Saturday 25 August 2007

Thank you, come again.

Warning and disclaimer: This post is likely to end up as some sort of angry rant. I've been meaning to mention this for a while now, so it may become messier than I would like. Caveat lector.

Anyway, the subject currently on my mind is something that ought to be, and was, in the distant days of my youth, a trivial act of common courtesy. I normally hold open doors for other people.

I used not to think more of it. I would hold a door open, the person for whom I held it would look at me, say, or even mouth, a brief 'thank you', then pass through the door.

Three actions, so, of course, there are three basic ways that this can go wrong:

It occasionally happens that the other chap (or chap-ess, but even more rarely) also wants to be polite, so they pause, either to offer to let me go first, or to make sure that I am holding the door for them. This momentary delay is elegantly and wordlessly polite. So much so, in fcat, that it hardly counts as going wrong.

Secondly, the other person may hold my gaze briefly, and then not say 'thank you'. I find this sort of behaviour unintelligible and quintessentially inhumane. To look into another human's eyes is to form some sort of brief connection with them, at the very least to acknowledge that they are, in fact, also human and real. So I genuinely fail to understand how person A can acknowledge person B, holding a door for person A, and not still fail to say thank you. Years ago, this used to annoy me so much that I made it a habit to say 'You're welcome' whenever this happened. Unfortunately, whenever I met someone who actually thanked me, the sheer shock induced me to blurt out something like 'You're more than welcome', which was normally too strange to pass unnoticed. For this reason, and the fact that it is needlessly rude in itself, I broke that habit.

Thirdly, there are those who fail to make eye contact, instead choosing to barge through the door without giving any of acknowledgment. These people rude, but in a more understandable way than the second sort; merely isolated, by habit, choice, or conditioning, from social interaction with those whom they do not know. Ad this is fine - understandable and even forgivable - especially in cities and busy people. (Sorry for the zeugma.)

This list is complete, but to use a mathematical analogy (a mathaphor), it is complete and also bounded. Outside of the thought process required to create that list, which I probably first picked up ten years ago, lies a more important question. Ad if, to my embarrassment, it never occurred to me to ask it, I would claim in my defence that the domain of thought which led to the list above is, mathaphorically, complete.

The really important question is: 'Why on Earth should I expect anyone to say 'thank you'? Unless they asked e to open the door, or they couldn't easily do so for themselves, why should they care whether or not I saved them an insignificant amount of effort? The only answer is that it corresponds to a social or cultural norm with which I am familiar ad happy, but by what right can I foist it on anyone else?

I do claim to be beyond that stage of boy-scout-gone-wrong pettiness during which I would feel virtuous for having 'better' manners than the other person in the sketch. And yet I have to admit that, in the final analysis, I hold open doors for others for reasons which are entirely my own.

Friday 24 August 2007

Napoleon going somewhere or other. Not sure where, but it must be important.

Here's a small image of a magnificent picture that I happen to like.

If you believe that ambiguity is essential in art, please go away.

I believe that a key function of art is to refine and distill qualities that are not entirely evident or accessible in ordinary life; really to present their quintessence. Or some such rot ...

Anyway, courtesy of David, I give you:

Monday 30 July 2007

The Periphrastic Do

I've recently been reading about the periphrastic 'do'. It's a bizarre construction found in English for at least four hundred years.

I have to admit that, from this point on, this post has been re-written. You see, I thought that I knew something about the usage of the periphrastic do. However, the better to serve you, my loyal readers, I decided to do some e-research about it before continuing.

(I use the term e-research for the extremely non-scholarly, lazy, and generally inaccurate combination of google searches and superficial skim-reading that most people use as a substitute for real research when they are straying out of their real area. But I digress ...)

It seems, from my brief reading of this subject, that there is not even agreement on the precise definition of the periphrastic do. Everyone knows the emphatic use (I do want some chocolate.), the interrogative use (Do you want some chocolate?) and the function of do as an auxiliary verb in the formation of the the past perfect (I did want some chocolate). It is even essential in forming a negative declarative, and although here it conveys no meaning, it cannot be removed. ("I want some chocolate" becomes "I do not want some chocolate".)

