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

 

From about 1630 onwards there were only two serious contenders under European astronomers, as the correct scientific description of the cosmos, on the one hand a Tychonic geo-heliocentric model, mostly with diurnal rotation and on the other Johannes Kepler’s elliptical heliocentric system; both systems had their positive points at that stage in the debate.

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A 17th century illustration of the Hypothesis Tychonica from Hevelius’ Selenographia, 1647 page 163, whereby the Sun, Moon, and sphere of stars orbit the Earth, while the five known planets (Mercury, Venus, Mars, Jupiter, and Saturn) orbit the Sun. Source: Wikimedia Commons

A lot of the empirical evidence, or better said the lack of that empirical evidence spoke for a Tychonic geo-heliocentric model. The first factor, strangely enough spoke against diurnal rotation. If the Earth was truly rotating on its axis, then it was turning at about 1600 kilometres an hour at the equator, so why couldn’t one feel/detect it? If one sat on a galloping horse one had to hang on very tightly not to get blown off by the headwind and that at only 40 kilometres an hour or so. Copernicus had already seen this objection and had actually suggested the correct solution. He argued that the Earth carried its atmosphere with it in an all-enclosing envelope. Although this is, as already mentioned, the correct solution, proving or explaining it is a lot more difficult than hypothesising it. Parts of the physics that was first developed in the seventeenth century were necessary. We have already seen the first part, Pascal’s proof that air is a material that has weight or better said mass. Weight is the effect of gravity on mass and gravity is the other part of the solution and the discovery of gravity, in the modern sense of the word, still lay in the future. Copernicus’ atmospheric envelope is held in place by gravity, we literally rotate in a bubble.

In his Almagestum Novum (1651), Giovanni Battista Riccioli (1598–1671) brought a list of 126 arguments pro and contra a heliocentric system (49 pro, 77 contra) in which religious argument play a minor role and carefully argued scientific grounds a major one.

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Frontispiece of Riccioli’s 1651 New Almagest. Mythological figures observe the heavens with a telescope and weigh the heliocentric theory of Copernicus in a balance against his modified version of Tycho Brahe’s geo-heliocentric system Source: Wikimedia Commons

Apart from the big star argument (see below) of particular interest is the argument against diurnal rotation based on what is now know as the Coriolis Effect, named after the French mathematician and engineer, Gaspard-Gustave de Coriolis (1792–1843), who described it in detail in his Sur les équations du mouvement relatif des systèmes de corps (On the equations of relative motion of a system of bodies) (1835). Put very simply the Coriolis Effect states that in a frame of reference that rotates with respect to an inertial frame projectile objects will be deflected. An Earth with diurnal rotation is such a rotating frame of reference.

Riccioli argued that if the Earth rotated on its axis then a canon ball fired from a canon, either northwards or southwards would be deflected by that rotation. Because such a deflection had never been observed Riccioli argued that diurnal rotation doesn’t exist. Once again with have a problem with dimensions because the Coriolis Effect is so small it is almost impossible to detect or observe in the case of a small projectile; it can however be clearly observed in the large scale movement of the atmosphere or the oceans, systems that Riccioli couldn’t observe. The most obvious example of the effect is the rotation of cyclones.

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Illustration from Riccioli’s 1651 New Almagest showing the effect a rotating Earth should have on projectiles.[36] When the cannon is fired at eastern target B, cannon and target both travel east at the same speed while the ball is in flight. The ball strikes the target just as it would if the Earth were immobile. When the cannon is fired at northern target E, the target moves more slowly to the east than the cannon and the airborne ball, because the ground moves more slowly at more northern latitudes (the ground hardly moves at all near the pole). Thus the ball follows a curved path over the ground, not a diagonal, and strikes to the east, or right, of the target at G. Source: WIkimedia Commons

Riccioli was not alone in using the apparent absence of the Coriolis Effect to argue against diurnal rotation. The French Jesuit mathematician Claude François Milliet Deschales (1621–1678) in his Cursus seu Mundus Mathematicus (1674) brought a very similar argument against diurnal rotation.

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Source: WIkimedia Commons

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Image from Cursus seu Mundus Mathematicus (1674) of C.F.M. Dechales, showing how a cannonball should deflect to the right of its target on a rotating Earth, because the rightward motion of the ball is faster than that of the tower. Source: Wikimedia Commons

It was first 1749 that Euler derived the mathematical formula for Coriolis acceleration showing it to be two small to be detected in small projectiles.

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A nearby star’s apparent movement against the background of more distant stars as the Earth revolves around the Sun is referred to as stellar parallax. Source:

The second empirical factor was the failure to detect stellar parallax. If the Earth is really orbiting the Sun then the position of prominent stars against the stellar background should appear to shift when viewed from opposite sides of the Earth’s orbit, six months apart so to speak. In the seventeenth century they didn’t. Once again supporters of heliocentricity had an ad hoc answer to the failure to detect stellar parallax, the stars are too far away so the apparent shift is too small to measure. This is, of course the correct answer and it would be another two hundred years before the available astronomical telescopes had evolved far enough to detect that apparent shift. In the seventeenth century, however, this ad hoc explanation meant that the stars were quite literally an unimaginable and thus unacceptable distance away. The average seventeenth century imagination was not capable of conceiving of a cosmos with such dimensions.

The distances that the fixed stars required in a heliocentric system produced a third serious empirical problem that has been largely forgotten today, star size.  This problem was first described by Tycho Brahe before the invention of the telescope. Tycho ascribed a size to the stars that he observed and calculating on the minimum distance that the fixed stars must have in order not to display parallax in a heliocentric system came to the result that stars must have a minimum size equal to Saturn’s orbit around the Sun in such a system. In a geo-heliocentric system, as proposed by Tycho, the stars would be much nearly to the Earth and respectively smaller.  This appeared to Tycho to be simply ridiculous and an argument against a heliocentric system. The problem was not improved by the invention of the telescope. Using the primitive telescopes of the time the stars appeared as a well-defined disc, as recorded by both Galileo and Simon Marius, thus confirming Tycho’s star size argument. Marius used this as an argument in favour of a geo-heliocentric theory; Galileo dodged the issue. In fact, we now know, that the star discs that the early telescope users observed were not real but an optical artefact, now known as an Airy disc. This solution was first hypothesised by Edmond Halley, at the end of the century and until then the star size problem occupied a central place in the astronomical system discussion.

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With the eccentricity of the orbits exaggerated: Source

The arguments in favour of Kepler’s elliptical, heliocentric system were of a very different nature. The principle argument was the existence of the Rudolphine Tables. These planetary tables were calculated by Kepler using Tycho’s vast collection of observational data. The Rudolphine Tables possessed an, up till that time, unknown level of accuracy; this was an important aspect in the acceptance of Kepler’s system. Since antiquity, the principle function of astronomy had been to provide planetary tables and ephemerides for use by astrologers, cartographers, navigators etc. This function is illustrated, for example, by the fact that the tables from Ptolemaeus’ Mathēmatikē Syntaxis were issued separately as his so-called Handy Tables. Also the first astronomical texts translated from Arabic into Latin in the High Middle Ages were the zījes, astronomical tables.

The accuracy of the Rudolphine Tables were perceived by the users to be the result of Kepler using his elliptical, heliocentric model to calculate them, something that was not quite true, but Kepler didn’t disillusion them. This perception increased the acceptance of Kepler’s system. In the Middle Ages before Copernicus’ De revolutionibus, the astronomers’ mathematical models of the cosmos were judge on their utility for producing accurate data but their status was largely an instrumentalist one; they were not viewed as saying anything about the real nature of the cosmos. Determining the real nature of the cosmos was left to the philosophers. However, Copernicus regarded his system as being a description of the real cosmos, as indeed had Ptolemaeus his system before him, and by the middle of the seventeenth century astronomers had very much taken over this role from the philosophers, so the recognition of the utility of Kepler’s system for producing data was a major plus point in its acceptance as the real description of the cosmos.

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The other major point in favour of Kepler’s system, as opposed to a Tychonic one was Kepler’s three laws of planetary motion. Their reception was, however, a complex and mixed one. Accepting the first law, that the planetary orbits were ellipses with the Sun at one focus of the ellipse, was for most people fairly easy to accept. An ellipse wasn’t the circle of the so-called Platonic axioms but it was a very similar regular geometrical figure. After Cassini, using a meridian line in the San Petronio Basilica in Bologna, had demonstrated that either the Earth’s orbit around the Sun or the Sun’s around the Earth, the experiment couldn’t differentiate, Kepler’s first law was pretty much universally accepted. Kepler’s third law being strictly empirical should have been immediately accepted and should have settled the discussion once and for all because it only works in a heliocentric system. However, although there was no real debate with people trying to refute it, it was Isaac Newton who first really recognised its true significance as the major game changer.

Strangely, the problem law turned out to be Kepler’s second law: A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. This seemingly obtuse relationship was not much liked by the early readers of Kepler’s Astronomia Nova. They preferred, what they saw, as the purity of the Platonic axiom, planetary motion is uniform circular motion and this despite all the ad hoc mechanism and tricks that had been used to make the anything but uniform circulation motion of the planets conform to the axiom. There was also the problem of Kepler’s proof of his second law. He divided the ellipse of a given orbit into triangles with the Sun at the apex and then determined the area covered in the time between two observations by using a form of proto-integration. The problem was, that because he had no concept of a limit, he was effectively adding areas of triangles that no longer existed having been reduced to straight lines. Even Kepler realised that his proof was mathematically more than dubious.

