The HISTSCI_HULK was gently easing his way into Monday morning, occasionally glancing over my shoulder at my Twitter stream, when a link posted in my notifications by the Aussie AnthropoidTM, John Wilkins, caught his eye. Before I could stop him, I knew no good could come of it, he had clicked on the link and as he read the linked article from The Observer, the steam started coming out of his ears.
Romanticised Victorian painting of Horrocks making the first observation of the transit of Venus in 1639. No contemporary portraits of Horrocks survive Source: Wikimedia Commons
A new play explores the short life of Jeremiah Horrocks, whose astonishing discoveries ‘changed the way we see the universe’
This is total hyper-bollocks as old Hulky is fond of screaming, when he gets really worked up. Horrocks made some important contributions to the development of astronomy in the early seventeenth century but none of them ‘changed the way we see the universe’.
The opening paragraph is OK…
On a cloudy afternoon in England in 1639, 20-year-old Jeremiah Horrocks became the first person to accurately predict the transit of Venus and measure the distance from the Earth to the sun.
But in the next paragraph the whole think develops into a major trainwreck of astronomical proportions:
His work proved, for the first time, that Earth is not at the centre of the universe, but revolves around the sun, refuting contemporary religious beliefs and laying the foundations for Isaac Newton’s groundbreaking work on gravity.
His work did nothing of the sort, but the claim gets repeated as a direct quote from the author of the play David Sears, a couple of paragraphs further on:
Now, a new play, Horrox, will attempt to reassert Horrocks’s rightful place in history as a British genius who, according to the playwright David Sear, “changed the way we see the universe”.
“We had no idea of the scale of the universe until Jeremiah Horrocks,” said Sear. “He was the first person to prove that the Earth was not the centre of creation, destroying key precepts of Christian teachings and the primacy of a literal interpretation of the Bible in the process.”
By the time poor old Hulky got this far in the article he was incandescent.
Sears is obviously under the mistaken impression that Horrocks’ observation of the transit of Venus was the first proof that Venus orbits the Sun and that this is a proof of the heliocentric model of the cosmos. Neither of these statements are true, as regular readers of the Renaissance Mathematicus will already know.
Telescopic observations of the phases of Venus by Thomas Harriot, Simon Marius, Galileo, and the Jesuit astronomers of the Collegio Romano, all made around 1611, so twenty-eight years before Horrocks observed the transit, had proven that Venus orbits the Sun and not the Earth. This is, however, totally consistent not only with a heliocentric model, but also with a geoheliocentric model, in which several or all the other planets orbit the Sun, which in turn orbits the Earth.
Sears also gets Horrocks’ determination of the astronomical unit (AU), distance between the Earth and the Sun, wrong. He says:
“The only way you could measure the distance to the sun at the time was by getting an object to fix on, between the Earth and the sun, and then triangulating through,” said Sear.
I’m not going to go through the method in detail that Horrocks used, it occupies several pages of Albert van Helden’s excellent Measuring the Universe: Cosmic Dimensions from Aristarchus to Halley (University of Chicago Press, 1985), which I recommend if you want all the grisly details, but Horrocks did not use triangulation as claimed here by Sears but a highly speculative method based on the diameters of the planets (he had measured the diameter of Venus during the transit) and a theory of Kepler’s that the diameters of the planets was proportional to their distance from the Sun. Using this highly dubious calculation he arrived at a figure of 59 million miles, much bigger than previous determinations but still well short of the actual value of 93 million miles.
We now get some more hyper-bollocks from Sears:
In 1687, Newton acknowledged the importance of Horrocks’s observations in his Principia: “Newton wouldn’t have been able to complete his work on gravity, if Horrocks hadn’t done these observations at the time he did,” said Sear. “Newton relied on this earlier work.”
Neither Horrocks’ observations of the transit of Venus nor his determination of the AU appear anywhere in Newton’s Principia. There are a couple of very brief references to the solar parallax value of Flamsteed and Horrocks, which Newton originally rejected but then latter adopted. Beyond this Horrocks’ main contribution to Newton’s work was his model for the Moon’s orbit around the Earth, which Sears nowhere mentions. Kepler, perhaps wisely, had not included the Moon’s orbit in his elliptical model of heliocentricity. Horrocks was the first to adopt an elliptical orbit for the Moon, which Newton briefly acknowledges in passing. Newton, in his failed attempts to make the Moon fit his model of universal gravity, used Flamsteed’s values for the lunar apogees, which he states are, “adapted to the hypothesis of Horrocks.” These are literally the only references to Horrocks in the whole of the Principia. This doesn’t quite seem to fit Sears’ grandiose claims.
Sears really piles on the pathos when it comes to the posthumous publication of Horrocks’ Venus in sole visa (Venus seen on the Sun).
Despite this, Horrocks’s great treatise on the transit of Venus was nearly lost for ever. Only a Latin manuscript survived the ravages of the civil war and the Great Fire of London. Passed from one astronomer to another for 20 years after Horrocks’s death, it would not be published until 1662, in an appendage to a Polish astronomer’s work.
Firstly, I strongly suspect that there were several copies of Horrocks manuscript made by NosKepleri the group of English supporters of the Keplerian model of the cosmos founded by Horrocks. It was John Wallis, who was a contemporary of Horrocks’ at university, who sent a copy of the manuscript to that Polish astronomer, who was none other than Johannes Hevelius, Europe’s most prominent astronomer, meaning Horrocks’ text got maximum exposure. Those who have been paying attention and remember their school history lessons will have noticed that Hevelius published Venus in sole visa in 1662, whereas the Great Fire of London was first four years later in 1666. It should also be noted that the Royal Society published Horrocks’ Opera Posthuma edited by William Crabtree and John Flamsteed in 1673.
Sears now tries his hand at a bit of biography:
Horrox, which will run in Cambridge’s ADC theatre from 28 March to 1 April as part of the Cambridge Festival, begins in 1632 as Horrocks makes his way to university in the city on foot. Sear said: “At the age of 14 or 15 – no one’s quite sure – he walked to Cambridge from Lancashire, to study the stars.”
The son of a watchmaker, who was largely self-taught, Horrocks worked as a sizar while studying at Cambridge, serving his fellow students and even emptying their bedpans to pay his way. “He begged and borrowed books from the various Cambridge colleges, and left without a degree, probably because he’d run out of things to read,” said Sear.
The Aspinwalls, Horrocks maternal grandparent, with whom his father worked, were very successful and wealthy watchmakers, so it is very unlikely that Jeremiah walked from his home in Toxteth Park to Cambridge. Both the Aspinwalls and the Horrocks were highly educated and not self-taught. They were also very strict Puritans, which would have explained why he was a sizar at Cambridge. Puritan ethics dictating that if you wanted a university education you worked for it and didn’t get it served up on a plate. Horrocks is known to have enquired about the latest and best book on astronomy, which would explain Sears’ “begged and borrowed books.” It is not known why he left university without a degree.
Sears makes a last attempt in this article for the most hyper-bollocking statement possible:
At his age, understanding the maths he did, making these amazing observations on rudimentary telescopes and then drawing conclusions that overturned established religious and scientific beliefs about the nature of the universe – he was a genius and 400 years ahead of his time.”
Jeremiah Horrocks was an intelligent and astute astronomer, but he did not overturn any “established religious and scientific beliefs about the nature of the universe,” and I fail to see how he was in anyway “400 years ahead of his time.”
The pain continues. On the webpage for the playHorrox. Here Sears writes:
The arc of his life is shown in parallel with that of his main inspiration, Johannes Kepler, the Copernican astronomer- mathematician who measured the movement of the planets. Kepler, called a heretic by the world, served three Holy Roman Emperors and a Duke (and wasn’t paid for his labours by any of them).
Kepler had his religious differences with the Lutheran Church because of his liberal ecumenical views but he wasn’t called a heretic by anybody. Whilst Kepler, at times, had difficulties getting the monies due to him from the Imperial treasury, to say that “wasn’t paid for his labours by any of them” is a crass exaggeration.
Sears delivers up a splendid example of how not to do the history of science. He appears to have gathered a small collection of half facts that he doesn’t really understand and woven a third-rate fairy story out of them. Apparently, the Observer doesn’t believe in fact checking and appears to believe that its readers will swallow any old garbage.
The descriptive panel below, from the Museum of the Bible in Washington DC was posted on Twitter by the historian of Chinese astrology, Jeffrey Kotyk, who posed the question, “I wonder whether Ptolemy would have considered himself “pagan”?”
Reading through the text I have several other comments and queries, but first I will address Jeffrey’s question. Ptolemy lived in the second century CE and was an Alexandrian Greek. At that point in time the Latin word pagan from pāgānus meant “villager, rustic; civilian, non-combatant”. Only in the fourth century did early Christians begin to refer to people who practiced polytheism, or ethic religions other than Judaism as pagans. The word pagan meaning “person of non-Christian or non-Jewish faith” first entered the English language around 1400 CE, so Ptolemy would definitely not have considered himself pagan.
Also referring to Ptolemy, one of the greatest mathematical polymaths of antiquity, as “scholar of the stars” is somewhat limited, not to say strange. The text then attributes a “passion for mathematics, geography, and astronomy” to him but leaves out optics, music theory, and, of course, astrology. Strangely the opening paragraph seems to attribute those things that developed out of astronomy all to Ptolemy alone. What about all the other astronomers, geographers, mathematicians, who existed before Ptolemy, contemporaneously with him, and after him, didn’t they contribute anything?
Of the things listed, “the ability to navigate the earth, determine agricultural seasons, and organise time into days, months, and years,” only the first, navigation, can really be said to have grown out of astronomy. Systematic agriculture and with it, knowledge of the agricultural seasons predates mathematical astronomy by about six thousand years. Days are a natural phenomenon of which homo sapiens would have been aware since they first evolved, although I assume that animals are also aware of days.
The same of course applies to the year of which every sentient creature that lives long enough becomes aware without any help from astronomers. Astronomers, of course, determined how many days there are in a solar year, but they took long enough to get it right.
