Tuesday, 16 December 2014

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!

Wednesday, 8 October 2014

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!


Saturday, 16 August 2014

Running trail in Amman

One drawback of spending the summer in Amman is that it's really hard to go out for a run.  With temperatures of 30-35° during the day, dry and dusty air, and pavements that are often blocked or end abruptly, running in the street isn't really an option.

I joined the al-Madina gym at Sport City.  It's a fairly reasonably priced, well equipped gym, but I find running on the treadmill just so dull.  So I was really pleased to find a shady, quiet trail nearby.  I'm writing this post to help other people find it.

I found it with the help of this blog post, which has pictures of the trail and some descriptions of the facilities in Sport City.  Sport City is a large complex that includes the national football stadium, some running tracks, a showjumping ring, squash courts, etc.  Just by the stadium is a wooded area with a small hill.  The trail goes back and forth under the pine trees, making a circuit of about 2 km.  The length isn't ideal (I had to do 11 laps last Thursday) but it's cool (and even smells good) under the trees, and there's no traffic noise.

On the map below (credit: Google Maps), Sport City (or Al Hussein Youth City) is the whole area bounded by the main roads (Queen Alia, Haroun al Rasheed, Al Riyada and the yellow one at the top whose name I forget).  Al-Madina gym is in the building next to the pool in the northwestern part of the complex (the pool is nice, but it costs 15 dinars a day).  There are entrances to the complex at that white building between the pool and the word "Queen", and almost due north of the stadium (I think you can probably work out where the stadium is).  The trail is in the triangular wooded area southeast of the stadium, right under the words "Al Hussein Youth City".  (You don't need to be a member of Al-Madina gym to use it, but if you are, you exit the gym through the disused lower-ground car park, skirt round the stadium, and cut across the main stadium car park.)


I'd really recommend this trail for anyone like me who can't face more than 20 minutes on the treadmill, but wants to get some decent miles while in Amman.  The shade isn't perfect (don't forget a cap and sunscreen) and it can still be hot, but it's definitely better than taking your chances among the traffic.

Saturday, 26 July 2014

Comprehensible input: vocabulary vs. grammar

What is "comprehensible input"?  What's just the right amount of it to be able to learn a language?  What's the relative importance of vocabulary and grammar in making input comprehensible?  And why do I always forget the word for "forget"?

I've spent the last month working almost exclusively on learning Classical Arabic.  It's a tough language for a native English speaker. Obviously it has a different alphabet and little common vocabulary - I look back fondly to my Spanish-learning days, restaurante, polĂ­tica, incendio and all that - but the learning process is also complicated by the fact that the formal classical language is quite different from that spoken every day.  It's not as different as, say, Latin is from English (or even from Spanish), but it is different enough to make talking with taxi drivers depressingly difficult.

In order to learn, I'm largely reliant on input in classes and from books, as well as the small number of other media that use the formal fussha version of the language.  Fortunately (honestly!), the school where I'm studying gives us plenty of homework - every week we have a whole list of vocabulary to take away and memorise.  The words and phrases in that list are defined only in Arabic, which not only forces us to think carefully about their meanings but also, more often than not, requires more new words to be learnt just to make the definitions comprehensible.

The problem is that most of the vocabulary isn't that relevant to my purposes.  I'm studying Classical Arabic in order to be able to read medieval astronomical texts, whereas most people on this course are Muslims or Islamic Studies students who would like to be able to understand the Qur'an, Hadith and other early religious texts.  So the vocabulary we have been learning, and the texts we read, have been tailored towards these subjects.  In the last few weeks I've learned the words for prayer mat, betrothal, and a battle at which the Prophet Muhammad was (or was not) present, as well as many different words for morality.

Have I not bothered learning this vocabulary, because it doesn't suit my purposes perfectly?  Of course not (pardon the double negative).  I've made a big effort, for three reasons.  First, I always do as I'm told.  Secondly, surely no learning is a waste, and you never know when a word will come in useful.  But thirdly and most importantly, learning the words makes the class input comprehensible - essential for acquiring the language.

Three ways to make a point comprehensible (at the Jordan Museum)
What is comprehensible input?  Put simply, it's the idea that if all the foreign language you encounter is on a spectrum from completely comprehensible (for you) to completely incomprehensible, the perfect level for you will be somewhere in the middle.  If you understand nothing, you'll learn nothing, but the same is true if you already understand everything.  The best situation is if you understand the gist of an utterance but not every word.  You will be able to absorb the meanings of the previously unknown words (imagine if you understood the gist of the previous sentence but not the word "utterance" - you'd probably guess what it meant with little or no thought).