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Ismaël Boulliau portrait by Pieter van Schuppen Source: Wikimedia Commons

The French astronomer and mathematician Ismaël Boulliau (1605–1694) was a convinced Keplerian in that he accepted and propagated Kepler’s elliptical orbits but he rejected Kepler’s mathematical model replacing it with his own Conical Hypothesis in his Astronomica philolaica published in 1645.

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He criticised in particular Kepler’s area rule and replaced it in his work with a much simpler model.

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Boulliau’s Conical Hypothesis [RA Hatch] Source: Wikimedia Commons

The Savilian Professor of astronomy at Oxford University, Seth Ward (1617–1689)

Greenhill, John, c.1649-1676; Seth Ward (1617-1689), Savilian Professor of Astronomy, Oxford (1649-1660), Bishop of Exeter and Salisbury

Bishop Seth Ward, portrait by John Greenhill Source: Wikimedia Commons

attacked Boulliau’s presentation in his In Ismaelis Bullialdi astro-nomiae philolaicae fundamenta inquisitio brevis (1653), pointing out mathematical errors in the work and proposing a different alternative to the area law.

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Source: Wikimedia Commons

Boulliau responded to Ward’s criticisms in 1657, acknowledging the errors and correcting but in turn criticising Ward’s model.

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Source: Wikimeda Commons

Ward in turn had already presented a fully version of his Keplerian system in his Astronomia geometrica (1656).

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The whole episode is known as the Boulliau-Ward debate and although it reached no satisfactory conclusion, the fact that two high profile European astronomers were disputing publically over the Keplerian system very much raised the profile of that system. It is probable the Newton was first made aware of Kepler’s work through the Boulliau-Ward debate and he is known to have praised the Astronomica philolaica, which as Newton was later to acknowledge contained the first presentation of the inverse square law of gravity, which Boulliau personally rejected, although he was the one who proposed it.

The Boulliau-Ward debate was effectively brought to a conclusion and superseded by the work of the German mathematician Nikolaus Mercator (c. 1620–1687), whose birth name was Kauffman. His birthplace is not certain but he studied at the universities of Rostock and Leiden and was a lecturer for mathematics in Rostock (1642–1648) and then Copenhagen (1648–1654). From there he moved to Paris for two years before emigrating to England in 1657. In England unable to find a permanent position as lecturer he became a private tutor for mathematics. From 1659 to 1660 he corresponded with Boulliau on a range of astronomical topics. In 1664 he published his Hypothesis astronomica, a new presentation of the Keplerian elliptical system that finally put the area law on a sound mathematical footing. In 1676 he published a much-expanded version of his Keplerian astronomy in his two-volume Institutionum astronomicarum.

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Mercator’s new mathematical formulation of Kepler’s second law ended the debate on the subject and was a major step in the eventual victory of Kepler’s system over its Tychonic rival.

Addendum: Section on Coriolis Effect added 21 May 2020

 

 

 

 

 

 

 

 

 

 

 

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A uniform collection of maps should have been a Theatre but became an Atlas instead but it might have been a Mirror.

Early Modern cartography was centred round a group of pioneers working in the Netherlands in the sixteenth century. The two best-known cartographers being Gerhard Mercator and Abraham Ortelius but they were by no means the only map publishers competing for the market. One notable engraver cartographer, who has slipped out of public awareness, is Gerard de Jode.

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Source: Wikimedia Commons

He was born in Nijmegen, then part of the Spanish Lowlands in 1509, which appears to be the sum total of all that is know about his origins or early life; a not uncommon situation with Renaissance figures. At some point he moved to Antwerp and in 1547 he was admitted to the Guild of St Luke. At the time Antwerp was a booming trading city, the second biggest city in Northern Europe after Paris and probably the richest city in Europe. Because of its large population and accumulated wealth it was also a major centre for both the book and map trades.

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Map of Antwerp around 1598 Hoefnaegels, cartographer XVIth century Source: Wikimedia Commons

The Guild of St Luke was principally the guild for painters and other artists and De Jode was an engraver. To become a guild member he would have had to have been a master, so we can assume that he had served an apprenticeship and worked as a journeyman engraver prior to becoming a guild member.  He received permission to set up a printing office in Antwerp in 1551.

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Coat of arms of the Antwerp Guild of Saint Luke

This was not a one-man business and he employed a number of skilled engravers, who are well known craftsmen. His workshop produced a wide range of engraved products but he appears to have specialised to a certain extent in cartography and map production. Antwerp was a major centre for the map trade and De Jode printed and published single maps by notable cartographers.

In 1555 he issued an edition of the world map of the renowned Venetian cartographer Giacomo Gastaldi (c. 1500–1566). Gastaldi had originally been an engineer working for the Venetian Republic but in the 1640s he turned to cartography. His 1648 edition of Ptolemaeus’ Geographia is notable for including regional maps of the Americas and for being reduced in size to produce the first ‘pocket’ atlas. It also represents a shift from woodblock to copper plate printing in cartography. His world map is interesting in that it shows the Americas and Asia as a single conjoined landmass, a common geographical misconception of the period.

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Paolo Forlani & Ferando Bertelli, world map based on world map of Giacomo Gastaldi Source: Library of Congress

In 1558 he produced an edition of Jacob van Deventer’s map of Brabant.

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hertogdom Brabant uit 1540 door Jacob van Deventer Source

Jacob van Deventer (c. 1500–1575) was born in Kampen, also in the Spanish Lowlands. He is part of the mathematical heritage of the University of Leuven, where he registered as a student in 1520. It was in Leuven that he developed his interest in geography and cartography. He later moved to Mechelen and in 1572 to Köln to escaped the Dutch Revolt against the Spanish. In 1536 he produced the map of Brabant that De Jode would later reprint. It is the earliest known map to use the method of triangulation first described in print by Gemma Frisius (1508–1555) in his Libellus de locorum describendorum ratione (1533).

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It was once thought that Deventer had learnt the technique from Gemma but given that Gemma’s book was only published in 1533 and Van Deventer’s map already in 1536 it seems improbable. Two other possibilities are that Gemma learnt the technique from Deventer or they both learnt it from a third unknown source. We will probably never know.

Deventer was appointed Imperial Cartographer by Charles V in 1540, the title being changed to Royal Cartographer after the emperor’s abdication in 1555. In 1559 he was commissioned to survey and map all of the cities in the Spanish Lowlands, a task that he completed with great competence. Due to their military significance the maps were never published.

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Town plan of Asperen c. 1560 by Jacob van Deventer Source: Wikimedia Commons

In 1564 De Jode published another world map by a famous cartographer, the eight-sheet wall map of Abraham Ortelius (1527–1598), which would later appear in reduced form in Ortelius’ Theatrum Orbis Terrarum (1570).

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Ortelius World Map in reduced form from Theatrum Orbis Terrarum (1570) Source: Wikimedia Commons

This was actually Ortelius’ first published map and De Jode would also produce a reduced version of it. The two cartographers would go on to become serious rivals.

It is not known if De Jode independently came up with the idea of producing a book of uniform maps, what we now call an atlas, or whether he was inspired by Ortelius’ endeavour but he produced his own Speculum Orbis Terrarum.

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Gerade de Jode’s World Map 1578 Source: Wikimedia Commons

Whereas Ortelius presented the world on a stage as a theatre, De Jode held a mirror up to the globe reflecting it in his maps.  It appears that Ortelius used his reputation and his influential connections to enforce his monopoly and De Jode’s Speculum first appeared in 1578, when Ortelius’ official printing privilege for Antwerp ended. However, by that time Ortelius had established himself so well in the market that De Jode’s atlas suffered the same fate as Mercator’s and flopped, although it was considered at least as good as if not actually superior to Ortelius’ Theatrum.

However, De Jode appears not to have been too dispirited by the failure of his project as he set about preparing a second expanded edition. Rather like Mercator, he died in 1591 before he could complete this work and like Mercator, it was his son Cornelius de Jode (1568–1600), who completed the work and issued the Speculum Orbis Terrae in 1593.

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Title page of Speculum Orbis Terrae. 1593 Source: Wikimedia Commons

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Africa Gerade de Jode 1593 Source: Wikimedia Commons

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Map Quiviræ Regnum cum aliis versus Boream from the Speculum Orbis Terræ. This map is one of the earliest depictions of the North American West Coast based on a veröffentlichten world map published by Petrus Plancius 1592 Source: Wikimedia Commons

This too failed to sell well. The book however, features a pair of interesting polar projection world maps strongly influenced by Guillaume Postel’s polar planisphère from 1578.

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Guillaume Postel polar projection world map 1578

Guillaume Postel (1510-1581) was a French polymath principally known as a linguist, he was also an astronomer, cosmologists, cartographer, cabbalist, diplomat and religious universalist.

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Postel as depicted in Les vrais pourtraits et vies des hommes illustres grecz, latins et payens (1584) by André Thevet Source: Wikimedia Commons

Tried by the Inquisition in 1553 for heresy he was found insane and imprisoned in the Papal prisons in Rome. He was released in 1559 but then confined in a monastery in Paris from 1566 till his death. Postel did not invent the polar projection; it had already been used by Walter Ludd (1448–1547)–administrator of the Gymnasium Vosagense, whose most well known member was the cartographer Martin Waldseemüller(c. 1470–1520)–for a diagram in Gregor Reisch’s Margarita philosophica (1512), but Postel’s was the first large scale use of the projection and it influenced not just De Jode.

