Most of us learnt at some early stage that we use “Arabic numbers”, as opposed to the clunky Roman system of putting together Xs and Is. But from Jerry Brotton’s The Renaissance Bazaar I have just learnt just how great a debt our maths (and indeed accounting) owe to the East (and that they should apparently be called Hindu-Arabic numbers).

The man who brought many of the concepts and symbols to Europe was Leonardo Pisan, known as Fibonacci, who is 1202 completed is Liber annaci. He explained:

“I joined my father … as an officer in the customhouse located in Bugia [in Algeria] for the Pisan merchants who thronged to it. He had me marvellously instructed in the Arabic-Hindu numerals and calculation. I enjoyed so much the instruction that I later continued to study mathematics while on business trips to Egypt, Syria, Greece and Provence and there enjoyed discussions and disputations with the scholars of those places. Returning to Pisa I composed this book of 15 chapters which comprises what I feel is the best of Hindu, Arabic and Greek methods.”

He brought to Europe not only the numbers, but carefully explained the decimal point system and methods of addition, subtraction, multiplication and division – (he also brought the signs for these operations to Europe), and their application to commercial problems such as weights and measures, bartering, interest and currency exchange.

The term “algebra” comes from the Arabic for restoration “al-jabru”. The term “algorithm” comes from the Latinised name of the Persian astronomer Abu Ja’far Mohammed ibn Musa al-Khowarizmi.

(Pages 42-44)

A tag: [history]

I’m a recent convert to cycling. I was lucky that my former employer was – once my fitness level and skills got to a reasonable level – only 20 minutes or so from home on two wheels, faster than any other method except for a taxi on a Sunday.

Then when I changed jobs it upped to 30 to 40 minutes, which covers about 5 miles. Hah, I hear the enthusiasts say, that’s crawling.

Well there are around 20 sets of traffic lights along that route, plus a section of the Thames path littered with dogs, tourists and small children. Some people do cycle it at road pace; I don’t trust my reflexes.

And the rest is through central London traffic – which is not as much of a problem as some suggest, since it is seldom going at any great rate, but between bendy buses (a nightmare – that is definitely not joined-up governmental thinking) and taxis that stop suddenly, to get a straight 500m run is a rarity.

To say cycling has changed my life would be a slight overstatement, but it has made me fitter than I’ve ever been before (not that I claim that is saying a lot), healthier, and generally happier. I cycle in any conditions short of icy – my “magic” fleece balaclava soon warms me up, and if I’ve worn it on an insufficiently cold day, cooks me.

Even on those days it is hard going, it is nice when you stop. That’s an emotion beautifully summed up by Zen and the art of fixing a flat tire [tyre]. (A belly-laughing hat-tip to One more cup of coffee, who is a real cyclist.)

It was from him that I also learned about the dreaded Kyphosis Bicyclistarum caused, they said in the 19th century, from bending over the handlebars.
From Manufacturer and builder
Volume 25, Issue 8, August 1893

“A word of warning is uttered by the well-known medical authority, London Lancet, which young men, and boys in particular, who have the ugly habit of riding the bicycle with a forward stoop, will do well to take seriously to heart. This pernicious habit is by some acquired unconsciously, and by others (and these constitute the larger number of examples) in foolish imitation of the stooping, or humped, posture of the professional racer. For those who are old enough to understand and appreciate the evil consequences of this unwholesome posture in wheeling, which robs the exercise of all its hygienic value, will need no persuasion to break themselves of it at once; while for the thoughtless boys, among whom the habit is most common, and, because of their immaturity, most injurious, the intervention of parental authority is urgently called for. “

There’s nothing new about health scares.

Luckily I’m safe from the affliction, since my back only allows me to ride in a “sit up and beg” posture. Looking on the Zen side, I say this is guaranteed to maximise wind resistance and therefore excercise.

Two tags: [history] [cycling]

For those who still make claims of European moral supremacy: did you know there were “native headhunters” across Europe in the Iron Age?

Browsing through Southern France: An Oxford Archaeological Guide, by Henry Cleere, I came across what he calls the ‘severed head’ cult.

