Renaissance science – XLI

The cabinets of curiosity featured in the last episode of this series often featured a section containing a mixed collection of stones, minerals, and fossils all thrown together in one category of natural history. This is not surprising when one thinks that the word fossil originally meant anything dug up out of the ground, from the Latin fossilis meaning dug up, and only acquired its modern meaning at the beginning of the eighteenth century. This is wonderfully illustrated by the fact that the first published description of a pencil is in Conrad Gessner De Omni Rervm Fossilivm Genere (1565), graphite being something that is dug up.

Whilst not necessarily to the extent that modern botany was formed by the Renaissance, the three disciplines of palaeontology, mineralogy, and geology also began to gradually emerge during the Renaissance. 

As with the other areas of natural history the Renaissance interest in things out of the earth begins with the recently published books from antiquity. Aristotle (384–322 BCE) wrote about the properties of minerals in terms of his general four element theory of all known substances. Theophrastus (370–285 BCE), Aristotle’s pupil and successor as head of the Peripatetic school, followed Aristotle in dividing minerals into two categories–those affected by heat and those affected by dampness–in his De Mineralibus. Theophrastus’ knowledge of a wide range of substances was quite extensive. He knew that both amber and magnetite had powers of attraction, that pearls came from shellfish, and that coral comes from India. He also knew about coal and the metal ores, and that pumice stone is volcanic in origin. He knew about the practical use of various minerals in production of glass, pigments, and plaster. He also describes precious stones. He is aware that minerals often come from mines and discusses gold, silver, and copper mines. He apparently also wrote a separate work On Mining, which is lost.

As is almost always the case, Theophrastus’ wide-ranging work on minerals is overshadowed by the much more extensive writings of Pliny (23/24–79 CE) in his Naturalis Historia in which books 33 to 37 in volumes IX and X are devoted to mining and mineralogy, especially as applied to life and art, work in gold and silver, statuary in bronze, art, modelling, sculpture in marble, precious stones, and gems. He describes many more minerals than Theophrastus, discussing their properties and applications. He was the first to recognise the correct origin of amber.

The other driving force, during the Renaissance, behind the increased interest in things out of the earth was the development of a major mining industry in Middle Europe for the extraction of metal ores. These developments are reflected in the publications of two significant and successful books on the practice of mining, the Pirotechnica of the Italian mining engineer, Vannoccio Biringuccio (1480­–1539), published posthumously in 1540 and De re metallica by the German physician Georgius Agricola (1494–155), also published posthumously in 1556.

Book I of Biringuccio’s Pirotechnica is titled Every Kind of Mineral in General and deals with the location of metal ores and deals separately with the ores of gold, silver, copper, lead, tin, and iron. Book II continues the theme with what Biringuccio calls the semi-minerals an extensive conglomeration of all sorts of things that we wouldn’t necessarily call minerals. Starting with quicksilver he moves on to sulphur then antimony, marcasite (which includes all the sulphide minerals with a metallic lustre), vitriol, rock alum, arsenic, orpiment, and realgar. This is followed by common salt obtained from mine or water and various other salts in general then calamine Zaffre and manganese. As with Theophrastus he also, under minerals, deals with loadstone, Theophrastus’ magnetite.

In Book I of De re metallica, Agricola deals with the industry of mining and ore smelting, moving on to finding minerals and metal ores in Book II. Book III discusses mineral veins and seams. After several books which discuss the smelting of various metal ores, the final Book XII, discusses salts, solvents, precipitates, and glass. 

Source: Wikimedia Commons

Unlike Biringuccio, who only discussed minerals in the context of his book on mining, Agricola wrote and published several other works on minerals. His earliest publication on mining Bermannus sive de re metallica dialogue (1530) also contained much on mineralogy, as did his De animantibus subterraneis (1549).

However, his major work was his De natura fossilium published in 1546; here the word fossil is used in the sense of things out of the earth. In the ten books of this work, he combined the extensive knowledge about fossils, minerals, and gemstones passed down from antiquity and the Middle Ages with the oral, vernacular, practical, traditional experience of the mineworkers, smelters, and stone masons about the occurrence, exploitation, appearance, structure, properties, and uses of those things found underground.

Title page of De natura fossilium Source: Wikimedia Commons

Anselmus de Boodt (1550–1632), who we met as the curator of the cabinet of curiosities of Rudolf II in Prague, was as a natural historian principally interested in cataloguing all know stones and mineral, a task to which he devoted a large part of his life.

Engraved Portrait of Anselmus Boetius De Boodt by Egidius Sadele Source: Wikimedia Commons

The results of his endeavours were published in Latin in his Gemmarum et Lapidum Historia (The History of Gems and Stones), the first edition, dedicated to Rudolf, appearing in Hanau in 1609. Two further editions appearing in Leiden in 1636 and 1647.

Title page of the Gemmarum et Lapidum Historia Source: Wikimedia Commons

The third and final edition of 576 pages was in two parts. The first part gave the various causes of minerals, heavily influenced by the Work of Aristotle and Theophrastus but nevertheless giving providing unique accounts of how minerals are formed. The second part catalogues methodically hundreds of specific minerals, describing in detail their various identifying and curative properties. 

Another specialist for minerals and fossils, who we met as curator of a cabinet of curiosities was Michele Mercati (1541–1593), who served the pope in this function as well as directing the Vatican botanical garden.

Portrait of Michele Mercati, artist unknown Source: Wikimedia Commons

The emphasis of his collection lay in stones, minerals, and fossils. Based on his work, he wrote his Metallothica. Opus postumum, auctoritate et munificentia Clementis undecimi pontificis maximi e tenebris in lucem eductum; opera autem et studio Joannis Mariae Lancisii archiatri pontificii illustratum, which, however, was first published in Rome in 1717. Mercati was one of the first to recognise that the chipped flints in his collection were not, as believed at the time, produced by lightning but were tools produced by humans. 

Engraving made by Antonio Eisenhot between 1572 and 1581, but published in 1717, representing the Vatican mineral collection as organized by Michele Mercati Source: Wikimedia Commons

The sixteenth century’s perhaps greatest natural historian, Ulisse Aldrovandi (1522–1605), also had a very substantial collection of minerals, fossils, and stones in his teatro di natura (theatre of nature), and he of course wrote about them, although his text on the topic was one of those unpublished at the time of his death and the eventual late publication of his monumental Musæum Metallicum in 1648, certainly affected its reception, giving it not the attention it deserved. Already in his will in 1605, Aldrovandi was the first to use the word giologia (geology) in the modern sense, although his introduction had little impact, the usage first becoming widespread in the eighteenth century. Previously the word geologia had been used to distinguish earthly philosophy from theology. 

Body fossils pictured in the Musaeum Metallicum. A. Aldrovandi describes this specimen as a ” rock pregnant with a shell. ” Aldrovandi considers most fossils to be of inorganic origin made in imitation of living beings. B. Although Aldrovandi believes that fossils are not of organic origin, he often compares them to existing animals. He calls this structure ” Rhombites, ” meaning a ” (stone) resembling a fish of the Rhombus kind. ” C. Detail from the plate entitled ” belemnitarum septem differentiae ” (seven varieties of ” belemnites ” ). D. Aldrovandi calls shark teeth ” glossopetrae, ” or ” tongue-like stones. ” This specimen is given the attribute ” Gesneri, ” or ” Gesner’s ” : naturalist Konrad Gesner (Gesner, 1565) had already described shark teeth as ” Glossopetre ” in 1565. E. Aldrovandi often calls echinoderm fossils ” astroitis, ” a word that comes from the Latin ” aster, ” meaning star. The ” star-echinoderm ” comparison is most likely based on echinoderms’ pentameral symmetry, resembling the stylized figure of a star. The comparison was already made by Gesner (1565) in his description of fossil crinoids similar to those depicted by Aldrovandi and shown here. F. Aldrovandi frequently uses the term ” ophiomorphites, ” or ” snake-like stones, ” in his descriptions of ammonites. G, H. Fossil sea urchins, presented as ” astroitis ” (see E). I. When describing this mammoth tooth, Aldrovandi speaks of ” petrifaction. ” See also Vai and Cavazza (2006, fig. 14) J. Fossil coral, also presented as ” astroitis ” (star-stone), presumably because of the polyps’ stellate morphology. K. Aldrovandi distinguishes two main types of ” glossopetre ” : dentate (as in D) and nondentate (as in K).  Source

In his Musæum Metallicum, rather than simply listing the minerals etc, Aldrovandi attempts to apply a systematic classification to the objects under examination. He appears to be clearly aware of the organic original of fossils; Aristotle had claimed that fossils were stones that grew in the ground and only imitated organic forms. Aldrovandi was the first to recognise and describe microscopic fossils on the surface of a calcareous marble-like block: He almost certainly used a magnifying lens to do so. Aldrovandi’s work was in many senses highly innovative but had little impact, his various discoveries being remade by later researchers.

The other mega Renaissance natural historian, Conrad Gessner (1515–1565), also, as already noted above, also wrote and published a substantial work in the year of his death, his De Rerum Fossilium, Lapid um et Gemmarum maxime, figuris et similitudinibus Liber: non solum Medicis, sed omnibus rerum Naturae ac Philogiae studiosis, utilis et juncundus futurus, usually simple referred to as Fossils, Gems, and Stones. Although, he didn’t recognise the true origin of fossils, he did realise that their unusual appearance deserved recognition, and his book contains the earliest extensive collection of fossil illustrations. 

Fossil illustrations from ‘De omni rerum fossilium’, showing shark’s teeth Source: Welcome images via Wikimedia Commons ( you can read more about Gessner’s fossil book with more illustrations including that pencil, here)

Gessner was not the first to published illustration of fossils, that honour goes to the German Lutheran rector Christoph Entzelt (1517–1583), who published a De Re Metallica: Hoc Est, De Origine, Varietate, & Natura Corporum Metallicorum, Lapidum, Gemmarum, atq[ue] aliarum, quae ex fodinis eruuntur, rerum, ad Medicinae usum deseruientium, Libri III, under the name Chistophorus Encelius, in 1557, which contains illustrations of four fossils. I have been unable to find out any more about Entzelt or his book.


Like Aldrovandi, Gessner tried to systemise his presentation of the objects describe in his book by dividing them up into fifteen classes. However, his classifications were, by modern standards, trivial and or illogical and had very little influence on the developments within the disciplines of mineralogy, geology, or palaeontology.

In their books on the mining industry both Biringuccio and Agricola drew attention to stratigraphy, the layers under the surface of the earth playing a significant role in the practice of mining. Whilst discussing the types of layers that would potentially lead to fruitful seams of whatever was being mined in a given situation, they gave no thought as to how they various layers came into existence. The first scholar to do so was the Danish anatomist, palaeontologist, and geologist Niels Steensen (1638­–1686), more generally known by the Latin version of his name as Steno. 

Portrait of Niels Steensen (1666–1677). Unsigned but attributed to court painter Justus Sustermans. Source: Wikimedia Commons

Born in Copenhagen, he studied medicine at Copenhagen University. After graduating he travelled first to Rostock and then on to Amsterdam and further to Leiden, where he studied anatomy together with Jan Swammerdam (1637–1680), Frederik Ruysch (1638–1731), Reinier de Graaf (1641–1673), and Franciscus de le Boe Sylvius (1614–1672). As an atomist he made important discoveries and contributions.

After travelling through France, he settled in Italy where he became a member of the Accademia del Cimento. Here, he first made a major contribution to palaeontology and then one to geology. In 1666, he dissected a female shark’s head and recognised the similarity between the shark’s teeth and the fossils known as glossopetrae or ‘tongue stones.’ Steno published his theories that fossils are organic material turned into stone in his Canis carchariae dissectum caput in 1667.

Elementorum myologiae specimen: Illustration from Steensen’s 1667 paper comparing the teeth of a shark head with a fossil tooth. Source: Wikimedia Commons

Previously, the Italian naturalist and botanist Fabio Colonna (1567–1640) had in his investigations found evidence that glossopetrae had organic origins, which he published in his De glossopetris dissertatio in 1616.

Portrait of Colonna 1572 artist unknown Source: Wikimedia Commons

Whilst walking along the coast in Northern Italy Steno began to take interest in the exposed layers in the earth. He developed theories of stratigraphy defining four laws or principles of how the layers came into being, which he published in his De solido intra solidum naturaliter contento dissertationis prodromus (Preliminary discourse to a dissertation on a solid body naturally contained within a solid) in 1669.

Source: Wikimedia Commons

Steensen, in his Dissertationis prodromus of 1669 is credited with four of the defining principles of the science of stratigraphy. His words were:

  1. The law of superposition: “At the time when a given stratum was being formed, there was beneath it another substance which prevented the further descent of the comminuted matter and so at the time when the lowest stratum was being formed either another solid substance was beneath it, or if some fluid existed there, then it was not only of a different character from the upper fluid, but also heavier than the solid sediment of the upper fluid.”
  2. The principle of original horizontality: “At the time when one of the upper strata was being formed, the lower stratum had already gained the consistency of a solid.”
  3. The principle of lateral continuity: “At the time when any given stratum was being formed it was either encompassed on its sides by another solid substance, or it covered the entire spherical surface of the earth. Hence it follows that in whatever place the bared sides of the strata are seen, either a continuation of the same strata must be sought, or another solid substance must be found which kept the matter of the strata from dispersion.”
  4. The principle of cross-cutting relationships: “If a body or discontinuity cuts across a stratum, it must have formed after that stratum.” 

