JoaLDG: Negative Reinforcement (or, Sin and Redemption in Mathematics)

In his book Innumeracy John Allen Paulos, the veteran professor and exegete of mathematics and statistics, recounts a story about some pilots and their instructors.

This phenomenon[, regression to the mean,] leads to nonsense when people attribute [the regression] to some particular scientific law, rather than to the natural behaviour of any random quantity. If a beginning pilot makes a very good landing, it's likely that his next one will not be as impressive. Likewise, if his landing is very bumpy, then, by chance alone, his next one will likely be better. Psychologists Amos Tversky and Daniel Kahneman studied one such situation in which, after good landings, pilots were praised, whereas after bumpy landings they were berated. The flight instructors mistakenly attributed the pilots' deterioration to their praise of them, and likewise the pilots' improvement to their criticism; both, however, were simply regressions to the more likely mean performance. Because this dynamic is quite general, Tversky and Kahneman write, "behaviour is most likely to improve after punishment and to deteriorate after reward. Consequently, the human condition is such that ... one is most often rewarded for punishing others, and most often punished for rewarding them." It's not necessarily the human condition, I would hope, but a remediable innumeracy which results in this unfortunate tendency.

He goes on to give two paragraphs' worth of further examples about movie sequels, music albums, baseball players (what is it with Americans and baseball?), and stock markets, but the lesson for would-be pedagogues is clear: don't treat your subject with statistical rigour and suffer the fate of all pseudosciences that came before.

The contrary view alluded to in the first quoted sentence, namely, the ascription of intentionality and significance where there are only the capricious mechanisms of probability, is, I believe, a symptom of a whole another and different ontology of the physical world than the scientist/naturalist's, one which is surely mistaken. And it is one which is far too vast to take on in the screed of a single evening. So we'll consider ourselves admonished on two levels, namely with regard to our evaluation of our methods, and with regard to our concepts of praise and blame, and press on.

(By the way, every living person in the developed world, I kid you not, should read one of Paulos' books. It doesn't really matter which one, they're all more or less the same. Innumeracy is good and A Mathematician Reads the Newspaper is too. Go read!)

Not to put it in too maudlin terms, but I think I believe in positive reinforcement. As a very general principle this is connected to the Nietzschean optimism that (on our weblog's happier days, if I have succeeded) is our spirit here. (I keep saying that's our spirit, anyway.) If one "doubts with well-founded suspicion" that good things are possible, I want the courage to build a world, speaking literally or of the world as a metaphor for my ontology, which those good possibilities populate. As a principle of pedagogy it is maybe a reaction to something, some grousey grouch in my past, or maybe a recognition that the undergrads of today are the colleagues of tomorrow -- put another way, that the aims of a class are largely but not entirely about the students' command of the syllabus material and I am judged not merely by the standard of review for an educator-as-mechanism.

On the face of it, there's something very suspicious about negative reinforcement. I don't insist on being loved or liked -- I'll settle for respected -- and I don't repudiate Burrhus Skinner (entirely). It's just unclear how this negativity is going to get any desired result, particularly when many students are already very anxious about math, or about their academic position. What intermediate steps have failed that we need to take out this big club with its dangerous and indeterminate consequences? I fear that its advocacy comes from exasperation, but my perverse optimism tells me it could still lead to good things.

Because there's exasperation to be had. I read an article, "Teaching Freshmen to Learn Mathematics," whose author, Steve Zucker, (a professor of mathematics), took the following extreme (?) position. "We shouldn't," he argues, "overlook the power of negative reinforcement." He goes on to describe two mathematical errors often committed (in the past -- he tells us that their frequency has since dropped off) by his Calculus II students which he calls the "ultimate sin" and the "penultimate sin."

(They are, for the interested and mathematically inclined, respectively (a) the belief that a series, say the harmonic series, converges if its terms vanish; and (b) the computation of a limit of a sequence whose terms are given by some expression in n, like (1 + 1/n)ⁿ, by selectively letting instances of n go to infinity -- in this case, inside and then outside, concluding that the limit is 1, when, as everyone knows, it is in fact e.)

He says that the demonstration of these sins by his students argues some very dire things about the relationship of the student to the course and even to the instructor. (It's clear at any rate that the students don't understand what they've been taught if they make such errors, but naively we might wonder about the value of introducing eschatological language to describe these mistakes.) He informs his students that commission of the penultimate sin on any submitted work will immediately earn zero credit for the problem, and commission of the ultimate sin will earn negative credit.

