Tag: Radio

In Our Time: Crystallography

Crystallography is a technique that uses the diffraction patterns created by passing x-rays through a crystallised substance to determine the structure of the substance. It was first described in 1912 & has become very important to many scientific disciplines since then. The experts who discussed it on In Our Time were Judith Howard (University of Durham), Chris Hammond (University of Leeds) and Mike Glazer (University of Oxford and University of Warwick).

The programme opened with a brief description of crystallography & its wide-ranging uses in the sciences and then moved on to discuss the history of the technique. X-rays were discovered by chance at the end of the 19th Century, and were given the name “x-ray” because they were unknown rays. One of the questions physicists were trying to answer about these new rays was “are they particles or waves?”. As I understand it the modern physicist’s answer to this would be “yes.” but at the turn of the 20th Century they were still trying to categorise things as one or the other. A German physicist called Laue figured out an experiment to look at this – light waves split and are diffracted if passed through a diffraction grating, but the holes in these are far too wide to do the same at the sorts of wavelengths that x-rays have. So when he learnt about crystals – that they are regular arrangements of atoms or molecules – he realised these might act as diffraction gratings for x-rays. As he was a theoretician he got his students to do the actual experiment (I thought Hammond was quite sarcastic about this as he was telling us about it) – which neatly showed both that x-rays act like light waves when you use a fine enough diffraction grating and that crystals have this regular structure.

The next step on the way to using crystallography to determine the structures of molecules was done by a father & son team called William Henry Bragg & William Lawrence Bragg. Glazer told us a bit about the family – that they came from Wigton, Cumbria (just like Melvyn Bragg, in fact) and William senior moved out to Australia where he met his wife & had children (including William Lawrence). The family moved back to England, where William senior became a professor of physics at Leeds University & Lawrence became a student at Cambridge University. And they both worked on x-rays & x-ray diffraction through crystals. It was Lawrence who figured out the formula (Bragg’s Law) that describes the way that x-rays pass through the crystal structure & how the interactions between the different wavelengths and the differing spaces between the parallel planes of atoms produce a particular configuration of spots on the photographic plate. This formula is now used to work out the structure of a molecule from knowing the wavelengths of X-rays that are put in, and analysing the diffraction patterns that come out.

William senior in parallel was developing the X-ray spectrometer which provides a quantitative measure of the diffraction patterns. The original set up for these experiments was to shine a beam of X-rays through a crystal onto a photographic plate, and then look at the intensities of the spots to work out what structure would’ve generated that pattern. And for simple structures this works out OK, but as it gets more complicated you have a much more complex pattern where differing dots of differing densities might be hard to tell apart. So William developed a technique & machine that shone different wavelengths of x-rays through the crystal at a variety of angles sequentially rather than simultaneously, and then passed the diffracted beam into an ionising chamber to measure the intensity. This was initially a slow & laborious process, but essentially the same principle is used in today’s crystallography experiments – just the advent of computers & more refined technology has made the whole process much easier.

The first structures solved were simple ones – the very first was that of salt, NaCl. People then moved on to slightly more complex molecules (such as the benzene ring). And from there to much more complicated things, like proteins which consist of hundreds of thousands of atoms. The first of these to be published was the structure of haemoglobin, which was solved by Max Perutz – I think I once went to a lecture given by Perutz (but about 20 years ago so I can’t really remember it). The most famous is the structure of DNA, the discovery of which was published by Watson & Crick but relied heavily on data from Rosalind Franklin (which she wasn’t aware had been given to the other two, and she wasn’t credited for her work at the time).

During the programme the conversation went off on some interesting tangents. The first of these was that there is a relatively large number of women working in crystallography at all levels, and has been since the early days of the science. Howard said that this was down to both the newness of the field (relatively speaking) and the attitudes of the initial founders. Both Braggs welcomed anyone who could do the work into their groups, and didn’t discriminate based on gender, and there weren’t previous entrenched attitudes about the “place of women” in the field to overcome.

They also briefly discussed the way that modern science funding would’ve stifled some of the pioneering work in the field. I shan’t get up on my soapbox here, but it’s something I’m in agreement with. The examples from this discussion include the discovery of both x-rays themselves, and the technique of crystallography, which revolutionised several scientific fields and wouldn’t’ve happened if the scientists had had to figure out in advance why it was worth spending the money on that research. And some of the initial work solving structures was incredibly long term by modern standards – it took Perutz 25 years to be able to publish the structure of haemoglobin, no direct pay off in a 3 year project that’s easy to point to when you’re writing a grant application. You need some blue skies research and long term projects, as well as the more directed and more obviously relevant stuff – that’s how you expand the boundaries of knowledge & find out truly new things.

And they discussed how crystallography is a multi-disciplinary field – and that’s one of it’s strengths. People come from different scientific backgrounds, and collaborate across the boundaries of these fields.