Months are a completely different problem. If we are referring to lunar months, and after all the word month derives from the word for moon, then the same applies, as to days and years. Although the astronomers had the problem of how to align lunar months with solar years, they don’t fit at all, as became obvious fairly early on and you don’t really want to know about the history of early calendrics. Trust me you don’t, that way lies madness! If, however, we are referring to our current system of twelve irregular months fitted into the solar year, then, although the astronomers played a role, they are largely the result of political decisions.
As a result, the Church was able to use scripture and science to identify and commemorate holy days such as Easter.
Knowing something about the history of the determination of the so-called movable Christian holy days, I cringed when I read this very short paragraph. I will pass over it with the simple comment that these holy days are determined not identified and that determination was a very complex religio-political process stretching over several centuries and astronomers had very little to do with it, other than providing the date of the vernal equinox, which in early days was falsely considered to be the 25 March and providing lunar tables.
I developed the most advanced geocentric model of the universe, at which I believed Earth was the center.
This sentence is, of course, wonderfully tautological, geocentric meaning the earth is at the centre. The sentence is also, as Blake Stacey pointed out on Mastodon after I posted this, “not only redundant, it’s not even grammatical.”
My geocentric model of the universe was accepted until Copernicus, Galileo, and others introduced a heliocentric model.
Ptolemy’s model was extensively modified by a succession of Arabic astronomers and “the most advanced geocentric model of the universe” before Copernicus was that of the Austrian, Renaissance astronomer, Georg von Peuerbach (1423–1461), whose system Copernicus studied as a student.
Galileo, who in reality contributed very little to the heliocentric model or to its acceptance, in fact by rejecting supralunar comets, which orbited the sun, and ignoring Kepler’s laws of planetary motions, he explicitly hindered that acceptance, gets a name check with Copernicus, whereas, Kepler, whose heliocentric model was the one that actually became accepted gets dumped under others!
This is a more than questionable piece of museum signage and I wish I could blame it on the religious nature of the museum but such ill researched signage is unfortunately too common.
The so-called European Age of Discovery is usually considered to have begun as adventurers from the Iberian Peninsular began to venture out into the Atlantic Ocean in the fifteenth century, reaching a high point when Bartolomeu Dias (c. 1450–1500) first rounded the southern tip of Africa in 1488 and Christopher Columbus (1441–1506) accidentally ran into the Americas trying to reach the Indies by sailing west. Those who made successful voyages, basically meaning returned alive, passed on any useful information they had garnered to future adventurers. It would be first at the end of the sixteenth century that the governments of the sea faring nations first began to establish central, national schools of navigation that accumulated such navigational and cartographical knowledge, processed it, and then taught it to new generations of navigators. Through out the sixteenth century individual experts were hired to teach these skills to individual groups setting out on new voyages of discovery.
In England this function was filled by Thomas Harriot (c. 1560–1621), who not alone taught navigation and cartography to Walter Raleigh’s sailors but also sailed with them to North America, making him that continent’s first scientist. John Dee (1527–c. 1608) supplied the same service to the seamen of the Muscovy Trading Company, although, unlike Harriot, he did not sail with them. Richard Hakluyt (1553–1616), a promotor of voyages of discovery, collected, collated, and published much information on all the foreign voyages but only passed this information on in manuscript to Raleigh.
In the 1580s Dee disappeared off to the continent, Harriot after returning from the Americas disappeared into the private service of Henry Percy, 9th Earl of Northumberland (1564–1632) and Hakluyt, a clergyman, after returning from government service in Paris, investigating the voyages of the continental nations, went into private service. In Paris, in 1584, Hakluyt noted that there was a lectureship for mathematics at the Collège Royal and wrote a letter to Sir Francis Walsingham (c. 1532–1590), the Queen’s principal secretary, the most powerful politician in England and a major supporter of voyages of discovery. In his letter, Hakluyt, urged Walsingham to establish a lectureship for mathematics at Oxford University for scholars to study the theory of navigation and the application of mathematics to its problem, and a public lectureship of navigation in London to educate seamen.
Walsingham undertook nothing and the demand grew loud for some form of public lectureship in mathematics to supply the necessary mathematics-based information in navigation and cartography to English seamen. In 1588, a private initiative was launched by Sir Thomas Smith (c. 1558–1625), Sir John Wolstenholme (1562–1639), and John Lumley, 1st Baron Lumley and Thomas Hood (1556–1620) was appointed Mathematicall Lecturer to the Citie of London.
Thomas Hood, baptised 23 June 1556, was the son of Thomas Hood a merchant tailor of London. He entered Merchant Taylors’ School in 1567 and matriculated at Trinity College Cambridge in 1573. He graduated BA c. 1578, was elected a fellow of Trinity and graduated MA in 1581. He was granted a licence to practice medicine by Cambridge University in 1585 and, as already mentioned, lecturer for mathematics in London in 1588. This appointment and his subsequent publications indicate that he was a competent mathematical practitioner but from whom he learnt his mathematics is not known.
Before turning to Hood’s lectureship and the associated publications, it is interesting to look at those who sponsored the lectureship. Thomas Smith was the son and grandson of haberdashers and like Hood attended Merchant Taylors School, entering in 1571.
Source: Wikimedia Commons
He entered the Worshipful Company of Haberdashers and the Worshipful Company of Skinners in 1580 and went on to have an impressive political career in the City of London, occupying a series of influential posts over the years. His father had founded the Levant Trading Company and Thomas was the first governor of the East India Company, when it was founded in 1600, but only held the post for four months having fallen into suspicion of being involved in the Essex Rebellion. He was reappointed governor in 1603 and with one break in 1606-7 remained in the post until 1621. Later, he was a subscriber to the Virginia Company, as was Hood, and obtained its royal charter in 1609 and became the new colony’s treasurer making him de facto non-resident governor until his resignation in 1620. His grandfather had founded the Muscovy Company and Smith also became involved in that. It’s easy to see why Smith was motivated to promote a lectureship in practical mathematics.
John Wolstenholme was cut from a very similar cloth to Smythe, son of another John Wolstenholme a customs’ official in London, he became a rich successful merchant at an early age.
An effigy of Sir John Wolstenholme (1562 – 1639), carved by master stone mason to Charles I, Nicholas Stone, for the old St John the Evangelist Church, Great Stanmore Source: Wikimedia Commons
Like Smythe a founding member of both the East India and Virginia Companies, he was also a strong supporter of the attempts to find the North-West Passage. He fitted out several of the expeditions, Henry Hudson (c. 1556–disappeared 1611) named Cape Wolstenholme, the extreme northern most point of the province of Quebec after him. William Baffin (c. 1584–1622) named Wolstenholme Island in Baffin Bay after him.
John Lumley was slightly different to the two powerful merchants, a member of the landed gentry, he was an art collector and bibliophile.
John Lumley 1st Baron Lumley portrait attributed to Steven van de Meulen Source: Wikipedia Commons
In the same year 1582, that the three founded Hood’s mathematical lectureship, Lumley founded with Richard Caldwell (1505?–1584), a physician, the Lumleian Lectures. Initially intended to be a weekly lecture course on anatomy and surgery they had been reduced to three lectures a year by 1616. They still exist as a yearly lecture on general medicine organised by the Royal College of Physicians.
The mathematical lectures finally came into being in 1588, following the threat of the Spanish Armada in that year. The original intended audience consisted of the captains of the city’s train bands or armed militia but also open to the ship’s captains, who rapidly became the main audience. The lectures were on geometry, astronomy, geography, hydrography, and the art of navigation. The lectures were originally held in the Staplers’ Chapel in Leadenhall Street but later moved to Smith’s private residence in Gracechurch Street, where he had held the inaugural lecture. In total Hood lectured for four years and later he attempted to obtain license to practice medicine in London from the Royal College of Physicians. This was denied him due to his inadequate knowledge of Galen. He was finally granted a conditional licence in 1597 and sometime after that he moved to Worcester, where he practiced medicine until his death in 1620.
His first publication was his inaugural lecture under the title, A COPIE OF THE SPEACHE:MADE by the Mathematicall Lecturer, unto the Worshipful Companye present. At the house of the Worshipfull M. Thomas Smith, dwelling in Gracious Street: the 4. of November, 1588. T. Hood. Imprinted at London by Edward Allde.
In this lecture he set out the reasons for the establishment of the lectureship and emphasised the importance of mathematics to people in all walks of life. He also sketched a history of mathematics from Adam down to his own times. The lectures were obviously successful, and he was urged to publish them, which he did to some extent.
His next major publication was The VSE OF THE CELESTIAL GLOBE IN PLANO; SET FOORTH IN TWO HEMISPHERES: WHEREIN ARE PLACED ALL THE MOST NOTa[ble] Starres of the heauen according to their longitude, latitude, magnitude, and constellation: Whereunto are annexed their names, both Latin Greeke, and Arabian or Chaldee; … (1590) They don’t write title like that anymore.
There is also an advert explaining that one can buy the hemispheres from the author at his address. He explains that he has presented the celestial spheres in plano in order to make it easier for seamen to read off the longitude and latitude of stars than it would be from a small globe. His beautifully coloured planispheres are the first printed planispheres in England. A seaman who bought Hood’s planispheres no longer needed to buy a celestial globe or planispheric astrolabe.
Thomas Hood celestial sphere in plano northern hemisphere SourceThomas Hood celestial sphere in plano southern hemisphere Source
Before he published The Use of the Celestial Globe, he published a pamphlet on the use of a novel cross-staff that he had devised. Hood’s cross staff was a significant step towards the back staff, which eliminated the necessity of looking directly into the sun to take readings. This was so successful that he was urged to produce a similar pamphlet for the Jacobs Staff, and he obliged publishing two pamphlets in 1590,The vse of the two Mathematicall instrumentes, the crosse Staffe … and the Iacobes Staffe in two parts with separate titles. The pamphlets attracted the attention of the Lord Admiral, Lord Howard (1536–1624), who became his patron. Hood dedicated a second edition of the double pamphlet to Howard in 1596.