I have to admit that I'm a little envious. I'm pretty sure I couldn't get away with that.

Anyway, since we're all here to hear about linear algebra, and not about calculus, which no one understands anyway, I have a couple of candidates for confusions that drive me up the wall. Following precendent, I would like to propose, as an "opening bid," the:

• Penultimate linear algebraic sin -- phrases like "the vector is linearly independent" or "the vector is linearly dependent." I would also like to take on the concept of a "redundant vector," which to my view is simply pedagogical lemonade encouraging a nonexistent intentionality, but them lemons are in the textbook, with a footnote about how "redundant vector" isn't actually a linear algebraic concept but the author has found it "useful" in teaching, if you can believe that, so I'll save that one for another post.


• Ultimate linear algebraic sin -- any sentence of general type, "a basis for the kernel of matrix A (or another space) is the span of such-and-such vectors."

I'm not wedded by iron chains to these as my two least favourite things to read on students' papers, but it's hard to take a shot at things like co-ordinate chauvinism or implicit inner products which are, among other things, too far advanced errors to strenuously indict. (We'll see if I still feel the same way about co-ordinate chauvinism in the next two weeks, when eigenvectors and similarity of matrices are the topics of discussion.) The two cited transgressions show, roughly, that the student is confused about the relationship between vectors and vector spaces: the role of linear combinations in general and their significance to the concepts of independent sets and spanning sets (and bases) in particular.

And besides, these not-silly-mistakes (as Zucker would put it) -- especially the ultimate linear algebraic sin -- show up with depressing regularity. So I think I can summon a roughly analogous frustration to our poor calculus instructors -- though, mind you, I'm just grading these papers, not teaching the class. So how do I feel now about negative reinforcement?

I'm giving it a try. As I said I don't think I could get away with negative credit for problems, and anyway it would be a completely unfounded move for someone who doesn't even have any interaction with the students to tell them why. I mean, I can't even explain to them verbally what's wrong with what they've written, but commission of the ultimate linear algebraic sin is cause for loss of two points from five, no matter what the problem was about, and no appeals, damn it. It's not right for this nonsense to get written and for me to say nothing: that doesn't do anyone at all any favour.

How's it working? It's a little tough to evaluate, as I said, not being the instructor. I don't recall reading an instance of that sin lately. It drives my blood pressure up a notch to see so I'm pretty sure I'd remember if it had been there -- and, hey, I have been privately calling it the ultimate linear algebraic sin for a couple months now. Forgetting that would be like forgetting another fall of man. On the other hand, the students haven't been asked too many times to give a basis for the kernel of some matrix, and when they do, now that I think about it, they've been saying things like "the kernel of A is the span of such-and-such vectors," and not even using the word basis, as though they'd like for me to draw an inference, just answered like they would have in the first weeks of the class.

I...

I think my plan may have had some unintended consequences. Like apostasy.

Negative reinforcement, huh --

At this stage I'd like to remind everyone that it's not my fault, I didn't do anything, it's just regression to the mean. Somehow.

I'm going to abruptly end this post on the pretext that it's already long enough and, umm, further data must be collected to continue the discussion.

Lost Blogging: from the Omo River Valley

Sometimes my notes disappear for a long time. It doesn't bother me much to have them sit unattended or even lost. From the writing point of view, if the note was to have prose value, it just allows for better editting. From the pedagogical point of view, if the note has a pedagogical purpose, it is true that almost no one learns something the first time they see it or write it down. And there is a certain strangeness to uncovering something a year or two past or older, a not unpleasant strangeness if it's not overcome by awkwardness. (Well, Aristotle's been dead a long time, so he can wait patiently while I change my mind about what I said about him.)

Usually the point is to polish them, if they're supposed to become journal entries, to embelish them with context and make out the rhythm of a full entry. It's not too infrequent that my point (there usually is one) is very short and I want to make it in a sentence or two. (I am reminded of the desire of my often-aphoristic dead German mentor to "say in twenty sentences what another would write a whole book on" -- I paraphrase this quote from memory -- good advice for philosophers.) But sometimes I think: These little sentences are just too cryptic. Who will know what they mean? If I had read them yesterday or the day before, would I know what I'm talking about? When I read them tomorrow, will I have an idea about what I supposedly meant? To be fair, do they really mean anything? If am I not understood, and there was something to understand, isn't it really my fault? (My "Gangasrotogati-living" dead German mentor, despite famously upset on this score, probably agreeing -- according to the proposition: man who uses Sanskrit in a passage about how he's not understood must be making a joke; I mean BGE section 27.) So I must draw out a verbal recording of mental context.

