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An open letter to an author

Dear Yuval,

if I may? Sometime around the publication in English of your trendy mega bestseller, Sapiens, I read something from you, I can’t remember if it was an essay or an extract from the book, on the Scientific Revolution, as part of the extensive sales campaign for your publication. To say the least, I was, to put it mildly, totally underwhelmed and decided that I really didn’t need to read your book. Since then whenever the subject of your book came up in conversations or on the Internet I made disparaging comments about your abilities as a historian of Early Modern science. Recently it occurred to me that I might be being somewhat unfair, my comments being based on a half remembered short piece of writing and that maybe I ought to give you a second chance. Eventually I ordered your book through interlibrary loan, my university library apparently doesn’t have a copy. When it arrived I sat down to read the Fourth Section of the book entitled The Scientific Revolution. You must excuse me but I have so much that I want to read that I don’t really have time to read your whole book.

The first page of waffle about time travelling peasants and battleships didn’t really impress me but then on the second page I stumbled across the following:

In 1500, few cities had more than 100,000 inhabitants. Most buildings were constructed of mud, wood and straw; a three-story building was a skyscraper. The streets were rutted dirt tracks, dusty in summer and muddy in winter, plied by pedestrians, horses, goats, chickens and a few carts. The most common urban noises were human and animal voices, along with the occasional hammer and saw. At sunset, the cityscape went black, with only an occasional candle or torch flickering in the gloom.

The evocative picture that you paint with your words in this paragraph reminds me of the Hollywood B-movie visions of medieval hovels and unwashed peasants that informed my childhood and in my opinion has about as much truth content as those movies of yore.

I am a historian of Renaissance science, hence the name of this blog, and I live just up the road from the German, Renaissance city of Nürnberg, where, belonging as I do the an active group of local historians, I conduct on a fairly regular basis guided tours of the history of astronomy of that city most, but not all, of which revolves around the year 1500, plus or minus 50 years. For your edification and education I would now like to take you on part of that tour to show what a Middle European city really looked like in 1500.

Before I start I will grant that few European cities had more than 100,000 inhabitants; Nürnberg, then the second biggest German city, only had a population of 40,000. Of course there were much bigger cities in other parts of the world, Middle East, India, China but as the entire world population has been estimated to lay between 400 and 500 million in 1500, it is not surprising that the major cities were much smaller than those of today. Scaling up proportionally a city of 40,000 in 1500 with a world population of 500 million is equivalent to a city of more than 500,000 in today’s world of 7,000 million inhabitants, slightly less than Nürnberg’s current population.

I always start my tour with this sundial, which was created in 1502.

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Lorenzkirche Sundial Source: Astronomie in Nürnberg

As you can see it is a quite sophisticated sundial and if you know how, you can read the time on it in three different ways, from sunrise, from midday and according to the Great Nürnberger clock: a system between the medieval local time system and our equinoctial hours: A bit beyond the primitive culture that you sketch. I hear you muttering but what about clocks. We’ll get to one of those a bit later.

The sundial is on the side of the Lorenzkirche, one of Nürnberg’s two parish churches started in 1250 and finished in 1477.

Nürnberg St. Lorenz Türme von Westen

Source: Wikimedia Commons

As you can see it’s a rather impressive sandstone building with a slate roof, as were most of the city buildings in 1500. By the way, the streets were also paved. No dirt tracks here.

Our next station is the Heilige-Geist-Spital built in 1399 as an old peoples residence, a function it still fulfils today.

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Heilige-Geist-Spital Source: Wikimedia Commons

Moving on, we come to the Market Place and the Frauenkirche built between 1352-1362.

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Frauenkirche Source: Wikimedia Commons

The mechanical clock on the facade was built in 1509.

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Source: Wikimedia Commons

The ball above the clock shows the phases of the moon, still accurate today. At twelve-noon everyday there is a complex mechanical display with fanfares by the trumpeters, drum rolls and bell ringing. This is followed by the seven Electors circling the Emperor in the middle, three times. Tourists from all over the world come to Nürnberg to witness this spectacle.