Thomas Hood cross staff Source: Wikimeia Commons
Hood’s finally publication of 1590 was a translation of The Geometry of Petrus Ramus, THE ELEMENTES OF GEOMETRIE: Written in Latin by that excellent Scholler, P. Ramus, Professor of the Mathematical Sciences in the Vuniverstie of Paris: And faithfully translated by Tho. Hood, Mathematicall Lecturer in the Citie of London. Knowledge hath no enemie but the ignorant.
Like many others in this period, Hood’s books were written in the form of dialogues between a master and a student, and he continued in this form with his next book on the use of globes in 1592. Serial production printed celestial and terrestrial globes had been in existence on the continent since Johannes Schöner (1477–1547) had produced the first pair in the second decade of the sixteenth century but none had been produced in England. Probably at the suggestion of John Davis (c. 1550–1605), a leading Elizabethan navigator, the London merchant William Sanderson (c. 1548–1638) commissioned and sponsored the instrument maker Emery Molyneux (died 1598) to produce the first English printed pair of globes, in the early 1590s. The globe gores were printed by the Flemish engraver Jodocus Hondius (1563–1612), at the time living in exile in London, who would go on to found one of the two largest publishing houses for maps and globes in Europe in the seventeenth century.
Sanderson request Hood to write a guide to the use of such globes and Hood complied publishing his THE VSE of both the Globes, Celestiall,and Terrestriall, most plainely deliuered in forme of a Dialogue. Containing most pleasant, and profitableconclusions forthe Mariner, and generally for all those, that are addicted to these kinde of mathematicall instrumentes in 1592.
In the same year Hood edited a new edition of the popular navigation manual A Regiment for the Sea by William Bourne (c. 1535–1582) which was originally published in 1574. Hood edition would be printed in two further editions.
In 1598 Hood published his The Making and Use of the Geometricall Instrument called a sector, the first printed account of this versatile instrument, which almost certainly informed the much more extensive account of the sector by Edmund Gunter (1581–1626) published in 1624.
Astronomical sector, 16th-century artwork. This device was used to make accurate observations of the position of an object in the sky, such as a star or the Sun. The sight (lower left) would be used to line up the hinged rulers (right) with the object being observed. The position of the star was recorded as an angle from the vertical or horizontal, as read from the curved area (left). Artwork from ‘The making and use of the geometricall instrument, called a sector’ (1598) by Thomas Hood.
Hood’s most peculiar publication was an English translation of the Elementa arithmeticae, logicis legibus deducta in usum Academiae Basiliensis. Opera et studio Christiani Urstisii originally published in 1579. Christiani Urstisii was the relatively obscure Swiss mathematician, theologian, and historian Christian Wurstisen (1544–1588).
Why Hood stopped his lectures after four years in nor clear, he seems to have been both popular and successful and later Smith and Wolstenholme would later employ Edward Wright (1561–1615), who we will meet again in the next post in this series, through the East India Company in the same role. However, after he ceased lecturing Hood continued to sell instruments and his hemisphere charts. Hood’s lectureship was an important step towards the professional teaching of navigation to mariners in England at the end of the sixteenth century.
The Conversations banner states, Academic rigour, journalistic flair. Apparently, that bit about academic rigour doesn’t apply when an astronomer tries her hand at the history of science.
The article is actually about sonification, which Ms Nazé turns her attention to rather briefly at the end of her essay. Sonification is a new technique in astronomy of turning satellite astronomical data into sound making the data available to blind people (as this article explains) but possibly revealing other aspects of the data not revealed by visualisation of the data.
There are other explanatory articles, both better than Nazé’s effort, here, and here
However, Ms Nazé thought she could give her essay on the topic a different spin by prefacing her comments on sonification with a look at the historical harmony of the spheres, a topic that should be well known to regular readers of this blog, and it is here that she caused old HULKY such anguish and drove him to distraction. Let us examine her excursion into the chilly waters of the history of science:
Music and astronomy: an ancient love story
Music and space might not seem like natural partners – after all, no air means no sound. But to our forebears, the links were obvious. In Ancient Greece, thinkers such as Aristotle believed the Earth lay at the centre of the universe. This didn’t make it an unchanging ideal, however: to the ancients, terrestrial phenomena were ever-changing, a reflection of our planet’s imperfection. The sky, by contrast, was seen as immutable and eternal, and so worthy of emulation.
Well, it might be true that “no air means no sound”, but our forebears had no idea that there was no air in the heavens. Not just Aristotle, but it was obvious to almost anybody with half a brain that the Earth lies immobile at the centre of the visible heavens. It’s actually very, very difficult to prove otherwise, without a couple of thousand years of evolution of astronomy.
There is more:
A few of the stars moved with respect to others – so-called “planets” in the etymological sense (for planet means “wandering star”). The ancients knew of seven of them: Mercury, Venus, Mars, Jupiter and Saturn, plus the Sun and the Moon. That number would go on to inform the composition of the days of the week as well as of the music scale.
Planet does not mean “wandering star”, it simply means wanderer. The Greek expression for wandering stars is asteres planetai,” from planasthai “to wander, asteres is of course stars. If you are trying to prove your linguistic sophistication, it pays to get things right.
The next sentence is simply bullshit. There was an intense discussion on HASTRO_L recently as to where the seven-day week comes from. The answer is we don’t actually know but it certainly predates the astrological week, which gave the weekdays their names based on the planetary hour that begins each day, which seems to be what Ms Nazé is referencing. Ms Nazé obviously doesn’t know very much about music as the seven-tone scale, most commonly used in western music, is only one of numerous music scales with varying numbers of tones. The Pythagorean scale, which is actually from ancient Mesopotamia and falsely attributed to Pythagoras is a twelve-tone scale. Very widespread throughout the world are pentatonic scales with five-tones. The oldest form of Greek music was based on the tetrachord, a scale of just four-tones. I could go one…
On a sidenote although Ms Nazé links to a rather bizarre website about Pythagorean music theory, as error strewn as her own efforts, nowhere in her excurse on harmony of the spheres does she mention the Pythagoreans, who actually invented the concept
Ms Nazé can be very inventive:
Indeed, to the Ancient Greeks, each planet hung on a sphere, which, in turn, revolved around the Earth. Given that movement emitted sound here – such as when two objects rubbed against one another or when feet hit the ground – it made sense that the moving spheres in the cosmos should also produce sounds.
I have no idea where she got this idea, and although I’ve read quite a lot about the harmony of the spheres, I’ve never come across an explanation remotely like this, so I must assume she simply made it up. Especially, as according to most accounts the music of the spheres could not be heard by normal mortals.
Contrary to those heard on Earth, these were thought to be perfect, prompting the Ancients to use the stars as a template for terrestrial music. [my emphasis]
They didn’t! What the Pythagoreans did was to apply the concept of terrestrial music to the planets.
This is why in the Middle Ages astronomy and music were grouped together in the quadrivium, which also included arithmetic and geometry, and lay the foundations of the liberal arts education.
Astronomy and music, the theory of proportions, were both part of the quadrivium–arithmetic, geometry, music, astronomy–but arithmetic and music were paired, and geometry and astronomy were paired. Music was arithmetic in motion, and astronomy was geometry in motion.
But how to weave together notes and planets? This is admittedly the trickiest part. Some scientists have linked a sound’s pitch to a planet’s distance, others with its speed. To add more intricacy to the compositions, at the time perceptions differed in the relative positions of the planets in the solar system.
Of course, the use of the term scientist is totally anachronistic, the people in question are astronomers or philosophers. Once again, I fear that Ms Nazé is simply making things up. I know of no great technical discussion, as to just how the music of the spheres was created.
The German astronomer Johannes Kepler (1571-1630) was one of the scientists to most notably draw on this Ancient Greek concept of “music of the spheres” (also known as musica universalis) to map out the planetary system.
She got something right! But it doesn’t last
Kepler’s findings would catapult us into the modern cosmos: he determined that not only was the Sun not at the centre of the solar system – as Nicolaus Copernicus had proposed in the previous century – but also that the planets revolved around it in an elliptical rather than circular motion.
[“…he determined that not only was the Sun not at the centre of the solar system…” Wow! Some really bad copy editing here. That should, of course, read the Earth. Even corrected it’s not true. Kepler, like everybody else, couldn’t actually deliver proof of the cosmos was heliocentric.]
Addendum 5 February: As can be seen in the comments a debate has developed in the comments about Ms Nazé’s statement and my interpretation of it, which I now believe to be wrong and have placed in square brackets. I think she is correctly saying that Kepler removed the Sun from the centre of a circle, where Copernicus had placed it and positioned at at one focus of an ellipse. It is actually correct to point out that in Copernicus’ system the Sun is not actually at the centre of the circle but, for mathematical reasons, slightly offset and in reality his system is strictly taken not heliocentric but heliostatic. However, as most people are not actually aware of this, I’m going to be generous and not criticise her for saying that Copernicus had placed the Sun at the centre of the solar system.
As a result, distance and speed changed in the course of the orbit. It became impossible to associate a single note with a single planet, driving him to the conclusion that planets sung melodies.
Here we have something that gets repeated ad nauseum on the Internet. By showing that the planetary orbits were ellipses, Kepler did not show that “distance and speed changed in the course of the orbit.” This had been known for centuries, as could be demonstrated by any good set of ephemerides. What he did, with his elliptical orbits, was to show why this was the case.
The bit about single notes and melodies is once again made up. In his Harmonice Mundi, Kepler investigated every possible arithmetical ratio of all aspects of a planets orbit, looking for harmonic ratios–octave, thirds, fifths etc. Out of these he then constructed melodies for each planet.
Of course, all this had to remain harmonious: for a planet to produce a melody, the highest sound had to chime well with the lowest. Eventually, Kepler abandoned his tunes to concentrate on spelling out his third law on planetary motion in 1619. [my emphasis]
It was at this point, that the HISTSCI_HULK, who had become increasingly agitated as he perused Ms Nazé’s essay. Let out the scream of anguish with which I opened this post.
