How did an Italian astrolabe end up on the New Zealand passport?

A few years ago I enjoyed a blog post in which National Maritime Museum curator Rebekah Higgitt wrote about the "navigation" theme of the new New Zealand passport design.  Higgitt discussed the use of John Harrison's H1 clock as an illustration in the passport.  She also noted that the description on the New Zealand government website mentioned an astrolabe, which piqued my interest.  I tried to find out more, but the website didn't include pictures, and none of my Kiwi friends had new-style passports.

So I forgot about it... - until last week when a friend of mine was talking about the designs that have been proposed to replace the current NZ flag.  I took the opportunity to ask to see his passport, and bingo! Here it is:

I was intrigued by the distinctive design and decided to see if I could find similar astrolabes in any published museum collections.  It didn't take me very long to track down this one:

Image courtesy of Museum of the History of Science, University of Oxford

This is astrolabe 50257 at the Museum of the History of Science in Oxford.  You don't have to be an expert to spot the similarities.  But the question is, are those similarities remarkable? How unusual is this design?

To answer that question, let's go back to basics for a moment.  The similarity you notice - the dark pattern of rings, heart shape and so on - is the rete of the astrolabe.  It was made by cutting holes in a sheet of brass, so that it resembles a net (that's what rete means in Latin) or, as Chaucer thought, a spider's web.  It sits inside the mater of the astrolabe, and rotates around that big pin in the middle.  Each of the pointers on the rete marks a star, making the rete a moving star map, able to simulate the daily (apparent) motion of the heavens around the earth.

This overall layout, with the rete turning above a plate engraved with a grid of coordinates and a horizon for a particular latitude, is by far the most common form of an astrolabe.  The basic concept goes back to Ptolemy in the 2nd century CE, and the instrument had this settled form, with the mater, interchangeable plates for various latitudes, the rete and rule (which also moves, as you can see from its differing position in the two pictures above), by the time John Philoponus wrote a description of it in the early 6th century.

But that still left a lot of flexibility for individual designers and craftsmen.  They could choose which stars to include on their rete, but more noticeably, the supporting brass "net" could be almost any shape, as long as it included that smallish eccentric (off-centre) circle which is the ecliptic, mapping the Sun's annual progress through the zodiac.  Craftsmen expressed their flair through ingenious designs - a favourite trick, as you can see here, was to make the rete symmetrical, even though the stars obviously weren't.

As far as I know, this particular design of rete is unique.  Luckily the astrolabe itself has the name of its designer on the back: Giovanni Domenico Fecioli of Trento, in the far north of Italy.  We also have the name of the man who commissioned it: Giulio Cesare Luchino, of Bologna.  The latitude of Bologna is 44° 30', which matches the astrolabe's single latitude plate.  It's dated 1558, just when the popularity of astrolabes in Europe was at its peak.

Image courtesy Museum of the History of Science, Oxford

In technical terms there's nothing particularly remarkable about this astrolabe, but the design is an attractive one.  The illusion of interlocking circles at the bottom of the rete was a popular motif in that period - compare, for example, this one by the prolific Arsenius workshop in Louvain.  Arsenius was famous for his tulip-shaped designs (can you see the tulip?), and Fecioli's rete doesn't quite match the delicacy of Arsenius's intricate brasswork, but it's still beautiful, and I'm sure it was much prized (and proudly displayed) by Luchino.

I have no idea why the New Zealand government chose a Fecioli astrolabe as an illustration for their passports.  But it's worth saying a few words about the place of this instrument in the overall design scheme.

Here's what their website says about it:

The passport’s new design evolved from the concept of navigation and our evolution from a place of discovery, to a place of destination and follows the journeys of the earliest explorers of New Zealand through to the journeys made by Kiwis today. Themes of arrival and departure, navigation and time are represented figuratively and metaphorically throughout the passport.

And about pages 20-21 specifically:

The astrolabe and chart – the astrolabe is an astronomical instrument used by astronomers, navigators, and astrologers. Its many uses included: locating and predicting the positions of the sun, moon, planets and stars; determining local time using local longitude and vice-versa; surveying and triangulation. 

