Breakthrough

I had an engineering breakthrough in my non-orientable manifold lab this past weekend and am pleased to announce a new and improved Klein Bottle construction technique. (That's quite alright, you can thank me later.) A key modification to the previous double-torus method virtually eliminates the need to reshape toruses and, consequently, to curse, and yields a Klein Bottle representation that permits hole-cutting tools to reach pretty much anywhere. (Ironically, in another breakthrough, I've overcome the need to cover the entire surface of my Klein Bottles with holes.)

The revised first step is to throw one classic torus and one torus with a collar. The diameter of the collar should be the same size as the diameter of the cross section of the first torus. Thank your subconscious for having made the hole of the first torus a little larger than the neck of the second torus, and promise you'll sing its praises for suggesting you use the first torus as a chuck to trim the second torus so that you don't squash the latter's neck.


Because you understand the importance of safety in the ceramics studio, do not assemble the Klein Bottle in your kitchen with a cat on your shoulders.

Wired up and ready to go

When I called the tech guy at L&L and told him what happened that fateful night, he said "that sure sucks" and sent us a free Brick Repair Kit. It took us a few tries, but we finally succeeded in patching the kiln floor. For all of you trying this at home, here are two helpful hints: (1) don't confuse "cement" with "grout," and (2) don't believe the instructions: wait way more than 24 hours for the cement to cure, and help it along with a heat gun.

Being married to an engineer who will spend upwards of two hours lovingly designing, cutting, smoothing, assembling, and mounting an elegant, weather-proof brass bracket outside the kitchen window to hold a cheapo $2 thermometer--the sort of engineer who defines "vacation" as visiting friends and relatives and repairing their broken doors and bathroom fixtures--has its advantages when it comes to making busted kiln floors look as good as new.

With the helpful upper-body strength of a few neighbors, we finally set the kiln walls atop the repaired floor last weekend. Our electrician came this morning to finish the wiring. He started two weeks ago, but was leery of mounting an outlet until we had completely assembled the kiln. His leericism* was well founded. In order to maximize the distance between the kiln (which will get mighty hot) and our combustible porch walls (protected by a free-standing non-combustible cement-board heat shield built by the aforementioned talented engineer), we ended up positioning the kiln too far from the wall for the cable to reach an outlet there. So as of this morning, the kiln plugs into the porch floor.

This weekend we'll assemble the vent system, and then it's just a matter of finding 16-19 hours when I can be constantly present for the initial test firing. For that, I will be vigilantly armed with my spiffy new infrared thermometer (a gift from my beloved engineer), so I can see how hot (or cool) various parts of the combustible porch get when the kiln is running.

*Not a real word, but it should be.

Spring has sprung

Spring (\ˈspriŋ\), noun: an annual period that, in the Piedmont of North Carolina, is characterized by an abundance of flowers, lasts approximately ten days, and inaugurates a month-long span known as allergy season.

Salvation is created

This spring has been a little insane. I have two part-time jobs that constitute official Work, plus a teeny tiny pottery teaching gig that constitutes official Recreation. My organ job is the Work that nourishes and sustains me. Alas, it's getting short shrift at the moment, due both to the demands of my other part-time job and to my aging brain's inability to focus on a bazillion different things at once, the way (I like to think) it used to.

Adding to the stress: someone's brilliant idea, several centuries ago, to precede a big holiday that demands special, festive music--like Easter--with a season that demands extra church services every week, cutting into choir practice time--like Lent. Yes, yes, there's a certain logic to spiritually preparing for the Resurrection, but for the professional church music director, these six weeks are laced with panic.

Thankfully, there come occasional nights like tonight, when, prepared to crumple into a desperate heap, I suddenly learn to breathe again.

Imagine: although Palm Sunday, Holy Week, and Easter loom, only half of the small choir is at rehearsal this evening; the other half is sick, or visiting far-away family, or having assorted joints surgically replaced. I resign myself to the low numbers and plan to make the best of it, when the cavalry unexpectedly arrives: two basses, an alto, and a soprano appear in the doorway, their previous scheduling conflicts resolved, and we're up to a good dozen singers.

I check the upcoming repertoire's vital signs: this Sunday's anthem seems to be in pretty good shape, as do the pieces for Palm Sunday and Good Friday; and the Hallelujah Chorus for Easter Sunday is for all practical purposes memorized. We're going to make it through the home stretch.

