In episode XIV of this series, we surveyed the final intellectual efforts within Europe to hold the knowledge accrued during antiquity upright for future generations in the work of such figures as Boethius (c. 480–524), Cassiodorus (c. 485–c. 585) and Isidore of Seville (c. 560–636). Efforts that were at least partially successful as that knowledge did not die out completely but took, so to speak, a rest for several centuries. Important to note, I wrote there in opposition to a widespread popular myth, propagated by many militant atheists, Christianity and Christians were not responsible for the decline and loss of classical learning in late antiquity. In fact, the opposite is true, what survived in Europe did so because it was conserved and copied in monastery libraries, which is where much of it was found by the manuscript hunters during the Renaissance.
As we have seen in the following six episode, following the decline of knowledge production within Europe, which reached a deep point in the seventh century, beginning in the eighth century the newly emerging Islamic culture originating in Western Asia took up the baton of knowledge production, first collecting, then translating, and finally analysing, commenting on, and expanding, not just the knowledge from European antiquity but also that from Persia, India, and even China.
We now turn back to Europe and the gradual reawakening of the acquisition of knowledge beginning in the eight and ninth centuries, which slowly gained momentum down to the twelfth century and the so-called Scientific Renaissance during which much of the knowledge acquired, analysed, expanded, and improved by the scholars of the Islamic period was translated back into Latin and became available again, or in some cases for the first time, to European scholars. I shall here only offer an outline sketch, as I have already dealt in detail with this process in my Renaissance Science series to which I will here supply links at the appropriate points.
Before moving on I will briefly mention three authors from the Early Middle Ages, that I didn’t mention earlier, whose books, whilst on a fairly low academic level kept the knowledge of and interest in the mathematic sciences throughout the medieval period.
The first is Martianus Capella, a Roman citizen of Madaura in North Africa, who was active in the early fifth century and who wrote De nuptiis Philologiae et Mercurii (On the Marriage of Philology and Mercury) a Neoplatonic, allegorical tale describing the seven liberal arts, trivium and quadrivium, who appear as the bridesmaids at the title’s wedding.
Grammar teaching, from a 10th-century manuscript of De nuptiis Philologiae et Mercurii Source: Wikimedia Commons
The seven liberal arts provided the backbone of the curriculum in the medieval cathedral schools and for the undergraduate degrees at the newly emerging universities in the High Middle Ages. This book was highly popular and very widely read, as can be attested by the, at least, two hundred and forty-one surviving manuscripts. It was first printed in Vincenza in 1499 and there was an edition published in in 1539 just four years before the publication of Copernicus’ Derevolutionibus.
There were numerous commentaries on the text by leading medieval scholars. Perhaps the most intriguing aspect of the book is that Capella introduces a geo-heliocentric system, in the astronomy section, in which Mercury and Venus orbit the Sun which in turn with the remaining four planets orbits the Earth. This is the earliest known presentation of a geo-heliocentric system although Capella introduces in a way that seems to suggest that it was already known. He and his system get an honorary mention in De revolutionibus.
Capella’s cosmological model Manuscript Florence, Biblioteca Medicea Laurenziana, San Marco 190, fol. 102r (11. Jahrhundert) Source:: Wikimedia Commons
Our second is a near-contemporary of Capella’s, the Roman citizen, whose origins are unknown, Macrobius Ambrosius Theodosius, usually referred to as Macrobius, whose Commentarii in Somnium Scipionis (Commentary on Cicero’s Dream of Scipio) expounds a series of theories on the dream from a Neoplatonic background, on the mystic properties of the numbers, on the nature of the soul, on astronomy and on music. His commentary was essentially an encyclopaedic rendering of the Platonic interpretation of terrestrial and celestial science. Like Capella’s De nuptiis this work was widely read and commented on by medieval scholars.
Image from Macrobius Commentarii in Somnium Scipionis: The Universe, the Earth in the centre, surrounded by the classical planets, including the sun and the moon, within the zodiacal signs. Source: Wikimedia Commons
We leave the fifth-century Roman Empire and travel to Britain in the seventh and eighth centuries, where we find the monk Bede (672/3–735) in the monastery of Jarrow. Known as the Venerable Bede (Beda Venerabilis), he is best known for his Historia ecclesiastica gentis Anglorum (Ecclesiastical History of the English People) written about 731. However, he also wrote an important text on measuring time, his De temporum ratione (The Reckoning of Time). The book covers basic cosmological topics before going on to calendrics and its main theme computus, the calculation of the dates of Easter and the other movable Church feast days.
De temporum ratione: This manuscript was made around 1100, possibly in France.
The work of these three together with that of Boethius (c. 480–524), Cassiodorus (c. 485–c. 585), and Isidore of Seville (c. 560–636), who I introduced in an earlier episode, meant that an awareness of the mathematical sciences was kept alive in the Early Middle Ages, although at a very low level, following the decline of the Roman Empire. This meant that when a higher level of learning and knowledge began to emerge in Europe later in the Middle Ages, there was a foundation on which to build.
The next step in the reintroduction of learning into Europe came when Karl der Große (742–814) (known as Charlemagne in English) had completed the conquest and unification of a very large part of Europe by the Franks. Although Karl himself was illiterate, he and his heir Louis the Pious (778–840) introduced an education programme for priest and increased the spread of Latin on the continent.
The programme was basically not scientific, it had, however, an element of the mathematical sciences, some mathematics, computus (calendrical calculations to determine the date of Easter), astrology and simple astronomy due to the presence of Alcuin of York (c. 735–804) as the leading scholar at Karl’s court in Aachen. Through Alcuin the mathematical work of the Venerable Bede (c. 673–735), who was also the teacher of Alcuin’s teacher, Ecgbert, Archbishop of York, flowed onto the European continent and became widely disseminated.
Karl’s Court had trade and diplomatic relations with the Islamic Empire, in particular with Abu Ja’far Harun ibn Muhammad al-Mahdi (c. 764–809), better known as Harun al-Rashid, the fifth Abbasid caliph, and there was almost certainly some mathematical influence there in the astrology and astronomy practiced in the Carolingian Empire.
In the eleventh century the three Ottos, Otto I (912–973), Otto II (955–983), and Otto III (980–1002), increased the levels of learning on the Imperial court and in the monasteries through contact with Byzantium. This renaissance acquired a strong mathematical influence through Otto the Third’s patronage of Gerbert of Aurillac (c. 946–1003). A patronage that would eventually lead to Gerbert becoming Pope Sylvester II. From his time living in Spain Gerbert introduced some of the basics of Islamic astronomy and mathematics into the rest of Europe.
In the eleventh and twelfth centuries two developments furthered and accelerated to growth in knowledge within Europe. On the one hand groups of students seeking advanced instruction and groups of teachers seeking students to instruct set up the first European universities. The Latin term universitas “being a number of persons associated into one body, a society, company, community, guild, corporation, etc.” These bodies became sanctioned by the Church and by local rulers and adopted the seven liberal arts, as propagated by the scholars of the early Middle ages, such as Boethius and Capella as their undergraduate curriculum. They developed three post graduate faculties, theology, law, and medicine.
Bologna University is the oldest medieval European university. Interior view of the Porticum and Loggia of its oldest College, the Royal Spanish College. Source: Wikimedia Commons
The second development was that scholars began to travel to the areas dominated by Islamic culture to acquire and translate the knowledge of the ancient Greeks and their Islamic interpreters and commentators from Arabic into Latin, during what is know known as the Scientific Renaissance. Europe was now there where the Islamicate culture had been in the seventh century, with an education establishment and the material on which to build or better rebuild an academic and especially a scientific culture.
The beginning of Aristotle’s De anima in the Latin translation by William of Moerbek.. Manuscript Rome, Biblioteca Apostolica Vaticana, Vaticanus Palatinus lat. 1033, fol. 113r (Anfang des 14. Jahrhunderts) Source: Wikimedia Commons
I have already written an extensive blog post on the Scientific Renaissance in my series Renaissance Science, and also one on the emergence of the medieval university, so I won’t repeat them here. Next time I shall be looking at medieval contributions to the development of some areas of physics.
Although people who compile such lists very often ignore it, there can be no doubt that William Gilbert’s De Magnete must be listed amongst the most important science books published in the Early Modern Period. It is the first printed book entirely dedicated to the study of the magnet, magnetism, and the magnetic compass and following Petrus Perigrinus de Maricourt’s Epistola de magnete only the second tome dedicated exclusively to the topic at all. It is a presentation of systematic, detailed, empirical, experimental science published thirty-eight years before Galileo’s Discorsi, often claimed to be the first such book.
Obviously the product of many years of dedicated research into all aspects of the magnet and magnetism, De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure (On the Magnet and Magnetic Bodies, and on That Great Magnet the Earth) was originally published in Latin by Peter Short in London in 1600. The English translation runs to three hundred and fifty pages. There appears to have been an edition in Amsterdam 1600, a new edition published in London in 1633, two editions published in Stettin in 1628 and 1633, two in Frankfurt 1629 and 1633, and one in Ferrara in 1629. The reception throughout Europe, which I will look at in some detail later, was generally very positive.
Source: Wikimedia Commons
The book opens with an address to the author by Edward Wright (1561–1615) the leading English expert on navigation in the period and author of Certaine Errors in Navigation printed in London by Valentine Sims in 1599. Gilbert couldn’t have had a better recommendation for his text. I will look at this address in the next blog post in this series. This is followed by an Author’s Preface, in which Gilbert justifies his publication in rather flowery terms towards the end of which he slags off the Ancient Greeks. The work is divided into six books each of which deals with a different aspect of magnetism.
Book I, Writings of Ancient and Modern Authors Concerning the Loadstone: Various Opinions and Delusions, whereby “delusions” is Gilbert’s opinion of virtually everything that had been written about magnets and magnetism in the past. He debunks the myths about garlic and diamonds blocking magnetism as well as other less well known ones; naming and shaming the authors who perpetuated them. He gives a long list of authors who mentioned magnets and magnetism the writes:
…by all of these the subject is handled in a most careless way, while they repeat only the figments and ravings of others.
Having made negative comments about Fracastoro, all he has to say about Perigrinus is:
Of date two hundred years or more earlier than Fracastorio, is a small work attributed to one Petrus Peregrinus, a pretty erudite book considering the time:
Considering that Gilbert took the idea of experimenting with terrella, i.e. small spherical loadstones, and quite a few of the experiments he did with them, from Perigrinus this is a rather thin acknowledgement. Perhaps surprisingly, one author who gets a modicum of praise is Giambattista della Porta and Gilbert also repeats some of the experiments from Magia Naturalis in his research. He continues slagging off authors on magnetism right, left and centre before closing the chapter with the little piece of chauvinism that I brought in the first episode of this series:
There are other learned men who on long sea voyages have observed the difference of magnetic variation; as that most accomplished scholar Thomas Harriot, Robert Hues, Edward Wright, Abraham Kendall, all Englishmen; others have invented and published magnetic instruments and already methods of observing, necessary for mariners and those who make long voyages: as William Borough in his little work the Variations of the Compass, William Barlo (Barlow) in his Supplement, Robert Norman in his New Attractive–the same Robert Norman, skilled navigator and ingenious artificer, who first discovered the dip of the magnetic needle.Many others I pass by of purpose: Frenchmen, Germans, and Spaniards of recent times who in their writings, mostly composed in their vernacular languages, either misuse the teachings of others, and like furbishers send forth ancient things dressed with ne names and tricked in an apparel of new words as in prostitutes’ finery; or who publish things not even worthy of record; who, pilfering some book, grasp for themselves from other authors, and go a-begging for some patron, or go a-fishing among the inexperienced and the young for a reputation; who seem to transmit from hand to hand, as it were, erroneous teachings in every science and out of their own store now and again to add somewhat of error.[1]
With his opening chapter Gilbert basically says, all that went before was rubbish, now I’m going to deliver up the real story of magnets and magnetism. He devotes the next fifteen chapters of book one to the loadstone, iron and iron ore, starting with the history of the loadstone and then moving on to its properties, its poles, their basic attraction and repulsion. He then moves on to the relations between loadstone, smelted iron and iron ore basically arguing that they are one and the same, loadstone being ‘a noble kind of iron ore.’ In passing he rejects the then still prevalent Aristotelian theory of metals In the seventeenth and final chapter of book one he presents the central thesis of his book, its title:
That the terrestrial globe is magnetic and is a loadstone; and just as in our hands the loadstone possesses all the primary powers (forces) of the earth, so the earth by reason of the same potencies lies ever in the same direction in the universe.
Gilbert argues that we can only infer this fact from the behaviour of magnets and compasses, as demonstrated in his experiments with his terrellas and versoria. A versorium was a miniature, adapted compass needle able to turn horizontally or vertically. We can not experience the earth’s loadstone nature directly because its surface, what we can the crust, is corrupted and degenerated.
Terrella with versoria
The next five books of De Magnete are each devoted to one aspect of the movement of magnets and compass needles, so we have–magnetic attraction, the directional property of compass needles, variation, dip, and revolution.
Book II: Of Magnetic Movement is after a first chapter listing the five movement, dedicated to magnetic attraction, although Gilbert rejects the term attraction as too aggressive preferring instead the term coition:
Coition, we say, not attraction, for the term attraction has wrongfully crept into magnetic philosophy, through the ignorance of the Ancients; for where attraction exists, there force sems in and tyrannical violence rules.
