Let the Sunshine in!

At almost the point in time that I will post this, the sun (viewed from the stand point of an inhabitant of the northern hemisphere, which I am) will reach the end of its journey to the south and turning start its long journey* to the north bringing in their turn the spring and eventually the summer to these latitudes. Of course if you live in the southern hemisphere, as does my friend the Aussie Anthropoid, then everything is reversed with the sun departing from their latitudes and letting the autumn and following it the winter in. But then again the antipodeans always do everything arse backwards.

At this turning point in the year I wish all of my readers much sunshine in their lives for the next twelve months and lots of good food and drink at the various celebrations for the winter solstice, which takes place at exactly 17:47 UTC (that’s what used to be called Greenwich Mean Time when I was a kid).

*this is of course just a figure of speech as it is not the sun that goes on a journey but the earth being tilted on its axis that changes its position relative to the sun on its annual journey around the same.

I’m back although I haven’t been away!

Things have been more than quiet around here for quite a long time. I have been swamped by work that left me feeling less than enthusiastic about sitting down and writing something for the blog. Added to this I have been fighting a war on two fronts with the tax people and with my health insurance. Now as a self-employed person to fight a war with either the tax people or with your health insurance is definitely not and I repeat not recommended. To fight a war with both simultaneously goes over the border into insanity. The result of all this is that I have not merely neglected my blog but have left it totally fallow.

Since the end of last week the work load has reduced substantially and I’m even looking forward to somewhat more than a week with no work at all, not good for my bank balance but very good for my mental health. Also I have more or less successfully concluded the war on both fronts and that more or less to my own satisfaction. So the Renaissance Mathematicus is back and will be posting again on a semi-regular basis.

I will note that Giant Shoulders #18 is up at Jost A Mon and as I shall be hosting Giant Shoulders #19 I have added my email address to the information available at the top of the page.

A boy from Essex who made good

Today’s birthday boy was a geographical, when not a temporal, neighbour of mine, is a special favourite of my blog friend John Wilkins and illustrative of a important point that I have already made several times on this blog and will certainly make often in the future. So who is this multi-functional scientific personality? John Ray was born on 26^th November 1627 in Black Notley in Essex, which is only about 30 miles from the Essex village where I spent the first fifteen years of my life. Anyone who regularly reads Evolving Thoughts will also know that Mr Ray regularly turns up in John’s posts the reason for which I will mention at the end of explaining my third point from the opening sentence.

As I have mentioned more than once on this blog the so-called scientific revolution is almost always described as a revolution in astronomy with a little bit of physics on the side. As I have also explained more than once this is in fact a myth as in the 16^th and 17^th centuries fundamental developments took place in many different sciences as well as in quite a few of the humanities. An area where this was very much the case was in what are now known as the life sciences. In the Middle Ages the life sciences together with what would develop into the earth sciences, i.e. geology, mineralogy, metallurgy etc., were all subsumed under the one discipline natural history the standard reference work for which was Pliny’s Naturalis historia. *  This started to change in the 16^th century following the introduction of the printed book, linear perspective and naturalism in art. Starting around 1520 a series of what I call coffee table books started to appear in Europe. These were large format books on plants, animals, mineralogy etc, which contained mind-blowing illustration of the subject discussed by the author. These illustrations were not simple pictures but scientific drawings illustrating the various features of the biological specimens being described. These in the mean time legendary volumes from such authors as Otto Brunfels, Leonhard Fuchs, Conrad Gesner, Georgius Agricola and Ulisse Aldrovandi are now regarded as the beginnings of the separate life and earth science disciplines, botany, zoology, geology etc. De fabrica from Vesalius, the book that founded modern anatomy also played a role as the Paduan school of anatomy that he started soon expanded to include comparative anatomy. However although the presentation of these books was new, modern and in some sense revolutionary their authors were still guided by the science and taxonomies of antiquity from Pliny and above all Aristotle. Even William Harvey the Paduan anatomist famous for his discovery of blood circulation and also for his claim that ‘everything comes from an egg’ was at heart a conservative Aristotelian. Ray coming at the end of the 17^th century was different he represents a break with the past and a step into the future. Together with Francis Willughby, “Ray prepared the first systematic flora for a region – at first of Cambridgeshire, and later of Britain” (Wilkins 2009). In this work is Ray’s greatest contribution, quoting Wilkins, “Ray needed to define species, and he was the first to do so entirely in a biological context”. Ray’s work was an important and highly significant contribution to the science of taxonomy and was an important influence on the defining work of Linnaeus. I think that in a fair world in which the history of scientific development were not defined as the history of physics that Ray would be acknowledged as standing on a level with Galileo or Newton and not be regarded as some obscure biologist.

