Over my lifetime the wheelie bin has become the standard receptacle for the disposal of household rubbish. The are usually fairly large capacity, easy to clean so, reasonably hygienic and their collection by municipal services is comparatively simply and cost effective. It require just one garbage truck and one driver.
German wheelie bins Source: Wikimedia Commons
On collection day they are placed out on the side of the road, on the sidewalk and the garbage truck drives passed halting briefly for its mechanical arm to pick up the bin and empty it into its interior, before replacing back on the side walk and therein lies the rub.
I have suffered from a degenerative spinal and pelvic girdle orthopaedic/neurological condition for more than thirty years. Since about fifteen years this has resulted in increasing difficulty in walking. By the beginning of last year, I was down to about five hundred metres with hiking poles before I needed to take a substantial break. In the autumn I suffered another major decline in my ability to walk. On a good day, I can now manage ten metres without aids, but those are very uncertain and with a high risk that I will fall. I have little or no stability. With my hiking poles or my rollator, I can manage about fifty metres, probably less. In my flat I use my rollator more than ninety percent of the time, although my flat is very small. For longer distances I am now dependent on my trusty electric wheelchair. Although not so extreme as my legs I suffer from similar problems with my arms so, I lack the strength necessary for a normal wheelchair.
The Mathematicus Moble
My Mathematicus Mobile is very zippy, has a top speed of 6 kph and can literally turn on a dime. I’m very happy with the boost in mobility that it has brought me. I can even travel with it on the bus and up till now the bus drivers were all very friendly and helpful. When it came to opening the ramp so, I could get on and off. But now back to the wheelie bins.
On refuse collection day, and there are separate ones for, household refuse, recyclable plastic, and waste paper, the bins are lined up along the sidewalk. If the sidewalk is wide enough, I can usually get past with my wheelchair without any problems. However, if the bins are not on the edge of the sidewalk but scattered all over it, which is often the case after the garbage truck driver throws them back empty, I have difficulty getting past. However, I have learnt to shove them out of the way with one hand whilst steering my wheelchair with the other. I’m also very adroit at clearing shopping trollies out of the way in supermarkets. The problems start when the sidewalks are narrow, as is the case in the side-street in which I live. If the wheelie bins are out on the sidewalk, even if the stand correctly on the edge, there is not enough space for me to get passed. And I’m forced to driver on the road! Just one of the minor irritants one has to live with when mobility disabled.
Towards the end of the last episode of this series where I outlined the early life of Isaac Newton, I noted that between 1664 and the early 1670s, he undertook one of the most impressive period of self-study ever. That period I outlined in a post debunking the myth of the mythical Annus mirabilis. A large part of that time was devoted to the experimental study of light, in particular what Newton terms “the phenomenon of colour.” Before Newton it was in general believed that colour resulted through the changing of white light by external influences, becoming discoloured when passing through a prism or a lens, for example. His research showed, as we all know today, that white light itself is actually composed of a myriad of colours each of which has a different index of refraction, the spectrum being produced by white light being refracted. The rainbow is produced by sunlight being refracted by drop of rain water. These discoveries led to Newton’s first appearances in public as a natural philosopher. The first of which was a resounding success and the second boarding on a disaster.
Godfrey Kneller portrait of Isaac Newton 1689 Source: Wikimedia Commons
Before addressing these we need to catch up with Newton’s progress with in the University of Cambridge. In 1669, Isaac Barrow (1630–1677) resigned as Lucasian Professor of Mathematics and recommended the then twenty-six year old Newton as his successor, a recommendation that was accepted by the college authorities and the young Isaac was duly installed.
Portrait of a young Isaac Barrow by Mary Beale (1633–1699) Source: Wikimedia Commons
This simple historical fact throws up several red flags. Firstly, by 1669 Newton had published absolutely nothing, he was a blank sheet but he gets appointed to a professorship? His extreme talent for mathematics had obviously become known to Barrow, who after all recommended him, as probably did others, and he seemed to be the best man for the job so, he was appointed. I once wrote a whole blog post titled, “Only 26 and already a professor” in which I analysed the seemingly extraordinary fact of a twenty six year old unknown being appointed to what is now regarded as the most prestigious chair for mathematics in the world.
In fact, in its early decades the Lucasian chair was anything but prestigious. Its raise to fame would first begin with Newton’s later career and then be extended by the long list of famous mathematicians and physicists who followed Newton as its occupants. In those early years it was in fact totally insignificant and on the basically still Aristotelian university it almost literally interested no one. This was why Barrow resigned; it didn’t appeal to his self-image. Very, very few students found their way to Newton’s lectures if at all and he oft lectured to an empty lecture hall cutting his lecture short and going back to his chambers. However, it did have a salary, meaning Newton was free to get on with his intensive research.
In the late 1660s Newton’s main area of activity was his research into optics and he now preceded to make an appearance outside the university walls on two levels, practical and theoretical.
His research had shown him that light was made up of a spectrum of colours each with a different index of refraction. This had major consequences for lenses and telescopes. The images in seventeenth-century telescopes was anything but sharp. They were fuzzy with coloured fringes. It was assumed that this was due to spherical aberration. A spherical lens does not focus all the rays passing through it at a single point but over a mall stretch, leading to a diffuse image. This had been first identified by Ibn al-Haytham (965–c. 1040) in his Kitāb al-Manāẓir, which had been translated in to Latin as De Aspectibus or Perspectiva and was very well known. The theorectical solution was also known. Lenses needed to be ground in other forms–parabolic, hyperbolic–however, people lacked the technical know how to achieve this. It was known that increasing the focal length of the objective lens reduced the spherical aberration leading to the spectacular aerial telescopes of Christiann Huygens (1629–1695) and Johannes Hevelius (1611–1687).
Newton realised that lenses, which are basically prisms, also suffered from chromatic aberration and that this contributed much more to the diffuse image than the spherical aberration. Newton thought that it would be impossible to constuct a lens free of chromatic aberration, a major scientic error in his life, and so he set about construction a telescope that used a mirror to focus the incomming light rays instead of a lens, a reflector.
Newton was by no means the first to think of using a mirror in place of a lens to focus light rays. The reflector telescope has a history that begins with Hero of Alexandia (1st century CE?) as I have documented here. As Newton was still an undergraduate, the Scotish mathematician and astronomer James Gregory (1638–1675) had published a design for a reflecting telescope in his Optica promota (1663) but found the mirrors too difficult to construct. He then moved to London with the hope that London’s best lens-maker, Richard Reeve, could make his mirrors, but he was also unable to achieve the necessary quality to produce a usable image.
Source: Wikimedia Commons
The isolated school boy, Isaac Newton had spent much of his time constructing things with his hands. During his time a grammar school in Grantham the stories say that he made furniture for the doll’s house of the step-daughter of Mr Clarke the apothecary in whose house he lodged. He also made a working model of a windmill which he mounted on the roof of the house. Now having decided that a reflector was the solution to chromatic aberration in telescopes, he set his manual talents to building one. He cast the mirror using an alloy of his own making consisting of copper, tin, and arsenic, which give the mirror a white surface colour, and devised a new method of grinding and polishing, using pitch, to polish the surface. He built the tube and the mounts. The telescope was only about six inches long but magnified nearly forty time in diameter, which made it more powerful that a six foot refractor. This was in 1668 and in 1671 he made a second one which at the urgings of Isaac Barrow he sent to the Royal Society in London, which immediately elected him a fellow in January 1672. The recluse, Isaac Newton, had arrived on the public stage.
It should be noted that although Newton had cracked the problem of producing a functioning reflecting telescope, it was found almost impossible to repeat his success. It was first fifty years later that the mathematician John Hadly (1682–1744) developed ways to make precision aspheric and parabolic objective mirrors for reflecting telescopes. Going on to manufacture both Newtonian and Gregorian telescopes.
In the same year Newton sent a letter to the Royal Society outlining his optical experiments with prisms and the conclusions he had drawn from them:
A Letter of Mr. Isaac Newton, Professor of the Mathematicks in the University of Cambridge; Containing His New Theory about Light and Colors: Sent by the Author to the Publishee from Cambridge, Febr. 6. 1671/72; In Order to be Communicated to the R. Society
If he had only expected praise for his scientific endeavours he must have been disappointed.
The two leading experts for things optical, at this time, were Robert Hooke (1635–1703) in London and Christian Huygens (1629–1695) in Paris, both of whom reacted very negatively to Newton’s paper. When asked for his opinion by Oldenburg, the secretary of the Royal Society, Huygens was at first lukewarm and did not appear to see anything new in Newton’s work, implying that he had not really read the paper, but, when pressed, rejected Newton’s theories out of hand. Newton was enraged and in his reply addressed Huygens, a leading figure in European natural philosophy, as if he were addressing a particularly ignorant schoolboy. Huygens said that if the discussion was to be conducted at that level, he would not contribute.
One of Newton’s major problems was that he had used his discoveries to support his own view that light was corpuscular in nature; he argued that the refracting medium imparted spin to a light particle (in the same way as a tennis player imparts spin to the ball, Descartes influence can clearly be seen here), and the different indexes of refraction are a result of the different degrees of spin imparted to the particles of each colour. Both Huygens and Hooke had developed wave theories of light, and it was Hooke who took up the attack. He interpreted Newton as saying that his theory of colour was dependent on a corpuscular theory of light. Yet, as he, Hooke, had already philosophically demonstrated that light was propagated in waves, then Newton’s theory must be wrong. This was just the main one of many criticisms that Hooke brought that led to a very tempestuous exchange of letters through Oldenburg over a period of several years.