Dawn over the Omo River Valley

Anyway, not to tediously furnish yet another example of what I'm talking about in Sun-Drunken's most common bit of irony, but this entry was just supposed to be about a short, expository note to myself I found that I wrote last summer, in July or August, I'm not sure, that I figured I'd post with only a few fingerfehlers ("finger blunders") corrected. Editorial parentheses [...] in the original. (It's a compulsion.)

There's a BBC program they['ve] show[n] on CBC Newsworld called Tribe. It follows a Brit, Bruce Parry, on travels to see and live among various indigeneous tribes of the world. Once he went to live with the Nyangatom of the Omo River Valley, in Ethiopia, near the Sudanese border. The Nyangatom are proud [warlike] people living in ancient-style huts, drinking cows' blood in the daytimes, and wearing traditional clothes and raiments, with a few recent additions: t-shirts, AK-47's, and pierced bullet jewelry. There he was adopted by the village elder and made an honorary member of the Ibex, their corps of young fighting men. During the initiation ceremony they were harangued by their elder, who remarked that today's young men aren't like those who came before, that they laze around all day and can't protect their cattle, and drink too much alcohol. He might as well have added that civilisation is doomed for it -- but the Ibex warriors were quite keyed-up by it, and vowed to shoot and kill anyone who tried to steal their cattle, as the womenfolk sang a song about "Lokloram, the lion" (Bruce Parry's adopted name) and about how their enemies were afraid to cross the river.

Call it: From the

civilisation is doomed! because the youth are unruly

file, thinking of an (apocryphal?) ancient Sumerian (Akkadian? Babylonian?) text said to already have been making that argument. Of all the things I wonder about Sumer, the one I'd want answered most is about what it's like to live in a world that has no history.

(Insert externally-silent mental struggle about how much to amplify that remark in an already-burgeoning entry. I'll just leave a reference to the last sentence of the previous entry so we remember there's a theme being developed. Myth only counts as history at half-weight.)

Bullet-case earring?

Three quick remarks about the quoted text:

• Brackets on "warlike" because this is a word that comes as naturally as it sounds cheesy. It makes me think I've been deeply influenced by Zulus with tanks in Civilisation. I mean, people don't really talk like that, do they?


• Yes, I really wrote "womenfolk." I'm sorry. I swear that would never make it to the second draft, nor would the massive run-on final sentence. It's just a summary note to myself, damn it.


• Check out the similarity to the Wikipedia entry, whose current revision I note uses the word "warlike," with a placeholder for a citation (!), in the first sentence.
  

More Lost Blogging to come. I have a thing somewhere around here on airplane pictures which I promised back in December but actually dates to September. And I have a full Page-a-Day Calendar page of subject titles for Journal of a Lower-Division Grader I scrawled the last time I was marking papers.

Bruce Parry &c at the well

Pictures shamelessly borrowed fairly used from the BBC Tribe website.

Journal of a Lower-Division Grader: Introduction (and if you warned me,...)

"I despise your despising," spoke Zarathustra. "And if you warned me, why did you not warn yourself?""

There's something very dubious about work-related blogging. It seems to get people into trouble (cf. brief remarks here under "the end of credibility," or elsewhere at more length and erudition), for one thing. But more than that, and in its pervasity worse still, it seems all-too-often both unprofessional and morosely self-indulgent. How often do we read only glib snark cooked up from the catalogue of the daily travail? Endow it with vices and malfeasance beyond its station, and speak of it with the dryly clownish condescension of sufferance yielding to exasperation! But sad occasions are only sadder still when they command the service of powerful prose.

How often have I jotted notes on nothing-in-particular only later, a day, two days later, to find that I no longer had any interest in the subject? It is not that I am fickle or capricious, though perhaps I am. It's that the fundamental cost of all art, all media is viewer attention. The literature of forgettable pettiness only worths its price when it seasons itself with bile and hyperbole. It's the thing-of-the-moment that mistakenly universalises itself in a search for absent significance when it in truth has no such power. It's Guildenstern stabbing the Player King.