As true periphrasis ought not to change the meaning of a sentence, I had been under the impression that the periphrastic do was a usage which was, well, periphrastic. And yet I couldn't think of an example of a sentence where the word 'do' does not change the overall meaning.

Now the weird thing is that there are plenty of interesting-sounding articles about periphrasis, and especially about the periphrastic do. Here's one, chosen at random.

Some articles say that the periphrastic do does exist in the way that I thought it did, but don't give examples. Others say that any of the structural sentence alterations listed above do count as uses of the periphrastic do, although these seem to be the less respectable articles. And anyway, periphrasis, by definition, cannot change a sentence's meaning.

Anyway, the really amazing thing is that most of these authors spend considerable time debating the origins of the periphrastic do. How can they do this, without even agreeing on its definition? Is this how other subjects operate?

Anyway, now you see that what was originally conceived as an informative post has degenerated into a mass of questions without answers.

So, while you and I may not have gained any knowledge about linguistics or periphrasis, we have at least gained some Socratic knowledge. We know a little more about the geography of an unexplored area.

Ho hum. Lets' call it a day.

Friday 27 July 2007

Chocolate

The New York Times recently had a wondeful feature about the differences between British and American chocolate bars. They writer interviewed several people who had moved from the UK to the USA and were now left with a perpetual craving for chocolate; as well as people who had gone the other way and who had been shocked by the difference in quality.

I'm talking, of course, about regular everyday bars of chocolate. Compare Smarties to M&Ms, Milky Ways to Mars Bars, or, and I find myself loathe even to put these in the same clause, Hershey's to Cadbury's.

The reviewer then gave pieces of Hershey's milk chocolate and Cadbury's Dairy Milk to several randomly chosen New Yorkers, and asked for their opinions. All were ecstatic about the Cadbury bar, saying that it made the ... other one ... taste powdery and bland.

So far, so what? Not so much a new opinion as a satement of fact, albeit one of which only those familiar with both the UK and the USA may be aware.

But the author then gave the two bars of milk chocolate to the Times's food critic. He said that neither was better or worse, but that they were both differently bad.

The problem is that food criticism, by and large, is about subtlety, about complicated combinations of flavours and textures. But not all foods can be meaningfully measured in this way.

A wine, for example, can have many different dimensions. It can, and indeed, in my not-entirely-humble opinion, ought to, combine several tastes. They can arrive at one's consciousness at different times and with varying intensities. They can be fleeting hints or be longer-lasting. Wines are therefore a fit subject for the attention of a critic who focuses on complexity, subtlety, and nuance. Entire books have been written about the tastes of wines, some astonshingly thick and scholarly; and entire vocabularies have been invented to describe them, although most of these words do seem designed to be unintelligible.

Alas, real chocolate lies at the other end of the spectrum from wine. In its purest form, it has an immensely sweet and creamy taste, and a smooth and creamy texture. The sweeter it is (as long as the taste is not artificial) the better. The creamier it is (as long as it stays solid) the better. End of description. It is just not fitted to lengthy discussion. And so a chap whose livelihood is dependent upon discerning, separating out, labelling, and describing nuances will be entirely uninterested.

But this is not a bad thing, This who prefer single source, organic, high cocoa-solid content, dark chocolate have missed the point. If you want sublety in your food, don't eat chocolate. Eat almost anything else. And leave the chocolate for those who really enjoy it.

Running down

This is supposed to be a short post. That is, of course, how I have, thus far, introduced my longest posts.

I like to run. I have enjoyed running for several years. I normally run on my own, and I suppose that I enjoy the calmness and solitude one obtains. One's mind is mostly preoccupied with the sheer physical effort involved, and the small part that is left over is just powerful enough to sift through one's memories and the more superficial of one's thoughts. In short, it allows one to unwind, just the right amount.

People often think I'm odd when I talk about the relaxing quality of running, so here' an attempt to explain:

I want to compare people to old, mechanical, watches. The analogy may not be especially exact or entirely meaningful, but it is sufficient unto my purpose here. Most people are like most watches: their springs are wound to about the right amount, and consequently they keep about the right time. They function well in life, but occasionally they need to be wound up again, and it is good for their spring for them sometimes to be unwound.