(Taken from Wikipedia)

Somewhat bizarrely Steno converted from the Lutheran Protestantism of his birth to Catholicism in 1667. He was ordained a priest in 1675. He was consecrated bishop in 1677 and went off to Lutheran North Germany as a missionary. Living in poverty he died in 1686 after severe illness. In 1988 he was beatified by Pope John Paul II.

Portrait of Steno as bishop (1868) Source: Wikimedia Commons

Although, the full development of palaeontology, geology, and minerology didn’t take place until the eighteenth century, during the Renaissance the first steps were taken in separating and defining the three as individual disciplines. 

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Filed under History of geology, History of mineralogy, History of palaeontology, Natural history

The Wizard Earl’s mathematici 

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

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

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

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

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

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

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

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

Syon House Attributed to Robert Griffier

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

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

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

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

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

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

Source: Wikimedia Commons

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Source: Google Books

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

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

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

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

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

François Viète Source: Wikimedia Commons

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


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

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

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


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

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


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

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

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


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

Renaissance science – XXXX

As we have seen in previous episodes, Ulisse Aldrovandi (1522–1605) was one of the leading natural historians of the sixteenth century. The first ever professor for natural history at the University of Bologna.

Ulisse Aldrovandi (1522 – 1605). attributed to Ludovico Carracci. Source: Wikimedia Commons

He created the university’s botanical garden, one of the oldest still in existence. Collected about 4760 specimens in his herbarium on 4117 sheets in sixteen volumes, which are still preserved in the university and wrote extensively on almost all aspects of natural history, although much of his writing remained unpublished at his death. However, despite all these other achievements in the discipline of natural history, visitors to Bologna during his lifetime came to see his teatro di natura (theatre of nature), also known as his natural historical collection or museum.  This was housed in the palatial country villa that he built with the money he received from the dowry of Francesca Fontana, his wife, when he married her. His theatre contained some 18,000 specimens of the diversità di cose naturali (diverse objects of nature). These included flora and fauna, as well as mineral and geological specimens. He wrote a description or catalogue of his collection in 1595. 

In 1603, after negotiation with the Senate, Aldrovandi arranged for his teatro di natura to be donated to the city of Bologna after his death in exchange for the promise that they would continue to edit and publish his vast convolute of unpublished papers. This duly took place, and his collection became a public museum in the Palazzo Poggi, the headquarters of the university, opening in 1617, as the first public science museum.

Palazzo Poggi Bologna c.1750 Source: Wikimedia Commons

As with all of his natural history undertakings, Aldrovandi’s natural history museum was not the first, there being already ones in the botanical gardens of the universities of Pisa, Padua, and Florence but none of them approached the scope of Aldrovand’s magnificent collection. Also, later, the University of Montpelier had its own natural history collection. However, it wasn’t just institutions that created these early natural history museums. Individual apothecaries and physicians also set about collecting flora and fauna. 

The apothecary Francesco Calzolari (1522–1609) had an impressive Theatrum Naturae in Verona with 450 species on display. 

Source: Wikimedia Commons
Francesco Calzolari’s Cabinet of curiosities. From “Musaeum Calceolarium” (Verona, 1622) Source: Wikimedia Commons

Likewise, the papal physician, Michele Mercati (1541–1593), who was superintendent of the Vatican Botanical Garden, had a notable collection concentrating on minerology, geology, and palaeontology in Rome 

Source: Wikimedia Commons
Engraving made by Antonio Eisenhot between 1572 and 1581, but published in 1717, representing the Vatican mineral collection as organized by Michele Mercati Source: Wikimedia Commons

The Neapolitan apothecary Ferrante Imperato (1523–1620?)  published Dell’Historia Naturale in Naples in 1599, which was based on his own extensive natural history collection and containing the first printed illustration of such a collection. 

Portrait of Ferrante Imperato by Tanzio da Varallo  Source: Wikimedia Commons
Title page of Dell’ historia naturale, Napoli, 1599, by Ferrante Imperato (1550-1625). Source: Houghton Library, Harvard University via Wikimedia Commons
Engraving from Dell’ historia naturale, Napoli, 1599, by Ferrante Imperato (1550-1625). Source: Houghton Library, Harvard University via Wikimedia Commons

In the sixteenth century it became very fashionable for rulers to create cabinets of curiosities also know by the German terms as Kunstkammer or Wunderkammer. These were not new and had existed in the two previous centuries but in the Renaissance took on a whole new dimension. These contained not only natural history objects but also sculptures and paintings, as well curious items from home and abroad, with those from abroad taking on a special emphasis as Europe began to make contact with the rest of the world. 

The curiosity cabinet is a vast topic, and I don’t intend to attempt to cover it in this blog post, also it is only tangentially relevant to the central topic of this blog post series. I will, however, sketch some aspect that are relevant. Although they covered much material that wasn’t scientific, they were fairly obviously inspired by various aspects of the increasingly empirical view of the world that scholars had been developing throughout the Renaissance. We don’t just go out and actually observe the world for ourselves, we also bring the world into our dwellings so that all can observe it there. They represent a world view created by the merging of history, art, nature, and science. Although principally the province of the rich and powerful, for whom they became a status symbol, some notable Wunderkammer were created by scholars and scholars from the various scientific disciplines were often employed to search out, collect, and then curate the object preserved in the cabinets. 

Some of these cabinets created by the Renaissance rulers also had sections for scientific instruments and their owner commissioned instruments from the leading instrument makers of the era. These are not the average instruments created for everyday use but top of the range instruments designed to demonstrate the instrument makers skill and not just instruments but also works of art. As such they were never really intended to be used and many survive in pristine condition down to the present day. One such collection is that which was initially created by Elector August of Saxony (1526–1586), can be viewed in the Mathematish-Physikalischer Salon in the Zwinger in Dresden. 

Portrait of the Elector August of Saxony by Lucas Cranach Source: Wikimedia Commons
Planetenlaufuhr, 1563-1568 Eberhard Baldewein et al., Mathematisch-Physikalischer Salon

Equally impressive is the collection initially created by Wilhelm IV, Landgrave of Hessen-Kassel, (1532-1592), who ran a major observational astronomy programme, which can be viewed today in the Astronomisch-Physikalische Kabinett

Portrait of Wilhelm IV. von Hessen-Kassel by Kaspar van der Borcht († 1610) Source: Wikimedia Commons
Equation clock, made for Landgrave William IV of Hesse-Kassel by Jost Burgi and Hans Jacob Emck, Germany, Kassel, 1591, gilt brass, silver, iron Source: Metropolitan Museum of Art, New York City via Wikimedia Commons

Not surprisingly Cosimo I de’ Medici Grand Duke of Tuscany (1519–1574)

Agnolo Bronzino, Porträt von Cosimo I de’ Medici in Rüstung, 1545, Source: Uffizien via Wikimedia Commons

had his cabinet of curiosities, the Guardoroba Nuova, in the Palazzo Vecchio in Florence, designed by the artist and historian of Renaissance art Giorgi Vasari (1511–1574), who, as I have documented in an earlier post, in turn commissioned the artist, mathematician, astronomer and cartographer, Egnatio Danti (1536–1586), to decorate the doors of the carved walnut cabinets, containing the collected treasures, with mural maps depicting the whole world. Danti also designed the rooms centre piece, a large terrestrial globe. 

Source: Fiorani The Marvel of Maps p. 57

The alternative name Wunderkammer became common parlance because various German emperors and other rulers somewhat dominated the field of curiosity cabinet construction. Probably the largest and most spectacular Wunderkammer was that of the Holy Roman Emperor, Rudolf II (1552–1612).

Rudolf II portrait by  Joseph Heintz the Elder 1594 Source: Wikimedia Commons

He was an avid art collector and patron, but he also collected mechanical automata, ceremonial swords, musical instruments, clocks, water works, compasses, telescopes, and other scientific instruments. His Kunstkammer incorporated the three kingdoms of nature and the works of man. Unusually, Rudolf’s cabinet was systematically arranged in encyclopaedic fashion, and he employed his court physician Anselmus de Boodt (1550–1632), a Flemish humanist, minerologist, physician, and naturalist to catalogue it. De Boodt had succeeded Carolus Clusius (1526–1609) as superintendent of Rudolf’s botanical garden.

Rudolf II Kunstkammer

Although it was a private institution, Rudolph allowed selected professional scholars to study his Wunderkammer. In fact, as well as inanimate objects Rudolf also studiously collected some of Europe’s leading scholars. The astronomers Nicolaua Reimers Baer (1551–1600), Tycho Brahe (1546–1601), and Johannes Kepler (1571–1630) all served as imperial mathematicus. The instrument maker, Jost Bürgi came from Kassel to Prague. As already mentioned, Carolus Clusius (1526–1609) and Anselmus de Boodt (1550–1632) both served as superintendent of the imperial botanical gardens. The later also served as personal physician to Rudolf, as did the Czech naturalist, astronomer, and physician Thaddaeus Hagecius ab Hayek (1525–1600). The notorious occultist Edward Kelly (1555-1597) worked for a time in Rudolf’s alchemy laboratory.

When Rudolf died his Wunderkammer was mostly transferred to Vienna by his brother and successor as Holy Roman Emperor, Matthias, where it was gradually dissipated over the years. Although, his was by far the most spectacular Rudolf’s was only one of many cabinets of curiosity created during the Renaissance by the rich and powerful as a status symbol. However, there were also private people who also created them; the most well-known being the Danish, naturalist, antiquary, and physician Ole Worm (1588­–1654).

Ole Worm and Dorothea Worm, née Fincke artist unknown Source: Wikimedia Commons

Son of Willum Worm a mayor of Aarhus, he inherited substantial wealth from his father. After attending grammar school, he studied theology Marburg and graduated Doctor of Medicine at the University of Basel in 1611. He also graduated MA at the University of Copenhagen in 1618. He spent the rest of his life in Copenhagen, where he taught Latin Greek, physics, and medicine, whilst serving as personal physician to the Danish King, Christian IV (1577–1648). He died of the bubonic plague after staying in the city to treat the sick during an epidemic.

As a physician he contributed to the study of embryology. Other than medicine he took a great interest in Scandinavian ethnography and archaeology. As a naturalist he determined that the unicorn was a mythical beast and that the unicorn horns in circulation were actually narwhal tusks. He produced the first detail drawing of a bird-of-paradise, proving that they, contrary to popular belief, did in fact have feet. He also drew from life the only known illustration of the now extinct great auk.

OLe Worm’s Great Auk Source: Wikimedia Commons

Worm is best known today for his extensive cabinet of curiosity the Museum Wormianum a great collection of curiosities ranging from native artifacts from the New World, to stuffed animals and fossils in which he specialised.

1655 – Frontispiece of Museum Wormiani Historia Source: Wikimedia Commons

As with other cabinets, Worm’s collection consisted of minerals, plants, animals, and man-made objects. Worm complied a catalogue of his collection with engravings and detailed descriptions, which was published posthumously in four books, as Museum Wormianum. The first three books deal respectively with minerals, plants, and animals. The fourth is archaeological and ethnographical items. 

Title page 
Museum Wormianum. Seu historia rerum rariorum, tam naturalium, quam artificialium, tam domesticarum, quam exoticarum, quæ Hafniæ Danorum in œdibus authoris servantur. Adornata ab Olao Worm … Variis & accuratis iconibus illustrata. Source

A private cabinet of curiosity that then became an institutional one was that of the Jesuit polymath, Athanasius Kircher (1602-1680). Kircher referred to variously as the Master of a Hundred Arts and The Last man Who Knew Everything belonged very much to the Renaissance rather than the scientific revolution during which he lived and was active.

Athanasius Kircher engraving by Cornelis Bloemaert Source: Wikimedia Commons

He was author of about forty major works that covered a bewildering range of topics, which ranged from the genuinely scientific to the truly bizarre. Immensely popular and widely read in his own time, he quickly faded into obscurity following his death. Born in Fulda in Germany, one of nine children, he attended a Jesuit college from 1614 till 1618 when he entered the Jesuit Order. Following a very mixed education and career he eventually landed in the Collegio Romano in 1634, where he became professor for mathematics. Here he fulfilled an important function in that he collected astronomical data from Jesuit missionaries throughout the world, which he collated and redistributed to astronomers throughout Europe on both sides of the religious divide. 

Given he encyclopaedic interests it was perfectly natural for Kircher to begin to assemble his own private cabinet of curiosities. In 1651, the Roman Senator Alfonso Donnini (d.1651) donated his own substantial cabinet of curiosities to the Collegio, and the authorities decided that it was best placed in the care of Father Kircher. Combining it with his own collection, Kircher established, what became known as the Musæum Kircherianum, which he continued to expand throughout his lifetime.

Musæum Kircherianum, 1679 Source: Wikimedia Commons

The museum became very popular and attracted many visitors. Giorgio de Sepibus published a first catalogue in 1678, the only surviving evidence of the original layout. Following Kircher’s death the museum fell into neglect but was revived, following the appointment of Filippo Bonanni (1638–1725), Kercher’s successor as professor of mathematics, as curator in 1698. Bonnani published a new catalogue of the museum in 1709. The museum prospered till 1773 till the suppression of the Jesuit Order led to its gradual dissipation, reestablishment in 1824, and final dispersion in 1913.

Filippo Bonanni, Musaeum Kircherianum, 1709 Source: Wikimedia Commons

As we have seen cabinets of curiosities often evolved into public museums and I will close with brief sketches of two that became famous museums in England in the seventeenth and eighteenth centuries. 

