Mathematical Intuition and Millennium Problems

I have been busy juggling these past few weeks. But now the most recent paper deadline is met; the presentation materials for Tuesday are in hand; my computers are stable and mutually consistent; my desk and my home are both clean and organized; and I lack neither staples to attach my papers nor staples to make my meals (man does not live on ramen alone). I've even managed to deal with most of my technical support mail. So this evening I sit with pen and pad and a pot of tea to finish a thought from the start of the month. (As an aside: I wrote most of this, including the previous sentence, on Thursday night -- but I'm just now typing on Saturday morning.)

At Half-Price books two weekends ago, I found Keith Devlin's book The Millennium Problems sitting neglected on a corner shelf. I have a special place in my heart for popular writing by mathematicians like Ian Stewart, Ivars Peterson, and Martin Gardner -- I had their books checked out from the Bel Air library half the time when I was in middle school, and I continue to find them entertaining and interesting today. I know a mite more mathematics now than I did then, but the writing often focuses on history, applications, intuitions, and puzzles centered around some mathematical idea or set of ideas; and so even when I'm familiar with the mathematical idea, I still enjoy the reading. For the same reason, I enjoy reading articles on science written for a popular audicence. Devlin, who may be most familiar as the Math Guy on NPR, has an engaging writing style, and his topic -- the Millennium Problems, seven great unsolved mathematical challenges with million-dollar bounties on their heads -- is something I wanted to know more about. After reading the introduction, I bought the book in happy anticipation of a good read.

Besides, the man has an extinct species of possum named after him. What's not to like?

As I read, I found exactly what's not to like -- at least, I found points in the presentation that I very much disliked. Devlin undertook a monumental task: not just to explain the history and the impact of the Millennium problems, but to give a flavor for the problems themselves -- assuming a reader with only a pre-calculus grounding in high school mathematics. As Devlin puts it,

Even achieving a layperson's knowledge of what [the Millennium problems] are about takes considerable effort. I believe the effort, however, is worthwhile. Aren't all pinnacles of human achievement of interest?

But the challenge was too great. Devlin explained the problems at a lay level better than I could have done; but then, I don't know how someone could think about some of these problems without knowing -- really knowing, not just having some vague familiarity with -- some group theory, elementery number theory, and the basics of differential calculus. Devlin gives a creditable introduction to some of this background, but it is not enough, and by the end he is reduced in his frustration to section titles like The Hard Stuff, Made as Easy as I Can and The Hodge Conjecture: Not for the Faint-Hearted.

For most readers, the description of cohomology classes in the last chapter would probably be impenetrable. For me, it was frustrating. After all the effort of sketching in the technical background, an effort which will likely go unappreciated by most of your readers, why not finish the sketch for me? Just a little more technical detail? Somehow I ceased to react to the book as the popular exposition it was meant to be, and started to treat it as an inadequately fleshed out technical work -- which it was certainly not meant to be.

I was irked. I was sufficiently irked that I wrote a letter to a friend which fell somewhere between a lecture and a tirade, in which I tried to describe what I disliked in Devlin's book. I wondered almost as soon as I sent the letter whether I hadn't been unduly harsh -- but Yi shared an office with me for a while, and had plenty of opportunity then (and since) to become accustomed to the flavor of my unprompted lectures. So I expect she will take it in stride.

---

After reading Devlin's book, and after spending some time grumbling, I began to think more about the nature of mathematical intuition. In the first chapter, Devlin has a section entitled Why Are the Problems So Hard to Understand? in which he argues that the level of abstraction from everyday reality makes mathematical ideas harder to explain to a lay audience than are ideas from any area of science. At the same time, as he says near the end of the book,

... a trained human mind that has thought long and hard about a particular problem frequently develops intuitions that prove to be correct.