Of course, there are people whose springs are wound a little too tightly. Watches that are wound far too tightly may run too fast, and in extreme cases they may break. And even so, people who are wound too tightly seem soemtimes to be a little too rushed (although not too fast), and are more prone to breaking than their less excitable fellows.

One of my (far too numerous to list here) faults is a tendency not to wind my spring. I am like a watch owned by a rather careless fellow; fine when primed and properly used, but sometimes found stopped when I oughtn't to be.

And so it seems that running is an appropriate form of unwinding for me. Those who are habitually wound too tightly need to unwind entirely when they rest. Those of us, on the other hand, who prefer not to be wound up quite as far as we go, have no need to do so; and running suits some of us just fine.

Friday 20 July 2007

Badger-Hair-Brush

I just realised that I may accidentally have caused some confusion in my recent post about shaving. The more lynx-eyed and elephant-memoried among you will recall that I mentioned a badger hair brush.

Not soon afterwards, I was asked how one could obtain a badger hair-brush, and I realied the unintentional ambiguity. Let me clarify my meaning once and for all, by putting the hyphen in the right place.

What one needs is a badger-hair brush. Badgers are notoriously fond of their hair-brushes, and not unreasonably, since they do have so much hair. They are therefore loathe to part with them, even when asked nicely.

In fact it is an astonishing fact that a badger hair-brush is very nearly as good (for shaving a human) as is a badger-hair brush. Owing, however, to the difficulty inherent in obtaining one of the former, and their consequent rarity, I would suggest using a badger-hair brush.

Newsworthy?

For those of you who have recently returned from a prolonged period of meditation in a very secluded cave, let me mention that hte final 'Harry Potter' book is being released this week. It is worth noting that no other books, to my knowledge, are 'released' in this manner. They are written; then they are published; and then, as and when individual booksellers see fit, they are sold. Or rather, they are offered for sale, and many, of course, do not sell.

In the case of the 'Harry Potter' books, of course, these steps are often put out of sequence. The books are writtend, then sold, then printed, and then distributed. That's somehwat odd, to begin with. But now, thanks to the New York Times, they have become just like other books in one way: the book being relased tomorrow was reviewed before it appeared in bookstores.

Let us consider this story for a moment.

The New York Times, one of the most highly respected papers on the planet, increased its readership, and made headlines around the world, by reviewing a children's book.

All bookshops that wanted to sell the book were asked by the publisher to sign contracts saying that they wouldn't sell it before tomorrow. So the shop that sold a copy to the Times was not doing anything illegal, but it was breaking a contract. Similarly, the Times itself broke no laws, but did knowingly purchase a book from a shop which was not contractually allowed to sell it. Whatever one's view one such morally grey areas, one must surely be surprised that the Times would be seen to act so seedily. This sort of behaviour is more becoming of a tabloid or a less reputable news source eager for mor exposure. Of course, we can dismiss the claims made by many that this somehow spoils a surprise for readers, since no one is at all compelled to read the Times.

No, the real issue here is why on earth this is news-worthy. Why did a prestigious paper involve itself in a transaction of dubious morality simply to bring a book review to the public's notice?

Some of you may remember the debacle over a series of inflamatory, supposedly anti-Muslim, cartoons that appeared in a Danish paper in the autumn of 2005. They were prominently discussed for many weeks. But the amazing thing is that almost no major western news media ever re-printed the cartoons.

So for months people discussed cartoons that were called offensive, without knowing how offensive they were, or why. At the time, many newspapers excused their bizzare, to put it mildly, behaviour by conflating it with sensitivity. Most said that, oh yes, they were all in favour of people knowing what all the fuss was about, but unfortunately it would not be just too mean to re-publish the cartoons. The Times, however, showed no such hesitation. It proudly announced that they were not newsworthy, and that they had been found to be offensive by the editorial staff of the Times.

Curiouser and curiouser.