Coition, a synonym for coitus, was a neologism meaning ‘coming together’ like two lovers’ bodies, by which Gilbert did no mean that two magnets made love but that their motions were governed by principles of mutual harmony. He demonstrates coition by placing two terrella on circular discs of wood that had hemispherical depressions in the centre to receive them and floating them on water. They begin to spin and circle each other until the opposing poles are drawn together. Interestingly Gilbert doesn’t think magnetic repulsion exists. If his two floating terrella repulse each other they continue to rotate until they come together in coition.
There is a long section in Book II devoted to static electrical attraction in order to explain why it is not the same as magnetic attraction. Today, this section gets as much attention as the rest of the book on magnetism and is regarded as the beginning of research into electricity, a term the coining of which Gilbert is indirectly given the credit for.
In the rest of book two he covers every possible aspect of magnetic attraction between loadstones, loadstones and iron, loadstones and the earth etc. Interestingly having dismissed the possibility that magnetic attraction is a force, Gilbert, who is generally anti-Aristotelian, turns to Aristotle’s four causes theory to explain it. Magnetic attraction is the form of the matter of the loadstone or the earth in the Aristotelian sense of the terms. Gilbert also investigated what we would call the magnetic field, which he called ‘Orbis Virtutis’ (the sphere of virtue). He carried out these investigations using his versoria.
Book III Of Direction, deals with the phenomenon that a magnetic compass needle, ignoring for the moment variation, always aligns in the same direction. He states that this is confirmed for the whole globe by the reports of mariners, naming dropping the personal reports of the circumnavigators, Francis Drake and Thomas Cavendish in the process. Once again Gilbert introduces his own terminology in the title of the second chapter:
Directive (or Versorial) force, which we call Verticity: What it is; how it resides in the loadstone: and how it is acquired when not naturally produced.
Sailing his miniature compass, the versorium around a terrella Gilbert demonstrates that, in terms of verticity, it behaves identically (ignoring variation) to the mariner’s compass on the terrestrial globe. In book two he had sliced loadstones and compasses into half to demonstrate that the two halves still have poles at both ends. Now he shows that his versorium behaves on a half terrellas exactly the same as on the complete one, the cut surface becoming the opposite pole, demonstrating that it is the poles towards which the versorium points. Gilbert uses these experiments and the real mariner’s compass behaviour data provided by the mariners to argue by analogy that the sphere of the Earth is indeed a compass. Gilbert believes that the magnetic poles of the Earth are identical to the geographical poles.
Book IV, Of Variation, opens with a confession:
Do far we have been treating of direction as if there were no such thing as variation; for we chose to have variation left out and disregarded in the foregoing natural history, just as if in a perfect and absolutely spherical terrestrial globe variation could not exist.
He now turns he attention to variation, systematically rejecting all the suggestions that had been put forth to explain it and such concepts as the zero variation meridian or graduated differences in variation around the globe, using the extensive empirical data available to do so. In this book. he surveys all the available information on variation. He dismisses the argument that variation could be used to determine longitude, well aware of the importance of finding a solution to the longitude problem.
Gilbert argues that variation is the result of damage or imperfection to the terrestrial globe, which is anything but a perfect sphere:
[The] globe of the earth is at its surface broken and uneven, marred by matters of diverse nature, and hath elevated and convex parts that rise to the height of some miles and that are uniform neither in matter nor in constitution … For this reason a magnetic body under the action of the whole earth is attracted toward a great elevated mass of land as toward a stronger body, so far as the perturbed verticity permits or abdicates its rights.
The variation takes place not so much because of these continental lands, as because of the inequalities of the magnetic globe and of the true earth substance which projects farther in continents than beneath the sea-depths.
Imperfections in a Terrell causing variations in the versoria
He dismisses the argument that variation could be used to determine longitude, well aware of the importance of finding a solution to the longitude problem. However, having made the error of believing that variation is constant, the temporal changes in variation were not known at this time, Gilbert endorses the scheme of Simon Stevin (1548–1620) put forward in his De Havenvinding (1599), also published in English as The Haven-Finding Art in the same year and included as an appendix in later editions Edward Wright’s Certaine Errors in Navigation, to provide tables of the correctly measured variation to compare with measured observations as an aid to navigation. The twelfth chapter of book four provides the best and most detailed description of how to determine variation published up till that time.
Gilbert’s instrument for determining variation of landInstruments to determine variation at sea
Book V, Of the Dip of the Magnetic Needle, is of course very much up to date, because although Georg Hartmann (1489–1564) had first discovered magnetic dip or inclination in 1544, the phenomenon had first become widely known in 1581 when Robert Norman published his The Newe Attractive. Gilbert mentions Norman and his book at the end of Book I and uses the illustration from The Newe Attractive in this Book V. Gilbert once again sets up experiments with his trusty terrella and versorium to demonstrate and measure magnetic dip. On his terrella he measures the dip for the latitude of London and shows it to be the same as the value measured by Norman for the city. He also discusses the possibility of using magnetic dip, as an alternative method for determining latitude. A scheme never realised.
An instrument for showing by action of a loadstone the degree of dip below the horizon in any latitude
The book closes in Book VI with the most spectacular claim of all, titled Of The Globe ofEarth as a Loadstone, it contains the startling claim that the earth’s diurnal rotation is due to its being a loadstone, based on the false belief that a suspended terrella rotates freely about its polar axis. Gilbert has been called a Copernican and although he names Copernicus amongst those who claim that the earth moves he can at best be called a semi-Copernican, as he only argues for diurnal rotation, a position first argued by Heraclides Ponticus in the fourth century BCE. Gilbert makes no mention of the heliocentric theory of the earth’s orbit around the sun.
The above is merely a sketch of the highly detailed contents of De Magnete, but if you wish to know more then I recommend reading the book, which in the English translation is actually very readable and in the Dover edition very affordable.
The book was on the whole well received and became a central text on empirical methodology for the early decades of the seventeenth century. The strongest reactions came from Galileo, Kepler, and Francis Bacon.
Galileo appears to have acquired a copy very soon after publication from a philosopher who feared that keeping it on the shelf would infest the other books with the novelties it contained. and inspired by the book took up his own investigations into magnetism. He mentioned the book frequently in his correspondence with Giovanni Francesco Sagredo (1571–1620) and Paolo Sarpi (1552–1623). Paolo Sarpi in one of his letters, names Gilbert, with François Viète, as the only original writer among his contemporaries. We know from the only surviving letter from Gilbert, about which more in a later episode, that Sagredo wrote to Gilbert, presumably in February 1602:
… a Secretary of Venice, he came sent by that State, and was honourably received by her Majesty, he brought me a lattin letter from a Gentle-man of Venice that is very well learned, whose name is Iohannes Franciscus Sagredus, he is a great Magneticall man, and writeth that hee hath conferred with diuers learned men of Venice and with readers of Padua, and reporteth wonderfull liking of my booke…
Sagredo is one of the three figures, together with Salviati (Copernican, Galileo), and Simplicio (Aristotelian), discussing the TwoChief World Systems in Galileo’s Dialogo from 1632, he represents the supposedly neutral, intelligent layman.
Source: Wikimedia Commons
On Day Three in the Dialogo Galileo includes a twenty-five page discussion of Gilberts theory that the Earth is a loadstone, initiated by Simplicio:
SIMPLICIO: Are you then one of those who subscribe to the magnetic philosophy of William Gilbert?
SALVIATI: I am indeed, and I think everyone who has read the book attentively and checked his experiments agrees with me.
Then Salviati goes off on a rant about thinkers who stick dogmatically to old ideas and are too cowardly to accept new ones. He then waxes lyrically about Gilbert and his ideas over many pages. However, towards the end of this section Salviati torpedoes Gilbert’s theory of diurnal rotation.
SALVIATI: […] Lest I forget, however, let me first tell you of one detail that I wish Gilbert had never considered. He allows that is a small sphere of loadstone could be perfectly balanced it would turn on its own axis; but there is no reason why it should do so.
Johannes Kepler was an even bigger fan of Gilberts theories than Galileo. Chapter 33 of his Astronomia Nova(1609) is titled, The power that moves the planets resides in the body ofthe sun and Chapter 34 The Sun is Magnetic, and Rotates. Here he writes:
The example of the magnet I have hit upon is a very pretty one, and entirely suited to the subject; indeed, it is little short of being the very truth. So why should I speak of the magnet as if it were an example? For, by the demonstration of the Englishman William Gilbert, the earth itself is a big magnet, and is said by the same author, a defender of Copernicus, to rotate once a day, just as I conjecture about the sun.
Chapter 57, Natural Principles of Reciprocation, presents Kepler’s proto-gravitational theory, which is based on magnetism. It is too complex to explain here but there are a couple of relevant Gilbert quotes:
What if all the bodies of the planets are enormous round planets? Of the earth (one of the planets for Copernicus) there is no doubt. William Gilbert has proved it.
For this magnetic power is corporeal, and divisible with the body, as the Englishman Gilbert, B. Porta, and others, have proved.
Source: Wikimedia Commons
Whilst the leading natural philosophers on the continent were praising Gilbert to the heavens, in Kepler’s case quite literally, at home in England Francis Bacon (1561–1626) was of a very different opinion concerning Gilbert and his book. In his De Augmentis Scientiarum (1623) he wrote:
Gilbert has attempted to raise a general system upon the magnet, endeavouring to build a ship out of materials not sufficient to make the rowing-pins of a boat.
In The Advancement of Learning (1605), Novum Organum (1620) and repeated in De Augmentis Scientiarum(1623) he wrote:
The Alchemists have made a philosophy out of a few experiments of the furnace and Gilbert our countryman hath made a philosophy out of observations of the loadstone.
In his History of Heavy and Light Bodies published posthumously, he wrote:
[Gilbert] has himself become a magnet; that is, he has ascribed too many things to that force and built a ship out of a shell.
At least Gilbert is in good company, Bacon also rejected Copernicus’ heliocentricity and William Harvey’s discovery of the circulation of the blood. The best comment on Bacon’s approach was supposedly made by William Harvey, in his Brief Lives, John Aubrey tells us that Harvey:
“had been physitian to the Lord Chancellour Bacon, whom he esteemed much for his witt and style, but would not allow him to be a great Philosopher. Said he to me, ‘He writes Philosophy like a Lord Chancellour,’ speaking in derision, ‘I have cured him.’”
Inspired by Gilbert the Jesuits took up research of magnetism in a big way, largely to prove Gilbert wrong. Niccolò Cabeo (1586–1650) in his Philosophia magnetica (1629) accepted Gilbert’s proof that the earth is a loadstone but recast all of his theories about magnetism in Aristotelean terms, of course, rejecting his argument for diurnal rotation.
Source: Wikimedia CommonsDip needle, engraving, from Cabeo, Philosophia magnetica, 1629 (Linda Hall Library)
The Jesuit polymath Athanasius Kircher (1602–1680) published a massive tome on magnetism, Magnes (The Loadstone), which launched a massive attack on the heretics Gilbert, Stevin, and Kepler but added little of substance to the work of Cabeo.
Next up was Jacques Grandami (1588–1672) a professor at La Flèche the Jesuit college where both Descartes and Mersenne had studied. He published his Nova Demonstratio Immobilitatis Terrae (A new Demonstartion of the Earth’s Immobility) in 1645, which contained a new experiment, à la Gilbert, which disproved Gilbert’s magnetic diurnal rotation theory.
Nova Demonstratio Immobilitatis Terrae
Grandami placed a terrella on a wooden disc in water, just as Gilbert had done, making sure that its axis was perfectly vertical. He marked the terrella’s equator with the 180° of longitude east and west. He set the terrella spinning having noted its orientation when it started and then again when it stopped. He repeated this experiment many times and each time the terrella stopped with the same east west orientation as when it started. He concluded that magnetism controlled not only North-South alignment but East-West alignment too. His conclusion:
…there is no doubt that the magnetic virtue that God gave to [the Earth] not only keeps its poles still and stable but also its other parts and points.[2]
He then tackled magnetic Copernicanism, which was:
…not only false, but clearly contrary to magnetic laws. They will have our demonstration, stick to their opinions more firmly, and refute opposing opinions more solidly. Then they can praise divine wisdom in earth’s magnetic quality, which causes its stability, and demolish the other useless and ridiculous effects of the Sun and other planets.
Grandami wrote up his claims in a manuscript that was circulated widely through Marin Mersenne’s network but which had very little resonance, although his experiment was widely repeated and found to be correct. The crunch came from a simple, rather obvious, comment from Mersenne, Jesuit educated but a Minim friar, provoked by Grandami’s conclusions. Mersenne pointed out that the analogy claims between the Earth and a terrella were invalid because the terrella was not free but was affected by the magnetic field of the Earth, torpedoing Grandami’s claims for a geo-static earth but at the same time Gilbert’s magnetic diurnal rotation. He published his thoughts in 1644, a year before Grandami finally commited his manuscript to print.