And it's really bad writing. Maybe not bad prose, maybe often not, but badly misspent. I think we ought to command better from ourselves. Call that a re-statement of our mission at Sun-Drunken.

If you remember the last time, or the time before that, or --, that I went on a tear immediately prior to doing, or while doing, exactly what I'd just railed against, I'm sure you know what comes next. It's not just self-conscious irony, the plainest special pleading, a seeking to convince the reader that really nothing wicked passes here by sending him through loops and whirls until he's too dizzy to figure out whether it's satirical or just crass. It was never the despising that was at fault. Returns are still being earned when Guildenstern furnishes his "art to creating suspense" with a "law of diminishing returns."

Here, however, Zarathustra interrupted the foaming fool and put his hand over the fool's mouth. "Stop at last!" cried Zarathustra; "your speech and your manner have long nauseated me. Why did you live near the swamps so long, until you yourself have become a frog and a toad?... Why have you not gone into the woods? Or to plow the soil? I despise your despising; and if you warned me, why did you not warn yourself?

"Out of love alone shall my despising and my warning bird fly up, not out of the swamp.

"... What was it that first made you grunt? That nobody flattered you sufficiently; you sat down to this filth so as to have reason to grunt much -- to have reason for much revenge....

"But your fool's words injure me, even where you are right. And even if Zarathustra's words were a thousand times right, still you would always do wrong with my words."

Anyway, when the preface puts the body of text into the smallest corner of its shadow -- it could be bad writing, or it could be the preface was the point.

* * * * *

Way-back-when at UBC I took a class in Euclidean geometry. After the midterm a friend told me a sad story about the grading of one of the problems. It had asked for a statement of some theorem or definition or thing like this. As always in Euclidean geometry a good diagram was central to the issue, and she had included a helpful exegetical diagram. Alas, the instructor had not found it so helpful.

"I didn't label it a circle," she explained to me at some length. "That's why he took points off. You tell me, what else could it be?"

Obviously I couldn't say. I'd labelled mine.

"He said, 'Maybe you thought it was an ellipse'! What? What?! When in this class have we talked about ellipses?"

Well, it wasn't the most circle-like circle. They're not the easiest thing to draw.

"When has Instructor-Man even mentioned the word 'ellipse'?!"

Never, of course; if you have neither co-ordinate geometry nor solid Euclidean geometry at your disposal, and this was a strictly plane-geometric class, it's a bother even to say what an ellipse is.

So she went to work on him again, but it didn't help. He was the kind of person who helps earn a reputation for eccentricity for mathematicians. (It's a math pun; click the link to convince yourself it might possibly be funny.)

In truth, although I wished I could back up the professor's take, I really couldn't figure it out. I dislike unlabelled diagrams as much as the next guy, but this ellipse business couldn't be a serious criticism.

I have since recanted my naivete. A term or two grading papers has given me a somewhat more storied perspective. My understandings about what other people might mean when they speak what they say or write what they scribble are no longer Earthbound -- heavy, constrained by the gravity of consequence. Rather they roam between the sky and the space which is beyond, fantastic, undreambound. It's the fog of the Nothing, of the confusion-of-being, of the not-understanding and the not-communicating. It's sadness on a page.

And that's why I couldn't give examples. It would take a callous knowledge-worker not to empathise. Or at least it would if the clever critters didn't try their damn'dest to dress it up. And yet, heavens guard us, maybe now and then I've only rouged it -- I am on a deadline.

Three Short Comments from Princeton

I. Many machines on Ix...*

Today as I went for dinner I saw a cardboard box, sitting by the trash at the bottom of the stairwell. A big Dell box, bigger than the one I found last time.

(Oh?... yes?)

So I took it. I have plans for it. Plans within plans. For storing things.

No laughing at my new box, now. It's a newcomer and doesn't have the history that the others do, but it will. It's strong. It's capable of eating the old box, as you can plainly see. I'm resisting saying that it can bend like a reed in the wind, because that attempt would likely destroy it.

* For many good reasons I translate any Latin that might come up, so why not Geek, which is still more obscure? Whatever you feel about the qualities of the adaptation, there are many wonderful things about David Lynch's Dune, and this snippet of dialogue is one of them.