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Gerard de Jode polar projection map of the Northern hemisphere. Color print from copper engraving (printer Arnold Coninx), Antwerp, 1593. Source: Wikimedia Commons

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Gerard de Jose polar projection map of the Southern Hemisphere Source: Wikimedia Commons

Following Cornelius’ death the plates for the De Jode Speculum were sold to the Antwerp book and print seller Joan Baptista Vrients, who also acquired the plates for Ortelius’ Theatrum at about the same time. Although Vrients published several very successful editions of the Theatrum in the early years of the seventeenth century, he never reissued the Speculum, so it appears he only acquired it to remove a potential competitor from the market.

It should not be thought that because his atlas project failed that De Jode was not in general successful. His business in Antwerp was very successful turning out prints of all kinds and he also had a flourishing stand at the Frankfurt Book Fair where he not only sold his wares but acquired foreign prints and maps that he then copied for his own printing office back home. Following the death of Gerard and his oldest son Cornelius the family business was set forth by his second son Pieter de Jode the elder (1570–1634), an artist and engraver, who became a master of the Guild of St Like in Antwerp in 1599.

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Pieter de Jode the Elder by Lucas Emil Vorsterman after Sir Anthony van Dyck Source: Wikimedia Commons

He in turn was succeeded by his son Pieter de Jode (1606–1674) the younger, also an artist and engraver.

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Portrait of Pieter de Jode the younger based on portrait by Thomas Willeboirts Bosschaert

The line ended with Pieter the younger’s son Arnold born in 1638, who although he studied engraving under his father never rose to the standards of his illustrious forebears.

I find it an interesting speculation that if De Jode’s Speculum had been successful, we today take down a mirror from the bookshelf to look at maps of the world.

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

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The seventeenth century is commonly called the scientific revolution principally for the emergence of two branches of science, although much more was actually going on. Firstly, the subject of this series, astronomy, and secondly the branch of science we now know as physics. The name physics had a significantly different meaning in the medieval Aristotelian philosophy. As we know astronomy and physics are intimately connected, in fact, intertwined with each other and this connection came into being during the seventeenth century. We have already seen in an earlier episode how the modern concepts of motion began to emerge from Aristotelian philosophy in the sixth century reaching a temporary high point in the early seventeenth century in the works of Galileo and Beeckman.

Galileo is often regarded as the initiator, founder of these developments and lauded with titles such as the father of physics, which is just so much irrelevant verbiage. In fact as we saw in the case of the laws of fall he was just following developments that had long preceded him. On a more general level the situation is no different. Kepler was apparently the first to use the concept of a physical force rather than a vitalist anima. Simon Stevin (1548–1620) resolved the forces acting on an object on an inclined plane, effectively using the parallelogram of forces to do so. In hydrostatics he also discovered the so-called hydrostatic paradox i.e. that the pressure in a liquid is independent of the shape of the vessel and the area of the base, but depends solely on its depth. Thomas Harriot (c. 1560–1621) actually developed a more advanced mechanics than Galileo but as usually didn’t publish, so his work had no impact. However, it clearly shows that Galileo was by no means the only person considering the problems. All of these early discoveries, including Galileo’s, suffered from a problem of vagueness. Nobody really knew what force was and the definitions of almost all the basic concepts–speed, velocity, acceleration etc.–were defective or simply wrong. The century saw the gradual development of a vocabulary of correctly defined terms for the emerging new physics and a series of important discoveries in different areas, mechanics, statics, hydrostatics, optics etc.

I’m not going to give a blow-by-blow history of physics in the seventeenth century, I would need a whole book for that, but I would like to sketch an aspect that in popular accounts often gets overlooked. The popular accounts tend to go Galileo–Descartes–Newton, as if they were a three-man relay team passing the baton of knowledge down the century. In reality there were a much larger community of European mathematicians and proto-physicists, who were involved, exchanging ideas, challenging discovery claims, refining definitions and contributing bits and pieces to big pictures. Each of them building on the work of others and educating the next generation. What emerged was a pan European multidimensional cooperative effort that laid the foundations of what has become known as classical or Newtonian physics, although we won’t be dealing with Newton yet. Once again I won’t be able to give all the nodes in the network but I hope I can at least evoke something of the nature of the cooperative effort involved.

I will start of with Simon Stevin, a man, who few people think of when doing a quick survey of seventeenth century physics but who had a massive influence on developments in the Netherlands and thus, through connections, in France and further afield. Basically an engineer, who also produced mathematics and physics, Stevin motivated Maurits of Nassau, Stadholder of the young Dutch Republic to establish engineering and the mathematical sciences on the new Dutch universities. Stevin’s work influenced both the Snels, Rudolph (1546–1613) and his son Willebrord (1580–1626), the latter translated Stevin’s work into French and Latin from the Dutch, making it available to a much wider audience.

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Source: Wikimedia Commons

Stevin set up a school for engineering at the University of Leiden with Ludolph van Ceulen as the first professor of mathematics teaching from textbooks written by Stevin. Van Ceulen (1540–1610), who was Willebrord Snel’s teacher, was succeeded by his pupil Frans van Schooten the elder (1581–1646), whose pupils included his own son, Frans van Schooten the younger (1615–1660), Jan de Witt (1625–1672), Johann Hudde (1628–1704), Hendrick van Heuraet (1633–1660?), René-François de Sluse ((1622–1685) and Christiaan Huygens (1629–1695), all of whom would continue their mathematical development under van Schooten junior and go on to make important contributions to the mathematical sciences. An outlier in the Netherlands was Isaac Beeckman (1588–1637), a largely self taught natural philosopher, who made a point of seeking out and studying Stevin’s work. This group would actively interact with the French mathematicians in the middle of the century.

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Portrait of Frans van Schooten the younger by Rembrandt Source: Wikimedia Commons

On the French side with have a much more mixed bunch coming from varying backgrounds although Descartes and Mersenne were both educated by the Jesuits at the College of La Flèche. Nicolas-Claude Fabri de Peiresc (1580–1637), the already mentioned René Descartes (1596–1650) and Marin Mersenne (1588–1648), Pierre de Fermat (1607–1665), Pierre Gassendi (1592–1655), Ismaël Boulliau (1605–1694) and Blaise Pascal (1623–1662) are just some of the more prominent members of the seventeenth century French mathematical community.

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Pierre de Fermat artist unknown Source: Wikimedia Commons

René Descartes made several journeys to the Netherlands, the first as a soldier in 1618 when he studied the military engineering of Simon Stevin. He also got to know Isaac Beeckman, with whom he studied a wide range of areas in physics and from who he got both the all important law of inertia and the mechanical philosophy, borrowings that he would later deny, claiming that he had discovered them independently. Descarte and Beeckman believed firmly on the necessity to combine mathematics and physics. Beeckman also met and corresponded with both Gassendi and Mersenne stimulating their own thoughts on both mathematics and physics.

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René Descartes at work Source: Wikimedia Commons

On a later journey to the Netherlands Descartes met with Frans van Schooten the younger, who read the then still unpublished La Géometrié. This led van Schooten to travel to Paris where he studied the new mathematics of both living, Pierre Fermat, and dead, François Viète (1540–1603), French mathematicians before returning to the Netherlands to take over his father’s professorship and his group of star pupils. Descartes was also a close friend of Constantijn Huygens (1596–1687), Christiaan’s father.

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Source: Wikimedia Commons

Peiresc and Mersenne were both scholars now referred to as post offices. They both corresponded extensively with mathematicians, astronomers and physicists all over Europe passing on the information they got from one scholar to the others in their networks; basically they fulfilled the function now serviced by academic journals. Both had contacts to Galileo in Italy and Mersenne in particular expended a lot of effort trying to persuade people to read Galileo’s works on mechanics, even translating them into Latin from Galileo’s Tuscan to make them available to others. Mersenne’s endeavours would suggest that Galileo’s work was not as widely known or appreciated as is often claimed.

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Nicolas-Claude Fabri de Peiresc by Louis Finson Source: Wikimedia Commons

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Marin Mersenne Source: Wikimedia Commons

Galileo was, of course, by no means the only mathematician/physicist active in seventeenth century Italy. The main activist can be roughly divided in two groups the disciples of Galileo and the Jesuits, whereby the Jesuits, as we will see, by no means rejected Galileo’s physics. The disciples of Galileo include Bonaventura Francesco Cavalieri (1598–1647) a pupil of Benedetto Castelli (1578­–1643) a direct pupil of Galileo, Evangelista Torricelli (1608–­1647) another direct pupil of Galileo and Giovanni Alfonso Borelli (1608-1679) like Cavalieri a pupil of Castelli.

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Benedetto Castelli artist unknown Source: Wikimedia Commons

On the Jesuit side we have Giuseppe Biancani (1565–1624) his pupil Giovanni Battista Riccioli (1598–1671) and his one time pupil and later partner Francesco Maria Grimaldi (1618–1663) and their star pupil Giovanni Domenico Cassini (1625–1712), who as we have already seen was one of the most important telescopic astronomers in the seventeenth century. Also of interest is Athanasius Kircher (1602–1680), professor at the Jesuit University, the Collegio Romano, who like Peiresc and Mersenne was an intellectual post office, collecting scientific communications from Jesuit researchers all over the world and redistributing them to scholars throughout Europe.

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Athanasius Kircher Source: Wikimedia Commons

Looking first at the Jesuits, Riccioli carried out extensive empirical research into falling bodies and pendulums. He confirmed Galileo’s laws of fall, actually using falling balls rather than inclined planes, and determined an accurate figure for the acceleration due to gravity; Galileo’s figure had been way off. He was also the first to develop a second pendulum, a device that would later prove essential in determining variation in the Earth’s gravity and thus the globes shape.