But then a disappointed alto asks, "the Hallelujah Chorus? That's all we're singing for Easter?" Usually we sing two pieces, but between my aging brain and the reduced rehearsal time, I've been grateful just to stay afloat lately. "Yes," I say with manufactured confidence, "that's all."

As I say it, I hear a flutter behind me. An unrehearsed anthem, still tucked in its folder on the piano, is calling to me. "I am one of the most gorgeous, luscious, goosebump-inducing sacred compositions ever written," it says, "and I am seasonally appropriate. Rehearse me now."

"Stop it," I reply telepathically, "you're a six-part anthem, and we barely have enough folks for the four-part stuff these days."

But the anthem doesn't listen: "Rehearse me," it says. "You know you want to."

And so I sigh skeptically and distribute it to the singers, who pick up on my tentativeness. They take one look and become skeptical too. Everyone vaguely recognizes the title page, but only two people claim to remember that we sang the piece three years ago.

They shake their heads, but we try it out anyway--and the metaphorical gray clouds hovering in the choir loft magically dissipate. In the beginning, sound rumbles out of the primordial depths--pianissimo, rich, resonant. And then there is light, so radiant and exquisite that it makes you want to cry. Salvation is created in the midst of the earth. Alleluia. The music enacts the text. Everyone is stunned by their sonorousness.

"Told you," says the anthem, who has just moved from an indeterminate, distant, if-we-can-manage-to-learn-this-in-time Sunday to top Easter billing.

Suth'n humor

One of my all-time favorite jokes is bilingual, involving English and French.

"Why do the French like to eat just one egg for breakfast?"

Give up?

--Because "one egg" is "un oeuf" (enough).

Driving E and D home from school this afternoon, I was treated to my very first bilingual joke involving English and Suth'n. Interestingly, like the English/French joke, the English/Suth'n joke also involves numbers and food. D read out loud from the student newpaper:

"Why is it dangerous to do math in the jungle?"

Ready?

--Because when you add four plus four, you get eight.
The kids said, "I don't get it." D had to read the punchline aloud a few more times before she and E burst out laughing. To their credit, they understand that around here, you're more likely to get et or eaten than to get ate, but as with un oeuf/enough, we allow precise pronunciations to slide for the pleasure of the bilingual riddle.

What I like best about the joke, in addition to what it presumes about readers' fluency in American regional dialects, is its easy-going insertion of Southerners into far-off exotic jungles in order to get them et. Surely sharks, alligators, and a myriad of urban predators resent arithmetic as much as their subtropical kin.

Math on the mighty Aeolian

Today I had a two-hour lesson with David A., organist extraordinaire, on the Aeolian organ in Duke Chapel. The electro-pneumatic organ was built in 1932, the last major instrument made by Aeolian before the company merged with Skinner. Duke refurbished the organ last year. With approximately 6,600 pipes, 120 stops, and 30 couplers, with four manuals plus pedals and three expression boxes, and with a digital sequencer that allows pre-programming hundreds of settings, the sleek Aeolian is capable of a range of sounds not possible on the Flentrop at the other end of the Chapel. Thus, as wonderful as the Flentrop is, and as befuddling as I find electro-pneumatic action, the Aeolian is my instrument of choice for Franck's Grande Piece Symphonique. Hence, multiple lessons with David to figure out how to register the piece.

I've been giving myself a hard time, wondering why I'm so incompetent at choosing stops without help. Franck himself offered suggestions in his score, and I know more than the basics about combining assorted sounds. Admittedly, I came to the organ relatively late in life, but after several years of playing, I really ought to be getting the hang of this. Happily, after this morning's lesson, I finally figured out why this is such a challenge.

Here is a photograph of the Aeolian console. There are approximately 120 of those white knobs. There are so many knobs, in fact, that I couldn't get all of them to fit into the photograph. They're new and pretty, and they glide out and in smoothly, quietly, satisfyingly. They're lovely.

The knobs are divided into different sections, corresponding to the four different manuals and the pedal board. Pulling out a knob sends a signal to the organ's innards, allowing air to flow through a subset of pipes that produce a characteristic sound--a reed, say, or a flute, or a diapason, or whatever timbre is indicated on the knob.