John Tradescant the Elder (c. 1570–1638) was an English, naturalist, gardener, and collector. He was gardener for a succession of leading English aristocrats culminating in service to George Villiers, 1st Duke of Buckingham. In his duties he travelled widely, particularly with and for Buckingham, visiting the Netherlands, Artic Russia, the Levant, Algiers, and France. Following Buckingham’s assassination in 1628, he was appointed Keeper of the King’s Gardens, Vines and Silkworms at Oatlands Palace in Surrey.

John Tradescant the Elder (portrait attributed to Cornelis de Neve) Source: Wikimedia Commons

On his journeys he collected seeds, plants, bulbs, as well as natural historical and ethnological curiosities. He housed this collection, his cabinet of curiosities, in a large house in Lambeth, The Ark.

Tradescant’s house in Lambeth: The Ark Source: Wikimedia Commons

This was opened to the public as a museum. The collection also included specimens from North America acquired from colonists, including his personal friend John Smith (1580–1631), soldier, explorer, colonial governor, and Admiral of New England.

His son, John Tradescant the Younger (1608–1662) followed his father in becoming a naturalist and a gardener.

John Tradescant the Younger, attributed to Thomas de Critz Source: Wikmedia Commons

Like his father he travelled widely including two trips to Virginia between 1628 and 1637. He added both botanical and other objects extensively to the family collection in The Ark. When his father died, he inherited his position as head gardener to Charles I and Henrietta Maria of France working in the gardens of Queens House in Greenwich. Following the flight of Henrietta Maria in the Civil War, he compiled a catalogue of the family cabinet of curiosities, as Museum Tradescantianum, dedicated to the Royal College of Physicians with whom he was negotiating to transfer the family botanical garden. A second edition of the catalogue was dedicated to Charles II after the restoration.

Source: Wikimedia Commons

Around 1650, John Tradescant the Younger became acquainted with the antiquarian, politician, astrologer and alchemist, Elias Ashmole (1617–1692), who might be described as a social climber.

Elias Ashmole by John Riley, c. 1683

Born into a prominent but impoverished family, he managed to qualify as a solicitor with the help of a prominent maternal relative. He married but his wife died in pregnancy, just three years later in 1641. In 1646-47, he began searching for a rich widow to marry. In 1649, he married Mary, Lady Mainwaring, a wealthy thrice widowed woman twenty years older than him. The marriage was not a success and Lady Manwaring filed suit for separation and alimony, but the suit was dismissed by the courts in 1657 and having inherited her first husband’s estate, Ashmole was set up for life to pursue his interests in alchemy and astrology, without having to work. 

Ashmole helped Tradescant to catalogue the family collection and financed the publication of the catalogue in 1652 and again in 1656. Ashmole persuaded John Tradescant to deed the collection to him, going over into his possessing upon Tradescant’s death in 1662. Tradescant’s widow, Hester, challenged the deed but the court ruled in Ashmole’s favour. Hester held the collection in trust for Ashmole until her death.

In 1677, Ashmole made a gift of the Tradescant collection together with his own collection to the University of Oxford on the condition that they build a building to house them and make them available to the general public. So, the Ashmolean Museum, the world’s second university museum and Britain’s first public museum, came into existence on 24 May 1683.

The original Ashmolean Museum building on Board Street Oxford now the Museum of the History of Science, Oxford Source: Wikimedia Commons

My second British example is the cabinet of curiosities of Hans Sloane (1660–1753), physician, naturalist, and collector.

Slaughter, Stephen; Sir Hans Sloane, Bt; Source: National Portrait Gallery, London via Wikipedia Commons

Sloane was born into an Anglo-Irish family in Killyleagh a village in County Down, Ulster. Already as a child Sloane began collecting natural history items and curiosities, which led him to the study of medicine. In London, he studied botany, materia medica, surgery, and pharmacy. In 1687, he travelled to Jamaica as personal physician to the new Governor Christopher Monck, 2nd Duke of Albemarle. Albemarle died in the following year, so Sloane was only in Jamaica for eighteen months, however, in this time he collected more than a thousand plant specimens and recorded eight hundred new species of plants, starting a lifetime of collecting.

Sloane married the widow Elizabeth Langley Rose a wealthy owner of Jamaican sugar plantation worked by slaves, making Sloane independently wealthy. There followed a successful career as physician, Secretary of the Royal Society, editor of the Philosophical Transactions, President of the Royal College of Physicians, and finally President of the Royal Society. Throughout his life, Sloane continued to collect. He used his wealth to acquire the natural history collections of Barbadian merchant William Courten (1572–1636), papal nuncio Cardinal Filippo Antonio Gualterio (1660–1728), apothecary James Petiver (c.1665–1718), plant anatomist Nehemiah Grew, botanist Leonard Plukenet (1641–1706), gardener and botanist the Duchess of Beaufort (1630–1715), botanist Adam Buddle (1662–1715), physician and botanist Paul Hermann (1646–1695), botanist and apothecary Franz Kiggelaer  (1648–1722), and botanist, chemist, and physician Herman Boerhaave (1668–1738).

 When he died Sloane’s collection of over seventy-one thousand items– books manuscripts, drawings, coins and medals, plant specimens and more–was sold to the nation for £20,000, well below its true value. It formed to founding stock of the British Museum and British Library, which opened in 1759.

Montagu House, c. 1715 the original home of the British museum

The natural history collection was split off to found the Natural History Museum, which opened in South Kensington in 1881.

The Natural History Museum. This is a panorama of approximately 5 segments. Taken with a Canon 5D and 17-40mm f/4L. Source: Wikimedia Commons

The Renaissance practice of creating cabinets of curiosities played a significant role in the creation of modern museums in Europe. It also provided scientists with collections of materials on which to conduct their research, an important element in the development of empirical science in the Early Modern Period. 





Filed under History of botany, History of medicine, History of science, History of Technology, History of Zoology, Natural history, Renaissance Science

The sixteenth century dispute about higher order algebraic equations and their solution

The Early Modern period is full of disputes between scholars about questions of priority and accusations of the theft of intellectual property. One reason for this is that the modern concepts of copyright and patent rights simply didn’t exist then, however, that is not the topic of this post. One of the most notorious disputes in the sixteenth century concerned Niccolò Fontana Tartaglia’s discovery of the solution to one form of cubic equation and Gerolamo Cardano’s publication of that solution, despite a promise to Tartaglia not to do so, in his book Artis Magnae, Sive de Regulis Algebraicis Liber Unus, commonly known as the Ars Magna in 1545. A version of this story can be found is every general history of mathematics book and there are numerous versions to be found on the Internet. I blogged about it twelve years ago and maths teacher and historian, Dave Richeson wrote about it just last month in Quanta Magazine

Despite all of this, I am going to review a book about the story that I recently acquired and read, Fabio Toscano, The Secret FormulaHow a Mathematical Duel Inflamed Renaissance Italy and Uncovered the Cubic Equation.[1] 

Unlike most of my book reviews this is not a new book, it was originally published in Italian as, La formula segreta, in 2009 and the English translation appeared in 2020. I caught a glimpse of it on the Princeton University Press website at half price in their summer sale and on a whim decided to buy it.[2] I’m glad that I did, as it is an excellent retelling of the story using all of the original documents, which adds a whole new depth to it, not found in the popular versions. 

Toscano’s book, which is comparatively short, has six chapters each of which deals with a distinctive aspect of the sequence of historical events that he is narrating. The opening chapters introduces one of the principal characters in this story Niccolò Fontana, describing his lowly birth, his facial disfigurement delivered by a soldier during the 1512 storm of Brescia, which gave him the stutter by which he was known, Tartaglia. How the autodidactic mathematician became an abaco master, a private teacher of arithmetic, algebra, bookkeeping and elementary geometry.

The second chapter is a brief sketch of history of algebra up to the Renaissance. The elementary nature of ancient Egyptian algebra, the much more advanced nature of Babylonian algebra including the partial general solution of the quadratic equation. Partial, because the Babylonians didn’t acknowledge negative solutions. Here we have one of the few, in my opinion, failures in the book. There is no mention whatsoever of the Indian contributions to the evolution of algebra. This is important as it was Brahmagupta who, in the sixth century CE, introduced the full arithmetic of both positive and negative numbers and the full general solution of the quadratic equation. More importantly the Islamic algebraists took their knowledge of algebra from the Indians and in particular Brahmagupta. Another failure in this section is that Toscano repeats the standard myth of the House of Wisdom. Very positive is the fact that he explains the terminology of rhetorical algebra, the problems are all written out in words not symbols. He also explains that whereas we now just handle quadratic or cubic equations through the general form, in the Renaissance every variation was regarded as a separate equation. So, for example, if the x2 is missing from a cubic equation, this is a new equation that is handled separately. There are in fact, according to Omar Khayyam, fourteen different types of cubic equation. Apart from the omission of Indian algebra this whole chapter is excellent.

Toscano, The Secret Formula page 39

The third chapter takes us to the heart of the story and the event that made Tartaglia famous and would eventually lead to his bitter dispute with Cardano, the public contest with Antonio Maria Fior. In the most influential mathematics book of the era, his Summa de arithmetica, geometria, proportioni et proportionalita (Summary of arithmetic, geometry, proportions and proportionality) published in Venice in 1494, Luca Pacioli (c. 1447–1517) had stated that there was no possible general solution to the cubic equation, Fior had, however, acquired a general solution to the cubic equations of the form x3 + bx = c  and thought he could turn this into capital for his career. He challenged Tartaglia to a public contest thinking he held all the trumps. Unfortunately, for him Tartaglia had also found this solution, so the contest turned into a debacle for Fior and a great triumph for Tartaglia. If you want to know the details read the book. Toscano’s account of what happened, based on the available original sources is much more detailed and informative that the usual ones. We also get introduced to Messer Zuanne Tonini de Coi, another mathematician, who doesn’t usually get mentioned in the general accounts of the story but who plays a leading role in several aspects of it. Amongst other things, he was the first who tries to get Tartaglia to divulge the partial solution of the cubic that he has discovered, and it was he, who he first told Cardano about Tartaglia’s discovery.

In chapter four we meet the villain of the story the glorious, larger than life, Renaissance polymath, Gerolamo Cardano. We get a sympathetic description of Cardano’s less than auspicious origins and his climb to success as a physician against all the odds. Toscano does not over emphasise Cardano’s oddities and he had lots of those. We now get a very detailed account, once more based on original documents, of Cardano’s attempts to woo Tartaglia and seduce the secret of the partial cubic solution out of him. Cardano’s seduction was eventually successful, and he obtained the solution but only after swearing a solemn oath to reveal the solution to nobody until Tartaglia had published in his planned book. 

Chapter five takes us to Cardano’s breaking of that oath, his, I think justifiable reasons for doing so, and Tartaglia’s understandable outrage. The chapter opens with more exchanges about Tartaglia’s solution, which Cardano hasn’t truly understood, because of an error in Tartaglia’s encrypted poetical revelation of it. Having cleared this up Tartaglia begins to panic because Cardano is planning to publish a maths book his, Practica arithmetice et mensurandi singularis (The Practice of Arithmetic and Simple Mensuration), and he fears it will include his solution, it didn’t, panic over for now. We now get introduced to Cardano’s brilliant pupil and foster son, Lodovico Ferrari. Between the two of them, starting from Tartaglia’s solution, they find the general solutions of the cubic and the quartic or biquadratic equations putting algebra on a whole new footing but are unable to publish because of Cardano’s oath to Tartaglia. However, in 1542, Cardano and Ferrari travelled to Bologna and discovered in a notebook of Scipione Dal Ferro Tartaglia’s partial solution of the cubic made twenty years earlier than Tartaglia and obviously the source of Fior’s knowledge of the solution. Cardano no longer felt constrained by his oath and in 1545, his Ars Magna was published by Johannes Petreius in Nürnberg, containing all the algebra that he and Ferrari had developed but giving full credit to Scipione Dal Ferro and Tartaglia for their contributions. Tartaglia went ballistic!

The closing chapter deals with the final act, Tartaglia’s indignation over what he saw as Cardano’s treachery and the reaction to his accusations. Tartaglia raged and Cardano remained silent. Although, he had been very vocal in obtaining the cubic solution from Tartaglia, Cardano now withdrew completely from the dispute, leaving Ferrari to act as his champion. Tartaglia and Ferrari exchanged a total of twelve pamphlets, six each, full of polemic, invective, accusations, and challenges. Tartaglia trying, the whole time, to provoke Cardano into a direct response, accusing him of ghost-writing Ferrari’s pamphlets. Ferrari, in turn, constantly challenged Tartaglia to a face-to-face public confrontation, which he steadfastly rejected. Toscano reproduces a large amount of the contents of those pamphlets, upon which he judiciously comments. It is this engagement by the author that makes the book such a good read. Tartaglia finally caved in, probably as a condition of a new job offer, and met Ferrari in the public arena in Milan, fleeing the city on the evening of the first day of the confrontation, his reputation in tatters. What exactly took place, we don’t know, as Cardano and Ferrari never commented on the meeting, and we have only Tartaglia’s account that relates that he realised that the crowd was stacked against him with Ferrari’s supporters, and he could never win and so he departed.

Given the nature of the book, it has no illustrations. However, given the authors extensive use of both primary sources as well as authoritative secondary sources, it has an impressive number of endnotes, unfortunately not footnotes. Most of these are simple references to the source quoted and here the book uses a convention that I personally dislike. These references are mostly just something like [21.e]. The authors in the bibliography are sequentially numbered and if the author of more than one text these are identified by the small case letters. So, you are interested in the origin of a quote, you go to the endnotes, find there such a number, and then leaf through the bibliography to find out who, what, why, where! I do not like! Many of the items in the bibliography are texts from Italian historians, so the English edition has a short, but high quality, extra list of English titles on the topic. There is an excellent index.