At first Newton was content to answer, and he even showed that his theory worked equally well for a wave theory of light at the same time producing the best mathematical model for such a theory in the 17th century. A Serie’s of Quere’s Propounded by Mr. Isaac Newton, to be Determin’d by Experiments, Positively and Directly Concluding His New Theory of Light and Colours; and Here Recommended to the Industry of the Lovers of Experimental Philosophy, as they Were Generously Imparted to the Publisher in a Letter of the Said Mr. Newtons of July 8.1672 published in the Philosophical Transactions of the Royal Society.
During this period Newton worked on a long exhaustive essay on optics covering all of his research work up until this time, which he intended to publish in the Philosophical Transactions as a glorious rebuttal of all of his critics. However, Hooke did not let up, and Newton was further beset by criticisms from Ignace Gaston Pardies (1636–1673), a highly respected Jesuit scientist living in Paris who was also something of an expert for optics, and a second Jesuit, the Englishman Francis Hall (1595–1675), also known as Linus of Liège. The dispute with Pardies passed off relative quietly, but the one with Linus dragged on for six years and was continued by his student John Gasgoines after Linus’ death.
Although Linus was not a well-known philosopher, his objections are interesting and significant from a methodological point of view: he complained that he had been unable to repeat Newton’s experiments! This was not an isolated incident as the same thing occurred to Italian Newtonians at the beginning of the 18th century. In the case of the Italians, it turned out that the problem lay in the quality of the glass prisms that they were using and when they replaced them with better quality glass they were able to achieve the same results as Newton. One can assume that something similar happened in the case of Linus, but we will never know.
The results of this mass of criticism were fairly monumental. Newton’s patience, never very good at the best of times, gave out. He withdrew the extended optics essay that he had been writing and refused to have any more direct dealing with the Royal Society until 1704. He never established a relationship with Huygens. The feud with Hooke was patched up, only to break out again in the 1680s when Hooke accused Newton of having stolen the inverse square law of gravitation from him (but that, as they say, is another story). In fact, Newton’s first venture into publishing as such a disaster that he published nothing else until 1687, when he published his magnum opus Philosophiæ Naturalis Principia Mathematica ( The Mathematical Principles of Natural Philosophy)[1].
In 1704, now that both Huygens and Hooke were finally dead, Newton published, in English, that “long exhaustive essay on optics covering all of his research work up until this time”, expanded into his Opticks: or, A Treatise of the Reflexions, Refractions, Inflexions and Colours of Light.
Source: Wikimedia Commons
A Latin edition was published in 1706. Opticks is the most comprehensive volume on the topic published in the early modern period and it covers all then known areas of optics experimentally and mathematically. The opening sentence reads:
My Design in this Book is not to explain the Properties of Light by Hypotheses, but to propose and prove them by Reason and Experiments.
This is a direct challenge to the Cartesians, of which Huygens was one, who expected philosophical explanations of optical phenomena. When he had published that original paper in 1672, one challenge from his critics was that he didn’t explain the nature of colour. Descartes as we saw believed that white light was homogeneous, that is monochrome, so, he had to explain the colours of the rainbow or the spectrum in general, as produced by a prism, for example. Experimenting with a prism Descartes produced the following argument. He stated that the particle of the second element, those that transmitted light, when refracted and rubbing against the particle of the third element, matter, acquired an uneven rotation which manifested itself as colours.
For Newton it was coloured light that was fundamental not white light and he considered that he had demonstrated this experimentally with his so-called Experimentum Crusis, Newton himself never used the term, (Book I, Part II, Theorem ii), Newton showed that the colour of light corresponded to its “degree of refrangibility” (angle of refraction), and that this angle cannot be changed by additional reflection or refraction or by passing the light through a coloured filter.
Folio 45v of Isaac Newton’s manuscript, New College MS 351/2, Oxford, which contains Newton’s diagram of the experimentum crucis, made at the request of Pierre Varignon for a French translation of the Opticks, 1722 (new.ox.ac.uk) Source Linda Hall Library
In his experiment he passed a beam of sunlight through a prism to produce a spectrum that he then masked so that only a single coloured ray, blue for example, progressed further. He passed this single ray of coloured light through a second prism and observed that although refracted again the ray didn’t change colour in any way. He concluded that the prisms were not added colour to the white light as it passed through, as had been previously believed.
Newton’s experimentum crucis . Within the darkroom a solar spectrum is projected onto the screen DE via the prism ABC and the aperture G in the screen DE . Only a monochromatic section of the spectrum passes through the small aperture in the screen, that is again deflected using a second prism abc but hardly undergoes any further spreading. In this way Newton showed that the colourless sunlight is made up of irreducible coloured light elements. The illustration is from Newton’s Opticks of 1704, but has been inverted here and has been reproduced with a retrospectively coloured spectrum. Source
Although it still had its critics Opticks became the standard work on optics during the eighteenth century only to be dethroned in the early nineteenth century, when Thomas Young (1773–1829), François Arago (1786-1853) , and Augustin-Jean Fresnel (1788–1827) produced a series of experiments that could not be explain by Newton’s corpuscular theory of light and replaced it with a wave theory.
As a small foot note, because of his theory of colour, Newton is considered one of those who provided the scientific explanation of the rainbow. We now teach schoolchildren that the rainbow has seven colures–red, orange, yellow, green, blue, indigo, violet–with lots of mnemonics to help them remember the correct order. Before Newton, people mostly thought that the rainbow had three, four or five colours and it was Newton who extended the list to seven. In his Opticks he wrote:
In the Experiments of the fourth Proposition of the first Part of this first Book, when I had separated the heterogeneous Rays from one another, the Spectrum pt formed by the separated Rays, did in the Progress from its End p, on which the most refrangible Rays fell, unto its other End t, on which the most refrangible Rays fell, appear tinged with this Series of Colours, violet, indigo, blue, green, yellow, orange, red, together with all their intermediate Degrees in a continual Succession perpetually varying . So that there appeared as many Degrees of Colours, as there were sorts of Rays differing in Refrangibility.
In a recent episode in this series, I presented the life and work of Elias Allen (c. 1588–1653), who was the most prominent scientific instrument maker in England in the first half of the seventeenth century. He was the master of many apprentices, several of whom went on to become master instrument makers themselves. As I wrote there the most prominent of these was Ralph Greatorex (c. 1625–1675), who interacted with a significant number of the leading figures in the English scientific community in the third quarter of the century. Today, I’m going to take a closer look at Ralph Greatorex.
As is unfortunately often the case with figures out of the mathematical practitioner milieu in the early modern period, we know very little about Greatorex’s origins and background. Greatorex came from Derbyshire, which is where the first record of this fairly rare family name can be found from the thirteenth century in the form Greatrakes taken from a small settlement of this name, now known as Great Rocks Farm.
The remains of Great Rocks Farm in the 1980s
His birth year is estimated on the assumption he was fourteen when he was bound an apprentice clockmaker for nine years on 25 March 1639. His first master was a Thomas Dawson (fl. 1630–1639) who was probably the husband of Elizabeth the daughter of Elias Allen. Greatorex then moved from Dawson to Allen where he remained until the end of his apprenticeship. Although his apprenticeship ended in 1648 he didn’t take his freedom until 25 November 1653 following Allen’s death. However, he acquired his own premisses in the Strand already in 1650, which later became known as the Sign of Adam and Eve. All we know of his family is that he married Ann Watson at All Saints Church in Derby.
All Saints Church Derby now the cathedral c. 1875
As I explained in the episode on him, Elias Allen had a good working relationship and friendship with the mathematician and rector of Albury near Guilford in Surry, William Oughtred (1574–1660). Allen manufactured the mathematical instruments that Oughtred conceived. Greatorex also had a close relationship to Oughtred and the two corresponded.
William Oughtred engraving by Wenceslaus Hollar Source: Wikimedia Commons
Oughtred designed his innovative double horizontal dial, which had two scales for reading the hours. Allen manufactured and sold it in his shop and there are two undated ones that were made by Greatorex.
This octagonal brass pedestal sundial is known as a double horizontal dial because it has two scales for reading the hours. The first is a standard scale, which is used with the polar edge of the gnomon. The second is formed by the vertical edge of the gnomon (set at the centre of the dial) and the lines of projection of the celestial sphere on to the plane of the horizon (the horizontal projection).
Greatorex is known to have visited Oughtred in Albury in December 1652 and after his return to London the mathematician, astronomer, and Bishop of Salisbury, Seth Ward (1617–1689), a one-time mathematics pupil of Oughtred, visited him and they discussed a letter the Oughtred had given him, which he had written on a recent comet.
John Greenhill portrait of Seth Ward (1617-1689), Savilian Professor of Astronomy, Oxford (1649-1660) Source: Wikimedia Commons
Another connection between Greatorex, Allen, and Oughtred was Christopher Brookes (fl.1649–1651 d. ). Brookes was a one time sea man, who had earlier served an apprenticeship under Allen (bound in 1629, free in 1639) as an instrument maker. Brookes had married Elizabeth a daughter of Oughtred’s. During the Protectorate he had moved to Oxford where he was employed by the polymathic natural philosopher, John Wilkins (1614-1672), at Wadham as a manciple, i.e. servant of the college, with £30 pa to make instruments. Brookes made:
A nevv quadrant, of more naturall, easie, and manifold performance, than any other heretofore extant framed according to the horizontall projection of the sphere, with the uses thereof. By C.B. maker of mathematic instruments in metall.(1649)
Brookes’ second endeavour was:
The Solution of all Spherical Triangles by the Planisphere (1651): Based with permission on notes by William Oughtred. The instrument and book being sold by Ralph Greatorex at his shop in the Strand.
Amongst Greatorex’s clints was Christopher Wren (1632–1723), today famous as the architect who rebuilt London after the Great Fire but during the seventeenth century known as a mathematician and astronomer.