The problem, then, is not that there is no intuitive picture of the ojbects of higher mathematics -- just that such pictures are inaccessible without a lot of patient thought. I disagree with Devlin's assessment only in one point: I believe there are concepts in modern physics and chemistry which require abstractions which are fully as inaccessible to the lay reader as any of the Millennium problems (which is probably why two of the Millennium problems -- mathematical understanding of the Yang-Mills field equations and the solution of the Navier-Stokes equations -- come directly from modern physics).

So why is popular science still so much more popular than popular mathematics? And why does modern math have such a reputation for impenetrability, particularly when -- in contrast to the experimental sciences -- intuition can be had for only the cost of time and thought? Part of the trouble, I think, is educational. Think when the scientific method was first mentioned to you in an elementary science class -- and then think when the idea of a mathematical proof was first introduced. Do you know more names of physicists from the past two centuries than names of mathematicians? Difficulty alone cannot account for the difference in perception; nor, I believe, can the relative distance from everyday reality.

I don't have good answers to the questions why is it so hard to understand? and why should science seem any easier? But I'm still thinking on it. Maybe one day I'll gain enough psychological intuition to understand how people gain intuition -- but I doubt it. Mathematics is easier to understand than people are.

---

Works considered

This started off longer, and got shorter as I realized I wasn't sure I agreed with my own ideas. Consequently, this list is not a collection of works cited, but rather writings that I looked at during some version of the above.

1. Nature's Numbers (Ian Stewart); Islands of Truth: A Mathematical Mystery Cruise (Ivars Peterson) -- Peterson's book was definitely one that I kept checking out from the library. I forget which of Stewart's books the library had, but Nature's Numbers is a good one in any case.
2. Mathematical Association of America -- The MAA does a lot with mathematics education and popularization. Both Ivars Peterson and Keith Devlin write regular columns for the MAA, which are available from the web site.
3. The Honors Class: Hilbert's Problems and Their Solvers (Paul Yandell) -- Perhaps a natural complement to a book on the Millennium Problems. The Millennium Problems were deliberately introduced 100 years after Hilbert introduced his list.
4. The Man Who Loved Only Numbers (Paul Hoffmann); A Beautiful Mind (Sylvia Nasar) -- Biographies of two modern mathematicians. I thought both books were fascinating. No, not all mathematicians are so nutty.
5. Men of Mathematics (E.T. Bell) -- Biographies of some major mathematicians up through the end of the nineteenth century. There are more accurate historically accurate books on the history of mathematics and on historical mathematicians; but it is hard to find another book which is so enthusiastically and charmingly written. Mathematicians were Bell's heros; and he made a few of them my heros, too.
6. Fermat's Engima (Simon Singh) -- I have intended to finish reading this book for years now. Two of them, actually. But I particularly wanted to mention a quote from the dust jacket, which I repeat here in full:

   Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. One goes into the first room and it's dark, really dark, and one stumbles around bumping into the furniture. Gradually you learn where each piece of furniture is, and finally, after six months or so, you find the light switch and suddenly it's all illuminated and you can see exactly where you are.
   -- Andre Wiles

7. The Value of Science: Essential Writings of Henri Poincare (Henri Poincare; ed. Stephen Jay Gould) -- Poincare has much to say about the role of intuition and experiment in mathematical inquiry. A profound and prolific mathematician, Poincare turned late in life to writing for a popular audience. His publications were deservedly successful, and are worth reading as a model of accessible exposition, as well as for the ideas they contain on the nature of mathematics and of science.
8. Linear Differential Operators (Cornelius Lanczos) -- Really, any of Lanczos's books would serve as well, but Linear Differential Operators has a few wonderful paragraphs at the beginning in which he describes the goal of his expository style. In contrast to the very formal presentations of N. Bourbaki (Bourbaki was actually the nom de plume taken by a school of French analysts), Lanczos concentrates less on the details of the analysis and more on high-level intuitions. The Variational Principles of Mechanics is another excellent text in the same style; it was one of my primary texts in learning about classical mechanics.
9. Catastrophe Theory (V.I. Arnol'd) -- Usually Arnold writes more technical books, and when I found this on the shelf at Black Oaks, I was delighted to find that it was written for a general audience. It's short, interesting, and full of both dry humor and intuition.

