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.

The Kalamazoo Medieval Experience

I recently attended my first ever Kalamazoo.  This is not a strange musical instrument, or a kind of olive.  It is an annual gathering of 3,000 medieval historians, which takes place on the campus of Western Michigan University, USA.  The breadth of scholarship on offer is legendary - as are the seediness of the campus accommodation, and the scariness of the dancing at the Saturday night disco.

You can watch a video of my conference presentation on vernacular astronomy here.  But in this blog post I've compiled some of my favourite tweets, to give you a flavour of my conference experience...

Friday, 29 May 2015

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!

Wednesday, 25 March 2015

Historic navigational instruments on trial

I started this blog when I reconstructed a medieval equatorium.  I wanted to understand how it worked, and the best way was to follow the instructions in the unique manuscript that describes it.

Last weekend I did it again, with three different instruments: a sextant, a cross-staff, and a mariner's astrolabe.

I only made two of these myself.
I'm a keen sailor, and one reason I first got interested in history of science was because of my fascination with navigational techniques.  Lots of stories are told about great explorers, but we rarely hear about their tools and techniques.  Sometimes we hear about great inventions, but those stories are often misleading.  So while everyone knows about John Harrison and his amazingly reliable clocks that helped solve the problem of finding longitude at sea (I recently reviewed the National Maritime Museum's wonderful exhibition on this subject), people don't always appreciate that knowing Greenwich time was only helpful if you could measure your local time accurately.  This was done by observing the altitude of the Sun.  And that was the purpose of all three of the instruments above.

Actually that's not quite right.  The mariner's astrolabe, which came into common use in the late 15th century, started out as an instrument for stellar, rather than solar observation.  It was well known that the altitude (angle above the horizon) of the Pole Star was almost equal to the latitude of the place of observation.  It was also known that the Sun's zenith distance (90° minus the altitude) at noon on the equinox was equal to the observer's latitude, but declination tables to simplify the calculations necessary on other days of the year were not drawn up until the very end of the 15th century.  That's why the first mariner's astrolabes measured altitude, while on later ones the scales were reversed to measure zenith distance.

Mariner's astrolabe in use. From Pedro de Medina's
Arte de navegar
The earliest mariner's astrolabes were made of wood - we know that Vasco da Gama had a large one, about 60 cm in diameter, on his first voyage to India in 1497.  Columbus also used an astrolabe (as well as a quadrant), though we can't be sure what it was made of.  The oldest surviving terrestrial globe, the Erdapfel of Martin Behaim, contains an inscription urging navigators to use an astrolabe.  These were soon made out of brass, which was a more durable material than wood.

From John Sellers'
Practical Navigation
The cross-staff (or Jacob's staff) incorporated simple trigonometry to measure the angle between two objects (such as the horizon and the Sun).  Although it was probably invented in the 14th century, it was not used for navigation until the 16th century.  Before then, most sea travel took place along known routes, staying within sight of land whenever possible - precise measurement of latitude was pointless.  It was only with the first trans-oceanic voyages at the end of the 15th century that the cross-staff and mariner's astrolabe became essential navigational devices.

The purpose of this blog post isn't to give the history of these instruments.  There are lots of great websites and books that do that.  I just want to write about what I learned at the weekend.

I made the cross-staff using the instructions at Richard Paselk's very informative site.  The mariner's astrolabe was just a copy of ones I've seen in books and museums.  They were both made out of off-cuts of wood I had lying around, which I sawed, glued and screwed into shape with the basic tools I have at home.  I finished them just in time for the trip I was skippering for Cambridge University Yacht Club.

I planned the trip for the new moon, hoping that we'd see some good stars (the partial solar eclipse on Friday morning was a bonus).  So, fuelled by chicken and chorizo pasta and some chocolate brownies, we set off from Ipswich on Friday evening at about 10.30 pm.  Sadly the cloud blocked our view of the stars that night.  The following day high winds and rough seas (not to mention more cloud) meant that we were more concerned with sailing the boat safely and effectively, than with astro-navigation.  But on Sunday afternoon the cloud finally cleared and we were able to try out the instruments.

Navigating Puffin up the Orwell
I took some sightings, compared them with my modern plastic sextant, and was pleased to see that both instruments were accurate to a degree or better.  I'd made two cross-pieces of different lengths for the cross-staff, and had done the trigonometry in advance, marking the angles directly on the staff (the further you push the cross-piece away, the smaller the angle between its two ends).  The result was a surprisingly versatile instrument: as well as measuring altitudes, it could also be used to measure the horizontal angle between two (or more) landmarks.  So if you have those landmarks on a chart, you can use the cross-staff to fix your position relative to them.  It was easy to make and pretty robust.  On the downside, it requires the user to point it directly at the Sun, which is pretty hard on your eyes!  It's not surprising that it was superseded by the back-staff, which could be pointed away from the Sun.

I was less impressed by the mariner's astrolabe.  It was more difficult to make: dividing a circle accurately was a major challenge.  For angles between 10 and 80 degrees it was harder to read than the cross-staff. And despite the fact that I'd made it with holes in the disc, it swung a little in the wind.  I probably should have made it out of brass instead of MDF, I suppose.  On the other hand, you can use it to measure the Sun's altitude without blinding yourself, by letting the shadow of the top sight fall on the bottom one.  But sadly the damp conditions on the boat softened the glue and one of the sights fell off... I bet that never happened to Columbus.

It was fascinating to compare these instruments with my modern sextant: the model I have can measure altitudes to 2' (1/300th of a degree).  My productions weren't that good, but I was pleased that they gave moderately accurate results even though I'm hardly a master craftsman.  Knowing your latitude to within 60 miles isn't much use if you're trying to thread your way through Suffolk sandbanks, but it might help with oceanic passages.  Above all though, I was impressed by the early-modern navigators, whose lives depended on their ability to take accurate sightings, no matter how rough the sea or how fleeting a glimpse of a star they could get.  It makes me appreciate our GPS all the more.

Wednesday, 21 January 2015

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.