I do not even wish to pursue those ways by which others believe that the Earth’s stability is proved from magnetic directions, since exactly the same thing happens to the magnet whether the Earth stands still or moves. So far, nothing from magnetic laws, any more from projectiles and the fall of heavy bodies can or ought to prove the double or triple motion of the Earth, the double rest of the Earth or its immobility
Universae geometriae synopsis (1644)
I will close this very brief survey of the reception of De Magnete with Isaac Newton. Challenged on the action at a distance concept of his law of gravity, Newton proffered both magnetism and static electricity as attractive forces that displays action at a distance.
As Attraction is stronger in small Magnets than in great ones in proportion to their Bulk, and Gravity is greater in the Surfaces of small Planets than in those of great ones in proportion to their bulk, and small Bodies are agitated much more by electric attraction than great ones; so the smallness of the Rays of Light may contribute very much to the power of the Agent by which they are refracted. And so if any one should suppose that Æther (like our Air) may contain Particles which endeavour to recede from one another (for I do not know what this Æther is) and that its Particles are exceedingly smaller than those of Air, or even than those of Light: The exceeding smallness of its Particles may contribute to the greatness of the force by which those Particles may recede from one another, and thereby make that Medium exceedingly more rare and elastick than Air, and by consequence exceedingly less able to resist the motions of Projectiles, and exceedingly more able to press upon gross Bodies, by endeavouring to expand itself. (Opticks, Queries 21)
As I stated at the beginning, there can be no doubt that Gilberts De Magnete is one of the most important science books published in the Early Modern Period a fact that should be more widely acknowledged than it usually is.
[1] De Magnete by William Gilbert Translated by P. Fleury Mottelay, Dover Publications, NY, 1958, pp. 14-15
[2] This quote, and several others, is taken from Stephen Pumfrey’s excellent but frustrating biography of Gilbert, Latitude & The Magnetic Earth: The True Story of Queen Elizabeth’s Most Distinguished Man of Science, (Icon Books, 2002). Frustrating because it has no academic apparatus, no foot or endnotes, no references and above all no index!
A couple of weeks back, another Renaissance Mathematicus friend, David Hop, drew my attention once again to the same Rogan/Tyson interview, this time a longer section in which NdGT extemporises about the space telescope, Hubble, and Antoni Leeuwenhoek before he reaches the section I dissected back in May last year. As to be expected Motor-Mouth-Tyson spews out a non-stop stream of pure drivel, which truly demands the attention of the HIST_SCI HULK:
NdGT: Why do you think the Hubble Telescope…the mirror issues notwithstanding, which were ultimately fixed when, it was first launched…Why was it so successful? Version of the Hubble telescope previously launched by the military, looking down. The model for that telescope had already been conceived and built and was operating. Then we said we want one of those OK but that’s not public that this is going on. The telescope gets designed has the benefit of previous versions of it having been used successfully but looking down. We look up, this the perennial two way street astronomy in the old days and in modern times astrophysics.
One doesn’t need to be a fucking rocket scientist to recognise that a military spy satellite, looking down, is technically, optically, functionally, conceptionally different to a space telescope, looking up. But is there any truth in Tyson’s stream of verbal garbage? Now neither Hulky nor I are experts on the Hubble Telescope, it wasn’t built in the seventeenth century, but Wikipedia has good articles on the history of Hubble and on the history of military spy satellites too. Tyson could have taken the time to read them before opening his mouth. But what the hell, why ruin a good story with facts? Neil, “who cares about facts”, Tyson obviously didn’t bother.
The Hubble Space Telescope as seen from the departing Space Shuttle Atlantis, flying STS-125, HST Servicing Mission 4. Source: Wikimedia Commons
To save you having to turn to Wikipedia, a brief synopsis. We start with the military as Motor-Mouth-Tyson thinks they started the ball rolling and NASA jumped on the bus having seen that it works.
The United States Army Ballistic Missile Agency launched the first American satellite, Explorer I, for NASA’s Jet Propulsion Laboratory on January 31, 1958. The information sent back from its radiation detector led to the discovery of the Earth’s Van Allen radiation belts.
Wikipedia
Note the date!
The theoretical idea goes back a bit further:
Herman Potočnik explored the idea of using orbiting spacecraft for detailed peaceful and military observation of the ground in his 1928 book, The Problem of Space Travel. He described how the special conditions of space could be useful for scientific experiments. The book described geostationary satellites (first put forward by Konstantin Tsiolkovsky) and discussed communication between them and the ground using radio, but fell short of the idea of using satellites for mass broadcasting and as telecommunications relays.
Wikipedia
Note once again both civil and military!
Turning to space telescopes and Hubble:
In 1923, Hermann Oberth—considered a father of modern rocketry, along with Robert H. Goddard and Konstantin Tsiolkovsky—published Die Rakete zu den Planetenräumen (“The Rocket into Planetary Space”), which mentioned how a telescope could be propelled into Earth orbit by a rocket.
Wikipedia
So not exactly a recent idea!
The history of the Hubble Space Telescope can be traced to 1946, to astronomer Lyman Spitzer’s paper “Astronomical advantages of an extra-terrestrial observatory.”
Wikipedia
Note the date, twelve years before that first military launch of a satellite looking down!
Spitzer devoted much of his career to pushing for the development of a space telescope. In 1962, a report by the U.S. National Academy of Sciences recommended development of a space telescope as part of the space program, and in 1965, Spitzer was appointed as head of a committee given the task of defining scientific objectives for a large space telescope.
Wikipedia
Liman Spitzer Source: Wikimedia Commons
Also crucial was the work of Nancy Grace Roman, the “Mother of Hubble”. Well before it became an officialNASA approved, she became the program scientist, setting up the steering committee in charge of making astronomer needs feasible to implement and writing testimony to Congress throughout the 1970s to advocate continued funding of the telescope. Her work as project scientist helped set the standards for NASA’s operation of large scientific projects.
Space-based astronomy had begun on a very small scale following World War II, as scientists made use of developments that had taken place in rocket technology. The first ultraviolet spectrum of the Sun was obtained in 1946, and NASA launched the Orbiting Solar Observatory (OSO) to obtain UV, X-ray, and gamma-ray spectra in 1962. An orbiting solar telescope was launched in 1962 by the United Kingdom as part of the Ariel programme, and in 1966 NASA launched the first Orbiting Astronomical Observatory (OAO) mission. OAO-1’s battery failed after three days, terminating the mission. It was followed by Orbiting Astronomical Observatory 2(OAO-2), which carried out ultraviolet observations of stars and galaxies from its launch in 1968 until 1972, well beyond its original planned lifetime of one year.
Wikipedia
I could go on, but I think that is enough to show that the Hubble Space Telescope was definitively not a case of the civil space programme copying an idea from the military space programme and that Motor-Mouth-Tyson is, as per usual, spreading high grade bovine manure.
NdGT: The invention of the telescope [babble between Tyson and Rogan] Galileo perfects the telescope He learns that the telescope has just been invented in the Netherlands the Dutch were opticians, so they invented the telescope and the microscope within a couple of years of one another This transforms science.
The Dutch were opticians! So what? So were people all over Europe. Funnily enough the man credited with having invented the telescope, Hans Lipperhey, lived in Middelburg in the Netherlands but was actually a German. The invention of the telescope and/or microscope had nothing to do with nationality.
Rogan: Why did they invent the eyeglass the reading glass?
NdGT: The reading glass was earlier than that, but I don’t know when, The real advance was putting two lenses in line with one another. Trivial in modern times but that was a huge conceptual leap and what you would accomplish [sic] and in so doing depending on how you curve them and how you grind the shape of those lenses you would get a microscope or a telescope. And we’re off to the races!
It you are going to pontificate about the history of optics and the invention of the telescope and the microscope, you really should know when eyeglasses were invented, as one of the central questions, in that history, is why did it take so long from the invention of eyeglasses, around 1260, to the invention of the telescope in 1608? The accepted thesis in answer to this question is contained in Rolf Willach’s magisterial Long Route to the Invention of the Telescope: A Life of Influence and Exile (American Philosophical Society, 2008). Willach argues convincingly that it was not putting two lenses in line with one another that led to the telescope, several people had done that without creating a telescope, but masking or stopping down the lens. The shape or form of a hand ground lens becomes more inaccurate the further one goes from the middle. These inaccuracies in the outer areas of the lens cause a distorted image, no problem in eyeglasses where one looks through the centre of the lens, but a major problem in the attempt to create a telescope. Lipperhey was probably the first to mask or stop down the lens so that only the central, correctly ground, portion of the lens gets used to create the image.
I could write a whole book about Motor-Mouth-Tyson, “depending on how you curve them and how you grind the shape of those lenses you would get a microscope or a telescope.” Let’s just say an explanation it is somewhat wanting in more ways than one.
NdGT: That’s basically the birth of modern science as we think of it and conduct it. Because you say to yourself, my senses I don’t trust them to be the full record of what’s going on in front of me.
That the telescope and the microscope extended human perception and added new layers of empiricism to the study of nature is beyond discussion but to call it the birth of modern science is typical Motor-Mouth-Tyson hyperbole.
NdGT: You pull out a microscope, oh my gosh, Leeuwenhoek , the microscope guy, he got a drop of pond water, puts it under his microscope, just to think to do this, it’s just water, why do you think that’s something interesting to do? He said, I wonder, he was curious and puts it under and sees little, what he described as animalcules happily aswimming.
Rogan: Animalcules!
NdGT: Animalcules, these are like the amoebas and paramecia. So, he writes to…he reports on this to the scientific authorities, and they don’t believe him. They say Van Leeuwenhoek, we think you might have had too much gin before you wrote this letter. Why would anyone believe this that there’s entire creatures, an entire universe of creatures thriving in a drop of pond water. And so, the way science works, one report does not make it true, you need verification. They sent people to the Netherlands to verify his results and there it was the birth of microscopy and then they look at everything. Cells you know, they need vocabulary to describe what you are seeing.
Antoni van Leeuwenhoek Portrait by Jan Verkolje, after 1680 Source Wikimedia Commons
Leeuwenhoek now gets the Motor-Mouth-Tyson stir some half facts with a portion of liquidbovine manure and splatter the result over the listener treatment. Leeuwenhoek did not put his drop of pond water under his microscope because that is not how his single lens microscopes worked. Wait a minute didn’t our narrator just explain that to make a microscope you need to put two lenses in line with one another? If you are building a compound microscope you do indeed need at least two lenses and often more, but Leeuwenhoek is famous for the fact that he used single lens microscopes of his own special design.
A replica of a microscope by Van Leeuwenhoek Source: Wikimedia Commons
The small spherical lens is embedded in a metal plate and the specimen to be viewed in placed on the spike behind the lens and the whole apparatus is held up to the light. At the time Leeuwenhoek examined pond water with his microscope, microscopists were examining anything and everything with their microscopes, so nothing very special in this act. “He reports on this to the scientific authorities” sounds like something out of a dystopian novel by Kafka or Orwell. At the time he was corresponding with the Royal Society in London, basically, at the time, a private gentleman’s club for those interested in natural philosophy, who were publishing the results of Leeuwenhoek’s microscopic investigation in the Philosophical Transactions.
The letter with the animalcules, a term coined by Henry Oldenburg Secretary of the Royal Society, when translating from Leeuwenhoek’ original colloquial Dutch was sent in 1676 and was by no means his first letter.
.. this was for me, among all the marvels that I have discovered in nature, the most marvellous, and I must say that, for me, up to now there has been no greater pleasure in my eye as these sights of so many thousands of living creatures in a small drop of water, moving through each other, each special creature having its special motion.
Leeuwenhoeks animalcules letter to Oldenburg
The prominent Dutch physician Reinier de Graaf made Oldenburg aware of Leeuwenhoek’s investigations in a letter from 1673:
That it may be the more evident to you that the humanities and science are not yet banished among us by the clash of arms, I am writing to tell you that a certain most ingenious person here, named Leewenhoek [sic], has devised microscopes which far surpass those which we have hitherto seen, manufactured by Eustacio Divini and others. The enclosed letter from him, wherein he describes certain things which he has observed more accurately than previous authors, will afford you a sample of his work: and if it please you, and you would test the skill of this most diligent man and give him encouragement, then pray send him a letter containing your suggestions, and proposing to him more difficult problems of the same kind.
Oldenburg followed de Graaf’s suggestion and from then on the Royal Society regularly published Leeuwenhoek’s letters with his latest investigations until his death in 1723.
Motor-Mouth-Tyson’ comment, “They say Van Leeuwenhoek, we think you might have had too much gin before you wrote this letter” is a piss poor joke and has no place in an account of the history of science. Leeuwenhoek’s discovery of single cell organisms did indeed cause some consternation because the Royal Society’s resident microscopists, Robert Hooke and Nehemiah Grew where initially unable to replicate his observations, their microscopes were not powerful enough. Later Hooke would succeed but in the meantime the Royal Society was justifiably sceptical. The situation was not improved by Leeuwenhoek’s refusal to explain his methods out of fear of being plagiarised.
Tyson is quite correct that scientific results have to be verified, usually by replication. Galileo’s telescopic discoveries, which Tyson introduces in the part of the interview that I dissected last time, were also initially met with scepticism, particularly as people were unable to replicate them. Something Tyson doesn’t mention. They were only accepted after the Jesuit astronomers of the Collegio Romano had finally succeed in replicating them.