The quotes above are from John Wilkins excellent Species: A History of an Idea, University of California Press, 2009. This is a splendid contribution to the history of ideas and will almost certainly become known as a classic in its field. I can recommend it to anybody with an interest in the history of science and I know from personal experience that if you buy a copy there’s a chance that the author will come by sometime and sign it for you.

* A good book on Pliny in the Middle Ages is Arno Borst, Das Buch der Naturgeschichte: Plinius und seine Leser im Zeitalter des Pergaments. Heidelberg 1994.

Astronomy and Astrology 0: Prelude

Some time back the Aussie Anthropoid (aka OOwilkins the Bond Professor) posted a Mr Deity video the theme of which was all of the gifts that he was going to bestow on his chosen people. Lucy compares his list with everything that Zeus is giving the Greeks such as science, medicine and astronomy at which point Mr Deity interrupts to say how much he loves astronomy and to ask if she had seen Larry’s horoscope for that day… Lucy answers “that’s astrology not astronomy” “yer, what’s the difference” asks Mr D. “About 50 IQ points!” Lucy fires back. A truly great line and one that John chose as the subtitle of his post. However one commentator spoiled the joke by pointing out that the Greek’s also practiced astrology to which John gave a short but fairly accurate answer. Inspired by this exchange I have decided to do a series of posts on the intertwined history of the two disciplines of which this forms a sort of introduction.

Words and Concepts:

Today most people have a fairly clear view of the division between astrology and astronomy but from the time of the ancient Greeks up to the 18^th century the lexicographical difference between the two concepts was anything but clear. In the first footnote to his brilliant book “ Mathematik und Astronomie an der Universität Ingolstadt im 15. und 16. Jahrhundert” * Christoph Schöner writes that in the Renaissance the words astrologus, astronomus and mathematicus are synonymous, a comment that could equally apply to the preceding two thousand years. In the literature from the Greeks up to the end of the 17^th century you will find authors who use astrology for what we consider to be astronomy and astronomy for that which we call astrology. Other authors use astrology or astronomy for both disciplines. In a famous quote Augustinus warns Christians to beware of mathematicians thus demonstrating for some people his anti science attitude. His defenders correctly point out that although he uses the word mathematici he is actually referring to astrologers. This defence is in fact correct and it’s obvious from the rest of the quote that Augustinus is indeed warning his fellow Christians of the dangers of astrology and other forms of divination. However the defence looses some of its strength if one realises that in the time of Augustinus mathematicians and astrologers were one and the same.

For the purposes of these posts I shall be ahistorical and treat the concepts astrology and astronomy as if they had always had clear and separate definitions and in fact those assigned to them by Ptolemaeus in the definitive Greek work on astrology his Tetrabiblos. Here Ptolemaeus writes that the study of the heavens is divided into two disciplines, astronomy, which is the study of the movement of heavenly bodies and astrology, which is the study of their influence. These are the definitions for the two words that I will be using but I should point out that Ptolemaeus himself did not stick to this clear division and in fact mixed up the two terms in his writing like everybody else.

Astrology is more than horoscopes:

Today when people hear the word astrology they, like Mr Deity, think automatically of horoscopes but in fact horoscope astrology is only one aspect, and a comparatively late one at that, of the discipline, which covers a very wide range of celestial influences. In the course of these posts I shall touch upon the origins of horoscope astrology and also deal in some detail with a couple of other aspect of astrology that are not based on horoscopes.

Astrology doesn’t actually exist:

This subtitle is not a sceptical rejection of the claims of astrology but in fact a denial that the discipline astrology exists at all. Anyone who has read so far will probably at this moment think that I have gone insane. I write a post explaining that I shall be writing a series of posts on the history of astrology and now I am denying that it exists at all, how come. The point that I wish to make and it a very important one is that people talk about astrology as if it were a clearly defined single discipline but this is not the case. One thing that makes the study of the history of astrology extremely difficult is that there is not one coherent astrology but literally hundreds of conflicting and even contradictory astrologies. In fact there are almost as many different astrologies as there are authors on the subjects and a large part of the astrological literature consists of the authors explain why their system is the one true correct one and all the others are wrong. What is interesting is that in their disputes mediaeval and Renaissance astronomers will often call upon the same Greek authorities to justify contradictory positions. On the whole I shall again be ahistorical and write as if there were one unified discipline of astrology throughout its history.

