Namespace Collision

Of distraction and potato chips

2005-09-09T20:12:00.000-07:00

So yes, I'm way behind on math, but there are reasons for that: I've just recently started teaching, and figuring out how to do right by the 29 kids whose only instruction is me for 4.5 hours a week has occupied much of my willingness to explain math for the last several weeks (before that there was another thing, but harder to explain -- I merely assure you of its presence). We'll see when it recovers.

However, via Making Light, I've come across the blog of one Chippie, taking particular interest in her recent potato-chip making foray. I started trying to comment about it, but it got so long it seemed like at least some of my regular readers might take an interest. So, in the spirit of unsolicited advice from strangers, here's what small wisdom I have about chip making (and I must say I can make some pretty decent chips):

-Potato choice. I've only ever fried russets, and I find that they come out remarkably well -- golden brown with a serious potato flavor I've never seen on other chips. I imagine most other potatos are also ok.

-Thin is key -- chips aren't fries. Short of a mandolin or v-slicer (devices that can cut foods into very thin strips), the best way to go is to use a vegetable peeler and peel long strips off the potato. You won't get that nice chip shape, but you will get thin without buying a gadget you may not otherwise need. Also, one potato makes a decent-sized collection of chips, but you'll probably need two or three to replace that Lay's party-size bag.

-Keep the proto-chips soaking in water, but dry them as well as you can (salad spinner, towels) before frying.

-General frying principles: more oil is better. Use a large, heavy vessel, so that the heat will return more quickly to the right temperature after you put in food (it drops due to the additional mass). I use a dutch oven and keep my oil in two green (keeps the light out) wine bottles. Get a fry thermometer and watch it like a hawk -- 375 is good for chips, but going over 400 will spoil your oil (it'll start to burn). Needless to say, use vegetable/canola/corn/peanut oil, not olive or something else with flavor, as such things burn way sooner than 375. You can (and should) save your oil from one session to another: let it cool, filter, store, and reuse.

-Drop in the chips a handful at a time, say 10-15 chips total in a single batch in a reasonable-sized pot (you'll do several). Pull them out when they've almost stopped bubbling, about 3 minutes (they'll still be good even if they've stopped). Remove to draining rack (I like paper towels on a plate), salt, pepper, enjoy. These are certainly my favorite chips (nice and potato-y!).

With practice, you can even peel the strips online -- peel 15, start frying, peel 15 more, pull the others out, start the new batch, season the old, peel 15 more...

The footnote: this recipe is essentially due to Alton Brown in his book "I'm Just Here for the Food," and the chips are extra-good with his version of homemade onion dip, and extra extra good if you make it with your own homemade mayo.

Math Post the Ninth: Group Actions

2005-08-16T11:54:00.000-07:00

Well it looks like that whole "I'll blog during the conference" idea petered out quickly; what with thinking about math enough hours a day to wear me out before blogging, there have been no posts in three weeks. So now, right back into it.

Following some extremely gentle chiding from Neil, along with a link to the following article, I've decided to again defer the promised note on factoring maps and talk instead about group actions, implicitly the subject of the piece linked (you don't need to read it yet).

One of the most fruitful ways to study something is to study its symmetries; correspondingly, one of the most fruitful ways to study groups is to study the things of which they are symmetries. So, how can a group be a symmetry of a thing? Practically every object (ok, every object) out there in the world of mathematics has what's usually called an automorphism (=isomorphism to yourself) group, denoted Aut(X). If X is a set, Aut(X) is composed of the bijections X->X; if X is a group (or other algebraic structure), the isomorphisms; if X is a polygon, the rigid self-maps (rotations and reflections); if X is some kind of bigger geometric object like the plane, symmetries are defined in close to the same way -- as invertible maps which preserve "the structure," where "the structure" is whatever structure you happen to care about at the moment. The simplest way to define a group action of G on a thing X is to say it's a homomorphism \phi:G->Aut(X). Equivalently, if X is a set with some additional structure (like all of our examples thus far), you can write it as a "multiplication" of elements of X by elements of G such (i) ex=x for all x, e the identity of G, and (ii) g(hx)=(gh)x,* as long as that multiplication "respects the structure."

Some examples of group actions include:

(1) A group G acts on the set of its elements by multiplication; just multiply in the group. This isn't a homomorphism, and in fact seems kinda dumb, but is still surprisingly important. Similarly, G acts on the (left) cosets of any subgroup in the same way.

(2) A group G acts on itself as a group by conjugation -- g acting on h is ghg^(-1). This actually is a homomorphism, since if you multiply two g-conjugates together the g's in the middle cancel; thus G acts by conjugation on its set of subgroups. Normal subgroups are precisely those stable under this action. This action is important enough that the subgroup of Aut(G) that is hit by it is called the inner automorphisms and written Inn(G); it is actually a normal subgroup (of Aut(G)!) in its own right, and Aut(G)/Inn(G)=Out(G), the outer automorphisms.

(3) Permutation groups act on the set they're permuting.

(4) Symmetries of polygons act on the polygons.

(5) A subgroup of a group acting on X also acts on X.

With these actions identified, I'll give a few more words. An element x in X has an orbit under G, consisting of all the other elements G can move x to; the subgroup of G which doesn't move x at all is called the stabilizer of x, written Stab_G(x) or myriad other ways that suggest the same thing. An action of G on a set X is called transitive if there is only one orbit; that is, if some element of G can move any element of X to any other. Every action is really a collection of transitive actions (that is, a collection of orbits), and any transitive action is the same thing as the action of G on cosets of the stabilizer of any point in the orbit, which takes some thought but isn't hard to see. An action is faithful if no two elements of G act the same way on X, or the map G->Aut(X) is injective, an action is free if no non-identity element fixes a point (or all stabilizers are trivial), and an action is simply transitive if it is transitive and free; this last implies that G and X have the same number of elements by the point about stabilizers above, since there are no stabilizers in this case. This also implies that a simply transitive action is faithful.

That may seem like a giant load of terminology, but the payoff is Cayley's theorem: every finite group is a subgroup of a permutation group. And in fact with all those words out of the way the proof is almost trivial: G acts on itself by left multiplication, giving a map G->Aut(G) as a set, and Aut(G) as a set is a permutation group. The action is simply transitive, hence faithful, so the map is injective and we're done. The argument here actually generalizes to geometric cases of various kinds, but we won't have to touch those for a long time yet.

Now, go read the article I linked above; it should be easy to figure out where he's going even before he goes there. The exercise to do is this: figure out what the author means by a "golden rule" in terms of group actions. The hint is that it can be said in five words, all of which I've defined already in some math post...

*Writing actions on the left (rather than the mathematically-equivalent right -- that is as gx rather than xg) is actually a slightly bad thing to do if the group G is not Abelian; for reasons that can be avoided if you don't want to dive deeply into the notation, you often want to act by the inverse of some natural action if you're acting on the left. However, it looks slightly more natural for most people, so for informal purposes I'll elide the concern. In fact, this issue is something I've seen distinguished professors argue about at length in class (young, distinguished, argumentative commutative guy didn't care where his action went; old, distinguished, noncommutative but slightly dyslexic guy wanted them on the right), so it should be clear why I'm hoping to skip out on the whole discussion.

Math Post the Eighth: Personal Interlude with Some More Definitions

2005-07-21T14:08:00.000-07:00

So I am now officially a doctoral candidate! Heck yeah! Also I'm now (or will soon) be attending a lengthy algebraic geometry conference in Seattle, so I'm not even in Michigan anymore. Perhaps most importantly from a blogging perspective, I'm not madly studying every second of my day anymore (merely some seconds), so I should be able to get back to blogging on a more regular basis. So nyah, say I!

I've also redone my links section, doing away with links to friends' livejournals because I couldn't think of a good way to separate them from links to friends' more serious blogs or therefore from other peoples' more serious blogs. Any complaint and I'll rethink it, but it seemed like the right way to go at the moment.

However, I've decided to defer my promised discussion of isomorphism theorems and universal properties so I can, in celebration of my prelims, explain that portion of my research that I'm currently prepared to discuss (that is, that part that shouldn't be much over anybody's head for reasons other than density). So, in broad strokes, here we go:

One first kind of assumption that mathematicians like to make is a finiteness assumption. It's usually easier to deal with things that are "small" than things that are "big," and indeed strange things can happen in the world of large objects (they can be the same as several copies of themselves stuck together, for one). One finiteness assumption we've already used is precisely that: that the number of elements in a group is finite. A lesser one harks back to my discussion of generation of a group, in particular that our group has a finite set of generators, or is finitely generated. Many (though not quite all) of the examples I've mentioned in that first group post are finitely generated (an exercise for the reader to figure out which!). Making an assumption like this is more about choosing a field of study than picking out a special case.

A second definition I'll need is the condition of a subgroup having finite index. The index of a subgroup H in a group G is the number of cosets that you can form from H with elements of G. In the integers Z, the subgroup 3Z has three cosets, the subgroup 5Z five, and so on. For finite groups, Lagrange's theorem tells us that the index of a subgroup is simply the ratio of the orders (i.e. the number of copies of the smaller group it takes to cover the large one is the number of elements in one divided by the number of elements in the other). If we consider the group of ordered pairs of integers, the subgroup generated by the pair (1,0) is of infinite index, while the subgroup generated by the elements (2,0) and (0,2) is of index 4 (consider quotienting it out and note that you get a (the) two-element group in each component).

The first big assumption I'd make is that of being just infinite. A group G is just infinite if it is infinite but has only finite quotients. I'll cut to the examples in a second, but I need to add one more assumption to get to what I'm actually studying: I don't just want G just infinite, I also want every finite-index subgroup to be just infinite as well -- a condition called being hereditarily just infinite. Our first example is the integers. Since every normal subgroup (in fact, since the integers are abelian, every subgroup) has finite index, there can be no infinite quotients. A slightly more complicated example is the group of symmetries of an infinite line with equally-spaced dots on it (like the integer points in the real numbers), written as D_\infty, where the notation means an infinity symbol. These come essentially in two kinds -- shifts some number of spaces in one direction or the other or reflection around a particular point (or combinations of the two). The group actually looks like (something I'll get to later) the semi-direct product of the integers (the line movements) with the two-element group (a reflection about some point -- you can "make" reflecting about any point by translating, reflecting, then translating back). Seeing that this group is hereditarily just infinite is most easily done by thinking hard about group actions, which I will also get to later.

Before finishing up, I need one more assumption: that the group is not something I'll call simple. A simple group has no nurmal subgroups and therefore no interesting quotients at all. The finite groups of prime order are all simple; showing any other group to be simple (that is, actually doing the proofs) is well beyond the scope of what I'll be able to consider here for some time. Computing all the finite simple groups was a major research project, popularly considered finished around 1980, and filling many thousands of pages (so many in fact that people still aren't completely sure it's all correct -- there's a major effort to write it in some comprehensible way that's still going on). Infinite simple groups satisfy the condition of being hereditarily just infinite trivially (for the mathematicians in the audience, this is because any finite index subgroup H in a group G has a finite-index subgroup H' normal in G inside it -- think about it), but aren't very interesting examples for this same reason.

(For genuine group theorists, the previous paragraph is an ersatz for simply assuming G to be residually finite, which is equivalent for just-infinite groups but harder to explain)

The last class of examples is something harder to get your hands on -- for the big-word-friendly audience, I'm talking about irreducible lattices in higher rank semisimple Lie groups -- and harder still to show in general (again for the big-words crowd, this is Margulis' stuff). For the near future, you can simply think of them as big groups of integer matrices (say 3x3 or larger). My project is to show that these are the only interesting examples. It's likely to be uphill work, but it should at least lead to some intriguing stops along the way.

Meme-ification

2005-07-17T04:24:00.000-07:00

Wow. I used to be behind two, now I'm behind like six or eight in terms of math. I beg preliminary exams on Tuesday, the last hurdle I have before my only goal in life becomes a dissertation. For now, though, I steal from my friend/cooking idol eclectician, and meme about food:

What is your first memory of baking/cooking on your own?

Unclear. I think I may actually have never done it until sometime during summer 2000 when I was living on my own for the first time -- and such memories are phrased purely in terms of an industrial kitchen at an MIT fraternity rather than in terms of one dish or another. Since then, more enthusiasm, more frequency, and more skill (I hope).

Who had the most influence on your cooking?

Again almost uselessly hard to say in terms of people I actually know. Looking back on it, my parents figured out cooking more or less as I grew up, so early memories are few. I suppose the most honest answer is my little brother, who started cooking seriously well before me and who I must always outdo.

Personality/reference-wise, definitely Alton Brown of Good Eats fame, who manages the right mix of improvisation, science, and art (though who can let me down when he cheats).

Do you have an old photo as 'evidence' of an early exposure to the culinary world, and would you like to share it?

Not to my knowledge, alas -- everything I know is lately acquired as these things go. For instance, everything I've yet posted about math I knew before I knew anything about food beyond how to eat lots of it.