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Riccioli as portrayed in the 1742 Atlas Coelestis (plate 3) of Johann Gabriel Doppelmayer. Source: Wikimedia Commons

Grimaldi was the first to investigate diffraction in optics even giving the phenomenon its name. Many of the people I have listed also did significant work in optics beginning with Kepler and the discovery of more and more mathematical laws in optics helped to convince the researchers that the search for mathematical laws of nature was the right route to take.

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Francesco Maria Grimaldi Source: Wikimedia Commons

As we saw earlier Borelli followed Kepler’s lead in trying to determine the forces governing the planetary orbits but he also created the field of biomechanics, applying the newly developed approaches to studies of muscles and bones.

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Giovanni Alfonso Borelli Source: Wikimedia Commons

Torricelli is, of course, famous for having invented the barometer, a device for measuring air pressure, of which more in a moment, he was trying to answer the question why a simple air pump cannot pump water to more than a height of approximately ten metres. However, most importantly his experiments suggested that in the space above the mercury column in his barometer there existed a vacuum. This was a major contradiction to traditional Aristotelian physics, which claimed that a vacuum could not exist.

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Evangelista Torricelli by Lorenzo Lippi (c. 1647) Source: Wikimedia Commons

Torricelli’s invention of the barometer was put to good use in France by Blaise Pascal, who sent his brother in law, Périer, up the Puy de Dôme, a volcano in the Massif Central, carrying a primitive barometer. This experiment demonstrated that the level of the barometer’s column of mercury varied according to the altitude thus ‘proving’ that the atmosphere had weight that lessened the higher one climbed above the earth’s surface. This was the first empirical proof that air is a material substance that has weight. One person, who was upset by Torricelli’s and Pascal’s claims that the barometer demonstrates the existence of a vacuum, was René Descartes to whom we now turn.

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Painting of Blaise Pascal made by François II Quesnel for Gérard Edelinck in 1691 Source: Wikimedia Commons

Descartes, who is usually credited with being one of, if not the, founders of modern science and philosophy, was surprisingly Aristotelian in his approach to physics. Adopting Beeckman’s mechanical philosophy he thought that things could only move if acted upon by another object by direct contact; action at a distance was definitely not acceptable. Aristotle’s problem of projectile motion, what keeps the projectile moving when the contact with the projector breaks was solved by the principle of inertia, which reverses the problem. It is not longer the question of what keeps the projectile moving but rather what stops it moving. He also, like Aristotle, adamantly rejected the possibility of a vacuum. His solution here was to assume that all space was filled by very fine particles of matter. Where this theory of all invasive particles, usually called corpusculariansim, comes from would takes us too far afield but it became widely accepted in the second half of the seventeenth century, although not all of its adherents rejected the possibility of a vacuum.

Descartes set up laws of motion that are actually laws of collision or more formally impact. He starts with three laws of nature; the first two are basically the principle of inertia and the third is a general principle of collision. From these three laws of nature Descartes deduces seven rules of impact of perfectly elastic (i.e. solid) bodies. Imagine the rules for what happens when you play snooker or billiards.  The details of Descartes rules of impact needn’t bother us here; in fact his rules were all wrong; more important is that he set up a formal physical system of motion and impact. Studying and correcting Descartes rules of impact was Newton’s introduction to mechanics.

Turning to another Frenchman, we have Ismaël Boulliau, who was a convinced Keplerian. Kepler had hypothesised that there was a force emanating from the Sun that swept the planets around their orbits, which diminished inversely with increasing distance from the Sun. Boulliau didn’t think that such a force existed but if it did then it would be an inversed square force in analogy to Kepler’s law for the propagation of light; a candidate for the first modern mathematical law of physics. The foundations of the new physics were slowly coming together.

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Ismaël Boulliau portrait by Pieter van Schuppen Source: Wikimedia Commons

Our last link between the Dutch and French mathematicians is Christiaan Huygens. Huygens initially took up correspondence with Mersenne around 1648; a correspondence that covered a wide range of mathematics and physics. In 1655 he visited Paris and was introduced to Boulliau and a year later began correspondence with Pierre Fermat. Frans van Schooten the younger continued to act as his mathematical mentor.

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Christiaan Huygens by Caspar Netscher, 1671, Museum Boerhaave, Leiden Source: Wikimedia Commons

Huygens absorbed the work of all the leading European mathematician and physicists and as an avowed Cartesian became acknowledged as Europe’s leading natural philosopher. He realised that Descartes rules of impacts were wrong and corrected them. Huygens was also the first to derive and state what is now know as Newton’s second law of motion and derived the law of centripetal force, important steps on the route to a clear understanding of forces and how they operate. Huygens also created the first functioning pendulum clock in the process of which he derived the correct formula for the period of an ideal mathematical pendulum. It is very easy to underestimate Huygens contributions to the development of modern physics; he tends to get squeezed out between Descartes and Newton.

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Spring-driven pendulum clock, designed by Huygens, built by instrument maker Salomon Coster (1657), and a copy of the Horologium Oscillatorium. Museum Boerhaave, Leiden Source: Wikimedia Commons

All the way through I have talked about the men, who developed the new physics as mathematicians and this is highly relevant. The so-called scientific revolution has been referred to as the mathematization of science, an accurate description of what was taking place. The seventeenth century is also known as the golden age of mathematics because the men who created the new physics were also at the same time creating the new mathematical tools needed to create that physics. An algebra based analytical mathematics came to replace the geometric synthetic mathematics inherited from the Greeks.

Algebra first entered Europe in the twelfth century with Robert of Chester’s translation of Muḥammad ibn Mūsā al-Khwārizmī’s ninth century Al-kitāb al-mukhtaṣar fī ḥisāb al-ğabr wa’l-muqābala (The Compendious Book on Calculation by Completion and Balancing), the word algebra coming from the Arabic al-ğabr, meaning completion or setting together (in Spanish an algebraist is a bone setter). This introduction had little impact. It was reintroduced in the thirteenth century by Leonardo of Pisa, this time as commercial arithmetic, where it, especially with the introduction of double entry bookkeeping, had a major impact but still remained outside of academia.

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Leonardo of Pisa Liber Abaci

It was first in the sixteenth century that algebra found its way into academia through the work of Scipione del Ferro (1465–1526), Niccolò Fontana known as Tartaglia (c.1499–1557)and above all Gerolamo Cardano (1501–1576), whose Artis Magnæ, Sive de Regulis Algebraicis Liber Unus (Book number one about The Great Art, or The Rules of Algebra) published by Johannes Petreius (c. 1496–1550) in Nürnberg in 1545 is regarded as the first modern algebra textbook or even the beginning of modern mathematics (which, as should be obvious to regular readers, is a view that I don’t share).

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Source: Wikimedia Commons

Modern readers would find it extremely strange as all of the formulas and theorems are written in words or abbreviations of words and there are no symbols in sight. The status of algebra was further established by the work of the Italian mathematician Rafael Bombelli (1526–1572),

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Source: Wikimedia Commons

(1572)

Another school of algebra was the German Cos school represented by the work of the

German mathematician Michael Stifel (1487–1567), Arithmetica integra (1544),

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Source: Wikimedia Commons

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Michael Stifel’s Arithmetica Integra (1544)

Simon Stevin in the Netherlands L’arithmétique (1585)

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and Robert Recorde (c. 1512–1558) in Britain with his The Whetstone of Witte (1557).

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The passage in The Whetstone of Witte introducing the equals sign Source: Wikimedia Commons

Algebra took a new direction with the French mathematician François Viète (1540–1603),

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François Viète Source: Wikimedia Commons

who wrote an algebra text based on the work of Cardano and the late classical work of Diophantus of Alexandria (2nd century CE) In artem analyticam isagoge (1591) replacing many of the words and abbreviations with symbols.

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Algebra was very much on the advance. Of interest here is that Galileo, who is always presented as the innovator, rejected the analytical mathematics, whereas the leading Jesuit mathematician Christoph Clavius (1538–1612), the last of the staunch defenders of Ptolemaic astronomy, wrote a textbook on Viète’s algebra for the Jesuit schools and colleges.  Two further important publications on symbolic algebra in the seventeenth century were the English mathematician, William Oughtred’s Clavis Mathematicae (1631),

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which went through several editions and was read all over Europe and Thomas Harriot’s unnamed (1631), the only one of his scientific works ever published and that only posthumously.

The development of the then new analytical mathematics reach a high point with the independent invention by Pierre Fermat and René Descartes of analytical geometry, which enabled the geometrical presentation of algebraic functions or the algebraic presentation of geometrical forms; a very powerful tool in the armoury of the mathematical physicists in the seventeenth century. Fermat’s pioneering work in analytical geometry (Methodus ad disquirendam maximam et minimam et de tangentibus linearum curvarum) was circulated in manuscript form in 1636 (based on results achieved in 1629) This manuscript was published posthumously in 1679 in Varia opera mathematica, as Ad Locos Planos et Solidos Isagoge (Introduction to Plane and Solid Loci).

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Descartes more famous work was published as La Géometrié, originally as an appendix to his Discours de la méthode (1637). However, much more important for the dissemination of Descartes version of the analytical geometry was the expanded Latin translation produced by Frans van Schooten the younger with much additional material from van Schooten himself, published in 1649 and the second edition, with extra material from his group of special students mentioned above, in two volumes 1659 and 1661. Van Schooten was the first to introduce the nowadays, ubiquitous orthogonal Cartesian coordinates and to extend the system to three dimensions in his Exercises (1657).