He says across the region sculptures of “what are indisputably human heads severed are found their bodies” are found, with some of the best examples at Entrement, as even the Tourist Office somewhat reluctantly admits.

There’s also documentary evidence, with the Greek scholar Posidonius, via Strabo …

“There is also that custom, barbarous and exotic, which attends most of the northern tribes…when they depart from the battle they hang the heads of their enemies from the necks or their horses, and when they have brought them home, nail the spectacle to the entrance of their houses. At any rate Posidonius says that himself saw this spectacle in many places, and that, although he first loathed it, afterwards through his familiarity with it, he could bear it calmly.” Strabo IV, 4,5. Speaking of the Gauls.” From this website which links it to stone carvings across Europe, although many of these are not necessarily “dead” heads.

Cleere notes that Strabo has, however, archaeological support, with “the discovery in excavations at the oppidium of La Cloche (Bouches-du-Rhone) where human skulls were found that appeared to have been mounted over the main gate”. (p. 128)

Which was, of course, just what was done with “traitor’s” heads over London Bridge many centuries later.

A tag: [history]

As promised, if slightly delayed …

Aristotle, having spent considerable time and philosophical ingenuity on trying to justify slavery by saying slaves were “naturally” inferior, goes on in the Politics to sum up the position of women in a few words: “A slave does not have the deliberative faculty at all, while a woman has it, but it lacks authority.” As Williams has it (see reference below) “the argument is of basically the same shape as that about slaves: there is a need for the division of roles, and nature provides the casting.”(p. 135)

And that’s about it really – doesn’t take you very far, except that it seems there’s nothing new about the resurgent claim that women just HAVE to have babies – it is their role in life to be barefoot and pregnant in the kitchen. (Haven’t you noticed how empty the world is getting?)

The other main element running through the book is a discussion of shame versus guilt cultures – something I feel I should have come across before but haven’t. Williams says: “The basic experience connected with shame is that of being seen, inappropriately, by the wrong people, in the wrong condition. It is straightforwardly connected with nakedness, particularly in sexual connections. The word aidoia, a derivative of aidos, shame, is a standard Greek word for the genitals, and similar terms are found in other languages.” (p. 78)

(Fascinating this – Williams doesn’t say if this means related European languages, or across the world. I’d imagine most cultures have the word – that would be a fascinating cross-cultural study of where it has come from within them.)

So, Williams says, shame involves an internalised figure of a watcher or a witness. (They don’t have to be actually present.) Guilt, however, involves an internalised figure that is victim or enforcer. “In guilt-centred, autonomous moralities the point is supposedly reached where there is no distance at all between subject and internalised figure, and guilt is pictured as an emotion experienced in the face of an abstraction, the moral law, which has become part of the subject itself.”

This usefully explains the whole Asian idea of “face”, and many of my difficulties in interacting with workmates when I was in Thailand. They were only concerned with a barely internalised other looking on – as long as what they had done looked OK; whether it was actually really OK, which my internalised guilt character worried about, was utterly irrelevant to them. A comment that was made to me several times was: “Don’t think so much – that’s a bad thing to do.”

Other snippets:

* Heracleitus said: “a man’s character is his fate”. (p. 136)

* In the Freud “would have had fun” category: Plato was fundamentally concerned with inner freedom of the soul. “In the tripartite soul that he introduced, the requirement was that its highest, reasoning part should not be tyrannized by its other parts, in particular by its desire. These desires present themselves as exigent, as making demands and imposing constraints.

He typically speaks of this as erotikai anangkai, sexual necessities. … a writer of the 2nd century AD tells us that the penis was then known as ‘the Necessity’.” (p. 154) (The reference says Artemidorus Oneirocriticon I 79) Somehow I suspect that’s a male rather than a female perspective!

A tag: [history]

Bush and Co. really couldn’t be stupid enough to invade, could they? Really?

Last week I came across two interesting articles, a review in the Times Literary Supplement of In the Rose Garden of the Martyrs, by Christopher de Bellaigue (which sounds well worth reading), and a piece about the acceptance there of gender re-assignment surgery, now unfortunately locked up in the LA Times archives.

