention-seeking whore that he needs to try and ruin the simple enjoyment of millions world-wide just to provoke a reaction on Twitter?

As a historian of both astronomy and astrology, I expect a man, who once upon a time in his life was an astrophysicist, not to display such ignorance, so publicly in such a spectacular manner. “Lunar eclipses are so un-spectacular…” really? “If nobody told you what was happening to the Moon you’d probably not notice at all,” only if you’ve got your head firmly entrenched in your posterior orifice.

The moon glows red over Columbus, Ohio on Sunday Source

The phenomenon of light pollution, which makes life so difficult for modern astronomers, is actually a very recent development that only became a factor in celestial observation during the course of the twentieth century. Before the eighteenth century, street lighting was confined to large towns and consisted candles or oil lamps and didn’t cause serious light pollution. Even the invention of gas street lighting in the eighteenth century, or of electric street lighting in the nineteenth had no noticeable effect on the night sky. It was first in the twentieth century with the widespread use of strong electric lighting at night that the night skies in towns and cities became so artificially bright as to obscure the night-time celestial sphere. Even then a full moon remains clearly visible for all who are not visually handicapped. 

In the millennia of human existence before the invention of street lighting, the moon was the brightest object in the sky, particularly when full, on a clear night. Lunar eclipses only occur at full moon, and if you happened to be outside in, shall we say, for example, in the eighth century CE, during full moon and the moon started to disappear finally vanishing completely behind a dark shadow, you just might happen to notice. “Just sayin’.” 

Of course, people fucking noticed! Every culture on the Earth, that existed before they discovered the scientific explanation of why lunar eclipses take place has myths, legends, and folktales to explain what happened, when the full moon suddenly started to disappear. For the Maya and the Inca in Middle America, the moon got devoured by a jaguar, which also explained the colour of the so-called blood moon. In ancient Mesopotamia, it was belived that the eclipse was the result of demons attacking the moon and that it presaged an attack upon, or even the death of the king. For the ancient Chinese a lunar eclipse was caused by a dragon biting the moon. For something they didn’t notice, people went to a lot of trouble to invent reasons to explain it.

Tyson, as per usual, doubled down on his mean-spirited tweet with a follow up:

Lunar eclipses occur on average every two or three years and are visible to all the billions of people who can see the Moon when it happens. So, contrary to what you may have been told, lunar eclipses are not rare.

Yes, Mr “I used to be an astrophysicist”, we now know the frequency of lunar eclipses, what sort of eclipse will occur, total, partial penumbral, and can predict the occurrence and duration down to the minute, but have you taken the trouble in your arrogance to ask how we acquired that knowledge? 

Tyson is one of those science communicators, who looks down his nose at the occult sciences, and if he mentions them at all, it is only to sneer at them and the gullible people who believe in them. However, it is to the Babylonian belief in astrology that we owe our original scientific knowledge of the frequency of lunar eclipses. The moon played a central role in Babylonian omen astrology and as noted above, lunar eclipses were considered to presage danger or even death to the king. Because of this, beginning in about 700 BCE the Babylonians began a series of systematic accurate observations and records of eclipses which they continued for about seven hundred years. From this accumulated data they derived the saros series an accurate predictive cycle for eclipses. To quote Wikipedia:

A series of eclipses that are separated by one saros is called a saros series. It corresponds to:

  • 6,585.321347 solar days
  • 18.029 years
  • 223 synodic months
  • 241.999 draconic months
  • 18.999 eclipse years (38 eclipse seasons)
  • 238.992 anomalistic months

The 19 eclipse years means that if there is a solar eclipse (or lunar eclipse), then after one saros a new moon will take place at the same node of the orbit of the Moon, and under these circumstances another eclipse can occur.

The saros series is still used today to predict eclipses. This is a first-class example of how science works: make observations, collect data, look for patterns, derive a law.

I could go on about full moons and lunar eclipses throughout the history of astronomy, but I think I have made my point and will just briefly mention a couple of other examples.

One of the early scientific societies, the Lunar Society of Birmingham, known popularly as The Lunatics, which included Erasmus Darwin, James Watt, Matthew Boulton, Josiah Wedgewood, and even Benjamin Franklin amongst its shifting membership over the years, derived its name from the fact that their meetings were always held at full moon, so that the members could safely find their way home. If a a lunar eclipse fell on a full moon, they would all, being amateur astronomers, have stayed at home to observe it.

As an American, one would have thought that Tyson might have mentioned one of the most famous lunar eclipse stories in history. On his fourth voyage in 1504, Columbus beached his last two remaining ships on the island of Jamaica on 25 June. The indigenous population of the island were reluctant after many months to continue feeding Columbus and his crew. He persuaded them to do so by using the ephemerides of Abraham Zacuto to predict the total lunar eclipse of 1 March 1504. 

Tyson could have used the total lunar eclipse of 16 May as a teaching moment to interest people for astronomy and its history, instead he chose to mock and ridicule those, who were looking forward to observing this celestial phenomenon. He has the cheek to call himself a science communicator, words fail me.