Christopher Wren portrait by Godfrey Kneller 1711 Source: Wikimedia Commons
He was Gresham professor for astronomy from 1657 to 1661 when he became Savilian professor for astronomy at Oxford a post he held until 1667. Earlier in his career in 1651 he ordered a perspectograph, an instrument to aid in making perspective drawings and a surveying instrument from Greatorex.
Christopher Wren’s perspectograph made by Ralph Greatorex
Historians, on the whole, differentiate between mathematical instruments and mechanical and philosophical instruments. Allen was definitively a mathematical instrument maker producing quadrants, sundials, sectors, etc. Greatorex was one of the earliest makers of mechanical and philosophical instruments:
Samuel Hartlib (c. 1600–1662) referred to Greatorex’s diving apparatus from 1653, a new kind of brewing vessel in 1655, and water-lifting and fire engines in 1656 (the latter praised by John Evelyn (1620–1606))[1]
Greatorex seems to have specialised to some extent in making pumps. The natural philosopher Robert Boyle (1627–1691) is famous for his experiments on the properties of air using a vacuum pump. In 1658, Boyle ordered a vacuum pump modelled on that of Otto Von Guericke (1602–1686) from Greatorex. Greatorex’s pump proved inadequate and Boyle called on his assistant Robert Hooke (1635–1703) to improve it. Hooke did so with one of his usual dismissive comment directed at Greatorex:
“In 1658 or 1659, I contrived and perfected the air-pump for Boyle, having first seen a contrivance for that purpose made for Boyle by Gratorix, which was too gross to perform any great matter.”[2]
Greatorex had other interests: he made implements for sowing corn and cutting tobacco, and in 1657 took a garden in Arundel House for experimental growing of exotic herbs. His chemical interests included inventing a new metal for coinage, corresponding with Robert Boyleon practical matters (1655–6), and demonstrating a new varnish (1663). Astronomy was another interest and in 1658 Greatorex advised on the terminology of scientific instruments to Edward Phillips, lexicographer. As a surveyor, he was employed by the crown in Hampshire (1664), at Woolwich (1668–9), in Whitehall (1670), and in Cambridgeshire (1674). He surveyed the town and castle at Windsor in 1672.[3]
Arundel House was the home of Thomas Howard, 14th Earl of Arundel (1585–1646), who was William Oughtred patron and Oughtred resided there when in London. It was literally just around the corner from the premisses of both Allen and Greatorex in the Strand.
Arundel House (viewed from the north), 1646 engraving by Adam Bierling after a drawing by its then occupant, Wenceslaus HollarMap of Arundel House, drawn by Ogilby and Morgan, c. 1676
One of Greatorex’s most interesting connections was that with the mathematician and engineer Jonas Moore (1617–1679). Moore was born in Pendle in Lancashire and in 1637 was appointed clerk to Thomas Burwell, Vicar-General of thediocese of Durham, a job requiring competence in the use of legal Latin, indicating that he had somewhere received a formal, probably grammas school, education. He married in 1638 and had two sons and a daughter.
Jonas Moore after Unknown artist, line engraving, published 1660
Moore had a strong interest in mathematics and somewhere down the line somebody introduced him to Oughtred’s Clavis mathematicae and he became another of the seventeenth-century mathematicians, who taught themselves mathematics using Oughtred’s tome. His involvement with Oughtred’s magnum opus went further:
In the 1647 Key of the Mathematics, the first English edition of Oughtred’s famous Clavis, an authorial preface pays glowing tribute to Moore and Thomas Wharton for the ‘exceeding great paines and expense’, they had bestowed in correcting and proof-reading the volume.[4]
In 1642 during the English Civil War, he lost his position and moved back to Lancashire where he became part of the group of mathematicians and astronomers around the aristocratic antiquarian, Christopher Towneley (1604–1674), which included William Crabtree (1610–1644), William Gascoigne (1612–1644), and Jeremiah Shakerley (1626–c. 1623) amongst others. This group stood in contact with Oughtred. Before 1649 he had moved to London where he took up residence in Elias Allen’s premisses, working as a mathematics teacher and surveyor. The preface to his to his 1650 Arithmetick is dated from Allen’s shop.
Title page of Moore’s Arithmetick in Four Books, by Jonas Moore (1627 – 1679) 4th edition 1688 Source
In 1650, he was appointed Surveyor to the Fen drainage Company of William Russell, 5th Earl of Bedford and worked on draining the Fens for the next seven years. In 1658, Moore was able to produce a 16-sheet Mapp of the Great Levell of the Fens, which provided an effective means of displaying the Company’s achievements in altering the Fenland landscape ofEast Anglia. Greatorex provided pumps for the drainage. Moore returned to London, where he now had his own house and worked mainly as a surveyor.
In 1661, England acquired the port of Tangier in northwestern Morocco from the Portuguese as part of the dowery of the Infanta Catherina of Braganza on her marriage to Charles II. The English planned to improve the harbour by building a mole. In June of 1662, Jonas Moore went to Tangier as part of the term to design the mole. On his return, he prepared a map with the title A Mapp of the Citty of Tanger with Straits of Gibraltar. Described by Jonas Moore Surveyor to his Royall Highness the Duke of York.
Greatorex had designed a diving bell, which he had demonstrated to fellows of the Royal Society, with the suggestion that it could be used in the construction of the mole. He also designed a device for lifting stones to help in the construction and in 1665 he too went to Tangier returning to London during April or early May 1666, intending to return after 2 July.
Incompetence, waste and outright fraud and embezzlement caused costs to swell; among those enriched was Samuel Pepys. The mole cost £340,000 and reached 1,436 ft (438 m) long before its destruction. (Wikipedia)
Plan of the Tangier mole Source: Wikimedia Commons
The mole construction project brought Moore and Greatorex together again and following the Great Fire of London in 1666, Greatorex assisted Moore who was part of a six man team commissioned to survey the ruined city. The results to the survey were reduced to a six sheet map by the mathematical practitioner John Leake (fl. 1650–1686), who became Master of the Christ’s Hospital Royal Mathematical School in 1673. Both Jonas Moore and Samual Pepys were governors of the Royal Mathematical School. Leake’s map was reduced again and engraved as a single map by Wenceslaus Hollar (1607–1677) another occupant of Arundel House.
Wenceslaus Hollar’s map of London following the Great Fire
Samuel Pepys (1633–1703) is today known as probably the most famous diarist in the English language but in the seventeenth century but he was a well-connected civil servant, who rose to became Secretary to the Admiralty from 1673 to 1679 and again from 1684 to 1689 on both occasions also serving as a member of parliament. Pepys is revealed in his diaries to be a womaniser and drinker and it appears he found a kindred spirit in Ralph Greatorex.
Greatorex was described by Hartlib as having ‘a most piercing and profound witt’ and by Sir Hugh Cholmley in a letter of 22 July 1665 as ‘a very ingenious person but … to much subject to … good Fellowshipp and to spend his time and money idelly … hee is not … to bee trusted with money’ (N. Yorks. CRO, zcg, v/1/1/1, fol.183). A decade earlier, in January 1654, he had been accused of harbouring loose women in his house in St Clement Danes, to which young apprentices and others constantly resorted.[5]
There are quite a lot of references to Greatorex in Pepys’ diary. I have only included the references to Greatorex not the whole entry for the given date. Note how often they go out drinking with each other:
10th January 1660 Tuesday Went out early, and in my way met with Greatorex and at the alehouse he showed me the first sphere of wire [probably an armillary sphere] that ever he made, and indeed it was very pleasant…
12th June 1660 To Mr. Crew wither came Mr. Greatorex and with him to the Faithornes and so to the Devils tavern
11th October 1660 After we had done there Mr. Creed and I to the Leg in King Street, to dinner, where he and my Will had a good udder to dinner, and from thence to walk in St. Jame’s Park, where we observed the several engines at work to draw up water, with which sight I was very much pleased. Above all the rest, I liked best that which Mr. Greatorex brought, which is one round thing going within all with a pair of stairs round; round which being laid at an angle of 45 deg., do carry up the water with a great deal of ease. [there will be a prize for anybody who can explain how Greatorex’s engine worked from Pepys’ description!]
24th October 1660. I went to Mr. Greatorex, where I met him, and so to an alehouse, where I bought of him a drawing-pen, and he did show me the manner of the lamp-glasses, which carry light a great way, good to read in bed by, and I intend to have one of them.
6th December 1660 From thence I walked to Greatorex (he was not within), but there I met with Mr. Jonas Moore, and took him to the Five Bells, and drank a glass of wine and left him.
23rd January 1661 At noon, without dinner, went into the City, and there meeting with Greatorex, we went and drank a pot of ale. He told me that he was upon a design to go to Teneriffe to try experiments there. With him to Gresham Colledge (where I never was before), and saw the manner of the house, and found great company of persons of honour there. [It is interesting that Greatorex was the first to take Pepys to Gresham College, where the Royal Society was formed in 1660. Pepys woulfdlater become its president.)
18th March 1661 I called her [his wife] home, and made inquiry at Greatorex’s and in other places to hear of Mr Barlow (thinking to hear that he is dead), but I cannot find it so, but the contrary. Home and called at my Lady Batten’s, and supped there, and so home.
30th May 1661 Back to the Wardrobe with my Lord, and then with Mr. Moore [not Jonas] to the Temple , and thence toGreatorex, who took me to Arundell-House, and there showed me some fine flowers in his garden, and all the fine statues in the gallery, which I formerly had seen, and is a brave sight, and thence to a blind dark cellar, where we had two bottles of good ale, and so after giving him direction for my silver side-table, I took boat at Arundell stairs, and put in at Milford…
2nd June 1661 Then home to dinner, and then to church again, and going home I found Greatorex (whom I expected today at dinner) come to see me, and so he and I in my chamber drinking of wine and eating of anchovies an hour or two, discoursing of many things in mathematics, and among others he showed me how it comes to pass the strength that levers have, and he showed me that what is got as to matter of strength is lost by them as to matter of time.