Disclaimer: I am not an expert:

Regular readers of this blog will know that my main interest as a historian of science is the evolution of the mathematical sciences between about 1400 and 1750 (I will explain those dates one day). Now nearly all of the practicing mathematicians in this period, at least up to about 1650, were not just astrologers but the wish to reform astrology and set it up on a firm empirical footing was one of the main driving forces of their work so if you really want to understand them as a historian you have to engage with astrology and its history, which over the years I have done. Now if somebody had said to me thirty years ago that I would spend substantial amounts of my time reading astrology books or books about astrology I would have recommended them a good psychiatrist, however that is exactly what I have done in the last years and although I now have a reasonable working knowledge of some aspects of the history of astrology and its practitioners, particularly in the Renaissance I am anything but an expert on the subject. The history of astrology is an incredible complex, multi-dimensional and twisted subject and I’m very glad that people, who are much better historians than I, have devoted their time and considerable talent to it thus enabling me to distil their collective wisdom from their books and papers. What will follow in the later posts in this series are some thoughts and conclusions that have crystallised out of my readings on the subject and are by no means authoritative but I hope will be at least somewhat informative and possibly stimulate the reader into rethinking their own view of the role of astrology in the history of western thought and in particular science.

* If you read German this book, Schreiner’s doctoral thesis, contains in the first 150 pages the best account of the teaching of mathematics in the European mediaeval universities that has ever been written (it’s one of my bibles!).

Cutting heroes down to size.

Professor Wilkins of the Bond University, Queensland has posted a truly excellent piece on his blog demythologising Darwin and The Origin of Species and placing its significance as a piece of scientific publishing into context. Now you may ask why I as a historian of Renaissance mathematics should comment on a blog post about a 19^th century work of biology and its author? The answer is quite simple; everything that John says about Darwin and his book can and should be applied to Copernicus, Kepler, Galileo, Descartes, Newton and a host of other scientist from the early modern period and their works.

Nothing that any of these scholars did or wrote existed in a vacuum and all of their achievements would have taken place roughly within the same period of time if they had never lived. Copernicus’ work built upon the work of Regiomontanus and Peuerbach and a host of Islamic astronomers, the only original contribution that he made was the concept of heliocentricity. You may think that this was unique but in fact heliocentricity and a moving earth had been in discussion for about 100 to 150 years before Copernicus published the De revolutionibus and if he had not come up with the concept then sooner rather than later somebody else would have done.

The same applies to Galileo’s contributions; his telescopic observations were also made independently and simultaneously by various other European astronomers such as Thomas Harriot, Johann Fabricius, Simon Marius and Paolo Lembo. His work on dynamics in the Discorsi were based on the work of the Oxford calculatores and the Paris physicist from the 14^th century and the work of Tartaglia and Benedetti in the 16^th century. In the 17^th century Harriot, Simon Stevin und Isaac Beeckman produced most of Galileo’s results independently.

The same can be shown to be true for all of the others as well, for example the orbit of Mercury was already considered to be an ellipse in the work of Peuerbach. It might well be that had Newton not lived then his achievements would have been spread out over the work of several scientists rather than one but that his results would still have emerge in much the same form in roughly the same time period is almost certain.

It is perfectly OK to acknowledge the achievements of the scientists who helped create modern science but as John so superbly demonstrates in the case of Darwin it is wrong to place them on a pedestal.

Isaac Newton perverts the course of science.

An investigation of the private correspondence of Isaac Newton and other members of the Royal Society has revealed that they were less than candid in their public utterances concerning science! All the truth that is fit to print here!

 

HT to John Lynch.

An important anniversary in the history of science.