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Filed under History of Astrology, History of Astronomy

A Clock is a Thing that Ticks

As I have mentioned a few times in the past, I came late to the computer and the Internet. No Sinclairs, Ataris, or Commadores in my life, my first computer was a Bondi Blue iMac G3. All of which is kind of ironic, because by the time I acquired that G3, I was something of an expert on the history of computing and computing devices. Having acquired my G3, I then took baby steps into the deep waters of the Internet. My initial interest was in music websites starting with the Grateful Dead. Did I mention that I’m a Dead Head? One day I stumbled across Mark Chu-Carroll’s Good Math, Bad Math blog, which in turn introduced me to the Science Blogs collective of which it was a part. Here I discovered, amongst other, the Evolving Thoughts blog of John Wilkins. Who, more than any other, was responsible for me starting my own blog. Another blog that I started reading regularly was Uncertain Principles by the American physicist Chad Orzel, who wrote amusing dialogues explain modern physics to his dog Emmy. A publisher obviously thought they were good, they were, and they soon appeared as a book, How to Teach Physics to Your Dog (Scribner, 2010), launching his career as a writer of popular science books. This was followed by How to Teach Relativity to Your Dog (Basic Books, 2012) with the original book now retitled as How to Teach [Quantum] Physics to Your Dog. Leaving the canine world, he then published Eureka: Discovering Your Inner Scientist (Basic Books, 2014) followed by Breakfast With EinsteinThe Exotic Physics of Everyday Objects (BenBella Books, 2018). 

All of the above is a longwinded introduction to the fact that this is a review of Chad Orzel’s latest A Brief History of TimekeepingThe Science of Marking Time, from Stonehenge to Atomic Clocks[1].

Astute, regular readers might have noticed that I reviewed Davis Rooney’s excellent volume on the history of timekeeping About TimeA History of Civilisation in Twelve Clocks (Viking, 2021) back in September last year and they might ask themselves if and how the two books differ and whether having read the one it is worth reading the other? I follow both authors, and they follow each other, on Twitter and there were several exchanges during last year as to whether they were covering the same territory with their books. However, I can honestly report that if one is interested in the history of time keeping then one can read both books profitably, as they complement rather than copy each other. Whereas Rooney concentrates on the social, cultural, and political aspects of measuring time, Orzel concentrates on the physics of how time was measured.

The title of this blog post is the title of the introductory chapter of Orzel’s book. This definition I viewed with maximum scepsis until I read his explication of it:

At the most basic level a clock is a thing that ticks.

The “tick” here can be the audible physical tick we associate with a mechanical clock like the one in Union’s Memorial Chapel, caused by collision between gear teeth as a heavy pendulum swings back and forth. It can also be a more subtle physical effect, like the alternating voltage that provides the time signal for the electronic wall clock in our classrooms. It can be exceedingly fast, like the nine-billion-times-a-second oscillations of the microwaves used in the atomic clock that provides the time signals transmitted to smartphones via the internet, or ponderously slow like the changing position of the rising sun on the horizon.

In every one of these clocks, though, there is a tick: a regular repeated action that can be counted to mark the passage of time. 

I said above that what distinguishes Orzel’s book is a strong emphasis on the physics of timekeeping. To this end, the book had not one, but two interrelated but separate narratives. There is the main historical narrative in language accessible to every non-expert reader describing forms of timekeeping, their origins, and developments. The second separate narrative, presented on pages with a grey stripe on the edge, takes the willing reader through the physics and technical aspects behind the timekeeping devices described in the historical narrative. Orzel is a good teacher with an easy pedagogical style, so those prepared to invest a little effort can learn much from his explanations. This means that the reader has multiple possibilities to approach the book. They can read it straight through taking in historical narrative and physics explication as they come, which is what I did. They can also skip the physics and just read the historical narrative and still win much from Orzel’s book. It would be possible to do the reverse and just read the physics, skipping the historical narrative, but I, at least, find it difficult to imagine someone doing this. Other possibilities suggest themselves, such as reading first the historical narrative, then going back and dipping into selected explanations of some of the physics. I find the division of the contents in this way a very positive aspect of the book. 

Orzel starts his journey through time and its measurement with the tick of the sun’s annual journey. He takes us back to the Neolithic and such monuments as the Newgrange chamber tomb and Stonehenge which display obvious solar orientations. The technical section of this first chapter is a very handy guide to all things to do with the solar orbit. The second chapter stays with astronomy and the creation of early lunar, lunar-solar and solar calendars. Here and in the following chapter which deals with the Gregorian calendar reform there are no technical sections. 

In Chapter 4, The Apocalypse That Wasn’t, Orzel reminds us of all the rubbish that was generated in the months leading up to the apocalypse supposedly predicted by the Mayan calendar in 2012. In fact, all it was the end of one of the various Mayan cycles of counting days. Orzel gives a very good description of the Mayan number system and their various day counting cycles. An excellent short introduction to the topic for any teacher. 

Leaving Middle America behind, in the next chapter we return to the Middle East and the invention of the water clock or clepsydra. He takes us from ancient Egypt and the simplest form of water clock to the giant tower clock of medieval China. The technical section deals with the physics of the various systems that were developed to produce a constant flow in a water clock. In the simplest form of water clock, a hole in the bottom of a cylinder of water, the rate of flow slows down as the mass of water in the cylinder decreases. 