The Royal Society did indeed send a delegation to control Leeuwenhoek’s results. This was not in anyway exceptional in the seventeenth century where personal testimony from reliable witnesses was a common form of verification. When the Royal Society doubted the accuracy of Johannes Hevelius’ astronomical observations, because he refused to use telescopic sights on his instruments, they sent Edmond Halley to Danzig to investigate the matter. The measuring of atmospheric pressure using a primitive barometer by Pascal’s brother in law, Florin Périer, was witnessed and confirmed by Minim Fathers from a local friary. Here we have an interesting aspect of personal witness verification, church officials, rather than natural philosophers, were regarded as the most reliable and trustworthy witnesses. The delegation that went to visit Leeuwenhoek to investigate his animalcules’ reports was led by Alexander Petrie, minister to the English Reformed Church in Delft; Benedict Haan, at that time Lutheran minister at Delft; and Henrik Cordes, then Lutheran minister at the Hague. The visit was for Leeuwenhoek a success and his observations were fully acknowledged by the Royal Society.
NdGT: … and there it was the birth of microscopy and then they look at everything. Cells you know, they need vocabulary to describe what you are seeing.
As I pointed out in an earlier post this was not the birth of microscopy, although Leeuwenhoek took it to a new level. Marcello Malpighi (1628–1694), Jan Swammerdam (1637–1680), Robert Hooke (1635–1703, and Nehemiah Grew (1641–1712) were all prominent microscopist contemporaries of Leuwenhoek, who all started their investigations and also published some of their results before Leeuwenhoek began his investigations. The were also not to first and these scholars, particularly Robert Hooke, had already been looking at everything. Ironically, Motor-Mouth-Tyson’s example “cells” had already been discovered by Hooke. His Micrographia (1665) contains a microscopic image of the cells in cork. Hooke coined the term because he thought they looked like the monk’s cells in monasteries.
Robert Hooke’s microscopic image of cork displaying the cell structure Source: Wikimedia Commons
NdGT That was the journey down small then the journey went big, and Galileo perfects the telescope…
This is where the section of the interview that we dissected back in May last year begins. Motor-Mouth-Tyson is slowly becoming the HISTSCI_HULKS favourite punch bag although the man is so dumb, it’s a bit like shooting fish in a barrel. On a serious note, NdGT is wildly successful all over the Internet and almost everything he spews forth, and there’s an awful lot fit, about the history of science is either highly inaccurate or simply false and unfortunately his adoring fans don’t know better. Equally unfortunate is the fact that he simply ignores the criticisms of those who know better.
I don’t remember ever coming across half a paragraph of just nineteen lines that manages to cram in so many history of science and technology myths, errors, and falsehoods as the one that I recently read whilst soaking in a hot bath. A truly monumental cluster fuck!
The offending object is on page 131 of David B. Teplow’s The Philosophy and Practice ofScience[1], which I will be reviewing in the not to distant future and which is much better than the handful of lines dumped on here and which I will almost certainly be recommending but for now the cluster fuck.
Revolutionary advance in science have been achieved through a number of mechanisms. Optics is a good example. Simple, but keen and thoughtful, observation of the worlds at a magnification of 1x, combined with logic, enabled Aristotle to lay the foundation for all of science and for Copernicus to propose a heliocentric solar system.
The statement about Aristotle laying the foundation for all science is definitely questionable given his rejection of mathematics but I’ll let it pass. Copernicus proposal of a heliocentric solar system was not in anyway based on observation but on rethinking elements of the existing geocentric system.
Copernicus’ heliocentric model from Andreas Cellarius’ Atlas Coelestis 1660
Galileo’s construction of the first telescope’s allowed him to observe the world at ≈30x and to confirm Copernicus’s theory of a heliocentric heavens.
Galileo by no means constructed the first telescopes. Apart from being preceded by the various inventors of the telescope such as Hans Lipperhey and Jacob Adriaenszoon, by the time he learnt about telescopes they were on sale all over Europe. The Venetian Senate was truly pissed off when they discovered this after giving Galileo a massive pay rise for presenting them with a telescope, having thought it was something very special. Galileo was also definitely preceded as a telescopic astronomical observer by Thomas Harriot and probably by Simon Marius. If I could get my hands on the idiot, who first perpetrated the myth that Galileo’s observations confirmed Copernicus’s theory of a heliocentric heavens, I would shove a Galilean telescope up his fundamental orifice. Galileo knew that nothing that he had observed confirmed Copernicus’s theory and he never claimed that he had. It would be 1725 before James Bradley produced the first telescopic observation that confirmed part of the heliocentric theory, when he observed stellar aberration.
Galileo’s “cannocchiali” telescopes at the Museo Galileo, Florence via Wikimedia Commons
It [optics] also enabled van Leeuwenhoek to study the microscopic world, at ≈250x, and in the process discover “animalcules” (from the Latin for “tiny animal”; animalculum) – including bacteria, protozoa, and spermatozoa – thus becoming the first microscopist and microbiologist.
Van Leeuwenhoek is a very long way from being the first microscopist. It’s actually difficult to establish who first began using microscopes as scientific instruments. Galileo knew of the microscope and almost certainly discovered the principle, as probably did many others, when looking through a Galilean or Dutch telescope ( one convex, one concave lens) the wrong way it, when it functions as a microscope, but he did make any systematic microscopic studies. The Dutch engineer, inventor, (al)chemist, optician, and showman Cornelis Jacobszoon Drebbel (1571–1631) was constructing and giving public demonstrations with Keplerian microscopes (two convex lenses) by about 1620. Galileo built a compound microscope in 1624, which he presented to Prince Federico Cesi founder of the Acccademia dei Lincei.
Anthonie van Leeuwenhek Portrait by Jan Verkolje, after 1680 Source: Wikimedia Commons
The first illustrations made with a microscope are attributed to Francesco Stelluti on a pamphlet published by the Acccademia dei Lincei to celebrate the election of Maffeo Barberini as Pope in 1623. The bees were the Barberini family emblem. Stelluti published further microscopic studies of bees in a Tuscan translation of an obscure Latin poem in 1630.
Stelluti Bees1630
In 1644 Giovanni Battista Odierna published a pamphlet of his microscopic studies of the fly’s eye, his L’Occhio della mosca and in 1656 Pierre Borel published a collection a collection of a hundred miscellaneous microscope observations, his Observationum microscopicarum canturia.
The Italian biologist Marcello Malpighi (1628–1694) observed capillary structures in frog’s lungs with a microscope in 1661 putting him ahead of van Leeuwenhoek as microbiologist.
With the help of the newly invented microscope, Marcello Malpighi (A) (1628–1694) solidified Harvey’s concepts and was the first man ever to describe the pulmonary capillaries and alveoli (B). Source:
Given his propensity to vehemently claim priority on every aspect of his research in his polymathic career, Robert Hooke would almost certainly be enraged by our authors claim, as his magnificent and ground-breaking microscopic study the Micrographia was published in 1665, eight years before van Leeuwenhoek’ first letter was published by the Royal Society. Hooke would probably also claim priority as the first microbiologist for his study of and naming of biological cells.
Source: Wikimedia Commons
The claims that van Leeuwenhoek was the first microscopist and microbiologist are total bullshit and display a level of ignorance and/or laziness, on Teplow’s part, who either didn’t bother to check his facts or to do the bloody research.
Electron and atomic force microscopes now allow scientists to see objects at magnifications up to ≈107x, opening up an immense sub-cellular world in which even individual atoms can be visualized. These instrumental advances expanded the observable universe, and the amount of information to which one has access, many orders of magnitude.
Nothing to complain about here.
The best example of a recent revolution in scientific method comes from computer science, a field that for all intents and purposes, did not even exist until the twentieth century.
Nor here, but the pain starts again in the very next sentence.
The development of mechanical computers (the “difference and analytical engines”) and arbitrary, user-defined programs (“weav[ing] algebraic patterns”) by Charles Babbage and Ada Lovelace, respectively, followed by the conception and development of electronic computers by John van [sic] Neumann and Alan Turing ushered us into the current “information age.”
Oh boy! Babbage’s Differential Engine, a special purpose computer designed to calculate and print error free mathematical tables using the method of differences was never realised, beyond a small working model, which he had his engineer Joseph Clement (1779–1844) construct in 1832, before the project was abandoned. The Analytical Engine, conceived as a grandiose multipurpose computer never got off the drawing board.
Portion of Charles Babbage’s calculating machine (Difference Engine No.1), built by Joseph Clement, London, 1832. Science Museum London
Although she described the concept of arbitrary, user-defined programs in her notes to her translation of Luigi Menabrea’s Notions sur la machine analytique de M. Charles Babbage (1842), the concept is from Babbage and not Lovelace. The full quote from Lovelace’s notes is “we may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard loom weaves flowers and leaves.”
The idea of a machine that could transcend number, as the Analytical Engine had transcended addition and had been generalized to other operations, had been in Babbage’s thoughts for some years. In a letter to Mary Somerville written 12 July 1836, he spoke of having “a kind of vision of a developing machine.” This was only twelve days after he had taken the decision to adopt punched card as input to the Analytical Engine, and two days after he mused in his notebook.
This day I had for the first time a general but very indistinct conception of the possibility of making an engine work out algebraic developments – I mean without any reference to the value of the letters. My notion is that as the cards (Jacquards) of the calc. engine direct a series of operations and then recommence with the first, so it might be possible to cause the same cards to punch others equivalent to any given number of repetitions. But these hole[s] might perhaps be small pieces of formulae previously made by the first cards and possibly some mode might be found for arranging such detached parts according to powers of nine numbers and of collecting similar ones [the entry breaks off here].
What he was groping for here was some means of bypassing or replacing the columns of numbers that are ordinarily the objects to be operated on, so that he could operate on symbols instead.[2]
Note that this is eight years before Ada translated the Menabrea article. Note also, whereas Ada drops the suggestion in a simple, highly quotable, poetic bon mot, Babbage was acutely aware of the problems involved in actually achieving this aim. As I’ve sodding well said a hundred bleeding times, before accrediting anything to Countess Lovelace see what Babbage has said on the subject in his correspondence and unpublished papers.
One should also note that there was no continuity or influence between Babbage’s schemes and the invention of the computer in the twentieth century. It was only with hindsight that historians began to praise Babbage as a pioneer of the computer age.
Neither Alan Turing nor John von Neumann conceived or developed the effing computer! Vannevar Bush (differential analyser, 1927), Konrad Zuse (Z2 1940, Z3 1941), Vincent Atanasoff & Clifford Berry (ABC, 1942), Howard Aiken (Harvard Mark I, 1944), Tommy Flowers (Colossus, 1943–45), and John Mauchly & J. Presper Eckert (ENIAC, 1945) did conceive and develop computers.
In 1936 Alan Turing published a meta-mathematical paper, On Computable Numbers, with an Application to the Entscheidungsproblem, which after other people had developed computers provided a succinct way of categorising the computing capabilities of a computing machine.
During WWII Turing, together with Gordon Welchman, developed the Bombe from the Polish Bomba, an electro-mechanical device used to help decipher German Enigma-machine-encrypted secret messages. The Bombe was designed and constructed by Harold Keen. After WWII, Turing worked on the design of the Automatic Computer Engine (ACE), which he presented in 1945. The ACE was never built.
Beginning in 1944, ENIAC inventors, John Mauchly and J. Presper Eckert, designed the Electronic Discrete Variable Automatic Computer (EDVAC) the machine being finally delivered in 1949. Brought in as a consultant, John von Neumann wrote a description of the EDVAC, First Draft of a Report on the EDVAC, which was published in 1945 and led to Mauchley and Eckert being denied a patent for EDVAC.
First Draft of a Report on the EDVAC Source: Wikimedia Commons
This totally lazy and factually incorrect Turing and von Neuman invented the computer that has become established in popular history of technology gets on my fucking wick. Teplow’s paragraph that I have dissected above is a glowing example of lazy, cliché filled, badly researched history of science and technology that should not be being published by a major academic publisher in 2023.
[1] David B. Teplow, The Philosophy and Practice ofScience, CUP, 2023
[2] Dorothy Stein, Ada: A Life and a Legacy, The MIT Press, 1985. pp. 102–103
Winter solstice at Stonehenge, which is thought to be astronomically aligned with sunrise on the winter solstice
You don’t have to delve very deeply into the history of astronomy to come into contact with the problems of time measurement. The three natural units of time measurement, the solar day, the solar year, and the lunar month are all astronomical phenomena. Unfortunately, these three units are all mutually incommensurable. That is, there is not a whole number of solar days in a solar year, or a lunar month, or lunar months in a solar year. This leads us into the problems of calendrics, that is the attempt to create a reasonable system incorporating the three basic units in order to be able to mark the passing of time. Humanity has come up with more than a handful of differing attempts to solve this problem over the millennia.
One initial problem is where to place the beginning or the end of one solar cycle. Currently, in the western world people, following the Gregorian solar calendar, use the more than somewhat arbitrary 31st day of December as New Year’s Eve, that is the end of a cycle and the following day 1st January as New Year’s Day the beginning of the next cycle. This choice doesn’t appear to have any rational or astronomical foundation; it just is. The Gregorian calendar is by no means the only calendar in use throughout the world and 1st of January is also not the only acknowledge starting point of a solar cycle.