The theory of comprehensible input (about which you can read more on the excellent LanguageSurfer blog) goes along with another theory (also credited to Stephen Krashen): that a distinction can be made between language acquisition and learning.  The former is an instinctive but slow process; the latter requires conscious effort.  The former is what you're doing if you read that sentence above and absorb the meaning of the word "utterance"; the latter might involve reading a grammar book and making notes.  And, says Krashen, the former is superior - it's the only way you can really know a language, rather than just knowing about it.  (Again, see LanguageSurfer for more on this).

Grammar fans may of course protest that understanding the structure of of a language is just as crucial to knowing it as knowing its vocabulary.  I don't know about that - many native speakers don't have the first clue about the structure of their own language and get on fine most of the time (at least until they try to teach it).  But it's surely true to say that for a foreign-language learner, a solid knowledge of grammar can only help with language acquisition.  If I know from my grammar studies that the muta prefix and i vowel in the Arabic word muta'allim make it the active participle of Form 5, from the Form 1 root 'alima, meaning "to know", and I know that Form 5 typically expresses the result of Form 2, which itself tends to indicate causation of Form 1 (so that Form 5 ends up being a gradual version of Form 1), then I might be able to guess that muta'allim means a learner or apprentice - though it's more often used in an adjectival sense, as "educated".  (If you're interested, the Form 2 verb 'allama means "to teach".)

This post is already getting quite long - so time to wrap up what all this has taught me about language learning.  The first thing to say is that vocabulary must be the most important part of learning a language.  If you want to ask the way to the railway station, no amount of grammar will help you if you don't know any of the relevant vocabulary (though you can always imitate a train, something I enjoy doing at every opportunity).  Secondly, I've learned much here about how vocabulary builds on itself.  If you know a few words in a sentence, you'll be more likely to learn other words.  I suffered in the first few weeks here because my vocabulary was very poor, but as I learned some of the words the teacher uses regularly (sometimes this had to be through the conscious process of looking them up in a dictionary), I was able to pick up others with less effort.  And finally, there's no substitute for using new vocabulary in as many contexts as possible.  No matter that I mainly just want to read classical texts: hearing, writing and speaking are all important ways to drive content into my brain, and it is much easier to learn vocabulary by using it in some kind of context than by memorising lists of words.

And why I always forget the word for "forget"?  I forget the answer to that one.  It might have something to do with the weak letter root, but more probably it's just my defective brain.

Friday, 27 June 2014

Arabic in Amman: Immersion?

This blog is taking a holiday from astronomical instruments, and turning its attention to language learning.  That's odd! I hear you exclaim.  Yes, it may seem that way, but I have long been fascinated by different languages, and passionate about learning them.  And now I am in Jordan, spending 2 months improving my Arabic.  I plan to write a short series of language-focused posts while I'm here.

The big question for this post: to immerse or not to immerse?  When is it better to learn a language in that language, and when is it better to do it in your native language?

This makes me feel exotic and special...
First, a bit about why I'm here and what I'm doing.  I'm studying at the Qasid Institute in Amman.  This is a specialist language school which started out teaching Classical Arabic to Americans who were keen to read the Qur'an and other religious texts, but over the last decade or so has expanded into Modern Standard (written) Arabic, and now has students who come to learn the language for all kinds of reasons (still mainly Americans, though).  This is the second time I've studied here (I spent 2 months here in Summer 2012 too) and I am impressed by their professionalism and the standard of teaching.  I'm here now because texts translated from Arabic were incredibly important in medieval astronomy, and I'd like to be able to access some of those texts (many of which remain unpublished) in their original language.

But what's the best way for me to do this? Should I be focused on immersing myself in Arabic, or should I be thinking about translating into English and understanding the structures of the language?

Now, I have some experience teaching English - both as a foreign language (EFL) and English literature, though it's obviously EFL that's relevant here.  When I trained as a TEFL teacher, the course included 4 hours of full immersion Swedish.  Why? In order to show us how a language can be taught from scratch without a word of the user's native language being used.  Many people believe this is the best way to learn: you are not constantly comparing the language to your own, you quickly learn to think in the language instead of translating, and you can somehow trick yourself into forgetting that you can use your native language.  That last point means you're less likely to switch back into your native language, and will instead force yourself to make the best use of whatever ability you have in the new language to communicate whatever it is you want to say.