II. More lock stories

I mentioned that I've not yet locked myself out. In truth when last fall I arrived on the contrary I felt locked in. The first time I put my key in the lock it became stuck; I had to brace myself against the door and hook two fingers in the ring of my key chain to wiggle/yank it out. This scene repeated itself. I began to fear that one day I would open my door and not be able to retrieve my keys. It would close and my housekey would just sit there. What would the lock do for me then?

But as often happens the problem went away by itself, or was helped by a little bit of use.

Now I have a different trouble. The lock is a deadbolt with one side tapered so that when the door falls into the frame the bolt draws back until it locks in place in the slot. I've noticed quite a bit over just the past 3 days -- already in the fall, irregularly, but often recently, right now, even -- the door not recessing the whole way. I've set my feet against the ground and pushed and the damn'd door doesn't fall far enough to let the bolt fall into place.

Just fiddling with the lock right now I've discovered that it has a second deadbolt, which can only be set into place from the inside, if you can make sense of that. (The key does draw it back, though.) It also has a little switch set into the side of the door which apparently toggles the autolock on the first deadbolt (the movement of the door-knob/handle draws that bolt back, and the switch releases or freezes the outside knob). Sometimes I wish I could live in an unlocked world, but my natural caution and my laptop make me think my wishes won't be like fishes.* Last year I left the door unlocked whenever I could, but those NGC buildings have a keycard entry system the OGC lacks.

I figure it -- the lock -- it's setting me up. When I stop compulsively jiggling the keys in my pocket every time I step through the threshold -- one day, somehow, I'll miss them and then it'll be click! like the assassin's blade. Sometimes, you know, I walk in and, carefree, drop my keys on the desk. They're camouflaged there. And then I think: that's just what it wants, and quickly replace them in my pocket. When those keys jingle on the desk, that to me should be like the sound of the nightingale floors of the Tokugawa fortress.

Apparently any life can be a little like an episode of The Outer Limits if you work hard enough at it. I'm thinking of the ones with a twisted set-up and diabolical reversal. Like the one about a (male) POW on an alien world who falls for the female human POW target of cruel alien interrogators and to whom he mentions, to cheer her a little, about the starships massing at the Lagrange point behind the sun that'll turn the war. Predictably (I always tried to figure out the most depressing ending possible consistent with the set-up, and wasn't too often surprised) she turns out to be an alien in human make-up, as it were. The next episode in this story line, by the way, has Wil Wheaton accidentally annihilating the Earth instead of the alien homeworld.


* "If wishes were fishes, we'd all cast nets" -- ancient Caladan proverb.



III. The end of credibility

I'm sure everyone's heard a story, probably many such stories, about someone who made trouble for themselves without quite realising it by posting something on-line. It might have been humourous or harmless, a little off-colour, a confession that shouldn't have been announced-in-principle to the entire English-speaking world, a phrase worded more strongly than it deserved, whatever. (Some of us are especially guilty of that one, multiple times per post, and a recent Globe and Mail column fairly took us to task. I've said it in passing, but just to be clear, the Lord Kelvin Useless Creation Award is firmly ironic in character.)

Some pundits even remark that future political careers are being ruined by such seeming-harmlessness. This on the face feels unduly pessimistic to me. After all, the underlying problem, as it so often is, is about data organisation, and not capacity. Still, perhaps there's something to it.

More worrisome to me at the moment is the casual and accidental intrusion of someone making a serious inquiry and getting their Google returns clogged with my useless prose. It doesn't happen so much, and there's a little thrill in the search engine's compliment. But something I read recently elsewhere (you know who you are) brought me back to the subject. Apparently someone got here looking for the Monster sporadic group, and I'd apologise to them, but I looked myself and I wasn't in the first fourteen pages, thank heavens. On the other hand, someone with a light-hearted interest in Ed Witten discovered me buried only three pages deep (mostly behind other, more well-known math-physics blogs) repeating a rumour that he sometimes plays at the local chess club. (At the time it was to me a rumour, anyway.) Frankly, half the embarassment in this "http referrer" business (when you click a link your browser tells the new site what page was linking to them) is that I feel like I'm snooping on someone else's affairs.