It may seem that I have revealed too much of the contents of the book to make it worth reading but I have only sketched the outline of the story as it appears in the book, a story, which as I said at the beginning is very well know, the devil is as they say in the detail. By his very extensive use of the original sources, Toscano has given the popular story a whole new dimension, making his book a totally fascinating read for anybody interested in the history of mathematics. His book is also a masterclass in how to write high quality popular history of mathematics. 

[1] Fabio Toscano, The Secret FormulaHow a Mathematical Duel Inflamed Renaissance Italy and Uncovered the Cubic Equation, Translated by Arturo Sangalli, Princeton University Press, Princeton and Oxford, 2020

[2] More accurately the dastardly Karl Galle drew my attention to it, and I couldn’t resist the temptation, as it was not only cheap but came with free p&p. When I ordered it, I had forgotten that PUP distribute their book in Europe out of the UK. I try to avoid ordering books from the UK because, since Brexit, I now have to pay customs duty on book from the UK, on top of which the German postal service adds a €6 surcharge for paying the customs duty in advance, this would, in this case almost double the cost of the book. Normally, when I receive books from the UK, I get a note in my post box and have to go to the post office to pay the money due and pick up the book. For some reason, in this case, the postman simply delivered the book despite the label saying how much I was supposed to pay and so I didn’t have to pay it. You win some, you lose some!


Filed under Book Reviews, History of Mathematics, Renaissance Science

Renaissance science – XXXIX

Over a series of episodes, we have followed how the Renaissance Humanists introduced materia medica into the university curriculum developing it from a theoretical subject to a practical empirical field of research and then over time, how the modern scientific study of botany developed out of it. We have also seen how some of the same energy was invested in laying down the beginnings of the modern scientific study of zoology. The beginnings of this evolution at the end of the fifteenth century coincided with the beginnings of the so-called Age of Discovery or Age of Exploration, which as I stated in the first episode on navigation I prefer to refer to as the Contact Period, when Europeans first came into contact with lands and peoples unknown to them, such as the Americas or sub-Saharan Africa, and at the same time vastly increased their knowledge of countries such as India; they also became acquainted with a vast number of new medicinal herbs and other plants as well as animals, which played an increasing role in their studies in these areas. 

Exotica out of the plant and animal kingdoms were not unknown to the European scholars, after all Alexander the Great had conquered Persia and Northern India and the Romans Northern Africa. They brought knowledge of these lands and their flora and fauna back into Europe and even imported many of those plants and animals. Famously, Hannibal crossed the Alps with his elephants and the Romans fed Christians to the lions in the Circus Maximus. Some of these exotica were also recorded in the works of Aristotle, Theophrastus, Dioscorides, and Pliny. Later in the Middle Ages the Islamic forces created an Empire that stretched from China to Spain and the Islamic scholars also recorded much of the flora and fauna of this vast Empire. A lot of that material came into Europe during the twelfth century Scientific Renaissance when large quantities of Arabic material was translated into Latin. 

However, this knowledge of natural historical exotica was purely second hand and the European recipients in the Middle Ages and Renaissance had no way of knowing how accurate it was or even if it was true. They had no first-hand empirical verification. Were the accounts of real plants and animals or mythical ones. Just looking at the proto-zoological works of both Conrad Gesner and Ulisse Aldrovandi illustrates this problem. Both of them include many animals that we now know never existed, myths and legends from other times and other cultures. They had no way of differentiating between the real and the mythical, although they both put hesitant question marks behind some of the mythical beasts that they served up for their readers.

The vastly increased voyages of trade and exploration, although one could simply write trade as almost all exploratory voyages where motivated by the hope of trade, during the contact period gave the Renaissance scholars the chance to go and search out and describe the exotica with their own eyes. When talking about Renaissance zoology we saw that the French naturalist Pierre Belon (1517–1564) travelled as a diplomate in Greece, Crete, Asia Minor, Egypt, Arabia, and Palestine between 1546 and 1549 and observed and wrote about natural history there. Under the botanists Carolus Clusius (1526–1609) translated Garcia de Orta’s important materia medica text Colóquios dos simples e drogas he cousas medicinais da Índia, into Latin from the original Portuguese and published it in Europe in 1567. He also acquired information about the flora of the Americas by questioning seafarers returning to the Iberian Peninsula from there. Clusius’ interest in the materia medica and natural history of the newly discovered Americas didn’t end with just collecting information from returnees, he also translated and published in Latin. the work of Nicolás Monardes (1493–1588)

Source: Wikimedia Commons

Monardes was born in Seville the son of Nicolosi di Monardis, an Italian bookseller, and Ana de Alfaro, the daughter of a physician. He graduated BA in 1530 and obtaining a first degree in medicine in 1533, began to practice medicine in Seville. He obtained a doctorate in medicine from the University of Alcalá de Henares in 1547. He wrote extensively on the materia medica of the Americas. In 1565, he published his Historia medicinal de las cosas que se traen de nuestras Indias Occidentales in Seville, which was based on the reports of a wide range of people returning from the Americas. In 1569, he published an extended version, his Dos libros, el uno que trata de todas las cosas que se traen de nuestras Indias Occidentales, que sirven al uso de la medicina, y el otro que trata de la piedra bezaar, y de la yerva escuerçonera. A second volume expanding on the material in the first two books, Segunda parte del libro des las cosas que se traen de nuestras Indias Occidentales, que sirven al uso de la medicina; do se trata del tabaco, y de la sassafras, y del carlo sancto, y de otras muchas yervas y plantas, simientes, y licores que agora nuevamente han venido de aqulellas partes, de grandes virtudes y maravillosos effectos appeared in Saville in 1571. A single edition of all three books, Primera y segunda y tercera partes de la historia medicinal de las cosas que se traen de neustra Indias Occidentales, que sirven en medicina; Tratado de la piedra bezaar, y dela yerva escuerçonera; Dialogo de las grandezas del hierro, y de sus virtudes medicinales; Tratado de la nieve, y del beuer frio was published in Saville in 1574, with a second edition appearing in 1580.

Source: Wikimedia Commons
Source: Wikimedia Commons

 In 1574, Platin in Antwerp published Clusius first translation De simplicibus medicamentis ex occidentali India delatis quorum in medicina usus est. Plantin published a revised edition, Simplicium medicamentorum ex novo orbe delatorum, quorum in medicina usus est, historia, in 1579. In 1582, Clusius produced a compendium of revised translations of the work of Garcia de Orta, Nicolás Monardes, and Cristóbal Acosta, to who we will return shortly. A further revised edition appeared in 1593 and a last revision in 1605. In 1577, John Frampton, a sixteenth century English merchant, published an English translation of the 1565 Spanish text, Ioyfull newes out of the newe founde worlde, wherein is declared the rare and singular vertues of diuerse and sundrie hearbes, trees, oyles, plantes, and stones, with their applications, as well for phisicke as chirurgerie in London. A new expanded edition based in the 1574 Spanish text appeared in 1580.

Source: Wikimedia Commons
Source: Wikimedia Commons

Before we turn to Acosta, we need to deal with Gonzalo Fernández de Oviedo y Valdés (1478–1557), who preceded him.

Gonzalo Fernández de Oviedo y Valdés Source: Wikimedia Commons

Oviedo was a Spanish, soldier, historian, writer, botanist, and colonist, who participated in the colonisation of the West Indies already in the 1490s. Born in Madrid, he was educated at the court of Ferdinand and Isabella, where he served as a page to the Infanta, Juan de Aragón, until his death in 1497. He then spent three years in Italy before returning to a position as a bureaucrat in the Castilian imperial project. In 1514, he was appointed supervisor of gold smelting in Santo Domingo and in 1523 historian of the West Indies. He travelled five more times to the Americas before his death. 

In 1526, he published a short work, La Natural hystoria de las Indias, with few illustrations, in Toledo. It was translated into Italian appearing in Venice in 1534, with French editions beginning in 1545, and English ones beginning in 1555. In 1535, part one of a longer and more fully illustrated Historia general de las Indias was printed in Seville, which contained the announcement of two further parts. He continued to work on a revised version of part one and on parts two and three until his death in 1557, but they were first published in an incomplete edition in 1851 entitled, Natural y General Hystoria de las Indias. English and French editions of the 1535 Seville publication appeared in 1555 and 1556 respectively. The Saville publication is a ragbag of topics but contains quite a lot of both botanical and zoological information. 

Source: Wikimedia Commons
Source: Wikimedia Commons

The Portuguese physician and natural historian, Cristóbal Acosta (c. 1525–c. 1594), whose work was partially included in Clusius’ 1582 compendium, is thought to have been born somewhere in Africa, because he claimed to be African in his publications.

Cristóbal Acosta Source: Wikimedia Commons

He first travelled to the East Indies, as a soldier, in 1550. He returned to Goa with his former captain, Luís de Ataíde, who had been appointed Viceroy of Portuguese India, in 1568, the year Garcia de Orta died. He worked as a physician in India and gained a reputation for collecting botanical specimens. He returned to Europe in 1572 and worked as a physician in Spain. In 1578, he published his Tractado de las drogas y medicinas de las Indias orientales (Treatise of the drugs and medicines of the East Indies). This work included much that was culled from Garcia de Orta’s Colóquios dos simples e drogas he cousas medicinais da Índia but became better known that Orta’s work. The last entry was a treatise on the Indian Elephant, the first published in Europe. The work was translated into Italian in 1585 by Francesco Ziletti.

Source: Wikimedia Commons

Cristóbal Acosta is not to be confused with José de Acosta (c. 1539–1600), the Jesuit missionary and naturalist.

José de Acosta Source: Wikimedia Commons

Born in Medina del Campo, Spain José de Costa joined the Jesuit Order at the age of thirteen. In 1569, he was sent by the Order to Lima, Peru. Ordered to cross the Andes to journey to the Viceroy of Peru, he and his companions suffered altitude sickness; Acosta, as one of the earliest to do so, gave a detailed description of the ailment, attributing it correctly to “air… so thin and so delicate that it is not proportioned to human breathing.” Acosta aided the Viceroy in a five-year tour through the Viceroyalty of Peru, seeing and recording much of what he experienced. He spent the year of 1586 in Mexico studying the culture of the Aztecs. In 1587, he returned to Spain. He published many, mostly theological, works in his lifetime but is best known as the author of De Natura Novi OrbisDe promulgatione Evangelii apud Barbaros, sive De Procuranda Indorum salute (both published in Salamanca in 1588) and above all, the Historia natural y moral de las Indias(published in Savile in 1590). 

Source: Wikimedia Commons

In his Historia natural y moral de las Indias he presented his observations on the physical geography and natural history of Mexico and Peru as well as the indigenous religions and political structures from a Jesuit standpoint. His book was one of the first detailed and realistic descriptions of the New World. Acosta presented the theory that the indigenous populations must have crossed over from Asia into the Americas. The work was translated into various European languages, appearing in English in 1604 and in French in 1617.

Historia natural y moral de las Indias Source: Wikimedia Commons

It should be noted that just as the early Renaissance natural historians in Europe relied, to a great extent, for their information on plants, herbs and animals on farmers, hunters, foresters, and others who lived and worked on the land, so the Europeans studying the materia medica and natural histories of Asia and the Americas depended very heavily on the information that they received from the indigenous populations. This was particularly the case in the next natural historians that I will briefly present.

Bernardino de Sahagún (c.1499–1590) was born Bernadino de Rivera in Sahagùn in Spain and attended the humanist University of Salamanca and there joined the Franciscan Order, changing his name to that of his birthplace, as was the Franciscan custom, and was probably ordained in 1527. He was recruited in 1529 to join the Franciscan mission to New Spain.

Source: Wikimedia Commons

He helped found the first European school of higher education in the Americas, the Colegio Imperial de Santa Cruz de Tlatelolco in 1536. He learnt the Aztec language Nahuatl in order to be able to confer with the indigenous population about materia medica and natural history. In 1558, he was commissioned by the new provincial of New Spain, Fra Francisco de Toral, to formalise his studies of native languages and culture. He spent twenty-five years researching the topic with the last fifteen spent editing, translating, and copying. He was assisted in his research by five graduates of the Collegio, all of whom spoke Nahuatl, Latin, and Spanish, and as well as helping him to interview the elders about the religious rituals and calendar, family, economic and political customs, and natural history, also participated in research and documentation, translation and interpretation, as well as painting the illustrations. In the text he credited them for their work by name. 

Out of this research Sahagún created a twelve volume General History of the Things of New Spain, the manuscript was sent to Philip II of Spain. It was never printed, and the manuscript was bought by Ferdinando de’ Medici, Grand Duke of Tuscany, in 1580. He put it on display in the Uffizi Gallery in Florence and it is generally known as the Florentine Codex. The volume that deals with natural history is titled Earthly Things and is the most heavily illustrated, containing paintings of thirty-nine mammals, one hundred and twenty birds and more than six hundred flowers. The hundreds of New World plants listed in the Florentine Codex are presented according to an Aztec system of taxonomy. The Aztec divided plants up into four main groups: edible, decorative, economic, and medicinal. 

The Florentine Codex Source: Wikimedia Commons
The Florentine Codex Source: Wikimedia Commons

Sahagún’s Historia general was not the only book on indigenous materia medica to emerge from the Colegio Imperial de Santa Cruz de Tlatelolco. In 1552, a native graduate, Martín de la Cruz wrote a Libellus de Medicinalibus Indorum Herbis (Little Book of the Medicinal Herbs of the Indians) in Nahuatl, which was translated into Latin by Juan Badianus de la Cruz (1484–later than 1552) an Aztec teacher at the Collegio. The original Nahuatl manuscript no longer exists. The manuscript is a compendium of two hundred and fifty medicinal herbs used by the Aztecs. The Latin manuscript sent to Spain changed hands many times over the years before landing in the Vatican Library. In 1990, it was returned to Mexico, where it now resides in library of the National Institute of Anthropology and History in Mexico City.

