June 13, 2008

Partial Order in Environmental Sciences and Chemistry, Rainer Brüggemann and Lars Carlsen, eds.

I have wondered, in some environmental or geomorphic courses, whether the drive to quantify wasn't slightly misplaced; whether it would be possible, and more reliable if less precise, to merely rank qualities without trying to rank them on a metric line. In this sense 'metric' doesn't mean 'meters, centimeters...', but any system in which there are distances that you can add up, and divide in half, etc., as one can meters or feet. There are plenty of systems, called generally 'topology', that describe complicated things/worlds that aren't metric; in which you can say that two things are near but not how near they are. (I gave up on the book Small Pieces Loosely Joined after way, way too much falling-about astonishment that the common users' Internet has more of a topology than a metric, without any sign that we were going to be introduced to the idea of a topology -- or graph, any name will do -- and the many things known about them.)

Then I had the mild shadow of a realization that if you have orders, you might have partial orders; for instance, you and your parents and your grandparents are in 'parent-child' orders with each other, but your maternal and paternal grandparents almost certainly can't be so ordered; none of them are parent or child to the other three. If you go back far enough, your tree of descent certainly does cross itself, though; very possibly with 'legs' of different numbers of generations; even this commonplace example doesn't nail down descriptions right away. Also, mm, ecosystems, they have both spatial and developmental nesting, partially ordered sets (posets) might arise very naturally.

So they do, and here are some examples. The book starts with an even lovelier natural source; you can't rank molecules into a single order of development, but there are obvious ways to put them into directed graphs with partial orders. If A is a sub-molecule of B and C, perhaps because B and C have different side-chains, that's the beginning of an order; and this happens rather a lot with organic molecules, since organisms would naturally rather not build everything from scratch. There might be a molecule D that has the side-chains of both B and C; or that might be impossible; so the 'family tree' of molecule A has a range of possible shapes.

There are metrics on some traits of molecules, e.g. their boiling-points, and there are some mappings from posets to metrics. (Much of this book is thinking about toxicology, for which it's handy to be able to guess from molecular data what the organism or system effects might be.)

A later chapter (Wayne L. Myers,G. P. Patil,Yun Cai) is describing biodiversity by posets> They start by pointing out that political contention 'need's a single ordering, and the bulk of the chapter is describing habitat diversity in a part of Pennsylvania. Handy, if you're trying to set policy for watershed protection.

I'm dubious that political matters naturally need a single ordering, though. Market contention surely does -- in fact, would like to translate everything into the single metric of price or price-of-tort. This seems to me to be one of the things we need political systems to avoid; we have alternate rankings, of things you cannot alienate, things you can give away but not sell or buy, things you can sell or buy only if some other characteristic is in play. In a partially-ordered mindset, you need not say that one of the characteristics is more protected than another, even if both are protected with regard to a third. It's hard to live up to this in reality, when we have limited resources and generally end up trying to minimize harm (for which we do need to rank the harms).

For that matter, the political process leads us to try and rank goods; the Democratic primary just concluded was rrrrather an example of that; every political platform with realistic goals must be. Somewhere along here we must hit Arrow's Impossibility Theorem; I am being very lazy about this post, because I am mostly trying to get a lingering urge to procrastinate off my desk, but does the AIT arise from a poset-ness in social goods?

Find in a Library: Partial Order in Environmental Sciences and Chemistry

Posted by clew at 02:53 PM

June 01, 2008

Living Alone, Stella Benson

A World War One novel ought to be strange and sad; this novel was published in 1919 and reprinted twice in 1920, seems to have hit a nerve in its day, and goes from the odd to the inconsolable.

The outward odd thing is a novel about bedsits and witches, in which a committee devoted to helping the deserving poor in WWI London is bewildered by a witch who happens to dogfight in the city's defense. Her magic is explained in terms of past lives; but, unusually, in this cosmology one only has magic power in one's first life; old souls are too worn down and sad. This is a recognizable view of The Cute and the Cool idealization of the young, and there are little bits of that, but mostly it's a principle of universal decline -- there is nothing to explain why the world is better off with old sad souls in it, or the souls better off, or the world lovable at all if this is what it turns us into.

Why the title? Much of the story is set in a boardinghouse in London which obliges its boarders to solitude, and discomfort, and scarce friendship. One bildungsroman character, poor and honorable, earnest and hardworking, moves in because there is no rent and she's broke. (The combination of London, poverty, gentility, and a war is another trope of universal decline.) In almost any story that we now have with witches and dogfights -- in Harry Potter or Dr. Who, let alone Disney -- this would be the heroine, and she would make some friend, acquire some skill, possibly be fallen in love with, and would leave the House of Living Alone as Inanna left the Underworld.

But no! it goes with her instead! The witch escorts her nearly to the New World and then abandons her with these words:

Dear Sarah Brown, you did mean well. How sad it is that people who have once lived in the House of Living Alone can never make a success of friendship. You say you left all you loved--what business have you with love? [...] Did you think you had destroyed the House of Living Alone? Did you think you could escape from it?

I seem never to have mentioned Paul Fussell's The Great War and Modern Memory, which is a terrible oversight, as it is an excellent book connecting the bored, bruised swoonings of the late Victorian poets -- A. C. Swinburne, etc. -- to the imaginative experience of World War One. (I remember Fussell citing a poet as describing going to war as 'into cleanness leaping'. I'm pretty sure that was before the actual war.) From there I can go by easy steps to Tolkien, and modern tastes for romantic adventure; and therefore Star Wars, the fictional one and the factional project.

What molded the architects of World War One? The long, long end of the nineteenth century reared up more than one biological generation of gilded youth into... bored, entitled fools who thought a war would be as manageable as a peace? (The film Oh! What A Wonderful War is amazing, by the way.) This bodes ill for us; Fareed Zakaria is probably right when he says that the U.S. could change course and lead a world of developing equals into peace; but I don't see why anyone should assume, on our current form, that we will.

History; did we think we could escape from it?

Living Alone, Stella Benson; Project Gutenberg etext 14907

Find in a Library: The Great War and Modern Memory, Paul Fussell

A. C. Swinburne, many works at Project Gutenberg

Find in a Library: Oh! What A Lovely War; if the blocking in the opening scene is inherited from a stage play, it's even more amazing

Posted by clew at 10:38 PM
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