Speaking of which, the good news is that I am no longer "south of zealots and smut-mongers". There are some strange things about that particular query (the titular quotation of this journal). For example, the third result is to a result page of another crawler that turns me up on a different query. My Blogger user profile is right below the afore-mentioned zealots but above an entry from oldpoetry.com, which error I now ameliorate. The smut doesn't make it into the first page, but truncating to just "sun-drunken delight" shifts things around -- now my user profile is below. On truncating yet further the good news is that we have considerable standing. The very bad, bad news is that there's an actual thing -- a thing with a website -- and, well, I didn't have the heart to pursue it much, but I suspect certain kinds of smut are unbeatable. I wouldn't mention it except that this has been an important source of incoming traffic for me lately. Oy.

[Predictably, I note in a brief update a little while after writing this, the presence of the keywords in this entry hasn't helped. Oh, well. Fight the fights you can win, they say.]

On a brighter note, and returning to the data organisation theme, if at the beginning of this year you searched a thing called IceRocket Blog Search (which I've never heard of until now but which site possesses a curiously Google-like layout) on a certain Dune-related theme, you might find your way here. The reason you'd have to do it then is that this search engine organises apparently returns first by date. I note with a hint of schadenfreude that someone else has mentioned this book in a parenthesis and thereby opened their own definitely-not-for-the-dinner-table discussion to public scrutiny. (Let's just say that I shortly determined that it wasn't grammatical ignorance causing all those first-person pronouns to be capitalised.) Fortunately for them, they're getting buried, day by day, by more of the same.

Home: "Behold! human beings living in a underground den"

Nervous prefaces should be expunged. It's elementary. At worst they're an ad misericordiam special plea, at best merely bad prose. But in the medium of the blog I think we will have to get used to them. There is a lot of nonsense out there and sometimes people realise when they're writing it. If you feel exasperated with mine, keep in mind I've already given you my one-page take on Hamlet. There are any number of indulgent existential whiners who couldn't write three coherent sentences on the man who beat them all to it.

This, then, is a nervous preface. This post is going to get a little weird, and I thought it would be best to explain beforehand, in the hopes that by the end the reader will think I'm a nervously clucking hen and the untoward sleeps breezily tonight. That would be ideal.

It's a certain special brand of weird. I've been putting it off. Today I was baking cookies, though, and remembered that once and not so long ago I posted my cookie recipe here. (Actually, I think it's at least half Grandmother's. Hi, Grandma.) So some curious things have shown up now and then. This is another cookie recipe.

So I've got some photos to show you. Here ends the nervous preface. There lie dragons.

* * * * *

Once and not so long ago a man packed his books and music and linens into eleven sturdy boxes and sent them off with a "Godspeed, sturdy boxes" to the other side of the world. They braved the road and the customs agent to arrive, eventually, safely, a little battered, with a little more packing tape than when they left, but whole. The man met them there and unpacked them with a "Thank you, brave boxes" and flattened them and put them under his bed. There they lay for a half-year, waiting for their time of glory.

And it came. They poured from the underworld and, armoured with the steel hide of duct tape, readied to once more take up their charge. And yet, and yet, they were too few: for in the intervening time the man had bought more books and more music and home appliances, and these things no longer fit into the eleven. "I need another box," the man said to his heart. "I have this one here spare, which someone sent to me and I kept safe; now they number twelve. And yet, and yet, they are still too few, and too small besides: my home appliances will not fit in a box a foot and a half on the diagonal."

So warned, he wondered where a youthful, bountiful box might bloom; but no one sold him boxes, not even the ineptly run local storage concern. Time passed and trees flowered -- until one morning something remarkable happened. The man awoke and stumbled from his home to break his fast; and there, on the side of the road beneath an arch, discarded haphazardly, unwanted, in a pile of refuse, lay a great bear of a box, two feet on a side! "This is it, my champion!" spoke the man to his heart. "A box of the proportions we desire. And yet, and yet -- is it possible -- could we -- might one just take it?" And he thought about it still. "Here it lies, on the side of the road in a pile of refuse," he mused. "Soon the garbageman will come and take it away. Look you here! No one wants it. Take it now!" And so ordered by himself, he obeyed, and took the box to his home. Now they numbered thirteen; and when the man returned not so much later from his breakfast the refuse all was gone.

