Fame and glory where it counts

How do you make a geek glow? You not only make her Klein bottle the pin-up model for October but also put it on the cover of the American Mathematical Society 2020 Calendar of Mathematical Imagery and then send her a bunch of copies. My math professor dad would have enjoyed this!

JMM 2019

I'm delighted that this Klein bottle representation* found an appreciative audience at the 2019 Joint Mathematical Meetings (the American Mathematical Society and the Mathematical Association of America) in Baltimore, where it won an award for "best textile, sculpture, or other medium." Hooray for clay! The gallery of exhibited art is here.

(*Since a Klein bottle has only one side, it can't actually have holes; those come from the artistic license of living in 3D.)

DT-MSH/TC Klein Bottle revisited

Longtime follower(s) of this blog might recall the DT-MSH/TC that I made in 2010; it waited patiently until 2011 to be fired, emerging from the Cedar Creek wood kiln covered with strange bubbly crusty purple stuff. Thereafter, it sat high up on a shelf in my study, hidden behind a bunch of other pots: too much work to throw away, but too ugly to look at. And then, last month, neighbor-potter Julie Jones said she had a little space left in her ^10 wood kiln and asked if I had anything I wanted her to fire for me.

Behold: no more bubbly crusty purple stuff! Thanks, Julie!

Post-firing debriefing

As always, I need time to come to terms with my pots post-firing. For example, what I considered yesterday to be disturbing crusty bubbly purple stuff, I now consider (just one good night's sleep later) merely befuddling crusty bubbly purple stuff. But I'm getting ahead of myself. Good news first:

The Moebius Diatom Boxes experienced minimal warpage, and none of the parts stuck together. The photos make them look toastier and bagelier than they are in reality. I expect future MDBs will end up electric or gas fired, maybe with some stains for color, to reduce preparatory exasperation.

My four favorite pieces are square boxes (wheel thrown and altered!) that I glazed top to bottom. They responded beautifully to the soda. The tallest box is about 5" high.

There are two fine pitchers, an excellent bottle, some lush double-walled bowls, a confident teapot, and a juicy green pear (looking artificially green in the photo; it's a little bluer in real life). I consider it a bonus that only one of the pitchers seeps, because--like every other pot I've produced in the past two years that has seeped--they're both made from Loafer's Glory clay. No more Loafer's Glory clay for me (regrettably; it's a lovely clay to work with when it's wet). I have a can of very dangerous highly toxic spray that's supposed to help seal pots, unless the can explodes or the spray poisons you in the process; I haven't tried it out yet, however, because I value functioning lungs, skin, and eyeballs more than I value my seeping pots, but maybe this spring I'll get out the goggles, gloves, and respirator and give it a whirl.


Here are some chickens mugging for the camera:

I will concede that the bubbly crusty purple stuff looks pretty good on chickens. Here's a close up of the crusty stuff on some cups, where it's less appealing (dry crusty stuff and lips don't go well together):

Upon pieces that are strictly objets d'art, the purple stuff is fine. The objet on the left is actually a vase form on its side, though I very much like the spherical look in the photo. I was planning to give up holes for a while, but I think I'm going to have to try making some hole-filled spheres.

On the Double Torus-Multiple Size Hole/Total Coverage Klein Bottle that's been patiently waiting to be fired since last summer, the purple is a little garish against the green glaze. What am I saying, the [w]hole thing is garish anyway:



I will try sanding the crusty bubbles off of pots that should be functional, such as this bowl and colander, as no one wants little bits of heavy-metal-laden glass to chip off into their noodles:

Also in the category of Pots-That-Have-Been-Waiting-Since-Last-Summer are several wheel thrown and altered oval boxes. Alas, instead of using my purple alumina hydrate wax on the lids, I wadded the lids--with the somewhat predictable result that most of the lids warped. Dang. From here on out, it's alumina hydrate wax for me.

In the Total Fail category are several pieces made from a highly recommended ^5-^8 porcelain that I purchased online. I'm used to porcelain being finicky and S-cracking in the bottoms of bowls and cups, but these pieces split in some very odd places. Several tumblers had vertical cracks down the side, often beginning well below the rim and ending well above the foot. In the photo below of the two tumblers, a long vertical crack cuts through the cup on the left, while some beads of water are leaking through a crack in the cup on the right. The salt-rock pear has a horizontal crack across the top that is, as far as I can tell, completely unrelated to the form. Homer Cat doesn't mind the cracks in the tumblers, since all he sees are People Cups, but these pieces are headed for the trash can. I bisqued all of my porcelain pots well before the outside temperatures dropped below freezing, so I'm at a loss to explain the defects. Schade.

To end on a more positive note, here are some non-crusty, lid-fitting oval jars (does that count as litotes?), and a picture of a flattery* penguin chatting it up with a chicken at an office party (penguin and penguin photo by Bob F.).

*as in, "imitation is the sincerest form of..."

Prototype

Announcing another breakthrough from the Non-Orientable Manifold Lab!

I said I was going to call it a "Bagel Box," but that's so 2010. It's a new year, and "Möbius Diatom Box"* has a better ring to it (so to speak).

I took advantage of Saturday's warm weather to throw some tori.


Then it rained for two days, so I moved the tori inside to dry; and then winter returned, so after I trimmed the tori outside in the subfreezing night air (brrr), I moved production into the dining room.

I carefully marked and cut the first torus, going for an angular look.


Silly me. Those 90^o angles locked the two rings together with impressive efficiency. I had to smoosh the clay to get the torus open, and both rings ripped a bit.


Oh well, back to the drawing board.

I carefully marked and cut the second torus. No sharp angles this time.