In Our Time: The Cult of Mithras

The cult of Mithras was one of several cults that sprang up in the Roman Empire during the 1st Century AD. It was a mystery cult and so what we know of it now comes from archaeological evidence and the writings of people who were not members. The experts who discussed it on In Our Time were Greg Woolf (University of St Andrews), Almut Hintze (SOAS, University of London) and John North (Institute of Classical Studies, University of London).

The historical origins of the Mithras cult aren’t clear – back in the late 19th Century it was thought that the cult had a direct connection to Zoroastrianism, mostly because there is a Zoroastrian god called Mithra. But more recent scholarship suggests that the connection isn’t particularly direct – it’s more like the Romans took the name & some very basic idea of the worship of Mithra and then reinvented it completely for their own cult. (Which meant it felt a little like Hintze was invited to the programme based on a faulty understanding, as she’s a Professor of Zoroastrianism – she did have other things to contribute, but I felt like she got unfairly cut off a few times.) Other cults that sprang up at the same time had similar types of origins, although possibly had closer links to their parent religion – things like the Roman Isis cult, or a Demeter cult. And of course Christianity can be seen as another of these – Pauline Christianity is partly a reinterpretation of Judaism for Gentiles.

The literary sources of information about the Mithras cult are pretty slim – a lot of it is written by Christians who are trying to show how their religion is a real one, and this Mithras nonsense is a work of the devil. That was apparently a mainstream Christian opinion during the first couple of centuries after Christ, that the devil had started up all these other cults so that the truth of Christianity would be obscured by competing cults. And later in the 4th & 5th centuries Christians were involved in the destruction of Mithraic temples (as part of a wider movement of the destruction of pagan temples).

The archaeology tells us more about the iconography & so on of the cult, but as I said at the start it was a mystery cult and so the iconography is not explained. One of the images that is present in nearly all excavated temples is of Mithras killing a bull, while a dog & a serpent lap up the blood and a scorpion & a raven are also involved in the killing. Hintze pointed out that this is very different from the Zoroastrian Mithra in the level of violence protrayed – whilst there is a Zoroastrian myth that death entered the world with the killing of a bull, it’s the force of evil who does the killing in Zoroastrianism and doesn’t come with so much violence. Whereas in the Mithras cult it’s the god doing this, and it’s a violent scene – still possibly having to do with creation of the cosmos in some fashion. Other scenes include some sort of story for how the bull ends up in the cave where it is killed (although these are not always in the same order which seems odd if they are a sacred narrative). And a meal that Sol & Mithras eat together.

The temples themselves represent a cave – the cave that the bull was killed in. And there are indications that the gathered worshippers (20-40 of them) ate a communal meal. There is also from one temple some recent evidence that there may’ve been some sort of ritual meal for non-initiates around the outskirts of the temple. But by the way this was presented on the programme it seems this is still very much a conjecture based on a single data point.

Another archaeological source for the cult are the dedicatory inscriptions from members of the cult. These are all from men, and as there are a few thousand of these (I think they said) this seems to suggest that there were no women members of the cult. They are also all from the middling sort of people – not poor, not rich. And are primarily members of the military or the bureaucratic hierarchy.

It seems that the cult had seven levels of initiate, the lowest ones were called ravens & the highest paters (fathers). One of the middle levels was called a leo (lion) and from some of the texts & inscriptions this seems to be the “normal” level of an initiate. There could only be one pater per temple, and when there were too many worshippers a new temple would be built. I think they have depictions of the initiation ceremonies for progressing up the levels & it seems that these were fairly brutal. Presumably they also involved transfer of the sacred knowledge, but we don’t have any record of this.

Towards the end of the programme they had a little segment doing a compare & contrast with Christianity, because that has always been one of the things that’s brought up when discussing Mithraism in a modern context. They talked about how the 25th December was supposed to be significant in the Mithras cult, but it seems this was based on a single calendar and it’s not even clear that that’s what the calendar meant! That’s the one I’d heard before, that Mithras’ birthday was the same as Christ’s but that doesn’t appear to be true. They also discussed how Christianity was actually more similar to the Demeter & Isis cult than it was to the Mithras cult – there’s no death & resurrection in the Mithras mythology (that we know of) for instance. And in the Mithras cult your position in the secular hierarchy was often reflected in your position in the initiate hierarchy – which is again not the case with Christianity.

When I set out to write this I wasn’t sure how much I was going to remember, but it seems the answer is “quite a lot” 🙂

In Our Time: Bertrand Russell

Bertrand Russell was, among many other things, one of the influential British philosophers of the 20th Century. The experts who discussed his life & ideas on In Our Time were A. C. Grayling (New College of the Humanities, London and St Anne’s College, Oxford), Mike Beaney (University of York) and Hilary Greaves (Somerville College, Oxford). The programme concentrated on his mathematical work and on his philosophical ideas. They started the programme with a brief description of Russell’s early life – he was born in 1872 as a part of an aristocratic family & didn’t go to school until his teens, just before he went to study at Cambridge University. The bit that stuck in my mind from this part of the programme is that he wasn’t sent to school because he was thought of as the sensitive sort – his brother went to school, but that was because he was more into sports & more robust.