Of course the theme of navigation is perfect for a passport.  But the astrolabe's place in that theme is less certain.  It was a multifunctional compendium of astronomical and astrological functions, not particularly suited to use at sea.  It's true that the mariner's astrolabe was a popular navigational device (I made and tested one for a previous blog post), but that was a quite different instrument.  It's certainly highly unlikely that Fecioli's beautiful piece ever went offshore.

Even if it had, it could never have been used to determine longitude (or to predict the positions of the Moon or planets).  The relationship between longitude and time was well known in the age of the astrolabe, and astrolabes could certainly be used to find local time.  But longitude is a relative measurement (these days we measure it east or west of Greenwich); if you want to go from local time to local longitude, you also need to know the time at the reference point (e.g. Greenwich) from which you're measuring longitude.  Local time was easy to find, but when Fecioli made his astrolabe, a reliable, robust method of keeping reference time - a clock that could withstand ocean passages - was still 200 years away.

But local time itself is unattainable with the astrolabe pictured in the passport, because the designers have cut off the suspension ring and throne that attaches it to the mater.  The ring is crucial for sightings of the Sun or a star, because the astrolabe has to hang vertically.  Without it, the astrolabe is no longer an observational instrument.

That may seem like nitpicking, but it tells us something about the way astrolabes are (and were) seen.  They have always had symbolic value, representing astronomical knowledge as well as artistry and the owner's wealth and status.  Today in many museums they are presented as art objects, out of context and, often, supported from below rather then suspended by the ring (admittedly for sound preservation purposes).  They now seem to symbolise ancient, arcane knowledge, and this symbolic value trumps accuracy, much like the "save" icon in most computer programs is a 3.5" floppy disk, though you're unlikely to be storing your work on those any more.

Of course I don't mind that - I'm happy people find astrolabes evocative and attractive.  And, as I say, they've always had symbolic value.  But once in a while it's worth reminding ourselves of the specific contexts where, for a thousand years, they were also complex scientific objects with practical purposes.

Update, 25/08/2015: I wrote to the New Zealand Passport Office to see if I could find out more, and received a very friendly response.  The officer wrote: "I have spoken directly with some of those involved in the design process of the latest version of the New Zealand passport, which was produced in 2009 and the astrolabe design appears because it is a symbol for travel and a relatively complex shape. [...]
The specific astrolabe was not chosen for any particular reason except that it fit with the overall theme.  I was unable to ascertain whether the astrolabe featured in the book is the specific 16th century Italian you have identified but your analysis would suggest that it is the case.  Unfortunately I am not able to be more specific than that.  
Thank you very much for writing to us and I have noted with pleasure your compliment for our 'beautiful' passport."

Geoffrey Chaucer's Inspirational Astronomy

OK, so I missed Andy Murray's Wimbledon semi-final.  And I missed seeing England hammer the Aussies in Cardiff.  But I didn't care.  Because I was incredibly excited to be at my first Chaucer conference.

The Biennial London Chaucer Conference took place at the Institute of English Studies last Friday and Saturday.  Given that the manuscript I work on has been (wrongly) attributed to Chaucer, and that the theme of this year's conference was "Science, Magic, and Technology", this was one conference I couldn't miss.

And I'm so glad I was there.  An inspiring series of presentations took hugely varied approaches to the theme.  Literary, historical or scientific, they were all fascinating and I learned so much.  If you want a flavour, check out the #Chaucer2015 hashtag on Twitter.  My cardboard astrolabe featured in the conference's most popular tweet!

You know it's an awesome #Chaucer & science conference when SOMEBODY busts out an #astrolabe. #medieval #Chaucer2015 pic.twitter.com/IUEn5iIvd9

— Jonathan Hsy (@JonathanHsy) July 10, 2015

If you want to know what I had to say about Chaucer and his influence on the Equatorie of the Planetis, why not watch the video of my presentation (above)?  Hope you enjoy it, and don't forget to comment!