Mageiricophobia - do you suffer from any cooking phobia, a dish that makes your palms sweat?

A dish, not really -- there's two Indian desserts of which I've yet to create even a remotely decent rendition (pedas and ras gulla, for anybody wondering), but I usually only make them for myself -- but for a more general phobia there's an easy answer: cooking for the current special someone. The girl's a vegetarian and I am so totally not. Also she has deeply serious taste (unlike many vegetarians) and obviously I'm loathe to disappoint. Between these two things I think that this particular fear has taught me more about cooking than anything else in recent memory.

What would be your most valued or used kitchen gadgets and/or what was the biggest let down?

I probably get most action either out of my chef's knife (ten inches, calphalon, $20) or my cast-iron skillet (twelve inches, I don't even know, $20) -- I suspect if you just left me these and a heat source I'd be able to accomplish 80% of my cooking without great difficulty. As to letdowns, I'd like to nail my ice-cream maker, but the real problem with that one is that I just don't have enough ice-cream consumption taking place in my house to support an ice-cream maker for anything but vanity. For real, I'd probably have to nail that jar-opener my roommate's aunts got us when we moved in -- they furnished the apartment with an impressive array of goods, but that one thing I've never even considered using.

Name some funny or weird food combinations/dishes you really like - and probably no one else!

I'm (alas) an impressively normal kid regarding food combinations. The one thing that people have been surprised about me enjoying is kheer: kheer with cocoa powder or kheer as breakfast with coffee, both of which seem utterly natural to me. After all, milk, sweet? Who cares about the rice component; sense is still made.

What are the three eatables or dishes you simply don’t want to live without?

Number one has got to be cow meat -- out in the midwest, nothing else is as cheap, as good, and as versatile. Number two is garlic, since whenever I manage to make a meal without adding at least a little bit I feel vaguely ashamed, as though I'd forgotten the existence of a family member. Number three is wine. Between the variety of flavors and the sheer utility of the alcohol (not to mention the intoxication value), when the roomie's in town I go through at least a bottle a week.

... that whole list, on reflection, actually sounds pretty bland until you've eaten at my place a few times. I do have a few decent tricks.

Your favorite ice-cream…

I'm tempted to go with my associate's mention of burnt caramel, but there's an institution back in Princeton called Thomas Sweet which produces a flavor called chocolate chip cookie. Not cookie dough, but the cookie itself -- tiny chips mixed into a base of salty-sweet butter. Every bite is pure tollhouse, but summery in a way cookies simply aren't.

You will probably never eat:

Many, many things, but at this point more mediated by my inability to get them than anything else.

Your own signature dish...

At this point, probably the steak I stole from an old New York Times recipe and modified until my roommate was weaned off a previous sauce addiction. Lamentably, I'm a much better thief than creative mind in the kitchen.

A common ingredient you just can’t bring yourself to stomach…

I haven't yet tried tounge...

Which one culture’s food would you most like to sample on its home turf?

Gujarati food. Blatantly self-serving, but these kids are the hardest veggies to impress I know of and I'd like to have a little better idea where it's all coming from.

The people I am tagging are:

Oddly, none of the bloggers I know who read this are foodies. Any are welcome to it, but if I had my choice of the whole wide world I'd pass the baton to Maggie the Mad Wine Girl over at the Wine Offensive, whose erstwhile wares I've sampled many a time and whose punk-gourmet attitude I simply adore.

More math soon, I promise!

Update and Apology

2005-06-28T11:45:00.000-07:00

So I've been vacationing a bit and am thus way way behind on math posts (two, I think, is the number of my behindness), and I've actually really wanted to say something about Grokster, but haven't been able to formalize my thoughts into something resembling a post. Regardless, there will likely be at least one math post will be here by tomorrow; falling behinder, however, is likely in the near future (after which I'll try to catch up lots).

Math Post the Seventh: Kernels and Quotients

2005-06-21T10:54:00.000-07:00

Last time I was talking about homomorphisms, the "nice maps" in the land of groups, and I gave some of the usual map definitions (injective, surjective, and so on). One of the things we (well, mathematicians -- I can't really answer for the rest of you) always want to know about maps is what the stuff over a particular point looks like; if you had a map to the integers, what stuff goes to three? Since this concept is so common, the set of stuff going to a particular point has a name: the fiber over that point. In the case of homomorphisms, the answer to this question has a simplifying wrinkle: the answer is the same for all points. To symbolify things a bit, let f:G->H be a homomorphism of groups and let h be in H. Now, say f(g)=f(g')=h, so both g and g' are in the fiber over h. Now, since f is a homomorphism, f(g^(-1)g)=h^(-1)h=e, so the difference between any two elements of the fiber over h are in the fiber over the identity; thus if you pick a particular element g in the fiber over h, and we call the fiber over the identity K (for reasons soon to become clear), the fiber over h is exactly gK. So all the information about the fibers is contained in the set K (called the kernel of the map f).

Now, we can say some quick things about K. First, K is a subgroup of G; two elements g and g' in K both map to the identity under f, so their product maps to the product of the identity with itself, which is still the identity, as is the inverse of the identity. However, K has one more special property: the left and right cosets of K are the same, that is for any g, gK=Kg (since both of these are precisely the fiber over the point f(g) in H). This implies the interesting property that gKg^(-1)=K, since this is the fiber over the identity again; this funny equation is called "conjugation by g". Now, if your group isn't abelian, conjugation may not fix all the elements of the subgroup K, but since K is a kernel, conjugation can only move an element of K to another element of K. Subgroups with the property of being fixed under conjugation are called "normal," in one of math's most badly overloaded terms.

Normal subgroups have one extra bonus fun property: their cosets form a group. Let N be a normal subgroup of G, and consider the cosets gN and g'N; if we try to multiply them in the straightforward way, we get gNg'N=gg'NN=gg'N (since N is closed under multiplication, NN=N). If N weren't normal, the left and right cosets wouldn't conicide, but since it is they do, and the cosets inherit all the group properties from the same properties of G. This new group is written G/N, and is called the quotient group of G by N. The easiest examples of this can be realized by the clock arithmetic groups Z/n (and now you understand the notation; because the integers are so familiar we omit the extra Z on the end) for various integers n; remember the cosets of the subgroup H=nZ are H, 1+H, 2+H, and so on up to (n-1)+H, and adding cosets is just adding the numbers out front and subtracting off n's if the number gets bigger than n. Of course, since Z is abelian, all subgroups are normal (the inverse just commutes through), so you need to be more careful in general.

G/N admits a nice map from G (an element g goes to the coset gN), nice in the way called "canonical," meaning that no choice is involved in determining the map -- we don't have to pick anything to make it up, it just comes to us. If you made a version of this map up, yours would be the same as mine. There are lots of non-canonical maps, and we'll meet plenty next time, but it's important to know about the differences in the kinds of nice maps.*

Next time: isomorphism theorems and factoring.

*And it's important to be specific about words; the inventors of a branch of mathematics called category theory, which is in some sense a language in which all other mathematics should be done, gave a definition for a kind of niceness they called "naturality." Fortunately for them (and us), the natural transformations of objects called functors are important and cool; unfortunately for us as students of math, people are sadly nonspecific with the word natural, rarely specifying when they mean the technical sense. One of my more trying math experiences was realizing after finishing a problem set (from the canonical algebraic geometry textbook) that when the word natural appeared in every problem it didn't just mean pleasant or straightforward but that there was suddenly much more work to do.

Math Post the Sixth: Isomorphism

2005-06-17T15:36:00.000-07:00

This is going to verge on the philosophical, since I'll have to justify a "why" inside, but I'll kick off with the answer to the question from last time: describe all the groups of prime order. Start with the hint; pick an element g in a group G of prime order p, and say that g is not the identity. Now, g generates a subgroup, say H, and it has some nonidentity element in it, since g is such an element. Now Lagrange's theorem tells us that the order of H divides the order of G, but the order of G is prime, so H must have order either 1 or p. Since H has at least two elements (the identity and g), H has order p, so H=G. This argument shows that any group of prime order is generated by any element not the identity, has no nontrivial subgroups, and is "structurally the same" as the group where we add hours on a p-hour clock. Now the only issue is what I mean by "structurally the same."

Consider two groups: one is the group S_3 (underscore is ASCII for subscript) of permutations of three elements (i.e. all the moves the three-card-monte-guy can do) and the other is D_3, the rigid symmetries of an equilateral triangle. Both of these groups have six elements, and they have much in common in terms of structure, since they both can achieve any configuration of three things being moved around (you can reflect the triangle on an axis as well as rotate it, and think of it as acting on the corners). I want to say that they're the same, but I can't quite; after all, they're given in different ways, written with different letters, and so on. On the other hand, the situation is the same as if I took a clock and rubbed off all the numbers, replacing them with fruits -- I might now be saying that pear plus strawberrry equals pineapple, but that doesn't stop it from being a clock. So the question is how to capture this notion of "identical except in name."

The first part of the answer starts with the notion of a homomorphism. A homomorphism is a "nice"* function between two groups, and the buzzword is that it "preserves the group structure." Homomorphisms are traditionally written with Greek letters which I'm not sure how to render here, so until I find a better way I'm going to do it with LaTeX (math typesetting) notation, which should be pretty straightforward: a small phi will be written \alpha, a capital one \Alpha, and so on. The symbolic way to write a map \phi from a set G to a set H is like this: \phi : G->H, where the arrow-looking thing is in fact an arrrow. If G and H are groups, the map \phi is said to be a homomorphism if for any g and g' in G, \phi(gg')=\phi(g)\phi(g'). The trick to this simpleminded equation is that the multiplication is carried out in G on the left and H on the right. Now, say we have two homomorphisms which are inverses, say \phi:G->H and \psi:H->G such that doing \psi first then \phi gets you back to where you started in H and doing \phi first then \psi gets you back where you started in G (\phi(\psi(h))=h and \psi(\phi(g))=g for all g in G and h in H); then we can multiply in G by going over to H, multiplying there, and coming back and vice versa. This means that we can think of either G or H as just alternate names for the other group, which tells you that they're really the same.

Before concluding I'll define quickly some relevent terms. A map is said to be one-to-one or injective if no element gets hit twice; symbolically, if f(x)=f(y) implies x=y. For people who remember precalculus, this is the "horizontal line test" for a graph. A map is onto or surjective if everything gets hit. A map which is both injective and surjective is bijective. Bijective maps are invertible**, and bijective homomorphisms have inverses and are called isomorphisms.

To restate the conclusion of the first paragraph in nicer language, we classified all groups of prime order up to isomorphism: a group of order p is isomorphic to a clock arithmetic (or cyclic) group of order p, via the isomorphism defined by taking any nonidentity element to the generator 1.

Next time: what groups are homomorphic images of other groups.

*Practically every definition in math is a definition of "nice," though the connotation that goes with it can be anything from "super duper extra bonus spiffy" to "not something you made up just to annoy me." Most branches of math have a fundamental definition of "nice function" that follows shortly after the definition of the objects under discussion; in most algebraic disciplines what this definition should include is obvious to anybody who's been doing algebra for a while. Geometry and topology have it slightly harder.

**If you need to convince yourself of this, draw two collections of dots and some arrows from one side to the other to make a function (each dot on one side gets exactly one outgoing arrow). Also, there is no short phrase for "one-to-one and onto," however little sense that may seem to make.

Math Post the Fifth: Cosets, Lagrange's Theorem, Generation

2005-06-15T12:23:00.000-07:00

I'm sorry for the lateness of this; I've had a busy weekend/early week.

I asked two questions last time, and while I was planning to answer the second one first, I realized there was a reason I asked them in that order. Silly me. The question was about the cosets of the subgroup H=5Z in the group G=Z (Z is the group of integers under addition). To answer it, let's start by doing out a few simple examples. For these, I'm going to break down and write the group operation with a + rather than simply omitting it, since if I leave it out it'll look like integer multiplication, which is not what I mean. The easiest coset to consider is 0+H; this is pretty obviously H back again. Slightly (but only slightly) less obviously, there is the coset 5+H, which is also H back again, since the element 5 in is the subgroup H. In fact, any element of H will simply give back H again as the corresponding coset, because H is closed under multiplication and inversion.

What about elements not in H? Well, 1+H is a coset -- it contains -4, 1, 6, 11, and so on in both directions. By the same principle that any element of H gives H back H, any other element of 1+H gives back 1+H: 6+H=1+(5+H)=1+H. A little more thought shows that there are exactly five cosets of H, one for each of the numbers 0-4. These are the possible remainders upon dividing by five, which I'll touch on again later, but for now just think of them as elements.

As to the second question, the first part is obvious: of course cosets of H cover G, since for any element g in G the coset gH contains g (the identity is in H). Whether they overlap is harder, and will be my first major invocation of equations on this string of posts. Say that two cosets, gH and g'H, for elements g and g' in G, overlap; this means there are elements h and h' in H such that gh=g'h', so g'=ghh'^(-1). So g and g' differ on the right by elements of H, meaning that they give the same coset by the reasoning in the first paragraph.