At the other end of the spectrum are the people who say that the best way to learn a language is to understand how it works, and it is much quicker and easier to do that through your native language.  These people tend to place emphasis on understanding the structures and grammar of a language, in contrast to advocates of immersion who focus on vocabulary and communication strategies.  This approach might well be suitable for someone like me, more interested in reading, understanding and translating texts than speaking.  Arguably it's well suited to Classical (and Modern Standard) Arabic in general, which are structured written languages, distinct from the spoken dialects ('Amia).  This way of learning is familiar to anyone who's learned Latin. (Are there any schools that teach full immersion Latin? That would be interesting.)  And since I've learned Latin on-and-off for a while, it might suit me quite well.

Now most people, when confronted by a spectrum of views like this, assume that the optimum is somewhere in the middle.  But for the immersionists, of course, there is no happy medium: if you get used to using your native language, particularly if you become accustomed to using it with a particular individual (your teacher, say), it immediately becomes much harder to use and to think in the target language.

Qasid have come up with a nice solution to this problem.  They split the class in two, with a different teacher for each half.  So each day I have two hours of "Skills", followed by two hours of "Sciences".  The Skills are taught exclusively in Arabic, including all instructions, definitions and feedback.  In these two hours we use the familiar four skills of reading, writing, listening and speaking - but no translation, you'll note.  In the Sciences class we study Arabic grammar, learning to analyse and parse the structures of texts, discussing the patterns of grammar and seeing how the texts fit together.

For me, this is a good compromise.  It has its drawbacks: grammar questions arise in the immersion (Skills) class, of course, and it's tricky to ask in Arabic why a verb has a certain ending, and even harder to understand the teacher's answer.  Meanwhile questions of vocabulary and usage arise in the grammar (Sciences) class, but asking them sometimes feels like a distraction, as if it's inappropriate to focus on minutiae when we're looking at the bigger picture.  But in general I like the approach.  There's not much space at present for translation, but that's a skill to work on in future.  For now, I'm happy getting my head around the 10 Forms in one class, and discussing the battle tactics of the companions of the Prophet Mohammed in the other.  Come back soon for an update on how it's going!

What are your experiences of language learning?  How do you prefer to learn?  Feel free to comment below!

Monday, 9 June 2014

Launch of the Digital Equatorium

I wrote this post for the Peterhouse Perne and Ward Libraries blog.  It is cross-posted from there with their kind permission.

28 May saw the launch at the Whipple Museum of the online Peterhouse Manuscripts Collection, housed in the Cambridge Digital Library. The collection aims to present highlights from the College’s collection of 276 medieval manuscripts, and will be developed as time and funding allow. High-quality images are presented alongside searchable transcription, commentaries and critical apparatus, making the Peterhouse manuscripts accessible to scholars around the world. Initial work on the collection has been made possible by generous funding from donors to the College, particularly Dr Joe Pesce.

The launch focused on the first manuscript to be digitised, the fourteenth-century Equatorie of the Planetis (MS 75.I). This manuscript has been at Peterhouse since at least 1538, but it was first brought to the world’s attention in the 1950s by the historian of science Derek (de Solla) Price. Price was a PhD student, conducting research into “the history of scientific instrument making”, and came to the Perne Library expecting to examine an unexceptional astrolabe treatise. He found something quite different, as he later recalled:
As I opened it, the shock was considerable. The instrument pictured there was quite unlike an astrolabe – or anything else immediately recognizable. The manuscript itself was beautifully clear and legible, although full of erasures and corrections exactly like an author’s draft after polishing (which indeed it almost certainly is) and, above all, nearly every page was dated 1392 and written in Middle English instead of Latin. [Science Since Babylon, enlarged edition, 1975, 26-27]
What Price saw, one cold December day in 1951...
Price realised straight away that the manuscript might be by the poet and astronomer Geoffrey Chaucer (c.1343-1400), whose Treatise on the Astrolabe, probably written in 1391, is a very early example of scientific writing in English. He quickly changed his PhD to focus exclusively on this manuscript, and the resulting thesis (published in 1955) included an edition and translation of the instrument treatise that takes up nine folios of the manuscript (alongside seventy folios of astronomical tables).

The instrument Price could not at first identify turned out to be an equatorium, a device designed to compute the positions of the planets. Few equatoria survive today, but they were popular tools of astronomy and astrology in the later middle ages. They were based on the models of planetary motion explained by the Greek astronomer Claudius Ptolemy (c.90-c.168) – essentially three-dimensional diagrams with moving parts. Medieval astronomers took pride in adapting and refining their predecessors’ designs, and the Peterhouse equatorium, whose construction is explained in detail in the manuscript, represents an improvement on the equatoria of notable astronomers such as Campanus of Novara (c.1220-1296) and Richard of Wallingford (1292-1336). Because the manuscript is a draft, we can see the author-translator working out and refining his ideas, learning new techniques and devising improvements as he goes.