Libellus de Medicinalibus Indorum Herbis Source: Wikimedia Commons
Libellus de Medicinalibus Indorum Herbis Source: Wikimedia Commons

In the seventeenth century copies of the manuscript were made by Cassiano dal Pozzo (1588–1657) and Francesco Stelluti (1577–1652), both members of the Accademia dei Lincei. The Dal Pozzo copy in now in the Royal Library at Windsor but the Stelluti copy has disappeared. 

For many years, Ulisse Aldrovandi hoped to get a commission from the Spanish Crown to study the natural history of New Spain but in the end, King Philip II sent his personal physician, Francisco Hernández de Toledo (1514–1587) there to study the medicinal plants and animals.

Source: Wikimedia Commons

Of Jewish extraction, he studied medicine at the University of Alcalá from 1530 to 1536 and was connected with the leading scholars of the period. In the area of botanical studies, he won a good reputation for his study of the medical effectivity of plants and his translation into Spanish of Pliny’s Naturalis historia. In 1570, Francisco Hernández shipped out to the Americas accompanied by his son Juan, and the cosmographer Francisco Domínguez, who had been commissioned by the king to map New Spain.

Like Sahagún he learnt Nahuatl and acquired most of his knowledge by interviewing the indigenous population. He was accompanied in his work by three Aztec painters– baptized Antón, Baltazar Elías, and Pedro Vázquez–who provided the illustrations for his work. His work describes over three thousand plants unknown to Europeans, an incredible number when one considers that Dioscorides’ Materia Medica only contains about five hundred. Hernández sent at least sixteen bound volumes of manuscripts back the Philip before he returned in 1577. Theses were three volumes of twenty-four books on plants, one volume of six treatises on animals, eleven volumes of coloured illustrations, and at least one volume of dried plant specimens, there may have been more. 

As with Sahagún, there were problems when it came to the publication of his work. He intended to publish three editions, one in Spanish, one in Latin, and the third in Nahuatl for the indigenous population of New Spain. However, his voluminous material was in a mess, and he was unable to complete the mammoth task that he had undertaken, so the book remained unpublished in his lifetime. Philip II placed the manuscript in the library of the Monasterio y Sitio de El Escorial en Madrid (Royal Site of San Lorenzo de El Escorial), where it was destroyed in a fire in 1671. 

In 1580, Nardo Antonio Recchi (1540–1594) was appointed Hernández’s successor as Philip’s personal physician and took on the task of trying to bring order into Hernández’s chaos. Recchi produced a four-volume edition of Hernández’s work and Juan de Herrera (1530–1597), the architect of El Escorial began the process of preparing it for publication in 1582. However, by the time of his death in 1587 little progress had been made and the project died with him. However, Recchi had taken a copy of his manuscript back to Naples with him and it became the grail for all of the European natural historians, including, Giovanni della Porta, Ulisse Aldrovandi and Carolus Clusius, were eager to study the treasures that Hernández had brought back from the New World.

Part of Hernández’s work, the Index medicamentorum, an index that lists Mexican plants according to their traditional therapeutic uses, was published in Mexico City; the index was arranged according to body part, and it was ordered from head to toe. A Spanish translation appeared as an appendix to the medical treatises of Juan de Barrios (1562–1645) in 1607.  

A Spanish translation of Recchi’s four-volume edition was prepared by Fra Francisco Ximénez with the title, Quatro libros de la naturaleza y virtudes de las plantas y animales and published in Mexico City in 1615.

Source: Wikimedia Commons
Source: Wikimedia Commons

The Accademia dei Lincei under the leadership of Prince Federico Cesi (1585–1630) took up the task of publishing a Latin edition of Recchi’s work. A partial, heavily redacted edition under the title Francisci Hernandez rerum medicarum Novae Hispaniae Thesaurus appeared in print in 1628, however the project was laid on ice when Cesi died in 1630. Finally, a complete Latin edition of Recchi’s four volumes, edited by Johannes Schreck (1576–1630) and Fabio Colonna (1567–1640), was published in Rome, including material from Hernández’s original manuscripts not used by Recchi, with the title, Nova plantarum, animalium et mineralium mexicanorum historia a Francisco Hernández in indis primum compilata, de inde a Nardo Antonio Reccho in volumen digesta (1648–51)

Source:Wikimedia Commons

Of course, what I have sketched above was only the beginning of the European awareness of the natural history of the world outside of Europe and down to the present-day thousands of research expeditions by scientists from all other the world have continued to add to our knowledge of the extraordinary diversity of flora and fauna on our planet. 


Filed under History of botany, History of medicine, History of Zoology, Natural history, Renaissance Science

Mathematician, astrologer, conjurer! 

It is almost impossible to imagine a modern university without a large mathematics department and a whole host of professors for an ever-increasing array of mathematical subdisciplines. Mathematics and its offshoots lie at the centre of modern society. Because popular history of science has a strong emphasis on the prominent mathematicians, starting with Euclid and Archimedes, it is common for people to think that mathematics has always enjoyed a central position in the intellectual life of Europe, but they are very much mistaken if they do so. As I have repeated on several occasions, mathematics had a very low status at the medieval European university and led a starved existences in the shadows. Some people like to point out that the basic undergraduate degree at the medieval university formally consisted of the seven liberal arts, the trivium and quadrivium, with the latter consisting of the four mathematical disciplines–arithmetic, geometry, music, and astronomy. If fact, what was largely taught was the trivium–grammar, logic, rhetoric–and large doses of, mostly Aristotelian, philosophy. A scant lip service was paid to the quadrivium at most universities, with only a very low-level introductory courses being offered in them. There were no professors for any of the mathematical disciplines.

Things only began to change during the Renaissance, when the first universities, in Northern Italy, began to establish chairs for mathematics, which were actually chairs for astrology, because of the demand for astrology for medical students. The concept of general chairs for mathematics for all educational institutions began with Philip Melanchthon (1497–1560), when he set up the school and university system for Lutheran Protestantism, to replace the previously existing Catholic education system, in the second quarter of the sixteenth century.

Melanchthon in 1526: engraving by Albrecht Dürer Translation of Latin caption: «Dürer was able to draw Philip’s face, but the learned hand could not paint his spirit».
Source: Wikimedia Commons

Melanchthon did so because he was a passionate advocate of astrology and to do astrology you need astronomy and to do astronomy you need arithmetic, geometry, and trigonometry, so he installed the full package in all Lutheran schools and universities. He also ensured that the universities provided enough young academic mathematicians to fill the created positions.  

Catholic educational institutions had to wait till the end of the sixteenth century before Christopher Clavius (1538–1612) succeeded in getting mathematics integrated into the Jesuit educational programme and installed a maths curriculum into Catholic schools, colleges, and universities throughout Europe over several decades. He also set up a teacher training programme and wrote the necessary textbooks, incorporating the latest mathematical developments.

Christoph Clavius. Engraving Francesco Villamena, 1606 Source: Wikimedia Commons

England lagged behind in the introduction of mathematics formally into its education system. Even as late as the early eighteenth century, John Arbuthnot (1667–1735) could write that there was not a single grammar school in England that taught mathematics.

John Arbuthnot, by Godfrey Kneller Source: Wikimedia Commons

This is not strictly true because The Royal Mathematical School was set up in Christ’s Hospital, a charitable institution for poor children, in 1673, to teach selected boys’ mathematics, so that they could become navigators. At the tertiary level the situation changed somewhat earlier. 

Gresham College was founded in London under the will of Sir Thomas Gresham (c. 1519–1579) in 1595 to host public lectures.

Gresham College 1740 Source: Wikimedia Commons

Sir Thomas Gresham by Anthonis Mor Rijksmuseum

Amongst other topics, professors were appointed to hold lectures in both geometry and astronomy. As with the Royal Mathematical School a century later these lectures were largely conceived to help train mariners. The instructions for the geometry and astronomy professors were as follows:

The geometrician is to read as followeth, every Trinity term arithmetique, in Michaelmas and Hilary terms theoretical geometry, in Easter term practical geometry. The astronomy reader is to read in his solemn lectures, first the principles of the sphere, and the theory of the planets, and the use of the astrolabe and the staff, and other common instruments for the capacity of mariners.

The first university professorships for mathematics were set up at Oxford University in 1619 financed by a bequest from Sir Henry Savile (1549–1622), the Savilian chairs for astronomy and geometry.

Henry Savile Source: Wikimedia Commons

Over the years it was not unusual for a Gresham professor to be appointed Savilian professor, as for example Henry Biggs (1561–1630), who was both the first Gresham professor and the first Savilian professor of geometry.

Henry Briggs

Henry Savile was motivated in taking this step by the wretched state of mathematical studies in England. Potential mathematicians at Cambridge University had to wait until a bequest from Henry Lucas (c. 1610–1663), in 1663, established the Lucasian Chair of Mathematics, whose first incumbent was Isaac Barrow (1630–1677), succeeded famously by Isaac Newton (1642–1726 os).  This was followed in 1704 with a bequest by Thomas Plume to “erect an Observatory and to maintain a studious and learned Professor of Astronomy and Experimental Philosophy, and to buy him and his successors utensils and instruments quadrants telescopes etc.” The Plumian Chair of Astronomy and Experimental Philosophy, whose first incumbent was Roger Cotes (1682–1716).

unknown artist; Thomas Plume, DD (1630-1704); Maldon Town Council;

Before the, compared to continental Europe, late founding of these university chairs for the mathematical sciences, English scholars wishing to acquire instruction in advanced mathematics either travelled to the continent as Henry Savile had done in his youth or find a private mathematics tutor either inside or outside the universities. In the seventeenth century William Oughtred (1574–1660), the inventor of the slide rule, fulfilled this function, outside of the universities, for some notable future English mathematicians. 

William Oughtred by Wenceslas Hollar 1646

One man, who fulfilled this function as a fellow of Oxford University was Thomas Allen (1542–1632), who we met recently as Kenhelm Digby’s mathematics tutor.

Thomas Allen by James Bretherton, etching, late 18th century Source: wikimedia Commons

Although largely forgotten today Allen featured prominently in the short biographies of the Alumni Oxonienses of Anthony Wood (1632–1695) and the Brief Lives of John Aubrey (1626–1697), both of them like Allen antiquaries. Aubrey’s description reads as follows: 

Mr. Allen was a very cheerful, facecious man and everybody loved his company; and every House on their Gaudy Days, were wont to invite him. The Great Dudley, Early of Leicester, made use of him for casting of Nativities, for he was the best Astrologer of his time. Queen Elizabeth sent for him to have his advice about the new star that appeared in the Swan or Cassiopeia … to which he gave his judgement very learnedly. In those dark times, Astrologer, Mathematician and Conjuror were accounted the same thing; and the vulgar did verily believe him to be a conjurer. He had many a great many mathematical instruments and glasses in his chamber, which did also confirm the ignorant in their opinion; and his servitor (to impose on Freshmen and simple people) would tell them that sometimes he should meet the spirits coming up his stairs like bees … He was generally acquainted; and every long vacation he rode into the country to visit his old acquaintances and patrons, to whom his great learning, mixed with much sweetness of humour, made him very welcome … He was a handsome, sanguine man and of excellent habit of body.

The “new star that appeared in the Swan or Cassiopeia” is the supernova of 1572, which was carefully observed by astronomers and interpreted by astrologers, often one and the same person, throughout Europe.

Star map of the constellation Cassiopeia showing the position of the supernova of 1572 (the topmost star, labelled I); from Tycho Brahe’s De nova stella. Source: Wikimedia Commons

Conjuror in the Early Modern Period meant an enchanter or magician rather than the modern meaning of sleight of hand artist and was closely associated with black magic. Allen was not the only mathematician/astrologer to be suspected of being a conjuror, the same accusation was aimed at the mathematician astronomer, and astrologer, John Dee (1527–c. 1609). At one public burning of books on black magic at Oxford university in the seventeenth century, some mathematics books were reputedly also thrown into the flames. Aubrey also relates the story that when Allen visited the courtier Sir John Scudamore (1542–1623), a servant threw his ticking watch into the moat thinking it was the devil. The anonymous author of Leicester’s Commonwealth (1584), a book attacking Elizabet I’s favourite Robert Dudley, Earl of Leicester (1532–1588) accused Allen of employing the art of “figuring” to further the earl of Leicester’s unlawful designs, and of endeavouring by the “black art” to bring about a match between his patron and the Queen. The same text accuses both Allen and Dee of being atheists. 

Anthony Wood described Allen as:

… clarrissimus vir [and] very highly respected by other famous men of his time … Bodley, Savile, Camden, Cotton, Spelman, Selden, etc. … a great collector of scattered manuscripts …  an excellent man, the father of all learning and virtuous industry, an unfeigned lover and furtherer of all good arts and sciences.

The religious controversialist Thomas Herne (d. 17722) called Allen:

… a very great mathematician and antiquary [and] a universal scholar. 

In his History of the Worthies of Britain (1662), the historian Thomas Fuller (1608–1661) wrote of Allen:

…he succeeded to the skill and scandal of Friar Bacon [and] his admirable writings of mathematics are latent with some private possessors, which envy the public profit thereof.