Let us repeat her sentence:
Eventually, Kepler abandoned his tunes to concentrate on spelling out his third law on planetary motion in 1619.
It would appear that Ms Nazé is not aware of the name of Kepler’s third law or where it originated. The third law is the Harmony Law and is the high point of the Harmonice Mundi! Far from abandoning his tunes, Kepler saw the discovery of his Harmony Law, as validation of his investigations of the harmony of the spheres.
Way back at the beginning of November I wrote what was intended to be the first of a series of posts about English mathematical practitioners, who were active at the end of the sixteenth and the beginning of the seventeenth centuries. I did not think it would be two months before I could continue that series with a second post, but first illness and then my annual Christmas trilogy got in the way and so it is only now that I am doing so. The subject of this post is a man for whom a whole series of mathematical instruments are named, Edmund Gunter (1581–1626).
Unfortunately, as is all to often the case with Renaissance mathematici, we know almost nothing about Gunter’s origins. His father was apparently a Welshmen from Gunterstown, Brecknockshire in South Wales but he was born somewhere in Hertfordshire sometime in 1581. Obviously from an established family he was educated at Westminster School as a Queen’s Scholar i.e., a foundation scholar (elected on the basis of good academic performance and usually qualifying for reduced fees). He matriculated at Christ Church Oxford 25 January 1599 (os). He graduated BA 12 December 1603 and MA 2 July 1606. He took religious orders and proceeded B.D. 23 November 1615. He was appointed Rector of St. George’s, Southwark and of St Mary Magdalen, Oxford in 1615, he retained both appointments until his death.
Whilst still a student in 1603, he wrote a New Projection of the Sphere in Latin, which remained in manuscript until it was finally published in 1623. This came to the attention of Henry Briggs (1561–1630), who had been appointed professor of geometry at the newly founded Gresham College in 1596, and as such was very much a leading figure in the English mathematical community. Briggs was impressed by the young mathematician befriending him and becoming his mentor. The two men spent much time together at Gresham College discussing topics of practical mathematics. In 1606, Gunter developed a sector, about which later, and wrote a manuscript describing it in Latin, without a known title. This circulated in manuscript for many years and was much in demand. Gunter gave into that demand and finally published it also in 1623.
When the first Gresham professor of astronomy, Edward Brerewood (c. 1556–1613) died 4 November 1613, Briggs recommended Gunter as his successor. However, Thomas Williams another Christ Church graduate, of whom little is known, was appointed just seven days later 11 November 1613. When Williams resigned from the post 4 March 1619, for reasons unknown, Briggs once again supported his friend for the position, this time with success. Gunter was appointed just two days later, 6 March 1619. Like his two rectorships, he retained the Gresham professorship until his death.
Gresham College, engraving by George Vertue, 1740 Source: Wikimedia Commons
Apparently, he was already spending so much time at Gresham College before being appointed that when the mathematician William Oughtred (1574–1660) visited Henry Briggs there in 1618, he thought that Gunter was already professor there.
In the Spring 1618 I being at London went to see my honoured friend Master Henry Briggs at Gresham College: who then brought me acquainted with Master Gunter lately chosen Astronomical lecturer there, and was at that time in Doctor Brooks his chamber. With whom falling into speech about his quadrant, I showed him my Horizontal Instrument. He viewed it very heedfully: and questioned about the projecture and use thereof, often saying these words, it is a very good one. And not long after he delivered to Master Briggs to be sent to me mine own Instrument printed off from one cut in brass: which afterwards I understood he presented to the right Honourable the Earl of Bridgewater, and in his book of the sector printed six years after, among other projections he setteth down this.
Gunter and Oughtred would go on to become firm friends.
William Oughtred engraving by Wenceslaus Hollar Source: Wikimedia Commons There are apparently no portraits of Briggs or Gunter
We now have the known details of the whole of Gunter’s life and can turn our attention to his mathematical output but before we do so there is an anecdote from Seth Ward (1617–1689), another mathematician and astronomer, concerning a position that Gunter did not get. In 1619, Henry Savile (1549–1622) established England’s first university chairs for mathematics the Savilian chairs for geometry and astronomy at Oxford. Savile’s first choice for the chair of geometry was Edmund Gunter and he invited him to an interview, according to John Aubrey (1626–1697) relating a report from Seth Ward:
[Gunter] brought with him his sector and quadrant, and fell to resolving triangles and doing a great many fine things. Said the grave knight [Savile], “Do you call this reading of geometry? This is showing of tricks, man!”, and so dismissed him with scorn, and sent for Henry Briggs.
Henry Briggs travelled all the way to Edinburgh to meet the inventor of this new calculating tool. After discussion with Napier, he received his blessing to produce a set of base ten logarithms. His Logarithmorum chilias prima, which were publish in London sometime before Napier’s death in 1617.
Many people don’t realise that Napier’s logarithmic tables were not straight logarithms but logarithms of trigonometrical functions. These are of particular use for astronomers and navigators. It is almost certainly through Brigg’s influence that Gunter’s first publication was a set of base ten, seven figure logarithmic tables of sines and tangents. His Canon Triangulorum sive Tabulae Sinuum et Tangentium Artificialum was published in Latin in 1620. An English translation was published in the same year. The terms sine and tangent were already in use, but it was Gunter, who introduced the terms cosine and cotangent in this publication. Later, on his scale or rule he introduced the short forms sin and tan.
In 1623, Gunter finally published his New Projection of the Sphere written in his last year as an undergraduate. He also published his most important book, Description and Use of the Sector, the Crosse-staffe and other Instruments. This was one of the most important guides to the use of navigational instruments for seamen and became something of a seventeenth century best seller in various forms. David Waters in his The Art of Navigation say this, ” Gunter’s De Sectore & Radio must rank with Eden’s translation of Cortes’s Arte de Navegar and Wright’s Certain Errors as one of the three most important English books ever published for the improvement of navigation.” [1]
Waters opposite page 360
His various publications were collected into The Works of Edmund Gunter, which went through six editions by 1680. Each edition having extra content by other authors. Isaac Newton (1642-1727) bought a copy of the second edition. The title page of the fifth edition is impressive:
The Workers of Edmund Gunter 5th ed. Title page with diagrams of the sector on the fly leaf
The Works of Edmund Gunter: Containing the description and Use of the Sector, Cross-staff, Bow, Quadrant, And other Instruments. With a Canon of Artificial Sines and Tangents to a Radius of 10.00000 parts, and the Logarithms from Unite to 100000: The Uses whereof are illustrated in the Practice of Arithmetick, geometry, Astronomy, Navigation, Dialling and Fortification. And some Questions in Navigation added by Mr. Henry Bond, Teacher of mathematicks in Ratcliff, near London. To which is added, The Description and Use of another Sector and Quadrant, both of them invented by Mr. Sam. Foster, Late Professor of Astronomy in Gresham Colledge, London, furnished with more Lines, and differing from those of Me. Gunter′s both in form and manner of Working. The Fifth Edition, Diligentyl Corrected, and divers necessary Things and Matters (pertinent thereunto) added, throughout the whole work, not before Printed. By William Leybourne, Philomath. London Printed by A.C. for Francis Eglesfield at the Marigold in St. Pauls Church-yard. MDCLXXIII.
The sector, also known as a proportional compass or military compass, was a major calculating instrument in use from the end of the sixteenth century until the nineteenth century. It is an instrument consisting of two rulers of equal length joined by a hinge. A number of scales are inscribed upon the instrument which facilitate various mathematical calculations. It was used for solving problems in proportion, multiplication, and division, geometry, and trigonometry, and for computing various mathematical functions, such as square and cube roots. Its several scales permitted easy and direct solutions of problems in gunnery, surveying and navigation. The sector derives its name from the fourth proposition of the sixth book of Euclid, where it is demonstrated that similar triangles have their like sides proportional. (Wikipedia)
The sector has many alleged inventors. The earliest was Fabrizio Mordente (1532–c. 1608). The invention is often credited to Galileo (1564–1642), who marketed a very successful variant in the early seventeenth century, including selling lessons and an instruction manual in its use. However, Galileo’s instrument was a development of one created by Guidobaldo dal Monte (1545–1607). It is not known if dal Monte developed the device independently or knew of Mordent’s. Thomas Hood (1556–1620) appear to have reinvented the instrument, a description of which he published in his Making and Use of the Sector, 1596.
Waters opposite page 345
Gunter developed Hood’s instruments adding addition scales, including a scale for use with Mercator’s new projection of the sphere.
Water opposite page 361Waters page 361
The French Jewish scholar, Levi ben Geshon (1288–1344), published the first description of the cross staff or Jacob’s staff, used in astronomy, surveying, and navigation, in his Book of the Wars of the Lord (originally in Hebrew but also translated into Latin).
Gunter image of a cross staff
Gunter’s book also describes the Gunter Quadrant, basically a horary quadrant for telling the time by taking the altitude of the sun but with some additional functions.
Gunter’s most popular instrument was his scale. The Gunter scale or rule was a rule containing trigonometrical and logarithmic scales, which could be used with a pair of dividers to carry out calculations in astronomy and in particular navigations. The Gunter scale is basically a sector folded into a straight line without the hinge.Sailors simply referred to the rule as a Gunter. William Oughtred would go on to place two Gunter rules next to each other thus creating the slide rule and eliminating the need for dividers to carry out the calculations.
Gunter scale front sideGunter scale back side
In 1622, Gunter engraved a new sundial at Whitehall, which carried many different dial plates supplying much astronomical data. At the behest of Prince Charles, he wrote and published an explanation of the dials, The Description and Use of His Majesties Dialsin Whitehall, 1624. The sundial was demolished in 1697.
Gunter’s most well-known instrument was his surveyor’s chain, which became the standard English Imperial chain. 100 links and 22 yards (66 feet) long, there are 10 chains in a furlong and 80 chains to a mile.