9th June 1662 Dined at home, and after dinner to Greatorex’s, and with him and another stranger to the Tavern, but I drank no wine. He recommended Bond, of our end of the town, to teach me to measure timber, and some other things that I would learn, in order to my office.
22nd September 1662 Thence I parted from them and walked to Greatorex’s, and there with him did overlook many pretty things, new inventions, and have bespoke a weather glass of him.
25th November 1662 … thence to Greatorex’s, where I staid and talked with him, and got him to mend my pocket ruler for me…
23rd March 1663 This day Greatorex brought me a very pretty weather-glass [thermometer] for heat and cold.
23rd May 1663 Thence to Greatorex’s, and there seeing Sir J. Minnes and Sir W. Pen go by coach I went in to them and to White Hall;
[…]
Thence back by water to Greatorex’s, and there he showed me his varnish which he had invented, which appears every whit as good, upon a stick which he hath done, as the Indian, though it did not do very well upon my paper ruled with musique lines, for it sunk and did not shine.
10th August 1663 After dinner I took leave and went to Greatorex’s, whom I found in his garden, and set him to work upon my ruler [slide-rule], to engrave an almanac and other things upon the brasses of it, which a little before night he did, but the latter part he slubbered over, that I must get him to do it over better, or else I shall not fancy my rule, which is such a folly that I am come to now, that whereas before my delight was in multitude of books, and spending money in that and buying alway of other things, now that I am become a better husband, and have left off buying, now my delight is in the neatness of everything, and so cannot be pleased with anything unless it be very neat, which is a strange folly.
29th October 1663 Being wearied with looking upon a company of ugly women, Creed and I went away, and took coach and through Cheapside, and there saw the pageants, which were very silly, and thence to the Temple, where meeting Greatoex, he and we to Hercules Pillars, there to show me the manner of his going about of draining of fenns, which I desired much to know, but it did not appear very satisfactory to me, as he discoursed it, and I doubt he will faile in it.
12th September 1664 Anon took boat and by water to the Neat Houses over against Fox Hall to have seen Greatorex dive, which Jervas and his wife were gone to see, and there I found them (and did it the rather for a pretence for my having been so long at their house), but being disappointed of some necessaries to do it I staid not, but back to Jane, but she would not go out with me.
4th February 1669 Thence out with my wife and him, and carried him to an instrument-maker’s shop in Chancery Lane, that was once a ’Prentice of Greatorex’s, but the master was not within, and there he [Gibson] shewed me a Parallelogram in brass, which I like so well that I will buy, and therefore bid it be made clean and fit for me
The list of Greatorex’s clients, friends and acquaintances reads like a who’s who of the English scientific community in the middle of the seventeenth century and is a good example of how interconnected that community was.
[1] Sarah Bendall, Greatorex, Ralph, ODNB, Print 2004 Online: 2004 This version: 03 January 2008
[2] Robert Hooke (c.1670), Posthumous Works (pg. iii-iv); cited by Richard Waller (1705) in “Life of Robert Hooke”
In the previous episode of this series, I took a look at the two English mathematicians, who most influenced the young Isaac Newton (1642–1726 os) in the early stages of his intellectual development, Isaac Barrow (1630–1677) and John Wallis ((1616–1703). Today we take a first of, probably, several looks at Isaac Newton, who played a highly significant role in the evolution of physics, although it still wasn’t called that yet, when he combined terrestrial mechanics with astronomy und the umbrella of universal gravity in his magnum opus, Philosophiæ Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy) 1687.
Source: Wikimedia Commons
The popular hyperbole calls Newton the greatest scientist of all time, which is of course rubbish. Apart from the fact that the use of the term scientist, first coined by William Whewell in 1831, is anachronistic it pays to pause and note that even as late as the end of the seventeenth century there was no such thing as a professional scientist in the modern sense and certainly no preprogrammed career path to become one. If we consider the period from the gradual revival of science in the High Middle Ages to the period of Newton the closest we get to professional scientists are the court astrologers, who were mostly also the astronomers. Even Kepler, who revolutionised astronomy and optics, earned his living mostly as a professional astrologer.
The medieval university didn’t really take mathematics seriously and there was almost never chairs for mathematics. They were predominantly Aristotelian and what are now the physical sciences were handled philosophically not mathematically. When chairs for mathematics began to be created during the Renaissance in the fifteenth century, first in Krakau and then in the Renaissance universities of northern Italy, there were actually created to teach astrology to medicine students because of the prevailing mainstream astromedicine, or iatromathematics to give it its correct name. To do astrology you need to be able to do astronomy and to do astronomy you need to be able to do mathematics. Even at the beginning of the seventeenth century Galileo, as professor of mathematics in Padua, would have been required to teach astrology to the medical students, although we don’t have a direct record of his having done so.
Chairs for mathematics and or astronomy gradually spread throughout Europe during the sixteenth century but Britain lagged well behind the continental developments. In England, Henry Savile (1529–1622), who travelled abroad to acquire his own mathematical education, established chairs for geometry and astronomy at Oxford University in 1619. Cambridge had to wait until 1663 before Henry Lucas (c. 1610–1663) bequeathed the funding for a professorship in his will, with Charles II establishing the Lucasian Chair in 1664. Newton was the second Lucasian Professor following in the footsteps of Isaac Barrow. Of course, the Gresham chairs for geometry and astronomy, set up at the beginning of the century, predate both of the university chairs but these were not teaching positions but public lectureships aimed at a general public. Henry Briggs (1561–1630) was both the first Gresham and the first Savilian professor for geometry.
To show that there no such thing as a science career path in the seventeenth century let us briefly recapitulate the life paths of four scholars who have featured in this series. who made serious contributions to the emerging mathematical sciences.
René Descartes (1596–1650) was the son of a minor aristocrat and politician. He was schooled in the Jesuit College of La Flèche meaning he received a first class education including probably the best mathematical education available in Europe at the time. He studied two years at the University of Poitiers graduating with a Baccalaureate and Licence in canon and civil law. However, instead of now becoming a lawyer he set off to become a military engineer but to do that he, a Catholic French aristocrat, went off to Breda in the Netherlands to join the Protestant Dutch States Army. Purely by chance in Breda, he met the Dutch candle maker turned school teacher Isaac Beeckman, who introduced him to both the corpuscular mechanical theory and mathematical physics. This set him off on a winding path to becoming a mathematician, philosopher and physicist.
Engraved portrait of Descartes based on painting by Frans Hals the Elder (c. 1582–1666) Source: Wikimedia Commons
Christiaan Huygens (1629–1695) was the son of a powerful aristocratic diplomat who enjoyed an absolutely first class private education before going to Leiden University to study law and mathematics followed by a period at the Orange College in Breda. He had been prepared his whole life to become a diplomat like his father but after one mission he decided the life was not for him he withdrew to the family home and supported by his father became a private scholar studying a wide spectrum of the mathematical sciences. Later he would be become a paid scholar in the new French Académie des sciences. That the Académie employed paid scholars was an advantage over the rival Royal society in London, which only paid Robert Hooke as curator of experiments.
As we saw John Wallis (1616–1703) had perhaps the weirdest life path for a scientist. The son of a cleric he also became a cleric occupying various church positions. Purely by chance he discovered a talent for cryptography and became the cryptologist of the parliamentary party during the Civil War and Interregnum. In 1649, Cromwell appointed him, a man with no formal education in mathematics, Savilian Professor of Geometry at Oxford, a post he held for fifty years going on to become one of Europe’s leading mathematical authorities having spent his first couple of years in the post teaching himself the full spectrum of mathematics.
Portrait of John Wallis by Godfrey Kneller Source: Wikimedia Commons
Isaac Barrow (1630–1677) the son of a draper born into a family of many prominent scholars and theologians. A graduate and fellow of Trinity College Cambridge he taught himself mathematics and the natural sciences with a small group of like-minded fellows. Leaving England in 1655 because of the rise of puritanism he travelled extensively through Europe and Asia Minor for four year, deepening his impressive linguistic abilities. Returning in 1659 he was appointed both Regius Professor of Greek at Cambridge and three years later Gresham professor of geometry. In 1663, he was appointed the first Lucasian Professor, resigning the Regius and Gresham professorships in 1664. In 1669, he resigned the Lucasian chair in order to devote his time to theology.
Portrait of a young Isaac Barrow by Mary Beale (1633–1699) Source: Wikimedia Commons
Although their life paths differ substantially, all four of our mathematical scholars have in common that they come from the upper, educated, well off strata of society, two of them were even aristocrats, and could afford the so-to-speak luxury of pursuing a career in still not really established mathematical disciplines. This, as we will see, was not true for Isaac Newton.
Born in manor house of the hamlet of Woolsthorpe-by-Colsterworth near Grantham in Lincolnshire on Christmas Day 1642, on the Julian calendar, Isaac was the son of the yeoman farmer Isaac Newton and his wife Hannah Ayscough. Isaac senior was not only uneducated but could not even sign his own name. He was however not poor and was a successful, prosperous farmer, who unfortunately died three months before his son’s birth.
Woolsthorpe Manor Source: Wikimedia Commons
His mother Hannah, however, came from higher social strata than her husband, from a family that valued education, her brother the Rev William Ayscough MA was a graduate of Trinity College Cambridge.
When Isaac was just three years old, Hannah married the Rev. Barnabus Smith and went to live with him in his parish of North Witham a mile and a half away, leaving Isaac in Woolsthorpe Manor in the care of his maternal grandmother. Eight years later Barnabus died and Hannah returned to Woolsthorpe with Isaac’s three step siblings. Two year later, Isaac, now twelve, was sent off to the grammar school in Grantham, where he lodged with the local apothecary, Mr Clark. Isaac lived an isolated life at school and tended to neglect his studies, which basically consisted just of Latin, but always did just enough to remain school primus.