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The other branch of analytical mathematics that was developed in the seventeenth century was what we now know as infinitesimal calculus, the mathematics that is necessary to deal with rates of change, for example for analysing motion. There is a prehistory, particularly of integral calculus but it doesn’t need to interest us here. Kepler used a form of proto-integration to prove his second law of planetary motion and a more sophisticated version to calculate the volume of barrels in a fascinating but often neglected pamphlet. The Galilean mathematician Cavalieri developed a better system of integration, his indivisibles, which he published in his Geometria indivisibilibus continuorum nova quadam ratione promota, (Geometry, developed by a new method through the indivisibles of the continua) (1635) but actually written in 1627, demonstrated on the area of a parabola. This work was developed further by Torricelli, who extended it to other functions.

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The other branch of calculus the calculating of tangents and thus derivatives was worked on by a wide range of mathematicians. Significant contributions were made by Blaise Pascal, Pierre de Fermat, René Descarte, Gregoire de Saint-Vincent, John Wallis and Isaac Barrow. Fermat’s work was the most advanced and included contributions to both integral and deferential calculus, including a general method for determining tangents that is still taught in schools. The Scottish mathematician, James Gregory (1638–1675), inspired by Fermat’s work developed the second fundamental theory of calculus, which states that the integral of a function f over some interval can be computed by using any one, say F, of its infinitely many anti-derivatives. Isaac Barrow (1630–1677) was the first to provide a full proof of the fundamental theorem of calculus, which is a theorem that links the concept of differentiating a function with the concept of integrating a function. Fermat’s work and John Wallis’ Arithmetica Infinitorum (1656) would be an important jumping off point for both Leibniz and Newton in the future.

Wallis_Arithmetica_Infinitorum

Source: Wikimedia Commons

By about 1670, the mathematicians of Europe, who knew of and built on each other’s work had made major advances in the development of both modern mathematics and physics laying the foundations for the next major development in the emergence of modern astronomy. However, before we reach that development there will be a couple of other factors that we have to consider first.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7 Comments

May 6, 2020 · 8:33 am

Doctor, doctor give me the news…

Meghan Daum, who describes herself as a writer, started a Twitter shit storm by tweeting the following:

Seeing “Dr. Ford” trending reminds me anew of how much I hate when PhDs who are not medical doctors want to be addressed as “Dr.” It undermines authority rather than underscores it. That goes for you, too, Dr. Jill Biden.

Now this tweet is several degrees of bollocking stupid but unfortunately many of the negative responses to it were even more stupid, as they were by people propagating historical knowledge of the awarding of doctoral degrees that was, mildly put, total and utter crap. Before I give a quick historical sketch of university doctorates, I will first describe, what I surmise to be the origins of Ms[1] Daum’s more than somewhat dated take on the subject, which I suspect is largely motivated by wanting to take a swipe at Dr Jill Biden.

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With thanks to Charlie Hurnemann

When I was growing up in the dim and distant past, in rural Essex, it was considered polite to address medical practitioners as Doctor irrespective of whether they possessed a MD or not. It was also considered bad etiquette to address non-medical holders of doctorates as Doctor, only the Germans do that sort of thing, if addressing them in writing they were Mr, or somewhat rarer Mrs, with their title appended to the end of their names in the form of the correct initials, D.D., M.D., D.Lit., PhD or whatever. Not being American I can’t be sure, but it is this bygone age that I think Ms Daum (see footnote) is appealing to.

When I moved to Germany, not quite so far in the dim and distant past, I discovered that it is de rigueur to address all holders of a doctoral degree as Doctor. However, medical practitioners, who do not possess an MD, are addressed as Herr or Frau. I don’t know whether this is still true, but the Austrians took it one stage further.  The wife of a man with a doctorate was referred to Frau Doctor, although she did not possess a doctorate. In the classical tradition of sexism the husband of a woman with a doctorate was not referred to as Herr Doctor, if he didn’t possess a doctorate.

However, times have changed and it is now considered correct in almost all countries to address somebody with a doctorate, irrespective of the academic discipline, as Doctor if they so wish it. If the wishes of the holder of the title are not known then etiquette demands the use of the title.

We now turn to the historical horrors on Twitter that have provoked this post. Numerous people claimed that the PhD was older than the medical degree and it was only in comparatively modern times that medical practitioners could even possess a doctorate. This is, I’m afraid to say, complete bollocks and I will now give a brief sketch of the history of the doctorate and its associated title.

As several people correctly pointed out the word doctor originally meant simply teacher, coming from the Latin verb docere meaning to teach. Interestingly the German word for a university lecturer, Docent, comes from the same root. As the European universities began to emerge in the eleventh century CE the term licentia docendi, licenced to teach was applied to somebody qualified in someway to teach at the university. With time a system of qualifications developed at the universities out of which the modern qualification developed over the centuries.

The fully developed medieval university had four faculties the lower or liberal arts faculty and three higher faculties, theology, law (with two divisions, canon and civil law) and medicine. A student started in the liberal arts faculty where he received a general education in the seven liberal arts, the trivium (grammar, logic and rhetoric) and the quadrivium (arithmetic, geometry, music and astronomy) this course of studies closed with the BA or baccalaureus atrium, modern Bachelor of Arts. Most students then left the university. Those that stayed continued their education in the same subjects advancing to the MA or Magister Artium, modern Master of Arts, which was now a licence to teach and qualified the holder to teach the undergraduate courses in the liberal arts faculty.

Some MAs were content to remain at this level but the majority enrolled in one of the three higher faculties to study theology, law or medicine. It was this course of studies that now closed with the degree of doctorate in the chosen faculty, qualifying the holder to now teach that subject. So the original three doctorates available at European universities all the way down to the eighteenth century were doctor of theology, doctor of law and doctor of medicine. This is of course a generalised, ideal model of the medieval university and many institutions deviated from it.

Turning to the doctor of medicine, those with a university degree were by no means the only medical practitioners in the Middle Ages and Early Modern Period with a wide range of others offering medical services, midwives, herbalists, apothecaries, surgeons etc. In fact most people would not have been able to afford the services of a university educated medical practitioner. Also someone with a doctorate in medicine would have been referred to as a medicus and not as a doctor. It was only in the late sixteenth century that people really began to generally refer to medical practitioners as doctors.

We now turn to the, in our day and age ubiquitous, PhD. The doctor of philosophy degree was first introduced in Germany in the late seventeenth century with 1652 being the earliest know award of the degree. The philosophy refers not to the discipline philosophy but to a much wider range of subjects, philosophy being used as a synonym for the liberal arts. By the nineteenth century this had become a research-based degree at German universities, the earlier medieval doctorates were entirely based on learning. These modern research doctorates PhD, DSc etc. slowly began to become accepted at American and British universities in the late nineteenth century. They still had the taint of something foreign and not quite wholesome when I was growing up in the 1950s and many university lecturers and even professors at British universities in this decade did not possess a doctorate.

Of course, nowadays in academia the doctoral degree in all faculties has become ubiquitous with universities churning out freshly backed doctors of everything under the sun at an alarming rate and if they desire to be addressed by their hard earned title as Doctor then please be so polite and have the decency to do so.

[1] It will come as no surprise to the reader that Ms Daum does not possess a doctorate

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Filed under Odds and Ends, University History

The Electric Showman

The are some figures in #histSTM, who, through some sort of metamorphosis, acquire the status of cult gurus, who were somehow super human and if only they had been properly acknowledged in their own times would have advanced the entire human race by year, decades or even centuries. The most obvious example is Leonardo da Vinci, who apparently invented, discovered, created everything that was worth inventing, discovering, creating, as well as being the greatest artist of all time. Going back a few centuries we have Roger Bacon, who invented everything that Leonardo did but wasn’t in the same class as a painter. Readers of this blog will know that one of my particular bugbears is Ada Lovelace, whose acolytes claim singlehandedly created the computer age. Another nineteenth century figure, who has been granted god like status is the Serbian physicist and inventor, Nikola Tesla (1856–1943).

The apostles of Tesla like to present him in contrast to, indeed in battle with, Thomas Alva Edison (1847–1931). According to their liturgy Tesla was a brilliant, original genius, who invented everything electrical and in so doing created the future, whereas Edison was poseur, who had no original ideas, stole everything he is credited with having invented and exploited the genius of other to create his reputation and his fortune. You don’t have to be very perceptive to realise that these are weak caricatures that almost certainly bear little relation to the truth. That this is indeed the case is shown by a new, levelheaded biography of Tesla by Iwan Rhys Morus, Tesla and the Electric Future.[1]

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If anyone is up to the job of presenting a historically accurate, balanced biography of Tesla, then it is Morus, who is professor of history at Aberystwyth University and who has established himself as an expert for the history of electricity in the nineteenth century with a series of excellent monographs on the topic, and yes he delivers.

Anybody who picks up Morus’ compact biography looking for a blow by blow description of the epic war between Tesla and Edison is going to be very disappointed, because as Morus points out it basically never really took place; it is a myth. What we get instead is a superb piece of contextual history. Morus presents a widespread but deep survey of the status of electricity in the second half of the nineteenth century and the beginnings of the twentieth century into which he embeds the life story of Tesla.

We have the technological and scientific histories of electricity but also the socio-political history of the role that electricity during the century and above all the futurology. Electricity was seen as the key to the future in all areas of life in the approaching twentieth century. Electricity was hyped as the energy source of the future, as the key to local and long distant communication, and as a medical solution to both physical and psychological illness. In fact it appears that electricity was being touted as some sort of universal panacea for all of societies problems and ills. It was truly the hype of the century. Electricity featured big in the widely popular world exhibitions beginning with the Great Exhibition at Crystal Palace in 1851.