The jurist John Selden (1584–1654), even in comparison with the historian William Camden (1551–1623), the diplomat and librarian Thomas Bodley (1545–1613) and the Bible translator and mathematician Henry Savile, called Allen:

…the brightest ornament of the famous university of Oxford.

So, who was this paragon of scholarship and learning, whose praises were sung so loudly by his notable contemporaries?

Thomas Allen was the son of a William Allen of Uttoxeter in Staffordshire. Almost nothing is known of his background, his family, or his schooling before he went up to Oxford. It is not known how, where, when, or from whom he acquired his knowledge of mathematics. He began acquiring mathematical manuscripts very early and there is some indication that he was largely an autodidact. He went up to Trinity College Oxford comparatively late, at the age of twenty in 1561. He graduated BA in 1563 and was appointed a fellow of Trinity 1565. He graduated MA in 1567. He might have acquired his mathematical education at Merton College. There is no indication the Allen was a Roman Catholic, but he joined an exodus of Catholic scholars from Trinity, resigning his fellowship, and moving to Gloucester Hall in 1570.

In 1598 he was appointed a member of a small steering committee to supervise and assist Thomas Bodley (1535–1613) in furnishing a new university library. Allen and Bodley had both entered Oxford at around the same time, graduating BA in the same year, and remained live long friends. Allen’s patrons all played a leading role in donating to the new library. About 230 of Allen’s manuscripts are housed in the Bodleian, 12 of them donated by Allen himself when the library was founded and the rest by Kenhelm Digby, who inherited them in Allen’s will. 

Through his patron, Robert Dudley, 1st Earl of Leicester, Allen came into contact with John Dee and the two mathematician/astrologers became friends.

Robert Dudley, 1st Earl of Leicester artist disputed Source: Wikimedia Commons

The Polish noble and alchemist Olbracht Łaski (d. 1604), who took Dee with him back to Poland in 1583, also tried to persuade Allen to travel with him to the continent, but Allen declined the invitation. 

Olbracht Łaski Source: Wikimedia Commons

In this time of publish or perish for academics, where one’s status as a scholar is measured by the number of articles that you have managed to get published, it comes as a surprise to discover that Allen, who, as we have seen from the quotes, was regarded as one of the leading English mathematicians of the age, published almost nothing in his long lifetime. His reputation seems to be based entirely on his activities as a tutor and probably his skills as a raconteur. 

As a tutor, unlike a Christoph Clavius for example, there is not a long list of famous mathematicians, who learnt their trade at his feet. In fact, apart from Kenelm Digby (1603–1665) the only really well-known student of Allen’s was not a mathematician at all but the courtier and poet Sir Philip Sidney (1554–1586) for whom he probably wrote a sixty-two-page horoscope now housed in the Bodleian Library.

Sir Philip Sidney, by unknown artist, National Portrait Gallery via Wikimedia Commons

He may have taught Richard Hakluyt (1553–1616) the promotor of voyages of explorations.

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

He did teach Robert Fludd (1574–1637) physician and occult philosopher

Source: Wikimedia Commons

as well as Sir Thomas Aylesbury (1576–1657), who became Surveyor of the Navy responsible for the design of the warships.

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

At the end of his life, he taught and influenced the German scientific translator and communicator, Theodore Haak (1605–1690), who only studied in Oxford between 1628 and 1631.

Portrait of Theodore Haak by Sylvester Harding.Source: Wikimedia Commons

As a member of Gloucester Hall, he tutored the sons of many of the leading, English Catholic families. In this role, he tutored several of the sons of Henry Percy, 8th Earl of Northumberland the highest-ranking Catholic aristocrat in the realm. He probably recommended the Gloucester Hall scholar, Robert Widmerpoole, as tutor to the children of Henry Percy, 9th Earl of Northumberland. Percy went on to become Allen’s patron sometime in the 1580s.

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

Allen became a visitor to Percy’s Syon House in Middlesex, where he became friends with the mathematician and astronomer Thomas Harriot (c. 1560–1621), who studied in Oxford from 1577 to 1580.

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

When he died Harriot left instructions in his will to return several manuscripts that he had borrowed from Allen. Percy was an avid fan of the sciences known for his enthusiasm as The Wizard Earl. He carried out scientific and alchemical experiments and assembled one of the largest libraries in England. Allen with his experience as a manuscript collector and founder of the Bodleian probably advised Percy on his library. Harriot was not the only mathematician in Percy’s circle, he also patronised Robert Hues (1553–1632), who graduated from Oxford in 1578, Walter Warner (1563–1643), who also graduated from Oxford in 1578, and Nathaniel Torporley (1564–1632), who graduated from Oxford in 1581. Torporley was amanuensis to François Viète (1540–1603) for a couple of years. Torpoley was executor of Harriot’s papers, some of which he published together with Warner. All three of them were probably recommended to Percy by Allen. 

When Allen died, he had little to leave to anybody having spent all his money on his manuscript collection, which he left to Kenelm Digby, who in turn donated them to the Bodleian Library. But as we have seen he was warmly regarded by all who remembered him and, in some way, he helped to keep the flame of mathematics alive in England, at a time when it was burning fairly low. 


Filed under History of Mathematics, Renaissance Science, Uncategorized

Renaissance science – XXXVIII

There is a strong tendency to regard the so-called scientific revolution in the seventeenth century as a revolution of the mathematical science i.e., astronomy and physics, but as I have pointed out over the years many areas of knowledge went through a major development in the period beginning, in my opinion around 1400 and reaching, not a conclusion or a high point, but shall we say a stability by about 1750. During the seventeenth century one area of knowledge that experienced major developments was that of the life sciences, mostly in combination with medicine. One area that had intrigued humanity for millennia, which found an initial resolution during the second half of the seventeenth and first half of the eighteenth centuries was the puzzle of conception and procreation; in simple words, how are babies made? The starting point of this development is usually taken to be the work of the English physician, William Harvey (1578–1657),

William Harvey portrait attributed to Daniël Mijtens, c. 1627 Source: Wikimedia Commons

better known for his discovery of the blood circulation, who wrote a Exercitationes de Generatione Animalium, which was first published 1651, the main message of which was summed up on the frontispiece by the inscription Ex ovo omnia – All things come from an egg.[1]

The frontispiece Exercitationes de Generatione Animalium showing Zeus freeing all creation from an egg with the inscription Ex ovo omnia – All things come from an egg. Source Welcome Collection

It is not a coincidence that Harvey acquired his doctorate in medicine in Padua a Northern Italian, Renaissance Humanist university. Towards the end of the sixteenth century some of the Renaissance Humanist natural historians and physicians had taken up the study of embryology, not as many as had taken to botany or even as many as had taken to zoology, but the most significant work was produced by Hieronymus Fabricius ab Aquapendende (1533-1619), who was Harvey’s teacher.

As we have seen in this series as a whole, and specifically in the episodes on natural history, the Renaissance Humanists, who regarded themselves as the inheritors of classical antiquity, turned to sources from classical antiquity as their inspiration, motivation, and role models, when undertaking scientific endeavours. For the transition from materia medica to botany the major role model was Dioscorides, for zoology Pliny and Aristotle. For embryology, although both the Hippocratic Corpus and the Galenic Corpus both contain writings on the topic, it was principally to Aristotle that the Renaissance humanists turned as role model.

It has become fashionable in recent times to heavily criticise Aristotle both as a scientist and as a philosopher of science, and even to suggest that he hindered the advancement of science through his posthumous dominance. His critics, however, tend to ignore that he was for his time quite a good empirical biologist. Yes, he got things wrong and also made some, by modern standards, ridiculous statements, but a lot of his biological work was based on solid empirical observation, so with his embryology.

In the Early Modern Period, there was a heated debate between the supporters of two different theories of embryology preformation and epigenesis. The theory of preformation claimed that the male sperm contained a complete preformed, miniature infant, or homunculus, that was injected into the female womb where it grew larger over the pregnancy before emerging at birth. 

A tiny person (a homunculus) inside a sperm as drawn by Nicolaas Hartsoeker in 1695 Source: Wikimedia Commons

Opposed to this the theory of epigenesis in which the form of the infant emerges gradually, over time from a relatively formless egg. The theory of epigenesis was first proposed by Aristotle in his De Generatione Animalium (On the Generation of Animals). This work consists of five books of which the first two deal with embryology. I’m not going to give an account of all that Aristotle delivers here but just note two things. For Aristotle human procreation is the male sperm, activating the female menstrual blood. 

A brief overview of the general theory expounded in De Generatione requires an explanation of Aristotle’s philosophy. The Aristotelian approach to philosophy is teleological, and involves analyzing the purpose of things, or the cause for their existence. These causes are split into four different types: final cause, formal cause, material cause, and efficient cause. The final cause is what a thing exists for, or its ultimate purpose. The formal cause is the definition of a thing’s essence or existence, andAristotle states that in generation, the formal cause and the final cause are similar to each other, and can be thought of as the goal of creating a new individual of the species. The material cause is the stuff a thing is made of, which in Aristotle’s theory is the female menstrual blood. The efficient cause is the “mover” or what causes the thing’s existence, and for reproduction Aristotle designates the male semen as the efficient cause. Thus, while the mother’s body contains all the material necessary for creating her offspring, she requires the father’s semen to start and guide the process.

Source: The Embryo Project Encyclpopedia

 Secondly, he developed his theory of epigenesis by the empirical examination of the foetuses in incubating birds’ eggs.

Guillaume Rondelet (1507–1566) in his Libri de piscibus marinis in quibus verae piscium effigies expressae sunt (1554) and Pierre Belon (1517–1564) in his Libri de piscibus marinis in quibus verae piscium effigies expressae sunt and his Libri de piscibus marinis in quibus verae piscium effigies expressae sunt were both heavily influenced by Aristotle, and both included discussion on reproduction in their works. Famously, Leonardo da Vinci (1452–1519) carried out studies of the human embryo and foetus amongst his more general anatomical investigations but these first became known in the nineteenth century so played no role in the historical development of the discipline. 

A page showing Leonardo’s study of a foetus in the womb (c. 1510), Royal Library, Windsor Castle via Wikimedia Commons

The Italian physician Julius Caesar Aranzi (1529–1589),

Portrait of Julius Caesar Arantius (Giulio Cesare Aranzi, 1530–1589). From the Collection Biblioteca Comunale dell’Archiginnasio, Bologna, Italy. Source.

who was lecturer for anatomy and surgery at the University of Bologna, published his De humano foetu opusculum, which contains the first correct account of the anatomical peculiarities of the foetus in Rome in 1564. Further editions appeared in Venice in 1572 and in Basel in 1579. 

As with much else in sixteenth century zoology, a lead was taken by Ulisse Aldrovandi (1522–1605), who followed Aristotle in making daily examinations of fertilised chickens’ eggs, to follow the development of the embryo. He wrote in his Ornithologiae tomus alter de avibus terrestribus, mensae inservientibus et canoris (1600):

Source: Wikimedia Commons

“ex ovis duobus, et vinginti, quae Galina incubabat, quotidie unum cum maxima diligentia, ac curiositate” (each day, with the greatest care and curiosity, I dissected one of twenty-two eggy which a hen was incubating).

Although he describes in detail his embryological observation the lavishly illustrated volume only contains one picture of embryological interest, that of a chick in the act of hatching. 

Volcher Coiter (1534–1576), a Dutch student of Aldrovandi’s, who, before his studies with Aldrovandi, also studied with Gabriele Falloppio (1523–1562) and Bartolomeo Eustachi (c. 1505–1574), and then Guillaume Rondelet(1507–1566) after his time in Bolgna, and who became town physician in Nürnberg in 1569, also took up the systematic study of the development of chicken embryos at Aldrovandi’s urging.

Source: Wikimedia Commons

He published the results of his studies in his Externarum et Internarum Principalium Humani Corporis Partium Tabulae in Nürnberg in 1572, that is twenty-eight years before Aldrovandi published his.

Source: Welcome Library via Wikimedia Commons

Skeleton of a child from Externarum et Internarum Principalium Humani Corporis Partium Tabulae

It has been speculated that Aldrovandi was in fact publishing the results of Coiter’s research without acknowledgement. In 1575, Coiter published his book on ornithology De Avium Sceletis et Praecipius Musculis, which contains detailed anatomical studies of birds. 

As already stated above the major Renaissance work on embryology was by Hieronymus Fabricius ab Aquapendende (1533-1619), or more simply Girolamo Fabrici.

Source: Welcome Library via Wikimedia Commons

Hieronymus Fabricius got his doctorate in medicine under Gabriele Falloppio (1523–1562) in Padua in 1562. He succeeded Falloppio as professor for surgery and anatomy. Fabricius was responsible for the construction of the university’s first permanent anatomical theatre. Here he gave lectures and anatomical demonstrations dissecting the uterus and placenta of pregnant women in 1586. He began lecturing on the foetus in 1589 and embryology in 1592. 

Fabricius’ work displays attempts to balance traditional views and the knowledge he has won from his work. His first book on embryology, De formato foetu was published in about 1600 with many editions appearing between 1600 and 1620. His studies in embryology were much more extensive than any previous researcher and in this, his first publication on the topic, he divides embryology into three areas, firstly semen and the organs that generate it, secondly how semen interacts and generates the foetus, and finally the form of the foetus. His planned book on semen never appeared and is considered lost and his book on the generation of the foetus, De formation ovi et pulli, was published posthumously in 1621.