I like this 19th-century picture showing the Schöner Brunnen (Beautiful Fountain), also on the Market Place, which was built between 1385-1396.

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Here it is in all its glory, today.

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Schöner Brunnen. In the backgrounfd you can see the towers of the other parish church St. Sebald (14th century) Source: Wikimedia Commons

You might like this house, it was the home of a local artisan, Albrecht Dürer (1471–1525), you might have heard of him?

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Source: Wikimedia Commons

In 1500, Nürnberg was a major industrial city, producing a very wide range of metal products, as well as being a leading European trading centre. In fact it was one of the biggest centres in Europe for the production of everything that could be made out of metal. For example, the Nürnberg craftsmen received an order from the Emperor, Charles V (1500–1558), for five thousand suits of armour, so we can assume that there was quite a lot of noise on the streets on the city. Nürnberg traded on a large scale with much of Europe. It was not unusual for the traders to attend the Frankfurter Fair with a waggon train of five hundred waggons

You can get a good overall impression of the city from this illustration out of the Schedelsche Weltchronik (known in English as the Nuremberg Chronicle), the world’s first printed encyclopaedia, printed and published in Nürnberg in 1493.

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Nürnberg as depicted in the Nuremberg Chronicles 1493

By now I hope you will realise that the real historical Nürnberg in 1500 was radically different from your fairy tale description of a city in 1500. Having recovered from having read the paragraph reproduced above, I tried to persevere with your book but having come across several more equally dubious paragraphs in the next few pages, I must honestly say that I can’t be bothered. I have better things to do with my time. I can’t claim that this is a review of your book but I certainly won’t be recommending it to anybody, anytime soon.

No hard feelings

Thony

 

 

 

 

 

 

 

 

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

Part I  Part II Part III

There is general agreement amongst historians of science that a major factor in the emergence of modern science in general and modern astronomy in particular was the (re)invention of moveable type printing and the arrival of the printed book in the middle of the fifteenth century. I say reinvention because moveable type printing emerged twice before in China in the eleventh century CE and in Korea in the fourteenth century, as I explained in an earlier post. For a long time it was a commonplace in the historical narrative that the printed book, like gunpowder and the compass, was a Chinese invention but extensive long-term research has failed to produce any evidence of a technology transfer and it is now thought that Johannes Gutenberg’s was an independent invention. Even within Europe Gutenberg was not the first to experiment with moveable type and his real invention was the printing press, inclusive printing ink.

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Book Printers from Jost Amman  Professionals and Craftsmen

Less than twenty years after Gutenberg published his Bible, Regiomontanus printed and published the first printed astronomy book Peuerbach’s Theoricae Novae Planetarum (Nürnberg, 1473) followed by a handful of other astronomy/astrology books. Unfortunately he died before he could publish their Epytoma in almagesti Ptolemei, which was first published by Ratdolt in Venice in 1496. Both titles became standard astronomy textbooks throughout Europe for more than one hundred years. Famously also being the texts from which Copernicus learnt his astronomy and cosmology.

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Theoricae Novae Planetarum Source: Wikimedia Commons

This marked the start of a wave of printed astronomy/astrology books throughout the sixteenth and seventeenth centuries including the works of Apian, Copernicus, Tycho, Kepler, Galileo and many other less well-known figures. Printing made reliable, consistent text available to a wide circle of readers. Whereas a copy of a manuscript in Copenhagen might well have serious deviations compared with a manuscript of the same work in Venice, printed copies of a book were in theory the same wherever their owners lived and worked.

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The Astronomer from Jost Amman’s Professionals and Craftsmen Source: Wikimedia Commons

As I pointed out in a reply to an earlier comment in this series the printed great works of astronomy, such as Copernicus’ De revolutionibusor Apian’s Astronomicum Caesareum, would have been way beyond the pocket of the average university student of the period but the professional astronomers, their patron and the institutions could and did acquire copies thus making them, at least potentially, accessible to those students. Interestingly Kepler bought a second hand copy of Copernicus’ De revolutionibus when he was still a student.