Chapter 6 takes us to the real tick tock of the mechanical clock from its beginnings up to the pendulum clock. Interestingly there is a lot of, well explained, physics in the narrative section, but the technical section is historical. Orzel gives us a careful analysis of what exactly Galileo did or did not do, did or did not achieve with his pendulum experiments. The chapter closes with the story how the pendulum was used to help determine the shape of the earth.

The next three chapters take as deep into the world of astronomy. For obvious reasons astronomy and timekeeping have always been interwoven strands. We start with what is basically a comparison of Mayan astronomy, with the Dresden Codex observations of Venus, and European astronomy. In the European section, after a brief, but good, section on Ptolemy and his epicycle- deferent model, we get introduced to the work of Tycho Brahe.

The rules of the history of astronomy says that Kepler must follow Tycho and that is also the case here. After Kepler’s laws of planetary motion, we arrive at the invention of the telescope, the discovery of the moons of Jupiter and the determination of the speed of light. If you want a good, accurate, short guide to the history of European astronomy then this book is for you. 

Chapter nine starts with a very brief introduction to the world of Newtonian astronomy before taking the reader into the problem of determining longitude, a time difference problem, and the solution offered by the lunar distance method as perfected by Tobias Mayer. Here, the technical section explains why the determination of longitude is a time difference problem, how the lunar distance method works, and why it was so difficult to make it work.

Of course, in a book on the history of timekeeping, having introduced the longitude problem we now have John Harrison and the invention of the marine chronometer. I almost cheered when Orzel pointed out that although Harrison provided a solution, it wasn’t “the” solution because his chronometer was too complex and too expensive to be practical. The technical section is a brief survey of the evolution of portable clocks. The chapter closes with a couple of paragraphs in which Orzel muses over the difference between “geniuses” and master craftsmen, a category into which he places both Mayer and Harrison. I found these few lines very perceptive and definitely worth expanding upon. 

Up till now we were still in the era of local time determined by the daily journey of the sun. Orzel’s next chapter takes us into the age of railways, and telegraphs and the need for standardised time for train timetables and the introduction of our international time zone system. The technical section is a fascinating essay on the problems of synchronising clocks using the telegraph and having to account for the delays caused by the time the signal needs to travel from A to B. It’s a hell of a lot more complex than you might think.

We are now firmly in the modern age and the advent of the special theory of relativity. Refreshingly, Orzel does most of the introductory work here by following the thoughts of Henri Poincaré, the largely forgotten man of relativity. Of course, we get Albert too.  The technical section is about clocks on moving trains and will give the readers brains a good workout. 

Having moved into the world of modern physics Orzel introduces his readers to the quantum clock and timekeeping on a mindboggling level of accuracy. We get a user-friendly introduction to the workings of the atomic clock. This was the first part of the book that was completely new to me, and I found it totally fascinating. The technical section explains how the advent of the atomic clock has been used to provide a universal time for the world. The chapter closes with a brief introduction to GPS, which is dependent on atomic clocks.

Einstein returns with his general theory of relativity and a technical section on why and how exactly gravity bends light. A phenomenon that famously provided the first confirmation of the general theory.

Approaching the end, our narrative takes a sharp turn away from the world of twentieth century physics to the advent and evolution of cheap wrist and pocket watches. In an age where it is taken for granted that almost everyone can afford to carry an accurate timekeeper around with them, it is easy to forget just how recent this phenomenon is. The main part of this chapter deals with the quartz watch. A development that made a highly accurate timepiece available cheaply to everyone who desired it. Naturally, the technical section deals with the physics of the quartz clock. 

The book closes with a look at The Future of Time. One might be forgiven for thinking that modern atomic clocks were the non plus ultra in timekeeping, but physicists don’t share this opinion. In this chapter Orzel describes various project to produce even more accurate timepieces.

Throughout the book are scattered footnote, which are comments on or addition to the text. The book is illustrated with grey scale drawing and diagrams that help to explicate points being explained. There is a short list of just seven recommended books for further reading. I personally own six of the seven and have read the seventh and can confirm that they are all excellent. There is also a comprehensive index.

Chad Orzel is a master storyteller and despite the, at times, highly complex nature of the narrative he is spinning, he makes it light and accessible for readers at all levels. He is also an excellent teacher and this book, which was originally a course that he teaches, would make a first-class course book for anybody wishing to teach a course on the history of timekeeping from any level from say around middle teens upwards. Perhaps combined with Davis Rooney’s About TimeA History of Civilisation in Twelve Clocks, as I find that the two books complement each other perfectly. Orzel’s A Brief History of TimekeepingThe Science of Marking Time, from Stonehenge to Atomic Clocks is a first-rate addition to the literature on the topic and highly recommendable. 


[1] Chad Orzel, A Brief History of TimekeepingThe Science of Marking Time, from Stonehenge to Atomic Clocks, BenBella Books, Dallas, TX, 2022

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Filed under Book Reviews, History of Astronomy, History of Physics