Rooibos

• Rooibos is actually pronounced roy-boss.
• Pico de gallo translates to rooster's beak -- a little peck of flavor.
• For complex symmetric M, K, the expression (v^T K v) / (v^T M v) is more accurate than the standard Rayleigh quotient for estimating an eigenvalue from an approximate eigenvector v, assuming v^T M v is nonzero.

So now you know.

Remote thoughts

It was spring or early fall, and the lot of us spilled onto McKeldin Mall, laughing and teasing. We were on the way to Plato's Diner for dinner, perhaps -- I know longer remember. There was a giggle and a charge, and then a weight on my back and shoulders. With no particular thought, I dropped my center of gravity, turning forward and aside just so -- and the weight was deposited in front of me on the grass.

I remember the smell of the grass. I remember she looked up at me from under a tumble of red hair. I don't think I've ever been so humiliated, she said. Have you ever tried to read an ambiguous expression on a face turned upside down? I'm not sure whether she was serious; but a moment later, she laughed, and we all continued our tumble toward whatever our destination might have been.

Nine years later, idly contemplating a laughing gaggle of undergrads sitting at a table across the room in La Burrita, it all came back. It was a minor incident, an acquaintance I saw little in my later undergrad years, and never since I graduated. I don't recall remembering it since. But for a moment, I smelled grass instead of salsa, and I remembered.

Memory's a funny thing.

On an unrelated note, the rdesktop protocol is pretty cool. My desktop at the office runs Linux, and I like it that way, but every now and then I have to work with Word documents or PowerPoint presentations. But since the department runs a Windows 2003 server that supports the rdesktop protocol, I can open a window that acts just like a Windows box. I'm restricted in what I can run on the server, so I can't use it to compile my codes for Windows; but even so, it's mightily useful.

• Currently drinking: Black tea scented with caramel and memory

Manners

Why would someone think that reminding me of a deadline in bright blue capital letters in a large font would be any more effective than sending something politely worded in ordinary text?

Perhaps I could figure out how to use PowerPoint as a mail filter, so that any letters which were intended to be bright blue never actually appeared on the screen; or at least, so that they didn't appear until I restarted PowerPoint.

Lanczos

In one of the (unfortunately lost) comedies of Aristophanes the Voice of the Mathematician appeared, as it descended from a snow-capped mountain peak, pronouncing in a ponderous sing-song -- and words which to the audience sounded like complete gibberish -- his eternal Theorems, Lemmas, and Corollaries. The laughter of the listeners was enhanced by the implication that in fifty years' time another Candidate of Eternity would pronounce from the same snow-capped mountain peak exactly the same theorems, although in a modified but scarcely less ponderous and incomprehensible language.
-- C. Lanczos, preface to Linear Differential Operators

A tale of three Jims

1. He taught my first undergraduate math course, a class on real analysis that gave most of us pause. When he explained things, he would lower his head and shake it from side to side, looking at you over his glasses. He gave us problems with the rejoinder That'll keep you out of trouble for the weekend! He constantly broke his chalk; and, like most of the professors I know who break chalk in mid-explanation, it caused him no end of irritation. In irritation, he once tossed a piece of chalk across the front of the room, sidehand, from where he was standing at the door. The chalk bounced four times; each time, the remaining chalk fragments snapped in half, so that a moment later, sixteen bits of chalk collided with the wall. It was all we could do to keep from laughing, but we managed it. He looked at the chalk for a moment, then returned to his lecture.