The Jewish calendar is a lunar solar calendar and has not just one but four different ends/starts to the year. These are 1st Nisan, the first month in the biblical calendar, the ecclesiastical new year. 1st Tishrei the seventh month in the biblical calendar, the civil new year, on which the year number advances; this day is known as Rosh Hashanah. The 1st of Shevat, the eleventh month in the biblical calendar, is the new year of trees. However, another school says it falls on the 15th of Shevat. The fourth is 1st Elui the sixth month in the biblical calendar. Due to the use of seven intercalery months over a cycle of nineteen years in order to bring the lunar year 354 days into line with the solar year of 365 days the four Jewish new years day fall on different days on the Gregorian calendar each year.
The Lunar New Year, celebrated in several East Asian cultures, based on a lunar solar calendar usually falls on the second new moon after the winter solstice (rarely the third if an intercalary month intervenes). In theGregorian calendar, the Lunar New Year begins at the new moon that falls between 21 January and 20 February.
The Persian calendar, currently used in Iran and Afghanistan, is a solar calendar that has been in use for about four thousand years during which time it has evolved. The Persian New Year begins at the midnight nearest to the instant of the northern spring equinox, as determined by astronomic calculations for the meridian (52.5°E). It is, therefore, an observation-based calendar, as is traditionally the Jewish calendar, observation of the new moon determining the beginning of the month, unlike the Gregorian, which is rule-based.
Because the Christian calendar was solar, at that time still the Julian calendar, and the Jewish calendar was lunar-solar, the, then new religion, Islam deliberately chose a pure lunar calendar to differentiate themselves from the other monotheistic religions. The Islamic New Year is the 1st of Muḥarram, the first month of the Islamic calendar. Because the lunar calendar is approximately eleven days shorter than the Gregorian calendar the Islamic New Year moves backwards by eleven days each year against the Gregorian calendar taking a bit more than thirty-three years to complete a cycle through it. Like the Jewish calendar the Islamic calendar is an observation-based calendar, the first of the month occurring when the new moon is first observed.
There are other calendars but the examples I have discussed, unlike the Gregorian calendar, all have a New Year’s day, which is defined astronomically and not arbitrarily. As a historian of astronomy and calendrics living in the northern hemisphere, I decided several years ago that the Renaissance Mathematicus end and beginning of the annual solar cycle takes place at winter solstice when the old year dies, and the new year is born. The northern winter solstice is the day in the year when the sun is directly overhead at noon at the Tropic of Capricorn, currently 23°26′10.2″ south of the equator. Tropic comes from Latin tropicus “pertaining to a turn,” from Greek tropikos “of or pertaining to a turn or change.” It is the point when the sun turns on its journey southwards and begins to journey northwards towards the Tropic of Cancer and the summer solstice. The northern winter solstice usually falls on the 21st or 22nd December on the Gregorian calendar.
Today is the northern winter solstice and I wish all my readers a healthy and happy start in the new solar cycle. I thank you for having read my scribblings over the last twelve months and hope you will continue to do so. I particularly thank all those, who have taken the time and trouble to comment and to correct my errors both orthographical and factual.
It is important to note, for the evolution of scientific thought in Europe throughout the centuries after Aristotle, that when applied to nature he didn’t regard mathematical proofs as valid. He argued that the objects of mathematics were not natural and so could not be applied to nature. He did however allow mathematics in what were termed the mixed sciences, astronomy, statics, and optics. For Aristotle mathematical astronomy merely delivered empirical information on the position of the celestial bodies. Their true nature was, however, delivered by non-mathematical cosmology.
In the next three episodes I will be taking a separate look to the three so-called mixed sciences–astronomy, optics, statics–starting with astronomy, because all three would go on to play a significant role in the development of physics in the Early Modern Period.
We have already seen that Aristotle propagated a homocentric, mathematical, astronomical model of the cosmos that was originally conceived by Eudoxus of Cnidus (c. 390–c. 340 BCE), and then further developed by Callippus (c. 370–c. 300 BCE) and Aristotle himself. However, we don’t have any real astronomical texts from any of the three. In what follows I shall be looking at the work of the practical astronomers Hipparchus (Greek: Ίππαρχος, Hipparkhos) (c. 190–c. 120 BCE) and Ptolemaeus (Greek: Πτολεμαῖος, Ptolemaios, English: Ptolemy), which basically means the work of Ptolemaeus, as most of what we know about Hipparchus is taken from the Geographica of Strabo (63 BCE–c. 24 CE), the Naturalis Historia of Plinius (23–79 CE), and Ptolemaeus’ Mathēmatikē Syntaxis or Almagest as it is more commonly known.
Although Ptolemaeus was one of the most influential scholars in antiquity we know almost nothing about him. He appears to have lived and worked in the city of Alexandria during the second century CE and that is quite literally all we know.
Sixteenth century engraving of Ptolemaeus being guided by the personification of astronomy, Astronomia – Margarita Philosophica by Gregor Reisch, published in 1508. Ptolemaeus is shown wearing a crown, as during the Middle Ages, he was thought falsely to be part of the ruling Ptolemaic dynasty Source: Wikimedia Commons19th-century engraving of Hipparchus Source: Wikimedia Commons
We have exactly the same problem with Hipparchus who was born in Nicaea, which is now in Turkey, and is said to have died in Rhodes. The dates given for his life are guestimates based on the known dates of some of his astronomical observations.
Starting with Ptolemaeus’ Mathēmatikē Syntaxis, what this represents is a fully fledged science in the modern sense but which in its development goes back more than a thousand years. The Mathēmatikē Syntaxis is a vast collection of empirical data, which is then analysed to produce a mathematical model of the observable celestial sphere. It is in this sense no different to the astronomical work of Copernicus or Tycho Brahe and the only thing that separates from the work of John Flamsteed, in the time of Newton, is that much of Flamsteed’s empirical data was acquired with a telescope, an instrument that the earlier astronomer did not have available to them.
A 14th.century Greek manuscript of the Mathēmatikē Syntaxis; it shows a table layout, and the functions of the columns, colours and rows are labelled in this depiction. Source: Wikimedia Commons Manuscript source
The Mathēmatikē Syntaxis was published sometime in the middle of the second century CE. It was translated into Arabic in total five times starting around eight hundred. Islamic astronomers studied, analysed, and criticised it. They added new mathematical methods to improve it, but they did nothing to change its fundamental structure.
Arabic Almagest beginnings of the star catalogue Source
It was translated both from the original Greek and from Arabic into Latin in the twelfth century, again without major change.
In the fifteenth century Peuerbach and Regiomontanus produced their Epitome of the Almagest, for Cardinal Bessarion, an updated, modernised, shortened, mathematically improved version of the Almagest.
Epytoma Ioannis de Monte Regio in Almagestum Ptolomei, Latin, 1496 Full manuscript source
The basic concept and structure, however, remained the same and this, in its printed version from 1496, became the standard advanced astronomy textbook in Europe. Copernicus, who learnt his astronomy from the Epitome of the Almagest, and modelled his De revolutionibus (1543)on it.The Mathēmatikē Syntaxis was and remained the archetype for a general presentation of astronomy.
Ptolemaeus’ model is a geocentric one for the obvious reason that it best fitted the available empirical data. As far as the observer is concerned there is no indication that the earth moves in anyway whatsoever, it’s a stable non-moving platform, as far as the observer can tell. This is what makes the mental leap to a heliocentric model so extraordinary. However, even within a heliocentric paradigm astronomical observation remain by definition geocentric until the late twentieth century when the human race made its first tentative steps into space.
Why am I saying this? There is a widespread misconception that somehow Copernicus created a completely new astronomy when he published his De revolutionibus, in reality he didn’t, he ‘merely,’ where merely is doing a lot of work, hypothesised a new model within the astronomical frame that Ptolemaeus had given him in his Mathēmatikē Syntaxis. Tycho Brahe did nothing other with his geo-heliocentric model. The observational astronomy remains the same the mathematical interpretation of the acquired data changes.
Regiomontanus, Wilhelm IV of Hesse-Kassel, and Tycho Brahe all recognised that the data set delivered up in the Mathēmatikē Syntaxis had become corrupted by constant copying of manuscripts and all set about creating new data but using the same basic techniques and instruments as Ptolemaeus. Regiomontanus died before his programme really got of the ground but both Wilhelm and Tycho created new accurate data sets. Tycho developed another new interpretation of the data with his geo-heliocentric model.
A simplified, short explanation of the emergence of modern science during the Early Modern Period is that the qualitative natural philosophy of Aristotle was replaced by a quantitative natural philosophy in which empirical data was analysed and interpreted mathematically. The oft quoted mathematisation of science of which Newton’s Principia Mathematica is held up as the prime example. Ptolemaeus’ Mathēmatikē Syntaxis already offered up a role model for this way of doing science. However, because Aristotle had claimed that mathematics does not or cannot describe reality the Mathēmatikē Syntaxis was generally interpreted, but not as we will see by Ptolemaeus, as being merely a calculating device to determine the position of the celestial object for astrology, cartography, navigation, etc. This, of course, changed with Copernicus, as astronomers began to regard their mathematical models as describing reality. Astronomy became one of the principle driving forces behind the seventeenth-century mathematisation of science.
I’m not going to give a detailed analysis of everything that is in the thirteen books of the Mathēmatikē Syntaxis. I would need a whole blog series for that. However, I will make some salient points of what Ptolemaeus delivers in his complete package.
In the first book he describes a basically Aristotelian image of the cosmos. The Earth a sphere at the centre of a spherical cosmos. Without mentioning either Aristarchus of Samos, who is credited by a couple of sources with having proposed a heliocentric cosmos, or Heraclides Ponticus (c. 390–c. 310 BCE), who proposed a geocentric system with diurnal rotation, Ptolemaeus criticises those who would attribute diurnal rotation to the Earth, anticipating a common criticism of Copernicus. He argues quite logically that if the Earth was rotating on its axis the resulting headwind would cause havoc. Copernicus opposed this argument correctly by claiming that the Earth carries its atmosphere with it in a sort of envelope but couldn’t explain how this physically functioned. Much of the history of physics of the seventeenth century are the incremental steps towards supplying the solution to this problem, culminating in Newton’s theory of universal gravitation.
Ptolemaeus deviates strongly from Aristotelian philosophy in two important aspects. Firstly, it is fairly obvious that he regards his mathematical models as describing reality and not just being a method of calculating the positions of celestial objects. This is something that tended to be ignored by the medieval Aristotelian philosophers, who used the Mathēmatikē Syntaxis. Secondly, because it was not capable of explain all of the properties of the planetary orbits, he abandoned the homocentric spheres model replacing it with variations on an deferent /epicycle model, combined with an eccentric, i.e., the deferent is not centred on the Earth but a point some distance away from it, and with the uniform circular motion measured from an equant point, an abstract point equidistant from the eccentric point as the Earth.
Ptolemaeus’ model of the planetary orbits
This complex geometrical construction led several times down the century to a rejection of the Ptolemaic astronomy and the demand for a return to the Aristotelian homocentric astronomer. The last attempt being by Girolamo Fracastoro (c. 1477–1553) and Giovanni Battista Amico (1511? – 1536), Fracastoro’s book Homocentricorum sive de stellis (Homocentric [Spheres] or Concerning the Stars) being published in 1538, just five years before De revolutionibus.
Portrait of Girolamo Fracastoro by Titian, c.1528 Source: Wikimedia Commons
Ptolemaeus was by no means the originator of all that is contained in his Mathēmatikē Syntaxis, which is a presentation of accumulated astronomical knowledge produced over a couple of thousand years. The most extreme view held by some historians is that he stole or plagiarised all of it from Hipparchus. Others are less drastic in their judgement. However, there is no doubt that he owed a major debt to Hipparchus, which he partially acknowledges.
The story, however, does not begin with Hipparchus. European astronomy has its principal roots in the astronomy of the Babylonians, who began systematic observations of the celestial sphere because of their astrological belief that the heavens controlled/affected life on Earth. Over the centuries they accumulated a vast amount of astronomical data out of which they developed accurate models to predict the movements of the celestial bodies. Unlike the Greeks, these were not geometrical models but numerical algorithms. They also developed an accurate algorithm to predict lunar eclipses. They also had an algorithm to predict when a solar eclipse might take place but could not predict whether it would or not.
Around five hundred BCE, the Greeks took over both the Babylonian astronomy and astrology. They developed both further and changed from algebraic to geometrical models of the celestial movements. Hipparchus at some point almost certainly produced something resembling the Mathēmatikē Syntaxis, which included, amongst other things, a significant star catalogue, giving the observed positions of numerous stars. Ptolemaeus’ most extreme critics accuse him of having taken his entire star catalogue, of 1022 stars, from Hipparchus and didn’t observe any himself.
Hipparchus’ greatest contribution is that he is credited with having produced the first trigonometrical table. This was a table of chords, whereby in a unit circle the chord of an angle is twice the sine of half of the angle. Ptolemaeus used a standard circle with a diameter of 120 so, chord 𝛉 = 120 sin(𝛉/2). Ptolemy includes a chord table giving values for angles from 0.5 to 180 degrees in 0.5 degree intervals and follows it with an introduction to spherical trigonometry. Improved, first by the Indian astronomer, who introduced the sine, and then by Islamic astronomers, whose work then entered Europe, where it was further developed, trigonometry became an important part of the mathematical canon in the Early Modern Period.