This non-overlapping of cosets yields an interesting result. Say the group G is finite (has only finitely many elements, like permutations of a set, symmetries of a regular polygon, or is a 'clock arithmetic' type group). Then if H is a subgroup of G, the cosets of H cover G without overlapping and are all the same size (they all have the same number of elements as H). This means that the number of elements in H divides the number of elements of G, so, for instance, a group with twelve elements can only have subgroups of size 1, 2, 3, 4, and 6. This fact is called Lagrange's Theorem, and has a fairly giant list of obvious corollaries of decreasing size (the professor who taught me this quipped, "we'll eventually get to the empty corollary."), which eventually end in most of the facts underlying public-key cryptography.

For next time, I'll leave you with one definition and one question which should now be soluble. If S is a set of elements in a group G, the subgroup generated by S, written with angle brackets usually but because I can't remember the way to get escape characters in HTML written here as [S], is the subgroup you get by starting with S and adding all the elements you can make by multiplying and inverting until you can't get any more. As an example, the subgroup H from the example way back at the beginning is generated by the number 5 (or equally by -5), so I might also write it as [5]. With this definition, the following question should be easy: describe all groups of prime order (that is, with a prime number of elements). It sounds big, but in spite of this it's easy enough I can bear to give only one hint: pick an element g in G.

Next time: what that act of "describing" really was...

Math Post the Fourth: Abelianness, Subgroups, Closure

2005-06-09T23:29:00.000-07:00

When last we left our heros, they were groups. They were a giant menagerie of strange examples, but they were groups. A new reader named Vito commented that I should talk about a thing called closure, so I will (disclaimer: I was going to anyway).

But before I get to the new stuff, something I forgot to mention last time. Some groups have an operation that, in addition to being associative, is also commutative. That is to say they satisfy the relation ab=ba for every a and b. Many familiar examples have this property, like the integers, like the integers on a clock (aka modulo some number n), or even like the real numbers (not including zero) under multiplication. Other examples don't: for instance, if we think about the permutations of a set of three elements, switching one and two first and then switching two and three gives a different result from if we to the switching in the opposite order. Groups that satisfy this property (like the integers), are called abelian, after a mathematician named Abel who was one of the fathers of group theory. This gives rise to one of the traditional math jokes: What's purple and commutes? An abelian grape. The more you know...

Sometimes, groups have other groups living inside them. For instance, the integers under addition are a group; the integers divisible by three, also under addition, are also a group. Permutations of five elements are a group; permutations of the first three of those five are too. One group sitting inside another group is called a "subgroup," just like a subset in quasi-technical parlance (ask me about the prefix quasi- in math sometime). This is where we care in an official sense about the property of closure: a subset of an ambient structure with an operation(s) on it is said to be closed under that(/those) operations if, when you do those operations to all the elements of the subset in all the possible ways, you don't get any new stuff. In our case, that is to say that if we multiply two elements together or invert a single element, we stay in the set; such sets are subgroups.

In order to set up for next time, let me start with this new definition: given a subset S of a group G and an element g of G, the set gS is the set of elements in S multiplied on the left by g, and similarly for Sg; in the same way, if T and S are subsets of G, the set TS is the set of elements of G ts, where t is in T and s in S. If H is a subgroup of G, we call a set of the form gH a left coset of H in G (there's actually no universal standard on this; a set gH is called a right coset roughly as often as it's called a righ coset. I'm sticking with where the element is). The questions for next time are these:

1) What are the cosets of the subgroup 5Z in Z, where Z is the integers?

2) Given any group G and any subgroup H, do the left cosets of H cover G? Do they overlap?

Until next time.

Math Post the Third: Groups and Axioms

2005-06-05T20:42:00.000-07:00

At last, I'm able to tackle my actual topic of interest: group theory. Groups are one of the simplest (not easiest) algebraic structures around, but in spite of the ease of giving an axiomatic definition, I'm going to start with examples before we start; it'll make things much easier.

The first example of practically everything in algebra is the same: the integers, those guys I've been talking about for a week, positive and negative whole numbers. I'll ignore multiplication for a moment and focus on the fact that you can add two integers together. And that, my friends, is algebra.

The canonical second example of a group is still just adding numbers, but adding them on a clock face. This is called "integers modulo twelve," or mod twelve for short, and the idea is just that twelve is the same as zero and otherwise we add normally (so 3+11=2*, and so on). Obviously twelve can be replaced by whatever number I want here; the concept will remain the same.

Less additively, imagine drawing a square on a table and putting down a square piece of paper with labelled corners (the same front and back) that fits directly on top of it. If you wanted to, you could pick up the paper and put it down with the corners in a different position. In fact, there's something like a "multiplication" that you can do on these motions: make a new motion by taking two old motions, doing one, then doing the other. This just physically realizes the symmetries of the square (rotate, reflect, and so on). In fact, symmetries of things (broadly construed) provide a wonderful source of groups (experts may here recall the old saw about the catagorical definition of group**, which I'll probably explain at some point). Another way to see this is to think about a Rubik's cube -- beyond just being a cube and having those symmetries, there are others you can get from the operation of twisting a face, since twisting a face keeps the cube a cube and just moves the colors around.

More abstruse examples abound. For anyone who recalls matrices, the set of n by n matrices with nonzero determinant is a group with matrix multiplication; so is the set of matrices with determinant equal to one (both of these are actually symmetry groups in disguise). The permutations of a set also constitute a group, called of course a permutation group. If you write down words composed of the letters a, b, a^-1, and b^-1, stipulating that a letter and its inverse cancel if they appear next to each other, you get a group by concatenating (and then reducing) words; just write one, then the other. And this is only the beginning; stranger examples will appear soon enough.

As you might expect, a definition that actually captures all of these examples is likely to be a little out-there. It'll involve many symbols when I give it, but first I'd like to say a word or two about axioms. Obviously there is a lot of theory you can give about all of these examples individually, but they do all involve some common features, and capturing them in and then working with an axiomatic defintion permits you to apply old theory in new situations (for the computer scientists in the audience, think of a well-documented code library). While it'll be a while before examples of this come up (though they will, fear not), it'll be handy to start collecting axiomatic structures now.

So, a group is a set, say G, with a multiplication, written here by juxtaposition of elements, which has:

Associativity: given any three elements g,h, and k in G, g(hk)=(gh)k.
A unit element: there is an element e in G such that for any g in G, eg=ge=g.
Inverses: for any g in G, there is an element g^-1 in G such that g(g^-1)=(g^-1)g=e.

Associativity just means that you don't have to worry about where you put the parentheses in a long list of elements being multiplied together; this is usually either pretty hard or pretty easy to prove (there are two or three examples above which require individual lengthy proofs of this; the others can be handled easily together if you're slightly clever). The other two are easier to understand; in fact, I'm going to leave understanding what they mean in all the above examples as an exercise. You can answer in comments for the harder ones (though please don't post a first response if you already know this stuff) the following question: for each example of a group listed above, what is the unit element, what is an inverse element, and how would you get one? It shouldn't take more than a few minutes of thought, but it's a good place to start getting a feel for how to think about this stuff.

Next time: subgroups, cosets, quotients, and one of my favorite cute little theorems ever.

*Technically, that equals sign should have three bars in it, signifying that it means equality modulo something, not normal integer equality. It's not strictly required, since the addition is really taking place within the mod twelve group structure anyhow, but it's sometimes nice to have.

**"A group is a category with only one object in which every morphism is an isomorphism."

Math Post the Second: On Factoring and Fermat

2005-06-03T02:40:00.000-07:00

Prime factorization of integers, as promised.

This is a strongly intuitive thing. Prime numbers don't have any divisors; any number not a prime has several prime divisors, and since when you divide a number by something it gets smaller, if you just keep dividing out primes you'll eventually just get a big list of primes with no more composite part left. That part isn't actually so strange or difficult to understand; the other part is very obvious and yet extremely subtle. It's this: that factorization is unique, at least the list of factors is unique (six is two times three as much as it is three times two, but the way this is non-unique is pretty dumb, so we don't count it). Part of the subtlety is that the way to see the uniqueness isn't something I can explain as glibly as I can the existence; I hope another part will be illustrated by the following story.

Some people in the world have still heard of Fermat's Last Theorem; it got lots of play ten years ago, when it was just proven after a 350-year wait. The statement is simple enough: for any integers x, y, z, and n, none zero and n bigger than two, it is not the case that x^n+y^n=z^n. What most moderately informed non-mathematicians know is that the statement appeared in the margin of a book owned by Fermat accompanied by a notation to the effect that he knew a beautiful proof, but that the margin was too small to contain it. What moderately informed non-mathematicians generally do not know is that Fermat, like Newton, was quite the ass. Fermat was a lawyer and did math in his spare time, which is well and good until it turns out that the primary way he did math was by sending other mathematicians letters that amounted to schoolyard teasing: "I can prove this and you-oo ca-aan't!" It wasn't yet the tradition of his day to actually tell people how you proved the things you proved (you wouldn't believe how long the cubic and quartic equations were unpublished; solving cubics was a courtly version of a party trick for some of these guys), but he did occasionally do it. Thing is, knowing his methods, some very smart guys in the 1800s came up with what we still think was the proof he had.

It doesn't work. And the reason it doesn't is that prime factorizations stop being unique when you start looking at things only slightly more complicated than integers, but it's desperately easy to assume that it doesn't, particularly if you live hundreds of years ago and don't have access to modern algebra. In fact, this failure was only discovered because of this proof, and the methods for getting around it (and what grew out of them) currently go by the name of algebraic number theory. So uniqueness of factorization is a bit subtle. I'll assume the fact until I need the other things I need to explain it for other things, but just understand that it's subtle.

Next time: introduction to Group theory, my actual honest-to-goodness field.

(For the record, the example of non-unique factorization appears if you start with the integers, but just for kicks throw in a square root of negative five and all the sums and products you can make with integers and this new number. 'Prime' still makes sense, as does 'factorization,' as does 'unique.' The trouble is that the numbers 2, 3, 1 + sqrt(-5), and 1 - sqrt(-5) are all prime, and 6=2*3=(1 + sqrt(-5))(1 - sqrt(-5)), so factorization is still good but uniqueness is out the window)

Math Post the First: Dividing and Primes

2005-05-30T03:52:00.000-07:00

Well, here goes... math post the first. Not background, real stuff.

I thought we'd start off with a little number theory; most people do actually know what integers are, and it's not as though this early chunk of math is hard or anything. It should be easy enough to understand what I'm saying here without anything like background.

The basic object of study here is the collection of integers: zero, one, two, three, and so on. Negatives, but not fractions. For at least the next while, I'll never even hint that fractions exist (much though it pains me to not be able to share with you, right now, the simple, brilliant, unforgettable, and world-shaking for the ancient Greeks at least, proof that the square root of 2 is irrational). This is important, because it's required to sensibly parse our first term, "divides," which is the same concept you called "divides evenly" back in elementary school. Formally, we say that a divides b if there is a number k such that ak=b. Two divides six because 2*3=6, for instance. Five doesn't divide six, as I'm sure is clear.

There are a few first easy results to be deduced. First, if a given number a divides a number b, a also divides any multiple of b. This follows more or less immediately from the associative law, a property of multiplication and addition that you probably learned without thinking about it in middle school. Multiplication and addition are binary operations: two numbers go in, one comes out. But you can also multiply or add a big line of things: 1+2+3+4+5, for instance. If I were being completely technical, this is utterly incorrect; should we add the two and three first, or start from the left, or what? Handily, it doesn't matter. As you almost certainly already know, the order in which I do the adding doesn't matter, just which numbers are involved, and this is the associative law. If you toss in the distributive law (that is, a(b+c)=ab+ac), you can also see that if a divides two numbers, it divides their sum. These two facts together are the "linear comination lemma."

Some numbers don't divide any number not themselves: zero, for instance, can never be multiplied by anything to make something other than zero. Zero is actually the only number with this property, as should be pretty clear. Other numbers divide every number: since for any x, 1*x=x, one is one of these. Similarly, negative one divides all the numbers because every number has a negative; such numbers are called "units." I mention this seemingly trivial situation because I'll need it soon, but also because some large number of posts down the road the concept of unit will become deep and interesting and important, but only after it gets generalized to the many more complex objects on the docket.

The reason I bring all this up at the moment is the concept of a prime number, whose elementary school definition is a number only divisible by itself and one. We'll have to go slightly further: a non-unit p is prime if whenever ab=p, either a or b is a unit. We need this extension because I also want to talk about negative numbers; seven is divisible by minus seven, so "itself and one" isn't quite going to cut it. I want to exclude units because the nice property of integers we all remember is that they uniquely factor into products of primes. I'll say a bit more about it on Wednesday, but for now I'll just give the basic property of primes: if a prime divides a product, it divides one of the factors. It's not that hard to understand why, but I'll leave it as an exercise until next time.