   He had a chair in his office for visitors: it was a drab upholstered affair, probably as old as I was; it looked like it would probably be comfortable. But it had no bottom to speak of, and so I would sit, precariously perched on the four inch width of board that formed the entire solid seating surface, and ask questions about tensors and algebraic k-theory. I used to ask his opinion on math courses at the start of the semester. That's a good course, he would say; take something with this guy, another time. Number theory! It's an interesting area, but here's the book they use for the undergrad course. You've had abstract algebra, and I know what you know. You could probably cover this material in a weekend, and a weekend spent in a bar, at that. When I told him I was going to graduate school to study numerics, he said numerical analysis!? in the tone most people would reserve for utterances like you're eating cockroaches!? But then he thought for a moment and said there was undoubtedly interesting stuff there, and I would do fine. Just don't forget the math.

   He gave us a homework entitled Eine Kleine Nachtmusik; one problem for each of us. He subbed for the graduate topology course once when I was taking graduate algebra; one of my classmates who took both courses summarized the lecture with the words Who was that masked man? It was in his class that I first really experienced mathematics as I see it now.

2. He has a beard and glasses, an occasionally owlishly-serious expression, and the ability to cover technical material at a phenomenal rate. I know people who speak faster, but most of them don't really say that much with their words, or become incomprehensible as their rate of speech increases. He doesn't become less comprehensible, but sometimes he saturates his listeners -- too much information, too fast. He covers his book in one semester; most others teaching from the same text only go through half of it.

   The problems in his book are labeled easy, medium, and hard, and it was those labels which first clued me in on how differently we think about mathematics. Some of his medium problems, I find easy or hard; some of the hard or easy problems, I would call medium; and rarely I'll find something that he thinks is hard to be easy, or vice-versa. He is an extraordinary algebraist, far more so than I. His favored languages are Fortran 77 and Matlab.

   He seems to be constantly under threat of a deadline, but usually manages anyhow. He drinks an immense amount of coffee, usually as lattes. I have seen him look stressed, but only once have I seen him look fatigued -- it was in a lecture, and I thought he might have fallen asleep, until he sat up and asked a penetrating question. Each of his students works on something different; but somehow he manages to keep up with them.

3. He was trained as an engineer, but was not happy working as one. He's a little shorter than I am, and nearly as lanky. I'm not sure he eats much more regularly. His passion is mountain climbing. His accent changes when he speaks with his grandmother on the phone; it changes from an American accent to a New Zealand accent. He's sometimes happy, sometimes brooding, rarely in the middle, always sardonic. He's laid back, with a quirky -- though sometimes ungracious -- sense of humor. He calls me guy, and I call him sir, and we get along just fine even when neither of us have the slightest clue what the other is talking about.

   He plays croquet, likes to have a beer with friends, enjoys rap music but listens to NPR when he's in a car -- which is rarely. He usually bikes or walks for transportation. He sometimes watches classic Star Trek re-runs on the Sci Fi channel, and sometimes I join him. He asked me today whether my shirt (which says Eschew Obfuscation) was geeky or nerdy. I told him I wasn't sure, and then explained what it meant. I wish you hadn't done that, he said, That wasn't the question I asked, was it? I think he was joking; but he delivers his jokes in a deadpan manner: the perfect straight man.

LCD Sunrise

An LCD Sunrise sounds like it ought to be some particularly toxic beverage, doesn't it? Something bright orange, naturally phosphorescent, and capable of stripping paint at twenty paces, perhaps.

I am writing this on my Thinkpad, now restored to normal function. The problem must have been a loose connector, since taking the thing apart and reassembling it seems to have restored it to normal function.

Wir-Do

It is the Way of the German First Person Plural Pronoun. It is not to be confused with the Way espoused by the Jedi Nuns: the Force of Habit. Will this punishing plethora of new paths never cease?

The Pile

The Pile on my shelf is coming of age. It used yo be a cute little pile -- you should see its baby pictures! -- but now it is sullen and wayward. If I do nothing, I fear it might spawn new baby piles, and then where would I be? Buried beneath a host of paper piles, that's where I'd be, or my name isn't Preserved Killick.