But my interest in Iran precedes the latest sabre-rattling from the world’s rogue super-power. Discovery of the two articles prompted me to dig out an essay on the Iranian Revolution that I wrote some 15 years ago, and it holds up pretty well.

And doesn’t this sound so familiar (across religious and cultural boundaries). “An editorial in a women’s magazine in 1984 set out the tenets. ‘In Western societies where capitalism is dominant, women’s liberation is nothing but the liberty to be naked, to prostitute oneself …

In Iran since the Revolution, ‘we witnessed the ultimate ideologisation and instrumentalisation of the woman question. … Kandiyoti* says that forcing women to conform to extreme Islamic ideas was at the heart of the ‘utopian populism’ which was trying to exclude the ‘Other within’ from the true community.”

Remind you of anywhere? “Abstinence education”, “banning abortion” …
and now, a small flood of books saying women will have to have more babies.

No mention of the environmental benefits of reduced populations, scarcely a thought for the possibility of changing to a simpler way of life to reduce consumption and thus economic need, or all sorts of other possibilities that might cope with falling, ageing populations.

* D. Kandiyoti ‘Introduction’ in Kandiyoti (ed) Women, Islam and the State, Philadelphia, Temple University Press, 1991, p. 8.

Bernard Williams, in Shame and Necessity, says that the ancient Greeks – here talking primarily of the Classical period – did not generally attempt to morally justify slavery.

Instead, since they believed that it was essential to the functioning of their society, particularly domestic slavery, they just hoped that this fate would never fall of themselves or their relatives, then otherwise ignored the problem. “If someone is a slave, he has the same flesh, for no one was ever born a slave by nature: it is chance that has enslaved his body.” (p. 109)

(Under Roman law apparently, if a woman conceived a child when she was free, but became a slave by the time that it was born, it was recognised as free.)

Later antiquity “seems to have given up on the question of slavery as a moral problem, trying, unedifyingly instead, to claim that real freedom was freedom of the spirit, also, perhaps even especially, available to slaves. So said Seneca: “It is a mistake to think that slavery goes all the way down into a man. The better part of him remains outside it. The body belongs to the master and is subject to him, but the soul is autonomous and is so free that it cannot be held in any prison … ” (p. 115)

(See where dualism gets you!)

But lest we indulge in a “reflex of self-congratulation”, Williams says: “We have social practices in relation to which we are in a situation much like that of the Greeks with slavery. We recognise arbitrary and brutal ways in which people are handled by society, ways that are conditioned, often, by no more than exposure to luck. … [But are uncertain whether to act] partly because we have seen the corruption and collapse of supposedly alternative systems, partly because we have no settled opinion on the question … how far the existence of a worthwhile life for some people involves the imposition of suffering on others.” (p. 125)

Some other snippets:

Quoting Wilamowitz: “To make the ancients speak, we must feed them with our own blood.” (p. 19)

On the lack of the mind/body dualism in Homer: “the word that came to mean something like ‘soul’ by the time of Plato, psuche, stands in Homer for something that is mentioned only when someone is fainting, dying or dead; when the person is dead, it is pictured as existing in a very flimsy, deprived and unenviable condition …. The later Greek word for the body as opposed to the soul, soma, means a corpse in Homer. (p. 23) The sensibility of Homer “was basically formed by the thought that this thing that will die, which unless it is properly buried will be eaten by dogs and birds, is exactly the thing that one is.” (p. 24)

“The Greeks tended to regard the capacity to hold out against feeling or desire as the same capacity, whatever the feeling or desire and however it originated — whether it was sexual desire or the desire to yield to pain or to run away or to take revenge. For this reason, they tended to put together strengths and weaknesses in ways different from those that have been familiar to what has been, at least until very recently, conventional modern opinion … they thought that men were better at resisting both fear and sexual desire than women were.” (p. 40)

To the claim that Homer’s heroes lack and inner life: “we must come back to the question of what the poem is doing. Some characteristics of these figures – the dignity, the distance, the grave acceptance of a fate or fortune that is given … are features of how they are presented, artefacts of the epic style.” (p. 46-7)

Tomorrow: the woman question.
A tag: [history]