Math Post the Zeroth: Fundamentals

2005-05-28T20:29:00.000-07:00

I have now lost this post twice. So I'm going to keep it short, in the hopes it'll actually get posted. This is the traditional (in basically all math books) "chapter zero," where all the stuff you're supposed to already know is quickly reviewed. Since you're not supposed to know much of anything, I'm going to say a very short word about explanations. This will be short and very easy and might be somewhat insulting-sounding, but just in case someone hasn't heard I need to say it all anyway. It's also very late because of losses and frustration -- rest assured the next/first installment will arrive on Monday.

I'm not going to give a lot of proofs of things in the usual sense -- formalisms often seem to hide the issue for non-mathematicians, even when they shouldn't really. I am, however, planning to give lots of basic explanations. The philosophy here is to say enough words that a student of mathematics could turn whatever is being said into a proof without difficulty, but not enough to break away from an explanation a non-mathematician can understand. There are just two principles I'll need: proof by contradiction and proof by induction. Contradiction is simple: you assume whatever you're trying to show is not true, then deduce something false. For example, if I wanted to show I haven't eaten today, I could say that if I had eaten my stomach would be full -- since it is empty, i couldn't have eaten recently.

Induction is somewhat subtler, but not a lot. The basic idea is probably best regarded as an aid to avoid writing arbitrarily long proofs, but maybe not best explained that way. Imagine you have to say how to walk from one end of a straight line to the other. To describe how to do this, you might say "take one step" the number of times required to get from one end to the other, but that would end up being a bit long-winded. More simply, you might say "walk in that direction, and when you get there stop." This is what induction is: you say how to do a little bit of the problem, and then you say to keep doing that until you're done. People also talk about it as a line of dominos: if you know that if one falls then the next one does and you push the first one over, they all must fall.

The formal version is this: if you have something you want to prove about all integers, say the proposition P, you would start by proving P(0), that is to say that P holds for zero. Then you show that P(n) implies P(n+1) for all n; in words, if P of one number, then P of the next. This second proposition sets up the line of dominos (true for zero implies true for one, true for one implies true for two, and so on) and the first pushes them all over.

There's a nice combination of these ideas that I hope to use with cavalier abandon: minimal counterexample. Whenever you're trying to show something about positive integers by contradiction, you can always assume you've got your hands on the smallest number that doesn't work. This is exactly the same as induction (since if you've got the smallest counterexample, the next smallest number isn't one; the nonexistence of a smallest is then the induction principle above), but applications of it look a little bit different, as you'll no doubt see soon enough.

Math Post the Minus First

2005-05-23T00:13:00.000-07:00

...I was thinking of this great proof of something you already know yesterday, and I wish I could tell you...

Most people have some idea what money is. Most people can identify what an interest rate is, and most people have an understanding of what it means to go into debt.

Most people have at least a vague notion of DNA -- it's that stuff that makes you a person rather than a chimpanzee, or vice versa. Most people know what an animal is, and most people know about cells.

Most people know about molecules. Most people (with kitchens) have worked with acids and bases, and most people understand that cold things freeze.

Most people have absolutely no idea about groups. Most people have no idea about varieties, and most people have no idea about manifolds, rings, sheaves, or differential equations.

Such are the plagues of the mathematician. When most other scientists talk about their profession, understandings of some of the basics can be assumed of anybody asking "what do you do?" We lose pretty hard on this score; even if I say "prime number," a notion hardly more complicated than "number" itself, I already lose half my listeners. Hrmph.

So, between now and (forever, probably), I'm going to try to write the gentlest possible introduction to advanced mathematics, particularly focusing on my advanced mathematics because I'm horribly egocentric. I'd love to eventually be able to post about the interesting things I hear in talks or classes or read in papers, but before I can even think about doing that I have to give a million back definitions and bend every reader's mind in at least twelve ways to make them care. I'm trying anyhow.

A few ground rules: I'm not requiring background, per se, but I am asking that readers be willing to think, since even the (relatively florid) stuff I want to write will require pondering to understand. I'll start with warmups, but I want to get to genuine stuff soon. I'll try to avoid proofs, much to my chagrin, because I recognize that most readers care much less than I do about what's really happening and really want to just get a vague idea of what's going on; also it cuts down on the writing to only give that vague idea. I'll try to sneak in some stuff about philosophy and methodology (since induction, for instance, really is interesting in its own right) in interludes here and there, but mostly I'll try to leave well enough alone. I'll ask that you be comfortable with symbols and equations, but I'll try to keep the optimal balance -- symbols only when they make things clearer. Lastly, I'll try to build in complexity, starting with the familiar so that reading the archives will get you ready for the exotic, but I want to start almost agonizingly simple and I therefore have to ask that you don't take my tone as too condescending. I'll feel really stupid explaining prime numbers, and many readers, I don't doubt, will feel condescended to, but if I don't start the discipline of talking slow with small words now I'll just start launching into discussions of positive-definite nodegenerate symmetric bilinear forms assuming everybody knows what I'm talking about, which would distinctly be a bad thing.

Well now. Time to commit before it gets too late. First, a brief interlude on symbols and logic; then, the beginnings of number theory.

This will be interesting...

PS: For the record, I'm aiming for Monday-Wednesday-Friday as a posting schedule until I'm remotely up to date. Also for the record, the proof was of why casting out nines works. It's really cute, and I do genuinely wish I could tell you.

Edit: I'm not so clever with the date-time settings sometimes -- this is supposed to be recent, not old. Sorry.

Meme again

2005-05-22T22:45:00.000-07:00

So Neil, having done another meme, has inspired me to finally complete the much-overdue Caesar's Bath meme handed me by Julie what is now quite a long time ago. I should beg some excuse, but the best I can come up with is that I have genuinely been thinking about it the whole time, and unfortunately I chose to interpret it fairly strictly: for me "I just don't get it" is not synonymous with "I don't like it." The game is finding something whose very appeal you simply don't see, which makes it rather harder. But without further ado:

Fantasy. As a genre. Science fiction I get, power fantasy I get -- the imaginary world that could never be and shows nothing special about the people that live in it just isn't obvious in its appeal from my perspective. This may be because my perspective is somewhat limited, but I genuinely don't think so.
Dancing. It occasionally happens that people I know want to go out dancing for the sake of dancing and not for the sake of something else (a reason to get drunk, getting play, what have you), and this boggles my mind. I get dancing as a social event, I get dancing as community, I even get dancing in some complicated fashion (English, line, etc.), I just don't get dancing for its own sake.
BDSM. Pain, restraint, power, just not appealing to me in an actual sexual situation and I don't even see why they could be. Sorry.
Lesbians as an object of male sexual desire. Say it along with me: lesbians aren't interested in you. By definition! That's what it is to be a lesbian! It could be that I've known a few too many lesbians too closely to even imagine lesbians as attractive to men anymore, but that's the way it is.
Personal relationships with God. This may be the only one that's even a minor cheat. Agnostic though I am (and unlike PZ over at Pharyngula, I'm a mathematician and not a scientist and therefore can't reject God merely based on a perponderance of the evidence), I do see at least the external signs of having deep belief, and they seem pretty good, so in that sense I understand the attraction. What I don't get is how a sensible person could possibly get to the point where they can accept such a seemingly crazy thing.

I toss the ball to Neil, Tony, and whoever comments first on this post, thus proving that they might actually see such a baton-passing...

Star Wars

2005-05-20T22:45:00.000-07:00

Hrm. Tony seems to think I should say things about Star Wars, and indeed I've got a few thoughts. I promise that only half of them will be nitpicky or snarky. They'll be plenty spoilerific though, but since I have no idea how to hide it below a fold, it's just going to be up top.

Firstly, my primary nitpick/snark: of course the film had a liberal bias, since none of the bad stuff could possibly have happened if the Jedi had access to non-abstinence-only sex ed. Or even decent reproductive health technology. Either way. Also of course the obvious takehome point: if he force-chokes you, leave him.

In reality, there's no strong political drive to the film -- epic is epic, and even the little bits of dialog that can be snipped out to pretend things swing one way or the other ("only a Sith thinks in absolutes," "from my point of view, the Jedi are evil!") can be snipped out in more or less equal proportion. The only good argument I can think of one way or the other is that the film definitely hews to the axiom that whichever side is committing the atrocities is the bad guys, and this is only left or right in the crazy version of politics. We may be living in crazy politics now, but that part of the movie was very much written in the eighties with the rest of the outline, before this axiom was twisted (like "we should listen to government policy experts," "reporters should ask everybody hard questions" or "evolution exists") into a partisan opinion, so I think we're safe on that score.

From having seen my esteemed college science fiction association's MSTing of Phantom Menace, I'm reminded of the parking shot phenomenon. For those not in the know, the parking shot is just that: a shot of something parking. While they can be establishing shots like any other, oftentimes, particularly in action movies, shots of planes, cars, spaceships, or whatever parking or coming in for a landing are just used gratuitously to add time. Phantom Menace features an approach to Coruscant involving eight separate parking shots with no dialog at all. Sith, at least, has relatively little parking, and is a relatively good movie, suggesting the value of "number of parking shots" as a measure of goodness of movie (what we might call a "cinemetric").

A nitpick more or less equal to the first is that Bail Organa seems to have forgotten to take the jets off of R2 when he had C3PO mindwiped. Funny he never gets to use them again... but that's not really the point. It seems to me that one thing that Lucas seems to get more and more into over time is slapstick. I can remember none in A New Hope, little in Empire, a bit more with Ewoks and Boba Fett in Jedi, and scads and scads in the new trilogy, all of which I've seen quite recently. In Episode III, there's a fair bit of gratuitous slapstick, and even though Lucas appears to have figured out how to make it work again after forgetting for the previous two movies, there's still enough dumb battledroid humor to bring things down. Humor is really important to the Star Wars films, but slapstick in the large sticks out unpleasantly. Most of the funny bits of episodes one and two were slapstick, so seemed annoying and out of place; episode three moved back to more character humor, which worked a lot better.

Even major points seemed, under further consideration, better than other recent movies -- even when characters seem to be carrying the idiot ball (most notably when Mace Windu spontaneously changes his mind about whether to arrest Palpatine or kill him, just in time for Anakin to see it go down) they basically act within the bounds of plausibility. I might want to shoot them for behaving in ways the movie doesn't quite motivate properly (particularly the rate at which Anakin turns evil, though smart people can disagree) but they basically don't do dumb things. So good on that.

When the apocalyptic battle between Yoda (who is, as always, awesome, not to mention the only character who should ever be permitted to say "youngling") and the Emperor starts up with the tossing around of flying donuts, y'think there's a metaphor of some sort going on? Heavy-handedness aside, the real issue for me here is that the Jedi don't have a place in the political structure. In Doc Smith's Lensman series, the Lensman (on whom the Jedi are based) are more or less in charge of everything, but nobody minds because they're also incorrruptible by authorial stipulation.* But here, who knows? Are the Jedi more or less the military? Are they in fact charged with protecting democracy? It seems like lots and lots of the plot hinges on Jedi not having a clear place in the political culture, and the exact meaning of the "Jedi code," in the sense that most of the issues seem like they'd go away if there were answers to these questions, almost regardless of what those answers are.

I think, on balance, that I liked it. Characters make hard choices, and that always wins points. Friends seem to like each other. Nobody has a thought quite as ridiculous as "I like you because you're not like sand." I'm not sure it's wholly redeeming, but it's definitely worth seeing.

*You might not want to read the Lensman novels, but let me at least say that they're kinda right-wing, very 30's, and probably the only piece of science fiction I've ever read that took science seriously (very seriously, actually) but didn't know about relativity. The really notable thing is the crazy level of homosocial stuff going on when our heros first become lensmen and see how incorruptible they all are. It's like they're lusting after each other's moral sensibility.

Hitchhikers' Movie

2005-04-30T19:42:00.000-07:00

So I saw the movie last night, and I've been trying to put my opinion into words. It's a little difficult to do; Neil Gaiman once mentioned that what you want from the new stuff from your favorite author (or artist of other description) isn't something like their last work, but something that makes you feel like you felt when you read their last work. Somehow I have to think about the movie this way, and somehow it lets me down.

Don't get me wrong, I am in the large quite affectionate towards the film. Having at last seen it I think the casting choices basically make sense, and I think it has a vastly better structure than anything a direct translation could form. I can really see the music video and commercial background of the directors at work -- they have a real talent for creating impressive visuals, and they've managed to get a movie with twenty million different looks but a distinct aesthetic. Take a moment for this point, because it's important. The Matrix (whatever you may think of it in the large) looked good because it had a unified aesthetic, an actual look; neither of the first two Star Wars' pulled this off, and they suffer a lot for it. Hitchhikers' is very comparable to Star Wars in this regard: both have a few dozen alien locales to create, and they all have to look very different from each other, but Hitchhikers' manages to fit the disparate pieces into a single puzzle. In some ways, I think the directors were actually perfect, since they got a visual sense of the books into the movie very very well. When a few dozen people lay on the floor of the local pub with bags over their heads, when Ford Prefect wheeled a shopping cart full of beer down a country road, or during the amazing opening montage of the Dolphins leaving (water ballet, more or less, with a full-blown production numbery song), my heart was filled with joy.