He started out studying mathematics, and then moved onto philosophy, and worked in both fields over his life. In mathematics he was particularly concerned with building the whole of maths up from logic alone – so in arithmetic instead of accepting as an axiom that 1+1=2 you first have to prove that. This was partly because of a philosophical point of view that why should you accept those axioms on trust, and partly because if your system of deciding if a proof is valid or not depends at any point upon intuition then it’s possible for different mathematicians to disagree about the validity of proofs.

So to derive something like 1+1=2 from logical principles alone he first had to define the numbers based on logical principles and the operation of addition. He used the then new idea of sets – called “classes” at the time. I think the idea for how to use sets to define numbers worked as follows: the idea of identity (something is identical to something else) is a logical principle. The idea of non-identity is also such a principle. If you have a set that contains all things that are not identical to themselves, then you have a set with nothing in it – this is the null set, or zero. This set is a singular object. If you have a set that contains the null set and nothing else, then it is a member of the set of all sets that only contain one thing. Which you can use as the definition of the natural number 1. Now you have two objects (the null set, and the definition of 1) and can use those in the same way to define the natural number 2. I am a little confused here why this isn’t using the number to define itself – but I suspect the confusion arises from me (and the experts on the programme) using words to discuss something that’s better done symbolically. They didn’t cover how Russell used sets to define the operation of addition, but I suspect that’s even more complicated.

But using sets to define the basic logical underpinnings of arithmetic introduces a paradox – called Russell’s Paradox, because he described this flaw. If you have a set that contains all sets that do not contain themselves, then does that set contain itself or not? The word picture they used to make the paradox more clear was to say imagine there’s a barber in a village who shaves all the men who do not shave themselves, and only the men who do not shave themselves. If he does not shave himself, then he is a man who does not shave himself and so must be shaved by the barber. But the barber is himself, so if he shaves himself then he is ineligible to be shaved by the barber. But the barber is himself, so now he is not shaved by himself and so must be shaved by the barber etc etc. So Russell took his theory back to pieces and tried to rebuild it without this flaw (and ultimately failed, I think they said). He tried to categorise the sorts of objects that can exist into a hierarchy – there are objects that aren’t sets, then there are level one sets that contain objects that aren’t sets, level 2 sets can contain objects that are level 1 sets etc etc.

And I was reminded that I should re-read “Gödel, Escher, Bach” at some point 🙂

On the philosophy side of things Russell was the founder of something called Analytic Philosophy, which is apparently the dominant philosophy in the English speaking world these days. He was reacting against Idealism which was the dominant philosophy when he was studying at Cambridge. I think the key thing was that the Idealists thought of the mind as the dominant thing, the world exists as it is perceived – essentially a sceptical philosophy where you don’t know if anything is real except that which you have perceived yourself. Russell was more of a Realist (technical term, I think) who was on the side where if you can express a thought about something then that thing must in some sense exist (even if what you are saying is “fairies don’t exist” then the very fact you can conceive of fairies means they do somehow exist even if not actually in the actual real world). Analytic philosophy isn’t as far from Russell’s mathematics as one might imagine at first glance – a large part of his system is breaking down language into logical components and using this to express ideas with clarity. I have a feeling I’ve completely mangled this explanation, and looking at wikipedia hasn’t helped. I do remember the example they gave of the sort of thing he was talking about, which is that the sentence “The present King of France is bald” is actually made up of three logical sentences. In words this would be “There is a thing that is the King of France”, “All things which fit the definition of this thing are this thing” and “The thing that is this thing, is bald.” So when you look at the original sentence it’s hard to tell if it’s true or false – and Russell wanted this to break down to a binary system, either a statement is true or it’s false. The original sentence is actually quite complex – with no King of France, is he bald or not? But if you look at the three logical sentences that make it up, then you can assign it to the “false” category because the very first logical part of it is clearly false (there is no thing that is the King of France).

They ended the programme by saying that Russell did lots of other things as well as mathematics & philosophy – for instance he was heavily in politics, wrote several popular books. But clearly there just wasn’t enough time in the programme to do more than scratch at the surface of his life. And even then it felt like one of the more complex episodes of In Our Time that we’ve listened to.

In Our Time: Shahnameh of Ferdowsi

The Shahnameh is an epic poem, twice as long as the Odyssey & the Iliad put together, written in 10th Century AD Persia about Persian history. It took its author, Ferdowsi, 30 years to write and is still regarded today as one of the important pieces of Persian literature. The experts who discussed it on In Our Time were Narguess Farzad (University of London), Charles Melville (University of Cambridge) and Vesta Sarkhosh Curtis (British Museum). The two women are Iranian, and particularly towards the end of the programme were very enthusiastic about how important this poem is to Iran & to the cultural identity of the Iranian people.