Drawing up a medieval horoscope

I've written a blog post entitled "How to cast a medieval horoscope" before.  But I didn't tell the whole story.

Regular readers of this blog (are there any?) will know that the main focus of my research is equatoria - devices designed to compute the positions of the Sun, Moon and planets.  I've made and used two of them - three if you count the fully functional virtual model which I helped create (though I can't claim much of the credit - that goes to the amazing Ben Blundell).

So I know how to find the locations of the celestial bodies - and how medieval astronomers did it, using instruments and tables.  But that's only one-third of the job.  Once you've found the planets, you still need to draw up the horoscope.  And then you need to interpret it.

This post is about the second part of the job - drawing up the horoscope.  What does that mean?  Simply put, it's no use just knowing the planets' positions in degrees of celestial longitude.  Most medieval horoscopes were based on their location in segments of the sky - the houses.  And dividing the sky into houses was no trivial matter.

The stars rotating at Race Rocks (photo: Ryan Murphy)

Astronomers (or astrologers - invariably the same people, who saw no distinction between aspects of their work that we like to divide into Science and Superstition) agreed that there were 12 houses.  But how to divide them up?  The simplest way was simply to make 12 segments of equal celestial longitude.  But that was not a common way of doing it.  A much more common way was to use two key points: midheaven and the ascendant.

Midheaven (or the meridian) is where the Sun reaches its highest point in the sky.  In geographical terms, that's south, but in celestial terms, because the celestial sphere is constantly rotating (think of how the stars rotate during the night), that could be any part of the heavens - any constellation, if you like - depending on when and where you are.

(Remember that the zodiac constellations are the stars that lie along the ecliptic - the apparent path of the Sun against the background of stars throughout the year.  Because the Earth always rotates around the Sun in more or less the same plane, the Sun moves through (passes in front of) a consistent pattern of constellations.)

The ascendant is the point of the ecliptic which is rising (crossing the horizon) at your chosen moment - again, remember the celestial sphere is constantly rotating.

Diagram from John North, Horoscopes and History (1986), p. 4

According to the most popular medieval method, the space between the ascendant and midheaven were the last three houses.  So that segment of the sky was divided into three.  The rest of the houses follow in the same way: the points opposite the ascendant (α1) and midheaven (α10) were used to divide up the remaining houses (those opposite points were called the nadir of the ascendant (α7) and the midnight line (α4)).  So, as you'll see in this diagram, there were 6 houses of one size, and 6 of another.

Easy, right?  No, because those 6 houses are the same size in right ascension, not in longitude.  In other words, the space between ascendant and midheaven was divided into equal rising times - equal segments of the celestial sphere according to how long they take to move through the sky.  Those are measured on the equator (since the equator is perpendicular to the earth's axis, equal arcs of the equator rise in equal times).  But longitude is measured on the ecliptic, which is inclined at an angle of roughly 23½° to the equator.  As a result, some pretty complicated trigonometry is required to convert houses that come up above the horizon in equal times, into (unequal) longitudes.

Fortunately for medieval astronomers, they could often rely on tables which would show the longitudes of the cusps of the houses for a given ascendant.  But someone had to draw up those tables, and that was a complicated business, involving some complex trigonometrical formulae and depending on your latitude. (If you want to know more, write a comment and I'll explain!)

The Peterhouse equatorium in action

Astronomers seemed to take pride in updating and improving the tables to suit their purposes.  For example, one set of tables I've been working on recently shows the longitudes for a given midheaven, rather than ascendant.  And it adds a column with corrections so that you can find the houses at any time of day.  Those changes required a phenomenal amount of re-computation.

Once you've done all that calculation (or used appropriate tables), you can draw up a chart that shows the division of the houses, and the placement of the planets within them.  I thought I'd give this a go for my son, who was born at 9.47 a.m. on 5th December. 

Using Excel, I was able to reproduce a medieval set of tables (which was very helpful in understanding how they were originally computed).  I used an astrolabe (following the instructions written in 1391 by Geoffrey Chaucer) to find the ascendant at that date and time, then looked up the divisions of the houses in my new tables.  Finally, I added in the locations of the Sun, Moon and planets, which I'd found using the virtual model equatorium.  (I checked them against Stellarium, a modern computer simulation, and the results were pretty close.