This is something of a new twist in the old debate about the place of the media in an increasingly internet-ised world. It is, of course, necssary for the editors of media to deicde which stories to discuss each day by some selective proccess. This will inevitably involve a degree of subjectivity. And this will, in its turn, lead to some people being happy with the selection, and others unhappy. But the ommission of some news is incontrovertibly necessary because of the finiteness of the space or time available. One man's meat is another man's dead animal tissue, and so on. Conflicting points of view, don't you know.

But during the debate about the cartoons, so many thousands of words were spent discussing the issues that it simply seems ludicrous and inexplicably that the cartoons themselves were never shown. They were made to seem so important that it would have been reasonable to cut anything else, even the Times' banner and masthead, to fit them in.

Friday 13 July 2007

Shaving

Oops. I had intended to alternate serious (you may substitute long-winded or boring) posts with lighter (read mindless, insubsantial) ones. Yet somehow I seem to have managed to follow up a long post on an esoteric piece of mathematical machinery with an equally long one on art history and ... yawn ... something or other. Hmm.

Anyway, here's a corrective.

I'm going to share a secret with any of my readers who happen to be men. Actually, I'm sharing it with all of you indiscriminately, but if you're not a man, it shan't be of much use to you.

In two words: Shaving soap. (In three words, 'use shaving soap'; but I can do it almost as well in two.) Try shaving with proper, old fashioned shaving soap.

I think that peoplle gave up using shaving soap because it takes slightly longer than modern gels and mousses. However, if you are at all used to shaving soap it may take less than one extra minute. And boy, is it ever worth it. You get a far closer shave. Far, far, far closer. There's just no comparison. Have you ever shaved against the grain just to get a closer shave? Well, if you shave with shaving soap you can get that finish by just going with the grain. And if you go against the grain too; well, wow!

You'll need a brush to whip up a nice rich lather on the surface of your soap. The purists recommend one with badger-hair bristles, but these are astonishingly expensive. (A couple of years ago a decent-sized badger hair brush was £40 in England.) Anyway, there's nothing like trying it out for yourself, so off you go. Run along and have shave.

But not at the same time - weren't you ever taught not to run with blades?

Civilisation

Welcome back.

I'm about halfway through watching an outstanding BBC documentary series called Civilisation. It was written and narrated by Kenneth Clark, who, I recenetly found out, was the father of Alan Clark.

Clark is magnificent in the series. The cinematography itself would make this series worthwhile, but his narration is beyond praise. He is absolutely clear, always intelligent, and almost never patronising.

The series is also impressive for the coherence of the thoughts and arguments expressed in it. Some of his slightly more xenophobic comments may be offensive to those who are easily offended; but they should also serve to remind one that the ideas and the narrative are the result of a single man's thoughts. That alone is worth applauding in an era of collectively produced, almost corporate entertainment.

It is also astonishing that there are only two signs of age shown by this work, apart from the obvious signs of the times in background, such as cars. The first is the occasional comments, mentioned above, which do not conform to the bland opionlessness of modern art documentaries. Secondly, the complexity of the thoughts expressed is significantly greater than anything else I have ever seen on television. It is a reminder that television can be educational and intellectually stimulating without failing to be entertaining.

However, the greatest quality of this documentary is its intellectual honesty. The presenter motivates his series with questions, and proceeds to attempt to answer them. But he does so in a scupulously open and honest way. There is none of the disingenuity which makes so many television programs look patronising, or even like propoganda. Where the evidence supporting his point is ambiguous he lets us know, and then explains his opinions, rather than prsenting an unbalanced narrative.

So many articles are written, or documentaries made, by people whose minds are already made up. Their contributions to the public discourse are an attempt to sell their position, and they do so without any regard for this sort of intellectual honesty.

This quality has all but dissappeared today; from political discourse where all issues are reframed by each side in ridiculous black and white, downwards (or upwards, according to one's tastes) through so much of society. It reflects a mind-set which is truly rare even in academic circles. It shows a man who is prepared to make his arguments seem weaker, in order to make them more honest.

Of course, Kenneth Clark was an emminent and distinguished scholar at the time he made the series; and this quality may have been extremely rare at the time. So this quality may never have been widepread in mankind. Nonetheless, I was glad to have caught this glimpse of it.