However, printing advanced the general dissemination and progress of astronomy and its related fields through purpose written textbooks. The most obvious example of this is Peter Apian’s Cosmographia, originally published by the author in Landshut in 1524. This was a basic introduction to astronomy, astrology, surveying, cartography etc. In total, over the sixteenth century, the book went through thirty-two expanded and improved editions all of which were, somewhat strangely, edited and published by Gemma Frisius and not Apian. Similar textbooks were produced by Oronce Fine, Michael Mästlin and many other sixteenth century mathematical authors.

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Title page of Apian’s Cosmpgraphia

It was not just major monographs that profited from the invention of movable type printing. Such astronomical/astrological tools as ephemerides benefited from a certain level of consistency given by print as opposed to hand written manuscripts with their copying errors. In fact a large part of Regiomontanus’ posthumous reputation was based on his printed ephemeris, one of the few books he was able to publish before his untimely demise.

Regiomontanus also led the way in producing printed astronomical/astrological calendars, volumes much in demand from all those working in the wider field of astronomy. In fact astronomical/astrological ephemera of all types–calendars, prognostica, single-sheet wall calendars, almanacs–became a mainstay of the early printing industry providing a much need flow of ready cash.

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Regiomontanus Calendar Source: University of Glasgow

To give an idea of the scope of this activity, one of the calendars of Simon Marius (1573–1625), which had to be withdrawn because of political complaints by the local authorities, was said by the printer publisher to have had an edition of 12,000. Marius was only a small local astrologer; the editions of the calendars and prognostica of an Apian or a Kepler would have been much larger. An astronomical monograph, such as De revolutionibus, would have had high production costs and an edition of maybe 500. It would take several years before it turned a profit for the printer publisher if at all. The author got nothing for his troubles. A calendar (wall or pocket), prognostica or almanac had comparatively low production costs, a large edition and if the author was established sold very rapidly. The profits were usually shared fifty-fifty between the printer and the author, a reliable stream of income for both parties. Gutenberg raised some of the finance for his Bible by printing and issuing an astro-medical single-sheet wall calendar.

In an important work, Astrology and the Popular Press: English Almanacs 1500–1800historian Bernard Capp showed that astrological ephemera made up by far and away the largest sector of publishing in the early centuries of printing and more importantly that the editorial sections of the cheap almanacs were one of the major sources for disseminating the latest developments in astronomy, in particular, in the seventeenth century, heliocentricity.

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Almanack by John Tulley, 1692. Book exhibited in the Cambridge Public Library, Cambridge, Massachusetts Source: Wikimedia Commons

Along with the development of moving type printing came an increased use of illustrations leading to a rapid development in the techniques used to produce them–woodblock printing, copperplate engraving and etching.

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Woodblock cutter Jost Amman’s Professionals and Craftsmen Source: Wikimedia Commons

These techniques were then extended to other field related to astronomy, cartography and globe making. Printed copies of Ptolemaeus’ Geographia with maps were already being printed in the last quarter of the fifteenth century. There also quickly developed a market for large scale printed wall maps, the most famous early example being Waldseemüller’s world map that gave the very recently discovered fourth part of the world the name America after Amerigo Vespucci (1454–1512). Waldseemüller also seems to have printed the first terrestrial globe, a small globe containing the same map of the world. Unfortunately we only have a small number of printed globe gores and no surviving finished globes.

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Waldseemüller World Map 1507 (Wikipedia Commons)

Johannes Schöner (1477–1547) was the first to start producing serial printed globes, his first terrestrial globe in 1515 and the matching celestial globe in 1517, establishing a tradition for matching pairs of printed globes that continued until the end of the nineteenth century. Judging by comments from his correspondence his globe printing enterprise was both very successful and very lucrative. Gemma Frisius (1508–1555) took up the baton producing printed globes to be sold with reprints of Schöner’s cosmographia, the descriptive book sold with each globe to explain how to use it. Gemma’s assistant was Gerhard Mercator, who would go on to become the most successful printed globe maker of the second half of the sixteenth century. Mercator’s globes inspired both the great Dutch cartographical houses of Hondius and Blaeu, who would dominate the European globe making and cartography industry in the seventeenth century. England’s first commercial globe printer, Joseph Moxon (1627–1691) learnt his handwork from Willem Janszoon Blaeu (c. 1570–1630). Printed globe making was big business in the sixteenth and seventeenth centuries and the globes were used to teach both astronomy and astrology.