It doesn't do to anthropomorphize piles of paper, though, at least not within their hearing. The biological analogy is purely an accident of the s-shaped behavior of a paper pile's growth, so much like the shape of a logistic model. The pile starts modestly enough, then grows at an accelerating rate, until an external concern (like stability of the pile) imposes some restraint. The pile then grows slowly or stagnates until some catastrophe, like a collapse or a spring cleaning, spells doom for the pile as a single entity.

UPS-y days, eh?

UPS delivered a book for me on August 31 -- but not to me. The customer representative was friendly, and figured out what went wrong.

It took me forever to figure out how to get parallel Matlab running on the local cluster (though Viral did most of the work). Eventually, I discovered it was an error in my .cshrc file. In the process of figuring that out, though, I learned some useful things about ssh, ssh-agent, and ssh-add.

A gentleman using my Matlab interface to the finite element code FEAP has been having persistent problems; I think this is because he is using an older version of the code. But he has done an excellent job in presenting his difficulties -- most people give too much information or too little -- and may go around the problem by upgrading his version of FEAP. And now I know another person interested in using my software.

A colleague is having problems getting results from ANSYS to match results from Sugar on some simulations. I have not yet determined the root of his problem, but I think I have a lead. If I'm right, it's not a bug in my software (hooray!), but a subtlety in the modeling. Modeling issues are much more interesting than software bugs. In addition, we have both learned a few things about frequency shifting due to residual stress -- a topic which I think does not relate to the mismatch between ANSYS and Sugar, but may explain some of the mismatch between the simulated and the theoretical results.

I looked up the warranty information for my laptop. The warranty period ended in May. But from the symptoms, the problem with my laptop is related to the backlight, which may have broken or may have simply become unplugged. Taking apart the screen to find out should be educational; and new backlights are cheap.

I am no Polyanna (though I could pretend to be a polyhedra if that would make a proof easier). But some days the world seems brighter for the bugs in it.

Boat Captain and the World of Yesterday

From O'Brian's The Fortune of War (p. 134), Dr. Stephen Maturin's comments on the merits of monarchy.

Man is a deeply illogical being, and must be ruled illogically. Whatever that frigid prig Bentham may say, there are innumerable motives that have nothing to do with utility. In good utilitarian logic a man does not sell all his goods to go crusading, nor does he build cathedrals; still less does he write verse. There are countless pieties without a name that find their focus in a crown. It is as well, I grant you, that the family should have worn it beyond the memory of man; for your recent creations do not answer -- they are nothing in comparison of your priest-king, whose merit is irrelevant, whose place cannot be disputed, nor made the subject of a recurring vote.

Squirrels cooked in madiera, indeed.

• Currently drinking: Russian caravan blend

LCD Twilight

The backlighting on my laptop screen is no more. The image on the LCD is too faint to be useful, but I can still connect to an external monitor. The screen has been slowly dying for a long time, now; first the image was reddish, then increasingly hard to see, and then... vanished.

A sunset is a much prettier sight.

I've attached my laptop to one of the monitors in the office, and I brought in my CD burner. This evening, I'm backing things up.

At the end of the tour

Last week, I had a productive week and an interesting weekend. This week, the semester starts in earnest. Tuesday is the first day of the course that I'm taking this semester (Convex and Nonlinear Optimization); next Wednesday is the first day of the matrix computations seminar; and various paper and presentation deadlines are fast approaching. It was a good summer; and now I'm glad it's over and another semester has begun.

Some lists from the summer now past:

• Beverages of choice:
  • Hong-Kong style coffee + tea -- This drink, which can be served hot or cold, consists of coffee mixed with English breakfast tea. Both the tea and the coffee are quite strong. When I had it, it was served with milk and sugar; it was a very good combination.
  • Pu-erh tea -- I've learned that the name sounds different in Cantonese, more like po li (though I've likely butchered the pronunciation). Pu-erh has a strong, earthy sort of black tea taste. I got brother Rick some for a birthday gift, and he thought it was reminiscent of beet juice. I think he'll appreciate it more with a little practice brewing it... but I'm biased.
  • Dragon well tea -- This is a particularly tasty variety of green tea.
  • Silver needle white tea -- Pu-erh and white tea are at far ends of the tea spectrum, insofar as it makes any sense to talk about a tea spectrum. White tea is light, and must be brewed at a lower temperature and for a longer time than even the green teas. The flavor is subtle.
  • Black coffee -- Of course! Peet's is offering a new special blend, their African Blend, which I quite like.
  • Hot water with lime -- I bought a new bottle of lime juice about a week ago, and can once again make one of my favorite late-evening beverages. This goes well with honey.
  • Red tea (rooibos) -- This is actually made from a type of African bush. It has a strong, mellow sort of flavor.
• Games and amusements
  • Eraser hurling -- Why are we scouring Iraq for Whiteboard Marker Dusters when we have so many of them here already? Upon hearing the tale of a professor who hurled his eraser at a student snoring in the middle of the class, I was inspired. Suppose I practiced hurling weighted erasers at a target in some very public place, then brought along a basketful of erasers with me to class. Would students remain awake? Could a potato cannon be adapted to make an eraser bazooka? This is, I think, my best idea in this area since Bread Do.
  • Survivor: College Tournament -- The name, I think, says it all. Survivor and the Jeopardy College Tournament both enjoy some popularity; why not combine the two? Yes, eraser hurling would be involved.
  • Embarrassingly parallel parking -- I'm not sure what this would involve. Perhaps a lot full of inexperienced teenage drivers playing musical parking spots? Alas, if the game was really embarrassingly parallel in nature, it probably wouldn't be very exciting.
  • People watching -- Finally, a real amusement.
• Books I want to read
  • Hackers and Painters (Paul Graham)
  • Programming as if People Mattered (I'm missing the author)
  • The Blue Bear (Lynn Schooler)
  • Black Lamb and Grey Falcon (Rebecca West)
  • In Season (Greg Atkinson)
  • The American Language (H.L. Menken)
  • Chasing the Sea (Tom Bissell)
  • A Year in Provence (Peter Mayle)
  • Walter Rudin's autobiography

Indian Summer

Summer comes late to Berkeley.

Throngs of students bustle or lounge, depending on their ages and attitudes. The sun is bright, the air is warm, and tight, sleeveless t-shirts are the norm. Doors are open, and the scents of food and sounds of laughter waft out. On a porch step, two middle-aged men sip their beers and watch the antics of the dog across the street.

A song drifts from the chancellor's lawn; it's something by The Cranberries, sung a capello. A man sipping coffee narrowly averts a disastrous collision with a young woman who is inexpertly trying to skate while walking her dog. A motorcyclist zooms by, oblivious to the drama on the sidewalk, intent only on crossing the intersection before the light change.

The air stays warm even when the sun sets. The horizon, at first bright with the setting sun, dims in color until night has fallen. The sidewalks stay crowded for a while longer: people meeting people, people getting lost, people experiencing Berkeley for the first time or just getting reacquainted with the streets. At last, quiet falls; I listen to the lingering sounds of traffic and insects and the radio.

Titles

I have added titles to the template. I've also added titles to the past several entries, though I'm too lazy to go back much farther.

I went out wandering...

Trees at twilight,
Sunlit sent'nels.
Gold on the ocean,
Fog on the hills.

Light the lamps
At ghost of the gloaming
For the walker
Watching still.

Meh. Perhaps I should stick to code. It was a nice walk, though. There's something fascinating about natural things lit from below, whether they're tree branches, water fountains, or faces.

• Currently drinking: White tea

We

While describing a train ride, I said We stopped at Coliseum station, and a bunch of Raiders fans boarded. Only a sentence or two later did I think: what we?

Mathematicians use we when writing proofs, even if the proof is not joint work. Supposedly the we in this case refers to the reader who will carefully follow the author's arguments; but I doubt many mathematicians deliberately choose we, any more than we deliberately choose the imperative voice when we write let n be an integer or suppose not. For good or ill, proofs are conventionally written in a particular style, and we is part of the style.

