Sunday, October 12, 2014

First and Last

For each letter A–Z, what is the alphabetically earliest word you can think of? How about the alphabetically latest? Words must have four or more letters.

No peeking at dictionaries! This is a mental exercise. I had fun with it by giving myself a time limit of 10 minutes. Alternatively one could take a perfectionist approach to each letter.

You can use any variety of words you like, but the words I like to work with are the “standard” word game variety: this means we avoid proper nouns, foreign words, slang, contractions, hyphenated words, or acronyms; personally, I also frown on jargon.

I'll post some answers next week. In the meantime, here's a worksheet you can use to record your answers (the letter A is done as an example).

Feel free to put answers in the comments, or post them online by taking a picture of the completed worksheet with your phone and uploading the image to www.imgur.com.

(Imgur is nice because you don't need to sign in. Just click the "upload images" button.)

Wednesday, August 13, 2014

Book Review: Jonathan Lethem

Two lesser-known books by Jonathan Lethem, author of Motherless Brooklyn and Fortress of Solitude.


Gun, With Occasional Music
Harvest Books, 2003 (reprint; originally published 1994)
Paperback, 271 pages

Fans of Raymond Chandler and Philip K. Dick will enjoy this hard-boiled science-fiction story. The novel is told in the first person by a Marlowe-type detective, Conrad Metcalf, who gumshoes his way around a futuristic East Bay, California. To solve his case, Metcalf must navigate the usual obstacles (femme fatales, bent cops) as well as some new ones: designer pharmaceuticals, animals who've evolved the capacity for speech, and the comically disturbing "babyheads," about which let me say no more. The prose is occasionally uneven, but this seems intentional, part of the narrator's actual voice (and a spoof on genre dialogue). The plot sometimes meanders, but no more than in Chandler, and again this seemed intentional. As in Chandler, the atmosphere is so rich you don't mind taking the long way round.


The Disappointment Artist: Essays
Vintage, 2006
Paperback, 160 pages

This short book of autobiographical essays is worth reading if you're a student of Lethem, or if you share his enthusiasms (such as comic books or Philip K. Dick). The confessional style hit me over the head a few too many times. I also have to admit that I seldom enjoyed teenaged Jonathan's company. By the end, however, the author's adolescent frailties came more subtly and sympathetically into focus in relation to his mother's death---a tragic death, from brain cancer, when Lethem was just 13.


Up to What Point?

This post is about the abortion debate, an atypical subject for me but I'll be writing about it in relation to my customary concerns about quantitative thinking. All I want to say about it is that whenever I try to follow the debate, I become frustrated by the vague propositions people use to frame the question. Here's an example, a graph from Pew:



















The poll asks, "Do you think abortion should be legal or illegal in all or most cases?" The trouble with this is that there's no time axis in the question. I think for a large fraction of people---not everyone, certainly, but for a significant number of people---their actual views about this question depend strongly on how far along the pregnancy in question happens to be.

For a significant number of people the answer is, "Legal up to a point"---which makes it important to ask, "Up to what point?" But none of the polls seem to ask this question.

For each n = 1, 2, 3, ..., what percentage of Americans would outlaw abortion-on-demand in week if they could do so? Is there any research on this?

Sunday, August 3, 2014

Notes from a cross-country drive


From Vermont to Detroit and back, October 2011


The meteor flew from left to right, halfway above the horizon, leaving behind an incandescent green trail that measured the width of my windshield. There was a sense of nearness, as if it weren't more than a couple of thousand feet high. The meteor moved more slowly than any I'd ever seen. In the end, the long green line forked into two dull-orange tracks: the meteor exploding in two. The pieces were extinguished, and the sky went black again.


Sitting on Scott's back deck, looking out over his neighbors' houses toward the flat horizon, I saw in the middle-distance a rank of towering maples, their huge canopies darkening to silhouettes as the evening fell. I'd forgotten about the ancient maple trees that still stand in the Detroit suburbs, like woody pins on a giant map.


The cornfields along my drive were being cut down to stubble. Good time of year to be a bird of prey. I saw plenty of falconiformes swooping down, coming up, or perching on fence-posts. Many held mice, or unidentifiable tasty-bits in their talons.


Passed through Ontario's level farmlands at one or two in the morning. A clear, cold sky had drawn vapor from the ground. Fog bunched itself in the hollows and lay roped across the land in silver skeins. Intermittently, all was white as my car pierced one of the swirling banks.


The beautiful weather in Detroit has followed me, and it's just the time to be tooling around the back-roads. The clouds are whipped cream and the hills are giant heaps of colored popcorn.



Concerning the meteor, I later searched the Web for similar reports and found these.