	So these are the Thirteen. Umm, except that there is obviously an even number of them. I guess I had already packed one and it's hiding behind the camera. (Also, this file is called "room_0.jpg". Some people like to start counting from zero, but I'd better just confess. Apparently I started numbering my pictures from the last in the series and couldn't count. Well, at least it's not room_negative_1.) This is the south-east corner of the room. (You can see one of my speakers, and the subwoofer under a pillow -- that was to hide the bright green light at its back, which was clearly visible from where my head lay at night. To regain a little lost cred, that book on the table is called "Automorphic Forms and Representations.") This was an ideal place to put the boxes, with one minor drawback--
	--namely, that if you wake up in the dull, suffused glow of dawn, it looks for all the world like there's a two-metre-tall thug with a Darth Vader-esque head standing at the base of your bed. (Apparently I was so shocked by the recollection that I called this file room_2. Oy.) This parable, by the way, has a moral; it is: "On a long enough timeline, good things happen, just by chance." I seriously was thinking (as opposed to thinking seriously) about this problem for four weeks before I found that discarded "Dell" box. Special thanks to A.N. for ordering a laptop at the end of the year.
	So this the south-west corner. My desk and shelving. It's looking like there's space because I've already started taking books down at this stage. A certain party was encouraging me for some time to take pictures of my living space but I the unruly son was quite belated about it. By this stage it was "If not now, when?" and "It's cleaner than usual, and anyway I can blame any disarray on the fact that I'm moving. That's the ticket." So that answers your question, if your question was, "Why are we getting a tour (of some place he doesn't even live in anymore)?" Click through for a bigger version, my voyeurs -- I mean, concerned parties. Umm... ignore all the Amazon boxes. They send huge boxes for the smallest items, a manifest waste of space, I swear. Moving on, I want to introduce someone:
	Say "hello" to Professor Albert. In tiger form. (Wait... room_5? I give up. Seriously, this time I just changed my mind about the flow of my narrative.) This one is really its own punchline. (In truth, I think he's adorable in addition to hilarious.) You may recall there was recently a major anniversary in the physics world -- one hundred years for the "Annus Mirabilis," the year in which Einstein published a large number of revolutionary papers, including the original Special Relativity paper and the Nobel-prize-winning paper on the photoelectric effect. You may not recall there was recently a major anniversary for the Institute for Advanced Study -- seventy-five years since its inception. You may also not recall that recently there was the fiftieth anniversary of Einstein's death. (Ugh.) These were the same years. I do not recall for which the plush is commemorative.
	Let's zoom out a bit. This picture has nothing of especial interest (no, I do not normally make my bed, this is not in situ, it is staged), it just completes the tour and gives the reader a break before we press on. If you look closely back at my desk, you can see another figure, adjacent to Professor Albert, partially obscured by a bag of tea leaves. Now who could that be?
	It's -- my word -- it's Little Richard Wagner! You can even wind him up, and he plays a music-box version of "Ride of the Valkyries." Now this demands an explanation. Back in March, two-thirds of Party the Third (that's Mom and Bruce, if you're keeping track) were passing through the area and took me to the New York City Opera, where we saw a production of -- Don Giovanni, by Mozart. At the gift kiosk downstairs they had Little Mozart and Little Wagner, too. Since stormy petrel Little Wagner is clearly superior to, umm, stormy petrel Little Mozart, the rest is clear. He comes with a little tag identifying the queer fish that made him: a little shop called the Unemployed Philosopher's Guild. A branch of their merchandise is a little suspect ("indictmints"?) but if you stick to the non-political you can spend a few happy minutes exploring their stock. I'll mention two I especially enjoyed:
	"Nietzsche's Will to Power Bar," his name spelled correctly on most pages. "When your Wille zur macht is a flagging or you're just a little tired of transvaluating all values.... These bars, like other 'energy bars' are packed with protein, vitamins and chocolatey goodness. Whether you're philosophizing with a hammer, or just trying to get through your day, these will help." In case you were wondering, that's an hilarious bit of copy.
	"What Would Nietzsche Do?" I ask myself now and then. I also ask myself if this "100% cotton" shirt is Egyptian or some low-quality knockoff, because this is about one of two pieces of apparel with text other than "No bleach, tumble dry medium" I'd consider wearing. I'd feel very cheeky doing so.
	That brings us to this guy, who you can't even see on my desk in that picture. His name is Sha-naqba-umuru, and everything about him clearly demands an explanation. Where to start? Hum, let me ponder for a line or two. All right, where it came from: Last year Craig (the other third of Party the Third) visited Las Vegas (with Cindy and their friend, Ted) for a weekend. They brought back a little present, this "Excalibear," which is what passes for clever at the hotel they were staying at. (Try to guess what it was called.) Which leaves the name: Sha naqba umuru is ancient Sumerian (or possibly Akkadian) for "He who saw the Deep." (There's no chance the punctuation is correct -- there's an apostrophe in there somewhere-- and I don't have my book handy to check.) It's a name for Gilgamesh, king of Uruk. (Now that I think on it I'm not entirely certain to what "the Deep" refers, although it's evidently a really cool sobriquet.) Anyway, in context of our magical bear here, it refers to his position as a personification, an avatar if you will, of my Platonist mysticism. That wand he carries is not fabric, cardboard, and glue, but a fantastic relic, the Reifying Juju, which instantiates in the physical world things which existed theretofore only as perfect, Platonic abstractions. To put it in more down-to-Earth terms, the Reify is to the Platonist as the Force is to the Jedi.