Although Gunter invented, designed, and described the use of several instruments, he didn’t actually make any of them. All of his instruments were produced by the London based, instrument maker Elias Allen (c. 1588–1652). Allen was born in Kent of unknown parentage and was apprenticed in 1602 to London instrument maker Charles Whitwell (c. 1568–1611) in the Grocer’s Company, serving his master for nine years. Following Whitwell’s death in 1611, Allen set up his own business. He rapidly became the foremost instrument maker in London, working mostly in brass, but occasionally in silver. He became very successful and made instruments for various aristocratic patrons and both James I and Charles I. Allen also produced the engravings in Gunter’s books, using them also as advertising in his shop.
He worked closely with various mathematicians including both Oughtred and Gunter. His workshop became a meeting place for discussion amongst mathematical practitioners. He was the first London instrument maker, who could make a living from just making instruments without working on the side as a map engraver or surveyor. His master Whitwell subsidised his income as a map engraver. He rose in status in the Grocers’ Company, becoming its treasurer in 1636 and its master for eighteen months in 1637-38. Over the years many of his apprentices became successful instrument maker masters in the own right, most notably Ralph Greatorex (1625–1675), who was associated with Oughtred, Samuel Pepys, John Evelyn, Samuel Hartlib, Christopher Wren, Robert Boyle, and Jonas Moore, the English scientific elite of the time.
Allen had the distinction of being one of the few seventeenth-century artisans to have his portrait painted. The Dutch artist Hendrik van der Borcht the Younger (1614–1676) produced the portrait, now lost, in about 1640. It still exists as an engraving done by the Bohemian engraver, Wenceslaus Hollar (1607–1677).
Edmund Gunter was not a mathematician as we understand the term today, but a mathematical practitioner, who exercised a large influence on the practical side of astronomy, navigation, and surveying in the seventeenth century through the instruments that he designed and the texts he wrote explaining how to use them.
[1] David Walters, The Art of Navigationin England in Elizabethan and Early Stuart Times, Yale University Press, 1958 p. 359
Using the simplest and widest definition as to what constitutes a scientific instrument, it is literally impossible to say who first created, devised, used a scientific instrument or when and where they did it. My conjecture would be that the first scientific instrument was some sort of measuring device, a rod, or a cord to standardise a unit of measurement, almost certainly taken from the human body: a forearm, the length of a stride or pace, maybe a foot, a unit that we still use today. It is obviously that all the early great civilisation, Indus valley, Yellow River, Yangtze River, Fertile Crescent and so on, definitely used measuring devices, possibly observational devices, instruments to measure or lay out angles, simple compasses to construct circles, all of them probably as much to do with architecture and surveying, as with anything we might now label science.
This is the Royal cubit rod of Amenemope – a 3320-year-old measuring rod which revealed that Egyptians used units of measurement taken from the human body. The basic unit was the cubit – the length from the elbow to the tip of the middle finger, about 45cm. Source: British Museum
Did the early astronomers in China, India, Babylon use some sorts of instruments to help them make their observations? We know that later people used sighting tubes, like a telescope without the lenses, to improve the quality of their observations, did those first astronomers already use something similar. Simple answer, we don’t really know, we can only speculate. We do know that Indian astronomers used a quadrant in their observation of solar eclipses around 1000 BCE.
Turning to the Ancient Greeks we initially have a similar lack of knowledge. The first truly major Greek astronomer Hipparkhos (c. 190–c. 120 BCE) (Latin Hipparchus) definitely used astronomical instruments but we have no direct account of his having done so. Our minimal information of his instruments comes from later astronomers, such as Ptolemaios (c. 100–c. 170 CE). Ptolemaios tells us in his Mathēmatikē Syntaxis aka Almagest that Hipparkhos made observations with an equatorial ring.
The easiest way to understand the use of an equatorial ring is to imagine a ring placed vertically in the east-west plane at the Earth’s equator. At the time of the equinoxes, the Sun will rise precisely in the east, move across the zenith, and set precisely in the west. Throughout the day, the bottom half of the ring will be in the shadow cast by the top half of the ring. On other days of the year, the Sun passes to the north or south of the ring, and will illuminate the bottom half. For latitudes away from the equator, the ring merely needs to be placed at the correct angle in the equatorial plane. At the Earth’s poles, the ring would be horizontal. Source: Wikipedia
At another point in the book Ptolemaios talks of making observations with an armillary sphere and compares his observations with those of Hipparkhos, leading some to think that Hipparkhos also used an armillary sphere. Toomer in his translation of the Almagest say there is no foundation for this speculation and that Hipparkhos probably used a dioptra. [1]
Ptolemaios mentions four astronomical instruments in his book, all of which are for measuring angles:
1) A double ring device and
Toomer p. 61
2) a quadrant both used to determine the inclination of the ecliptic.
Toomer p. 62
3) The armillary sphere, which he confusingly calls an astrolabe, used to determine sun-moon configurations.
Toomer p. 218
4) His parallactic rulers, used to determine the moon’s parallax, which was called a triquetrum in the Middle Ages.
Toomer p. 245
Ptolemaios almost certainly also used a dioptra a simple predecessor to the theodolite used for measuring angles both in astronomy and in surveying. As I outlined in the post on surveying, ancient cultures were also using instruments to carry out land measuring.
Graphic reconstruction of the dioptra, by Venturi, in 1814. (An incorrect interpretation of Heron’s description) Source: Wikimedia Commons
Around the same time as the armillary sphere began to emerge in ancient Greece it also began to emerge in China, with the earliest single ring device probably being used in the first century BCE. By the second century CE the complete armillary sphere had evolved ring by ring. When the armillary sphere first evolved in India is not known, but it was in full used by the time of Āryabhata in the fifth century CE.
Armillary sphere at Beijing Ancient Observatory, replica of an original from the Ming Dynasty
A parallel development to the armillary sphere was the celestial globe, a globe of the heavens marked with the constellations. In Greece celestial globes predate Ptolemaios but none of the early ones have survived. In his Almagest, Ptolemaios gives instruction on how to produce celestial globes. Chinese celestial globes also developed around the time of their armillary spheres but, once again, none of the early ones have survived. As with everything else astronomical, the earliest surveying evidence for celestial globes in India is much later than Greece or China.
The Farnese Atlas holding a celestial globe is the oldest known surviving celestial globe dating from the second century CE Source: Wikimedia Commons
In late antiquity the astrolabe emerged, its origins are still not really clear. Ptolemaios published a text on the planisphere, the stereographic projection used to create the climata in an astrolabe and still used by astronomers for star charts today. The earliest references to the astrolabe itself are from Theon of Alexandria (c. 335–c. 414 CE). All earlier claims to existence or usage of astrolabes are speculative. No astrolabes from antiquity are known to have survived. The earliest surviving astrolabe is an Islamic instrument dated AH 315 (927-28 CE).
North African, 10th century AD, Planispheric Astrolabe Khalili Collection via Wikimedia Commons
Late Antiquity and the Early Middle Ages saw a steady decline in the mathematical sciences and with it a decline in the production and use of most scientific instruments in Europe until the disappeared almost completely.
When the rapidly expanding Arabic Empire began filing their thirst for knowledge across a wide range of subjects by absorbing it from Greek, Indian and Chinese sources, as well as the mathematical disciplines they also took on board the scientific instruments. They developed and perfected the astrolabe, producing hundreds of both beautiful and practical multifunctional instruments.
As well large-scale astronomical quadrants they produced four different types of handheld instruments. In the ninth century, the sine or sinical quadrant for measuring celestial angles and for doing trigonometrical calculations was developed by Muḥammad ibn Mūsā al-Khwārizmī. In the fourteenth century, the universal (shakkāzīya) quadrant used for solving astronomical problems for any latitude. Like astrolabes, quadrants are latitude dependent and unlike astrolabes do not have exchangeable climata. Origin unknown, but the oldest known example is from 1300, is the horary quadrant, which enables the uses to determine the time using the sun. An equal hours horary quadrant is latitude dependent, but an unequal hours one can be used anywhere, but its use entails calculations. Again, origin unknown, is the astrolabe quadrant, basically a reduced astrolabe in quadrant form. There are extant examples from twelfth century Egypt and fourteenth century Syria.
Horary quadrant for a latitude of about 51.5° as depicted in an instructional text of 1744: To find the Hour of the Day: Lay the thread just upon the Day of the Month, then hold it till you slip the small Bead or Pin-head [along the thread] to rest on one of the 12 o’Clock Lines; then let the Sun shine from the Sight G to the other at D, the Plummet hanging at liberty, the Bead will rest on the Hour of the Day. Source: Wikimedia CommonsAstrolabic quadrant, made of brass; made for latitude 33 degrees 30 minutes (i.e. Damascus); inscription on the front saying that the quadrant was made for the ‘muwaqqit’ (literally: the timekeeper) of the Great Umayyad Mosque of Damascus. AH 734 (1333-1334 CE) British Museum
Islamicate astronomers began making celestial globes in the tenth century and it is thought that al-Sufi’s Book of the Constellations was a major source for this development. However, the oldest surviving Islamic celestial globe made by Ibrahim Ibn Saîd al-Sahlì in Valencia in the eleventh century show no awareness of the forty-eight Greek constellations of al-Sufi’s book.
Islamicate mathematical scholars developed and used many scientific instruments and when the developments in the mathematical sciences that they had made began to filter into Europe during the twelfth century scientific renaissance those instruments also began to become known in Europe. For example, the earliest astrolabes to appear in Europe were on the Iberian Peninsula, whilst it was still under Islamic occupation.
Canterbury Astrolabe Quadrant 1388 Source Wikimedia CommonsAstrolabe of Jean Fusoris, made in Paris, 1400 Source: Wikimedia Commons
The medieval period in Europe saw a gradual increase in the use of scientific instruments, both imported and locally manufactured, but the use was still comparatively low level. There was some innovation, for example the French Jewish scholar, Levi ben Geshon (1288–1344), published the first description of the cross staff or Jacob’s staff, used in astronomy, surveying, and navigation, in his Book of the Wars of the Lord (originally in Hebrew but also translated into Latin).