The 24^th of November is a very significant date in the history of science. On this date an event took place that would contribute to a major change in the way humanity viewed the world and its place in it. On this day in 1639 the British astronomers Jeremiah Horrocks and William Crabtree became the first observers to record a transit of Venus. *

 

If people list the supposedly great astronomers who made major contribution to the evolution of astronomy in the 17^th century they almost never mention Horrocks but they should. Born in 1618 in Toxteth Park, now part of Liverpool, Horrocks he went up to Emmanuel College Cambridge in 1632. Whilst in Cambridge he became interested in astronomy and because the mathematical sciences where not taught at that time he acquired the astronomical text of the age and taught himself mathematics and astronomy. Wanting to acquire the most modern astronomical tables he obtained a copy of those of Philip Landsberge but soon determined that they were inaccurate. Looking for better tables he came across the then still relatively unknown Rudolphine Tables calculated by Johannes Kepler from the data collected by Tycho Brahe. Realising that these were far superior to Landsberge’s Horrocks became and convinced Keplerian and later with Crabtree and William Gascoigne, who introduced the cross-hairs into the telescope ocular, he formed a group calling themselves “Nos Keplari” dedicated to propagating the elliptical astronomy.

 

However even Kepler’s calculations were far from perfect and Horrocks, still a teenager, set about correcting errors in the Rudolphine Tables. He realised that Kepler had made an error in his calculation of the orbit of Venus and that there would be a second transit of Venus in 1639 eight years after the one predicted by Kepler for 1631. Having left Cambridge in 1635 Horrocks was installed as a private tutor to the Stone family in Much Hoole in Lancashire and it was here that he made the first ever observation of a transit of Venus. This proved that Venus like Mercury, whose transit had been observed by Pierre Gassendi in 1631, orbited the Sun and not the Earth a highly significant step on the way to the acceptance of heliocentricity.

 

If this had been Horrocks’ only achievement it would place him in the top grade of 17^th century astronomers but there was considerably more. Based on a rather dubious piece of Keplerian number mysticism Horrocks used a parallax measurement made during the transit observation to calculate the size of the astronomical unit, the distance between Earth and Sun, and although his figure of 59 million miles was way below the real figure of 95 million miles it was significantly larger that all previous estimates and played a role in the reconsideration of the dimension of the solar system that took place in the 17^th century. Horrocks also tackled the problem of the Moon’s orbit. Kepler had not included the Moon in his elliptical astronomy because had he done so it would have caused him great problems with his astrophysics in which he claimed that the planets were moved by a magnetic force emanating from the Sun. Horrocks now provided the missing Keplerian elliptical orbit for the Moon, a model that was taken over by Flamsteed and also by Newton in his Principia. The Moon’s orbit is highly irregular and extremely difficult to capture mathematically and although still deficient Horrocks’ Moon model was the best one produced up till the 18^th century; the problem of the Moon’s orbit was finally solved by Laplace. Horrocks’ also made significant contributions to that which would become the theory of gravity.

 

All of this would be highly impressive for any 17^th century astronomer but it should be noted that Horrocks died in 1640 aged only 22! There has been much speculation as to what he might have achieved if he liked Newton had lived into his eighties.

 

* By a strange coincidence an English naturalist called Darwin also published a book about species on the same date in 1859 **

 

** Actually it’s not the same date as Horrocks made his observation on 24^th of November by the Julian calendar and Darwin’s book was published on the 24^th by the Gregorian calendar.

The day my world turned pear shaped

At one o’clock in the afternoon on Monday almost four weeks ago I was feeling fine by five o’clock I felt like shit and thought I was developing a healthy dose of the man-flu. At some point on Tuesday I realised that the tissue under my jaw was extremely swollen and very painful so early on Wednesday morning I made my way to my friendly GP. She took one horrified look at my swollen throat and said, “I not touching that” and sent me to my local neighbourhood ears, throat and nose specialist. He in his turn also took one horrified look and told me to ‘go direct to the local ears, throat and nose clinic, do not pass Go and do not collect 200 Euro’. I should point out that by now I was doing a pretty good impression of a bullfrog as the saliva glands in my throat were swollen up to the size of golf balls and were extremely painful. Having spent the afternoon sitting around the waiting area of the clinic I was finally examined at about five o’clock and dispatched to a ward where I would spend the next twelve days laying on my back with a drip feed in my arm through which vast quantities of very powerful antibiotics were poured into my body. It would appear that I had a fairly serious bacterial infection of the cell tissue of my throat and jaw. A serious infection would have meant that the surgeons would have started chopping bit out of my body! In addition to this I was required to swallow large numbers of pills of unknown function. After having enjoyed this therapy for seven days I suffered an acute loss of hearing in my left ear. This meant that for the next five days in the gaps between the litres of antibiotics I received several litres of a poisonous cocktail through the tube in my arm. This cocktail was so poisonous that I had to sign an extra disclaimer absolving the doctors should my head turn green and start revolving at high speed before departing for distant parts of the universe!

