Tall, Dark, and Mysterious

10/24/2005

Ode to general knowledge

File under: I Made It Out Of Clay, No More Pencils, No More Books. Posted by Moebius Stripper at 9:55 pm.

I’ve stated before that I don’t believe that college is for everyone. For example, college is not for Stacy Perk, who just wants to write for Glamour magazine, but her dumbass school is making her learn stuff, and she doesn’t care enough about stuff to actually go to class and do her homework and shit, so her GPA is suffering and so she might get kicked out of j-school, OH THE INJUSTICE OF IT ALL. (Where did I find this again?) There’s cheap dig about Glamour magazine (Americans spell ‘glamour’ with a U? Who knew?) just asking to be made, but I can’t be bothered to make it. As for the rest of the piece - it’s been a long day, and fisking is a delicate art as it is, and fisking something that so spectacularly transcends parody? Forget it.

So I’m going to talk about how a broad and general technical background has served me in the place where I most flagrantly avail myself of the right hemisphere of my brain: the pottery studio.

For instance, I minored in physics for a spell - more than long enough that I can answer the question that every beginner potter asks: “why is everything I make turning into a bowl?” That’s Newton’s first law in action: if you pull the clay directly upward, it’ll bowl out, because as soon as you lose contact with your form, you’re releasing the centripetal force that keeps your clay close to the centre of the wheel. Compensate by pushing inward, toward the centre of the wheel, if you want to throw forms that don’t widen at the top.

…A solid background in elementary geometry was enough to enable to me to help a fellow potter who was throwing a drum. On top of the thrown drum body she planned to stretch a circle of drum skin, which she’d tie on by looping a string through “twelve or fourteen” holes spaced equally on the perimeter. Twelve, I explained, would be better than fourteen, and we could space them equally using nothing but pencil and a straightedge. And I understood the reflection properties of conics deeply enough to explain why it was suggested that drum bodies be paraboloids.

…My studies of chemistry ended when I graduated high school - something that I didn’t start regretting until I started working regularly with clay. But I stuck around long enough to learn the difference between temperature and quantity of heat - a difference that is paramount to everyone who works with kilns. Potters talk about firing at various cones rather than at various temperatures - whether your kiln temperature rises at 50 degrees per hour or 150 degrees per hour makes a huge difference in how your glazes will come out. I stuck around long enough to understand that the evaporation of the water molecules in wet clay - which happens when clay is left in the air to dry - is a physical change, whereas the driving off chemically bonded water from clay molecules - which happens in the bisque firing - is a chemical change. This distinction explains why clay will disintigrate if you dip it in glaze - a suspension of insoluble particles in water - before it’s been fired, but not after; it also explains why unfired clay can be recycled, but bisqueware can’t. I don’t know enough chemistry, however, to make glaze-mixing anything other than random, which is why I’m positively salivating over this book. (I do know enough to remember that copper turns green when it’s been exposed to oxygen - witness the roofs of our Parliament buildings, among countless others - which is why I’m not surprised that copper oxide in glazes only gives brilliant reds in reduction firings, such as raku, in which the interior of the kiln is starved of oxygen.)

…And damned if I have the physics/kinesiology background to explain this one adequately, but every time I teach a beginners’ workshop, I recall a certain experiment that I found in one of the children’s science magazines I used to read when I was a kid. Try this one at home: have a partner - preferably a strong one - extend his or her arms, with elbows locked, and fists pressed together as tightly as possible. You won’t have much trouble knocking your partner’s fists apart, regardless of how strong they are or how weak you are. Now have your partner try this again, but with his or her elbows bent and fists pressed together close to the body. That’s a much more stable position, and it’s how I motivate the throwing posture: you use your entire upper body - not just your hands - when you’re on the wheel. You tuck your elbows into your hips, you bring your chair right up to the wheel, and you lean downward into the clay; otherwise you’re no match for it when you try to centre it. Take it from a certain beginner I taught once: he was six inches taller and nearly a hundred pounds heavier than me; he had biceps the size of my thighs; and when he sat back at the wheel with arms extended, he was no match for a 500g lump of clay.

That’s how my “useless general knowledge” has come up in the pottery studio alone. I owe a huge debt not only to the artists, but to the mathematicians and scientists who have laid the groundwork for my craft. I suppose I don’t really need to know why I need to lean inward why I throw; why I can’t seem to control a pound of clay unless I tuck my elbows into my hips; why we can’t get bright red glazes with our electric kilns…but my time in the studio is richer because I do.