…of a staff of 4.5 feet (1.4 m) long and about one inch (2.5 cm) wide, with six or seven perforated tablets which could slide along the staff, each tablet being an integral fraction of the staff length to facilitate calculation, used to measure the distance between stars or planets, and the altitudes and diameters of the Sun, Moon and stars
A Jacob’s staff, from John Sellers’ Practical Navigation (1672) Source: Wikimedia Commons
Also, the magnetic compass came into use in Europe in the twelfth century, first mentioned by Alexander Neckam (1157–1217) in his De naturis rerum at the end of the century.
The sailors, moreover, as they sail over the sea, when in cloudy whether they can no longer profit by the light of the sun, or when the world is wrapped up in the darkness of the shades of night, and they are ignorant to what point of the compass their ship’s course is directed, they touch the magnet with a needle, which (the needle) is whirled round in a circle until, when its motion ceases, its point looks direct to the north.
Petrus Pereginus (fl. 1269) gave detailed descriptions of both the floating compass and the dry compass in his Epistola de magnete.
However, it was first in the Renaissance that a widespread and thriving culture of scientific instrument design, manufacture, and usage really developed. The steep increase in scientific instrument culture was driving by the substantial parallel developments in astronomy, navigation, surveying, and cartography that began around fourteen hundred that I have already outlined in previous episodes of this series. Renaissance scientific instrument culture is too large a topic to cover in detail in one blog post, so I’ll only do a sketch of some major points and themes with several links to other earlier related posts.
Already, the first Viennese School of Mathematics, which was heavily involved in the development of both astronomy and cartography was also a source of scientific instrument design and manufacture.Johannes von Gmunden (c. 1380–1442) had a notable collection of instruments including an Albion, a multipurpose instrument conceived by Richard of Wallingford (1292–1336).
Georg von Peuerbach (1423–1461) produced several instruments most notably the earliest portable sundial marked for magnetic declination.
Folding sundial by Georg von Peuerbach
His pupil Regiomontanus (1436–1476) wrote a tract on the construction and use of the astrolabe and there is an extant instrument from 1462 dedicated to Cardinal Bessarion and signed IOHANNES, which is assumed to have been made by him. At least eleven other Regiomontanus style astrolabes from the fifteenth century are known.
Stöffler also made celestial globes and an astronomical clock.
Celestial Globe, Johannes Stöffler, 1493; Landesmuseum Württemberg Source: Wikimedia Commons
Mechanical astronomical clocks began to emerge in Europe in the fourteenth century, but it would not be until the end of the sixteenth century that mechanical clocks became accurate enough to be used as scientific instruments. The earliest clockmaker, who reached this level of accuracy being the Swiss instrument maker, Jost Bürgi (1552–1632).
Bürgi made numerous highly elaborate and very decorative mechanical clocks, mechanised globes and mechanised armillary spheres that were more collectors items for rich patrons rather than practical instruments.
Bürgi Quartz Clock 1622-27 Source: Swiss Physical Society
This illustrates another driving force behind the Renaissance scientific instrument culture. The Renaissance mathematicus rated fairly low in the academical hierarchy, actually viewed as a craftsman rather than an academic. This made finding paid work difficult and they were dependent of rich patrons amongst the European aristocracy. It became a standard method of winning the favour of a patron to design a new instrument, usually a modification of an existing one, making an elaborate example of it and presenting it to the potential patron. The birth of the curiosity cabinets, which often also included collections of high-end instruments was also a driving force behind the trend. Many leading instrument makers produced elaborate, high-class instruments for such collections. Imperial courts in Vienna, Prague, and Budapest employed court instrument makers. For example, Erasmus Habermel (c. 1538–1606) was an incredibly prolific instrument maker, who became instrument maker to Rudolf II. A probable relative Josua Habermel (fl. 1570) worked as an instrument maker in southern Germany, eventually moving to Prague, where he probably worked in the workshop of Erasmus.
1594 armillary sphere by Erasmus Habermel of Prague.
Whereas from Theon onwards, astrolabes were unique, individual, instruments, very often beautiful ornaments as well as functioning instruments, Georg Hartmann was the first instrument maker go into serial production of astrolabes. Also, Hartmann, although he didn’t invent them, was a major producer of printed paper instruments. These could be cut out and mounted on wood to produce cheap, functional instruments for those who couldn’t afford the expensive metal ones.
One of the most beautiful sets on instruments manufactured in Nürnberg late 16th century. Designed by Johannes Pretorius (1537–1616), professor for astronomy at the Nürnberger University of Altdorf and manufactured by the goldsmith Hans Epischofer (c. 1530–1585) Germanische National Museum
As well as astrolabes and his paper instruments Hartmann also produced printed globes, none of which have survived. Another Nürnberger mathematicus, Johannes Schöner (1477–1547) launched the printed pairs of terrestrial and celestial globes onto the market.
Celestial Globe by Johannes Schöner c. 1534 Source
In France, Oronce Fine (1494–1555), a rough contemporary, who was appointed professor at the Collège Royal, was also influenced by Schöner in his cartography and like the Nürnberger was a major instrument maker. In Italy, Egnatio Danti (1536–1586) the leading cosmographer was also the leading instrument maker.
Egnation Danti, Astrolabe, ca. 1568, brass and wood. Florence, Museo di Storia della Scienza Source: Fiorani The Marvel of Maps p. 49
Sternwarte im Astronomisch-Physikalischen Kabinett, Foto: MHK, Arno Hensmanns Reconstruction of Wilhelm’s observatoryTycho Brahe, Armillary Sphere, 1581SourceTycho Brahe quadrant
Their lead was followed by others, the first Vatican observatory was established in the Gregorian Tower in 1580.
View on the Tower of Winds (Gregorian tower) in Vatican City (with the dome of Saint Peter’s Basilica in the background). Source: Wikimedia Commons
In the early seventeenth century, Leiden University in Holland established the first European university observatory and Christian Longomontanus (1562–1647), who had been Tycho’s chief assistant, established a university observatory in Copenhagen
Drawing of Leiden Observatory in 1670, seen on top of the university building. Source: Wikimedia CommonsCopenhagen University Observatory Source: Wikimedia Commons
As in all things mathematical England lagged behind the continent but partial filled the deficit by importing instrument makers from the continent, the German Nicolas Kratzer (c. 1487–1550) and the Netherlander Thomas Gemini (c. 1510–1562). The first home grown instrument maker was Humfrey Cole (c. 1530–1591). By the end of the sixteenth century, led by John Dee (1527–c. 1608), who studied in Louven with Frisius and Mercator, and Leonard Digges (c. 1515–c. 1559), a new generation of English instrument makers began to dominate the home market. These include Leonard’s son Thomas Digges (c. 1546–1595), William Bourne (c. 1535–1582), John Blagrave (d. 1611), Thomas Blundeville (c. 1522–c. 1606), Edward Wright (1561–1615), Emery Molyneux (d. 1598), Thomas Hood (1556–1620), Edmund Gunter (1581–1626) Benjamin Cole (1695–1766), William Oughtred (1574–1660), and others.
The Renaissance also saw a large amount of innovation in scientific instruments. The Greek and Chinese armillary spheres were large observational instruments, but the Renaissance armillary sphere was a table top instrument conceived to teach the basic of astronomy.
In navigation the Renaissance saw the invention various variations of the backstaff, to determine solar altitudes.
Davis quadrant (backstaff), made in 1765 by Johannes Van Keulen. On display at the Musée national de la Marine in Paris. Source: Wikimedia Commons
Also new for the same purpose was the mariner’s astrolabe.
Mariner’s Astrolabe c. 1600 Source: Wikimedia Commons
Edmund Gunter (1581–1626) invented the Gunter scale or rule a multiple scale (logarithmic, trigonometrical) used to solve navigation calculation just using dividers.
All of which were of course also used in cartography. Another Renaissance innovation was sets of drawing instruments for the cartographical, navigational etc draughtsmen.
Drawing instruments Bartholomew Newsum, London c. 1570 Source
The biggest innovation in instruments in the Renaissance, and within its context one of the biggest instrument innovation in history, were of course the telescope and the microscope, the first scientific instruments that not only aided observations but increased human perception enabling researchers to perceive things that were previously hidden from sight. Here is a blog post over the complex story of the origins of the telescope and one over the unclear origins of the microscope.
The Renaissance can be viewed as the period when instrumental science began to come of age.
[1] The information on Ptolemaios’ instruments and the diagrams are taken from Ptolemy’s Almagest, translated and annotated by G. J. Toomer, Princeton Paperbacks, 1998
God made all things by measure, number and weight[1]
The first history of science, history of mathematics book I ever read was Lancelot Hogben’s Man Must Measure: The Wonderful World of Mathematics, when I was about six years old.
It almost certainly belonged to my older brother, who was six years older than I. This didn’t matter, everybody in our house had books and everybody could and did read everybody’s books. We were a household of readers. I got my first library card at three; there were weekly family excursions to the village library. But I digress.
It is seldom, when people discuss the history of mathematics for them to think about how or where it all begins. It begins with questions like how much? How many? How big? How small? How long? How short? How far? How near? All of these questions imply counting, comparison, and measurement. The need to quantify, to measure lies at the beginning of all systems of mathematics. The histories of mathematics, science, and technology all have a strong stream of mensuration, i.e., the act or process of measuring, running through them. Basically, without measurement they wouldn’t exist.
Throughout history measuring and measurement have also played a significant role in politics, often leading to political disputes. In modern history there have been at least three well known cases. The original introduction of the metric system during the French revolution, the battle of the systems, metric contra imperialism, during the nineteenth century, and most recently the bizarre wish of the supporters of Brexit to reintroduce the imperial system into the UK in their desire to distance themselves as far as possible from the evil EU.
It was with some anticipation that I greeted the news that James Vincent had written and published Beyond Measure: The Hidden History of Measurement.[2] Vincent’s book is not actually a history of measurement on a nuts and bolts level i.e., systems of measurement, units of measurement and so on, but what I would call a social history of the uses of measurement. This is not a negative judgement; some parts of the book are excellent exactly because it is about the use and abuse of methods of measurement rather than the systems of measurement themselves.