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Pair of globes by Gerard Mercator (Globe Museum, Austrian National Library).

Of course all of the above applies equally well to printed maps. Along with the demand for large wall maps, a market developed for collections of printed maps, what we now call atlases. Bound collection of manuscript maps existed before the invention of printing but being the product of hundreds of hours of manual labour these tended to be art treasures for rich patrons rather than practical books for everyday usage. The man, who did most to change this was Abraham Ortelius (1527–1598), whose Theatrum Orbis Terrarum, a bound, standardised, collection of maps, produced especially for traders first published in 1570 was a runaway success. Initial less successful was the more academic Atlas of his good friend and rival Gerhard Mercator. However, both publications laid the foundations for the commercial success of the cartographical publications of Blaeu and Hondius.

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Theatrum Orbis Terrarum Title Page Source: Wikimedia Commons

A somewhat different approach was taken by Sebastian Münster (1488–1552), with his Cosmographia, first published in 1544, which was not just a collection of maps but also a full geographical and historical description of the world. In its numerous editions it was almost certainly the biggest selling book in the sixteenth century.

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Title page of the first edition of Münster’s Cosmographia Source: Wikimedia Commons

Like nearly-all-the-other globe makers and cartographers described here Münster was an astrologer and astronomer. Other astrologer/astronomers in the sixteenth century, who were also commercially successful as cartographers were Peter and Philipp Apian, Oronce Fine and Michael Mästlin.

It should be clear from the above that the advent of movable type printing had a very large impact on the dissemination of astronomy and its related fields at the same time raising its status in the Early Modern Period in Europe and bringing it to a much wider audience.

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

You can read Part I here

Before we progress we need to take stock and deal with a couple of points that came up in a comment to Part I. This series is about the factors that led to the emergence of heliocentricity in Europe in the Early Modern Period. It doesn’t deal with any of the factors from earlier periods and other cultures that also explicitly and implicitly flowed into European astronomy. If one were to include all of those, it would be a total history of western astronomy that doesn’t even start in the West but in Babylon in about 2000 BCE. That is not what I intend to write and I won’t be doing so.

The other appears to contradict what I said above. At my starting point circa 1400 CE people became aware of a need to increase their usage of mathematical astronomy for a number of reasons that I sketched in Part I. Ptolemaic mathematical astronomy had been available in Europe in two Latin translations, the first from Greek the second from Arabic, since the twelfth century. However, medieval Europeans in general lacked the mathematical knowledge and to some extent the motivation to engage with this highly technical work. The much simpler available astronomical tables, mostly from Islamic sources, fulfilled their needs at that time. It was only really at the beginning of the fifteenth century that a need was seen to engage more fully with real mathematical astronomy. Having said that, at the beginning the users were not truly aware of the fact that the models and tables that they had inherited from the Greeks and from Islamic culture were inaccurate and in some cases defective. Initially they continued to use this material in their own endeavours, only gradually becoming aware of its deficiencies and the need to reform. As in all phases of the history of science these changes do not take place overnight but usually take decades and sometimes even centuries. Science is essential conservative and has a strong tendency to resist change, preferring to stick to tradition. In our case it would take about 150 years from the translation of Ptolemaeus’ Geographiainto Latin, my starting point, and the start of a full-scale reform programme for astronomy. Although, as we will see, such a programme was launched much earlier but collapsed following the early death of its initiator.

