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.

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.

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.

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.