Monday, 29 February 2016

Leap years and astrolabes

Since today is 29th February, a leap-year-themed post is in order.  This one answers the question you've all been asking: how are leap years represented on astrolabes?

Astrolabe-equatorium at Merton College, Oxford
First, a word about the Julian calendar.  Most astrolabes were made before the Gregorian calendar reform (1582), and that made life a bit simpler for instrument-makers.  In the Julian calendar, leap years happen every four years, without exception.  On the other hand, the Gregorian calendar got rid of 3 leap days in every 400 years, by decreeing that centurial years (1700, 1800, 1900...) would not be leap years, unless they were divisible by 400.  That's why 2000 was a leap year, but 2100 won't be.

Still, astrolabes have to deal with the fact that one year in four has an extra day.  And astrolabes basically only map celestial motions over a single year.  So how did makers handle the irregularity?

This astrolabe at the Oxford Museum of the History
of Science says it has 28 days in February, but there
seem to be 29. A mistake?
They certainly knew about it.  For the most part they made their instruments to be correct 2 years after a leap year, thus averaging out the errors (which were insignificant anyway).  But that approximation didn't satisfy everyone.

Jean Fusoris, the Parisian craftsman - and alleged English spy - whose trial for treason was taking place exactly 600 years ago, wrote in detail about astrolabe calendars.  He argued that
"Their major defect is that they assume that the Sun on its deferent circle traverses the entire zodiac in precisely 365 days, which is not true."
Fusoris proposed that marks could be added to an astrolabe's alidade (the rule used to read information between the solar and Julian calendars), so that the calendar could be read differently for different years in the leap cycle.

But this still doesn't solve the problem of the Julian calendar.  Fusoris was well aware that one leap day every four years was too much - it meant the Sun effectively moved 1 minute and 46 seconds too far every four years (there are 60 minutes in a degree).  So he suggested you could customise your astrolabe to keep it up to date.

How?  Simple.  Just file down the alidade a tiny bit:
"In this way the instrument will show the true place of the Sun precisely for the lifetime of a man and more, so it is a good way of putting the motion of the Sun on the back of an astrolabe.  It can be done just as the zodiac of the rete of an astrolabe is commonly filed down."
It's important to remember that instruments were frequently customised in this way - they weren't kept in pristine condition as museum pieces, but were designed to be working objects, to be altered and added to just as you might buy a new case for your smartphone.  (Though it may be fair to say that most medieval astrolabe-owners were about as capable of performing these kinds of upgrades as most people today are of repairing their phones.)

However, some instruments were designed to make leap year calculation easy.  The instrument pictured at the top of this post is a combination astrolabe-equatorium from Merton College, Oxford.  It was made around 1350, when Merton was Europe's centre of astronomical and mathematical learning.  The picture just above shows a segment of the same instrument's solar and Julian calendars.  (They're usually on the back of an astrolabe, but they're on the front of this instrument in order to make space on the back for a planetary equatorium.)  Above where it says "Pisces" in the middle of the picture, you can see there are four curves arcing across the photo from the top-left corner to the lower-right side.  They're crossed at an angle by more-or-less vertical lines.  Those allow the calendars to be read differently in different years.  Depending on which year you were at in the leap cycle, you simply read from the calendar to the solar longitude (or vice versa) using a different one of the four circles.

It's an ingenious solution to what was a pretty complex problem.  Of course the results weren't exact, but they never were with these instruments.  That wasn't the point.  Astrolabes - not unlike like your smartphone today - were designed to be quick and clear, convenient and user-friendly.  And attractive of course.  This one's designer succeeded admirably.

Wednesday, 24 February 2016

Medieval (g)astronomy: my PhD in biscuit form

The Equatorie of the Planetis, from
Peterhouse, Cambridge MS 75.I, f. 74r
I submitted my PhD thesis last week (and now have a little more time to post on this blog).  In large part it's a study of this fascinating instrument.

If you've read this blog before, you'll know I've studied a 1950s replica of this equatorium, made my own replica - and then made it again in a smaller form and (slightly) more authentic materials.

But until now, I'd never made an edible equatorium.

I made the face out of chocolate shortbread (an adaptation of Jamie Oliver's recipe, with 3 tbsp of cocoa added per equatorium).  The epicycle was gingerbread.

It was a bit tricky to get everything the right shape, and the gingerbread expanded more than I had expected in the oven, but it all came out pretty well...

Add a screw and nut to hold the rule to the epicycle, position them correctly, and here's your complete equatorium!

Sunday, 21 February 2016

Masculine Mars? Planetary degrees in medieval astrology

I handed in my PhD thesis earlier this week, so I finally have time for a new blog post.  It's another small step towards the blogging task I've been putting off for months: using my son's horoscope as a way in to understanding medieval astrology.