At the time it was written it was a few centuries after Persia had been conquered by the Muslim Arabs at a time when the Caliphate was no longer a strong force across the Islamic Empire. The Persian people had kept oral traditions of their culture, and their own language, and during this period there was a reassertion of Persian culture. Ferdowsi was writing as part of this cultural movement & he was setting out to retell pre-existing prose records & oral tradition as poetry because he believed this would be easier to remember. So it was a self-conscious effort at writing something for posterity. It’s written in early modern Persian, so is still understandable today even if somewhat archaic. The format is rhyming couplets, and a specific meter – I think they said it was 11 syllables, a pause, 11 more syllables for each line, and the middles and the ends of the lines in a couplet rhyme. I’m not sure if that means it’s A: A, A: A, B: B, B: B or if it means it’s A: B, A: B, C: D, C: D (if you see what I mean). They said he was a very good poet and within the strict meter he uses the feel of the language to fit the things he’s writing about. So battles have words that feel short and energetic, but scenes like banquets are more flowing words.

The poem is split into three parts – myths, legends & history. The myths are what we might think of as pre-history – the first people (cave dwellers), the coming of gods, that sort of thing. The legends are the stories of heroes, and of early kings and early battles (and these may or may not’ve happened, but certainly didn’t happen like they’re told). And the history is the stories of the Kings of the Sassanid Empire – which runs from around 200AD to the Islamic conquest of Persia in about 650AD. This is accurate in the sense that the right kings are named in the right order, but it’s not really telling you about what happened when, it’s more of a manual for “how to be a good Persian King”. There are lots of dialogues where the wise advisor tells the new King how to rule – reminds me a bit of Ancient Egyptian literature which has a whole genre of that sort of thing.

After it was written it wasn’t all that popular at first – it must’ve survived, and been copied around because it’s referred to in other literature. But it comes into its own once the Mongols conquer Persia, as a way of Persianising the new rulers and of showing what it means to be Persian. Since then it’s occupied a central role in Persian education & culture – they were saying that it’s taught in schools and that even people without formal schooling would learn sections of the poem.

In Our Time: The Borgias

The Borgias have a bit of a reputation – poisoning, murder, incest & all sorts of bad behaviour. And particularly shocking in a family that includes two Popes! The experts who discussed this on In Our Time were Evelyn Welch (Queen Mary, University of London), Catherine Fletcher (University of Sheffield) and Christine Shaw (Swansea University).

The programme started with a brief run-down of the salacious details of the “Black Legend” (much as I did just now, but they did it with a quote). Then they moved on to set the Borgia family in context with a description of Italy in the fifteenth century – unlike today it wasn’t a single unified state, instead there were several different states on the peninsula. Some were city states ruled by aristocracy, some were republican city states, other areas were kingdoms (like the Kingdom of Naples), and there were also the papacy. The political interactions of all these various states, and of the families that ruled them were complex and sometimes the rivalries were so bitter that states would rather invite in foreigners than be ruled by a neighbouring state. The papacy had only relatively recently returned to Italy & to Rome, and so was in the process of establishing itself (in temporal terms) in the network of relationships. The Pope held a lot of lands within Italy, including the Kingdom of Naples.

The Borgias enter the story with Alphonso Borgia who came with the King of Aragon when he conquered Naples, as a secretary & lawyer. He was then made a Cardinal, and became Pope as a compromise candidate when there was stalemate between the two leading candidates. Once he became Pope he did the traditional papal thing of making a nephew or two into Cardinals. They were saying on the programme that this nepotism (the word is derived from the Italian for nephew) was fairly standard – that there were really two sorts of Cardinals, those that were respected theologians or churchmen, and those that were there to be part of the government for the Pope’s temporal domains. And promoting your own family to these positions would give you some men on whose loyalty you could count.

So Rodrigo Borgia is one of these new Cardinals and he stayed a Cardinal under several popes for thirty-something years, gaining experience and power as he did so. The experts were saying that he was a very politically savvy man. He was elected as Pope in 1492 and took the name Pope Alexander VI – he’s the (in)famous Borgia Pope. Here’s where in the programme we had the first debunking of a popular legend – he is generally said to have bribed his way to the papacy, but the experts were keen to point out that bribery isn’t quite the right way to describe it. Yes, his various bishoprics were handed out to various Cardinals etc after he became Pope but this was the standard way that things were done. And obviously people who were on good terms with him would be more likely to get given these, but it wasn’t that he systematically went out to gain votes by promising people rewards. Any of the candidates for the papacy would’ve given out their bishoprics to allies after they got the office.

Rodrigo had several children, eight I think they said, and particularly doted on the eldest four (who all had the same mother). These included Cesare Borgia and Lucrezia Borgia who are the other main subjects of the salacious legends. They said on the programme that it wasn’t particularly shocking that a Pope had children – but he did raise eyebrows by actually having children whilst he was Pope and by legitimising his children.