Although roughly chronological, the book is not a systematic treatment of the use of measurement from the first group of hunter gatherers, who tried to work out an equitable method of dividing the spoils down to the recent redefinition of the kilogram in the metric system. The latter being apparently the episode that stimulated Vincent into writing his book. Such a volume would have to be encyclopaedic in scope, but is rather an episodic examination of various passages in the history of mensuration.
The first episode or chapter takes a rather sweeping look at what the author sees as the origins of measurement in the early civilisations of Egypt and Babylon. Whilst OK in and of itself, what about other cultures, civilisations, such as China or India just to mention the most obvious. This emphasises something that was already clear from the introduction this is the usual predominantly Eurocentric take on history.
The second chapter moves into the realm of politics and the role that measurement has always played in social order, with examples from all over the historical landscape. Measurement as a tool of political control. This demonstrates one of the strengths of Vincent’s socio-political approach. Particularly, his detailed analysis of how farmers, millers, and tax collectors all used different tricks to their advantage when measuring grain and the regulation that as a result were introduced is fascinating.
Vincent is, however, a journalist and not a historian and is working from secondary sources and in the introduction, we get the first of a series of really bad takes on the history of science that show Vincent relying on myths and clichés rather than doing proper research. He delivers up the following mess:
Consider, for example, the unlikely patron saint of patient measurement that is the sixteenth-century Danish nobleman Tycho Brahe. By most accounts Brahe was an eccentric, possessed of a huge fortune (his uncle Jørgen Brahe was one of the wealthiest men in the country), a metal nose (he lost the original in a duel), and a pet elk (which allegedly died after drinking too much beer and falling down the stairs of one of his castles). After witnessing the appearance of a new star in the night sky in 1572, one of the handful of supernovae ever seen in our galaxy, Brahe devoted himself to astronomy.
Tycho’s astronomical work was financed with his apanage from the Danish Crown, as a member of the aristocratical oligarchy that ruled Denmark. His uncle Jørgen, Vice-Admiral of the Danish navy, was not wealthier than Tycho’s father or his independently wealthy mother. Tycho had been actively interested in astronomy since 1560 and a serious astronomer since 1563, not first after observing the 1572 supernova.
After describing Tycho’s observational activities, Vincent writes:
It was the data collected here that would allow Brahe’s apprentice, the visionary German astronomer Johannes Kepler, to derive the first mathematical laws of planetary motion which correctly described the elliptical orbits of the planets…
I don’t know why people can’t get Kepler’s status in Prague right. He was not Tycho’s apprentice. He was thirty years old, a university graduate, who had studied under Michael Mästlin one of the leading astronomers in Europe. He was the author of a complex book on mathematical astronomy, which is why Tycho wanted to employ him. He was Tycho’s colleague, who succeeded him in his office as Imperial Mathematicus.
It might seem that I’m nit picking but if Vincent can’t get simple history of science facts right that he could look up on Wikipedia, then why should the reader place any faith in the rest of what he writes?
The third chapter launches its way into the so-called scientific revolution under the title, The Proper Subject of Measurement. Here Vincent selectively presents the Middle Ages in the worst possible anti-science light, although he does give a nod to the Oxford Calculatores but of course criticises them for being purely theoretical and not experimental. In Vincent’s version they have no predecessors, Philoponus or the Arabic scholars, and no successors, the Paris physicists. He then moves into the Renaissance in a section titled Measuring art, music, and time. First, we get a brief section on the introduction of linear perspective. Here Vincent, first, quoting Alberti, tells us:
I set this up between the eye and the object to be represented, so that the visual pyramid passes through the loose weave of the veil.
The ‘visual pyramid’ described by Alberti refers to medieval theories of optics. Prior to the thirteenth century, Western thinkers believed that vision worked via ‘extramission,’ with the eye emitting rays that interacted with the world like a ‘visual finger reaching out to palpated things’ (a mechanism captured by the Shakespearean imperative to ‘see feelingly’). Thanks largely to the work of the eleventh-century Arabic scholar Ibn al-Haytham, known in the West as Alhacen, this was succeeded by an ‘intromisionist’ explanation, which reverses the causality so that it is the eye that receives impressions from reality. It’s believed that these theories informed the work of artists like Alberti, encouraging the geometrical techniques of the perspective grids and creating a new incentive to divide the world into spatially abstract units.
Here, once again, we have Vincent perpetuating myths because he hasn’t done his homework. The visual pyramid is, of course, from Euclid and like the work of the other Greek promoters of geometrical optics was indeed based on an extramission theory of vision. As I have pointed out on numerous occasions the Greeks actually had both extramission and intromission theories of vision, as well as mixed models. Al-Haytham’s great achievement was not the introduction of an intromission theory, but was in showing that an intromission theory was compatible with the geometrical optics, inclusive visual pyramid, of Euclid et al. The geometrical optics of Alberti and other perspective theorists is pure Euclidian and does not reference al-Haytham. In fact, Alberti explicitly states that it is irrelevant whether the user of his system of linear perspective believes in an extramission or an intromission theory of vision.
Linear perspective is followed by a two page romp through the medieval invention of musical notation before turning to the invention of the mechanical clock. Here, Vincent makes the standard error of over emphasising the influence of the mechanical clock in the early centuries after its invention and introduction.
Without mentioning Thomas Kuhn, we now get a Kuhnian explanation of the so-called astronomical revolution, which is wonderfully or should that be horrifyingly anachronistic:
This model [the Aristotelian geocentric one] sustained its authority for centuries, but close observation of the night skies using increasingly accurate telescopes [my emphasis] revealed discrepancies. These were changes that belied its immutable status and movements that didn’t fit the predictions of a simple geocentric universe. A lot of work was done to make the older models account for such eccentricities, but as they accrued mathematical like sticky notes, [apparently sticky notes are the 21st century version of Kuhnian ‘circles upon circles’] doubts about their veracity became unavoidable.
Where to begin with what can only be described as a clusterfuck. The attempts to reform the Aristotelian-Ptolemaic geocentric model began at the latest with the first Viennese School of Mathematics in the middle of the fifteenth century, about one hundred and fifty years before the invention of the telescope. Those reform attempts began not because of any planetary problems with the model but because the data that it delivered was inaccurate. Major contributions to the development of a heliocentric model such as the work of Copernicus and Tycho Brahe, as well as Kepler’s first two laws of planetary motion also all predate the invention of the telescope. Kepler’s third law is also derived from pre-telescope data. The implication that the geocentric model collapsed under the weight of ad hoc explanation (the sticky notes) was Kuhn’s explanation for his infamous paradigm change and is quite simply wrong. I wrote 52 blog posts explaining what really happened, I’m not going to repeat myself here.
We now get the usual Galileo hagiography for example Vincent tells us:
It was Galileo who truly mathematised motion following the early attempts of the Oxford Calculators, using practical experiments to demonstrate flaws in Aristotelian wisdom.
Vincent ignores the fact that Aristotle’s concepts of motion had been thrown overboard long before and completely ignores the work of sixteenth century mathematicians, such as Tartaglia and Benedetti.
He then writes:
In one famous experiment he dropped cannonballs and musket balls from the Leaning Tower of Pisa (an exercise that likely never took place in the way Galileo claims [my emphasis]) and showed that, contra to Aristotle, objects accelerate at a uniform rate, not proportionally to their mass.
Galileo never claimed to have dropped anything from the Leaning Tower, somebody else said that he had and if it ‘never took place’, why fucking mention it?
Now the telescope:
From 1609, Galileo’s work moved to a new plane itself. Using home-made telescopes he’d constructed solely by reading descriptions of the device…
The myth, created by himself, that Galileo had never seen a telescope before he constructed one has been effectively debunked by Mario Biagioli. This is followed by the usually one man circus claims about the telescopic discoveries, completely ignoring the other early telescope observers. Copernicus and Kepler now each get a couple of lines before we head off to Isaac Newton. Vincent tells us that Newton devised the three laws of motion and the universal law of gravitation. He didn’t he took them from others and combined them to create his synthesis.
The fourth chapter of the book is concerned with the invention of the thermometer and the problems of creating accurate temperature scales. This chapter is OK, however, Vincent is a journalist and not a historian and relies on secondary sources written by historians. There is nothing wrong with this, it’s how I write my blog posts. In this chapter his source is the excellent work of Hasok Chang, which I’ve read myself and if any reader in really interested in this topic, I recommend that they read Chang rather than Chang filtered by Vincent. Once again, we have some very sloppy pieces of history of science, Vincent writes:
Writing in 1693, the English astronomer Edmond Halley, discoverer of the eponymous comet…”
Just for the record, Halley was much more than just an astronomer, he could for example have been featured along with Graunt in chapter seven, see below. It is wrong to credit Halley with the discovery of Comet Halley. The discoverer is the first person to observe a comet and record that observation. Comet Halley had been observed and recorded many times throughout history and Halley’s achievement was to recognise that those observations were all of one and the same comet.
A few pages further on Vincent writes:
Unlike caloric, phlogiston had mass, but Lavoisier disproved this theory, in part by showing how some substances gain weight when burned. (This would eventually lead to the discovery of oxygen as the key element in combustion.) [my emphasis]
I can hear both Carl Scheele and Joseph Priestley turning in their graves. Both of them discovered oxygen, independently of each other; Scheele discovered it first bur Priestly published first, and both were very much aware of its role in combustion and all of this well before Lavoisier became involved.
Chapter five is dedicated to the introduction of the metric system in France correctly giving more attention to the political aspects than the numerical ones. Once again, an excellent chapter.
Chapter six which deals primarily with land surveying had a grandiose title, A Grid LaidAcross the World, but is in fact largely limited to the US. Having said that it is a very good and informative chapter, which explains how it came about that the majority of US towns and properties are laid out of a unified rectangular grid system. Most importantly it explains how the land grant systems with its mathematical surveying was utilised to deprive the indigenous population of their traditional territories. The chapter closes with a brief more general look at how mathematical surveying and mapping played a significant role in imperialist expansion, with a very trenchant quote from map historian, Matthew Edney, “The empire exists because it can be mapped; the meaning of empire is inscribed into each map.”