Similarly, Ms. Perk technically doesn’t need to know damn near anything outside how to write a sentence if she wants to write. But she sure won’t have enough perspective to write anything worth reading. Not even in Glamour magazine.

9/6/2005

Get out of the classroom and start learning

Ontario Premier Dalton McGuinty is often said to be the Canadian politician who broke the greatest number of campaign promises in the shortest amount of time. No joke: his throne speech was pretty much, “Yeah, so all that stuff I said I’d do? I didn’t mean that.” So I’ll believe his latest promise when I see it, but in the meantime, I can’t find fault with his plan to give high school students the option of continuing their education in co-op programs, trace apprenticeships, and on-the-job training rather than in a traditional classroom setting. After all, I said something similar myself.

[McGuinty] said it’s time to explore “different avenues for success,” adding that for some students, studying Shakespeare can amount to “cruel and unusual punishment.”

“But on the other hand, they could take apart a car engine and put it back together like nobody else could.”

Agreed. I would also add that teaching Shakespeare (or factoring quadratics, or world history, or what not) to some students can amount to “cruel and unusual punishment”. I’m well aware that many of the students in my service classes I’ve taught (excluding statistics, which I think everyone in a university should study at some level) will never use the subject in any capacity whatsoever once they’re out of my class - particularly since a good many of them didn’t even learn the prerequisite material well enough to be getting anything out of my class at all. Oftentimes, I know that the variety of answers I give to the question of why students have to learn this stuff, anyway fall flat.

I support the idea of a core curriclum (which includes math, and Shakespeare, and history) in the lower grades, but it’s hypocritical to be continuing to impose one on students who will soon be trusted to make all of their educational choices.

8/21/2005

You won’t find yourself in university if you got lost somewhere else

File under: No More Pencils, No More Books, I Read The News Today, Oh Boy. Posted by Moebius Stripper at 3:21 pm.

This article from the Georgia Straight does a decent job of quantifying and probing some observations I made in some earlier posts I wrote about the contradictory messages students receive on the relationship between university and employment. University, it seems, is neither a path to a career nor a place to develop intellectually - rather, it’s a place to wander about aimlessly with little guidance on either front:

  • About half of postsecondary students drop out or change programs by the end of their first year
  • Up to four out of five students don’t know what they want to do with their education when they start it
  • Just 75 percent of students completed the college or institute credential they set out to earn
  • Just 44 percent of former students reported that their job is “very related” to the training they took (Aside - I’m surprised it’s that high, actually.)

Unfortunately, the writer then muddies the waters by lamenting the rising cost of tuition. Which is a barrier to higher education for many, to be sure, but the rest of the article makes a pretty compelling case for just how overly accessible university educations are to a large contingent of people who have no clue what to do with them. I also disagree with a statement made by Phillip Jarvis, developer of career-exploration tests, who remarks, “Education changes slower than anything else in the country, and career is changing at an accelerated rate.” Having seen the changes undergone by high school and university mathematics curricula in the past decade, I’m inclined to disagree that education is stagnant. I’ll concede, however, that high school and university education are diverging from the practical, career-related goals they’re purported to fill.

Nevertheless, the main point of the article is a good one: that career counselling and skills training in the university are vitally important, and that both are between bad and nonexistent.

So, can someone remind me a) why it’s taken for granted that everyone who can afford it (and many who can’t) should go to university, b) why students are expected to go straight from high school to university, c) why university is the canonical setting for self-discovery among middle-class children of professionals, d) why, given the facts, many employers will overlook applicants with “only” two-year diplomas or hands-on training in a trade, and e) why government organizations and activists concerned with education accessibility focus their energies almost exclusively on the Rising Cost of a University EducationTM, and not on alternatives to same?

5/15/2005

Everything I ever needed to know about grad school, I learned the hard way

File under: Righteous Indignation, No More Pencils, No More Books. Posted by Moebius Stripper at 2:30 pm.