They talked about how the generally politically astute Rodrigo had a blindspot when it came to his children. He was trying to ensure the survival of his dynasty after his death and granted Cesare a lot of lands that had belonged to the Pope, which unsurprisingly didn’t particularly go down well. Rodrigo was effectively trying to sweep aside all of the delicate alliances & networks of relationships that existed in Italy and to install his son in a fiefdom of his own. He also once left Lucrezia to handle the papal correspondence whilst he was away from Rome – shocking because women weren’t even supposed to be in the Vatican, let alone be in a position of responsibility. This helped fuel rumours of indecent relations between father & daughter.

When they came to discuss the rumours and legends they were fairly unanimous that most of it was made up by enemies of the Borgias either at the time or after one of Rodrigo’s main rivals had succeeded him as Pope. There probably was one orgy, but there is no evidence of poisoning or of incest. The incest rumours in particular are probably due to someone who would have a distinct bias against the Borgias – Lucrezia’s first husband. At the time the rumours start Rodrigo is trying engineer his daughter’s divorce (because he wants an alliance with someone more useful), and is trying to get the chap to sign off on an annulment on the grounds that he was incapable of consumating the marriage. Which the soon-to-be-ex-husband isn’t particularly happy about, so he’s spreading rumours about how rather than him being impotent it’s more that Rodrigo wants Lucrezia for himself.

However it is likely that the talk of murders was true – some of them at least. But this is not confined to the Borgia family, and it’s worth remembering that not only were the politics of the time fairly cut-throat in general but also the whole period is a time of war. The King of France is marching his armies through Italy (at, I think, the request of some states that are hoping he’ll back them against other states – that whole thing where the internal rivalries are stronger than the external). There’s definitely evidence that Lucrezia’s second husband was murdered on the orders of the Borgia. And perhaps one of the Borgia sons was murdered by Cesare – but there are several other candidates for his murderer. However, Shaw made the point that the Borgias seem to’ve been particularly feared as a family that you shouldn’t cross, and even Rodrigo seems to’ve thought that Cesare overreacted when he felt he’d been insulted. So they certainly weren’t a nice family.

They talked a bit about the later lives of Cesare & Lucrezia – Cesare basically declined from power & ended up dying in some minor conflict in Navarre. Lucrezia died in childbirth at the age of 39, and at that point had a reputation for piety & good business sense – not what you’d think if you believed the stories told about her now.

So the take home message was that the Black Legend of all the evil doings of the Borgias was pretty much propaganda. They weren’t nice people by any means, but they weren’t unusual for a ruling family of the time.

In Our Time: The Upanishads

The Upanishads are some of the sacred texts of Hinduism, originally transmitted orally from father to son in the priest families they were written down in the 6th Century AD. They consist of a series of dialogues about the nature of the universe and the nature of knowledge. And I’d not even heard of them before listening to the In Our Time episode about them. The experts on the programme were Jessica Frazier (University of Kent and University of Oxford), Chakravarthi Ram-Prasad (Lancaster University) and Simon Brodbeck (University of Cardiff).

They started by putting the texts in context – the oral versions date from about 700BC and are the last part of the Vedas, which are the rituals performed by Hindu priests. The Vedas are part of the ancient concept of religion as control of the world – these rituals are spoken in the right way at the right time, with the right ceremonies, and then the gods and world will become ordered in the way you desire. The Upanishads were developed during a time when the tribal societies of the Indian subcontinent were starting to coalesce into kingdoms, with larger urban centres, and are concerned with the meanings and knowledge behind the rituals. They’re presented mostly as a series of dialogues between pupil and teacher (with the roles of teacher & pupil being taken by various different people – sometimes father & son, sometimes husband & wife, sometimes King and sage (in either role)). I’m not quite clear on why they started to be written down, perhaps it was just a more general transition from oral to written culture? But even after they were first written down they were still for the priestly class, not for general consumption. Over time commentaries on them were written by religious leaders, and closer to modern times they were translated first into Persian and then into Western languages & became more widely known.

There was an interesting division between the experts. Brodbeck seemed to concentrate on how the texts were about knowledge and about how to transmit and to learn that knowledge. And the other two were more interested in what the texts had to say about the Hindu beliefs about the nature of the universe. Interestingly they were saying that the Hindus were not interested so much in “who created the world” like many other religions, but more in what came before there was a world and before there was a creator – this is the concept of Brahman (I think) which is the universal cosmic power & is described using many different analogies in the Upanishads. They also discussed the desire for immortality reflected in what the Upanishads said, and how this is different from the Western concepts of immortality. In our culture immortality is about the continuation of the personality – either living forever or dying and going to an eternal afterlife as yourself. But in the Hindu religion it can be about the immortality of one’s lineage – one’s children are one’s immortality, they carry on the line. Or it can be about the immortality of the Atman (which again is described with many analogies in the Upanishads but roughly translates as the self). And this isn’t your personality, if the Atman is reincarnated the new life isn’t related to the old one & doesn’t remember it or anything, even tho it’s the same immortal Atman. And a goal is to die finally and become part of the Brahman, in an immortal existence that has no more personality or suffering like there is in the world.