Plot alterations. As I've said, there are many many plot changes, and they tend to transform the movie into something substantially more movielike than any previous incarnation of Hitchhikers' has been. A few of them, however, seem to stray from the spirit of the thing -- I can't say too much about the changes that really bothered me because most of them qualify as major spoilers, and of course they're mostly little spiritual kinds of bothering. On the other hand, the dialogue isn't quite on that level.

I remember reading the screenwriter Karey Kirkpatrick's self-interview last summer and it filled me with hope. He said so much good stuff about loving the language and ideas of Douglas Adams. Unfortunately, while he seems to understand good words and understand good ideas, he definitely doesn't understand the rhythm of dialogue. Brilliant phrase after brilliant phrase just got slightly changed, just the tiniest little bit, turning hilarious jokes into unfunny ones. Easy example to cite (because it's on the website):

"... Arthur went to a fancy-dress party, and met a very nice young woman, who he totally blew it with."

in the movie, versus

"... Arthur went to a very nice party, and met a very nice girl, who he totally failed to get off with."

in the book. Crying shame after crying, crying shame. Whether the alterations are for clarity or de-Britishization or just 'cause, I can't quite deal. There's also a strange affection for punning that Adams basically avoided; it may just be a subtle thing that only bothers a ridiculous fanboy like me, but the many visual puns are just ... off.

I think the basic punchline is that this edition of Hitchhikers' fails me not because it's bad, but (ironically) because however much I may love brilliant visuals and stunning dolphin songs, it just doesn't make me feel the way Hitchhikers' should. Crying shame.

I heart the Daily Show

2005-04-20T20:29:00.000-07:00

I am, as always, charmed by the Daily Show almost beyond words. The story on the students who created Harvard's new maid (sorry, cleaning professional) service was entirely too delightful in every way.

I'm even learning to appreciate the new Dennis Miller. Segment one of him was an amazing tour de force of logorrhea (which word, interestingly enough, google cannot spell) that was completely hilarious. Segment two was the same ... or would have been if it hadn't been filled with the kind of unbearable stupidity that is now his trademark. But I'm trying to like it in the same spirit Jon Stewart seems to: purely as a superlative demonstration of craft. Kind of in that way one appreciates Wagner or Pound or any other brilliant artist whose unsavory political beliefs occasionally creep into their art.

And now we get last night and Frank Luntz. Heart heart heart.

Note to Rahm Emmanuel

2005-04-15T15:00:00.000-07:00

When soliciting DCCC contributions, even from relatively generous (for a grad student) donors, some days are definitely better than others.

Dropping Arguments

2005-04-13T10:54:00.000-07:00

At the peril of actually commenting on something happening in the blogosphere, I wanted to talk about Democrats and culture. All this argument is probably good for us, but most of it seems to miss the correct starting point.

Back in high school, I was a debater for a very brief time. Since the activity, like most longstanding extracurriculars, had developed a rich technical language for describing various bits of itself, I almost can't comment on public debate without using its terms. One in particular comes to mind: spreading. What is called "policy debate" denudes the argument of all pretensions towards persuasiveness or rhetorical technique, encouraging everyone to simply speak as fast as possible; "spreading" was the art of making as many arguments as you can, talking like the micro machines guy all the while, in the hopes that your opponent wouldn't respond to some of them. Any dropped argument you then snap back: "since they dropped (whatever), they concede the point, and therefore their plan leads to nuclear war."

(for those who don't know, every negative in policy debate leads to nuclear war)

National politics doesn't quite have spreading, but in this case of culture we do have something close: lefties don't want to censor (not to mention that we tend to get exercised about different bits of potentially-censorable stuff), but also don't want to have to put it quite that way, so we tend to say nothing. Argument dropped, the opposition then says we want nuclear culture war. Badness ensues. The strangeness is that even the pro-censorship folks don't really want to do much, and even can't -- even nibbling on the edges of "obscenity" doesn't affect the issue at the root of the demagoging.

As far as I'm concerned then, the local point is that we do need to be saying stuff about culture and media, even if it is bloviation or non sequitur -- there's just no response that's worse than not responding, however logically incoherent that response may be. Even saying "I'm not happy, but I can't do anything" is probably better than nothing. We don't need to be anti-media crusaders, but our response to events can't be mumbling and feet-shuffling.

The global point is more interesting: find things Republicans don't want to talk about and bring them up. Stupid, yes, but it's impressive how little we do this on a national level, particularly because we miss the point about not needing to take strong action against the issues under discussion. For instance, we could talk more deeply about in vitro fertilization (yay, but hardcore pro-lifers can't support it), toxic chemical pollution, even infant mortality would be plenty good enough -- smarter people than me should be able to think of better points, but the idea is simple enough and woefully unexploited.

I have created a monster

2005-04-12T23:23:00.000-07:00

The esteemed Neil has, having never previously enjoyed mayonnaise, become addicted to my current version (champagne vinegar and chili oil); I fear this may imply more worry in future. On the other hand, it may enhance my argument that he should learn how to cook (cheap+skill=good is an equation any utilitarian can love).

On the gripping hand, it's not like he's outpaced my own gluttony yet. So we'll see...

For the Record

2005-04-10T11:57:00.000-07:00

My Unitarian Jihad Name is: Brother Immaculate Gatling Gun of Loving Non-Dualism. What's yours?

Simply too charming to pass up.

Junk Food Ninjitsu

2005-04-02T20:44:00.000-08:00

I love cooking.

Final four party.

Roommate says: "I could do with some cheese fries." Great: frozen fries, check. Provolone, check. Tinfoil, check. Toaster oven, check. Junk food aplenty, ten minutes tops. A gracenote on the chips and dip (god, homemade onion dip may be the most addictive smell I've ever smelled -- browning the onions half to death is the thing) (and the fries probably would have been homemade if I had another russet; the oil from the chips was still cooling in the pot).

Guest says: "I could do with cheese fries with gravy."

Gravy!?! A Canadian thing. Chicken or turkey, apparently. We can swing with that.

Medium roux. No roast, so improvise. Nuke cup and a half of stock from the freezer, add sherry up to two cups, peppercorns, bay leaf, reduce to one. Rouxify, taste.

Disaster.

Sherry too sugary. Gravy (of all things) cloying.

Salt, yes -- none from the nonexistent pan drippings -- but more than that. Must beat the sweet. So: rice wine vinegar.

Add. Fries. Taste. Correct. Simmer. Doublecheck. Cheese. Decant. Melt. Serve.

Win.

I love cooking.

Goodness later -- I promise.

Anti-Labor

2005-03-30T13:42:00.000-08:00

So here's something that utterly, utterly confounds me.

I enjoyed Easter dinner with some very earnest, friendly, nice people over in Lansing. I met them through theater stuff, and I'm trying to do the whole big-brother thing for their daughter, who reminds me of myself at age 12 (bright, but in desperate need of a social skills transplant). The mother of the family is a geology grad student here, and was firmly opposed to the recent job action undertaken by the grad student union. She seemed to think that the grad students were being whiny (which is arguable), but more importantly she said that her husband and family had recently had their healthcare costs raised appreciably by her husband's employer (something like $5 per prescription to $25 per, for instance), and that this invalidated grad student agitation here. I asked why she didn't try to do something about it and she said, for the second time, "I'm just anti-labor."

This is something I absolutely do not get. I understand why one might be opposed to a particular union and its demands, for reasons running a gigantic gamut from outright corruption through to owning the company employing the labor, but none of these objections have any connection to an objection to labor in the abstract. You might suppose that labor is really communism, but despite communitarian impulses universal to labor this view isn't supportable anymore. You might suppose that labor undercuts individualism, but the same objection would carry over to all forms of collective action, so is unworkable. Even rabid free-marketers shouldn't object to labor -- every individual should, in their worldview, be allowed to try to get the most profit on their labor that they can, however they can. So where is the principled objection to labor as labor? I'm genuinely curious...

Easter Quickie

2005-03-27T08:18:00.000-08:00

Since I'm actually doing something this Easter without getting paid for it, time to be a good little heathen and post about the Left Behind novels, about which I'm sure all three readers already know. I just caught a review (horrible, politicized, missing the point, and elsewise generally crappy) which sparked an interesting thought.

Current best speculation about how the Book of Revelation came to be (and what its authors intended it to be) suggest that it was essentially a political allegory, satire dressed up as prophecy; the analysis even goes far enough to venture fairly specific mappings onto then-current trends and events. The idea that the current series of novels whose entire premise is to take everything in the Book of Revelation completely literally ends up being political allegory anyhow tickles my irony bone.

More later on being good, including the luscious pie theory!

Ethics and Emotional Distance

2005-03-21T22:30:00.000-08:00

So this is one of those posts where I solicit my three readers, none of whom know anything about the given field and of whom at least one (the wolf fashioned from straw, for anyone wondering) is unlikely to remotely support the view being presupposed, to give me input on something bothering me recently: to what extent can I ignore the problems of the far away and still be a more or less "good" person? That is to say, if a friend appears in front of me and needs taking care of in some way I feel like I would be a bad person if I failed to supply that care; if my buddy needs a hand, I think I would be remiss in some way if I didn't supply my buddy with it. On the other hand, it's not as though there aren't many many people all over the world requiring of equal hands, so why shouldn't I help them too? While sometimes convenience is a factor, money certainly moves fast, so it's not as though I couldn't offer comparable assistance to anybody out there. At the same time, I feel (in my horrible, flawed, moral intuition kind of way) like it's okay to neglect at least minor needs of people "farther" from me in some emotional sense; equivalently, I think it's not a problem that I'm more inclined to be helpful to people I know/am closer to, at least not in a way that imperils my standing as a decent human being. Then there ought to be some criterion capturing people it's okay to not help -- but I have no idea what it could possibly be.

Anybody with insight on this?

In a life update, it looks like I'll be participating in my first picket line on Thursday. Time to take part in the labor negotiations process for a job I'm not yet (but will soon be) doing!

When it rains

2005-03-19T18:05:00.000-08:00

It would appear to pour. Maybe if Tony's still linking me every other day I'll actually get some visitors to appreciate it, but eh.

This time, I'm thinking about (inevitably) Terry Schiavo. I don't want to jump into the huge moral quandry, but something small to think about: her husband is being prevented from carrying out her will because her parents are trying to intervene. That is to say that the wingnuts are trampling all over traditional marriage. So I ask, how much does this threaten marriage relative to the right to marry for gay people? The state taking away marital rights versus men kissing in public.

I'm just waiting for our side to learn to use unapologetically definitive rhetoric about things we feel nuanced about.

MacGyver

2005-03-19T17:46:00.000-08:00

So I promised to come through on MacGyver; I figured I'd best do it now.

The basic ID complaint about evolution is based in "irreducible complexity," a slightly-updated and technobabbled version of the "what good is half an eye" argument (for the record, half an eye is quite useful: computer simulations have evolved eyes from light-sensitive membranes selecting only for goodness of seeing); on the molecular level, it says that because some protein chains and messenger paths break if you remove any part (beware though, since this argument isn't actually formalized in any way), they could not have evolved. Since the parts are useless, so it goes, the idea that the whole could evolve is making something from nothing.

However, there is an obvious flaw here: there isn't nothing. Any organism has a bunch of stuff around already (limbs, organs, proteins, etc.) before a feature evolves, so the proper analogy, rather than to making something from nothing, is to making something from whatever you happen to have on hand (gum, needles, jam, bottles, baking soda, etc.). And now everything should be clear: evolution says "Hey! Whatcha got? Input/output channels, mitochondria, some control of the cell membrane? Presto, flagellum!"

Also, of course, this is appropriate because evolution is Canadian, a pacifist, and looks oddly like that guy who used to be on Stargate...

Memely memes

2005-03-15T00:21:00.000-08:00

So I started this a while back, and it no longer really applies to the very moment, but here it is anyhow.

Wow. Spring break over already (that is to say a week and a half later) and I'm still not quite back in the swing of things. Fine.

I'm simultaneously glad and chagrined that so many people (i.e. Diana and Tse-Wei) discovered my blog while I was spring-breaking and thus paying absolutely no attention to it; rest assured that I saw the comments and extend hearty welcomes. For now, I'm still post-birthday (not mine), which means little intelligent thought, but a few new memes. And of course, by memes here I genuinely mean memes, not the specialized blogospheric variety; spread these, for lo they are good and fruitful!