Going into some detail on points from the first post. I listed Peuerbach’s Theoricarum novarum planetarum(New Planetary Theory), published by Regiomontanus in Nürnberg in 1472, as an important development in astronomy in the fifteenth century, which it was. For centuries it was thought that this was a totally original work from Peuerbach, however, the Arabic manuscript of a cosmology from Ptolemaeus was discovered in the 1960s and it became clear that Peuerbach had merely modernised Ptolemaeus’ work for which he must have had a manuscript that then went missing. Many of the improvements in Peuerbach’s and Regiomontanus’ epitome of Ptolemaeus’ Almagest also came from the work of Islamic astronomers, which they mostly credit. Another work from the 1st Viennese School was Regiomontanus’ De Triangulis omnimodis Libri Quinque (On Triangles), written in 1464 but first edited by Johannes Schöner and published by Johannes Petreius in Nürnberg in1533.

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Title page of a later edition of Regiomontanus’ On Triangle

This was the first comprehensive textbook on trigonometry, the mathematics of astronomy, published in Europe. However, the Persian scholar Abū al-Wafā Būzhjānī (940–988) had already published a similar work in Arabic in the tenth century, which of course raises the question to what extent Regiomontanus borrowed from or plagiarised Abū al-Wafā.

These are just three examples but they should clearly illustrate that in the fifteenth and even in the early sixteenth centuries European astronomers still lagged well behind their Greek and Islamic predecessors and needed to play catch up and they needed to catch up with those predecessors before they could supersede them.

After ten years of travelling through Italy and Hungary, Regiomontanus moved from Budapest to Nürnberg in order to undertake a major reform of astronomy.

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City of Nürnberg Nuremberg Chronicles Workshop of Michael Wohlgemut Printed by Aton Koberger and published in Nürnberg in 1493

He argued that astrological prognostications were inaccurate because the astronomical data on which they were based was also inaccurate, which it indeed was. He had an ambitious two part programme; firstly to print and publish critical editions of the astronomical and astrological literature, the manuscripts of which he had collected on his travels, and secondly to undertake a new substantial programme of accurate astronomical observations. He tells us that he had chosen Nürnberg because it made the best scientific instruments and because as a major trading centre it had an extensive communications network. The latter was necessary because he was aware that he could not complete this ambitious programme alone but would need to cooperate with other astronomers.

Arriving in Nürnberg, he began to cooperate with a resident trading agent, Bernhard Walther, the two of them setting up the world’s first printing press for scientific literature. The first publication was Peuerbach’s Theoricae novae planetarum (New Planetary Theory)

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followed by an ambitious catalogue of planned future publications from the astrological and astronomical literature. Unfortunately they only managed another seven publications before Regiomontanus was summoned to Rome by the Pope to work on a calendar reform in 1475, a journey from which he never returned dying under unknown circumstances, sometime in 1476. The planned observation programme never really got of the ground although Walther continued making observations, a few of which were eventually used by Copernicus in his De revolutionibus.

Regiomontanus did succeed in printing and publishing his Ephemerides in 1474, a set of planetary tables, which clearly exceeded in accuracy all previous planetary tables that had been available and went on to become a scientific bestseller.

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However he didn’t succeed in printing and publishing the Epytoma in almagesti Ptolemei; this task was left to another important early publisher of scientific texts, Erhard Ratdolt (1447–1528, who completed the task in Venice twenty years after Regiomontanus’ death. Ratdolt also published Regiomontanus’ astrological calendars an important source for medical astrology.

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Calendarius by Regiomontanus, printed by Erhard Ratdolt, Venice 1478, title page with printers’ names Source: Wikimedia Commons

The first printed edition of Ptolemaeus’ Geographia with maps was published in Bologna in 1477; it was followed by several other editions in the fifteenth century including the first one north of the Alps in Ulm in 1482.

The re-invention of moveable type printing by Guttenberg in about 1450 was already having a marked effect on the revival and reform of mathematical astronomy in Early Modern Europe.