Wednesday 11 July 2007

Everything you've ever wanted to know about Etale Cohomlogy but were afraid to ask

This is going to be a short post to attempt to explain the 'point' of etale cohomology and the etale fundamental group. The latter is often called the algerbaic fundamental group.

In case you don't know what any of these things are, they are important in the study of arithmetic algebraic geometry. It is an area of mathematics somewhere between algebraic geometry and number theory. Lang called it Diophantine geometry. If you don't know what those words mean, what follows will not make sense to you.

To begin with, the most readable introduction to this area across which I have come is in Milne's online notes. They are incomplete and lack many proofs, but they give one the general idea. I don't aim here to teach anyone about etale cohomolgy or the fundamental group, but if you are learning about them and you happen to stumble across this site (a concurrence which is mind-bogglingly unlikely), then this may help you to see the big picture.

First of all, start by understanding the fundamental group. Consider two cases. If our base space is a field, the fundamental group is its absolute Galois group. If the base is a complex variety, the etale fundamental group is closely related to its regular fundamental group. For any other scheme, it is different, but you should understand that it generalises these very different notions, one purely geometric and the other purely algebraic.

Its importance in the study of etale cohomolgy lies in the following statement: Connected etale covers of a scheme correspond to transitive sets acted on by the etale fundamental group. The analogy with the geometric case is perfect, because connected covering spaces of a nice (if these comments are making sense to you so far, you'll know what nice means) space correspond to transitive sets acted on by the regular fundamental group.

Then the basic construction of the machinery of etale cohomology is very similar to that of regular sheaf cohomology, but extra algebraic input is often need for standard proofs.

However, the cohomology groups produced by etale cohomology are very different from those produced from Serre-style quasi coherent chomolgy theory. The real value of etale cohomology lies in these differences. They are sufficiently many and large to require little comment.

It is often said that etale cohomology (especially in characteristic zero) has two main ingredients: Galois cohomology and clasical topology. This is made most concrete by comparing the cohomlogy of a k-scheme to that of its base change to the algebraic closure of k. The relationship is broken down by Grothendieck's spectral sequence theorem into precisely the algebraic and geometric data for which one would hope.

If you make it this far, please leave a comment. I'd love to discuss this with someone.

Explanation

Some people share their lives through their blogs. I wouldn't presume that anyone would rather read about my life than get on with their own. So instead I intend mainly to share my thoughts. Hopefully someone or other will find them entertaining, thought-provoking, or otherwise worth reading.

Tuesday 10 July 2007

Indian (English) and American (English)

Welcome back. I would like to talk to you this evening about two languages that I know and ... well, perhaps love is a little too strong, so let us say, in which I take more than a passing interest.

They are American English and Indian English. I make some claim to impartiality in this discussion because I was raised in England. I can make some claim to knowledge too, because I have frequently visited India, and currently live in the USA. Objectivity and knowledge are essential when analysing a topic. Alas, they are also often illusory.

Let's start at the beginning, which is a very good place to start. We consider the development of these two languages. The vast majority of the (modern-era) settlers of this country were native English speakers. They arrived, however, before the modern fad for widespread literacy had truly taken off. They therefore arrived knowing how to speak, but not how to spell, the English language. This had the following two consequences.

Firstly, the standard American accent is, objectively, somewhat similar to the standard English accent. (These are both, of course, entirely fictitious beasts; but this is not a sholarly article, only a pretentious blog aping the mien of one. We proceed, then, free from the possibility of serious scholarly scrutiny.) One could argue that the American accents one hears today are descended directly from accents once heard in England, as people learnt English from their parents and grew up in a society where English was spoken.

Yet American English exhibits drastically different spelling conventions from English. Furthermore, where these differences appear, the American spelling is almost invariablysimpler or more natural. Standard examples include flavour becoming flavor; skilful becoming skillful; analogue becoming analog; and (my perennial favourite) plough being transmogrified into plow.

Indian English is somewhat widespread in India today. Yet even a generation ago it was far less common, something of an achievement. Those who spoke it several generations ago would mostly have been well educated and extremely well read.

However, the number of native speakers of English English in India was never high enough to teach all, or even most, of those learning English in India. Thus most Indians learning English have, for generations, been very carefully how to read and write, but not at all how to speak, English. Again, this may have had two consequences.