L0008411 Plate from “De formato foetu…” Fabricius, 1604 Credit: Wellcome Library, London. Wellcome Images Plate from “De formato foetu…” Fabricius, 1604 Engraving 1604 De formato foetu. [De brutorum loquela. De venarum ostiolis. De locutione et eius instrumentis liber / Fabricius Published: 1604] Copyrighted work available under Creative Commons Attribution only licence CC BY 4.0

In part one of De formato foetu, Fabricius discusses the form of the foetus and uterus based on his dissections. He discusses and criticises Aranzi’s De humano foetu opusculu.

L0008414 Plate from “De formato foetu…” Fabricius, 1604 Credit: Wellcome Library, London. Wellcome Images – Engraving De formato foetu. [De brutorum loquela. De venarum ostiolis. De locutione et eius instrumentis liber Fabricus, Hieronymus Published: 1604 Copyrighted work available under Creative Commons Attribution only licence CC BY 4.0

In part two he discusses the umbilical vessels, placenta etc. He follows the views of Galen and Aristotle although he gives some original but mistaken views on the placenta, which he had examined in greater detail than any previous investigators. 

L0008418 Plate from “De formato foetu…” Fabricius, 1604 Credit: Wellcome Library, London. Wellcome Images – Engraving De formato foetu. [De brutorum loquela. De venarum ostiolis. De locutione et eius instrumentis liber Fabricus, Hieronymus Published: 1604 Copyrighted work available under Creative Commons Attribution only licence CC BY 4.0

De formation ovi et pulli (On the Formation of the Egg and of the Chick) was earlier work than De formato foetu but only appeared in print two years after his death.


This book is also in two parts the first of which deals with the formation of the egg, whilst the second covers the generation of the chick within the egg.

L0012570 Plate from “De formatione ovi et pulli”, Fabricius 1621 Credit: Wellcome Library, London. Wellcome Images Chicken and egg. Engraving De formatione ovi et pulli Fabricius, Hieronymous Published: 1621 Copyrighted work available under Creative Commons Attribution only licence CC BY 4.0

As before, the book is a balance act between the traditional views of Galen and Aristotle, and the knowledge that Fabricius had gained through his own research. Once again, he discusses and criticises Anzani’s views.

Both books are richly illustrated with engraved plates. 

Hieronymus Fabricius books represent the high point of Renaissance embryology and whilst far from perfect they laid the foundations for the work of his most famous student William Harvey. 

[1] The information on Harvey and his book is taken from Matthew Cobb’s excellent, The Egg & Sperm RaceThe Seventeenth-Century Scientists Who Unravelled the Secrets of Sex, Life and Growth, The Free Press, 2006, which tells the whole story outlined in it’s almost 19th century title.


Filed under History of medicine, History of Zoology, Renaissance Science

Astrology, data, and statistics

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

His justification for having written this book is interesting:

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

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

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

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

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

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

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

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

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

Boxer goes complexly overboard about the Astronomica. He writes:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

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

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

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

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

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

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

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

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

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

Further on Boxer writes:

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

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

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

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

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

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

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

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

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


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

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

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

Source: Wikimedia Commons

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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

Renaissance science – XXXVII

Over a series of posts, we have followed the emergence of the science of botany out of the Renaissance humanist physicians’ endeavours to integrate materia medica, the study of simples or medical herbs, into the Renaissance university teaching curriculum. By the end of the sixteenth century the books on plants that were being published were definitely works of botany and no longer works of medicine. However, one of the books that helped launch the gradual rise of botany during the century, Pliny’s more than somewhat disputed[1]Naturalis historia was actually encyclopaedic in its scope covering much more than just the flora of antiquity, which only made up sixteen of the thirty-seven books. Four of the other books were devoted to the fauna of antiquity, covering mammals, snakes, marine animals, birds, and insects. Aristotle had also written two books on the fauna his De Partibus Animalium and his Historia Animalium as well as the De Generatione Animalium, which is attributed to him. All three books were well known and published in the Renaissance. Albertus Magnus (c.1200–1280), who digested, interpreted, and systematized the whole of Aristotle’s works in the thirteenth century, also wrote a De animalibus, which was known and read in the Renaissance.

Albertus Magnus De animalibus (c. 1450–1500, cod. fiesolano 67, Biblioteca Medicea Laurenziana) via Wikimedia Commons

All of this raises the question, was there development of zoology as a discipline during the sixteenth century similar to that of botany? The answer is both yes and no. A much smaller number of authors wrote books on the fauna and the development, at that time, progressed by no means as far as that of botany. However, as we will see two authors in particular stand out and they can and have been labelled the founders of modern zoology, they are the Swiss polymath Conrad Gesner (1516–1565) and the equally polymathic Italian natural historian Ulisse Aldrovandi (1522–1605). However, before we look at the work of these two intellectual giants, and it is not an exaggeration to call them that, we will first take a look at the others, who published on fauna in the period and, to begin, briefly discuss why the development of zoology lagged behind that of botany.  

When you spell out the reasons why the development of zoology in the Renaissance lagged behind that of botany, they seem pretty obvious, but you first have to think about the problem.  Whereas the ongoing botanist could and did send each other, seeds, bulbs, dried plants in the form of herbarium sheets, and even living plants carefully packaged in letters and packages with the post you can’t pop a rhinoceros in an envelope and send it to someone. 

My example may seem more than somewhat ridiculous, but it refers to a real, notorious, historical occurrence. Perhaps the most well known of all Renaissance prints is Albrecht Dürer’s Rhinoceros, which we will meet again later. Dürer’s print is based on verbal descriptions of an Indian rhinoceros that was sent, by ship, as a gift to King Manuel I of Portugal in 1515. Manuel actually staged a combat between his rhinoceros and a young elephant to test Pliny’s account that elephants and rhinoceroses were enemies. The young elephant fled, and the rhinoceros was declared the winner. Manual decided to give his rhinoceros to the Medici Pope Leo X, and it embarked one again on a ship across the Mediterranean, but this time did not survive the journey dying in a shipwreck off the coast of Italy. Dürer’s print was based on a letter and sketch of the beast sent from Lisbon to Nürnberg. As we shall see, many of the early printed accounts of animals were based on verbal descriptions and sketches rather than actual encounters with the animals themselves. The animal studies of Renaissance artists like Dürer or Leonardo also played a role in stimulating interest in animals amongst the humanist scholars. 

Albrecht Dürer’s Rhinoceros woodcut Source: Wikimedia Commons

Another major problem is that if you go out on excursions or field trips to empirically study plants, the plants remain quietly where they are whilst you examine, sketch, or even dig them up to take them home with you. Most animals aren’t as accommodating. In fact, most wild animals will take to their heels and disappear when they hear humans approaching. Proto-zoologists were dependent on the second hand reports of hunters, field workers, or foresters of animals they didn’t get to observe themselves. Putting this all together, it is simply much more difficult to conduct empirical research on animals than on plants. It therefore comes as no surprise that the first zoological publications in the Renaissance were about fishes and birds, animals that humans eat and are thus more accessible to the researcher. It should be noted that in the Early Modern period people ate a much wider range of birds than we do today and that whales were also extensively eaten throughout Europe. In fact, the European whaling industry began in the Middle Ages because the Church classified them as fish, meaning they could be eaten on a Friday, a fast day when eating meat was forbidden. 

Before turning to the early Renaissance zoologists, we will take a brief look at the medieval manuscripts of animals, the bestiaries. Unlike the medieval herbals, which served a practical medical function, the bestiaries served a philosophical or religious function. The natural histories and illustrations of the individual beasts were usually accompanied by a moral lesson. The animals served a symbolic function rather than a practical one. The illustrations were mostly copied from earlier ancient Greek sources, the earliest known example is the second century Greek work, the Physiologus, which draws on earlier authors such as Aristotle, Herodotus, Pliny, and others.

Panther, Bern Physiologus, 9th century Source: Wikimedia Commons

The genre was further developed by Isidore of Seville and Saint Ambroise, who added a religious dimension. Bestiaries were very popular in the High Middle Ages, but had little or no influence on the beginnings of zoology in the Renaissance, unlike the influence herbals had with plants. 

Detail from the 12th century Aberdeen Bestiary Source: Wikimedia Commons

The earliest zoological text from the sixteenth century was published by the English naturalist William Turner (1509/10–1568), who, as we saw in the episode on herbals, was motivated by his travels and studies in Northern Italy. Before he began publishing his more famous herbal in 1551, he had already published Avium praecipuarum, quarum apud Plinium et Aristotelem mentio est, brevis et succincta historia (The Principal Birds of Aristotle and Pliny…), which not only discussed the birds to be found in the two authors from antiquity but contained descriptions of birds based on his own empirical observations.

Title page of Avium Praecipuarum, 1544, by William Turner. This was the first ever printed book devoted wholly to ornithology. Source: Wikimedia Commons

Much more extensive are the zoological works by the French traveller and naturalist, Pierre Belon (1517–1564).

Pierre Belon artist unknown Source: Wikimedia Commons

Little is known of his origins, but in the early 1530s he was apprenticed to the apothecary René des Prey. He entered the service of René du Bellay Bishop of Le Man (c. 1500–1546) in the second half of the 1530s, who permitted him to study medicine at the University of Wittenberg under Valerius Cordus (1515–1544).[2] He travelled through Germany with Cordus in 1542, continuing on through Flanders and England alone. He continued his studies in Paris, and then became apothecary to Cardinal François de Tournon (1489–1562) in whose service he undertook diplomatic journeys to Greece, Crete, Asia Minor, Egypt, Arabia, and Palestine between 1546 and 1549. An avid polymath he recorded everything he saw and experienced on his travels. During a Papal conclave, 1549–1550, he met up with Guillaume Rondelet (1507–1566), who would be appointed professor for medicine in Montpellier, and the Italian physician Hippolyte Salviani (1514–1572). Returning to Paris he began to sort his notes and publish his zoology texts. In 1557 he undertook another journey to Northern Italy, Savoy, the Dauphiné, and Auvergne. In 1558 he obtained his medical licence and began to practice medicine. He became a favourite of the Kings Henry II (1519–1559) and Charles IX (1550–1574). The latter providing him with lodgings in Château de Madrid in the Bois de Boulogne. His promising career was cut short when he was murdered in 1564.

Between 1551 and 1557 he wrote and published a series of books based on his travel observations. His first book was his L’histoire naturelle des estranges poissons marins, avec la vraie peincture & description du Daulphin, & de plusieurs autres de son espece. Observee par Pierre Belon du Mans published in Paris in 1551.

L’histoire naturelle des estranges poissons marins A Paris :De l’imprimerie de Regnaud Chaudiere,1551. Source: Wikimedia Commons

This is a description of the fish and cetaceans, such as dolphins and porpoises, that he had observed and dissected on his travels. Aristotelean in nature the work contained a classification system for marine fish, including both cetaceans and hippopotami under fishes, although he recognised that cetaceans had mammalian milk glands and were air breathing. Two years later he published a more general book on fish, his De aquatilibus. Libri duo Cum eiconibus ad vivam ipsorum effigiem, Quoad eius fieri potuit, expressis, also in Paris. This contained descriptions of 110 fish species and is a founding text of the discipline of ichthyology. A French edition De aquatilibus. Libri duo Cum eiconibus ad vivam ipsorum effigiem, Quoad eius fieri potuit, expressis was published in Paris in 1555.

In 1553 he also contributed to the botanical literature with his De arboribus Coniferis, Resiniferis aliisque semper virentibus…, a book on confers, pines and evergreen trees. It was published in both Latin and French in the same year. The same year saw the publication of his more general Les obsevations de plusieurs singularitez et choses memorables trouvées en Grèce, Asie, Judée, Egypte, Arabie et autres pays étrangèrsas well as a three-volume work on funerary customs in Antiquity. A revised edition of his Observations was published in 1555 and Clusius translated them into Latin for an international readership in 1559.

In 1555 he turned his attention to birds publishing his Histoire de la nature des oyseaux in Paris. It describes about 200, mostly European, birds. This book is particular notable for its comparison of the skeletons of a bird and a human, one of the earliest examples of comparative anatomy.

A comparison of the skeleton of birds and man in Natural History of Birds, 1555 Source: Wikimedia Commons

He rounded off this burst of publications with his Portraits d’oyseaux, animaux, serpens, herbes, arbres, hommes et femmes, d’Arabie et Egypte, in Paris in 1557.

Portraits d’oyseaux, animaux, serpens, herbes, arbres, hommes et femmes, d’Arabie et Egypte, 1557 Source: Wikimedia Commons

Much of the information in his books on both fishes and birds was obtained by investigating those that came to market in the towns that he visited. On his trip to England, he also met the Venetian humanist scholar and architect, Daniel Barbaro (1514–1570), Palladio’s patron, who had made many drawings of Adriatic fish. 

Etching of Daniele Barbaro by Wenzel Hollar Source: Wikimedia Commons

The Italian physician, humanist scholar, and naturalist Hippolyte Salviani (1514–1572), who as we saw above met Belon at the Papal conclave in 1549–1550, was the personal physician to the House of Farnese from 1550 till 1555 and taught at the University of Rome until 1568.

Frontispiece of Hippolyte Salviani’s Aquatilium animalium historiae  Source: Wikimedia Commons

Like Belon he wrote and published a work on fish Aquatilium animalium historiae (1554-1558), which depicted about one hundred Mediterranean fish species and some molluscs. He was aware of the difference between cephalopods and fish. This work was based on his own empirical observations, and he was supported financially in his work by Cardinal Marcello Cervini (1501–1555), later Pope Marcellus II. The work was dedicated to Cervini’s successor Gian Carafa (1476–1559), Pope Paul IV. Like Belon most of his fish research was done with fish from the markets.