In Our Time: The Anarchy

The Anarchy is a 19th Century term for a period of civil war in England in the 12th Century. The three experts who discussed it on In Our Time were John Gillingham (London School of Economics and Political Science), Louise Wilkinson (Canterbury Christ Church University) and David Carpenter (Kings College London). It turned out to be quite a lively discussion – Gillingham and Carpenter in particular seemed to disagree quite vigorously over how poor (or otherwise) a king Stephen was.

The period of time in question is about 80 years after the Norman Conquest, William the Conqueror was succeeded by his son William Rufus. Who in turn was succeeded by his brother Henry I. Henry had only two legitimate children (and about 20 illegitimate ones) – William and Matilda. William died young, drowned when the White Ship sank in the English Channel in 1120, and so Henry had no male heir. He promptly re-married but that marriage had no children. So he reluctantly designated Matilda as his heir, and made his nobles swear an oath to support her as heir.

Matilda had been married to the Holy Roman Emperor, she was sent to Germany at the age of 8 and educated there. When she married at the age of 12 she started to take on the role of Empress – in Germany the wife of the ruler was to some degree a co-ruler, so she granted charters etc. Wilkinson was saying that when Matilda was 12 her exercise of power was probably under the guidance of the Emperor’s advisers as part of her education, part of her training to rule. Once the Emperor died in 1125 she was summoned to return to England by her father to be designated as his heir, and re-married to Geoffrey d’Anjou in the hopes that this second marriage would produce offspring (it did).

Despite saying that she was his heir it seems that Henry didn’t really do much to make sure she had a chance of holding the throne. All three experts were in agreement that he didn’t let her establish a power base of any sort in England – he assigned her no lands, no castles. So really he was responsible for what happened after he died in 1135 – instead of Matilda inheriting, the throne was seized by her cousin Stephen de Blois. And the nobles in England were all perfectly happy to let this happen. The nobles in Normandy would’ve preferred his older brother to take the throne, but no-one was really on Matilda’s side (or at least not publicly). This was partly because she was a woman, and partly because she was foreign-educated. She was also widely regarded as proud and arrogant – Wilkinson was clear that she thought this was primarily because Matilda was a woman. That the same characteristics and actions as a man would’ve brought Matilda praise. The other two seemed to think that there was more truth to this than that – that Matilda might’ve been able to make life easier for herself if she’d been a little less concerned with her status as Empress.

Stephen was the sort of man who got along with everyone – he’d not been intended to be King & in many ways stayed more first-among-equals with the Barons, rather than their ruler. Carpenter was fairly anti-Stephen, he thought that he showed poor judgement in choosing who to please, whose side to take in disputes. Gillingham felt rather that Stephen had inherited a bad situation, and did as well as he could. But whichever is true, after a while Robert Earl of Gloucester (one of Henry’s illegitimate children) went over to Matilda’s side. He escorted her to England and his holdings gave her the power base she’d not had before. Stephen had the chance to capture Matilda at one point during this journey, but didn’t do so – which Gillingham thought was the right course of action due to the potential effects on Stephen’s reputation, but Carpenter thought was a ludicrous mistake.

The conflict dragged out for nearly 20 years, although there weren’t many actual battles. Stephen’s wife, another Matilda, was instrumental in both the negotiations and in raising armies particularly during a period where Stephen had been captured by the Empress. She wasn’t regarded with as much distaste by the nobles, because she managed to do this while still behaving femininely enough for the standards of the time. Despite the lack of battles the war had a lot of effect on the country – hence the later name of the Anarchy. One of the standard strategies in warfare at the time was to ravage the lands around your opponents castles – so burn the crops, burn the villages, ruin the economy of the area as well as deny the fortresses food. Gillingham and Carpenter disagreed on how much and how widespread this was. Carpenter was presenting a picture of the whole country in flames and turmoil, but Gillingham felt that outside a few areas it was pretty much business as usual for the peasantry.

The war was finally over when Stephen and Matilda’s son Henry came to an agreement that once Stephen died then Henry would be heir.

In Our Time: Fermat’s Last Theorem

Fermat was a 17th century lawyer who did maths in his spare time, corresponding with many other mathematicians around Europe. He had a habit of setting little challenges to his correspondents – “I can prove this, can you?”. He’s famous now for an annotation he made in a book – that he had found a proof that an + bn = cn has no positive integer solutions when n>2 “which this margin is too narrow to contain”. The guests on the episode of In Our Time that discussed it were Marcus du Sautoy (University of Oxford), Vicky Neale (University of Cambridge) and Samir Siksek (University of Warwick).

They started off by setting the theorem in context. It’s a generalised form of Pythagorean Theorem – the one we all (probably!) learnt at school. For a right-angled triangle the sum of the squares of the two shorter sides is equal to the square of the longer side (the hypotenuse). And du Sautoy pointed out that this has a very practical application – if you have a rope with equally spaced knots in it and you arrange it into a triangle with sides 3, 4 and 5 then you are guaranteed a right-angle between the sides of length 3 & 4. Useful for building pyramids. And other things you want the corners to be right-angles on. So for n=2 we know there are some positive integer solutions.