The grammar school in Grantham, Lincolnshire, attended by Isaac Newton. Engraving, ca. 1820. Welcome Collection
At the age of sixteen Hannah removed him from the school and by 1659 he was living back in Woolsthorpe, where Hannah tried to make a farmer out of him. This proved to be a dismal failure and the school master Henry Stokes and his uncle William Asycough persuaded Hannah to let him finish his education and go to university. Stokes even remitted his school fees to convince the reluctant widow.
He graduated school primus and in June 1661 he was admitted to Trinity College Cambridge as a subsizar, this is a student whose fees are partially remitted in return for which he works as a servant for other students. Hannah Ayscough Newton Smith was a very wealthy woman so, why did she force her son to earn his way through college? She also only gave him an allowance of £10 pa. The major theory is that this was her revenge for being pressured into letting him go to university at all but I think there was an element of puritanism, he should not expect to be spoon fed but should learn the value of money.
575 map showing the King’s Hall (top left) and Michaelhouse (top right) buildings before Thomas Nevile’s reconstruction. Source: Wikimedia Commons
It would seem logical to assume that Isaac went up to Trinity because it had been the college of his maternal uncle, William Ayscough, who had pressured Hannah into sending him to university but there is a second possible source of influence in this issue. There is slight evidence that Isaac served as subsizar to the Trinity fellow, Rev. Humphrey Babington, rector of Boothby Pagnell and brother of Katherine Babington, a friend of Hannah’s and the wife of William Clark the Grantham apothecary where Newton boarded as a schoolboy. Later, Newton stayed with Babington for a time during the summer in 1666-67. It is possible that that the Rev. Babington had recognised Newton’s abilities and taken him under his wing in 1661.
“Sir Isaac Newton. when Bachelor of Arts in Trinity College, Cambridge. Engraved by B. Reading from a Head painted by Sir Peter Lily in the Possession of the Right Honorable Lord Viscount Cremorne.” National Portrait Gallery vis Wikimedia Commons
The undergraduate curriculum in Cambridge in the 1660s was little changed from that when the university was founded more than four centuries earlier. This meant Aristotle, Aristotle and more Aristotle, a diet that didn’t appeal to the young Isaac, who remained a mediocre student. Newton was a disciplined note taker all of his life and we know from his own records that he didn’t actually finish any of his set books. By the 1660s standards had fallen so low in Trinity that basically any student who stayed the course for four years could graduate. So, despite his lack of engagement Isaac duly graduated BA in 1664.
The next step was to apply for a scholarship, which would enable him to continue his studies, and this is where his lack of effort almost caused him to stumble. There were a limited number of scholarship and a larger number of excellent potential candidates and it seemed that the lacklustre Isaac was not in the running. However, somebody in the background pulled some strings and he was granted a scholarship on 28April 1664, enabling him to study for another four years for his MA and making him financially independent for the first time in his life. It is not clear who did the string pulling. It might possibly have been Isaac Barrow who had examined Newton on Euclid for his scholarship and found him wanting or more possibly the Rev Babington, now a highly influential figure in Trinity. In 1667, Babington became one of the eight senior fellow, the group that controlled the college.
What now followed in the years from 1664 up to 1672, when Newton published his first paper, is one of the most impressive period of self-study ever undertaken, including the mythical Annus mirabilis, the year that Newton spent at home in Woolsthorpe Manor having been sent down from Cambridge because of the plague in 1665-66. During this period Newton taught himself the modern mathematics, astronomy, mechanics, and optics utilising the work of the leading scholars in these fields, extending and going beyond them and creating his first contribution to these fields. I’ve written a long blog post outlining all that he did over the second half of the 1660s and am not going to repeat it here. When he entered the 1670s Isaac stood at the beginning of the process that would see him become the most powerful natural philosopher in Europe.
Regular readers will be well aware that a Renaissance Mathematicus book review is usually anything but short. I try as far as possible to give an accurate, informative, outline sketch of the actual contents of the book under discussion. This leads automatically to a lengthy essay style review, the aim of which is to give potential readers a clear picture of what exactly they can expect if they decide to invest their time and money in the volume in question. Given this approach to reviewing, how can I produce a Renaissance Mathematicus style review of a book that is seven hundred and forty pages long and contains thirty nine academic papers covering a very wide array of different aspects of a single topic without it turning into a seemingly never ending essay? The simple answer is, I can’t so, what follows will be far less detailed and informative than is my want.
So, what is the topic and what is the book that gives this topic so much attention? The topic is one that has fairly often put in an appearance here at the Renaissance Mathematicus, zero and the book is The Origin and Significance of Zero: An interdisciplinary Perspective.[1]
The book is the result of a cooperation between Closer to Truth, a broadcast and digital media not-for-profit organisation presenting a weekly half-hour television show which airs continuously since 2000 on over 200 PBS and public TV stations, and the Zero Project Foundation, which was set up in the Netherlands in 2015. Closer to Truth is the baby of the book’s one editor Robert Lawrence Kuhn and the Zero Project Foundation was set up by the book’s other editor Peter Gobets, who unfortunately passed away just before the book was published. You can view a Closer to Truth video on the Zero Project here. and read about Closer to Truth here
The book opens with a ten page preface in which Kuhn, a philosopher, talks about his life-long obsession with the concept of nothing and discusses a hierarchy of definition of nothing. The twelve page introduction from Gobets explains the motivation behind the Zero Project, its cooperation with Closer to Truth and the structure and intention of the book itself.
The book is in four parts, whereby Part 0 consists of fifteen papers on Zero in Historical Perspective. Part 1 has sixteen paper on Zero in Religious, Philosophical and Linguistic Perspective, the papers are as wide ranging as the title suggests. Part 2 Zero in the Arts is very short consisting of a very brief introduction by Gobets to eight art works by the artist British-Indian sculptor Sir Anish Mikhail Kapoor (b. 1924) devoted to Kapoor’s visualisation of the Buddhist concept of the void. Part 3 has seven papers under the title Zero in Science and Mathematics.
The papers vary considerably, in length, in academic depth, some are fairly general and superficial, some are deeply researched, and writing quality i.e. readability but this is too be expected in a book that tries to pack so many different viewpoints into one volume. At times I got the feeling that some judicious editing would have improved it in general, less would have been more.
As somebody, who is primarily a historian of mathematics it is, of course, Part 0 Zero in Historical Perspectivethat most interested me. The section opens with two papers relating to the multiple appearances of zero as a concept, as a placeholder and as a number in different cultures and the historical problems of trying to establish if, when and how influences or exchanges took place between those cultures and concepts. Neither paper is particularly helpful and the second Connecting Zeros by Mayank N. Vahia gives prominence to an ahistorical myth. He writes:
Indians were the first to work out the algebra of zero and opened the window to a completely new class of mathematics.
This was not true for the Europeans, to whom life without one was unimaginable. One was the natural smallest number for them. Zero made them uncomfortable. All cultures believed in one form or another, that there exists a Great God. This was the proverbial “One”. This Great Got then created the universe and the many variation in life. The one therefore pervades everything and remains even when all else is gone.
In early Europe it was forbidden to study zero [my emphasis] as it was considered unnatural and against the working of the Great One who would always be present.
I could write a whole blog post taking this heap of garbage apart. It comes as no surprise that it was written by a retired engineer who “has become interested in understanding the origin and growth of astronomy and science in India”. He should start by learning something about comparative religion about which he displays an unbelievable ignorance. Perhaps he could explain who the “Great God” is/was in pantheistic Hinduism? Although he doesn’t define what he means by early Europe, one has to assume he means the Middle Ages with its Christian culture, which I’m sorry to tell him, which, despite the widespread myth, never forbade the study of zero.
Things improve when we get to the histories of zero in the individual cultures. There is an excellent paper, Babylonian Zero on the sexagesimal place-value number system in Mesopotamia and the introduction of a place holder zero and the separate concept of nothing as the result of an arithmetic operation.
There are two good papers on the Egyptian concepts of zero and nothing, Aspects of Zero in Ancient Egypt and The Zero Concept in Ancient Egypt, the latter includes a brief section on the Mayan concept of zero. Followed by an equally good one on zero in ancient Chinese mathematics, On the Placeholder in Numeration and the Numeral Zero in China.
As to be expected India features next with a short paper on the appearance of numerals in Reflection onEarly Dated Inscriptions from South India followed by a longer one tracing the path from the religious term Śūnyameaning empty or void to the numeral zero, From Śūnya to Zero – an Enigmatic Journey, which includes section on the Egyptians, the Babylonians, the Incas, the Maya, China, Greece and India with reflection of the reception in Arabic and European culture. The two paragraphs here on the Incas and the Maya are the only mention of the development of zero in Middle America a serious lacuna in the book. This is followed by an essay on The Significance ofZero in Jaina Mathematics an interesting branch of Indian mathematics, somewhat outside the mainstream.
Now we get the bizarre rantings of Jonathan J. Crabtree, Notes on the origin of the First Definition of Zero Consistent with Basic Physical Laws. Crabtree has been wittering on about his “great discovery” in elementary mathematical pedagogy to my knowledge for at least twenty years and an Internet search shows that it is closer to forty years. Crabtree thinks that English language elementary mathematics teaching is a disaster because it uses an at best ambiguous at worst false definition of multiplication. I write English language because the pesky British spread this abomination through the textbooks it distributed throughout the Empire. Crabtree attributes this pedagogical error to Henry Billingsley’s false translation of Euclid’s definition of multiplication. To this he has added that Europe didn’t understand the true nature of zero because the Arabs mistranslated Brahmagupta.