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In these world fairs electricity literally outshone all of the other marvels and wonders on display.

The men, who led the promotion of this new technology, became stars, prophets of an electrical future, most notably Thomas Alva Edison, who became known as the Wizard of Menlo Park.

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Far from the popular image of Edison being Tesla’s sworn enemy, he was the man, who brought Tesla to America and in doing so effectively launched Tesla’s career. Edison also served as a role model for Tesla; from Edison, Tesla learnt how to promote and sell himself as a master of the electric future.

Morus takes us skilfully through the battle of the systems, AC vs. DC in which Tesla, as opposed to popular myth, played very little active part having left Westinghouse well before the active phase. His technology, patented and licenced to Westinghouse, did, however, play a leading role in Westinghouse’s eventually victory in this skirmish over Edison, establishing Tesla as one of the giants in the electricity chess game. Tesla proceeded to establish his reputation as a man of the future through a series of public lectures and interviews, with the media boosting his efforts.

From here on in Tesla expounded ever more extraordinary, visionary schemes for the electric future but systematically failed to deliver.

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His decline was long drawn out and gradual rather than spectacular and the myths began to replace the reality. The electric future forecast throughout the second half of the nineteenth century was slowly realised in the first half of the twentieth but Tesla played almost no role in its realisation.

Morus is himself a master of nineteenth century electricity and its history, as well as a first class storyteller, and in this volume he presents a clear and concise history of the socio-political, public and commercial story of electricity as it came to dominate the world, woven around a sympathetic but realistic biography of Nikola Tesla. His book is excellently researched and beautifully written, making it a real pleasure to read.  It has an extensive bibliography of both primary and secondary sources. The endnotes are almost exclusively references to the bibliography and the whole is rounded off with an excellent index. The book is well illustrated with a good selection of, in the meantime ubiquitous for #histSTM books, grey in grey prints.

Morus’ book has a prominent subtext concerning how we view our scientific and technological future and it fact this is probably the main message, as he makes clear in his final paragraph:

It is a measure of just what a good storyteller about future worlds Tesla was that we still find the story so compelling. It is also the way we still tend to tell stories about imagined futures now. We still tend to frame the way we think about scientific and technological innovation – the things on which our futures will depend – in terms of the interventions of heroic individuals battling against the odds. A hundred years after Tesla, it might be time to start thinking about other ways of talking about the shape of things to come and who is responsible who is responsible for shaping them.

If you want to learn about the history of electricity in the nineteenth century, the life of Nikola Tesla or how society projects its technological futures then I really can’t recommend Iwan Rhys Morus excellent little volume enough. Whether hardback or paperback it’s really good value for money and affordable for even the smallest of book budgets.

[1] Iwan Rhys Morus, Tesla and the Electric Future, Icon books, London, 2019

 

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Filed under Book Reviews, History of Physics, History of science, History of Technology

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

Without any doubt the biggest impact on the discussion of astronomy and cosmology at the beginning of the seventeenth century was made by the invention of the telescope in 1608 and the subsequent discoveries that were made by astronomers with the new revolutionary instrument. That the Moon was not smooth and perfect as claimed by Aristotle but had geological features like the Earth, that the Milky Way and some nebula resolved into separate stars when viewed through the telescope, that the Sun had spots, that Jupiter had four Moons orbiting it and lastly that Venus displayed phases showing that it must orbit the Sun and not the Earth. All of these, for the times, amazing discoveries were made between the end of 1609 and 1613 then the stream of new discoveries dried up as suddenly as it had begun, why? The problem was a technological one.

All of these initial discoveries had been made using so-called Dutch or Galilean telescopes that consisted of a simple tube with two lenses a convex objective at the front and a concave eyepiece at the back.

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Optical diagram of Galilean telescope y – Distant object ; y′ – Real image from objective ; y″ – Magnified virtual image from eyepiece ; D – Entrance pupil diameter ; d – Virtual exit pupil diameter ; L1 – Objective lens ; L2 – Eyepiece lens e – Virtual exit pupil – Telescope equals Source: Wikimedia Commons

A simple instrument with a serious drawback, by adjusting the focal lengths of the lenses one can increase the magnifying power of the instrument but the greater the magnifying power the smaller the field of vision. Most of the discoveries were made using telescopes with a magnifying power of between twenty and thirty. With such telescopes, for example, Galileo could only view about one quarter of the Moon at a time. With magnifying powers above thirty the Dutch telescope becomes effectively useless as an astronomical instrument. The discoveries that had been made by 1613 marked the limit of discoveries that could be made with the simple Dutch telescope, another instrument had to be found if new discoveries were to be made.

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Galileo’s sketches of the Moon from Sidereus Nuncius. Source: Wikimedia Commons

The solution to the problem had already been presented by Johannes Kepler in his Dioptrice published in 1611.

In this important contribution to the science of optics Kepler not only explained, for the first time, how the Dutch telescope functioned but also what became known as the Keplerian or astronomical telescope with a convex objective and a convex eyepiece. He also described the function of the so-called terrestrial telescope with three convex lenses. The astronomical telescope had a much bigger field of view than the Dutch telescope and could thus be constructed with a much higher magnification.

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Source: Wikimedia Commons

It, however, suffered from the problem that whereas the image in the Dutch telescope was upright, in the astronomical telescope it was inverted. Thus the terrestrial telescope the third lens functioning as an inverter, righting the image.

Christoph Scheiner constructed astronomical telescopes for his work observing the Sun.

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Scheiner’s astronomical telescope for recording sunspots Source: Wikimedia Commons

However, Scheiner remained an exception, if a prominent one, and in general it took three decades before other astronomers turned from the Dutch telescope to telescopes with convex lenses. This of course raises the question, why? The inverted image in the simple two lens astronomical telescope was one problem, however not for Scheiner, who projected the Sun’s image onto a sheet of paper and could thus simply invert his drawn image when finished. There is, however another reason for the very protracted move away from the Dutch telescope to the astronomical telescope and that reason bears the name Galileo Galilei.

Since the publication of his Sidereus Nuncius in 1610, Galileo had become the authority for all things connected with telescopic astronomy.

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Title page of Sidereus nuncius, 1610, by Galileo Galilei (1564-1642). *IC6.G1333.610s, Houghton Library, Harvard University Source: Wikimedia Commons

Galileo was also arrogant enough to reject anything that he didn’t discover or originate. He made rude noises about the astronomical telescope praising the advantages of the Dutch telescope against the astronomical telescope, even though they didn’t exist. He was also very rude about and dismissive of Kepler’s Dioptrice claiming that it was unreadable. His authority was sufficient to hinder the adoption of the astronomical telescope.

One of the first to go against the authority of Galileo and construct and observe with an astronomical telescope was the Italian astronomer Francesco Fontana (c. 1558–1656), who as we saw earlier made the telescope with which Zupi first observed the phases of Mercury.

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Fontana drew a new more accurate map of the Moon, discovered the bands visible on Jupiter. He made the first drawings of Mars and discovered its rotation also inferring the rotation of both Jupiter and Saturn. He published a book of all of his discoveries Novae coelestium terrestriumque rerum observationes, et fortasse hactenus non vulgatae  in 1646.

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Italian astronomer Francesco Fontana created woodcuts showing the Moon and the planets as he saw them through a self-constructed telescope. In 1646, he published most of them in the book Novae Coelestium, Terrestriumque Rerum Observationes, et Fortasse Hactenus Non Vulgatae. Source

This turned out to be a major problem as the book also contained discoveries that Fontana claimed to have made, for example new moons of Jupiter Saturn and Venues, which simply didn’t exist. The charitable explanation is that these were optical artefacts produced by his telescope. This highlights another major problem of early telescopic astronomy, the quality of the early telescopes ranged from bad to abysmal.

The quality of the glass used to make the lenses was usually fairly poor. Often discoloured and equally often containing inclusions, bubbles created during the cooling of the glass, which interfered with the optical quality of the glass. All the early lenses were spherical, i.e. their curvature was segment of the surface of a sphere. This was the only shape that could be ground and polished with the technology available at the time. Even so, the further one got from the centre of a lens the more it tended to deviate from the correct form. This meant that the image formed by such lenses tended to be fairly severely distorted. The current theory is that the invention of the telescope occurred not when somebody succeeded in grinding and polishing lenses, spectacle makers had been doing that for three hundred years before the telescope emerged, or when somebody came up with the right combination of lenses, there is evidence that the magnifying property of the combination of a convex and a concave lens was known sometime before the breakthrough, but when somebody (Hans Lipperhey?) first came up with the idea of masking the outer edges of the objective lens reducing the available area to the truly spherical centre and thus creating a sharp image at the cost of a loss of light. Another problem was so-called spherical aberration. A spherical lens doesn’t actually focus light to a single point but the image is spread out over a small area causing it to blur. This was already known to Ibn al-Haytham (c. 965–c. 1040), who also knew the solution, lenses shaped according to the surfaces of ellipsoids or hyperboloids but lens makers in the seventeenth century were incapable of grinding such shapes. A much bigger problem was chromatic aberration. This is caused by the fact that simple lenses focus different wavelengths and thus different colours of light at slightly different points, causing coloured fringes on the images.  However, the discovery of chromatic aberration by Isaac Newton still lay in the future and its solution even further in the future. Over time the telescope makers discovered that making objective lenses with very long focal lengths reduced the problem of spherical and chromatic aberration and so throughout the seventeenth century the telescopes got longer and longer. Given all of these optical problems it is not surprising that astronomers made discoveries that were illusions; it is to a certain extent a wonder that they discovered anything at all.