Unfortunately, this chapter also contains some more sloppy history of science, Vincent tells us:
In such a world, measurement of the land was of the utmost importance. As a result, sixteenth-century England gave rise to one of the most widely used measuring tools in the world: the surveyor’s chain, or Gunter’s chain, named after its inventor the seventeenth-century English priest and mathematician Edmund Gunter.
Sixteenth or seventeenth century? Which copy editor missed that one? It’s actually a bit of a problem because Gunter’s life starts in the one century and ends in the other, 1581–1626. However, we can safely say that he produced his chain in the seventeenth century. Vincent makes the classic error of attributing the invention of the surveyors’ chain to Gunter, to quote myself from my blog post on Renaissance surveying:
In English the surveyor’s chain is usually referred to as Gunter’s chain after the English practical mathematician Edmund Gunter (1581–1626) and he is also often referred to erroneously as the inventor of the surveyor’s chain but there are references to the use of the surveyor’s chain in 1579, before Gunter was born.
Even worse he writes:
Political theorist Hannah Arendt described the work of surveying and mapping that began with the colonisation of America as one of three great events that ‘stand at the threshold of the modern age and determine its character’ (the other two being the Reformation of the Catholic Church and the cosmological revolution begun by Galileo) [my emphasis]
I don’t know whether to attribute this arrant nonsense to Arendt or to Vincent. Whether he is quoting her or made this up himself he should know better, it’s complete bullshit. Whatever Galileo contributed to the ‘cosmological revolution,’ and it’s much, much less than is often claimed, he did not in anyway begin it. Never heard of Copernicus, Tycho, Kepler, Mr Vincent? Oh yes, you talk about them in chapter three!
Chapter seven turns to population statistics starting with the Royal Society and John Graunt’s Natural and Political Observations Made Upon the Bills of Mortality. Having dealt quite extensively with Graunt, with a nod to William Petty, but completely ignoring the work of Caspar Neumann and Edmond Halley, Vincent now gives a brief account of the origins of the new statistics. Strangely attributing this entirely to the astronomers, completely ignoring the work on probability in games of chance by Cardano, Fermat, Pascal, and Christian Huygens. He briefly mentions the work of Abraham de Moivre but ignores the equally important, if not more important work of Jacob Bernoulli. He now gives an extensive analysis of Quetelet’s application of statistics to the social sciences. Quetelet, being an astronomer, is Vincent’s reason d’être for claiming that it was astronomers, who initial developed statistics and not the gamblers. Quetelet’s the man who gave us the ubiquitous body mass index. The chapter then closes with a good section on the abuses of statistics in the social sciences, first in Galton’s eugenics and secondly in the misuse of IQ tests by Henry Goddard. All in all, one of the good essays in the book
Continuing the somewhat erratic course from theme to theme, the eighth chapter addresses what Vincent calls The Battle of the Standards: Metric vs Imperial and metrology’s culture war. A very thin chapter, more of a sketch that an in-depth analysis, which gives as much space to the post Brexit anti-metric loonies, as to the major debates of the nineteenth century. This is mainly so that Vincent can tell the tale of his excursion with said loonies to deface street signs as an act of rebellion.
In the ninth chapter, Vincent turns his attention to replacement of arbitrary definitions of units of measurement with definitions based on constants of nature, with an emphasis on the recent new definition of the kilogram. At various point in the book, Vincent steps out from his role of playing historian and presents himself in the first person as an investigative journalist, a device that I personally found irritating. In this chapter this is most pronounced. He opens with, “On a damp but cheerful Friday in November 2018, I travelled to the outskirts of Paris to witness the overthrow of a king.” He carries on in the same overblown style finally revealing that he, as a journalist was attending the conference officially launching the redefining of the kilogram, going on to explain in equally overblown terms how the kilogram was originally defined. The purple prose continues with the introduction of another attendee, his acquaintance, the German physicist, Stephan Schlamminger:
Schlamminger is something of a genius loci of metrology: an animating spirit full of cheer and knowledge, as comfortable in the weights and measures as a fire in a heath. He is also a key player in the American team that helped create the kilogram’s new definition. I’d spoken to him before, but always delighted in his enthusiasm and generosity. ‘James, James, James,’ he says in a rapid-fire German accent as he beckoned me to join his group. ‘Welcome to the party.’
We then get a long, overblown speech by Schlamminger about the history of the definitions in the metric system ending with an explanation, as to why the kilogram must be redefined.
This is followed by a long discourse over Charles Sanders Peirce and his attempts to define the metre using the speed of light, which failed. Vincent claims that Peirce was the first to attempt to attempt to define units of measurement using constants of nature, a claim that I find dubious, but it might be right. This leads on to Michelson and Morley defining the metre using the wavelength of sodium light, a definition that in modified form is still used today. The chapter closes with a long, very technical, and rather opaque explanation of the new definition of the kilogram based on Planck’s constant, h.
The final chapter of Vincent’s book is a sociological or anthropological mixed basket of wares under the title The Managed Life: Measurements place in modern society in our understanding of ourselves, which is far too short to in anyway fulfil its grandiose title.
The book closes with an epilogue that left me simply baffled. He tells a personal story about how he came to listen to Beethoven’s Ninth Symphony only when he had a personal success in his life and through this came to ruin his enjoyment of the piece. Despite his explanation I fail to see what the fuck this has to do with measurement.
The book has a rather small, random collection of colour prints, related to various bits of the text, in the middle. There are extensive endnotes relating bits of the text to there bibliographical sources, but no separate bibliography, and an extensive index.
I came away feeling that there is a good book contained in Vincent’s tome, struggling to get out. However, there is somehow too much in the way for it to emerge. Some of the individual essays are excellent and I particularly liked his strong emphasis on some of the negative results of applying systems of measurement. People reading this review might think that I, as a historian of science, have placed too much emphasis on his truly shoddy treatment of that discipline; ‘the cosmological revolution begun by Galileo,’ I ask you? However, as I have already stated if we can’t trust his research in this area, how much can we trust the rest of his work?
The obligatory Winter Solstice at Stonehenge image
In 1965 the LA folk rock band, The Byrds, had a major international hit with a song written by folk singer Pete Seeger. Turn! Turn! Turn! (To Everything There Is a Season):
To everything turn, turn, turn There is a season turn, turn, turn And a time to every purpose Under heaven
A time to be born, a time to die A time to plant, a time to reap A time to kill, a time to heal A time to laugh, a time to weep
To everything turn, turn, turn There is a season turn, turn, turn And a time to every purpose Under heaven
A time to build up A time to break down A time to dance, a time to mourn A time to cast away stones A time to gather stones together
To everything turn, turn, turn There is a season turn, turn, turn And a time to every purpose Under heaven
A time of love, a time of hate A time of war, a time of peace A time you may embrace A time to refrain from embracing
To everything turn, turn, turn There is a season turn, turn, turn And a time to every purpose Under heaven
A time to gain, a time to lose A time to rain, a time of sow A time for love, a time for hate A time for peace I swear it′s not too late
Text by Pete Seeger
It is based on the Bible text Ecclesiastes 3:1-8, as rendered in the King James Bible:
To every thing there is a season, and a time to every purpose under the heaven: A time to be born, and a time to die; a time to plant, a time to reap that which is planted; A time to kill, and a time to heal; a time to break down, and a time to build up; A time to weep, and a time to laugh; a time to mourn, and a time to dance; A time to cast away stones, and a time to gather stones together; A time to embrace, and a time to refrain from embracing; A time to gain that which is to get, and a time to lose; a time to keep, and a time to cast away; A time to rend, and a time to sew; a time to keep silence, and a time to speak; A time of love, and a time of hate; a time of war, and a time of peace.
Seasons define our year and are the result of the fact that the ecliptic, the Sun’s apparent path around the Earth, is not parallel to the celestial equator but tilted by 23.4°. Viewed from the Earth in the northern hemisphere, during the year the Sun appears to travel from a point in the north in the middle of summer southwards to turn in the middle of winter, and travel back to the north. Those two turning points are the Tropic of Cancer in the north and the Tropic of Capricorn in the south. Tropic comes to us from the Latin tropicus, which comes from the Greek tropicos both words meaning pertaining to a turn. Those points where the Sun turns on its annual journey are known as the summer and winter solstices. Solstice is a combination of sol(the sun) and the past participle stem of sistere meaning stand still. So, solstice means the sun stands still. The Sun never stands still but if you track the annual path of the Sun along a ridge, then when it reaches the turning point, it appears to stay in the same place on the horizon for a couple of days.
A Renaissance armillary sphere, an instrument for teaching the parts of the celestial sphere. The celestial equator is the band with the Roman numbers. At an angle to it running between e and f is the ecliptic. At e it meets the Tropic of Cancer, the point of the northern hemisphere summer solstice. At f it meets the Tropic of Capricorn, the point of the northern hemisphere winter solstice.
The winter solstice 2022, the turning point, will take place at 21:48 UT (that’s GMT in astronomical talk) today. As I have said in the past I regard the winter solstice, where the old year comes to die, and the new year is born as a much better day to celebrate than the totally arbitrary 31 December-1 January. This being so, I wish all my readers a happy solstice and hope the ending solar cycle was a good one for them and the one now beginning will prove to be a good one. I thank you all for taking the time to read my scribblings and for all the comments and criticism over the last 365 days.
This year I would particularly like to say thank you for all of the kind and encouraging words both here on the blog and out on social media during my very recent and far too long bout of illness. As I was highly contagious, I was isolated in the real world and my Internet family came up trumps. Thank you!
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.
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.
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:
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.
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?
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.
If your philosophy of [scientific] history claims that the sequence should have been A→B→C, and it is C→A→B, then your philosophy of history is wrong. You have to take the data of history seriously.
John S. Wilkins 30th August 2009
Culture is part of the unholy trinity—culture, chaos, and cock-up—which roam through our versions of history, substituting for traditional theories of causation. – Filipe Fernández–Armesto “Pathfinders: A Global History of Exploration”
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