But I formed the we habit long before I started writing proofs. When Mom asked what I'd done during a day of elementary school, I would say we ate lunch; and we had recess... Everyone else in the class was doing the same thing as me, at the same time, sometimes even in cooperation with me. And so I said we.

And now? I stare into space; I went for a walk this evening. But if there is any hint that someone else might be staring into space at the same time, or going for a walk in the same direction, I'll revert to we.

If this seems like a lot of hot wind for a two-letter pronoun, consider the following line from an e-mail I sent during a coffee break this afternoon:

Hack hack hack. Boing boing. Hack. Boing. Um.

The response? Dude. Which is another very interesting word...

Wolfhounds on wheels

While walking to Safeway, I passed a woman walking a dog in a wheelchair. Yes, the dog was in the wheelchair; the woman was not. This curious canine contraption consisted of a pair of wheels and an axle, on which there was a sort of blue sling to support the dog's hindquarters. There was also a metal crossbar on which the dog could prop its legs, in addition to two crossbars which seemed primarily to be there for structural stability. It was a big dog, about three feet tall at the shoulder and husky as well, so those additional crosspieces were probably necessary.

Does anyone ever do stress analyses for dog wheelchairs? What about stress tests? What factors of safety go into the design? Or are dog wheelchairs only subject to an eyeball analysis? I think there could be business opportunities for designers of high-quality pet wheelchairs -- but perhaps that's just an indication that I've never studied business.

On typing

From a letter by Mark Twain to his brother upon the acquisition of a Remington typewriter (quoted in Faster by James Gleick, p. 117):

I am trying t to get the hang of this new f fangled writing machine ... The machine has several virtues I believe it will print faster than I can write. ... It piles an awful stack of words on one page.

(The typographical errors are copied from Faster, and presumably in turn were copied from the original letter.)

Savagery

From a letter from Bertrand Russell to the editor of The Observer (12th Jan, 1963, p. 30). Via Yours faithfully, Bertrand Russell (ed. Ray Perkins, Jr.), pp. 406--407.

   Have we all become savage? Why do we turn, inevitably, towards ferocity in dealing with political opponents -- towards maiming or killing or sentencing them to disproportionately long imprisonment?
   I think it is because we live in an atmosphere of fear bred by present political policies. We have been conditioned to accept cruelty, even the threat of extermination, as the sole means of defending a way of life that seems to prove itself, by such a result, hardly worth defending.

Salsa

The best thing about dinner at Cancun Taqueria this evening? Mango salsa. We ran out of chips before we ran out of salsa, so I drank the rest without chips.

They have pretty good agua fresca, too, with bits of fruit floating in it.

• Currently drinking: Cold water. But maybe I'll have hot water and lime soon.

A Specious Odyssey

I've got a great idea for a movie. I call it Y2K+1. In it, a maintenance programmer discovers a mysterious monolithic code of unknown origin. I haven't worked out the details, but I have a few lines of dialogue...

• What does this code do? It's origin and purpose are a total mystery
• The editor is opening. I can see the C code. My god, it's full of stars!
• Just what do you think it's doing, Dave?
• The 9K series is the most reliable computer program ever made.

On hash function security

Researchers have found flaws in the MD5 and SHA0 hash functions. A hash function is a function which takes a large amount of data (a document, say) and from it generates a much smaller number. Ideally, it should be very hard to find a collision, or two inputs which generate the same output. The recently-discovered flaws in MD5 and SHA0 mean that it's possible to find collisions in these functions much more quickly than anyone had previously realized.