The major breakthrough in the use of the astronomical telescope came with the invention of the multiple lens eyepiece by Anton Maria Schyrleus de Rheita, born Johann Burkhard Schyri  (1604–1660), an Capuchin monk, who had studied optics and astronomy at the University of Ingolstadt, the university of Christoph Scheiner and Johann Baptist Cysat, which, although they were no longer present when he studied there, still maintained a high standard in these disciplines. Schyri built his own telescopes and made astronomical observations. In 1643 he published his observations in his Novem stellae, which was full of new discoveries but like those of Fontana they mostly weren’t. Much more important was the publication in 1645 of his Oculus Enoch et Eliae in which he describe, without illustrations, a terrestrial telescope with a three lens eyepiece, as well a description of a pair of binoculars.

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Beginning in 1643 he had already begun to manufacture his new telescope together with the Augsburger instrument maker and optician Johann Wiesel (1583–1662), Germany’s first commercial telescope maker.

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Johann Wiesel with one of his telescopes. Copper engraving by Bartholomäus Kilian, 1660 Source: Wikimedia Commons

The Wiesel/ Schyri terrestrial telescope, which had an upright image, a wide field of vision and high-level magnification, was a huge success throughout Europe. Not only did they sell well but they were soon copied and used not just on land but also as astronomical instruments. In his book Schyri also coined the terms ocular and objective for telescopes.

The Wiesel/ Schyri telescope broke the dam and opened the market for convex lens, astronomical telescopes. In Italy Eustachio Divini (1610–1685) a clockmaker began to manufacture optical instruments becoming by 1646 the leading optician in Italy selling astronomical telescopes throughout Europe.

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Portrait of Eustachio Divini in Carlo Antonio Manzini’s “Dioptrica Pratica” Bologna 1660 Source: Wikimedia Commons

In 1649 he published his first book of observations centred round a spectacular selenography.

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Eustachio Divini Selenography

He would later go on to make detailed observations of Jupiter, the changing shape of the belts, the big red spot and the shadows cast by the satellites. His observation confirmed the axial rotation of the planet.

Divini’s reputation as Europe’s leading telescope maker/astronomer was usurped in 1656 by the still young Dutch polymath Christiaan Huygens (1629–1695), who designed his own astronomical telescope, which he constructed with his brother Constantijn (1628–1697) and with which he discovered Titan the largest of Saturn’s moons.

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Christiaan Huygens by Caspar Netscher, 1671, Museum Boerhaave, Leiden Source: Wikimedia Commons

The year before he had already staked his territory by explaining that the strange observations made by various astronomers of Saturn were in fact differing views of rings surrounding the planet. He explained this in his Systema Saturnium in 1659, which also contained the first telescopic sketches of the Orion Nebula. His explanation of the rings led to a major dispute with Divini, who was convinced that they were a belt of satellites.

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Huygens’ explanation for the aspects of Saturn, Systema Saturnium, 1659 Source: Wikimedia Commons

In the same year he made the first observations of a surface feature of another planet, Syrtis Major, a volcanic plain on Mars, using it to determine the length of the Martian day.

Divini lost his status as Italy’s prime telescope maker to the Campani brothers Matteo (1620–after 1678) and Giuseppe (1635–1715) in a series of contests staged the Accademia del Cimento to test the quality of their telescopes in 1664, which the Campani brothers won, although largely through skulduggery. Of interest is that the quality of the telescopes were compared by reading printed letters though them, a forerunner of the letter charts in the practice of every ophthalmic optician.

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Giuseppe Campani (1635-1715) Telescope with four tubes, Rome, 1666 Florence, Istituto e Museo di Storia della Scienza, inv. 2556

Although Giuseppe Campani was an active astronomer, who made his own observations and discoveries it is their most famous customer, who made the biggest impact, Giovanni Domenico Cassini (1625–1712), who became Jean-Dominique when he moved to France in 1669.

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Giovanni Cassini artist unknown Source: Wikimedia Commons

Employed as an astronomer at the observatory in Panzano by the Marquis Cornelio Malvasia (1603–1664) from 1648, Cassini was able to study under Giovanni Battista Riccioli (1598–1671) and Francesco Maria Grimaldi (1618–1663), themselves important telescopic astronomers, who produced an important lunar map, at the University of Bologna.

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Riccioli/Grimaldi Lunar Map Source: Wikimedia Commons

In 1650 he was appointed professor for astronomy at the university. During his time in Bologna Cassini was able, with the assistance of Riccioli and Grimaldi, using a meridian line in the San Petronio Basilica to prove that that either the Sun’s orbit around the Earth or the Earth’s orbit around the Sun was an ellipse thus confirming a part of Kepler’s astronomical system. The experiment was unable to determine if the system was geo-heliocentric or heliocentric.

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San Petronio Basilica The winter solstice end of the meridian line Source: Wikimedia Commons

As Europe’s leading telescopic astronomer Cassini discovered and published surface markings on Mars, determined the rotation periods of Mars and Jupiter, discovered four satellites of Saturn–Iapetus and Rhea in 1671 and 1672 followed by Tethys and Dione in 1684–he is also credited with the co-discovery with Robert Hooke of the big red spot on Jupiter. He was able to determine the orbits of the moons of Jupiter with enough accuracy that they could be used as a clock to determine longitude, as originally suggested by Galileo. A spin off of this research was the determination of the speed of light by Cassini’s assistant, Ole Rømer (1644–1710). He also showed that both the moons of Jupiter and Saturn obeyed Kepler’s third law, a fact used later by Newton in his Principia Mathematica.

The problem of aberration and the semi-solution of having objectives with ever-longer focal lengths led to the development of the aerial telescope. These are extremely long focal length telescopes that have an objective lens and an eyepiece but no tube, instead having some mechanism to keep the two lens units aligned. Christiaan Huygens constructed one with a cord between the objective and the ocular.

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An engraving of Huygens’s 210-foot aerial telescope showing the eyepiece and objective mounts and connecting string. Source: Wikimedia Commons

The most famous aerial telescope, however, was that of Johannes Hevelius (1611–1687), a wealthy beer brewer and amateur astronomer who lived in Danzig.

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Johannes Hevelius and his wife Elizabeth observing together Source: Wikimedia Commons

Hevelius constructed a telescope with a focal length of 150 feet, which became a tourist attraction.

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1673 engraved illustration of Johannes Hevelius’s 8 inch telescope with an open work wood and wire “tube” that had a focal length of 150 feet to limit chromatic aberration. Source: Wikimedia Commons

He also built a fully equipped observatory on the roof of his brewery and undertook extensive astronomical observations. He, like other, produced a very detailed map of the Moon, discovered four comets and hypothesised that comets obit the Sun on parabolic orbits, created an extensive star atlas in which he described and named ten new constellations, seven of which are still included in official star maps.

With the exception of the discovery of the five largest moons of Saturn, this second wave of seventeenth century telescopic astronomy, starting in about 1640 and continuing till the end of the century, was not as spectacular as the first one. However by the end of the century the small discoveries had accumulated to create a completely different picture of the heavens to the one that existed at the beginning. Planets were no longer Aristotle’s perfectly smooth, spherical bodies but had satellites and surface features, rotated on their axes and had determinable day lengths. The Moon had been accurately mapped by several independent astronomers and there was absolutely no doubt in the minds of the observers that it was fundamentally earth like. The position of many more stars had been accurately mapped and the orbits of the newly discovered satellites had been accurately determined. The celestial spheres of Aristotle and Ptolemaeus had been totally banished. During this second wave of telescopic observation and discovery telescopic astronomy came of age and became a recognised scientific discipline.

In 1669 Cassini was appointed the first director of the Paris Observatory, which had been founded in 1667 by the French minister of finance, Jean-Baptiste Colbert (1619–1683).

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An engraving of The Paris Observatory in the beginning of the 18th century with the wooden “Marly Tower” on the right, erected by Cassini to support both tubed and aerial very long telescopes Source: Wikimedia Commons

The founding of the Paris observatory was followed in 1675 with the founding in England of the Royal Observatory in Greenwich by Charles II, with John Flamsteed appointed in the same year as the first Astronomer Royal.

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Royal Observatory Greenwich Source: Wikimedia Commons

Berlin came somewhat later in 1700 with the appointment of Gottfried Kirch (1639–1710) but who never lived to see his observatory, which first opened in 1711. What we see here is a radical change in the status of astronomy. Whereas for most of the seventeenth century astronomy had been the province of either private citizens or university professors it now became the province of governments with astronomers appointed as civil servants required to deliver astronomical data for cartographical and navigational purposes.

 

 

 

 

 

 

 

 

 

 

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Annus mythologicus

Almost inevitably Newton’s so-called Annus mirabilis has become a social media meme during the current pandemic and the resulting quarantine. Not surprisingly Neil deGrasse Tyson has once again led the charge with the following on Twitter:

When Isaac Newton stayed at home to avoid the 1665 plague, he discovered the laws of gravity, optics, and he invented calculus.

Unfortunately for NdGT and all the others, who have followed his lead in posting variants, both positive and negative, the Annus mirabilis is actually a myth. So let us briefly examine what actually took place and what Isaac actually achieved in the 1660s.

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Portrait of Newton at 46 by Godfrey Kneller, 1689 Source: Wikimedia Commons

We will start with the calculus, which he didn’t actually invent at all, neither in the 1660s nor at any other time. Calculus has a more than two thousand year history stretching back to fourth century BCE. The development of calculus accelerated in the seventeenth century beginning with Kepler and Cavalieri and, previous to Newton, reaching a high point in the work of John Wallis. What Newton, like Leibniz, did was to collate, order and expand the work that others had already produced. Let us take a closer look at what Newton actually achieved in the 1660s.

