Miscellanea

I've been busy this month. On January 23, I'll be accompanying the Vocal Arts Ensemble of Durham in a performance of Leonard Bernstein's fabulous Chichester Psalms. The concert will be at Judea Reform Synagogue, as part of the synagogue's 50th anniversary celebrations. In addition to spending extra time practicing, I've also been teaching some writing workshops for grad students in the Engineering School. Thus, dear reader(s), I trust you will understand the recent lack of blog posts. Today, however, I bring you two exciting tidbits that I hope you'll find were worth the wait.

Tidbit 1

The writing workshops have made me refreshingly more attuned to things like this Tom's of Maine toothpaste tube:


In case you can't read the blurry photo, the text says (in part):

"Embrace the Power of Mother Nature! At Tom's of Maine that means we use authentic and effective natural ingredients.^[1] We use zinc citrate sourced from zinc--a naturally occurring mineral and xylitol, a natural ingredient derived from birch bark or corn.^[2]"

^[1] Did you catch the missing comma after the introductory element? Tolkien left those commas out all the time, which I'm told is common in British English. Since Tom's of Maine is located in Maine, U.S.A., I hold the company to American English standards for comma usage. Aside from that, can anyone tell me what an "inauthentic" ingredient would be?

^[2] I think they meant "We use zinc citrate (synthesized from naturally-occurring zinc ore) and xylitol (a natural ingredient derived from birch bark or corn)," but hey, I'm not a chemist. By the way, isn't saying "we use zinc citrate sourced from naturally-occurring zinc" kind of like saying "we use water sourced from naturally-occurring hydrogen and oxygen"?

Tidbit 2

While driving home the other day, I happened to observe that if the sum of the digits in a number is a multiple of 9, the number itself is evenly divisible by 9 (an extension of the similar tidbit about numbers being divisible by 3 if the sum of their digits is divisible by 3). This is old news to mathematicians, but brand new news to me. I don't know about you, but I feel empowered knowing, without doing any long division, that one trillion four billion seven hundred thousand five hundred one is divisible by 9.

My mathematician dad would want me to understand why this works, as opposed to simply knowing it works. I never appreciated that attitude when I was a kid bumming help from him on my math homework--in fact, I distinctly resented it--but I appreciate it now. So here you go, dad:

One trillion four billion seven hundred thousand five hundred one
= 1,004,700,501
= 1*(1+999,999,999) + 4*(1+999,999) + 7*(1+99,999) + 5*(1+99) + 1
= 1 + 4 + 7 + 5 + 1 + (a bunch of numbers divisible by 9).
Thus, if 1 + 4 + 7 + 5 + 1 is divisible by 9 (it is) then 1,004,700,501 is too.

In case you're wondering, I was thinking about nines because I've been doing a lot of Ken-Ken recently, a habit that started as a way to procrastinate finishing the Lord of the Rings trilogy (which, incidentally, I finished on Dec. 31, 2010).

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."