Like the Babylonians, Ptolemaeus’ astronomy was closely related to his astrology. He wrote what would become the standard astrological text, his Tetrabiblos (Τετράβιβλος) ‘four books’, also known in Greek as Apotelesmatiká (Ἀποτελεσματικά). In this work he stated that the science of the stars, astrologia, has two aspects:
One, which is first both in order and in effectiveness, is that whereby we apprehend the aspects of the movements of sun, moon, and stars in relation to each other and to the earth, as they occur from time to time. [The Mathēmatikē Syntaxis]
The second is that in which by means of the natural character of these aspects themselves we investigate the changes which they bring about in that which they surround. [The Tetrabiblos].
In the Early Modern Period the Tetrabiblos was as influential in academic circles as the Mathēmatikē Syntaxis.
Opening page of Tetrabiblos: 15th-century Latin printed edition of the 12th-century translation of Plato of Tivoli; published in Venice by Erhard Ratdolt, 1484.
For the astrologers and other users of astronomical data Ptolemaeus produced his Handy Tables (PtolemaiouProcheiroi kanones), to quote historian of Ancient Greek astronomy, Alexander Jones:
Ptolemy’s Handy Tables, the corpus of astronomical tables that he produced after completing the Almagest, largely adapting them from the tables embedded in that treatise, was a work of immense importance in later antiquity and in the medieval traditions of the Eastern Mediterranean and the Middle East. If the Almagest was the primary transmitter of the theoretical foundations of Greek mathematical astronomy, the Handy Tables was par excellence the practical face of that astronomy.
The Handy Tables were at least as influential as the Mathēmatikē Syntaxis during late antiquity and also during the Islamic Middle Ages.
Ptolemaeus also wrote a cosmology, the Planetary Hypotheses (Greek: Ὑποθέσεις τῶν πλανωμένων, lit. “Hypotheses of the Planets”). This is a physical realisation of the cosmos with his deferent/epicycle models of the planetary orbits embedded in the Aristotelian crystalline spheres. With the orbits determining the inner and outer surfaces of the spheres, Ptolemaeus was thus able to determine the dimensions of the cosmos. He estimated the Sun was at an average distance of 1,210 Earth radii, much too low, as we now know, while the radius of the sphere of the fixed stars was 20,000 times the radius of the Earth.
No Greek of Latin manuscript of the Planetary Hypotheses is known from antiquity, and it was long thought to be a lost work. In the fifteenth century, the Austrian astronomer, Georg von Peuerbach (1423–1461), produced his Theoricae Novae Planetarum (New Planetary Theory), which was the first book printed and published by his pupil Regiomontanus (1436–1476), in 1473, and it was the first ever mathematical/scientific book to be printed with movable type. This work of cosmology was, together with the Peuerbach’s and Regiomontanus’ Epitome of the Almagest, the textbook from which Copernicus learnt his astronomy.The Theoricae Novae Planetarum also presents Ptolemaeus’ deferent/epicycle models of the planetary orbits embedded in the Aristotelian crystalline spheres and was for several hundred years thought to be an original work by Peuerbach.
Peuerbach Theoricae novae planetarum 1473 Source: Wikimedia Commons
In the 1960s a previously unknown Arabic manuscript of Ptolemaeus’ Planetary Hypotheses was discovered, and it was obvious that Peuerbach’s work was an updated version of Ptolemaeus’, just as the Epitome of the Almagest was an updated version of the Almagest.
Ptolemaeus was also authored his Geōgraphikḕ Hyphḗgēsis, which became known in Latin as either the Geographia or Cosmographia, together with the Mathēmatikē Syntaxis and the Tetrabiblos it forms an interrelated trilogy of books. The Geōgraphikḕ Hyphḗgēsis is in different ways related to both books. It and the Mathēmatikē Syntaxis both use a longitude and latitude system; the Mathēmatikē Syntaxis to map the heavens, Geōgraphikḕ Hyphḗgēsis to map the Earth. However, they differ slightly, as Ptolemaeus uses and ecliptical system for the heavens and an equatorial one for the Earth. Hipparchus had used an equatorial system to map the heavens. It is important to notethat the latitude/longitude system of mapping was first devised to map the celestial sphere and only later brought down to Earth to map the globe. Ptolemaeus adds in his Geōgraphikḕ Hyphḗgēsis thatusing astronomy is the best way to determine longitude and latitude for cartography. On a superficial level the three books are connected by the fact that one needs to know the latitude of a subject’s place of birth in order to cast their horoscope. However, for Ptolemaeus the connection between astrology and geography goes much deeper. Ptolemaeus thought that each of the four quarters of the Earth was connected to one of the four astrological triplicities–
Fire (Aries, Leo, Sagittarius), characteristics: hot, dry – the north-west quarter Europe
Earth (Taurus, Virgo, Capricorn), characteristics: cold dry – the south-eastern quarter Greater Asia
Water (Cancer, Scorpio, Pisces) characteristics: cold, wet –the south-western Ancient Libya
These connections determined the general characteristics of each area and the population that lived there.
Jacobus Angelus’ Latin translation of Ptolemaeus’ Geographia Early 15th century Source via Wikimedia Commons
The Geōgraphikḕ Hyphḗgēsis was translated into Arabic by the nineth century and had a major impact on Islamic cartography. However, unlike the Mathēmatikē Syntaxis and the Tetrabiblos it was not translated into Latin in the twelfth century but first in 1406 by Jacobus Angelus. It had a fairly direct influence on European cartography changing the European approach to map making extensively and also very importantly, the need to accurately determine longitude and latitude, done astronomically as Ptolemaeus had recommended, was a major driving force in the attempts to reform astronomy, one aspect of which was Copernicus’ heliocentric system. That reform movement was also driven by a desire for more accurate astronomical data to improve astrological prognostications, due to rising status of astrology particularly in astro-medicine.
Often in popular literature written off as the out dated representative of an ignorant geocentric astronomy, Ptolemaeus’ publications actually had a major impact on and played a significant role in the renewal and modernisation of science in the fifteenth, sixteenth and seventeenth centuries that usually gets called the scientific revolution.
Readers of this blog will know that I’m a Brit living in German. Well, since Brexit only half a Brit, as I’m now a dual national. In the good old pre-Brexit days, I could buy books, have books sent as presents from friend and relatives, and receive review copies from publishers from the UK without any problems. Sometimes they took a long time getting here but they did get here. Since Brexit this has all changed. I have been charged custom’s duty on books that should have been duty free and discovered that there is virtually no way to get my money reimbursed. I have had a Dutch publisher refuse to send me a review copy because their warehouse is in the UK, and they don’t/can’t send books to the EU anymore! In that case the author sent me one of his personal copies. I’ve had one publisher only supply me with a digital copy, ignoring the personal requests of the author to please send me a dead tree copy. In the end, I read and reviewed the digital copy against my better judgement because the book was important to me. Once again, the author trumped up with a personal copy. However, the latest saga of a book sent from the UK to Germany really takes the biscuit, so I have decided to relate the whole sorry affair step by step for your amusement.
Before I start the background:
Aviva Rothman is Associate Professor of History at Case Western University in Cleveland, Ohio. She is a historian of science who focuses on the early modern period and is the author of the highly praised author of Harmony: Kepler on Cosmos, Confession and Community (Chicago University Press, 2017), which is on my infinite reading list. Some time back, I can’t remember exactly when, she contacted me and asked me if I would cast my jaundiced eye over something she had written. People do this you know; I don’t understand why but I’m mostly willing to undertake the task and did so in this case.
This summer Aviva was in Germany with her family and also visited Nürnberg. She asked me if I would do my infamous history of astronomy tour of Nürnberg for her, which of course I was quite happy to do. We spent a happy morning walking around the Renaissance city of Nürnberg, talking history of science, and getting to know each other. During lunch, my tour always ends with lunch, she mentioned that her new book, The Dawn of Modern Cosmology: From Copernicus to Newton (Penguin Classics, 2023), a source book, was due to be published soon and we agreed that she would arrange for me to receive a review copy.
Now the saga starts:
On 19 September I received an email from an editor at Penguin Classics with the following:
I’m an editor at Penguin Classics in the UK – I’m sending you a copy of Aviva Rothman’s new book, The Dawn of Modern Cosmology, by courier, but they’re asking for an EORI number. I just wanted to check if you had one that I can pass on to DHL.
I had no idea what an EORI number is, so I googled it:
Die EORI-Nummer (Economic Operators´ Registration and Identification number – Nummer zur Registrierung und Identifizierung von Wirtschaftsbeteiligten) ersetzt als in der gesamten Europäischen Union gültige Beteiligtenidentifikation die deutsche Zollnummer.
I’m not going to translate the whole definition, but an EORI number is basically the customs registration number for commercial businesses. I immediately wrote a reply email back to the editor explaining that I’m a private person and not a business and so I don’t have an EORI number. The email bounced! I tried a second time and it bounced again. Now, I tried sending a fresh email rather than replying and this email also bounced!
What to do now?
I then wrote an email to Aviva:
I got an email from K*** W****** at Penguin Classics yesterday in which he wrote:
“I’m an editor at Penguin Classics in the UK – I’m sending you a copy of Aviva Rothman’s new book, The Dawn of Modern Cosmology, by courier, but they’re asking for an EORI number. I just wanted to check if you had one that I can pass on to DHL”.
I tried to reply to his email twice and it bounced both times, I then tried emailing him directly instead of replying and that also bounced.
If you have contact with him, could you tell him what happened and also tell him that I, as a private person, don’t have and don’t need an EORI, which is a thing for businesses.
She replied:
I actually just got an email from K*** this morning asking for additional contact info for you. Instead, I passed along your message, and I’ll let you know what he replies. I hope it arrives soon, and would love to hear your thoughts once it does!
I now received a new email from the Penguin Classic’s editor via a different email account:
I’m an editor at Penguin Classics.
Aviva mentioned to me that your emails to me have been bouncing back, so I thought I’d get in touch via Gmail.
I’ve informed DHL via our post room that there’s no need for an EORI given that you’re a private citizen – hopefully that will get things moving now.
I replied to this:
thank you for your latest missive. I think my connection with Aviva is cursed.
I communicate via email with hundreds of people all over the world. My emails have only ever bounced from two addresses, yours and Aviva’s university address! [another story]
I assume that Aviva has already given you my postal address.
This produced the reply from Penguin:
I have a feeling that our spam filter at Penguin is overzealous. Apologies for that.
The package (containing a copy of the book) was sent from here in London a week ago, but it’s currently sitting in a warehouse in Leipzig.
I’ve followed up with the post room here so that DHL can contact you by email if absolutely necessary, and I’ve passed on the message about the EORI number.
Hopefully the next stage will be them delivering the thing to you, but if I hear anything more/need any more details, I’ll be in touch via this email address.
Then on the evening of 21 September I got a telephone call from a very nice lady at DHL in Leipzig trying to determine who or what I am, in order to decide the status of the package that was sitting in her office. After a very pleasant conversation, she informed me that she would be sending me an email which I had to answer before she could send me my book. The email arrived almost instantly:
Guten Tag,
vielen Dank für das freudliche Gespräch.
Um Ihre Sendung als eine Geschenksendung abfertigen zu können, benötigen wir ergänzende Informationen/Angaben. Wir können die Sendung erst abfertigen und ausliefern, wenn uns diese Angaben vorliegen:
eine schriftliche Erklärung, dass es sich um eine Geschenksendung handelt
eine Angabe zum konkreten Inhalt der Sendung mit einer Einzelauflistung aller Artikel/Gegenstände
eine Wertangabe (darf auch geschätzt sein) zu den einzelnen Artikeln/Gegenständen
den vollständigen Vor- und Zunamen des Absenders
die private Adresse des Absenders für die elektronische Zollanmeldung
Bitte halten Sie gegebenenfalls mit dem Versender Rücksprache, um weitere Informationen über den genauen Inhalt der Sendung zu erhalten.
Vielen Dank.
Thank you for the friendly conversation.
In order to process your package as a gift we require the following supplementary information/declarations. We can first clear and deliver your package when these declarations are available:
a written explanation that it is a gift parcel.
a declaration of the actual content of the package with an individual list of all articles.
a declaration of its value (may also be estimated) of all individual articles.
the complete forename and surname of the sender
the private address of the sender for the electronic customs declaration
If necessary, please contact the sender, in order to obtain further information about the exact contents of the package.
Back to Penguin:
Dear K***,
sorry to be a pain but I now need for the German Customs, who have contacted me personally, the exact name and address of the sender as it stands on the parcel. Could you please supply me with this information. I’m going to give up reading books!
He replied:
Sorry about this – I blame Brexit, obviously (I’m Irish).
My name is on the label as a contact (K*** W******, Penguin Press)
The sender address is
Penguin Random House UK 20 Vauxhall Bridge Road London SW1V 2SA
My reply:
Thank you and yes it is Brexit!
I’m British born of British parents, in Clacton-on-Sea of all places but I’m now a dual national German/British thank to Brexit.