Up next we next have a somewhat bizarre four page paper, Puttinga Price on Zero about a historian of mathematics asking a class of mathematicians to explain how they would allocate royalties to the various cultures which are claimants for the invention of zero. A waste of printing ink in my opinion.
Returning to more scholarly realms we now have an interesting article on a famous zero artifact, Revisiting Khmer Stele K-127. This stone stele discovered in1891 on the east bank of the Mekong River in Sambaur contains the date 604 of the śaka era, i.e. 682 CE, and is the oldest known inscription of the numeral zero.
Moving forward in time we get an essay on zero in Arabic arithmetic, The Medieval ArabicZero. Comprehensive, detailed and highly informative this article meets to highest standards and one wished that it might have been used as a muster for the whole volume. This is followed by an excellent paper on Islamic numerals, Numeration in the ScientificManuscripts of the Maghreb.
The final paper in Part 0, The Zero Triumphant is about the Tarot. This, however, is not the fortune telling Tarot but the original 15th century Italian card game, which was originally called ‘trionfi’ (i.e., ‘triumphs’ or ‘trumps’). This was played with an amalgamation of two packs of cards, the four-suited deck of playing cards brought into Europe via the Mamluk Empire from the Muslim Near East and a deck of 22 allegorical images originating in medieval Christian iconography. The Islamic deck was numbered with Hindu-Arabic numerals and the European Trumps cards had Roman numerals. The Fool or Crazy One (Il Mato or le Fol) is numbered 0.
A fascinating paper that is however flawed by repeating the myth served up in the second paper Connecting Zeros:
The concept of zero did not exist in the classical mathematics of the Greeks and Romans. And it was an abomination at first to the Christian West. What use did good Christians have for nothingness? God created something not nothing.
As noted above this is ahistorical bullshit.
Each of the papers as footnotes and its own, oft very extensive, bibliography, and the book has a usable general index. Some but not all of the papers are illustrated. The book closes with an Epilogue by Peter Gobets with more thoughts about the Zero Project and the books role in it.
Based on what I’ve read, and I admit to not having read the whole volume, I could have titled this review, The Good, The Bad and The Ugly. There are some excellent papers, some that are somewhat iffy and some that probably should not have made it into print. It is actually quite affordable given that it’s a Brill publication the hardback and the PDF both waying in at €100 plus VAT on the publishers website but I’m not sure I would recommend buying it rather than borrowing it from a library to read the bits that interest the individual reader. I do have one last complaint, the book is so thick, so heavy, and so tightly bound that I literally found it impossible to find a way to read it comfortably.
[1]The Origin and Significance of Zero: An interdisciplinary Perspective, edited by Peter Gobels and Robert Lawrence Kuhn, Brill, 2024.
In the early modern period England lagged well behind the European continent in the development of the natural sciences and mathematics. We are now rapidly approaching the man whose work would not only caught up to these developments but also took the lead in mathematics, optics, physics, and astronomy, Isaac Newton (1642–1726 os). Newton represents a high point in this series but not yet the end point. As we have already seen in recent episodes, Newton’s work was heavily influenced by continental scholars. His foundational three laws of motions in Principia took the law or principle of inertia from Isaac Beeckman (1588–1637) via René Descarte (1596–1650) and were influenced in their conception and form by the three laws of motion in the Horologium Oscillatorium (1673) ofChristiaan Huygens (1629–1695) However, before we plunge into Newton and his work, I want to take a brief look at two English scholars, Isaac Barrow (1630–1677) and John Wallis (1616–1703), who exercised a strong influence on Newton’s mathematical approach to physics, which stood in strong contrast to the prevailing mechanical approach of the European scholars. Contrary to popular opinion Barrow never taught Newton but did, famously, recommend him as his successor as Lucasian professor of mathematics. It should be noted that Newton’s Cambridge was still basically a medieval Aristotelian university in which mathematics played a very minor role so, his adoption of a mathematical approach to physics was a radical move.
Isaac Barrow was born, the son of a draper, into a family with many prominent scholars and theologians. He originally attended Charterhouse School but because of his bad behaviour, his father transferred him to Felsted School in Essex where John Wallis had also been educated. He entered Trinty College Cambridge in 1646, graduated BA in 1649, was elected fellow and graduated MA in 1652.
Portrait of a young Isaac Barrow by Mary Beale (1633–1699) Source: Wikimedia Commons
In the 1650s Barrow devoted much of his time and efforts to the study of mathematics and the natural sciences together with a group of young scholars dedicated to these pursuits that included John Ray (1627–1705) and Ray’s future patron Francis Willughby (1625–1672) who had both shared the same Trinity tutor as Barrow, James Duport (1606–1679). Barrow embraced the mathematical and natural science of Descartes, whilst rejecting his metaphysics, as leading to atheism. In this period Barrow produced epitomes of Euclid’s Elements and his Data, as well as of the known works of Archimedes, the first four books of Apollonius’ Conics and The Sphaerics of Theodosius. Barrow used the compact symbolism of William Oughtred (1574–1660) to produce the abridged editions of these classical works of Greek mathematics.
Because of the rise of puritanism Barrow left England in 1655 and ravelled extensively through Europe and Asia Minor, first returning to Cambridge in 1659. Through the support of John Wilkins (1614–1672) he was appointed Regius Professor of Greek at Cambridge followed in 1662 by his appointment as professor of geometry at Gresham College. On the creation of the Lucasian Chair for Mathematics in 1663 Barrow was, once again on the suggestion of Wilkins, appointed as it first occupant. In 1664 he resigned both the Regius and the Gresham professorships. As Lucasian professor he lectured on geometry and optics. He was immensely knowledgeable of the new analytical mathematics possessing and having studied intently the works of Galileo, Cavalieri, Oughtred, Fermat, Descartes and many others however he did not follow them in reducing mathematics to algebra and analysis but went in the opposite directions reducing arithmetic to geometry and rejecting algebra completely. As a result, his mathematical work was at one and the same time totally modern and up to date in its content whilst being totally old fashioned in its execution. Although presented geometrically Barror developed a fairly advance system of calculus containing amongst other things the first generalised formulation of the fundamental theorem of calculus. Newton acknowledged his influence and although Gottfried Leibniz (1646–1716) denied being influenced by Barrow, he is known to have bought the Lectiones geometricae when they were published in 1670.
Barrow prepared his optics lectures for publication assisted by his successor as Lucasian Professor, Isaac Newton, who was at the time delivering his own optics lectures, and who proof read and corrected the older Isaac’s manuscript. Building on the work of Kepler,Scheiner and Descartes, Barrow’s Optics Lectures was the first work to deal mathematically with the position of the image in geometrical optics and as such remained highly influential well into the next century. It is important to note that Barrow rejected the Cartesian mechanical interpretation of optics preferring a return to a purely mathematical presentation. In general, he believed in a mathematical presentation of all of the physical science echoing and almost certainly influencing Newton’s own Philosophiæ Naturalis Principia Mathematica with its emphasis very much on the Mathematica.
Matthew Noble (1817–1876) ; Isaac Barrow (1630-1677); Trinity College, Cambridge;
Barrow’s further career as a theologian doesn’t interest us here so we can turn our attention to John Wallis. Wallis, who went on to become one of the most important English mathematicians in the seventeenth century was a mathematical autodidact. Wallis was born the third child of John Wallis minister of the church at Ashford in Kent, who died when he was six years old. He attended various grammar schools and learnt Latin, French, Greek and Hebrew as well as studying but didn’t learn any mathematics, which was not taught at these schools because as Wallis wrote in his autobiography:
For mathematics, at that time with us, were scarce looked on as academical studies, but rather mechanical – as the business of traders, merchants, seamen, carpenters, surveyors of lands and the like.
However, during the Christmas holidays in 1631 his brother introduced him to arithmetic which he was learning it as preparation for a trade. Wallis remarked that mathematics:
… suited my humour so well that I did thenceforth prosecute it, not as a formal study, but as a pleasing diversion at spare hours …
Around Christmas 1632, he went up to Emmanuel College Cambridge, where he graduated BA in 1637 and MA in 1640. During this time, he studied little or no mathematics. He was ordained and appointed chaplain first to Sir Roger Darley at Butterworth in Yorkshire and the between 1642 and 1644 at Hedingham in Essex. Around this time, he discovered a talent for cryptography:
… one evening at supper, a letter in cipher was brought in, relating to the capture of Chichester on27December1642, which Wallis in two hours succeeded in deciphering. The feat made his fortune. He became an adept in the cryptologic art, until then almost unknown, and exercised it on behalf of the parliamentary party.
In 1644, Wallis became secretary to the clergy at Westminster and at the same time became a member of one of the groups that would later go on to found the Royal Society. In 1647, he stumbled across Willian Oughtred’s Clavis Mathematicae, which he proceeded to devour in a couple of weeks, finally becoming the mathematician that was apparently his destiny, writing his first mathematics text, Treatise of Angular Sections, which remained unpublished for forty years.
In 1649, seemingly out of the blue, Cromwell appointed him Savilian Professor of Geometry at Oxford. It should be pointed out that he had no formal mathematical education, had never worked as a mathematician, nor had he ever published any mathematics. He would, however, go on to hold the post for more that fifty years filling it with distinction.