Stellarium: soften the Sun, cut the clouds, lose the land, and that's the sky on the morning of 5th December

So, here's the result - pretty, don't you think?

Now all we have to do is interpret it... I predict that will be the subject of a post in the near future.

The vernacular in medieval astronomy - at Kalamazoo

I recently returned from the International Congress on Medieval Studies.  It's held every year at the University of Western Michigan in Kalamazoo (USA), and this year was the 50th congress.

3000 medievalists met to discuss everything from Viking archaeology to Middle English poetry - and of course there was a mead and ale tasting.  I'll put together some tweets from the congress in a future post.  For now, here's a recording (with PowerPoint slides) of my presentation at the conference.  Hope you enjoy it, and don't forget to comment!

Precision and accuracy in medieval astronomy

What is the difference between precision and accuracy?

In modern English they are used almost interchangeably.  But there is a difference, of course.  I wonder what time it is now, when you are reading this.  Is it about eleven o' clock?  Or is it 09:34?  Of course, I have no way of knowing which of those guesses is more accurate.  But the second is obviously more precise.

Which of these two timepieces
is more accurate? Well,
they've both stopped...

That distinction may be more or less clear to us.  But that wasn't always the case for medieval astronomers.  What if I were to refine my guess, and say you're reading this at 09:34:27?  Is that any better? It's obviously more precise.  But when is it preferable to be more precise?  The answer to that might be more complicated than it appears.  In general, we might say that precision is only preferable when it increases accuracy.  But medieval scholars didn't always see it the same way.

I study astronomical tables.  Take a look at this amazing digitised version for an example.  That link points to a table of the daily precession of the stars and planetary apogees.  It's a lot more exciting than it sounds!

(Here's a brief astronomical explanation: skip it if you want...  Precession is the phenomenon that means that the stars appear to move very gradually around the sky, so that they're not in exactly the same place from year to year.  I don't mean the obvious daily rotation around the North Star that's caused by the Earth spinning on its axis - I mean a much slower change, caused by a "wobble" in the tilt of the Earth's axis.  The stars are moving 1° every 72 years - pretty hard to spot, but it explains why, right now, the Sun is still just about "in" the constellation Sagittarius (i.e. in front of those stars) even though it ought to be passing from Capricorn into Aquarius.  To be clear: the astrologers haven't got that wrong, because when they say it's the cusp of Aquarius, they mean the Sun has gone 120° around the sky (in modern terms, we've completed a third of our orbit) since the last equinox.  It's just that the background of stars has moved since the Ancient Greeks assigned them to their positions between equinoxes and solstices.)

So what?  The point is, precession is a VERY slow motion.  It's obviously almost impossible to observe with the naked eye.  It's impressive enough that ancient astronomers had even noticed it, so we shouldn't be surprised that their estimate of the rate was a bit different from ours.  That's why the table I linked above represents a precession of 1° every 136 years (their theory of precession included a separate, non-linear component that made up most of the difference).

But I said above that that table is a table of DAILY precession.  What's the point of tabulating daily values for something that changes one degree every 136 years?!

Good question! Here's another one: What's the point of tabulating those daily values to a precision of billionths of billionths of degrees?!  I don't even know what a billionth of a billionth of a degree is called, but that is the precision represented by the daily value of 0;0,0,4,20,41,17,12,26,37.  (That's a sexagesimal number: 0°, 0 minutes, 0 seconds, 4 thirds... In decimal terms it's 0.0000201148235466718.)  The 37 in the final column of the table is 3.67 x 10^-15.  To put that in context, that's one 98,000,000,000,000,000th part of a complete circle. It would take approximately 750 billion years for these daily 37s to accumulate to even a degree’s difference.