First, Jon Chait over at TPM (for the moment) compares private accounts to a plan to save social security by creating statues of W in every town square in America. While this is a great and important idea (that is that a plan doesn't count as doing something if it only does it barely better than doing nothing), I must in my Buffy fandom ask that this concept be relabeled (rememed?): the canonical null plan is, as we all know, "we attack the mayor with hummus!" It could even be summarized by the word hummus alone so as to be invokable more conveniently; we do need the concept. (So, what do you think of the Bush plan? Hummus!).

Second (and third), I wanted to say a little bit about intelligent design. At Tales from the Culture Wars, there's a great post about doubting evolution in an ID-kinda way being akin to doubting gravity because of the procession of Mercury, Lastly, evolution is like MacGyver, a point which maybe I'll elaborate in a later post...

I suppose that ended up being a very little about intelligent design, but eh.

In Defense of the Core

2005-02-24T12:30:00.000-08:00

I try to follow the blogospheric wars about my esteemed alma mater, and some comments about the core disturbed me. So, a defense.

First, I come to bury the core, not to praise it, and unlike Marc Antony I mean it. The modern core has many, many problems -- large classes, sometimes a lack of intellectual rigor, appearance of being about nothing (a linguistic proof: many a student describing their schedule will list off a bunch of titles, ending with "...and a core."), and I think scrapping it and starting over is a great idea. The trouble is that, on paper, the core makes plenty of sense, which is why it was implemented in the first place. If a student is going to take one course in your discipline and forget most of the material after the fact, what do you want them to get out of it? Most likely an introduction to your methods, approaches to problems, and so on -- you want them to be able to think about things your way rather than name all the characters in some book. And you want the classes taught by good senior professors, so the students get exposure to top faculty rather than whichever postdoc drew the short straw, so you let them talk about whatever interests them while they try to make students understand how to tackle their problems. And yes, there are better and worse works to introduce to people, but who better to judge that than the professor of the class anyhow? Unless you particularly believe in a fairly specific curriculum that everybody should learn, the core is a much better way to go. In theory.

The real trouble, in my opinion, is that there's too little effort to teach students the methods of thinking that are the purported purpose of the core -- some classes do, others just assume that everyone can do it when they come into the class. If I could make just one change to reform the core, it would be to try to do this more formally: every area has to figure out what methods of analysis they're trying to teach, then actually teach them in some way rather than merely hope the students can osmose it from their TFs. It's the mismatch of this idea to actual core areas (the core is split by vague topic-area division rather than reasoning method) that seems to breed the trouble. And it's a lot of trouble. The core in the real world is horrible, but that doesn't mean the philosophy is broken.

Leftovers

2005-02-22T21:06:00.000-08:00

I've been thinking politics, god, complexity, probability, and other abstractions all day, some with a mind for a blog post. But will I post on any of them? Nope. Time for food.

So I've finally decided to start roasting chickens seriously, figured it all out, and now do it fairly regularly; I try to pick up a roaster every time I go to the store. It's way too easy to not, and has the benefit of producing a mountain of leftovers when I do it for just me and Kara. On the other hand, now I have to figure out what to do with a mountain of leftovers.

I recognize this should be easy. Cooked chicken in little bits is in a million dishes and is half the point of roasting a bird for two people to begin with (the other half is that it's great to have the carcass around for stock and I'm kinda ashamed of buying parts), but I feel I'm coming up short of ideas. With spring break coming fast, I need answers soon. Soup, hash, quiche -- what else?

Two caveats though: my roommate likes neither Asian cuisines of any type or any dish involving rice. Don't ask, just believe. Second, I have a longstanding visceral dislike of chicken salad -- it's a ridiculous prejudice, but I think it's slimy. Tuna's fine, but no chicken.

PS: Joy of Cooking's recipe for "Turned Roast Chicken" is the best I've found -- you get a whole, well-cooked bird at the end with a bunch of pan drippings for gravy (their recipe plus a shallot works surprising wonders) for about 1:15 roasting time.

Recruitment

2005-02-14T11:22:00.000-08:00

My stoop is filled with packages, seemingly mostly flowers and chocolate, for occupants of other apartments.

Anybody want to help me promote fertility and the civic good by running through the streets naked, whipping the young maidens with bits of wolfhide?

Memeing

2005-02-13T23:35:00.000-08:00

Trying in my vain way to help produce the college-prof-thanking meme that Brad DeLong's been talking about, shoutouts to (in no particular order; non-me-in-college profs not on the list):

Leslie Valiant, Noam Elkies, Salil Vadhan, Michael Rabin, Lisa Carbone, Nathan Dunfield, Steve Rosen, my amazing history of technology prof whose name I have utterly forgot (crying shame because I think she's here now), Andreea Nicoara, John Boller, Andy Engleward, Gerald Sacks, and many more.

Doing the math

2005-02-13T00:27:00.000-08:00

There's a part of me that wants to devote lots of time and energy to rebutting Ross Douthat's ridiculous articles and books about Harvard; he's a huge liar, he knows it, and he should be ashamed. There's another part of me that, unlike any part of him, is doing something constructive with its time, and it's this part that complains about me arguing too hard. So on the off chance he reads this, let me simply say that just because you're a dumbfuck doesn't mean Harvard was bad in any of the ways you describe.

The thing that pisses me off today though is misuse of math. Supply-siders like to claim that since a tax rate of 100% would yield no government revenue, lower taxes must always increase revenue, because people will work harder if they can keep some money. However, a tax rate of zero also produces no revenue; what we can conclude (if everything is smooth) is only that there are points where higher taxes mean more income and points where higher taxes mean less. So we can argue about where the changeover point is (or how many there are), but in reality both of these things must be true. Conservatives can't really debate this because it would lead to the obvious truth that current tax rates are on the wrong side of the local maximum for supply-side arguments (nobody fails to start new projects because they're taxed at 39% rather than 36%); all I'm saying to people is do the damn math, draw the conclusions, then argue from there.

Unsubstantiated Thoughts

2005-02-10T11:32:00.000-08:00

It occurs to me that I miss Douglas Adams. Perhaps this sensation of missing will be enough to make me dive through the giant stack of boxes of books that now takes up the better part of my bedroom.

Many topics seem to have, at least in terms of public debate, a fairly constrained space of tropes that can be invoked in favor of or opposed to any position on them (foreign policy, Social Security); moreover, some of these are clearly better than others and once one side uses a given trope it stops being available to the other side. That said, since there are currently no repercussions for using rhetoric bearing no relation to the policy actually being advocated, it seems like a strong strategy for many political arguments is simply to grab up the good tropes before anybody else gets to them.

Reductions are like homotopies. Hrm.

The current crop of AI contenders have absolutely no ability to learn lyrics. No brain whatsoever. Hrm again.

I'm guessing

2005-02-08T21:46:00.000-08:00

... that my hypothetical readers don't care to hear me muse about spectral sequences (a chunk of math which is basic but of technical complexity high enough that the only way to understand is to work it out for yourself); if this isn't the case, let me know. Otherwise, I'll keep my mouth shut.

On the other hand, they are an example of a kind of intellectual phenomenon I have seen rarely outside of math: machinery. Within math, this term refers to a theory not a priori interesting in its own right, but potentially very enlightening for dealing with other stuff, usually connoting a high degree of internal technical complexity that may not be necessary for the use of the theory for its desired purpose. I suppose math itself may function this way in other fields, but somehow that seems too conceptual to count (though of course I would say that in any case); machinery is characterized by being somehow un-conceptual, while math used in other fields is usually used because it makes sense in that context. Hrmph.

Inevitably, of course, I can't elucidate the concept via example without explaining something non-mathematicians haven't even heard of. So hrmph.

By the way, "musing" would be a written record (presumably half in pseudo-tex) of me trying to figure out spectral sequences, i.e. many sentences filled with strange symbols and stranger attempts to write them in ascii. Just be aware.

Current Reading

2005-02-06T23:02:00.000-08:00

A friend gave me "What's the Matter with Kansas" for my birthday; I'm pretty sure that all actual contents of this book are seriously old hat, so it's not worth mentioning the obvious conclusions (Dems need to link capitalism and mass-produced culture better, intellectuals need to grab some victimhood), but I did have one thought not entirely implied by the book -- the larger an organization gets, the worse it is at complex optimization strategies. In particular I was thinking about the way that bigger corporations get worse at worrying about things that aren't the bottom line, particularly things that seem like they ought to be constraints like the law or treating people like humans. And it seems to me that in general bad corporate behavior, when not orchestrated from the top, can be completely emergent since more layers of management make it harder to explain why a particular action is the best permitted by constraints. If anybody knows about anybody I could read on this point I'd be gratified.

In the meantime, I went to the supermarket today and saw low-fat butter. Aaaaarrrrggggghhh.

I'm still waiting for low-meat steak.

State of the Union

2005-02-03T15:51:00.000-08:00

I would like to let it be known that I have a plan to solve our {social security, foreign policy, terrorism, tort, medical, energy, budget} crisis. It will make us all healthy, wealthy, and wise, not to mention better people. Also, it will ensure that our children will all be all of these things too, not to mention attractive and tall. But we must not content ourselves with these victories; I will give every child in America a puppy, wish away everyone's extra pounds, and supply every man with a pliant supermodel for a girlfriend, and anybody who questions any of this must hate America.

So whose job is it to make sure statements agree with some semblance of reality? The disinterested public? Right.

Fun with math

2005-02-02T17:55:00.000-08:00

So I was pondering life today and thinking about the joy of mathematics and about how life works, politics, the whole bit, which inevitably led into one of my favorite facts about probability: the Chernoff bound. I fairly regularly bemoan the general public ignorance of probability, so I explain as a service, but hopefully also 'cause other people will think it's cool too.

Of course, like most cool things, it's both simple and complex; the complex version is all jazzy with symbols and precision and generality (in fact, so much that there are many different statements called Chernoff bounds for different situations), but the simple one just has a few words: if you flip n coins, the chance that you'll get more than a fixed bit off from n/2 heads decreases exponentially as n gets bigger. Another version: the longer you play, the more likely you get closer to expectation. If the coin is biased, it just changes that last fraction. It's a little subtle to get properly, but explanation won't help, so some exercises for the reader:

1) Why does polling work?
2) How do you explain why casinos make crazy profits, but backing a roulette game is a crappy thing to do with your life savings?
3) Why is social security privitazation bad?

I'll post my answers some other time if anyone cares. In the meantime, it's cool to ponder...

Waiting for the inevitable

2005-01-25T20:48:00.000-08:00

At some stage the slow transformation of Bush administration rhetoric will reach its final destination, and, drunk with power, Scott McClellan will insist that the press refer to Republican Social Security plans only as "orgasmaccounts." Shortly thereafter the press will be required to no longer refer to "Democrats," only "America-Haters." I await the day I'll see on the bottom of my TV the letters "Teddy Kennedy AH-MA."

Regardless, I hope we can all agree that while words do carry political charge, there's no need to describe anybody's plans only with the words they use, though it's always acceptable to do so even if they're not using the words anymore.

Food post

2005-01-02T21:44:00.000-08:00

Ok, so I know I haven't posted in ever, but I'm hoping any rss feeds out there are getting this. I'm just too mindboggled for words.

I'm watching a dvd, and someone started talking about "low-fat hollandaise sauce" on their eggs benedict. Friggin' buckwheat bagel I could take, but low fat? Hollandaise is a dynamic combination (and oh, what a dynamic combination it is) of cooked egg yolks and melted butter, which is to say this: it's *fat* mixed with *fat*. Lemon, salt, sure but mostly fat and fat. There's no way to reduce the fat in a fat-fat blend. Argh and double argh.

Defaulting

2004-11-28T19:44:00.000-08:00

Between several good posts in several places and the holiday, I have more than a few things to say, notably about religon and morals. However, I'm exhausted and don't want to write, as I've been doing light design all day. Why write then? Because I must procrastenate; through a convoluted internet process, I've received the single most boring introductory email ever written by man. Lest the author ever read this, I'll be circumspect, but I have to complain. I netstalked this person good and proper before getting this email, so I know with complete certainty that they could have said something interesting, and yet no. Argh. Time to go deal; more either later or tomorrow.

Democratic Morality

2004-11-08T02:17:00.000-08:00

As I've commented over at Neil's place, there is at least something to be said for moral issues in this past election and most particularly looking forward. I've been (obviously enough) seduced by George Lakoff's philosophy about morality, but it's more than that. I've been talking to a red-state, conservative christian friend and feel it's worth talking about what I've heard, even though people don't necessarily explain properly what's going on in their minds.

First, it should be clear enough that, much though we lefties like to talk about homophobia and hatred and closed-mindedness, what accessible values voters care about is what we might call societal morality -- the idea that we as a people should approve certain behaviors and disapprove others based on our shared morals. Now the more raving postmodernists among us probably abhor that idea, and even I'm made philosophically uncomfortable by it, but I think most of us would be willing to pony up that such a thing is practically important. After all, half of marriage is societal expectations of the married couple, and these things help make marriages work.