Portrait of John Wallis by Godfrey Kneller Source: Wikimedia Commons
With a rare energy and perseverance, he now took up the systematic study of all the major mathematical literature available to him in the Savilian and the Bodleian libraries in Oxford. According to the statutes of his chair, Wallis had to give public lectures on the thirteen books of Euclid, on the Conics of Apollonius, and on all of Archimedes’ work. He was also to offer introductory courses in practical and theoretical arithmetic—with a free choice of textbooks therein. Lectures on other subjects such as cosmography, plane and spherical trigonometry, applied geometry, mechanics, and the theory of music were suggested but not obligatory according to the statutes. (Christoph J. Scriba, Isaac Barrow, Complete Dictionary of Scientific Biography)
Firmly established in the leading position for mathematics in England, Wallis went on to write and publish books that introduced the newly developing continental mathematics to the island. His first publication in this direction was De sectionibus conicis (1655), a seemingly traditional topic but which he presented in a new way. Having introduced the conic sections, he handled them analytical as algebraic curves, not as geometrical forms, in the style of the analytical geometry of Descartes, actually improving on Descartes presentation. This was before van Schooten’s expanded Latin edition of Descartes’ Géométrie had been published.
In the same year Wallis also finished his most important book Arithmetica Infinitorum, although the official publication date was 1656. This systemised and extended the analytic methods of Descartes and above all Cavalieri’s geometry of indivisibles, which he had already introduced in De sectionibus conicis:
“I suppose any plane to be made up of an infinite number of parallel lines, or as I would prefer, of an infinite number of parallelograms of the same altitude; (let the altitude of each one of these be an infinitely small part1/∞ of the whole altitude, and let the symbol ∞ denote Infinity) and the altitude of all to make up the altitude of the figure.”
Although he learnt the method from Torricelli’s Opera Geometrica (1644), Wallis attributes this new methodology to Cavalieri, because Torricelli does, without acknowledging Torricelli’s own substantial contributions, of which he was not aware, not having read Cavalieri’s own work.
In 1685, Wallis published in English his Treatise of Algebra, Both Historical and Practical, which as the title states contained a historical survey of the subject. Amongst other things it contained the first complete publication of the Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas of Thomas Harriot (c. 1560–1621). It had been first published posthumously in 1631 but unfortunately his mathematical executors Torporley (1564–1632) and Walter Warner (1563–1643) did not understand his innovations, such as negative and complex roots of equations and removed them before publication. Wallis who was virulently nationalist, actually accused Descartes of having plagiarised Harriot’s work. Unlike Descartes, Wallis fully accepted both negative and complex roots whilst also demonstrating that Descartes rule of signs was incorrect.
In physics, as already noted in an earlier episode, Wallis was one of those, along with Christopher Wren (1632–1723) and Christiaan Huygens (1629–1695), who corrected Descartes false laws of collision in 1668. However, unlike the other two who confined their theory to perfectly elastic bodies (elastic collision), Wallis considered also imperfectly elastic bodies (inelastic collision). This work introduced the concept of the conservation of momentum, which played a central role in Newton’s dynamics. This was followed in 1669 by a work on statics(centres of gravity), and in 1670 by one on dynamics: these provide a convenient synopsis of what was then known on the subject.
Newton studied Wallis’ Arithmetica Infinitorum intensely in the years 1664 and 1665 and it exercised a major influence on his mathematical development. Newton later acknowledge that influence in a letter to Leibniz. Later Newton and Wallis became friends and Wallis was one of Newton’s most vocal supporters in his dispute with Leibniz over the calculus. He also continually pressured Newton to publish his Opticks, which had been essentially composed in the 1670s but which he held back do to the aggressive criticism of his first paper on optics in 1671.
The influence of both Isaac Barrow and John Wallis played a significant role in the intellectual development of both Isaac Newton the mathematician and Isaac Newton the physicist as the young scholar worked his way from the philosophical science of Descartes to his own mathematical presentation.
After Newton and Babbage, today we look at the surviving images of the astronomer Johannes Kepler (1571–1630). Kepler was born the son of an innkeeper’s daughter and a mercenary, who deserted his family when Johannes was just five years old. This is not the environment in which parents have portraits painted of their children. In fact, there are very few portraits of Johannes Kepler at all and we don’t know the source of most of them and several are clearly produced posthumously and we don’t know is they’re are based on an existing image or are just the artist’s imagination.
There is one contemporary painting by the German artist Hans van Aachen (1552–1615), a leading representative of Norther Mannerism. It is described as the portrait of a young man thought to be Johannes Kepler but the attribution is not certain.
Hans van Aachen’s supposed portrait of Kepler
There is another portrait in the Galleria degli Uffizi in Florence, which is labelled Johannes Keplerus, but neither the artist nor when it was painted is known. It is, however, attributed to the seventeenth century.
Johannes Kepler portrait by an unknown artist
There is a nineteenth century engraved portrait by the English watercolourist and architectural draughtsman Frederick Mackenzie (1787–1854), which is now in the Smithsonian Dibner Library of the History of Science and Technology. The caption says From a Picture in the Collection of Godefrey Kraemer Merchant of Ratisbon. Ratisbon is an English alternative name for Regensburg the city in which Kepler died and was buried.
The Dibner also has a copy of the Uffizi Kepler engraving, as well as an undated engraved portrait in profile.
Also in the Dibner is an engraving of a portrait of Johannes Kepler from a 1620 painting that was given to the Strasbourg Library in 1627, artist unknown. There is a painting from 1910 based on the engraving in the Kepler-Museum in Weil der Stadt, Kepler’s birth-place, by the German painter August Köhler (1881–1964).
1910 painting boy August Köhler based on the above engraving
Amongst all this doubt about the various portraits of Kepler the most surprising is the fact that a very impressive portrait in the possession of a Benedictine monastery in Kremsmünster, Austria, that was thought to be Kepler painted in 1610 is now thought to have been first painted in the nineteenth century and probably not Kepler at all. I myself have used it several time on Kepler posts in the past but no longer.
Nineteenth century portrait supposedly of Johannes Kepler claiming to be a copy of a lost original from 1610. Now considered to be a forgery and not Kepler at all.
Addenda 31.12.2025
In the comments, Laura quite correctly drew my attention to the fact that I hadn’t included the wedding portraits of Barbara and Johannes Kepler. I couldn’t find any information on these portraits anywhere on the Internet so I asked Professor Aviva Rothman, Inaugural Dean’s Associate Professor and Director of Graduate Studies at Case Western Reserve University, who is a Kepler expert and currently writing a new biography of Kepler. She directed my attention to the paper The Fate of Kepler’s Handwritten Heritage by Irina Tunkina in Culture and Cosmos Vol. 25, Spring/Summer & Autumn/Winter 2021. Tunkina writes:
In 1876 the Pulkovo Observatory acquired the family treasures from the direct descendants of Kepler’s first wife, Barbara Müller von Mülek (the sisters Emma, Ottilie and Augusta Schnieber) for 400 marks. These were added to the collection.53 There was a pair of miniature oil portraitsof Johannes and Barbara Kepler from 1597, made during their lifetime
Yesterday, we took a look at some of the many portraits of Isaac Newton the second Lucasian professor of mathematics at Cambridge, today, we are turning our attention to a nineteenth century occupant of that honourable chair, Charles Babbage (1791–1871).
Although Babbage came from a very wealthy family with a high social status there are no know childhood portraits. The earliest portraits seem to be from 1833, when he was already forty-two years old and Lucasian Professor. There is a stippled engraving made by the English engraver John Linnell (1792–1863). The son of a carver and guilder he had contact with several painters as a pupil before being admitted to the Royal Academy in 1805. He was only sixteen when left the Academy and went on to long and successful career as painter and engraver.
Self-portrait of John Linnell c. 1860Linnell’s portrait of Babbage
There is a second stippled engraving of Babbage from 1833 as Lucasian Professor by Richard Roffe (fl. 1805–1827) about who very little is known.
Roffe’s portrait of Babbage
There is an early painted portrait of unknown date and by an unknow artist, now in the National Trust’s collection.
British (English) School; Charles Babbage (1792-1871) ; National Trust
There is a painted portrait in the National Portrait gallery from 1876 by Samuel Lawrence (1812–1884) a British portrait painter, who painted the cream of the mid Victorian society, ncluding the polymath William Whewell, a student friend of Babbage’s.
Samuel Lawrence attributed to Sir Anthony Coningham Sterling, salt print, late 1840sSamuel Lawrence portrait of Babbage
There is lithographic portrait from 1841 now in the Wellcome Collection by D. Castellini after the pencil drawing Carlo Ernesto Liverati (1805–1844). I can find nothing on either Liverati or Castellini.
L0020480 Charles Babbage Credit: Wellcome Library, London. Wellcome Images Portrait bust of Charles Babbage with facsimile Lithograph By: D. Castellini after: Liverati, C.E.Published: –
Babbage was a man of his times and a major technology fan so we naturally have quite a lot of photographic portraits. There is a daguerreotype from around 1850 made by the French photographer and artist Antoine François Jean Claudet (1797–1867).
Antoine Claudet in 1850Claudet’s daguerreotype of Babbage
Claudet was active in the Victorian scientific community and was working with Charles Babbage on photographic experiments around the time this compelling portrait of him was made. In it, the pattern of embellished fabric on the side table is picked up in Babbage’s waistcoat. (National Portrait Gallery).
Claudet also took one of the only two surviving photographs of Ada Lovelace in c. 1843 or 1850
Claudet’s daguerreotype of Ada Lovelace
There is a seated photographic portrait of Babbage:
Half-length portrait of Babbage, seated, body turned to the left as viewed, Babbage looking to camera. The image is embossed “J M MACKIE PHOTO”. The reverse has two inscriptions. Top, in ink: “For my dear Aunt Fanny from her affectionate nephew B Herschel Babbage”. [Benjamin Herschel Babbage (1815-1878)]. Below “Copied from a negative taken for the Statistical Society about 1864. Charles Babbage was elected a Fellow of the Royal Society in 1816. (Royal Society)
There is another undated seated photographic portrait of an elder Babbage with the caption,” Charles Babbage (1792-1871). English mathematician and mechanical genius.”
