How to cast a medieval horoscope

I wrote this post for the blog of the 24th International Congress of History of Science, Technology and Medicine (iCHSTM), which takes place in Manchester on 21-28 July 2013.  Loyal readers of this blog won't find much new here, but it's a fair summary of my research so far.

I have modified my views slightly since writing this, mainly about how sophisticated an astronomer the equatorium's creator was, and how sure we can be about Schöner's purposes.  I'm looking forward to discussing these issues with people at the conference.

Posted on 20 June 2013 by admin

In preparation for iCHSTM 2013, I’ve spent the last few weekends indulging my creative side.  Sawing and filing wood and brass into a disc, ring and pointer may have disturbed the peace of my neighbours’ Saturday afternoons, but it has meant I will be able to demonstrate a particularly ingenious, user-friendly medieval device: a planetary equatorium.

I have recently begun PhD research into a unique fourteenth-century manuscript.  Known as The Equatorie of the Planetis, it describes how to construct an equatorium.  This makes it one of the earliest pieces of writing about a scientific instrument in the English language.  The first person to study it, Derek de Solla Price, was convinced not only that it was written by Geoffrey Chaucer, but that it was a draft in Chaucer’s own handwriting.  The authorship debate still rages; meanwhile, I am looking at some of the other fascinating aspects of this manuscript.

The equatorium nears completion

Much like their better known cousins, astrolabes, equatoria were medieval calculating devices.  These devices made use of astronomical theories and models that were long-established, having first been refined around 150 CE by the Greek astronomer Ptolemy.  In both cases, they existed in something close to their complete form in the late Classical period, before being further developed in the Islamic world from around the tenth century, and refined still further in western Europe between the thirteenth and sixteenth centuries. While astrolabes could be used for a range of functions, from telling the time to measuring the height of a building, equatoria just did one thing: modelled the motions of the planets.

They did this by recreating the essentials of Ptolemy’s planetary theories as a kind of diagram with moving parts.  These became progressively simplified, so that a single device could model the motion of the Sun, the Moon and the five known planets.  After an initial investment of time making his equatorium, an astronomer could then predict the location of the planets to a high degree of accuracy, far faster than by the alternative method – trigonometric calculation.  Using this basic computer, planetary astronomy could be as simple as looking up a couple of values in a table, and using them to place some pieces of brass, wood and string.  The question is: why?

For early modern astronomers such as Johannes Schöner, who included cut-out-and-build equatoria in his 1521 Aequatorium Astronomicum, they had a largely educational purpose: they could be used to demonstrate the fundamentals of the Ptolemaic theories, just as many classrooms today use globes (another favourite device of Schöner’s) to teach children about latitude and longitude. [I'm no longer so confident about this claim: Schöner’s equatoria could be used for practical astrology, though it's hard to be sure that they actually were.]

But equatoria also had practical importance.  Although nowadays we are dismissive of astrology, and think of horoscopes as a simple matter of making (up) predictions about people’s future fortunes based on the month of their birth, it wasn’t always that way.  In the medieval period there was no hard distinction between astronomy and astrology, and the calculations that could be made using personal and planetary information were complex and varied.  They had a range of possible uses, too, guiding anything from political decision-making to the timing of medical procedures.

In the case of The Equatorie of the Planetis, the simplifications made by its designer make it less suitable as a demonstration device, but much easier to make, transport and use to calculate planetary positions.  The designer has shown great imagination in paring the instrument down to its bare essentials.  It could be argued that by simplifying the Ptolemaic model, he demonstrated a lack of understanding and precision, but I think it is the reverse: he showed great sophistication in understanding where approximations could be made for the sake of greater usability, without sacrificing too much accuracy.

It’s sometimes suggested that these medieval “instruction” texts were not really designed to be followed except in the reader’s imagination. Certainly it’s true that it would be expensive and rather unwieldy to make it at its full six-foot scale! (Though that is precisely what Derek de Solla Price did in 1952.)  But with my newly built equatorium I’m looking forward to showing people at iCHSTM that these six-hundred-year-old instructions can be followed to produce a user-friendly, and useful, little computer.

This blog post is based on the paper , “Putting classical astronomy to work: the design and use of a medieval equatorium,” which [I am] due to give as part of symposium T157, “Pre-modern astronomy and cosmology,” on Saturday 27th July at ICHSTM.