 

After ten days of lazing around doing nothing I was discharged from the clinic and sent home with a couple of kilos of tablets to consume for the next week. I was glad to get out of the hospital but to put it mildly I felt like shit warmed up. As well as the after effects of my infection that had left me feeling as weak as a day old kitten I had still only about 50% of the hearing of my left ear an intense tinnitus at about two and a half kilohertz and permanent vertigo. Not exactly the condition in which I felt like pontificating on the subtleties of Renaissance mathematics or anything else for that matter.

 

At the beginning of this week I started working again although my loss of hearing, it’s improving slowly, and my tinnitus are still causing me a fair amount of distress. To add to my problems I had been offered a temporary job working as a substitute English teacher at our local Waldorf School the start of which had been stymied by me being incarcerated in the clinic. So this week I had my first days teaching a somewhat stressful situation.

 

But your friendly neighbourhood Renaissance Mathematicus having survived the evil attack of the killer bacteria, as a historian of science I was comforted by the fact that if this had happened to me 100 years ago I would be dead by now, is now back in business and normal postings on all things renaissancently mathematical will start as of today.

In defence of the indefensible.

Friday was the 23^rd of October and the Internet sceptics had a field day mocking one of their favourite punching bags James Ussher (1581 – 1656) Archbishop of Armagh. Ussher is notorious for dating the creation of the world to 6 pm on the 22^nd of October 4004 (and not 9 am on 23^rd October as Pharyngula falsely stated) a fact that the hordes of Pharyngula and other similar self appointed defenders of scientism love to brandish as a proof of the stupidity of Christians.

However Ussher has a right to be judged by the social and cultural standards of his own time and not those of the twenty first century. Who knows which things that we hold sacred will be ridiculed by sneering sceptics in three or four hundred years? “Can you believe it in the early 21^st century they actually believed…?” How much and how fast social norms can change is illustrated by the fact that as I was growing up in Britain in the 50s and 60s, in what was then one of the most open and liberal societies in the world, sexism, racism and homophobia were all acceptable and widespread social attitudes, a thought that makes me shudder today. I, at least, had the good fortune to have parents who openly rejected and condemned such behaviour and so never had to go through the painful process of adjusting my own warped prejudices.

But back to Ussher, in reality he was a widely respected, highly intelligent, well-educated scholar who was also an excellent mathematician. When considering his Bible chronology one has to take the following facts into consideration, firstly almost all well educated Europeans of the period believed in the literal truth of the Bible. Secondly, a large number of them were chiliast or millenarianists, i.e. people who believed in the second coming of Christ when the earth would be six thousand years old; a belief based on a Biblical saying. Now the generally accepted interpretation of the Bible placed the creation of the earth somewhere between 3000 and 5000 BC so for a chiliast, in the middle of the 17^th century, determining the correct date of the creation was very important. If the world had come into being 4500 BC then your whole theory was wrong but if it materialised in 4300 BC then you had better start preparing for the return of Christ. Ussher was by no means the only prominent Bible chronologist of the 16^th and 17^th centuries the most famous being the philologist and historian Joseph Justus Scaliger and of course Isaac Newton; others such as Johannes Kepler and Phillip Melanchthon also dabbled.

How did Ussher arrive at his strange date? He originally determined on theoretical theological grounds that the creation took place in 4000 BC and proceeded to fit the entire Old Testament history into those 4000 years but then corrected the birth of Christ to 4 BC, due to the calculation errors of Dionysius Exiguus when he first set up the AD/BC dating system, and so pushed creation back to 4004 BC. Ussher’s achievements in his analysis of Old Testament history are in fact a great feat of scholarship and earned him the accolades of his fellow chronologists. But why 6pm and the 22^nd of October? Here we see a reflection of a belief commonly held by scientists in the early modern period, God is a Geometer i.e. Mathematician i.e. Astronomer, all three names being synonymous in this period. For many scientists in the early modern period the concept of a rational mathematical God whose creation was a logical scientific structure functioned as a fundamental heuristic principle, most notably for Galileo, Kepler, Boyle and Newton. Ussher shared this belief and like many chronologists he believed that the point of creation would be determined by some sort of logically reasonable astronomical event, i.e. God setting the great astronomical clock in motion. For various reasons Ussher chose the autumnal equinox and placed the moment of creation on the beginning of the Sunday preceding the 4004 BC equinox, 25^th October, that he had determined using Kepler’s Rudolphine Tables. He chose the Sunday as the first day of creation because the Bible says that the creation took six days and God rested on the seventh, which is the Jewish Sabbath, the Saturday. The point of creation is 6pm on Saturday the 22^nd October because in the Jewish calendar the new day starts at 6 pm. All of this is within the social and cultural norms of his times perfectly sensible and rational and only appears idiotic when viewed from our perspective. Ussher was not the fool that he is presented as being by the modern sceptics but a highly regarded scholar of his times.