Friday, July 18, 2014

Book Review: Robert Hass (Ed.),The Essential Haiku

The Essential Haiku: Versions of Basho, Buson, and Issa

Edited and with Verse Translations by Robert Hass

Paperback, HarperCollins 1994

Years ago, a friend who was visiting Japan sent me a beautiful volume of haiku by Kobayashi Issa. I also needed a general collection of haiku for my library, so a few weeks ago I purchased The Essential Haiku, edited by former Poet Laureate Robert Hass. I'm very happy with it.

Hass covers the three great masters, Basho (1644–1694), Buson (1716–1783), and Issa (1763–1827). The language in the translations is gorgeous. In addition to the poems, there are some pages from the poets' journals. The book also includes introductory material for each poet (which looks interesting but I'm saving it for another day).

Here are just a few of the many poems that made a strong impression.


     Even in Kyoto—
hearing the cuckoo's cry—
     I long for Kyoto.


     Year after year
on the monkey's face
     a monkey's face.


     Felling a tree
and seeing the cut end—
     tonight's moon.


     That wren—
looking here, looking there.
     You lose something?


     Lime blossoms!
let's talk about the old days
     making dinner in the kitchen.


     New Year's Day—
everything is in blossom!
     I feel about average.


     These sea slugs,
they just don't seem
     Japanese.


     A bee
staggers out
     of the peony.


     A snail
waving its horns
     uncertainly.



The journal entries include a section from Issa's Journal of My Father's Last Days, translated by Robert N. Huey. In these pages, Issa recorded his father's grueling illness and eventual death. An entry from the early days of the journal: 

Tears were streaming down my face. I just sat there, looking down and unable to say anything. Because of his kindness, my debt to Father is deeper than the matchless snows of Mount Fuji, unmelted by the summer sun, and deeper than a twice-dyed crimson. Yet I hadn't stayed at home and taken care of him. Instead, I had drifted around just like a floating cloud; before I could wonder whether I had gone east, off I was to the west. The days and nights rolled on like a wheel going downhill, and twenty-five years had passed. To have stayed away from my father's side till my hair was white as frost--I wondered whether even the Five Violations could be worse than this.

In my heart, I prostrated myself and thanked Father. But if I were to openly shed tears, it would surely make him feel even worse. So I wiped my eyes and said with a smile, "Now put things like that out of your mind. Just hurry up and get well." I gave him some medicine, and added, "If you get better soon, I'll become the perfect son of a farmer, the Yataro you used to know. I'll cut hay, plow the land, and really set your mind at rest. Please forgive me for what I've been until now." When Father heard this, his joy was boundless.

The most direct reflection of this time, among the poems in the book, is this:


     Last time, I think,
I'll brush the flies
     from my father's face.


Thursday, June 26, 2014

An Interesting Web Magazine: Public Domain Review

Recently I stumbled across a web magazine called The Public Domain Review. Here is what the homepage looks like today:



There are illustrated articles about such diverse things as the Krakatoa sunsets, the first children's picture book, medieval-era animal trials, and a time when Maupassant and Swinburne shared a pretty bizarre lunch.

Oh one more thing: I have made some updates to the previous post, about the brachistochrone problem.

Thursday, June 19, 2014

A Brachistochrone Problem




A dog running on a polished floor spies a bone out of the corner of its eye and begins scrabbling like mad to reach it.

Given the dog's initial speed and initial distance from the bone, and taking the dog's acceleration vector to be constant in magnitude, find the shortest time in which the dog may reach the bone.

Mathematically, the problem I'm posing is this: Given parameters \(d>0\), \(v>0\), and \(a>0\) (defined below), find the smallest time \(T>0\) so that there exists a piecewise-continuous direction function \(\theta(t)\) governing the motion \((x(t), y(t))\) as follows:

\[(x(0),y(0))=(0,d)\] \[(x(T),y(T))=(0,0)\]
\[(v_x(0),v_y(0)=(v,0)\]
\[(a_x(t),a_y(t))=-a(\cos\theta(t),\sin\theta(t))\,.\]

There is no constraint on the final velocity.

I haven't solved the problem. I conjecture that the shortest time is

\[T=\sqrt{2}\cdot \frac{d}{v}\cdot\sigma\cdot\sqrt{1+\sqrt{1+\frac{1}{\sigma^2}}}\]
where \(\sigma\) is a "slipperiness factor" defined by \(\sigma = v^2/ad\). This value of \(T\) is achieved with a constant acceleration vector (i.e., \(\theta(t)\) constant). Here is a movie showing this motion:

video


This is better than a guess in that I've looked at some particular perturbations of the constant-acceleration trajectory and have also computed some specific non-nearby solutions as well. It'd be cool to see a faster, less obvious solution if there is one!

This problem is related to one solved a few years ago by Williams College faculty and students, concerning the optimal path for baserunning. More generally, both problems are about how best to navigate in space subject to a condition on the acceleration vector.

Be sure to let me know if you can improve upon my answer! And in the meantime, here's a funny video of dogs sliding on wood floors. (You can see the physics better if you mute the audio.)