Above the uppermost manual is a row of about 30 coupler tabs. Couplers allow you to take sounds from one manual and add them to another manual or pedals. They also allow you to take the stops you've chosen for one manual, knock the frequency up or down an octave, and fold them back into the same manual, either with or without the original octave.

Now let's do some math. If you have 120 knobs to pull, how many different combinations of pulled knobs are within your grasp? Why, 2ⁿ-1, that's how many! When n=120, there's not much point in subtracting 1, since 2⁽¹²⁰⁾ is about 1.3 x 10⁽³⁶⁾. That's a lot, and that's not even counting the couplers.

Of course, you wouldn't ever dream of actually using all of those combinations. You're not going to accompany a nearly inaudible four-foot flute in the swell with a bombastic 32-foot diapason in the pedals, or combine a tuba mirabilis with a gamba. So let's say you'll never use 99.99% of the available possibilities. That leaves 1.3 x 10⁽³²⁾ options, still a ridiculously large number. Let's chuck a few more. Say I can ignore a whopping 10⁽³³⁾ of the combinations--99.9999999999999999999999999999999%, poof, gone.

Lucky me, I have only 1300 combinations of stops to learn. Now all I have to do is remember which 1300 of the original 1.3 x 10⁽³⁶⁾ they are.

Vermin update

Cats 2: Mice 0.

Did you know that bats can bite you while you're sleeping, and you might never even notice? Generally not clear-thinking, healthy bats, of course--rather, bats who aren't in their right mind, like bats who are so befuddled by rabies that they think your bedroom is a better place to find mosquitoes than the good old out of doors. Did you know that post-exposure rabies shots, while not as excruciating as they used to be, are still a royal pain in the butt? Did you know that the only places in Durham, NC, that have rabies shots available on short notice are hospital emergency rooms, where co-pays are an order of magnitude greater than at a doctor's office? Alas, C knows.

Kiln bottom free fall

I am the proud owner of a spankin' new L&L e23T-3 Easy Fire electric kiln. All 310 pounds of this baby plus 150 pounds of accompanying parts were unloaded on a wooden pallet into the street in front of our house this evening.

I expect, thirty years from now, after we have hundreds of firings behind us and the kiln is running better than I am, I will look back on this evening and laugh--ha ha--about how it wasn't until after someone started opening the lid that we noticed, for shipping, the kiln bottom was packed atop the kiln top, and the bottom began its free fall toward the pavement.

We might have had an easier time avoiding calamity had the UPS guy come between 4-6pm, as scheduled, rather than at 6:45, well after sunset (and, as I predicted to the friends who came over for dinner, exactly when the oven timer dinged to let us know the popovers were done).

Fortunately, kiln triage conducted on the front porch suggests the damage is nothing that a spankin' new L&L Brick Repair Kit can't fix (assuming the injured patient survives the critical first night).

Thirty years from now, we'll also have learned whether launching vital kiln parts onto the street brings good luck, like christening an airplane; and whether, having survived its harrowing maiden flight, the kiln will choose a quiet life (bisquing greenware, cone 6 glazing) over an exciting one (igniting the front porch and burning down the house).

More on Klein Bottles

I do believe I have conquered my addiction to holes.

Here are instructions for another genre of Klein Bottle.

1. Throw a bottle. Throw a conical spout. Throw a torus. The diameter of the bottle neck, spout neck, and torus cross section should be more or less equal.

2. Cut, nudge, score, slip, and assemble the parts into a Klein Bottle. If you really must insist on poking holes in the thing (don't you have anything less compulsive to do?), remember to cut them into the conical spout before assembling.




The advantage of this model is that when you call it a "Klein Bottle," people understand the bottle part, if not the Klein part. I suppose it should be called a Klein-Bottle Bottle.

The Klein-Bottle Bottle is fine, but I'm more partial to the Diatomaceous Double Torus model. Please amend the previous instructions: do whatever steps you can while the clay is still wet. In this endeavor, malleable toruses are your friends.

This time, I made the toruses more bagel-like, and they fit together better, but it was nearly impossible getting the hole-cutting tool into the tighter spaces. Clearly, further refinement is necessary. Or fewer holes. Indeed, I rather like the Klein-Bottle Bottle with the mostly solid surface and the holes only in the ingress. It's a little more suggestive and a little less measles-ish.