## March 14th, 2005

Good time with

**atleastdefiant**today. Indeed.

Lots of good

**homovegetarian**yesterday---with an ending that was both reintegrative and its opposite, and sticks with me like a Dan Rather metaphor. Or, rather,

*un*like one, as those don't seem to have stuck. Funny what remains the open question: not the one begged.

At the public library this weekend I was, for the first time, approached in public by a "stranger" after being recognized from this very livejournal you hold in your hands, in a manner of speaking. Nice to meet you,

**trollhagen**.

And so here we are.

I am in a curious state. Not in the depths of uck in which I was mired a week ago. Curious. Curious about how curiously odd in my curiosity I feel. The world is turning and turning in an ever-widening spiral of self-referential curiosity; can the center hold? The best lack all conviction.

Alas, the ladies would not fly; they wanted to, but it was not the time. Amelia's spine is severely fractured, and her tails are fraying, but we shall overcome.

I am hungry for something, I know not what.

Enter I a contraction period where none, or few, do appear? Will I not henceforth for some interval eschew the apostrophe n t? Moreover, if I persist in this biliousness, will my "friend of" list itself contract? Moreover than that, what of the future of meaning? Without faith, can gravity find meaning and give it weight, or will meaning for me remain a tumbleweed, sore pressed for friction?

And why again is it we need things to have meaning?

*Confidential to You Know Who You Are*: If in some ways small or not-so you are now to play my part, may all its cursedness fall hard upon you tenfold what it was for me.Mostly I think of Knuth in association with T

_{E}X, the mark-up language for mathematical notation, but I see the occasional piece by or about him. Often his stuff has a context we lay folk understand, so he stands out for that; I can sometimes relate not only to his desire for aesthetically pleasing typesetting, but also to the curiosity about everyday stuff behind some of the problems he looks into. Here's a funny one that came from his musings in the restrooms at Stanford:

`[copy eds---and ALG---missed the comma that should have gone here!]`

Amer. Math. Monthly

The toilet paper dispensers are designed to hold two rolls of tissues, and a person can use either roll. There are two kinds of users. A big chooser always takes a piece from the roll that is currently larger, while a little chooser does the opposite. When the two rolls are the same size, or when only one is nonempty, everybody chooses the nearest nonempty roll. Assume that people enter the toilet stalls independently at random, with probability $p$ that they are big choosers and probability $q=1-p$ that they are little choosers. If two fresh rolls of toilet paper, both of length $n$

**MR0761401 (86a:05006)**

The toilet paper problem.The toilet paper problem

Amer. Math. Monthly

**91**(1984), no. 8, 465--470.The toilet paper dispensers are designed to hold two rolls of tissues, and a person can use either roll. There are two kinds of users. A big chooser always takes a piece from the roll that is currently larger, while a little chooser does the opposite. When the two rolls are the same size, or when only one is nonempty, everybody chooses the nearest nonempty roll. Assume that people enter the toilet stalls independently at random, with probability $p$ that they are big choosers and probability $q=1-p$ that they are little choosers. If two fresh rolls of toilet paper, both of length $n$

`are installed, let $M\sb n(p)$ be the average number of portions left on one roll when the other one first empties. The purpose of this paper is to study the asymptotic value of $M\sb n(p)$ for fixed $p$ as $n\to\infty$. Let $M(z)=\sum\sb {n\ge1}M\sb n(p)z\sp n$, and $C(z)=\sum\sb {n\ge1}c\sb nz\sp n$, $c\sb n={2n-2\choose n-1}/n$ (Catalan numbers) be the generating functions. It is proved that $M(z)=(z/(1-z)\sp 2)((q-C(pqz))/q)$. Let $r$ be any value greater than $4pq$; then $M\sb n(p)=p/(p-q)+O(r\sp n)$ if $q`[...html freaked out here, where a "<" appeared...]

`p$, $M\sb n(p)=((q-p)/q)n+p/(q-p)+O(r\sp n)$ if $q`[...html freaked out here, where a ">" appeared...]

`p$, and $M\sb n({1\over 2})=2\sqrt{n/\pi}-\frac 14\sqrt{1/\pi n}+O(n\sp {-3/2})$.`

S'okay, when it turns into what is apparently a version of Banach's matchbook problem, most of us just toss our hands up in the air & let it go, but it's fun anyway. Some part of me still likes a puzzle, especially when it has that for-its-own-sake purity that seems in part to embody a childlike innocence in its pursuit of joyous cognitive play.

From the story this morning: "He wears his bike helmet indoors because, well, he's going to have to put it back on a little later anyway." Not entirely unlike my personal resistance to, say, closing kitchen cabinets I'm just going to be opening again soon enough. (For the record, I've been much better at closing them lately than I was in the first months after H's departure. I really do like the feel of the kitchen better when it's orderly, yet it's an ongoing struggle---though prob'bly not so much against the mistaken instinct to save energy at all costs as against that old deleteriously rebellious reaction against housekeeping as oppression.)

Knuth: "There's ways to amuse yourself [chuckle] while you're doing things, and that's the way I look at efficiency: it's an amusing thing to think about, but not that I, that I'm obsessed that it's got to be efficient, you know, or else I, uh, go crazy."

He makes it sound easy to strike a balance there, doesn't he.

*from his website:*

During our summer vacation in 2003, my wife and I amused ourselves by taking leisurely drives in Ohio and photographing every diamond-shaped highway sign that we saw along the roadsides. (Well, not every sign; only the distinct ones.) For provenance, I also stood at the base of each sign and measured its GPS coordinates.

This turned out to be even more fun than a scavenger hunt, so we filled in some gaps when we returned to California. And we intend to keep adding to this collection as we drive further, although we realize that we may have to venture to New England in order to see `FROST HEAVES'.

Here are the images of our collection so far.