Equatorium made at Cavendish Laboratory for
Derek de Solla Price, 1952. Now at Whipple Museum
of the History of Science, Cambridge (Wh.3271).
Price decided to build the equatorium, following the manuscript’s instructions. In an era when historians favoured intensive textual scholarship and did not particularly value reconstruction, this was unusual. So why did Price do it? The answer perhaps lies in his biography. He was from a working-class, Jewish background in the East End of London, and had taken his first PhD in metal physics at the South-West Essex Technical College in 1946. He came to Cambridge from the University of Malaya, where he had been teaching applied mathematics. He arrived in Cambridge in 1951, the year that the University set its first exams in History of Science, and the Whipple Museum of the History of Science opened. The discipline of history of science was in its infancy, and scientists and historians were competing for authority as its boundaries were laid out. In this context, Price clearly felt he needed to establish himself; the publicity surrounding the discovery of a manuscript that might be written in the hand of Chaucer allowed him to do that. Price had worked in the Cavendish Laboratory, helping organise its archives and historic apparatus, and had a good relationship with the Cavendish Professor Sir Lawrence Bragg. Bragg helped him organise a full-scale model of the equatorium to display at an event at the Royal Society in 1952. The model, pictured above, is now at the Whipple Museum. An account of its construction, later loss and rediscovery, has just been published in the Royal Society journal Notes and Records, written by current Petrean Seb Falk.

Now, though, another model of the equatorium has been made – but this one is virtual. Produced by programmer and designer Ben Blundell, in collaboration with Scott Mandelbrote and Falk, the model is embedded in the Digital Library website alongside the manuscript. It allows users to gain the full experience of using the equatorium, giving results for the longitudes of the planets very close to those achieved by modern astronomical computation. In order to produce the model, Blundell needed to create his own calendar that transitioned seamlessly between the Julian and Gregorian systems, and to write new programming language to simulate movement of the equatorium’s silken threads!
Virtual equatorie created by Ben Blundell for the Peterhouse
collection at the Cambridge Digital Library
It is hoped that visitors to the website will gain a new understanding of how the equatorium works and might have been used. It is based on a simplified version of Ptolemy’s planetary models, ignoring the planets’ motions in latitude, and by scaling the parameters of the different planetary models to give them all equally sized deferent circles, their motions in longitude can all be modelled on a single disc. A single epicycle is used, its radius corresponding in size to the common deferent radius; a rotating rule is fixed at its centre and marked with the radii of the planets’ epicycles, which are thereby traced out as it rotates. The longitudes of the planets are found by taking easily calculated linear components of their motion from pre-prepared tables, and transferring those values to the equatorium by laying threads on the scales on the circumference of the disc and epicycle. (For more information, see the explanation on the Digital Library website, and try the model there!)
Study of the manuscript has not been confined to its technical content. At the launch, Professor Kari Anne Rand explained how linguistic and palaeographic evidence has been used to locate the manuscript’s production to the periphery of London, and to cast doubt on its attribution to Chaucer. She showed how certain characteristic features of the scribe’s practised, informal hand appeared in another manuscript that she has found, raising the possibility that an alternative candidate for the authorship of MS 75.I may soon be identified.
Detail from British Library MS Burney 275, f.390v (early 14th century). The illustrator of this copy of Ptolemy's Almagest clearly had some understanding of the use of astronomical instruments.
Whoever wrote the manuscript was part of a thriving astronomical culture, based in but not restricted to the growing universities of Oxford and Cambridge. Instruments like this equatorium were used not just for astrology, or to model the movements of celestial bodies with greater ease, but as a route to greater comprehension of the cosmos. As the picture above indicates (and as Dr Catherine Eagleton reminded us at the launch), devices like astrolabes were familiar features of literate culture. The equatorium was undoubtedly a more complex device but, as the references to the Treatise on the Astrolabe in the Equatorie suggest, it might be a suitable next challenge for someone who had already mastered that more commonplace tool. If the fox could learn from nature with the help of his astrolabe, so too could the medieval English readers who, for the first time in the Peterhouse manuscript, had the opportunity to learn about equatoria in their mother tongue.

Friday, 30 May 2014

Cambridge in 1945

I've just come across this fantastic propaganda film from 1945.  It is a detailed picture of life in Cambridge as the second world war came to a close.  It's fascinating to see what's changed (co-education being the most obvious thing) and what hasn't (just about everything else!).

Readers of this blog might also be interested to see a clip of Sir Lawrence Bragg, then Cavendish Professor, lecturing - it's at 5:52.


Cambridge (1945) from British Council Film on Vimeo.