 

 

 

 

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Filed under Early Scientific Publishing, History of Astronomy, History of Cartography, History of Mathematics, Uncategorized

Christmas at the Renaissance Mathematicus – A guide for new readers

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Being new to the Renaissance Mathematicus one might be excused if one assumed that the blogging activities were wound down over the Christmas period. However, exactly the opposite is true with the Renaissance Mathematicus going into hyper-drive posting its annual Christmas Trilogy, three blog posts in three days. Three of my favourite scientific figures have their birthday over Christmas–Isaac Newton 25thDecember, Charles Babbage 26thDecember and Johannes Kepler 27thDecember–and I write a blog post for each of them on their respective birthdays. Before somebody quibbles I am aware that the birthdays of Newton and Kepler are both old style, i.e. on the Julian Calendar, and Babbage new style, i.e. on the Gregorian Calendar but to be honest, in this case I don’t give a shit. So if you are looking for some #histSTM entertainment or possibly enlightenment over the holiday period the Renaissance Mathematicus is your number one address. In case the new trilogy is not enough for you:

The Trilogies of Christmas Past

Christmas Trilogy 2009 Post 1

Christmas Trilogy 2009 Post 2

Christmas Trilogy 2009 Post 3

Christmas Trilogy 2010 Post 1

Christmas Trilogy 2010 Post 2

Christmas Trilogy 2010 Post 3

Christmas Trilogy 2011 Post 1

Christmas Trilogy 2011 Post 2

Christmas Trilogy 2011 Post 3

Christmas Trilogy 2012 Post 1

Christmas Trilogy 2012 Post 2

Christmas Trilogy 2012 Post 3

Christmas Trilogy 2013 Post 1

Christmas Trilogy 2013 Post 2

Christmas Trilogy 2013 Post 3

Christmas Trilogy 2014 Post 1

Christmas Trilogy 2014 Post 2

Christmas Trilogy 2014 Post 3

Christmas Trilogy 2015 Post 1

Christmas Trilogy 2015 Post 2

Christmas Trilogy 2015 Post 3

Christmas Trilogy 2016 Post 1

Christmas Trilogy 2016 Post 2

Christmas Trilogy 2016 Post 3

Christmas Trilogy 2017 Post 1

Christmas Trilogy 2017 Post 2

Christmas Trilogy 2017 Post 3

 

 

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It’s Solstice Time Again!

We are deep in what is commonly called the holiday season. For personal reasons I don’t celebrate Christmas and as I explained in this post starting the New Year on 1 January on the Gregorian Calendar is/was a purely arbitrary decision. I wrote there that I consider the winter solstice to be the best choice to celebrate the end and beginning of a solar cycle in the northern hemisphere.

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Stonehenge Winter Solstice

Today at 22:23 UTC the sun will turn at the Tropic of Capricorn and begin its journey northwards to the Tropic of Cancer and the summer solstice.  Tropic comes from the Latin tropicus “pertaining to a turn,” from Greek tropikos “of or pertaining to a turn or change.”

I wish all of my readers a happy solstice and may the next 365 days, 5 hours, 48 minutes and 45 seconds bring you much light, joy, peace and wisdom. We can only hope that they will be better than the last 365 days, 5 hours, 48 minutes and 45 seconds (length of the mean tropical or solar year).

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Internalism vs. Externalism?

This is one of those blog posts where I do some thinking out loud[1]. I not really sure where it’s going and it might not end up where I intended it to. I shall be skating on the thin ice of historiography. The dictionary defines historiography as follows:

  1. The wring of history
  2. The study of the development of historical method, historical research, and writing
  3. Any body of historical literature[2]

I’m using the term in the sense of definition (2) here. Formulated slightly differently historiography is the methodology of doing history, i.e. historical research and the reporting of that research in writing. Maybe unfortunately there isn’t just one historiography or methodology for doing history there are historiographies, plural that often conflict or even contradict each other, dividing historians into opposing camps indulging in trench warfare with each other through their monographs and journals.

On the whole I tend to view historiographies with a jaundiced eye. I have a maxim for historiographies: ‘Historiography becomes dogma and dogma blinds.’ I like to mix and match my methodologies according to what I happen to be engaged in at any given moment. A single methodology or historiography is just one perspective from which to view a given historical topic and it is often useful to view it from several different perspectives simultaneously, even seemingly contradictory ones.