But before we start, one point that various people have made on the Internet is that during this time Newton was a completely free agent with no commitments, obligations or burdens, a bachelor without children. In college his chambers were cleaned by servants and his meals were prepared by others. At home in Woolsthorpe all of his needs were also met by servants. He could and did devote himself to studying without any interruptions.

Newton, who entered Trinity College Cambridge in June 1661, was an indifferent student apparently bored by the traditional curriculum he was supposed to learn. In April 1664 he was due to take a scholarship exam, which would make him financially independent. The general opinion was not positive, however he did pass as he also passed his BA in the following year, when the prognosis was equally negative. Westfall suggests that he had a patron, who recommended that Cambridge retain him.

Freed by the scholarship, Newton now discovered his love and aptitude for the modern mathematics and set off on a two-year intensive study of the subject, almost to the exclusion of everything else, using the books of the leading mathematicians of the period, Descartes (but in the expanded, improved Latin edition of van Schooten), Viète and Wallis. In October 1666 Newton’s total immersion in mathematics stopped as suddenly as it had begun when he wrote a manuscript summarising all that he had internalised. He had thoroughly learnt all of the work available on the modern analytical mathematics, extended it and systematised it. This was an extraordinary achievement by any standards and, although nobody knew about it at the time, established Newton as one of the leading mathematicians in Europe. Although quite amazing, the manuscript from 1666 is still a long way from being the calculus that we know today or even the calculus that was known, say in 1700.

It should be noted that this intense burst of mathematical activity by the young Newton had absolutely nothing to do with the plague or his being quarantined/isolated because of it. It is an amusing fact that Newton was stimulated to investigate and learn mathematics, according to his own account, because he bought a book on astrology at Sturbridge Fair and couldn’t understand it. Unlike many of his contemporaries, Newton does not appear to have believed in astrology but he learnt his astronomy from the books of Vincent Wing (1619–1668) and Thomas Street (1621–1689) both of whom were practicing astrologers.

I said above that Newton devoted himself to mathematics almost to the exclusion of everything else in this period. However, at the beginning he started a notebook in which he listed topics in natural philosophy that he would be interested in investigating further in the future. Having abandoned mathematics he now turned to one of those topics, motion and space. Once again he was guided in his studies by the leaders in the field, once again Descartes, then Christiaan Huygens and also Galileo in the English translation by Thomas Salusbury, which appeared in 1665. Newton’s early work in this field was largely based on the principle of inertia that he took from Descartes and Descartes’ theories of impact. Once again Newton made very good progress, correcting Descartes errors and demonstrating that Galileo’s value for ‘g’ the force of acceleration due to gravity was seriously wrong. He also made his first attempt to show that the force that causes an object to fall to the ground, possibly the legendary apple, and the force that prevents the Moon from shooting off at a tangent, as the principle of inertia says it should, were one and the same. This attempt sort of failed because the data available to Newton at the time was not accurate enough. Newton abandoned this line of thinking and only returned to it almost twenty years later.

Once again, the progress that the young Newton made in this area were quite impressive but his efforts were very distant from his proof of the law of gravity and its consequences that he would deliver in the Principia, twenty year later. For the record Newton didn’t discover the law of gravity he proved it, there is an important difference between the two. Of note in this early work on mechanics is that Newton’s concepts of mass and motions were both defective. Also of note is that to carry out his gravity comparison Newton used Kepler’s third law of planetary motion to determine the force holding the Moon in its orbit and not the law of gravity. The key result presented in Principia is Newton’s brilliant proof that Kepler’s third law and the law of gravity are in fact mathematically equivalent.

The third area to which Newton invested significant time and effort in the 1660s was optics. I must confess that I have absolutely no idea what Neil deGrasse Tyson means when he writes that Newton discovered the laws of optics. By the time Newton entered the field, the science of optics was already two thousand years old and various researchers including Euclid, Ptolemaeus, Ibn al-Haytham, Kepler, Snel, and Descartes had all contributed substantially to its laws. In the 1660s Newton entered a highly developed field of scientific investigation. He stated quite correctly that he investigated the phenomenon of colour. Once again his starting point was the work of others, who were the leaders in the field, most notably Descartes and Hooke. It should be clear by now that in his early development Newton’s debt to the works of Descartes was immense, something he tried to deny in later life. What we have here is the programme of experiments into light that Newton carried out and which formed the basis of his very first scientific paper published in 1672. This paper famously established that white light is made up of coloured light. Also of significance Newton was the first to discover chromatic aberration, the fact that spherical lenses don’t sharply focus light to a single point but break it up into a spectrum, which means the images have coloured fringes. This discovery led Newton to develop his reflecting telescope, which avoids the problem of chromatic aberration.

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Newton’s sketch of his crucial experiment. Source: Royal Society

Here trying to establish a time line of when and where he carried out these experiments is very difficult, not alone because Newton’s own statements on the subject are contradictory and some of them are provably false. For example he talks about acquiring a second prism from Sturbridge Fair in a year when one didn’t take place. Also Newton’s source of light was sunlight let into a darkened room through small hole in the shutters. This was only possible at certain times of year and certain times of day when the sun is in the right position respective the window. Newton claims experiments made at times where these conditions weren’t met. That not all the experiments were made in Woolsthorpe Manor is clear, as many of them required two operators, which means that they were made when Newton was back in his chambers in Trinity College. The best guestimate is that this programme of experiments took place over the period 1660 to 1670, so once again not in Newton’s year of quarantine.

Another thing that keeps getting mentioned in connection with this story is that during his experiments on light Newton, shock-horror, stuck a pin in his eye! He didn’t. What he did was to insert a bodkin, a flat, blunt, threading needle, into his eye-socket between his skull and his eyeball in order to apply pressure to the back of his eyeball. Nasty enough, but somewhat different to sticking a pin in his eye.

All in all the developments that the young Newton achieved in mathematics and physics in the 1660s were actually spread out over a period of six years. They were also not as extensive or revolutionary as implied in Neil deGrasse Tyson brief tweeted claim. In fact a period of six intensive years of study would be quite normal for a talented student to acquire the basics of mathematics and physics. And I think we can all agree that Newton was very talented. His achievements were remarkable but not sensational.

It is justified to ask where then does the myth of the Annus Mirabilis actually come from? The answer is Newton himself. In later life he claimed that he had done all these things in that one-year, the fictional ones rather than the real achievements. So why did he claim this? One reason, a charitable interpretation, is that of an old man just telescoping the memories of his youth. However, there is a less charitable but probably more truthful explanation. Newton became in his life embroiled in several priority disputes with other natural philosophers over his discoveries, with Leibniz over the calculus, with Hooke over gravity and with Hook and Huygens over optics. By pushing back into the distant past some of his major discoveries he can, at least to his own satisfaction, firmly establish his priority.

The whole thing is best summarised by Westfall in his Newton biography Never at Rest at the end of his chapter on the topic, interestingly entitled Anni mirabiles, amazing years, not Annus mirabilis the amazing year, on which the brief summary above is largely based. It is worth quoting Westfall’s summary in full:

On close examination, the anni mirabiles turn out to be less miraculous than the annus mirabilis of Newtonian myth. When 1660 closed, Newton was not in command of the results that have made his reputation deathless, not in mathematics, not in mechanics, not in optics. What he had done in all three was to lay foundations, some more extensive than others, on which he could build with assurance, but nothing was complete at the end of 1666, and most were not even close to complete. Far from diminishing Newton’s stature, such a judgement enhances it by treating his achievements as a human drama of toil and struggle rather than a tale of divine revelation. “I keep the subject constantly before me, “ he said, “and wait ‘till the first dawnings open slowly, by little and little, into full and clear light.” In 1666 by dint of keeping subjects constantly before him, he saw the first dawnings open slowly. Years of thinking on them continuously had yet to pass before he gazed on a full and clear light.[1]

Neil deGrasse Tyson has form when it comes to making grand false statements about #histSTM, this is by no means the first time that he has spread the myth of Newton’s Annus mirabilis. What is perhaps even worse is that when historians point out, with evidence, that he is spouting crap he doesn’t accept that he is wrong but invents new crap to justify his original crap. Once he tweeted the classic piece of fake history that people in the Middle Ages believed the world was flat. As a whole series of historians pointed out to him that European culture had known since antiquity that that the world was a sphere, he invented a completely new piece of fake history and said, yes the people in antiquity had known it but it had been forgotten in the Middle Ages. He is simply never prepared to admit that he is wrong. I could bring other examples such as my exchange with him on the superstition of wishing on a star that you can read here but this post is long enough already.

Bizarrely Neil deGrasse Tyson has the correct answer to his behaviour when it comes to #histSTM, of which he is so ignorant. He offers an online course on the scientific method, always ready and willing to turn his notoriety into a chance to make a quick buck, and has an advertising video on Youtube for it that begins thus:

One of the great challenges in this world is knowing enough about a subject to think you’re right but not enough about the subject to know you’re wrong.

This perfectly encapsulates Neil deGrasse Tyson position on #histSTM!

If you want a shorter, better written, more succinct version of the same story then Tom Levenson has one for you in The New Yorker 

[1] Ricard S. Westfall, Never at Rest: A Biography of Isaac Newton, CUP; Cambridge, ppb. 1983, p. 174.

 

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Filed under History of Astronomy, History of Mathematics, History of Optics, Myths of Science, Newton