What do values voters think about societal morality? Mostly that we should have some, it appears -- that it's important that our culture embrace some set of values. Politically, "American Values" certainly is a concept, and since it's ill-defined, it's not even that hard to stand for. Culture warriors certainly do, filling that empty idea with racism, sexism, religious intolerance, and homophobia*, and they then roundly denounce the left not so much for not having their morality but for not having any morality at all. This one we walk into eyes open: the continuing fashion of moral relativism makes embracing morality of this type and on this plane profoundly distasteful, even to me, and much though I hold myself and those around me to strong moral standards, the idea that we as a society should advocate morality is something I, as a good lefty intellectual, want to distance myself from. All of this is in spite of the fact that progressives have a strong shared moral code -- we just don't talk about it.

So let's step up. I don't just mean articulating values that drive us to enact policies here, I mean firmly and powerfully advancing a (the) coherent societal morality that guides progressives in their political thinking -- respect for others and fundamental fairness being two of the first pieces. After all, it's hard to fight something with nothing.

PS: I've been watching D. L. Hughely on Bill Maher's show -- there's a man we should send to Congress right quick. He's no Obama, but his heart and his rhetoric are very much in the right place.

*Some open and some not; my associate's positions, on closer examination, are based more on a 50's style "traditional morality" mixed with genuine Christian love, which admittedly carries its own dose of homophobia and sexism, but of a type I think non-radicals would find less vicious.

Well &*&%

2004-11-02T22:38:00.001-08:00

One way or another, there are a few things that this election makes clear, in two big points with two corollaries:

-It's time to give up argument. George Lakoff's position about framing and values (see Moral Politics and Don't Think of an Elephant) I believe completely, but they're not enough. To even contest your opponent's points coherently seems to be useless, so it's time for the power of talking points and repetition. We'd do best to pick the five most plausible things we can agree on doing and spin them forever.

-This means truth is definitely dead. The simple fact that large majorities of W's supporters believe proven false things about the war on terror is everything we need to demonstrate that you win no points for being right. By this I mean let's get comfortable with lying a lot and the rest of the disingenuous business.

-Managing the press is everything. I'm talking tequila and I'm talking brown-nosing, leaking, spin, and large-scale manipulation, and I mean now.

-Therefore, negativity is unbeatable. A negative story endures, it has substance and depth and exploration; a positive story lasts one day and dies. Attack and defense is all that cuts through the screen, and which would you rather be doing?

In short, Neil, you finally win this one -- it's time for some of us to lower ourselves to their level. Let's cowboy up.

Holidays

2004-10-25T11:34:00.000-07:00

Chris Mooney reminds me today that there is, as usual, a furor over Halloween in the satanic-holiday sense. This puts me in mind of a longstanding opinion I have as a fan of Judaism: it's good to separate your serious religious holidays and your party-down holidays. That is to say, Yom Kippur and Passover are serious and about religion, while Chanukah and Purim are about remembering your culture and having a big friggin' party, including ritual gambling and drunkenness, respectively. That way you don't get confused about all the "real meaning of Christmas" questions; sometimes you pray to God, other times you party to God, and you don't particularly comingle the two.

(Short sidenote: a postdoc from Assam told me recently of a local holiday with a story and set of customs essentially identical to those of Purim, down to getting so drunk you can't tell the difference between the good guy and the bad guy. Anybody out there in cyberland have more information for me?)

But today I wondered this: what should we make of Halloween and Mardi Gras? Neither seems technically a "Christian" holiday (and Halloween, in spite of being All Hallows' Eve, does indisputably have some pagan roots; on the other hand, so do Easter and Christmas), though inasmuch as they have stories, the stories are indisputably Christian, as are the cultural associations. So are these simply Christian party holidays (maybe a few centuries away from being properly of the faith)? Or is there some other story we should tell?

Bible Quotes

2004-10-13T23:17:00.000-07:00

But when thou doest alms, let not thy left hand know what thy right hand doeth: That thine alms may be in secret: and thy Father which seeth in secret himself shall reward thee openly. And when thou prayest, thou shalt not be as the hypocrites are: for they love to pray standing in the synagogues and in the corners of the streets, that they may be seen of men. Verily I say unto you, They have their reward. But thou, when thou prayest, enter into thy closet, and when thou hast shut thy door, pray to thy Father which is in secret; and thy Father which seeth in secret shall reward thee openly. But when ye pray, use not vain repetitions, as the heathen do: for they think that they shall be heard for their much speaking. Be not ye therefore like unto them: for your Father knoweth what things ye have need of, before ye ask him.

Matthew 6:3-8.

There are lessons from my good Catholic upbringing that I forget, and there are lessons I remember, and this almost more than anything else I remember: virtue, sacred more than secular, is to be practiced without hope of reward or praise, and is not to be inflated in hopes of achieving either. Religious nobility, and religious principle, is never to be claimed, only to be received.

These days, much though I wish I could hold religious faith, I'm a fervent agnostic, though Jesus' words still run through me, and I can only hope his virtue does as well, but my morals say one thing strongly: believe fervently, but don't proclaim it hoping for benefit. And when even Jesus literally believes I'm in the right, I think I'm in business, and when I hear even my lapsed faith implicitly derided, let alone my lack thereof, I can't help but be angered. I'm as good as the next guy, and better, not worse, because I don't tell people.

Most Disingenuous Point?

2004-10-13T22:44:00.000-07:00

So I've heard all the truths, all the lies, all the claims of various kinds, but my theory on Bush's truth is as follows:

Anytime Bush begins a statement with "Of course," he's pulling it out of his ass.

"Of course," I'm protecting America.

"Of course," I'm improving healthcare.

"Of course," I'm doing my best to pay down the deficit.

From here on: "Of course I'm doing x" means exactly and precisely "I'm not doing x, but I should be to the extent that you'd rather think I were."

Hell.

Continuous Prisoner's Dilemma

2004-10-07T13:29:00.000-07:00

I've been reading up recently on how to talk about politics in a politically useful way (mostly Lakoff), and I find it progressively more frustrating. Perhaps most telling for me are the tales of the pizza fund in Republican offices: you have to donate a quarter every time you use the wrong language, like "estate tax" rather than "death tax," "freedom to marry" rather than "gay marriage," or "tax cuts" rather than "tax relief." It seems regrettably obvious that this is necessary; after all, Republicans have been doing it for years and Democrats haven't, and the Republicans control everything. But this is only one example of the game of politics over policy.

So why play politics? Because it helps you play policy; after all, you don't need to outargue the opposition if you have a majority for you anyway. To me, at least, the game is so inherently undesirable that there can't be any other reason for it. But then, why did we get here?

I think the answer is essentially a prisoner's dilemma issue; both sides playing politics makes universally worse policy, and neither side makes better. However, if only one side plays they get everything they want, and we land in the ratting/not ratting game, to which the best strategy is tit-for-tat (i.e. always screw the other guy once if he screwed you once, otherwise play fair). There's a problem here, then, as if both sides play tit-for-tat, we end up with cooperation, and we haven't been cooperating since the Era of Good Feelings.

I think part of the issue is in passing from the discrete to the continuous case: if we think of the prisoner's dilemma being played at every moment, rather than at some discrete set of times, tit-for-tat is invalidated since there's no good notion of "once." We could imagine discretizing the continuous game by making decisions for a fixed interval, but it's not clear to me that that's a reduction. Even more, it's probably possible to cooperate or not on a continuous scale, with corresponding rewards and punishments. So, having rediscovered a presumably-well-developed area of economic research, anybody know what it says? Google seems to think that people (evolutionary biologists particularly) have pondered continuous payoff stuff and gotten some partial results about how to get cooperation evolutionarily, but can't easily discover anything on what happens if we play continuously rather than cooperate continuously. So, anything?

Tough Crowd and Terrorists

2004-10-05T22:40:00.000-07:00

I recognize that watching Tough Crowd is my first error, but this is such a common source of annoyance for me I had to vent. Why is it that so many people in the world somehow think that asking if we did anything wrong re: terror, where we are, and how to fix it is somehow morally reprehensible for "blaming America?" Then there's moral outrage at supposedly self-hating liberals. Hrmph.

Once and for all: the Muslim world is not currently all terrorists, the Muslim world didn't attack us on 9/11, and while there was a lot going on, most Muslims were sympathetic. Nowadays, a surprisingly large portion of the Muslim world would like to attack us, and the number's getting higher. We'll be better off fewer suicide bombers wake up tomorrow, and wanting to reduce that number by trying to placate centrist Muslims is no less patriotic or sincere or important than wanting to reduce that number by killing lots of people. So let's not get all outraged when someone suggests that mainstream Muslims think we've done wrong.

Required Debate Post

2004-09-30T18:36:00.000-07:00

I'm watching with rapt attention, but I have a problem: I find, and have always found, George W. Bush totally insuffferable in manner. Much though what he says disagrees with my thinking, all those "likeability" things that are supposed to be so much in Bush's favor make him utterly unlikeable to me, and I suspect would even if I agreed with the man.

On the other hand, I thought Al Gore was funny, charismatic, and empathetic. So it could be I'm just so far off the normal wavelength that I can make no sensible judgement on these issues.

Antonin Scalia: Confirmed Insanity

2004-09-29T19:26:00.000-07:00

At the peril of saying something remotely topical (and worse, something remotely topical I stole from somewhere else), Atrios just pointed me towards an article about Scalia appearing at the K-School. I'll leave aside the poorly-written nature of the article and merely observe that however poor a job the reporter did, any of those quotes are well implausible and off-topic enough that I can only assume he's nuts. If only a single quote indicated plausible argument! “Is it racial profiling prohibited by the Fourth Amendment for the police to go looking for a white man with blue eyes? Do you want to stop little old ladies with tennis shoes?” Yes, and no, and duh, and none of that is relevent. “Would you rather have the president of the United States decided by the Supreme Court of Florida?” Well, you sure should, based on your precedent. None of these comments remotely make me suspect the man has a coherent judicial philosophy; I wish someone could tell me he had one so I could sound less shrill saying why it's dumb, but honestly only one decision has ever made me feel the man is a Kantian rational being, so none of this probably ought to surprise me. It's like the Bush administration: every time I suspect they couldn't really be that bad, they turn out to be worse. I just keep hoping I don't have to be that cynical. Oh, dire, dire gods!

... I suspect that's enough topicality to keep me going for a good long time. Also hopefully a lot more interesting that whatever is going on in my own life or work (for the record: horrible, horrible depression, and a dynamic combination of nothing, stacks, and comma categories). We'll see if any of the above drive me to more posting...

Campaign Salsa!

2004-09-26T13:16:00.000-07:00

At the risk of saying something precisely topical (rather than only vaguely topical), I have to mention the New Democrat Network's new song. It's jumpy peppy salsa, sung in Spanish, and the harshest attack on Bush I've seen yet. So obviously I love it. However, it's worth noting that I'm more enthused about the possibility of a real campaign song for 2004 than the asskicking, and of course most enthused about the particular song itself. My toes are a-tappin'!

"...Ten cuidado del nombre Bush..."

Blind Criticism

2004-09-25T22:04:00.000-07:00

Back to posting, at long last.

I just caught Bowling for Columbine on late night deep cable, and I am as usual not sure what to say. Michael Moore is a highly problematic filmmaker and a more problematic spokesman for me; at the same time, I don't have to agree with everything in a piece of art to think it's valuable. The film is a typical product of his, much like F9/11: affecting, serious, important stuff, tastefully handled, mixed together with cheap shots and cheaper arguments. I really think that everyone will see what they personally want to see in his films, be it crazy liberal propaganda or the serious work of a firebrand for the people, and his style is such that you can pick and choose what you want to see and believe that that's what he is almost without noticing you're doing it. As for me, I can't take his blind admirers or his blind detractors, but the one thing that gets me every time is protesters who haven't seen the films. There's a lot to like and a lot to hate, and I respect intelligent criticism (god knows I have enough of it myself), but I hear this "Michael Moore is a crazy propagandist who hates America" meme, knowing it comes from people who've never seen one of his films, and I can't take it, because the one thing you know beyond doubt when you see his work is that the man loves and respects his country and its people. He may not love it the way you do, but he loves it just the same.

I suppose that went nowhere; it's just time for me to vent some rage on the subject. There are inappropriate works of art in the world; I'm pretty sure his movies aren't among them, but I'm absolutely certain that you can't make up your mind about that question without seeing the films.

More media strategy

2004-09-01T23:36:00.000-07:00

Immediately after posting a small addition to Mycroft's comment, I had a large thought. Then I had a better one, midway through writing about the previous thought. Here we go.

Let's add to our theories about best strategy two assumptions about the way the world works. Both should be pretty obvious:

(1) Only change is newsworthy. That is, if nothing happened, there's nothing to report. Enough new stuff happens each day that our papers are filled, and we have to construe "change" as including "things that happened," but it should be clear that stories that report more change are bigger news.