I now replied to DHL in Leipzig:
Die Sendung beinhaltet eine Kopie des Buchs, „The Dawn of Modern Cosmology: From Copernicus to Newton“ herausgegeben von Aviva Rothman und erschienen bei Penguin Classics. Professor Rothman hat den Verlag veranlasst mir das Buch als Geschenk zu schicken, weil ich eine frühe Fassung zur Korrektur gelesen habe. Ich soll es auch rezensieren.
Amazon.co.uk für £14,29 = €16,50, am Amazon.com $25,91 = €24,33
Absender:
Penguin Random House UK
20 Vauxhall Bridge Road
London
SW1V 2SA
Kontaktperson: K*** W******, Penguin Press
I’ll leave the translation to the reader as an exercise!
I sent this off to DHL and got an almost immediate computer reply acknowledging receipt of my email and informing me that it would be dealt with in due course and please don’t mail them asking when I would receive my package in the meantime.
We now have the 21 September.
On the 22 September I received the following from Aviva:
K*** passed along your message on Wednesday—did the book ever arrive?
To which I replied:
I haven’t got the book yet which is sitting in Leipzig but I think I’m on the home straight!
The whole thing is developing into a comic opera and I’ve decided I’m going to write a blog post about it, so you’ll just have to wait to get the grisly details.
She replied:
Haha, I look forward to reading it (and I’m sorry it’s been such a lengthy and difficult process!).
Yesterday I got the following from Penguin:
I just wanted to follow up to see if you’ve heard from DHL.
As I was busy, I decided to wait till this afternoon before replying. Then at midday today the book finally arrived! It was posted on 14 September!
The sentence on the label of the package that caused the whole farce was:
SAMPLE DUMMY BOOK NOT FOR RESALE
German customs deduced from this that this was a goods sample and that I was some sort of book dealer!
I informed Aviva that it had arrived:
Just a brief note to say that your wonderful book finally arrived about an hour ago.
The full saga will be appearing on my blog shortly.
She replied:
Yay! [FINALLY!] I look forward to hearing the saga and also your thoughts about the book more generally!
I also informed Penguin:
I put answering your email till this afternoon because I wanted to give a blow by blow account of my exchanges with DHL in Leipzig. However, instead I’m happy to report that Aviva’s book arrived safe and sound in my humble abode about an hour ago!
I have decided to write a blog post detailing every step of this sorry saga and will send you a link when I post it.
The reply:
I’m very glad it arrived.
The moral of this story is that if you send a single book as a present or a review copy from the UK to Germany declare it as a gift on the customs declaration with a value of €20 or less then the customs will let it go through without any problems (probably!).
In the last episode I was rude about the pre-Socratics and today I intend to be rude about another more noted Ancient Greek philosopher. Quite logically, Socrates (c. 470–399 BCE) follows on from the pre-Socratics, who was followed by his pupil Plato (c. 428–348 BCE), in turn followed by his pupil Aristotle (384–322 BCE). Socrates, Plato, and Aristotle the much-heralded triumvirate of Ancient Greek philosophy. Socrates left no writings and most of what we know about him comes from his pupils Plato and Xenophon. He needn’t bother us here as he wasn’t really interested in natural philosophy. To quote James Hannam:
Late in his [Socrates] life, he was scornful of natural philosophers, not least because the concocted a multiplicity of explanations for phenomena and never agreed on anything. From this, he concluded that none of them knew what they were talking about.[1]
Portrait of Socrates. Marble, Roman artwork (1st century), perhaps a copy of a lost bronze statue made by Lysippos. Source: Wikimedia Commons
On the other hand, Plato and Aristotle, are the dynamic duo of the history of European science from the fourth century BCE down to the seventeenth century CE, continually weaving in and out of the main narrative. In the case of Plato, viewed rationally there is very little reason why he should have featured in any way prominently in the European history of science; put in modern terminology Plato was not a scientist and his extensive writings contain next to nothing that could be termed science. However, in a couple of his dialogues he includes aspects of cosmology, mostly borrowed from the pre-Socratics, that continued to feature prominently down the centuries, attached to the name Plato.
Plato holding his Timaeus, detail from the Vatican fresco The School of Athens by Raphael Source: Wikimedia Commons
Plato’s acceptance of mathematics as a medium to describe natural philosophy (although it’s not something that he did himself) in contrast to Aristotle’s rejection of mathematics (because the objects of mathematics were not part of nature) led earlier historians to claim that the mathematization of science, in the early modern period, a prominent feature of the so-called scientific revolution, came about through a change from qualitative Aristotelian philosophy to a neo-Platonic quantitative philosophy. I personally, as I explained in my Renaissance Science series, think there are other more significant drivers of the mathematization of the scientific disciplines in the early modern period, although a more favourable view of Platonic philosophy might have played a minor role in that transition.
Plato’s first significant contribution to the scientific debate was the fact that he provides the earliest extant reference to a spherical earth. Previously, all advanced cultures had assumed that the earth was flat. In the Phaedo, Socrates talking about reading Anaxagoras “I assumed that [Anaxagoras] would begin by informing us whether the Earth is flat or round, and then he’d explain why it had to be that way because that was what was better.”[2] We don’t know who first hypothesised that the world was a sphere, Diogenes Laertius (fl. first half 3rd century CE), writing more than five hundred years later says it was Parmenides but he also said it was Pythagoras, Hesiod, and Anaximander. Remember why I’m sceptical about the things attributed to the pre-Socratics. It is obvious from the Plato quote that a discussion of the hypothesis was already taking place, when he wrote the Phaedo, and it is possible that he had the idea from the Pythagorean, Philolaus (c. 470–c. 385 BCE), but nothing is known for certain. Later in the Phaedo, Socrates says, “In the first place the Earth is spherical and in the centre of the heavens. It needs neither air nor any other such force to keep it from falling. The uniformity of the heavens and the equilibrium of the Earth itself are sufficient to support it.” Although spoken by Socrates it is fairly obvious that Plato is presenting his own view here; a view that adopted by Aristotle would become standard in European cosmology.
The nearest that Plato comes to a scientific text is in his Timaeus, a dialogue on the nature of the world, but like all his other works really a dialogue on ethics. Far from being the, from philosophers, much heralded logos in place of mythos, the Timaeus is a highly mythological tale about the creation of the world by a demiurge or divine craftsman. I’m not going to give an account of the metaphysical twists and turns of the Timaeus and simply filter out those ideas that found its way into mainstream European natural philosophical. One almost bizarre aspect of the dialogue is that although Timaeus gives a fairly detailed explanation of the creation of the Earth by the demiurge, he adds that one “should not look for anything more than a likely story.”
The universe is a sphere with the Earth at its centre. The Earth is not explicitly described as a sphere although it implies that it is a sphere. The demiurge creates the Earth out of Empedocles’ four element–earth, water, air, fire–in varying combinations. For Plato, with his belief in a mathematical world, the four elements now have the forms of four of the regular geometrical solids– Fire-Tetrahedron, Air-Octahedron, Water–Icosahedron, Earth–Cube–a concept that remains in discussion down to at least Kepler.
For Plato, once again borrowing from Empedocles, the planets orbit the Earth, at the centre of the universe, in circular orbits at a uniform speed. Another concept that continued to be largely adhered to down to the seventeenth century. Famously, Galileo in his Dialogo held firm to Plato’s circular orbits, despite the work of Kepler showing the orbits of the planets to be ellipses, which vary in speed.
Adhering to the conditions prescribed by Plato, Eudoxus of Cnidus (c. 480–c. 355 BCE), who is said to have been a student of the Pythagorean Archytas (c. 425–c. 350 BCE) and I member of Plato’s school, the Academy, constructed the earliest known Greek geometrical model of the cosmos, a homocentric or concentric spheres model. Each celestial body has a set of nested spheres with the Earth as a common centre but differing axels. But careful choice of the diameter of the spheres and the position of the axels, Eudoxus was able to create a reasonable model of the seeming irrational movement of the planets using only uniform circular motion.
In most modern reconstructions of the Eudoxan model, the Moon is assigned three spheres:
The outermost rotates westward once in 24 hours, explaining rising and setting.
The second rotates eastward once in a month, explaining the monthly motion of the Moon through the zodiac.
The third also completes its revolution in a month, but its axis is tilted at a slightly different angle, explaining motion in latitude (deviation from the ecliptic), and the motion of the lunar nodes.
The Sun is also assigned three spheres. The second completes its motion in a year instead of a month. The inclusion of a third sphere implies that Eudoxus mistakenly believed that the Sun had motion in latitude.
The five visible planets (Mercury, Venus, Mars, Jupiter, and Saturn) are assigned four spheres each:
The outermost explains the daily motion.
The second explains the planet’s motion through the zodiac.
The third and fourth together explain retrogradation, when a planet appears to slow down, then briefly reverse its motion through the zodiac. By inclining the axes of the two spheres with respect to each other, and rotating them in opposite directions but with equal periods, Eudoxus could make a point on the inner sphere trace out a figure-eight shape, or hippopede.
Wikipedia
Simplified schematic of Eudoxus’s concentric sphere model. The Earth (blue) sits in the center of the nested spheres that control the motion of the planet (red). The planet is shown embedded in a tilted sphere that carries it around the zodiac. This sphere is nested in a sphere that rotates daily on the polar axis of the fixed stars.When all four spheres start rotating on their axes, the planet will appear to move along a complex path that resembles its observed motion across the sky.Source
Callippus (c. 370–c. 300 BCE), a student of Eudoxus and of the Academy, extended Eudoxus’ model, adding seven spheres to the original 27, one for the sphere of fixed stars. As we will see, this was the model that Aristotle, with modification, adopted, but which was already rejected by other astronomers in antiquity. However, it enjoyed several revivals over the centuries.
Benjamin Jowett (1817–1893), a Plato expert and translator said, “Of all the writings of Plato, the Timaeus is the most obscure and repulsive to the modern reader.” In the normal run of events the Timaeus should not have had much impact on the unfolding of the history of science. Unfortunately, in late antiquity and the early medieval period the only work of Plato that was widely available to a Latin reading audience was the partial translation of the Timaeus by Cicero (106–43 BCE) and the almost complete translation by Calcidius (late 4. Century CE). George Sarton (1884–1956) one of the founders of the modern history of science in the twentieth century said this about the Timaeus, in his A History of Science (Harvard University Press, 1959)
The influence of Timaeus upon later times was enormous and essentially evil. A large portion of Timaeus had been translated into Latin by Chalcidius, and that translation remained for over eight centuries the only Platonic text known in the Latin West. Yet the fame of Plato had reached them, and thus the Latin Timaeus became a kind of Platonic evangel which many scholars were ready to interpret literally. The scientific perversities of Timaeus were mistaken for scientific truths. I cannot mention any other work whose influence was more mischievous, except the Revelations of John the Divine. The apocalypse, however, was accepted as a religious book, the Timaeus as a scientific one; errors and superstition are never more dangerous than when offered to us under the cloak of science.
[1] James Hannam, The Globe: How the Earth Became Round, Reaktion Books, London, 2023 p. 74
The Renaissance is a period of intense mathematical activity, but it is not mathematics as somebody who has studied mathematics at school today would recognise it but rather practical mathematics, that is mathematics developed and utilised within a particular practical field of work or study. It should be emphasised that this is not what we now know as applied mathematics, which is, as its name suggests, the application of an area of pure mathematics to the solution of problems in other fields. Practical mathematics is, as already stated above, mathematics that evolves whilst working on problems in a variety of field, which are susceptible to mathematical solutions. This is, of course, the province of the Renaissance Mathematicus the eponym of this blog, and as I wrote in an earlier blog post, Why Mathematicus?
If we pull all of this together our Renaissance mathematicus is an astrologer, astronomer, mathematician, geographer, cartographer, surveyor, architect, engineer, instrument designer and maker, and globe maker. This long list of functions with its strong emphasis on practical applications of knowledge means that it is common historical practice to refer to Renaissance mathematici as mathematical practitioners rather than mathematicians.
One major area of practical mathematics that bloomed and flourished in the Renaissance was surveying, as I described in detail in a post in my Renaissance science series. The root word survey has over the centuries acquired many different meanings, but it has a visual origin from the Medieval Latin supervidere “oversee, inspect,” from Latin super “over” plus videre “to see”. Renaissance land surveying is totally dependent on line-of-sight observations. The legendary straight Roman roads were so straight because the engineers laid them out from high point to high point by line of sight and then instead of going around obstacles cut through them, bridged them or whatever. Triangulation, the major advance in surveying that emerged during the Renaissance, also relies on direct line-of-sight observation from high point to high point to construct its triangles.
What, however, happens when you need to survey a territory were you literally can’t make direct line-of-sight observations? This is exactly the problem that had to be solved with the massive expansion in metal ore mining that took place during the Renaissance in eastern Europe. To solve it the miners developed their own form of practical mathematics that became known as Markscheiderkunst and its practitioners as Markscheider. Thomas Morel has written a fascinating and highly informative book, Underground Mathematics: Craft Culture and Knowledge Production in Early Modern Europe[1] that investigates the origins and evolution of this branch of practical mathematics from its origins up to the beginning of the nineteenth century.