Tweets from the Biennial History of Astronomy Workshop - Part 2

Here is the second instalment of my tweets from the Eleventh Biennial History of Astronomy Workshop.  If you missed the first batch, you can read them here.

Once again, if you enjoy reading them, don't forget to follow me on Twitter!




Congratulations for making it through all those!  Remember, if you missed the first instalment, you can find them here.

Tweets from the Biennial History of Astronomy Workshop - Part 1

I've spent the last few days at the Eleventh Biennial History of Astronomy Workshop, at the University of Notre Dame (in the USA, not Paris).  It was a tremendous learning experience and very enjoyable.

I hope to post some reflections on the conference soon, but first, I've collated all the tweets I wrote during the last five days.  I found the 140-character limit made for an interesting challenge in summarising what was being said.  As there were quite a few tweets, I've split them in two (you can find the second batch here).  If you enjoy reading them, don't forget to follow me on Twitter!



Wow! Did you really read all those tweets?  If you're a glutton for more punishment, click here for the second instalment.

Making a brass equatorium

I'm flying to Chicago on Wednesday.  There'll be an unusual object in my luggage (is it wise to put that kind of statement online?).  Yes, you guessed it: it's another equatorium.

Loyal readers will remember my early series of posts (here, here and here) in which I described how I made, and learned to use, a medieval equatorium.  Although I am no great artist, I managed to create a passable replica of the instrument described in the manuscript I'm studying.  In the process, I also had to think a little about the tools and techniques that medieval craftsmen would have used.

But I didn't learn much about materials - I made my replica out of MDF, the cheapest and most manageable material I could find in my local DIY store.  So, when I arranged to speak about the equatorium at a conference in the USA, and I realised that my first replica was too big to fit in my suitcase, I decided to make another one using a more authentic - and challenging - material: brass.

The word "more" is crucial in that last sentence.  When I went online, researched a few different suppliers, ordered a 360 x 400 x 1.2 millimetre sheet of brass, and paid for it using my credit card, I was hardly recreating the experience of the medieval instrument-maker.  It's important to note that even the basic material is quite different: brass is an alloy of copper and zinc, but the ratio of these two elements can vary substantially.  The melting together of metallic copper and zinc, which is necessary to produce the high-zinc brass that can be rolled into thin sheets, was a seventeenth-century innovation.  (Before then, copper was heated with zinc oxide and charcoal.  This produced zinc gas, which diffused into the melted copper.)  And of course medieval metalworkers didn't roll their brass into sheets either - they hammered it out.

For the face, I used an off-cut from the Epicycle of the
last equatorium - so you can see the difference in scale.

But I still felt there was something to be learned (and a prettier end result could be achieved) by working in brass.

Whereas the full-size equatorium would be six feet in diameter and my first one was half that, I had to scale it down again.  In order to avoid making the calculations and measurements too complicated, I decided the easiest thing would be simply to use a 1:1 ratio of inches to centimetres.  The effect is of course to reduce the dimensions by a factor of 2.54.  So my new equatorium is 36 cm in diameter.

The manuscript instructions specify a face (see the earlier posts for what this is) of wood, and all that brass is expensive so I was happy enough to follow that.  But the Epicycle and label (pointer) had to be cut out of brass.  With only a basic hacksaw and file, this was quite a challenge, especially when it came to cutting out the semicircles from the inside of the Epicycle.  Although I bought a nice new workbench and some clamps, it was still a tough job drilling the starter hole - I broke two or three drill bits during this stage of the process.  (If there's a next time, I'll be tempted to invest in a drill press.)

Still, it was very satisfying filing the brass down to precisely the right shapes, and I'm pretty pleased with the final result:

So, what have I learned?  Well, working in brass is hard!  And although I'm no artisan, it must still have been hard for craftsmen in the Middle Ages, whose tools were even more basic than my cheap set.  This raises a number of questions for my research.  For example, does the difficulty of working in brass make it more likely that an astronomer collaborated with an artisan to make this, rather than doing it himself?  Frankly, having had to make it myself, I am more sympathetic to the suggestion that this instrument wasn't actually made in the fourteenth century...  Or, at least, that it wasn't made at full size.  Working with a thin sheet of brass is hard enough when it's a 36 cm ring, and the brass has been rolled on an industrial machine.  I can't begin to imagine how tough it would have been not only to hammer out a 72" ring of brass, but to work with it without it bending out of shape.

It's all fodder for future research.  For now, I'm just curious to see what the friendly folk at United States customs will think of my unusual item of baggage...