Over at Toilet Paper With Page Numbers, a new-to-me blog that’s going straight into my bookmarks, some advice on picking your poison - that is, selecting an advisor for grad school. TPWPN’s taxonomy of advisors (Micromanager, Ambitious Geek, Absentminded Professor) is geared at science students, but anyone considering studying math at the graduate level should read it, too. Now. Seriously, git; TD&M will still be here when you’re done. If it were up to me, which it isn’t, that post would be included in every science grad student orientation booklet. I don’t remember what was in my orientation booklet way back when, but it wasn’t as useful as, say, this:

The Creative Genius: An older researcher who, at one point in the past, struck a home-run or two and is now flush with cash. Usually has more than one sub-group, and misuses time switching his or her attention back and forth between them as fancy strikes. Usually gives students a lot of room to pick their own projects, and has the money to let you develop your ideas. That’s great if you, yourself are creative, but a nightmare of a 7-year Master’s degree if you are not. (For real. I know of at least one 10 year Master’s). Be honest with yourself, and if you are just not that creative, go for the Micromanager.

Advantages: Money, money, money, and room to run free.

Disadvantages: Has a lot of ideas to start you out with in your first year. No one in the history of the lab has ever gotten any of them to work in the advisor’s entire 20 year career, so find a new idea quick, or prepare for Master’s hell.

Ah, that brings me back. Which reminds me, what is a certain student of my former advisor’s doing these days? Last we spoke, he was wrapping up his seventh year as a grad student and celebrating his 34th birthday, ostensibly making some progress on his thesis. Lifelong Student’s (15 years in postsecondary education and counting) graduate career had seen him switch departments twice, make enemies out of more or less everyone in all three of above, postpone his quals until Year 6, and finally get our mutual advisor (hereafter “Eccentric Genius”) to just solve his research problem for him so that LS’s Ph.D. thesis was reduced to a paraphrasing of someone else’s work. If Lifelong Student actually did manage to defend, then that would make him EG’s second graduate. In fourteen years. I lost track of EG’s refugees sometime into my second year: in my three year stint in grad school, a good half dozen students had signed up, or seriously considered signing up, to work under EG and then came to their senses before I did. The other student of EG’s who obtained her Ph.D., did so just before I arrived; I heard through the grapevine (LS, in particular), that she hadn’t understood any of the first sixty pages of a paper she’d cowritten with EG, and that she had understood only approximately half of the last ten. After finishing her seven-year graduate school career, she took an unrelated job in industry.

But that’s beside the point I was planning to make, which is this: if you’re a Master’s student, it’s nigh irrelevant whether or not your supervisor is a leading expert in their field. In fact, I’d advise against working with leading experts, as I’d wager that they’re probably less likely than non-leading-experts to be able to communicate effectively with amateurs. Master’s students do not need leading experts. Master’s students need supervisors who are solidly grounded in their subject, yes, but nearly everyone with a Ph.D. in the appropriate discipline can be counted on for that. What Master’s students really need, and what are in considerably shorter supply, are advisors who can advise. Master’s students, particularly ones who’ve never done any thesis-like research before, need advisors who can identify, to the uninitiated, the steps of the research process and guide their students through them.

I wish someone had told me that when I was assigned to Eccentric Genius, a world-renowned researcher in Impenetrable Geometry; knowing that would have saved me more than two years of grief. Actually, I didn’t even need to be told that I didn’t need to work with a world-renowned expert; I would have settled for not being told, repeatedly, from professors and peers alike, that I was so lucky to be working with EG, that so many other students would kill to be in my position, that I would be insane to even consider working under anyone else, yadda. When other schools saw that I’d worked under EG, I was told repeatedly, the academic world would be my oyster, and this was truly the opportunity of a lifetime.

People kept telling me this, and I believed it. I believed it when, after our very first meeting during which EG told me to study up on a certain invariant, I read a paper and an appendix on the subject and tried, to no avail, to compute some examples myself. During our next meeting, I reported on my lack of progress, and asked EG if he could show me an example or two. For the next - no lie - FOUR HOURS, EG paced back and forth in front of the blackboard trying, and failing, to work through a handful of examples. “I haven’t done this in years,” he explained, “usually I use computations other people have done. But you can probably figure out from these papers…” Later that week, I pored through handful of papers he’d given me. Each used a different formula to compute the invariant; none of the formulas worked for the examples in the other papers.

I believed it the next week, when, in passing, one of EG’s colleagues at the grad school told me that he was impressed that I was reading those papers, which were high-level research papers, didn’t I know, certainly not the sort of thing that most graduate students get weaned on. I pointed out that there was nothing impressive about being assigned high-level papers to read. If I were able to understand them, that would be impressive. Still, though, I blamed myself for not living up to what I foolishly thought were reasonable expectations.