Indinan speakers of English would have grown up in a society where other languages were much more common, and this would undoubtedly have affected the development of the Indian English accent.

Hence an objective judge (probably another fiction, but ably substitued for by the author) would probably judge the Indian English accent to be further from English than is American English. And yet variations in spelling are remarkably few.

Aside from the radically different pronunciation, an interesting difference between Indian English and English is created by a certain ruthless Indian logic. The English appear willing, and even happy, to accept irregularities in their language, but the Indians do not. For example, the English word 'postpone' dates back to at least 1496 (according to the OED). It lived a happy life for many centuries. When it moved to India, however, Indians seem to have become unhappy that such a word has no opposite, and very soon created 'prepone'. It was an entirely logical, and thouroughly welcome addition, but very un-English.

A final, comical, example is provided by the word 'pyjamas'. In English the word is spelt with a 'y', but pronounced as if it were an 'a'.

In American English, it is thus pronounced 'pajamas', and, this being so, it is only reasonable for it to be also spelt with an 'a'.

The word probably reached India in written form, so it is still spelt with a 'y', but it is now pronounced 'pie-jamas'. I find that rather funny.

Sunday 8 July 2007

Aims

I'm not sure what made me write that. It looks fairly pretentious, and entirely pointless, now that I have finshed it.

Most of my posts will not be that long. If I have a thought that I think is interesting, and do not change my mind in the time it takes me to come to my computer and post it here, I may post it. Otherwise, this may be a sort of diary.

Materialism

I think that it is clear to most of us that there are, at least, two forms of materialism. Let's be simplistic for a moment and consider only one extreme, to show that there are many forms. And rather than calling the sort that I believe that I display, Good, and the other, Bad; I shall, in a radical departutre from my usual form, strive for an approximation to objectivity.

In my bathroom sits a spongebag. It is a truly beautiful spongebag. Made of a rich, deeply coloured, lustrous brown leather, it holds my attention every time I see it. (Lest you think too poorly of me, I may add that it is somewhat new.) It is a distinct pleasure to use it now; and even with the passage of time, I don't doubt that it will be more pleasurable to use it than it was to use my old, rather ordinary one.

Now, to dwell upon the purely physical qualities of such an object may be called materialistic. However, there is now venality, no greed in my thoughts. I am happy to have it, no doubt, but I would have absolutely no use for another.

This is not the end of the moral aspect. A digression, into waters of which I know little. Hopefully the ship of my allegory shall not run aground on the rocks of my ignorance.

At the beginning of the Renaissance, Humanist architects and artists produced work on a human scale. One identifies this period with small, but beautifully proportioned, rooms in small, but beautifully proportioned, houses.

Later, towards the Baroque, this sense of proportion was lost or discarded. Palaces became bigger (or rather, bigger palaces were made), works of art became more ornate, involved, and extravagant. Did this immediately lead to a decline in quality? No, but we can crudely characterise this progression as one from the building of wonderful houses to the building of, admittedly more, wonderful palaces; from achitecture designed for the enjoyment of individual human beings to architecture designed to overawe and to overwhelm.

So how on Earth does this relate to my spongebag? The point is that I don't intend to show it to anyone. I don't intend to compare it to other people's spongebags, and so the pleasure that it gives me is, in the sense above, humanist and even humane.

It is also reassuringly physical. Its seductive smell, and it smooth, sensuous finish are, of course, entirely irrelevant to its function. But they are to be enjoyed by only me, and so have a different impact on my thoughts than would the beauty of an object designed for ostentatious display, or indeed any sort of display.

The final measures, I feel, are given by how a material object may affect my actions, and my happiness.

The fact is that I didn't covet this spongebag before I bought it. I didn't dream of, one day, buying such a bag. Thus I was not at all unhappy without it, yet I was made marginally more happy by its acquisition. And doubtless, when it is gone, I shall not shed tears for its passing, nor attempt to replace it.

It entered my life unasked, its tenure in my life is marked by a slight increase in my happiness, and at its passing I shall be unmoved. If only I could feel this way about all of my possessions.