That level of precision in the tables clearly didn't arise from naked-eye observation of the stars.  No, it's a result of the way the tables were computed.  And astronomers clearly realised that - they understood that such precision was unobservable.  Yet they maintained it when they copied and recomputed the tables.  Why?  Because, I suppose, they reckoned that more precision is better than less.  To put it another way: you say why keep those 37s?  They would say, what makes you so sure you can get rid of them?

Isn't that silly?  Hold on a moment - you may not be much better.  A friend of mine recently posted this on Facebook:

I know how these things work: authors of recipe books work out their recipes in their own ways.  Delia Smith was obviously used to using pounds and ounces.  She used 2 oz of sugar.  2 oz is about 56.75g, but no editor will let that go into the published cookbook.  So it gets rounded down to 50g.  Then when Delia calls for 6 oz (about 170.25g), it gets rounded up to 175g.

Here's the weird bit: I know this is what's happening - I even have a magnetic converter on my fridge door that tells me that 2 oz is 50g and 6 oz is 175g.  But that doesn't stop me measuring out the quantities with exaggerated care, paying attention to the slightest fluctuation on the scales.  And what about the eggs?  I'm precise to the last gram of sugar even in recipes that use eggs, when I'm well aware that the size of eggs can vary widely.  If I can sustain this kind of cognitive dissonance, perhaps I shouldn't be too critical of the medieval astronomers.

Is the Moon a planet or a star?

It's rare that shopping channels grapple with complex problems in astronomy - but miracles do happen.  Here's the contributors to QVC discussing whether the moon is a planet.  An important consideration is apparently that "things live on it".

I'm posting this for your amusement, but you could make a serious discussion out of it.  After all, what does it mean to be a planet?  The word comes from the Ancient Greek meaning wanderer, because astronomers spotted that some heavenly bodies moved against the background of fixed stars during the year.  In that sense, the Sun was a planet too.

Ancient and medieval astronomers could see obvious differences between the Moon and the Sun and the other planets in the Solar System, but there were lively discussions about precisely what they were, and how we could know.  They also calculated the relative distances of the Sun and Moon with impressive accuracy, simply by observing eclipses!

In modern terms, we say the Moon is a moon because it orbits a planet, but it might be worth noting that the situation is more complex: in fact, because the Earth and the Moon exert force on each other, they both orbit a point between their centres (though, since the Earth is much larger, the centre of gravity of the Earth-Moon couple is still within the Earth).

And remember, it was a change to the definition of a planet by the International Astronomical Union in 2006 that caused Pluto to fall out of that category (the IAU has a good explanation of their reasoning here).

So a silly discussion can raise some serious questions.  One thing we can be pretty sure about, though: although the Moon has definitely had life on it in the past (12 Apollo astronauts), there's nothing there now.

Thanks to Christopher Graney and the HASTRO contributors for posting this video and discussing it so interestingly.

String Theory - Medieval-style

Apologies for the long hiatus!  I've been busy with lots of things, among them the birth of my first child.  I'll post his horoscope here soon!  But first, here's a few thoughts I've been mulling over for a while...

My research centres on scientific instruments.  I study descriptions and images of them, attempt to follow the instructions to make and use them, examine the instruments themselves, and sometimes review or help curate exhibitions of them.  With all this, I spend a lot of time thinking about materials.

When we think about astrolabes, we tend to think of the shiny brass objects that are most common in museums.  Lots of attention has been paid to the kinds of metals that were used, and how they were shaped.  (Recent increases in the affordability of analytical technology means that this area is ripe for new discoveries - and I hope to blog soon about some research I've been involved in.)

But there are other materials too.  You don't have to think about this subject for very long to realise that the ornate astronomical instruments now on display in museums were probably not the same ones used for practical navigation at sea: sailors would have taken advantage of simpler designs and cheaper materials, principally wood.  Nor were they the same ones used for study in the new universities: teaching and learning took place with instruments made of parchment or paper.

Equatorium of Jupiter, from Peter Apian's
Astronomicum Caesareum (1540)

But one material is rarely mentioned in the scholarly literature: string.  This is despite the fact that it appears in many descriptions of instruments, and a good number of the surviving examples too.  The image on the right shows the equatorium for Jupiter, from Peter Apian's Astronomicum Caesareum (1540).  This sumptuous work, dedicated to Emperor Charles V, is hardly an ordinary equatorium treatise, but in its use of string it is entirely typical.