I believed it when I finished the summer research term with nothing to show for my work. I was lucky, I knew, to be working with Eccentric Genius. The reason I wasn’t making any progress was because I wasn’t smart enough. I just needed to work harder.

I started to grow doubtful a few months later, when I noticed that EG’s solution to my complete lack of progress and utter inability to make heads or tails of any of the papers he gave me, was to give me more papers to read. After a year I had some thirty high-level research papers in my office, and I’d started working with Lifelong Student on one of them. We were able to make some sense of it, but neither of us could see how on earth it applied to our assigned research topics. Still - I was lucky to be working with such an expert, and I knew I should be grateful.

I was frustrated and upset, but still grateful in some perverted way, when my questions about how the subject matter was motivated were brushed off. “That doesn’t matter,” he said, “just use the axioms.” It was true that those axioms had been developed in response to some other research problems, rather than being handed down by God Himself to his prophets in Impenetrable Geometry, but the fact of the matter was that I had a thesis in Impenetrable Geometry to write, and that it behooved me not to worry about what all of this stuff meant. There just wasn’t any time for that kind of thing. Meanwhile, had I managed to compute those invariants yet? I explained - again - that each of the research papers computed the invariants with a different formula that seemed to come out of nowhere, and perhaps I could make some sense of the formulas if I had some context, or something. None was provided; just trust the formulas, I was told, and don’t worry about where they come from.

It was at this point that I began to see clearly the roots of my frustration: I had decided to study math specifically because I thought I would never be expected to trust in tradition, to take any theory for granted. But I also knew that if I was going to accomplish anything under EG, it would have to be at his level, so far removed from the more elementary material that I couldn’t possibly learn all of the background in the time I had and that I would consequently have to start by accepting some results that I had neither the background nor the intuition to comprehend deeply. I had been working - or, more accurately, “working” - under EG for nearly two years at this point, and had gotten nowhere with him.

He realized it too, and decided to try something different. He started meeting with me and Lifelong Student together, and assigned us to dig through yet another collection of papers to see if there was anything useful there. I am not omitting details here: he handed us three hundred pages of mathematics with the explicit instructions, and I quote, “See if there’s anything useful here.” Anyone who’s ever taken a serious math course knows how absurd this is: getting through even a twenty-page pager will often take an entire weekend,

And I, beaten into submission and resigned to never being able to earn a Master’s degree, set to it with LS. We pored over the three hundred pages of mathematics, meeting periodically with EG. I couldn’t for the life of me tell what on earth anything in these three hundred pages of mathematics had to do with my research problem (which I still didn’t really understand, but whatever), but I plodded through (a subset of) them anyway. After all, I knew why it was that I wasn’t understanding anything: it was because I was stupid. And how could I squander the opportunity to work with a leading expert in Impenetrable Geometry?

A few months into this, LS commented in passing, “You know, I can sort of see what these three hundred pages of mathematics have to do with my research problem - however, from what Eccentric Genius told me, I don’t see what they have to do with yours.”

I suddenly felt ill. The next day, I composed an email to EG, asking, not in so many words, that question: how was the research problem I didn’t understand related to these three hundred pages of mathematics that I also didn’t understand? EG wrote back, calmly, “That’s a good question” (!!!) and then explained that it seemed I’d “lost interest” in my original research problem, so he’d taken it upon himself to give me another one, one related to what LS was working on.

He’d never bothered to tell me this.

This was two weeks before I was to take off for my summer job, which I spent variously distracted and in despair. I knew that I would not get a Master’s degree under Eccentric Genius. Classmates of mine who’d struggled through graduate level classes and had routinely solicited help from me, were getting their diplomas in two years. I didn’t know if I’d be done in three.

The next fall, fortunately, luck was on my side. Two things happened. One, I attended a conference of six talks, five of which I didn’t understand even slightly, and the sixth of which had me excited about math all over again; two, my grad school had just hired a young professor whose area of expertise was related to the topic of the sixth talk. I started working with him, first unofficially, then officially. It took me a few months to work up the courage to abandon EG, but finally I said to myself, out loud, you will never graduate with him. If you want to avoid hurting his feelings, keep working with him. If you want to graduate, jump ship, NOW.