Source: Wikimedia Commons

Guillaume Rondelet (1507–1566), who was also at that Papal conclave, went on to become professor for medicine at the University of Montpellier, where he taught several important natural historians including Charles de l’Écluse (Carolus Clusius) (1526–1609), Matthias de l’Obel (Matthias Lobelius) (1538–1616), Pierre Pena (c. 1530–c. 1600), Jacques Daléchamps (1513–1588), Jean Bauhin (1511–1582), and Felix Platter (1536–1614).

Guillaume Rondelet Source: Wikimedia Commons

Although he was one of the greatest teachers of medicine and natural history in the sixteenth century, he published very little himself. However, like Belon and Salvini, he published a work on marine life, his Libri de piscibus marinis in quibus verae piscium effigies expressae sunt (Lyon, 1554).

Libri de piscibus marinis, 1554 Source: Wikimedia Commons

Although the title refers to fish (piscibus), the book actually deals with all aquatic animals. Rondelet makes no distinction between fish, marine animals such as seals and whales, crustaceans, and other invertebrates. He investigated the difference between fresh water and saltwater fish. His approach was Aristotelean emphasising function. He dissected and illustrated many of his specimens and his anatomical drawings off a sea urchin is the earliest know drawing of an invertebrate. He made anatomical comparisons and found similarities between dolphins, pigs, and humans. The book became a standard reference work for many years and was translated into French in 1558 as L’histoire entière des poissons (The complete history of fish). 

Extract from Rondelet’s 1554 work De piscibus Source: Wikimedia Commons

Without doubt the most influential text on the road to the discipline of zoology published in the sixteenth century was the more than four-thousand-and-five-hundred-page, five-volume Historia animalia issued by the Swiss polymath Conrad Gessner (1516–1565) between 1551–1558 and 1587 posthumously in Zurich.

Source: Wikimedia Commons

I have written about Gessner in the past, but the short version is, he was the polymath’s polymath. A humanist, encyclopaedist, philologist, bibliographer, zoologist, botanist, alpinist, linguist, and professional physician. He was not only an encyclopaedist but a completist. His Bibliotheca universalis (1554–) was an attempt to list alphabetically all of the books printed and published in Latin, Greek, and Hebrew since the invention of printing with movable type. He followed this with a thematic index to the Bibliotheca universalis, the Pandectarum sive Partitionum universalium Conradi Gesneri Tigurini, medici & philosophiae professoris, libri xxi with thirty thousand entries in 1548. 

His approach to the Historia animalia was the same, it was an attempt to provide descriptions of all known animals. The animals were listed alphabetically but divided up in divisions in the style of Aristotle. Volume I Quadrupedes vivipares. 1551 (Live-bearing four-footed animals), Volume II Quadrupedes ovipares. 1554 (Egg-laying quadrupeds, reptiles and amphibia), Volume III Avium natura. (Birds) 1555, Volume IV Piscium & aquatilium animantium natura 1558 (Fish and aquatic animals), Volume V De serpentium natura (Snakes and scorpions).

Tiger and leopard, Book 1:Viviparous Quadrupeds Source: Wikimedia Commons

In 1638 a further volume on insects was published from his Nachlass. To write his book, Gessner drew on multiple sources giving credit to their authors. As well as an illustration of each animal, here he famously used Dürer’s rhinoceros, he included vast amounts of information–the animal’s name in all the languages know to him, habitat, description, physiology, diseases, habits, utility, diet, curiosities, all crossed referenced to ancient and modern authorities. Gessner, in has attempt at completeness, also included some mythical creatures, in some cases stating that he didn’t know if they existed or not.

Source: Wikimedia Commons

The Historia animalia was immensely successful and an abbreviated version, the Thierbuch, appeared in German in 1565. 

Fantastical creatures in a copy of Historia Animalium in The Portico Library in Manchester, England. Source: Wikimedia Commons

Just as encyclopaedic as Gessner’s work were the volumes on animals put together by the Italian natural historian Ulisse Aldrovandi (1522–1605), whose five hundredth birthday we will be celebrating on 11 September.

Ulisse Aldrovandi (1522 – 1605). Ornithologiae, hoc est de avibus historiae libri XII. (De avibus), Bologna, 1599. Source: Wikimedia Commons

He was born in Bologna into a noble family, a nephew of Pope Gregory XII. He father, a lawyer, died when he was seven. In his youth he studied first mathematics and then Latin under prominent private tutors. Following his mother’s wish he studied law but shortly before graduating he switched to philosophy. To complete his philosophy studies, he switched to the University of Padua, where he began to study medicine in 1545. In 1549 he was accused of heresy and had to go to Rome to clear his name. In 1550, he met Guillaume Rondelet, whom he accompanied on his visits to the local fish markets to study fish, which awakened Aldrovandi’s interest in zoology. Returning to Bologna he met Luca Ghini (1490–1556), who played such a central role in the early study of plants, and this awakened his interest in botany. When Ghini returned to Pisa, Aldrovandi followed him to attend his lectures on medical simples. In 1552 he graduated in philosophy at Bologna and a year later in medicine. In 1554 he was appointed lecturer for logic at the university and in 1559 professor for philosophy. 

In 1561 he became the first professor of natural history at Bologna, Lectura philosophiae naturalis ordinaria de fossilibus, plantis et animalibus. Aldrovandi devoted the rest of his life to the study and propagation of natural history. He set up the university botanical garden in 1568 and a museum for natural history, which I will look at more closely in a later post. Like Gessner, he spent years collecting material for a Historia Animalia, but didn’t start writing it until he was seventy-seven-years-old. He only managed to publish three of the eventual eleven volumes before he died aged eighty-two. The other eight volumes were published posthumously by Johannes Cornelius Uterverius (1592–1619), Thomas Dempster (1579–1625), and Bartholomäus Ambrosinus. Ornithologiae, hoc est, de avibus historiae libri XII. Agent de avibus rapacibus (1600); 

Aldrovandi Owl Source: Wikimedia Commons

Ornithologiae tomus alter de avibus terrestribus, mensae inservientibus et canoris (1600); De aninialibus insectis libri VII (1602); 

De animalibus insectis libri septem, cum singulorum iconibus ad vivum expressis, Bologna, 1602. Source: Wikimedia Commons

Ornithologiae tomus tertius ei ultimus de avibus aquaticis et circa quas degentibus (1603); De reliquis animalibus exanguibus, utpote de mollibus, crustaceis, testaceis et zoophytis, libri IV (1606); Quadrupedum omnium bisulcorum historia (1613); 

Aldrovandi Red Hartebeest and Blackbuck Source: Wikimedia Commons

De piscibus libri V et de cetis liber unus (1613); De quadrupedibus digitatis viviparis libri III, et de quadrupedibus oviparis libri II(1637); Historiae serpentum et draconum libri duo (1640);

Basilisk from Serpentum, et draconum historiae libri duo (1640) Source: Wikimedia Commons

 Monstruorum historia(1642)

Harpy. Ulisse Aldrovandi, Monstrorum historia, Bologna, 1642. Source: Wikimedia Commons

There were also some smaller individual studies published in the sixteenth century. The Cambridge scholar and physician John Caius (1510–1573)

John Caius, Master (1559-1573); Gonville & Caius College, University of Cambridge; artist unknown Source: Wikimedia Commons

was a correspondent of Gessner’s and produced a study of British dogs for him, which Gessner didn’t publish, so he published it himself in 1570, De Canibus Britannicis.


In the same year he also published De Rariorum animalium atque stirpium historia, libellus (Of Some Rare Plants and Animals).

The Bologna senator, Carlo Ruini (1530–1598) wrote a very accurate and comprehensive Anatomia del cavallo, infermità, et suoi rimedii (On the Anatomy and Diseases of the Horse), which was published posthumously in Venice, in 1598.

Source: Wikimedia Commons
Source: Wikimedia Commons

Finally, the English student of Felix Platter, Thomas Moffet (1533–1604) compiled the Insectorum sive Minimorum Animalium Theatrum (Theatre of Insects) based on his own work and that of Gessner, Edward Wotten (1492–1555) and the physician Thomas Perry (1532–1589).

Source: Wikimedia Commons

Edward Wotten, a graduate of Padua, had earlier published his Aristotelian research on animals De differentiis animalium libri decem, in Paris in 1552. 

Edward Wotton an engraving by William Rogers c. 1600 Source: Wikimedia Commons

Although the developments in zoology in the sixteenth century were not as widespread or as progressive as those in botany as we have seen they were not insubstantial and laid foundations that were developed further in the late seventeenth and eighteenth centuries. 

[1] For details of that dispute see Episode XXXII of this series

[2] For more on Valerius Cordus see Episode XXXV of this series


Filed under History of science, History of Zoology, Natural history, Renaissance Science


Today the Renaissance Mathematicus officially became a teenager, although I think it’s been one since it first emerged into the digital world thirteen years ago, snotty-nosed, stroppy, belligerent, argumentative, anti-authority, whilst at the same time oscillating between bursting with energy and sloth like behaviour. Did I mention self-opinionated and convinced it knows better than everybody else?

Thirteen is, in the Germanic languages, the first number with a compound name, three plus ten, eleven and twelve having single names. It is the sixth prime number and the second two-digit prime forming a twin prime with eleven, the first two digit prime. 

In some countries, including the UK and the USA, thirteen is considered an unlucky number, with people going as far as to not having a thirteenth floor in a building or a room 13 in a hotel. This superstition has been given the wonderful name Triskaidekaphobia from the Ancient Greek treiskaídeka for thirteen and phóbos meaning fear. There are various attempts to explain the historical origins of this phobia but none of them can actually be substantiated. Friday 13th is considered particularly unlucky in these cultures and has the equally splendid name paraskevidekatriaphobia from the Greek Paraskevi for Friday, reiskaídeka for thirteen, and phóbos meaning fear. In the Gregorian calendar, Friday 13th occurs at least once every year and can occur up to three times. Although there is evidence of both Friday and thirteen being considered unlucky, the earliest reference to Friday 13th as unlucky is in the nineteenth century. Once again, the origin of the superstition is a mater of speculation. 

One common occurrence of the number thirteen in the English language is the baker’s dozen. Whereas a dozen is a group of twelve, a baker’s dozen is a group of thirteen. The term dates back to the fifteenth century and refers to the habit of baker’s selling their wares in units of thirteen rather than twelve as the law required. As bakers could be fined for selling their wares underweight, it is thought that they included an extra item to avoid the risk of a fine.

As usual the Renaissance Mathematicus blog anniversary is an occasion for reflection, looking inward and questioning, a period of introspection. Why do I do this at all? What is my motivation? What do I hope to achieve? 

I’ve actually been thinking about these questions for sometime now. I am a self-confessed music junkie, who has spent a large part of my life working as a very small cog in the music business, as a stagehand, club live sound man, jazz club manager and chief cook and bottle washer. I also possess an obscenely large album collection, which I relativise by pointing out that other music junkies I know have much larger collections. One of my favourite rock guitarists is Robert Fripp, the genius behind King Crimson. Fripp is very philosophical for a rock musician and one of his sayings is, “don’t become a professional musician unless you can’t do anything else.” This statement is of course ambiguous. It could mean, if you are physically or mentally incapable of doing anything else or on the other hand you are so obsessed that nothing else comes into question. 

I prefer the second interpretation and it neatly sums up my relationship to history in general and the history of science in particular. I have been addicted to history for as long as I can remember, history in general, history of mathematics, history of science, history of food… What ever else I’ve done in my life, I’ve always studied history simply because. However, as I have revealed in the past, I am an AD(H)Dler and this means I tend to get easily distracted in my studies, research, and readings. Oh look, there’s another aspect I could follow up over there and isn’t this fact interesting, maybe I could find out something about that! This means I have in my life a strong tendency never to get anything finished, because there are always twenty other different pathways I want to go down first. Forcing myself to write a weekly blog post helps me to stay focused, to concentrate, and get at least one thing finished.  When I’m not writing blog posts my mind still wanders off in twenty different directions at once, but that’s OK; that’s have I come up with new topics for blog posts. 

All of the above basically covers the first two of my questions, why and motivation and there isn’t really any other explanation. This still leave the third question open; what do I hope to achieve? I don’t really have a general answer to this. I don’t actually think I want to achieve anything in particular. Initially, as I have said in the past, I wanted to teach myself to write, and I think I fulfilled that aim some time ago. I wrote my, The emergence of modern astronomy – a complex mosaic series to prove to myself that if I wrote in slices; I could write a book. Another aim that I think I successfully fulfilled. I might even get around to turning it into a proper book manuscript and trying to find a publisher this summer! The Renaissance Science series was just, you’ve written one long series, what could you write a second one about? 

On the whole I try not to think about potential readers but to write just for myself. This is a safety mechanism to stop me putting myself under any sort of pressure, will I fill my readers expectations!? Of course, I’m happy that people do read my scribblings and some of them even appear to enjoy them. Truth be told, the actual number of people who regularly read this blog scares me somewhat, in particular the successful professional historians of science, who I know do so. Imposter syndrome, what moi? As I have been known to say on occasions, even my imposter syndrome has imposter syndrome. One very concrete thing that I have aimed to achieve with my scribblings since the day I started this blog, is to try and clear away at least some of the myths that plague the popular perception of the history of science. It’s a Sisyphus task but it helps to keep me motivated and focused. 

Having mentioned my readers, I will close this anniversary post by saying I’m grateful for every person, who takes the time to read my weekly outpourings and I hope they gain something for the time taken. I’m also grateful to all those, who take the time to provide feedback, through comments: I thank all of you both readers and commentors and hope you stay on bord for the next twelve months.


Filed under Autobiographical, Myths of Science