Before being incorporated into astronomical compendia like this, threads had been used for centuries in practical surveying instruments such as quadrants.  The easiest way to measure an angle, such as the height of a building, was via a plumb-bob (a lead weight hanging on a string) that could move over a circumference marked on a brass or wood quarter-circle (see the image below).

It's a small step from that to the use of threads as pointers, to read angles on scales on the circumference of more theoretical instruments.  It's easy to see why this step was taken: they were flexible, easy to attach, use and replace; they were narrow and thus relatively precise.  And crucially, of course, they were cheap.

Detail from British Library MS Burney 275, f.390v (early 14th century). The
bear and goat on the right are using a surveying quadrant with plumb-bob.

 How cheap? Of course that depended on what the threads were made of.  Sadly most instrument treatises are silent on the subject of what kind of string to use, where to find it and how to cut it.  So we have to assume that instrument makers used the cheapest thing they could find, or whatever was to hand.  This probably meant threads made of hemp or flax.


Unusually, though, the Equatorie of the Planetis (the manuscript that's the focus of my research) does talk about materials.  (One of the reasons I find it so fascinating is that it goes into many of the practical details that are absent from most medieval scientific treatises.)  It says:

Note that every centre [of each planet's equant circle] must be also small as a needle, and in every equant must be a silk thread.

Why silk? Was silk finer than other threads, and thus more precise? Was silk in this context meant metaphorically, and the writer really just wanted some very soft and flexible thread? Was it included to give a sense of luxury or importance to the astronomical work, as if only the finest materials were suitable for the tasks undertaken? Or is the whole thing a flight of fancy, in which the writer was indulging his imagination in describing an instrument that he had no intention of making?

I'm not sure, but I'd like to think there is a practical reason.  After all, the Equatorie of the Planetis design also includes a revolving metal pointer, which was the standard device used on astrolabes.  A metal pointer was needed on the brass epicycle because the radius of each of the planets needed to be marked at the appropriate point along its length.  But on the face of the equatorium, with an equant centre for each planet, something more manageable was required.  So we can see the designer of the equatorium choosing appropriate techniques and materials at each stage, with the clear goal of producing a user-friendly, effective planetary computer.

And what difference would a material other than silk, say flax, hemp or polypropylene, make?  I don't know, but I'm starting to think another reconstruction experiment is required!

Ships, Clocks & Stars

I recently visited, and very much enjoyed, the exhibition at the National Maritime Museum about the quest for longitude.  It's on until 4th January, and I highly recommend it.  I liked it so much I wrote a review of it for the Science Museum journal!

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.

What's the difference between an astrolabe and an equatorium?

This is a question I've been asked several times, and it's a reasonable one given that this blog is called "Astrolabes and Stuff", yet I've mainly been posting about equatoria.  So I'm going to answer it in this post.

14th-century astrolabe at the Whipple Museum of the History of Science

First, it's important to stress the one thing astrolabes and equatoria have in common.  They are both tools, calculating devices.  As such, they simplify (and approximate) tasks that could have been done by geometrical calculation - but the astrolabe and equatorium get them done much faster.

So, what are they calculating?  Here's the key difference.  An astrolabe (from the Greek astro-, meaning "star", -labos, meaning "instrument", "measurer", "meter") tracks the stars.  On the other hand the word "equatorium" comes from the Latin æquatio, which generally means "correction" rather than "equation", and refers to the correction that needs to be made to convert a planet's mean position to its actual position.  So this is an instrument squarely focused on the planets.

What about the Sun and Moon?  Are they stars or planets?  The answer is of course neither - but also both, in some ways.  This is where we come to the more fundamental difference between astrolabes and equatoria: the timescales on which they operate.