Under my new supervisor, I saw for the first time what the grad student/advisor relationship could be. My new advisor gave me bite-sized pieces of work to do. Each week I’d read over a small section, work on some problems, and come up with questions. Later on, I’d work on more involved questions, and get stuck; during my meetings with him, he’d give me just the push I needed to get unstuck. I’d give him drafts every few weeks, and he’d make copious notes explaining what I needed to correct or clarify. I submited my thesis six months after I officially started working under him.

A year after I snagged the Master’s, I don’t blame my former advisor. Not every professor can be all things to all people; EG was an expert, suited to working with other experts, and perhaps some postdocs. A handful of Ph.D. students might have thrived under him, but I’m skeptical: when I left the school, his most promising Ph.D. student was frustrated by his lack of progress and was thinking of leaving. (EG’s response was to tell this guy to “think it over” at a conference in Europe that he could attend that summer, at EG’s expense.) I do blame the school, though, for assigning me to work with him, even though I’d never expressed an interest in his particular flavour of Impenetrable Geometry. I wish I’d been given an explicit idea of my responsibiltiies to my advisor, and his to me, as a graduate student doing research , so that I wouldn’t, in the absence of any clear guidelines or expectations, conclude that the reason for my lack of progress was because I was too stupid to do graduate level mathematics. I wish I’d been given explicit deadlines and tractable goals against which I could measure my progress. Instead, I was given one goal and told, “Once you can do this, you’ll have a good thesis.” And I couldn’t meet that goal.

I wish I’d been told that my job as a Master’s student was to build a solid background in my chosen field - not to build a reputation in it. I wish I’d been told that I did not need a big-name mathematician to help build a solid background in a respectable field - and that many a big-name mathematician wouldn’t help me get any closer to that goal.

In retrospect, all of this seems so obvious, but it wasn’t to me at the time. When I was in grad school, each failure of mine, contrasted with each success of a student working under a different advisor, eroded further my ability to look clearly at my situation. It blinded me even to the simple possibility that I could ask my peers about how they did their research; when I did find out some details, I wondered what I would do if I quit working under EG. By the end of my second year I was virtually paralyzed with self-loathing, at least as far as my work was concerned. I couldn’t even contemplate an advisor switch; I wasn’t worthy. I couldn’t see past my own inadequacies in assessing the sorry state of my research. It took me two years in grad school before I realized that I could, and should, demand better than what I was getting. It took year away from grad school before I was able to put everything in focus, before I could articulate a clear answer to “why did you leave before you got a Ph.D.?” that didn’t sound to me like an excuse.

Still, though, I can’t help but think that I could have learned at least some of this before. Would have made for a more helpful orientation than the “let’s meet the faculty and then have some cookies” one I attended, that’s for sure.

4/28/2005

Unqualified

In spite of…well, most of what I post here, I am confident that I have done a respectable job of working with my raw material (fundamentally uninteresting and inapplicable mathematics, students who should be in grade seven instead of university) this semester and last. When I emerged from a week-long isolation grading exams, I was able to step back and realize that a healthy majority of the papers I was grading belonged to students who had known nothing about the subject three months earlier, but who now had a working knowledge of it. Because of me. And the comments I got from students, for the most part, reflected that as well, not that I am above distributing course evaluations the day after a test, when my laziest and most obnoxious pupils can be counted on not to attend class.

My negative comments, unsurprisingly, came mostly from my precalculus students. Apparently, I am “too hard” and “too abstract”; I don’t “make the material interesting enough”, nor do I “relate it to real life.” (Of course, my attempts to make the material interesting and relate it to real life (see “word problems”, September 2004-present) meet with just as much hostility (see “too hard”, above).) Guilty, alas, on all charges; but I don’t see what I could have done differently while still teaching the material I was hired to teach. In any event, imagine my glee upon discovering, last week, that my successor is apparently a newly-minted Ph.D. whose area of expertise is - wait for it - category theory. Yes, the students who barely squeaked out of Precalculus 1 because they thought that equations were boring, abstract gibberish, have spent this past term learning Precalculus 2 under the tutelege of an individual who saw fit to devote his entire life to actual boring, abstract gibberish. *

Our resident category theorist (who I’ve previously referred to in this space as “Poor Sap”, a moniker that is actually more applicable now than ever before, for reasons I’ll get into as soon as I close these parentheses) will taking leave of Island U this month, after one brief term of employment. Reason: as it turns out, his category-theoretic ways were incompatible with the pedagogical needs of mathematical illiterates. Who’da thunk it? Perhaps both he and Island U would be happier if he were to find employment elsewhere, and we wish him the best of luck in his job search. Not that we’ll be providing glowing references.