It’s also a sort of equation called a Diophantine Equation – these are polynomials that only have positive integer values of their variables. So other examples are things like x2=y3-2 (which has at least one solution – 52=33-2). Some Diophantine Equations have no solutions, some have finite numbers of solutions, some have infinite. And the question is what sort of equation Fermat’s Last Theorem is.

Fermat never wrote his proof down anywhere, and the experts were suggesting that perhaps he never actually had a generalised one. That his proof by infinite reduction of the case where n=4 was all he’d done (and then was suggesting that must be the case for all the other possible values). The equation itself isn’t a particularly interesting one and hasn’t any direct practical applications, but it became famous because no-one could find the proof that Fermat said he had. Various famous (and otherwise) mathematicians tried to find the proof – the one that they discussed that I particularly remember is Sophie Germain, who was a French mathematician in the late 18th/early 19th Century. At that time she couldn’t study mathematics formally because she was a woman, so she was self-taught & corresponded with other mathematicians using a male pen-name. She found a way to inspect particular values for n to show that there were no solutions – and used this to prove the theorem for values of n up to 100. Neale clearly found Germain particularly interesting as she nearly got side-tracked into a bio of her before being pulled back to the subject at hand 🙂

During the 19th & 20th Centuries there were several monetary prizes on offer to people who found a proof, but no-one did until Andrew Wiles in 1997 (just before the time limit on that particular competition). They did discuss a bit about what his proof was, but I didn’t follow it well enough to remember it well enough to explain it – it had something to do with mapping these sorts of algebraic equations to elliptic curves, and if you could show there was no possible curve then there must be no solutions to the equation.

They summed up the programme (very briefly) by saying that even though the equation isn’t itself terribly important the effect of the competition to solve it was to drive forward several other areas of mathematics that do have practical applications.

In Our Time: Caxton and the Printing Press

The printing press was invented in Germany around 1440, and by 1476 had even been brought to the relative backwater of England, by a man named William Caxton. The guests on the episode of In Our Time that talked about this were Richard Gameson (University of Durham), Julia Boffey (Queen Mary, University of London) and David Rundle (University of Oxford). I’d heard of Caxton before, because he’s the subject of one of the mini biographies in a book I read earlier this year (“Renaissance People” ed. Robert C. Davis & Beth Lindsmith), but didn’t know much about him.

He was in his 40s by the time he became a printer – prior to that he was a mercer, that is a merchant involved in the cloth trade. He was clearly of some importance, he spent time in Bruges (in Burgundy) as the Governor of the Company of Merchant Adventurers of London in Bruges (I think I have the title right) – basically the representative of all the London merchants to the officials in the city & to the other trading nations there. They got side-tracked when talking about it, so I’m not quite sure why Caxton left Bruges and why he changed career, but in his 40s that is what he did. Moving first to Cologne where he got involved in the new trade of printing, then he went back to Bruges (probably) and proceeded to set up shop printing not just Latin & French books (which would have an international readership) but also books in English for import into England (and pretty much nowhere else, because English wasn’t an international language).

He then moved to Westminster, where he set up shop as the first printer in England (and he remained the only English printer for some time, other printers were of continental origin). They spent a while discussing why Westminster and not London (and as always I was momentarily taken aback that they aren’t the same place – I know this, but I have to remind myself every time). Partly it seems because there was already a book trade in the city of Westminster, so selling print books as well as manuscripts was in some ways more of the same and your customers would already be there. Partly because Westminster had the Abbey and all the religious related printing needs (like indulgences). Partly because the niche that Caxton was trying to fit into was more Westminster oriented than City of London oriented – he wasn’t doing legal documents and such, or pamphlets, he was primarily printing books. And partly because there were taxes and restrictions on who could produce books in the City of London, so setting up shop outside gave him more freedom (and lower bills).

So Caxton’s clientèle were primarily the religious institutions and the nobility – and a large part of what he printed was books in English, which was unusual. He is most remembered for his editions of Chaucer’s Canterbury Tales, and they spent a while talking about that on the programme. Caxton is credited with helping to cement Chaucer’s status as the première English writer, but they were pointing out that this wasn’t a new thing that Caxton did, he was very much building up an existing reputation (partly as a way of marketing his editions of the books).

Caxton is also credited with starting the standardisation of written English. But the guests on this programme were pretty clear that this wasn’t really the case – yes, printed books did do this (because you didn’t have local scribes copying texts with their local spelling, everyone bought the same edition) but Caxton himself didn’t really have much to do with it. They seemed clear that he did edit things, but was inconsistent within his own works. Also early printed books actually used the vagaries of spelling to their advantage, which I didn’t know before! So if it was more convenient to have a few letters more on a line to make the edges line up nicely then the typesetter would sprinkle a few “e”s on the ends of words, or double a letter or two. Or if you need some less, perhaps you’d take out a “u” or two.