The Illustrated London News published an obituary portrait of Babbage
Obituary portrait of Charles Babbage (1791-1871). The caption is The late Mr Babbage. Illustration for The Illustrated London News, 4 November 1871. This portrait was derived from a photograph of Babbage taken at the Fourth International Statistical Congress which took place in London in July 1860. (Science Museum)
Most of the images shown here were used multiple times in writings about Babbage-.
Humans are strongly guided by their visual perception. Naturally the other senses—smell, hearing, taste, touch—play a role but seeing is predominant. This is reflected in everyday speech. When we want to draw somebody’s attention to something or emphasise a point we often say “Look!” or “Look here!” even when we are only going to say rather than show something. We use the word “see” to signal understanding, “I see” or “do you see”.
Visual perception also played a strong role in the early evolution of science. People developed theories to try and explain what they could see. This was particularly true in astrology-astronomy where the only empirical evidence available was visual. It is significant that the period that most people believe is the nativity of modern science, the early seventeenth century, saw the invention of both the telescope and the microscope, the first instruments to extend the perception of one of the senses, namely vision, allowing researchers to see and examine things that were previously hidden from their sight.
Visual presentation plays an increasing role in the presentation of the history of science with historians examining and interpreting visual representation from times past. One thing that interests people, and not just historians, is what did a given scientist look like. Unfortunately, in popular presentations the portraits or photographs used tend to be those of said scientist as a dignified senior citizen, maybe when receiving that Nobel Prize or the tenth honorary doctorate, rather than as a young researcher when they were actually doing the work for which they were honoured. The further back we go the real difficulty is knowing whether the visual representation is real, i.e. true to life, or some artists ideal of the person in question.
Over the next three days I going to be taking a look at the surviving portraits of the three scholars, who make up my Christmas Trilogy every year—Isaac Newton, Charles Babbage, and Johannes Kepler.
Newton’s family were not by any means poor, when he inherited the family estates they provided him with an income of £600 p.a. at a time when the income of the Astronomer Royal was £100 p.a., but they were relatively simple puritan farmers so, there are no youthful portraits of Isaac, as a child. This, of course, all changed when he became the most famous natural philosopher and from the later part of his life we have quite a lot of portraits which documents his advancing age.
There is however one engraved portrait from 1677 on which the caption reads “Sir Isaac Newton. when Bachelor of Arts in Trinity College, Cambridge. Engraved by B. Reading from a Head painted by Sir Peter Lily in the Possession of the Right Honorable Lord Viscount Cremorne.”
Source: National Portrait Galery vis Wikimedia Commons
Sir Peter Lely was actually Pieter van der Faes, a Dutch portrait painter, who became a master of the Guild of St Luke, the city guild for painters, in Haarlem in 1637.
Peter Lely self-portrait c. 1660 Source: Wikimedia Commons
He moved to London in 1643 and succeeded Anthony van Dyck (1599–1641) as London’s most fashionable portrait painter going on to paint portraits of the rich, powerful, and famous including both Charles I and Oliver Cromwell, as well as Charles’ most famous mistress Nell Gwynne.
Peter Lely: long-time mistress of Charles II of England, Nell Gwynne as Venus, with her son, Charles Beauclerk, as Cupid.
Interestingly when Robert Hooke first came to London it was an apprentice to Lely but he then attended Westminster school instead.
Probably the most well-known portraits of Newton are those painted by Sir Godfrey Kneller (1646–1723). Kneller like Lely, whom he succeeded as London’s most fashionable portrait painter, was like him not English.
He was born Gottfried Kniller in Lübeck the son of Zacharias Kniller a portrait painter. He first studied in Leiden but then became a pupil of Ferdinand Bol (1616–1680) a pupil of Rembrandt Harmenszoon van Rijn (1606–1669) and of Rembrandt himself. Together with his brother Johann Zacharias Kniller (1642–1702) he spent the early 1670s painting in Rome and Venice before the two moved to London in 1676 and Godfrey inherited Lely’s crown as the in portrait painter. Kneller set up a portrait studio and specialised almost exclusively in painting portraits. His production rate was almost unbelievable and he achieved it by a streamlined work process. At sittings he only made sketches of the face of the sitter and then filled in the rest without reference to the sitter. We don’t know if his Newton portraits were done in this manner.
Godfrey Kneller portrait of Isaac Newton 1689 Source: Wikimedia CommonsGodfrey Kneller portrait of Isaac Newton 1702 Source: Wikimedia Commons
There are a series of four formal portraits of Newton in his eighties as the President of the Royal Society. These were painted by John Vanderbank (1694–1739), this time an English born painter but the son of the Huguenot refugee from Paris, John Vanderbank Snr. well-to-do proprietor of the Soho Tapestry Manufactory and Yeoman Arras-maker to the Great Wardrobe, supplying the royal family with tapestries from his premises in Great Queen Street, Covent Garden.
John Vanderbank self-portrait drawing c. 1720 Source: Wikimedia Commons
John Vanderbank studied composition and painting first under his father and then the painter Jonathan Richardson (1667–1745) before becoming a pupil of Godfrey Kneller in 1711 at his art academy in Great Queen Street, Covent Garden next door to his father’s tapestry workshop. Like Kneller, Vanderbank became a renowned portrait painter.
Vanderbank, John; Isaac Newton ,1725 Fellow, Source: Trinity College, Cambridge; Vanderbank, John; Isaac Newton 1726; Source: The Royal SocietyVanderbank, John; Isaac Newton 1727, Source: Trinity College, Cambridge; Vanderbank, John; Isaac Newton not dated; Source: The Royal Society;
There is a single, oft reproduced, portrait of Newton by the Irish painter Charles Jervas (c. 1675–1739) who was another pupil of and assistant to Godfrey Kneller and succeeded Kneller as Principle Painter in Ordinary to George I in 1723.
Self Portrait aged fifty, 1725 (oil on canvas) by Jervas, Charles (1675-1739) oil on canvas Newton portrait by Charles Jervas Source: Royal Society
John Smith (c. 1652–c. 1742), a very prolific English mezzotint engraver, was also a member of Godfrey Kneller’s circle and, as to be expected, he also produced an engraved portrait of Newton.
John Smith the Engraver 1696 painted by Sir Godfrey Kneller 1646-1723 Source: Tate GalleryJohn Smith’s engraved portrait of Newton
Also from the Godfrey Kneller’s circle was the English engraver George Vertue (1684–1756), who produced an engraving of a Vanderbank portrait.
George Vertue, portrait by Jonathan Richardson (1733) Source: Wikimedia CommonsGeorge Vertue’s portrait of Newton Source: Royal Society
There is a single portrait of Newton by Enoch Seeman the Younger (1689–1745), who was born in Gdańsk and was brought to London by his father Enoch Seeman the Elder, also a painter, in around 1704. He also painted in the style of Godfrey Kneller.
Self-portrait of Enoch Seeman Source: Wikimedia CommonsEnoch Seeman the Younger; Isaac Newton (1642-1727), Trinity College Cambridge
There is a portrait of Newton painted in 1712 by the English artist James Thornhill (1675/6–1734)
Self-portrait James Thornhill
Purchased for the Newton family home of Woolsthorpe Manor. It is a rare depiction of the great man without a wig.
Woolsthorpe Manor portrait of Newton by James Thornhill
There is a second Thornhill portrait, also without wig, in Trinity College Cambridge
James Thornhill; Isaac Newton Trinity College, University of Cambridge;
Trinity College Cambridge, Newton’s college has a full sized marble statue of Newton produced by the French sculptor Louis-François Roubillac (1702–1762), who moved to London in 1730. This was presented to the college by the mathematician and Master of Trinity Robert Smith (1690–1768) in 1755 and cost £3000, a vast sum in those days.
Louis-François Roubillac marble statue of Isaac Newton, Trinity College Cambridge Source: Wikimedia Commons
Posthumously Newton rose to the status of a scientific god so, there are many engraved portrait from the later eighteenth and the nineteenth century often based on the Kneller portraits. Due to his fame and status, especially in later life, there are many portraits of Isaac Newton and I’m sure I’ve missed one or the other but the selection above should give you an impression of what England’s most famous scientist looked like.
Today at 15:03 UT (that’s GMT for all those still living in the past) the Sun on its apparent journey to the south will briefly stand still above the Tropic of Capricorn before turning and beginning its climb northwards up to the Tropic of Cancer. The brief still stand gives the moment its name Solstice from the Latin Solstitium, point at which the sun seems to stand still. A composite noun set together from sol the sun and past participle stem of sistere, stand still, take a stand; to set, place, cause to stand. Tropic comes from Latin tropicus pertaining to a turn, from Greek tropikos of or pertaining to a turn or change. This moment marks the winter solstice in the northern hemisphere and the summer solstice in the southern hemisphere.
As I note at this time every year, rejecting the purely arbitrary convention of midnight on 31 December marking the beginning of the New Year, here at the Renaissance Mathematicus my New Year is the winer solstice, the point in the astronomical calendar in the depth of winter, when the light begins to return.
I wish all of my readers a happy solstice and may you enjoy whatever seasonal events you participate in. I personally don’t celebrate any of them. I thank all of you for your engagement, for reading my verbal outpourings, for your comments and your criticisms and hope you will continue to do so in the year to come.
If your philosophy of [scientific] history claims that the sequence should have been A→B→C, and it is C→A→B, then your philosophy of history is wrong. You have to take the data of history seriously.
John S. Wilkins 30th August 2009
Culture is part of the unholy trinity—culture, chaos, and cock-up—which roam through our versions of history, substituting for traditional theories of causation. – Filipe Fernández–Armesto “Pathfinders: A Global History of Exploration”
The Renaissance Mathematicus 