The terms Markscheider and Markscheidekunst are German and Morel’s book concentrates on the mining history of the mining regions in Eastern Germany because that is where the then modern mining industry developed and as Morel explains the knowledge that the German miners developed was then exported all over Europe. If you wanted to start your own mining endeavours, you imported German miners. As I explained in an earlier post this is why Nürnberg developed into a major centre for the manufacture of pencils. Miners in the service of Nürnberg companies were drafted into Borrowdale in Cumbria to exploit the recently, by accident, discovered graphite deposits in the sixteenth century and brought back the knowledge of this new writing material with them when they returned home to Nürnberg.
The Markscheidekunst, ‘the art of setting limits’, comes from the German words Mark, here with the meaning of boundary, and Scheiden meaning separate, so it means the setting of boundaries, originally between mining claims and the Markscheider is the surveyor, who determines those boundaries. On the surface, no different to other surveying but determining the same boundaries under ground becomes a whole different problem, which led to the Latin translation of Markscheidekunst, geometria subterranea.
The obvious difference between the German Markscheidekunst a term of the Bergmannsprache (the miners’ dialect) and the scholars’ Latin term geometria subterranean displays a divergence between the two worlds that illustrates one of the central theses of Morel’s narrative, which begins in the first chapter.
Morel starts there where somebody, like myself, with only a superficial knowledge of Renaissance metal ore mining would expect him to start with Agricola’s De Re Metallica. The first chapter covers both the publications on mining of Georgius Agricola (1494–1555) and of Erasmus Reinhold the Younger (1538–1592), the son of the famous astronomer, Erasmus Reinhold the Elder (1511–1553). Both authors were humanist Renaissance scholars writing in Latin and Morel shows that their presentations of underground surveying don’t match with the reality of what the Markscheider were actually doing. More generally the work of the Markscheider in the Bergmannsprache was largely incomprehensible to the educated scholars.
Morel’s second chapter goes into the detail of how the Markscheider actually went about their work. Firstly, how mining claims were staked out above ground and secondly how they measured and mapped the underground mine galleries, which followed the twist and turns of the veins of metal ore. Also, how they ensured that the underground galleries didn’t extend beyond the boundaries of the claim staked out on the surface. The Markscheider developed a practical mathematical culture that was substantially different from the learned mathematical culture of the university-trained scholars. In the early decades, the world of the Markscheider was, like other trades, one of an oral tradition with apprentices learning the trade orally from a master, who passed on the knowledge and secrets of the trade. Morel traces the evolution of this oral tradition and also the failure of university trained mathematicians to comprehend it
Despite their differences to their learned colleagues in the sixteenth century, because of the economic importance of the metal ore mines the Markscheider acquired a very high social status and achieved standing at the courts in the mining districts. They became advisers to the aristocratic rulers and their expertise was requested and applied in other areas of mathematical measurement such as forestry. All of this is dealt with in detail in Morel’s third chapter.
The seventeenth century saw the development of a scribal tradition with the appearance of the manuscript Geometria subterranea or New Subterranean Geometry, allegedly written by the mining official Balthasar Rösler (1605–1673). These manuscripts evolved over the century as did the methods of surveying and the instruments used by the mine surveyors. Surprisingly this literature remained in manuscript form for most of the century only appearing in print form with Nicolaus Voigtel’s Geometria subterranea in 1686. In his fourth chapter, Morel gives a detailed analysis of this manuscript tradition and offers and explanation as to why it remained unprinted, which has to do with the way these manuscripts were used to train the apprentice surveyors.
Chapter five takes into the late seventeenth early eighteenth centuries, following the publication of Nicolaus Voigtel’s Geometria subterranea and the life and work of Abraham von Schönberg (1640–1711), Captain-general of the Saxon mining administration, and his endeavours to revive the local mining districts in the aftermath of the Thirty Years War. Central to Schönberg’s efforts was the development of the mining map of which the most spectacular example in the Freiberga subterranea, a gigantic cartography of the Ore Mountains running continuously over several hundred sheets. Ordered by Schönberg and realised by the surveyor and mine inspector, Johann Berger (1649–1695).
First sheet of the Freiberga subterranea
Morel’s sixth chapter takes the reader into the eighteenth century and the attempts to raise the academic level of the mathematical knowledge of the mine surveyors and engineers leading up to the establishment of the Bergakademien (in English, mining academies). As Morel explains these were initially not as successfully as might be supposed. Morel takes his reader through the problems and evolution of these schools for mine surveyors. He also follows the significant developments made outside such institutions, particularly by Johann Andreas Scheidhauer (1718–1784). A recurring theme is still the inability of university educated mathematicians to truly comprehend the work of the practical mathematicians in the mining industry. As Morel writes at the beginning of his summary of this chapter, “Teaching a mathematics truly useful for the running of ore mines was a daunting task that underwent important transformations during the eighteenth century.”
Morel’s final chapter is dedicated to the story of the Deep-George Tunnel, a 10 km long drainage tunnel at a depth of 284 m, which connected up numerous mines in the Harz mining district. An extraordinary project for its times. Morel shows how the planning, for this massive undertaking, was based on data recording techniques for the run of the mine galleries developed in the preceding centuries rather than new surveying. The theoretical planning was on a level not previously seen in ore mine surveying. Morel also describes in detail an interesting encounter between the practical mining engineers and a theoretical scientist. The Swiss scholar Jean-André Deluc (1727–1817) visited the area in 1776, just before the start of the project, to test the calibration of his barometers to determine altitude by descending into the depths of the mine, having previously calibrated them by ascending mountains. Impressed by the undertakings of the mining engineers he returned several times over the years observing the progress of the tunnel and reporting what he observed to the Royal Society of London.
The story of the Deep-George Tunnel is a very fitting conclusion to Morel’s narrative of the evolution of the practical mathematical discipline of subterranean surveying in the ore mines of eastern Germany. The breadth and depth of Morel’s narrative is quite extraordinary and my very brief outlines of the chapters in no way does it justice, to do so I would have to write a review as long as his book. Morel is an excellent stylist, and his book is a real pleasure to read, a rare achievement for a highly technical historical text. There are extensive footnotes packed with sources and information for further reading. There is an almost thirty-page bibliography of manuscript, printed primary, and printed secondary sources, and the book closes with an excellent index. The book is nicely illustrated with grayscale reproductions of original diagrams.
This is truly a first-class text on an, until now, relatively neglected branch of practical mathematics, which should appeal to anyone interested in the history of mathematics or the history of mining. It will also appeal to anybody interested in a prime example of the narrative history of a technical disciple that combines mathematics, technology, politics and economics.
[1] Thomas Morel, Underground Mathematics: Craft Culture and Knowledge Production in Early Modern Europe, Cambridge University Press, 2023.
Today we celebrate the completion of the fourteenth journey around the Sun by the Renaissance Mathematicus. Yes folks, the Renaissance Mathematicus has now been dispensing history of science gems for fourteen long years. It seems that he’s here to stay, so what has he got to say for himself on this auspicious occasion?
Unlike thirteen, a year ago, or twelve, the year before, at first glance fourteen appears to be a rather boring number, not immediately suggesting a topic that we could spin out into today’s birthday blog post. However, appearances are deceptive. Fourteen delivers up a mathematical object that connects Archimedes, Luca Pacioli, Leonardo da Vinci, linear perspective, indirectly Paracelsus, Wenzel Jamnitzer, and Johannes Kepler all of them very much grist to the Renaissance Mathematicus mill. So, what is this wonderful mathematical object? It’s the truncated octahedron!
I can already hear a number of my readers muttering, what is a truncated octahedron when it’s at home? A truncated octahedron is a regular octahedron, which has six right square pyramids removed, one from each vertex. The resulting semi-regular solid has fourteen faces–eight hexagons and six squares.
Truncated octahedron Source: Wikimedia CommonsTruncated octahedron net Source: Wikimedia CommonsTruncated octahedron construction Source: Wikimedia Commons
There are five regular geometrical solids, known as the Platonic solids–tetrahedron (4 faces), cube (6 faces), octahedron (8 faces), dodecahedron (12 faces), Icosahedron (20 faces).
In geometry a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidian space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (allangles congruent and all edges congruent), and the same number of faces meet at each vertex. There are only five such polyhedra. (Wikipedia)
Famously, in his Mysterium Cosmographicum, Kepler argued that there were and only could be six planets in his heliocentric system because there were separated by the five Platonic solid of which there could only be five.
Kepler’s Platonic solids model of the Solar System from Mysterium Cosmographicum Source: Wikipedia Commons
The proof that there are only five Platonic solids is actually fairly easy, so I’ll leave it for my readers as an exercise.
They are known as the Platonic solids because, in his Timaeus, Plato hypothesized that the four classical elements were made of the first four–Earth/Cube, Water/Icosahedron, Air/Octahedron, Fire/Tetrahedron. Much later the Dodecahedron was attributed Aristotle’s Aether.
Kepler’s presentation of the five Platonic solids as the five ancient elements
There are thirteen semi-regular solids, known as the Archimedean solids. These are convex uniform polyhedra composed of regular polygons meeting in identical vertices, excluding the five Platonic solids. Like the truncated octahedron they are all basically modified forms of the Platonic solids. They are known as the Archimedean solids because Archimedes is said by Pappus to have discussed them in a now-lost work.
Following the discovery of linear perspective in the Renaissance it because a standard exercise for mathematici and artists to display their talent by producing three dimensional drawings of regular and semi-regular solids with the correct perspective.
Luca Pacioli (c.1447–1517) was one of the most important and influential Renaissance mathematici.
Portrait of Luca Pacioli attributed to Jacopo de Barbari Source: Wikimedia Commons
He wrote and published two major works, the first of which was his Summa de arithmetica, geometria, proportioni et proportionalita (Summary of arithmetic, geometry, proportions and proportionality) published in 1494.
It is a book on mathematical proportions and their application to geometry, to linear perspective and to architecture. The third part of this book is a translation into Italian of Piero della Francesca’s Latin book De quinque corpibus regulaibus [On [the] Five Regular Solids], without acknowledgement.
Title page of De quinque corporibus regularibus Source: Wikimedia Commons
There are two sections of illustration at the end of the book, the first section is letters of the alphabet drawn by Pacioli and the second section contains woodcuts, including the regular and semi-regular solids, drawn by Pacioli’s friend and mathematics student Leonardo da Vinci (1542–1519), which include both a solid and a skeletal drawing of our truncated octahedron.
Leonardo’s truncated octahedron solid drawing
The only authenticated portrait of Paracelsus (c.1493–1541) was made by the Nürnberger engraver, mathematician, and cartographer Augustin Hirschvogel (1503–1553).
Das ist Ein fleyssige Fürweysung, Wie die Fünff Regulirten Cörper, darvon Plato inn Timaeo, Unnd Euclides inn sein Elementis schreibt, etc. Durch einen sonderlichen, newen, behenden und gerechten weg, der vor nie im gebrauch ist gesehen worden, gar Künstlich inn die Perspectiva gebracht …
This is a studious demonstration, how the five regular solids, of which Plato in his Timaeus and Euclid in his Elements, wrote, etc. through a special, new, adroit, and correct way, that has never been seen in use before, brought artistically into perspective…
Jamnitzer, who covers far more than the five Platonic solids, presents each solid in its pure form and then develops it in numerous fascinating geometrical directions. Our truncated octahedron is one of the developments of the octahedron and is in turn geometrically developed.
SourceTruncated octahedron upper leftTruncated octahedron upper left
Johannes Kepler (1571–1630) devoted the first two books of his Harmonices mundi libri V(TheHarmony of the World in Five Books), published in 1619, to geometry.
Source: Wikimedia Commons
The first book dealt with the construction of plane figures and contains, amongst many other things, his criticism that Dürer construction of a heptagon in his Underweysung der Messung mit dem Zirkel und Richtscheyt (Instruction in Measurement with Compass and Straightedge), published in 1525, is that it is at best a good approximation. The second book deals with the solids, including the Archimedean semi-regular solids, and contains the earliest known proof that there can only be thirteen of them. He also gave them the names that they still bear today. On the truncated octahedron he writes:
There are thirteen solid congruences which are perfect in an inferior degree. From these thirteen we obtain the Archimedean solids.[1]
[…]
Since the two kinds of plane figure will no longer include trigons the smallest figure involved will now be a tetragon. Three tetragon angles with one larger angle come to more than four right angles and by definition IX we know we cannot combine two tetragon angles with one larger angle, since only two of the larger figures will occur in the resultant solid. The case of one tetragon angle combined with two pentagon angles is rejected, by XXIII, but one tetragon angle will go with two hexagon angles, and six tetragons and eight hexagons will fit together to make a tessarkaedecahedron which I call a truncated octahedron (Octaëdron truncum). It is shown as number 5 in the diagram below.[2]
The fourteen faces of the truncated octahedron stand here for fourteen years of this blog and maybe fourteen facets of the Renaissance mathematicus, who is definitely at best semi-regular.
If your philosophy of [scientific] history claims that the sequence should have been A→B→C, and it is C→A→B, then your philosophy of history is wrong. You have to take the data of history seriously.
John S. Wilkins 30th August 2009
Culture is part of the unholy trinity—culture, chaos, and cock-up—which roam through our versions of history, substituting for traditional theories of causation. – Filipe Fernández–Armesto “Pathfinders: A Global History of Exploration”
The Renaissance Mathematicus 