Now don't I feel silly. That wasn't curious at all. You know, it's good to branch out a little. With so many varied people potentially reading, I worry about what people see. Falling silent -- driving the readers away -- solves it simply.

* * * * *

Update, the next morning. I changed the pictures so that they're now thumbnails (width 240) for slightly larger pics (width 320, except for the two "this is just a picture of my room" shots, which I think were 640) to correct the unreadable vertically-stretched text in the second column. (Well, that's just what bad planning gets you.) As a bonus for your forbearance, here's another picture of someone else's merchandise (which is, umm, maybe not for public use, now that I think of it, just like the other two):

"Here's Looking at Euclid"

That, by the way, is the diagram for the elegant and extremely useful Proposition I.1 of the Elements, "To construct an equilateral triangle on a given line segment AB." Snazzy, but a little on the nose, don't you think?

Redemption: "for that I must descend to the depths"

I think I have made an error.

What kind of fool tells his audience that they should go away and return in two weeks or so because in the meantime things are going to be very, very boring? Zarathustra tells his disciples to leave and denounce him, but he's a mighty philosopher-poet. I'm just a hack job going out with an accidental whimper.

Clearly I need to rectify this blunder. Rectifying blunders is a slippery proposition, mostly because "rectify" is a worse idea than "ameliorate." In chess it is well-known that the most dangerous time, psychologically speaking, is just after you realise you've made the mistake. The impulse is to correct it by lashing out, with brutal violence hatched from desperation and chagrin, but the patient man knows that a minor misstep is not enough to ruin the position and that this is the moment to pull it together, man! and settle in for the long haul, play it stingy, rather than risk everything on a shoddy throw of the dice -- a dice-throw likely to fail, since the blunder has already put the gambler at a disadvantage.

I always say: "I'm a patient man." In as Croat-like an accent as I can muster, "I'mma pay-shyunt mann," I tell them.

Still, I have just the thing -- So: "as close to the gutter as I'm likely to get." Avert the eyes of the little ones, the sun is about to go under.

On a lark I did a Google search on Sun-Drunken's titular quotation. Pause a moment, selah, as I did not, and wonder what might come up. What I found -- if you guessed occultist textbooks and gay erotica, you were bang on. Apparently everyone else had the sense to keep their prose blue or red but not both at once.

The Google search summary left a tantalising dangling simile: "...set his locks on fire; his skin was sun drunken like a..." -- like a what, now? What's the end of that sentence? Ancient Bacchanallian reveller? Avatar of Eros? I have it -- icon of Icarus, apt and alliterative. But no: then it would not be "a" but "an." Instead they had a Mesopotamian theme going on:

"Enkidu!" My soul mate.... The light, now a pleasant, soft crimson, set his locks on fire; his skin was sun drunken like a peach.

Oh. So, anyway, that's "sun-drunken." What about "quivering" and "delight"? Well, naturally someone was saying something with "quivering" voice, dicit Google, and if you want to know what went with "delight," you can look it up yourself. I didn't bother. I couldn't quote it to anyone, anyway, for obvious reasons.

So that's where I am now: somewhere south of zealots and smut-mongers. Huzzah.

Back to high-minded parables next time, lads. That's how we're going to climb this valley.