(2) Credibility is key to popularity. Nobody would read a newspaper that said nothing true. Now, being credible enough isn't that hard, but being on top means being very credible.

Observe that these factors work in opposition to each other. If what people know is determined by what they read in the paper, and the newsworthy things are the things different from what people know, then reporting newsworthy things must inherently undermine the credibility of a news source, and thus be a bad strategy. In other words, a particular news source feels pressure to not contradict what it has said in the past, making it difficult to report news.

The payoff is that this explains media narratives. How do you deal with having a disincentive to report contradictory information? Choose a big story, then fit the events of the future in as supporting evidence. That way, nothing new has to go against the old information; indeed, there's the payoff in credibility coming from accurate prediction of future stories. And once some outlet has made up its mind on some narrative, it's bad strategy to go against it unless you have a more likely narrative. So there is a good strategic reason why narratives solidify. I wonder what more is needed to explain most major media behavior; any more examples of simple principles, or things that need explaining?

How should the media behave?

2004-09-01T16:06:00.000-07:00

During this week of convention randomness, I'm again pondering how the media should work. Not how it should work if all were right with the world, mind you; how it should work theoretically if the media looks more or less the way it does at the moment (corporate control, profit motive), but is playing its optimal strategy in terms of market success. Is there some source I should go to to figure out the theory here? Failing that, here are my thoughts thus far:

-Scandal sells. This implies that if there's a way to legitimize a scandal, it goes on the air.

-Conflict sells. Conflicts are exciting; people want to watch rivalry. So better than a scandal is a disputed scandal.

-Conflict lasts. Conflicts are the news version of cliffhangers: a major question is a reason to tune in the next day. As a corollary, since the news decides what the facts are, they decide when conflicts are over.

-The news cycle exists. I'm not sure why, but there is one, and I'd like to understand why it is the way it is.

Can anybody add anything useful? I'm looking for more basic principles, but I can't think of any at the moment.

Judicial Activism

2004-08-25T11:02:00.000-07:00

Hey again guys. Sorry for the lack of posting -- I've been off packing spheres and thinking about computing cohomology. But I'm back now.

With all the renewed gay marriage talk, I've been thinking again about judicial activism and have arrived at a simple conclusion: I have no earthly idea what it is. From the way it gets talked about and reported, it seems synonymous with "liberal," which is probably what they mean but philosophically useless (and definitely useless for convincing me that it's bad). And while I suspect an intellectually honest conservative would say something more like "enacting a social agenda through judicial decree," that's equally flawed; nobody can disagree that the court should strike down a modern-day Sedition act, and neither can they claim that the loudest complainers about activism wouldn't be only too happy to pack the court to overturn Roe v. Wade, both of which seem like social agendas enacted by courts to me (not to mention that I see no reason that activism should only apply to social policy and not, say, economic policy).

Also, to me, it would have been activist had the court taken a pro-God position in the Pledge case on the merits (rather than dismissing because of standing); near as I can tell, the Constitution and its current interpretation would consider that an establishment of religion, so supporting it would change the law, and that leads me to suspect that most people's idea of judicial activism is probably tied to the political ideas they already have.

So does anybody have a good, value-neutral definition? Is there one that doesn't inherently tie into a theory of legal interpretation? The best metric I've yet heard is along the lines of "number of cases overturned," (by which measure, incidentally, the Rhenquist court is more activist than the Burger court, which was more activist than the Warren court), but that's not a definition. So can anyone tell me what's really going on?

Slow Week

2004-08-15T11:00:00.000-07:00

So I've got some stuff to post. but it looks like I'm about to be AFK for about a week (maybe not, but posts will certainly be more sporadic, if that is indeed imaginable). I'll catch you later.

Anonymous Comments

2004-08-12T11:15:00.000-07:00

I just wanted to preempt this one. I'd like to permit anonymous comments on this blog, but only for the convenience of people who don't have accounts or something comparable. As such, here's a request for any anonymous posters: please sign your (a consistent) name in your posts. I just don't want to mess with trolls, and I think it's not excessive to ask a reasonable person to take responsibility for their words.

Policy Thought

2004-08-11T14:33:00.000-07:00

So I've been thinking about some variant on these proposals for a while, but hear me out.

I hope my loyal fans (yes, I mean all two of you) recall when FOX News threatened to sue the Simpsons over a segment parodying their rightward bias. I'd be pleased if my loyal fans remembered when the RIAA threatened to sue Ed Felten for publishing his success at their watermark-breaking challenge. I'd be surprised if my loyal fans recall when my friend Tom Lotze was threatened with a copyright lawsuit over his mirroring of the hamster dance, a webpage of animated gifs and 30 seconds of music (the ones on the first link) taken from the Disney animated film Robin Hood (by its creator, not Disney).

Now the Simpsons got very lucky: the corporation suing them happened to be a fellow subsidiary of a larger company, so they just pointed this out and walked away with a stern warning never to do anything like it again. Ed Felten got less lucky: he got to publish his paper, but he actually had to file a lawsuit to get that far (in which, by the way, the respondents claimed they'd never threatened a lawsuit). If either hadn't been lucky, the smart move for each would have been to let themselves be bullied. And while I've admittedly just cherry-picked the first examples I remembered, these cases are far from the only ones where people who were clearly in the right almost backed down because of the threat of legal trouble.

Things are worse because of the internet; what if the FOX News parody segment had been on homestarrunner.com, or this website? Individuals have tended to let their rights be trampled by big corporations with lawyers who send them threatening letters, and the reason is clear: properly defending a even a frivolous lawsuit by a rich entity is a huge cost in time and money. Even if the case is immediately dismissed, it probably costs thousands of dollars to get that far. This happens because going to court is a prisoner's dilemma-type situation even in the best of cases: if either party decides not to settle, that means huge sunk costs for both, making it often infeasible for a smaller party to be sued by a larger one. That leads us to the situation we have now: corporations with plenty of resources, in-house lawyers, and so on, send letters threatening lawsuits against individuals doing things they don't like even if those things are almost certainly not grounds for a suit, and the individuals back down because they can't afford the cost of fighting.

How do we negate, or at least blunt, this power? I have two thoughts. First is making it easier to seek large damages in court for legal extortion of this kind; if someone threatens a frivolous lawsuit, the threatened individual can seek compensation in court. While some version of this might be the right way to go, it suffers from two obvious problems. First, in order to be substantially deterrent, the amount of damages would need to be set fairly high for even sending a threatening letter (how much money to deter Disney?), which seems way out of proportion. Second, the whole regime seems ripe for abuse by unscrupulous lawyers, which is never a good way to set out on new policy.

My second suggestion, which I had just today, seemed better: since current charitable free legal services aren't stopping the problem, why not have public defenders for civil suits? Simply have the court provide the defendant with an attorney if they need one and cover legal costs. If the cost is excessive, you could restrict the program to cases in which the plaintiff's net worth exceeds that of the defendent by (several?) orders of magnitude or cut off the support after some amount of work had been done. I admit readily that I've yet to estimate the costs on this one (I don't know how much public defenders make), but I wonder if it might not take a large bite out of the problem; when Fox comes knocking on the humorist's door, the humorist has a free lawyer to go into court and say "it's a parody, idiot" and the suit goes away. In fact, it probably never got filed in the first place.

I'm sure there are a few obvious minor holes. But why would this not be a good idea in general?

PS: The last tale is less clear-cut than the others; I intend it to bring home the point that threats of hard-to-defend lawsuits are neither far away nor abstract, but rather can happen to you or people you know.

Left-Wing Dirty Tricks

2004-08-09T12:48:00.000-07:00

While I'm at it, I thought I might ask a quick question to my (very few) loyal readers: does anybody know about any Democrat dirty tricksters? It's not so difficult to list off obviously-dirty political techniques (like push polling, flyering neighborhoods with false information to suppress turnout, paying preachers to suppress black turnout, and DoSing the opposition campaign headquarters) that Republicans across the country (the Bushies in particular) have been guilty of in the last ten years, but I can't think of a single example of similar bad acts by Democrats. This may be because I'm reading the wrong things, but I don't think so, and I'd like to suppose that electoral corruption isn't a hallmark of the Republican party. So, what dirty tricks are Democrats guilty of, and who are the people behind them (again, for the Republicans I can name names)?

Media Balance

2004-08-09T11:27:00.000-07:00

Many many many words have been said about bias in the media on both sides of the aisle, but having just reread this article about political polarization from the Washington Monthly (which even the knee-jerk conservatives should read; it's mostly a list of facts), I'm again struck by my pet peeve media bias: the need for balance.

Don't get me wrong, I'm not arguing that balance is bad in all cases, I just think that in many cases where journalists are called upon to draw conclusions they tend to either back off or draw a conclusion that treats both left and right in a balanced way even when the facts don't support such a conclusion. Three quick examples are the article above, science coverage in general (though particularly on global warming, and for more of which see Chris Mooney's blog, and coverage of supply-side economic theories. The way it usually goes in (natural or social) science coverage is a he said/she said type article, even when the vast majority of scientists thinking about an issue come down strongly on one side or the other. This mentality even extends to policy questions, where most reporting fails to explain what the results of a particular policy would most likely be, rendering it almost useless to ponder the outcome of policy, since most of the public doesn't have the information or background knowledge to accurately estimate. And admittedly sometimes we don't know, but we do have at least some decent idea more often than not, and reporters often know. The trouble is that balance isn't really a primary virtue we should expect of our press; we should ask, first of all, that stories represent a best-effort attempt to report the truth. Sometimes this means being balanced and sometimes it doesn't, and while I'm all for an honest attempt to be unbiased and evenhanded, I have to think that truth beats balance every time.

How to fix it? I think reporters striving to report the truth (and being willing to take the criticism for it) more than they do now would be going a long way, and I hope that the emergence of better lefty media criticism will help (brave reporters at least) do just this. There are some mechanisms I could propose, but the best first step is just to ask for truth over balance.

Update: Just when I think it's safe to speak my mind, Chris Mooney posts something directly on point; apparently the AP is dissecting stem-cell spin in stories, certainly a truth-seeking step in the right direction.

Minority rights and direct democracy

2004-08-04T12:52:00.000-07:00

My esteemed friend Neil has posted about direct democracy versus representative democracy on the issue of minority rights. Read his post, then come back. While I mostly disagree with Neil's result on face, it seems to me that the real problem is that his model of a populace oppressing a minority seems in error; to wit, governments don't make oppressive laws on a whim, but because some constituency is actually calling for them. What I mean by this is that we shouldn't model this situation as one minority strongly in favor with a majority mildly against, but as two minorities, each strongly on their own side (in Neil's situation, gays v. christian conservatives) with a majority leaning one way or another. I'm not sure how the numbers balance out in all situations (haven't done the math), but the if we consider the symmetric case, we see that representatives should vote with the majority or their conscience, just as we end up with in the direct democracy situation.

It should be noted that I am in favor of a representative system, for a lot of reasons (some mathematical), just not because they respect minority rights better for any structural reason.

Picking Causes

2004-08-03T23:38:00.000-07:00

Well, it seems like time to have some nontrivial content here, even if this one's fairly facile...

Environmentalism occasionally crosses my mind, and when it does it usually strikes me how extreme a shame it is that its strongest proponents are motivated by the wrong things, notably natural beauty and endangered species. Now I'm hardly opposed to either, but when policy rubber hits the road it's difficult to argue to politicians that the costs (in terms of money and people) of protecting these things are worth it; just as bad, activists are made to seem lightweight with treehugger images and tales of spotted owls, which is a shame since the important bits of environmentalism are about people.

I believe environmental fights are pivotal. When individuals litter, streets get dirty; when corporations litter, people die. From heavy metals in water supplies to air pollution to bioaccumulation in fish to vicious, antibiotic-resistant bacteria getting free from the giant lagoons of pig feces that surround factory farms, today's environmental issues aren't about trees and birds, but today's environmentalists haven't made that case well enough. It's probably just a feature of the movement: young environmentalists will always get motivation from nature, not cancer, the fundamental texts will always be more like Rachel Carson's Silent Spring than Neal Stephenson's Zodiac, and the money will always come from pictures of cute animals, not sick people. Unfortunately, real policy clout will never come from issues about animals and trees. I'm just hoping that the people who really do these things can start choosing (and sticking to) the right battles soon, and keep it up long enough to turn their image around.

Why?

2004-08-02T13:02:00.000-07:00

With the seemingly-sudden proliferation of blogs written by friends and classmates, it seemed at last to be time to get in the game. I suppose chances are I'm going to end up just another kinda dumb non-personal-thoughts thing, since I'm not enough of a newshound to be filled with link-y goodness, but I thought I'd enjoy having a place to record some of the things I think that might be not too stupid. Nothing at the moment, really, but there'll be plenty soon I have no doubt.

Me-Tooism

2004-08-02T12:47:00.000-07:00

Bandwagon, bandwagon, here I come...