Since I have been involved in the history of science, and I realise with somewhat horror that is a good half century now, one of the on going historiography debates, or even disputes, within the disciple has been Internalism vs. Externalism.

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Definitions are very slippery things but if I was asked to explain what this means my first simple answer would be internalism is the historical study of the facts, hypotheses, theories etc. that science has produced and externalism is the historical study of the contexts in which those facts, hypotheses, theorems etc. were discovered, developed, formulated etc.

To give an abstract example from the history of mathematics an internalist would be interested in when mathematician X first proved theorem Y and the technical method that he used to do so. They might investigate on whose or which work X built his own work  and also possibly, who picked up on X’s proof and extended it mathematically; anything extraneous to that wouldn’t not be the concern of our imaginary internalist. An externalist would, however, be at least as interested in the context in which X carried out his mathematical endeavours. They would possibly look at X’s biography, how X came to be doing this work at all, what were X’s motivations for this particular piece of research, in which context (university, court mathematicus, insurance mathematician etc.) X was carrying out this work, who was financing it and why etc., etc. From this brief description it should be clear that the perspective of the internalist is a very narrow, very focused one, whereas that of the externalist is a very broad, very sweeping one, although any given externalist investigation might only concentrate on one or two of the various perspectives that I have listed.

Extreme internalism assumes that just presenting the ‘facts’ in the history of science is adequate because science is somehow independent of the world/society/culture in which it arose/developed/originated. Science is totally objective in some way and doesn’t need a context. Extreme internalism also tends to be highly presentist. That is it looks back through history and selects those events/developments in science that can be identified within science, as it exists today. It sees science as cumulative and progressive even teleological. It’s destination being some sort of complete truth.

Externalism sees science at any given point in time as a product of the world/society/culture in which it arose/developed/originated. The externalist historical picture includes all the bits the researchers of the period got wrong and were subsequently jettisoned somewhere down the line on the way to the present. Externalism sees any period of science, as not just embedded in its world/society/culture but as an integral part of the whole of that world/society/culture that cannot and should not be viewed independently.

To give just a couple of very simple examples out of my own main personal historical area of interest: An internalist is only interested in Kepler’s three laws of planetary motion as results that are still valid today. They are not interested in the complex twists and turns of Kepler’s battle to find the first two laws, which he outlines in great detail and great depth in his Astronomia nova. As for the third law, they take it gladly and ignore all of the remaining five hundred pages of the Harmonice Mundi, with its bizarre theories of consonance and dissonance, and cosmic harmony. As for Kepler’s distinctly unscientific motivations, the internalist shudders in horror. For the externalist everything that the internalist rejects is an interesting field of study. They are not just interested in Kepler’s laws as results but in how he arrived at them and what was driving him to search for them in the first place.

Turning to Newton, it is now a commonplace that he devoted far more time and energy to studying alchemy and theology that he did to either physics or mathematics. For the internalist these ‘non-scientific’ areas are an irrelevance to be ignored, all that matters are the scientific results, the law of gravity, the calculus etc. Externalists have shown that the various diffuse areas of Newton’s thoughts and endeavours are intertwined into a complex whole and if one really wants to understand the man and his science then one must regard and attempt to understand that whole.

Where do I stand on this issue? I think it should be obvious to anybody who regularly reads this blog that I am a convinced externalist. I am, however, happy to admit that when I first became interested in the history of mathematics as a teenager I was to all intents and purposes an internalist. Who discovered this or that theorem and when? Who developed this or that method of solving this or that type of problem? These were the questions that initially interested me. I also had strong presentist and even Whiggish tendencies. For those who have forgotten or maybe don’t know yet, the Whig theory of history is the belief that human existence or in this case science, is progressing towards some sort of final truth. Over the years, as I learnt more, my views changed and I became slowly but surely an externalist. This change was, at the latest, completed as I worked for many years, my apprenticeship, in a research project into the history of formal logic. This project was official called, Case Studies into a Social History of Formal Logic, where social is a synonym for external.