TECHNICAL BIT (feel free to skip this paragraph).  Ancient astronomers noted two kinds of regularity in the planets' motions: tropical and synodic periods.  The tropical period of a planet is the average amount of time it takes to go all the way around the ecliptic (i.e. to travel round all the stars).  The synodic period is the amount of time between periods of retrograde motion.  (For a quick explanation of the significance of retrograde motion, see this post of mine.)

Of all the planets known since antiquity, Saturn takes the longest to go all the way around the ecliptic - to pass all the constellations and end up back where it started.  The 4th-century-BCE astronomer Eudoxus estimated that this tropical period took 30 years; we now say 29.42 years, so he wasn't too far off.  An equatorium has no problem showing this.  Of course there are many ways in which you could say that we require even longer periods of time to be shown - for example, the Greeks adopted the Babylonian idea of great cycles - the amount of time it took before a planet was behaving in the same way at the same place on the ecliptic.  Jupiter's great cycle is 83 years.

Whereas an equatorium tracks planets over years, most of the functions of an astrolabe are best appreciated within a single day, and the information provided by a normal astrolabe repeats after one year.  Here are some of the things it can tell us:
1.  Where a star, or the Sun, will rise on the horizon
2.  How long a star, or the Sun, will stay above the horizon (i.e. the time between rising and setting)
3.  The longitude of the Sun (i.e. its position on the ecliptic) on a given day

Detail of the same astrolabe as above (Wh.1264),
showing the calendar for January/Aquarius,
with various saints' days in the inner circles.

4.  The height of the Sun (or any star) at noon
5.  How long it will take after sunset to get dark (or to get light before sunrise)
6.  The time of day, for a given date
7.  The date, if you observe the Sun at noon, sunrise or sunset
8.  The height of a building, if we know how far away from it we are

There may be many other functions too.  For example, an astrolabe may operate in unequal hours (where there are always 12 hours between sunrise and sunset) as well as equal hours; it may show us the astrological Great Houses, and the calendar on the back may feature a range of saints' days as well as the months and zodiac signs.

Smaller than an astrolabe,
but less likely to work after
being dropped in the bath

This dazzling array of functions means that astrolabes are sometimes compared to Swiss Army knives.  But these days I'm more struck by the comparison to a smartphone.  They are both up-to-date technological items, but more importantly they are both amalgamations of quite a lot of previously existing technology in one easily portable and user-friendly unit.  I suspect they also have in common the fact that despite their enormous range of functions, it tends to be the more basic functions that get/got used most often.

A 20th-century astrologer?

Which brings us to another crucial point: smartphones and astrolabes are both must-have status symbols, valued as much for their visually (and tangibly) attractive design as for their practical functions.  I suppose in a sense smartphones are now too common for the analogy to work perfectly - astrolabes were perhaps more like the earliest mobile phones for the 1980s yuppies - a sign of success, with a faint but perhaps false suggestion of technological know-how.

An equatorium, on the other hand, is a decidedly specialist item.  Its lack of functions - as we've seen in previous posts, it can tell us the longitudes of the Sun, Moon and planets, the latitude of the Moon, but not much else - raises the question of who would want one, and why.

These are very important and hotly debated questions.  I'll return to them in future posts, but for now it's probably fair to say that whereas astrolabes had wide-ranging appeal, equatoria were mainly for people with narrow astrological interests.  Not only did they not tell you as much, but they were harder to use and the theory underpinning them was more complex.

Less attractive equatorium

As a result, they never developed into status symbols in the same way that astrolabes did.  Equatoria could be made shiny and attractive - check out this one at the Museum of the History of Science (MHS) in Oxford - but that was much rarer.  (It's possible that such shiny equatoria were as much demonstrations of the maker's knowledge and skill as items that customers actually wanted.)

Such shininess may account for one key difference between astrolabes and equatoria today: there are way more astrolabes!  There are 182 in the MHS collection, but only a handful of equatoria survive in the whole world.  It's a handy reminder that the survival of objects, and their display in museums today, depends on more than just their significance (however you'd define that).

I'll come back to some of these issues in future posts.  If you are burning to find out more about astrolabes right now, I recommend this excellent site.