Incidentally, in preparation for this experiment, this weekend I tried (and failed) to slice four bagels into interlocked halves; the near-lack of bagel holes left no room to maneuver the knife. I can now say it's significantly easier to cut a clay torus this way than a bagel, but the rough edges stand out more in the clay than on the bagel, mainly because a linked-sliced bagel is almost entirely rough edges, whereas a hollow clay torus has the potential to be lovely and smooth all over.

Despite some jagged lines, the slicing achieved the desired outcome.


It turns out that this kind of box is a two-person job. My beloved engineer patiently held each ring in succession while I tidied up the other ring's rough edges.

Of course, no clay math toy is complete without holes.


*George Hart calls the cut surfaces "two-twist Möbius strips." Although that second twist means the cut surface isn't really a Möbius strip, I'm sticking with the name "Möbius diatom box."

Resolutions

I need to start an Etsy store. That will go on my list of New Year's resolutions, along with coming up with a way to take decent photos of my work, building a gas or soda kiln in the back yard, and learning to repair plaster walls. Can you tell which of the Klein Bottles below were photographed by a professional photographer and which were photographed by me using a low-tech piece of white poster board propped on a chair as a backdrop?

I didn't make any specific New Year's resolutions on January 1, 2010, but some goals did crop up along the way. I'm pleased to report that I have successfully renewed my devotion to Robert Schumann (to whom, incidentally, I dedicated my Master's thesis in Astronomy way back in 1989) by learning the six B-A-C-H fugues for organ. For those who question the absolute brilliance of the fugues, might I recommend several months of worshipful practice and analysis?

By comparison, I've been resisting my way through The Lord of the Rings, but with December 31 looming, I've bumped things up a notch and am now a mere 200 pages away from finishing The Return of the King (not counting the hundreds of pages of appendices). By New Year's Eve, I hope to call my cultural literacy oath to Tolkien fulfilled.

DT-MSH/TC

Holes accomplished. Classic Koosh Ball included for scale only; will not be bisqued with Klein Bottle.

Cutting edge

I told myself "No More Holes." But then another voice in my head said "Aww, for old time's sake." Thus I find myself immersed in making a Double-Torus Klein Bottle with Total Hole Coverage.

Last time around, I made several Single Sized Hole/Total Coverage models (item number DT-SSH/TC in my as-yet-unwritten mail-order Klein Bottle catalog), and several Multiple Sized Hole/Partial Coverage models (DT-MSH/PC). This one's going to be the first--and I swear, the last (although really, who am I kidding?)--DT-MSH/TC model. It is going to be the 3D Klein Bottle model to end all Klein Bottle models.

Unless, of course, the weight of the in-progress bottle starts to weaken and then crush one of the toruses along its seam. In an ideal world, my clay toruses wouldn't have seams. As I make them on real-world pottery wheels, however, there's no way to avoid the join.

I know how to successfully repair cracks in leather hard clay, but I have zero experience repairing cracked and dented hole-filled toruses, particularly when I can't access the weak seam because it's on the inside surface. I did my best, levering out the dent with a wooden skewer, scoring and slipping and filling in the cracks, and re-piercing the holes, after which I turned to the internet for technical and moral support.

Cliff Stoll's company, ACME Klein Bottle, is the best online reference for anyone considering Klein Bottle manufactury, but it focuses almost exclusively on Pyrex and woolens, and the only references to repairs are for 50-year-old Friden calculators.

When it comes to repairing leather-hard clay Klein Bottles, Google's search engine failed me.

And that's when it hit me: what I'm doing isn't just a bizarre, pitiful waste of time, it's also cutting edge ceramic topological research. No one else on the planet is doing this sort of work--or if they are, they aren't blogging about it. So I shouldn't be surprised that I'm hitting the occasional bump in this never-before-traversed road (although how the road got there in the first place, if no one has ever traversed it, is an interesting question). I guess that makes my work pretty special.

It occurs to me that I haven't posted any photos from the wood firing back in June. Below are two shots of a DT-MSH/PC, a bottle now in a private collection in Wisconsin. It also occurs to me that maybe a bent paperclip is the right tool for accessing that inner seam of my wounded torus, so it's back to the grindstone for me.

Möbius strip joke

I was at Claymakers last week, gently chiseling bisqued clay goobers out of the holes of one of my Klein bottles before glazing it, when a gentleman asked me what a Klein bottle was. I explained that it is basically what you get when you sew two Möbius strips together.

After we talked topology, he said:

"Why did the chicken cross the Möbius strip?"*

I thought the best answer was "KABLOOIE!" (the sound of a brain self-destructing when faced with the oxymoronic contradiction of anything getting to the other side of a Möbius strip), but he said "to get to the same side," which is almost as good.

Other interesting questions are why a chicken is on a Möbius strip in the first place, and what happens to it once it reaches the same side. According to Frederick Winsor, author of The Space Child's Mother Goose, animals don't necessarily do well in Möbius environments:

Flappity, Floppity, Flip!
The Mouse on the Möbius Strip.
The Strip revolved,
The Mouse dissolved
In a chronodimensional skip.**

Incidentally, in Winsor's world, my high flying chicken*** might have enjoyed a happier ending:

Humpty Dumpty sat on a wall.
At three o'clock, he had his great fall.
The King set the Time Machine back to two.
Now Humpty's unscrambled and good as new.**

*And to think that we hadn't talked about chickens at all!

**The Space Child's Mother Goose, verses by Frederick Winsor, illustrations by Marian Parry (1958; first paperback edition, 1963).

***Consider the amazing power of punctuation: compare a high, flying chicken to a high-flying one. You won't find this example in Eats, Shoots & Leaves: The Zero Tolerance Approach to Punctuation by Lynne Truss (2004).

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.