A lot of what is known about Caxton comes from his editorial work, in particular the prologues & epilogues that he added to his books. They did stress, however, that these are often full of clichés so need to be taken with a large pinch of salt. He was clearly good at being a publisher/editor/printer though, because he didn’t go bankrupt which a lot of early printers did. This was due to the high start up costs (you need all the equipment) and because you needed to figure out how many copies of something you wanted in advance, guessing demand right could make the difference between staying in business or going bankrupt. Caxton clearly did, as his business was inherited after his death by his foreman, who gradually moved towards printing things for the legal trade and printing pamphlets. And after a while he moved the business to the City of London – to Fleet Street.

The three guests all seemed very enthusiastic about the subject, and all keen to have their say on every bit, but I did end up feeling a little sorry for Julia Boffey who got talked over more than once. She’d start making a point and one of the others would jump in and she’d be reduced to saying “yes, yes” while they talked.

In Our Time: Hannibal

The famous Carthaginian general Hannibal was the subject of the In Our Time episode that we listened to on Sunday … unfortunately I can’t hear the name without thinking of Hannibal the Hamster, the hero of a book I had when I was little (and my pet hamster was his namesake). But I did manage to put that aside, and listen to the story of a much more impressive Hannibal. The experts on the programme were Ellen O’Gorman (University of Bristol), Mark Woolmer (University of Durham) and Louis Rawlings (Cardiff University).

They opened by setting the scene – Rome and Carthage each with an empire facing off across the Mediterranean. The Carthaginian empire had grown from Phoenician trading outposts, and was centred on the western Mediterranean with important holdings in Sicily and Spain as well as their North African heartland. Rome, obviously centred on Italy, were the new kids in town and the first war between Rome & Carthage (the First Punic War) started over control of Sicily. Hannibal’s father Hamilcar Barca was the general in charge of the Carthaginian army during the last part of this war – he didn’t win, but it seems he was probably never actually expected to win as the army was underprovisioned for that sort of undertaking. Also after the end of the war (Carthage lost) he wasn’t punished, which supports this – the Carthaginians had no qualms about executing generals that they felt had failed.

After the First Punic War Carthage’s finances were in trouble, which was even more of a problem than you might expect because their army was made up of mercenaries who promptly revolted when they weren’t paid. Hamilcar put down this rebellion, and then took the army off to Spain to secure & improve the Spanish holdings – Spain being a major source of wealth for Carthage due to the silver mines. And this is where Hannibal enters the story – he’s 9 at this point, and gets taken along with his father to Spain to live and campaign with the army. And this is really where & how he learns to be such a good general – he lives with the army so knows the men and what will motivate them etc. And gets to see how to run campaigns first hand.

Once Hamilcar dies (in battle) Hannibal’s brother-in-law takes over the army and gives Hannibal the job of cavalry commander. Once his brother-in-law dies (assassinated) Hannibal gets the job of overall commander – he’s only about 25 at this point, but has 16 years of military experience. Then Second Punic War kicks off – starting over control of a particular Spanish settlement which is under the protection of Rome. And right from the outset Hannibal demonstrates some of the genius for which he’s remembered – one of his key qualities is the speed at which he (and his army) reacts to events. Rome warned Hannibal off attacking the Spanish settlement, but by the time either Rome or Carthage had reacted Hannibal had already seiged and razed the city.

This is the point where Hannibal starts the journey that he’s most remembered for – he marches his 80,000 strong army north through Spain and into Gaul, then east to the Alps and across them to northern Italy. He had to do this because Carthage were no longer the major naval power in the Mediterranean, and if they’d sailed to Rome they would have had even more trouble. They had to fight their way through both Spain and Gaul, and provision the army from the land they march through. Then they crossed the Alps during the winter. This whole journey reduces his army to approximately 26,000 men – through desertions, through leaving garrisons behind en route and through deaths as they cross the Alps. He still has some of the war elephants too! Despite these crippling loses Hannibal goes on to win over 20 battles against Roman armies that outnumber him, due to his superior tactical skills (including paying a lot of attention to and making use of the lay of the land he’s fighting on) and the superior mobility of his troops. At one point he has the chance to march on Rome, but doesn’t take this opportunity – opinion is divided on whether this was the right decision. Perhaps he might’ve won the war if he’d marched on Rome then, perhaps he was right and didn’t have enough troops to properly seige the city for long enough for it to fall.

Eventually the Romans stopped trying to meet his army on his terms – instead they used delaying tactics to avoid battle but keep the army occupied. And then attacked Carthage itself forcing Hannibal to bring his army back home to save the city. This is the battle he lost, losing the war for Carthage – a while afterwards this was used as an excuse to send him into exile and he lived in a series of provinces/kingdoms that were being threatened by Rome offering them his advice on how to campaign against the Romans. Eventually one of these handed him over as part of their peace treaty with Rome, and rather than be captured he took poison.

Hannibal is still remembered (and respected) today because the Romans were impressed with him, and afraid of him. He was apparently used as a bogeyman for Roman children. And his tactical skill was respected even into modern times.