Meanwhile, I also handed in my textbooks and keys ** this week. My time at Island U has also come to an end; but unlike Poor Sap, who didn’t make it through the mandatory probationary period that precedes an offer of permanent employment, I’d actually originally been hired for a single term, and managed on the basis of good work to get my contract extended for a second one. But that won’t turn into a permanent offer, because, well, I don’t have a Ph.D. in, for instance, category theory. Really - you can’t make this stuff up. Department Head and I parted on good terms: as far as he’s concerned, he told me, I’ve done Island U a huge favour this past year and he’d love it if I could stay on, but his hands are tied. He wishes me the best of luck in my job search, and I should know that he’ll be happy to provide a good reference whenever I ask for one.

And I know he’s sincere, and I feel badly for him, because now he has to go through the hiring process again. But feeling bad doesn’t get me a paycheque next month. Still, I reckon there aren’t droves of people out there who a) have Ph.D.’s, b) have the skills and the temperament to teach mathematical illiterates, and c) are willing to move to Island Town; so I wish Department Head the best of luck.

But I think that the most ironic thing to come out of all of this is that there’s actually a real-life use for a degree in category theory.

* Yes, I have studied algebraic topology and algebraic geometry, both of which make copious use of category theory, so I realize that I owe a debt to this bizarre field. I maintain, however, that category theory talis qualis is just so much abstraction piled upon abstraction, and I have no interest in entertaining arguments to the contrary in this space. That said, some of my best friends are category theorists.

** Oh, crap, forgot about the keys.

4/11/2005

Ten inches

File under: 1000 Words, I Made It Out Of Clay, No More Pencils, No More Books, Hubris. Posted by Moebius Stripper at 8:44 pm.

My graduate school had a pottery studio on campus. I joined the pottery club during the first year of my Master’s, but this was a full year before I’d completely lost my motivation to do schoolwork, so I spent little time in the studio.

During my second year, the only course I was taking some ill-conceived algebraic geometry class whose audience consisted of eight graduate students taking the course for credit, and eight professors and postdocs. Two months into the class, the professors and postdocs had taken leave. “No point sticking around when I don’t understand anything,” one of them told me in confidence, and I agreed. Unlike the profs and postdocs, however, I needed the credit, so I compromised by attending the class and not stressing over it. The course was cotaught by two experts, one of whom was clearly more of an expert than the other. One day, after class, as Alpha wrapped up the lesson, Beta turned to me and whispered, I am SO lost in this class.

I took this as permission to ignore all homework assigned by Alpha. A few months later, I gave up on Beta’s assignments as well. Me and five of my classmates.

That year, I was productive in other ways.



When I moved to the Island, one of the first things I did was seek out a pottery studio. I also wanted to take lessons; I felt I’d progressed as far as I could on my own. I soon discovered, to my dismay, that although I now lived in a region known for its potters, none in my city were available to offer lessons. There were two types of lessons, it seemed: ones for student artists studying to be professionals; and one for children and adults who just wanted to poke around with clay.

“We don’t usually offer intermediate-level lessons,” said the artist who apparently was the one to talk to about that sort of thing. “Not much demand for it.” He glanced over at my station, which was surrounded by small misshapen bowls, which were all I’d been able to make this first day working on a new wheel with unfamiliar clay. I can only imagine what he must have been thinking; probably something close to what I think when my C students tell me that they typically get A’s in math. “In order to be eligible for my intermediate-level class,” he said, “You have to be able to throw five ten-inch cylinders, one after another. Can you do that?”

“With certain types of clay,” I replied. “Ones with more tooth than this stuff,” I added, hoping he’d be impressed by my use of the jargon.

He looked skeptical. “There’s still room in my beginner class,” he told me.

I took this all rather personally; I’d taught beginner-level classes, after all. In any case, I knew what one did in such classes, and that wasn’t what I needed to learn. So I set out, during the ten hours a month I could get into the studio, to master the ten-inch cylinder.





They aren’t cylinders, I know. but they were originally. And before they were fired, they were ten inches.

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