As I see it extreme internalism is not just too narrow, too focused but is actually distorting. The internalist history of mathematics, for example, when considering antiquity tends to concentrate on what could be called higher mathematics–the Euclids, Archimedes et al– who only represent a very small minority of those engaged in mathematical pursuits in their period and whose results were only interesting to an equally small minority. In doing so they ignore the vast majority of mathematical practitioners surveyors, bookkeepers extra, whose work actually contributed more in real terms to their societies than that of the ‘star’ mathematicians. A good example is the much-touted Babylonian mathematics, which was largely developed by clerks doing administration not by mathematicians. This fact is simply ignored by internalist historians of mathematics, who are only interested in the results.

Turning to the High Middle Ages and Renaissance, traditional internalist history of mathematics tend to simply ignore this period as having no mathematics worth mentioning. In reality it was the mathematical practitioners of this period–astrologers, astronomers, geographers, cartographers, surveyors, architects, engineers, instrument designers and makers, globe makerset al.–who created the mathematics that drove the so-called scientific revolution.

Having being very rude about internalist history of science I should point out that I by no means reject it totally, in fact exactly the opposite. Anybody who opens Newton’s Principia for the first time, even in the excellent modern English translation by Cohen and Whitman would probably understand very little of the mathematics and physics that they would find there. They have a choice either to spend several months chewing through Newton’s masterpiece or alternatively to turn to Cohen excellent internalist guide to the contents. The same is true of virtually any historical STEM text. Close internalist readings and interpretations help the historian to comprehension. Having gained that internalist comprehension they should, in my opinion, embed that comprehension into its wider externalist context.

Historians of science should be simply historian, in the first instance, investigating the breadth and depth of a discipline within its social context. However this also implies a solid understanding of the science involved, i.e. the internal aspects. You can’t investigate the role of a scientific discipline within a social context if you don’t understand the science. This means for me, that a good historian of science must be both an internalist and an externalist, weaving together both approaches into a coherent whole.

All of the above is of course my own subjective take on the dichotomy and they are certainly other viewpoints and other opinions on the issue. As always, readers are welcome to ventilate their views in the comments.

For any future historian, who might be interested in my motivation for writing this post, it was inspired by a request from a reader to write something on the ‘conflict’ between internalist and externalist histories of science and illustrate it with examples of the two different approaches with reference to my own blog posts. I’m not sure if that which I have written really fulfils their request and as should be obvious I, as a convinced externalist, can’t really supply the desired examples. However I am grateful to the reader for having motivated me to write something on the topic even if it not really what they wanted.

[1]If I was being pretentious I might have said, “Where I philosophise” but I don’t regard my stream of consciousness meanderings as rigorous enough to be dignified with the term philosophy.

[2]Collins English Dictionary online.

 

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Printing the Hindu-Arabic numbers

Arte dell’Abbaco, a book that many consider the first-ever printed mathematics book, was dated four hundred and forty years ago on 10 December 1478. I say many consider because the book, also known as the Treviso Arithmetic, is a commercial arithmetic textbook and some historians regard commercial arithmetic as a separate discipline and not really mathematics.

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Calculation from the Arte dell’Abbaco

The unknown author explains his book thus:

I have often been asked by certain youths in whom I have much interest, and who look forward to mercantile pursuits, to put into writing the fundamental principles of arithmetic, commonly called abbacus.

The Treviso Arithmetic is actually an abbacus book, those books on calculating with the Hindu-Arabic numerals that derive their existence from Leonardo Pisano’s Liber Abbaci. Like most abbacus books it is written in the vernacular, which in this case is the local Venetian dialect. If you don’t read 15thcentury Venetian there is an English translation by Frank J. Swetz, Capitalism and Arithmetic: The New Math of the 15thCentury Including the Full Text of the Treviso Arithmetic of 1478, Open Court, 1987.

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Filed under Early Scientific Publishing, History of Mathematics, Renaissance Science, Uncategorized