Now I hear the thoughts of a potential reader who is thinking that this is all well and good but when Ussher wasted his time and intellectual energy on a subject that viewed from the modern perspective is pure rubbish why should we cut him some slack now? At first this attitude seems to be correct and Ussher and his ilk should probably be assigned to the dustbin of history only to be pulled out and dusted off for a bit of healthy mockery on the anniversaries of their inanities but appearances can be, and indeed in this instance are, deceptive. The popular presentation of the scientific revolution usually presents it as fundamentally a revolution in astronomy and physics with a bit of medicine tacked on to justify the wider concept science, however this view is highly restrictive and fundamentally wrong. In the 16^th and 17^th centuries the fundaments were laid for a very wide range of modern academic disciplines and amongst them history and archaeology. In antiquity and the Renaissance the understanding and function of history was very different to that of today and a factual reconstruction of the past was not the aim of historians. The original concept of history was to use historical figures to tell moral or political fables for educational purposes. This concept changed radically in the 16^th and 17^th centuries towards our modern conception of history, this change was to a large extent due to the work of the chronologists. In their attempts to accurately reconstruct the march of time they started to develop and utilize methods of philological analysis and dating that had not existed previously and in so doing laid the foundation of both modern history and archaeology. Although their motivation was one that seems totally ridiculous from a modern standpoint the results of their efforts still play a central role in our academic world.  As so often in the history of the sciences rational results can and do emerge from irrational motivations.

Not just an architect.

Today is the birthday of Britain’s most famous architect, the man who built St. Paul’s Cathedral, Sir Christopher Wren (1632 – 1723). My first knowledge of Wren was as the subject of an oft-repeated Clerihew,

Sir Christopher Wren

Went to dine with some men

He said, “If anyone calls

Say I’m designing St. Paul’s”

Most people don’t realise that as well as being Britain’s most famous 17^th century architect, Wren was also a highly respected mathematician. In fact Isaac Newton named him along with John Wallace and William Oughtred as one of the three best English mathematicians of the 17^th century. As a young man he was an active astronomer and was a highly vocal supporter of the then still relatively young elliptical astronomy of Johannes Kepler.

In 1657 he was appointed Gresham Professor of Astronomy one of the two top positions for astronomers in Britain at the time. Gresham College had been founded, at the end of the 16^th century, with a bequest from Sir Thomas Gresham, he of the bad money law, and consisted of eight professorships, the holders of which were expected to hold public lectures both in English and Latin in their appointed subjects for the benefit of the artisans of London. As such the Gresham Chairs for Geometry and Astronomy were the first ever chairs for mathematics established in England. During the 17^th century many notable English scientist occupied one or other of these chairs.

It was during his time as Gresham Professor that the semi-formal group of scientists came together at Gresham in the grouping that led to the founding of the Royal Society, in which Wren played a leading role serving at times as its president.

In 1661 he was appointed to the other chair for astronomy, the Savilian in Oxford, the same route taken by some of his predecessors such as Briggs and his successors such as Halley. Whilst at Oxford he developed his interest in architecture, which led to him being appointed Surveyor of Works to Charles II. Wren was a true polymath whose scientific activities covered a very wide range of bases. Both the Wikipedia and the MacTutor articles are worth a read for more details and for anyone really interested in Wren the scientist I recommend Jim Bennett’s  The mathematical science of Christopher Wren (Cambridge-New York, 1982).

In the history of astronomy Wren occupies a legendary position as the man who offered a book token as a prize for the first person who could demonstrate that an inverse square law of gravity would lead to elliptical planetary orbits. Unable to solve the challenge Edmond Halley famously asked Isaac Newton, the start of a process that would culminate  in the publication of the Principia.