This chart has been pinned above my desk for some months:
Horoscope from Peterhouse 75.I, f. 64v
Much of my research investigates how medieval astronomers found the locations of the planets, using instruments and tables.  I explained in an earlier post how, in order to cast a nativity (an astrological analysis of the moment when someone was born), the first step was usually to find the locations of the planets in the 12 astrological houses.  The chart above is a traditional layout (here's the same layout used in a 9th-century horoscope, copied in the 14th-century manuscript at the centre of my research). It shows the cusps (boundaries) of the houses, and the locations of the planets within them.  They start in the middle on the left, and go round anticlockwise.  So in my chart, the first house starts at the 4th degree of Capricorn, the second house starts at the 16th degree of Aquarius, and Mars was at the 29th degree of Capricorn.

Now, the location of the planets in the zodiac was thought to determine the strength and nature of their influence.  But this basic astrological axiom could be interpreted in many ways.

The Declarations, a brief manual written for "The Queen" (probably Philippa of Hainault, the wife of Edward III) by the great astronomer Richard of Wallingford, who was Abbot of St Albans 1327-36, begins thus:
If there be a question made of the nativity of a man, and the planets be in masculine degrees, that shall be to him a strength.  And if there be a question made of the nativity of a woman, and the planets be in feminine degrees, that shall be to her a strength.
What are masculine and feminine degrees?  Ptolemy (whose Tetrabiblos is as important a text in astrology as his Almagest is in astronomy) had written that the stars were masculine when they rose and set before the Sun, and feminine when they followed it.  But here we see a different doctrine, in which certain degrees within each sign are assigned one or other sex.

Here, as on so many other topics, medieval astrologers were following the authority they knew as Alkabucius or Alchabitius.  This was (Abu as-Saqr 'Abd al-'Aziz ibn Uthman ibn 'Ali) al-Qabisi, a 10th-century Syrian who, along with the 9th-century Persian Albumasar (Abu Ma'shar), wrote the works of astrological theory that were most popular in the Middle Ages.  Al-Qabisi stated that the first 11° of Capricorn were masculine; the next 8° feminine; and the last 11° masculine again.  Each sign was divided in a similar way (but always in different proportions) into between 3 and 7 groupings of masculine and feminine degrees.

Opening of the Declarations, in Wellcome Library 8004, f. 31v
You'll already have worked out that for my little boy, Mars was in a masculine degree on the day of his birth.  (Matters weren't always this easy: in a table found with one copy of Richard of Wallingford's Declarations, individual hours of the week were assigned sexes.  On the other hand, the 11th-century Persian scholar al-Biruni thought the whole idea of masculine and feminine degrees was confused and lacking in substance.)

Anyway, if I use al-Qabisi's layout for little ADJF's horoscope, Mercury is also masculine; all the others (the Moon, Jupiter, Saturn, the Sun and Venus) are feminine.

This could be interpreted in a number of ways, depending on what we're interested in: are we investigating the subject's health, wealth, chances in life and love?  And how do we balance this information against other data in the horoscope concerning the Signs and planets?  I'll explain some of this in the next post (coming soon!), when I talk about the very important doctrine of planetary dignities, which considers the locations of the planets in the Signs and their relationships with each other.

For now, though, we can say that Mars and Mercury are strong in my son's nativity.  Mars, according to al-Qabisi,
indicates tyranny, bloodshed, conquering, highway-robbery, wrongful seizure, the leadership of armies, haste, inconstancy, smallness of shame, journeys, absence, indulgence in love-making, miscarriages, middle brothers, and the management of riding animals. (translation by Burnett, Yamamoto and Yano)
 Meanwhile Mercury suggests
public address, rhetoric, and activities which arise in mathematics like business, calculation, geometry, philosophy, taking omens, sorcery, writing, poetry, and all kinds of calculation . . . It indicates fear, fighting, killing, enmity, tyranny, opposition, prosperity, craftsmanship, kindness in deed, investigation, and everything else concerning commerce and contentions.
Does this mean that little A is going to be a tyrannical accountant? Well, it does run in the family.  But the more important point is that it took an experienced astrologer to interpret all the data in a horoscope.  This whole post is based on just the first two sentences of Richard of Wallingford's Declarations, and already we have a bewildering array of options.  What I thought was a simple little square diagram turns out to be surprisingly complex - in my attempts to read it, I'm beginning to understand why astrology was thought to be such an advanced science in the Middle Ages.

Sunday, 16 August 2015

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."

Monday, 13 July 2015

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!

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!

Friday, 5 June 2015

Angry Birds in Medieval Manuscripts

I'm just back from two very enjoyable days in Oxford, at the Bodleian Library's wonderful new Weston Library.  Apart from looking at some fascinating and important manuscripts, I snuck a peek at their Marks of Genius exhibition, which I'd strongly recommend if you're in town (it's free, and on until 20 September).

The view from the David Room on the fifth floor of the Weston Library is pretty special:

...though I do still have a soft spot for Cambridge's University Library - this is the equivalent view:

But of course the manuscripts were the main reason I was there.  Hopefully I'll get a chance to post about some of the things I found soon.  But for now, here's a picture of a feathered fellow who seems rather frustrated by Geber's technique for finding the latitude of a star:

MS Ashmole 1796, ff. 188v-189r

Tuesday, 2 June 2015

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 1) and midheaven 10) were used to divide up the remaining houses (those opposite points were called the nadir of the ascendant 7and the midnight line 4)).  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.