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.

Sunday, 18 January 2015

Is the Moon a planet or a star?

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

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

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

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

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

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

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

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!