Cryptographically secure hash functions are key to generating digital signatures. To digitally sign a document D, I would compute a hash function H(D), then compute another function S(H(D), K) based on my secret key K. Only I can easily evaluate S, but anyone can check to see that what I've evaluated is correct. We evaluate S(H(D), K) instead of S(D, K) because the output of S is the same size as the input, and we don't want a signature that takes as much space as the original document. Also, we can compute S much more quickly if the input is small. However, we don't want it to be easy for someone to cut our signature and attach it to another document, which they could do if the fake document F had the same hash as D does (i.e. H(D) = H(F)). That's why finding these collisions is considered a big deal.

However, the sky is not falling (except insofar as the sky is always falling locally in areas where convection cycles in the atmosphere produce a downdraft). If I can come up with an input file that produces the same MD5 hash as the mortgage you digitally signed, then I could replace your mortgage with my file, and the signature would still check. But finding some input file that produces the same MD5 hash as your mortgage is a far cry from finding some meaningful input file that produces the same MD5 hash as your mortgage. For the time being, the easiest way to forge an electronic signature on a document in which you will me all your money is to hire goons to steal your key.

• Currently drinking: Black coffee (Peet's African blend)
• Current password: Squeamish ossifrage

Ink in the drink

I have two fountain pens in Berkeley. One of them takes Parker ink cartridges; the other takes Waterman cartridges, or uses an adaptor to take ink from a bottle. It is a corrolary to Murphy's law that if I can't find one of the pens, I will be out of ink for the other. This evening, Murphy did not strike. I found Waterman cartridges, and had the appropriate pen close at hand. I had no problem taking out the old cartridge, putting the new one in, or reassembling the pen.

I should have been worried. Murphy always gets his due.

Half an hour later, I had an envelope with holes scratched into it, ink stains along my index fingers, a bottle cap full of inky water, and a renewed appreciation of water-soluble inks. I haven't left so many finger prints on a paper since the last time I spilled coffee on my hand while juggling a clipboard.

Just as my pens sometimes run dry, so do my creative juices. At least, so went my thought as I cleaned up and tried to figure out what I wanted to write with my newly-charged pen. Perhaps pouring a little water in my ear would help? Right -- and if the eyes are windows to the soul, then the virtuous should buy stock in eyeball squeegies?

• Currently drinking: Black tea flavored with osymanthus flowers and water-soluble ink

Thinking time

A few years ago, I bought a copy of James Gleick's Faster: The Acceleration of Just About Everything. I enjoyed his Chaos: The Making of a New Science when I was in high school, and the title tickled my fancy. I enjoyed it enough that I took it home for my parents to read. I spent part of yesterday evening browsing through the shelves around my old room, saw that Faster was still there, and picked it up. I think I might take it back to California with me.

There's a semi-humorous You might be a graduate student if... list that used to occasionally make it into my inbox. It was funnier before I passed through the 20th grade. One of the bullets is you find the bibliographies of books more interesting than the actual text. I don't feel exactly that way, but besides the re-read value, a strong reason for bringing Faster back to Berkeley with me is for the references, both in the Acknowledgements and Notes section and in the body of the text. More book recommendations!

(I've barely scratched the list of books recommended from reading From Dawn to Decadence, but since when has that factored into my reading habits?)

Vacations are a good time to think about time. What does mail have over e-mail? I've mentioned the aesthetics of pen and paper before. But I think another attraction of hand-written letters is the time they take, both in the drafting and in the sending.

I can type faster than I write, faster even than I can draft a coherent sentence. So when I type, my hand has the tendency to run ahead of me; then I backspace; and then my fingers run ahead again. The mental image I have is of a man walking a crazed little dog -- the type that runs in circles and yips impatiently at the staid pace of its owner. That's an exaggeration, but it captures the feeling. It's a sort of fidget. When I write with pen and paper, or with pencil and paper, I have much less difficulty keeping up my hands in sync with my thoughts. Furthermore, I often write letters in parts; a paragraph or two one day, a few more the next. I rarely write e-mail that way.

Then there's the sending. Write an e-mail, hit send, and you can expect the message to arrive in a matter of minutes. Write a letter, drop it in the mailbox, and you can expect it to arrive in a few days. And that's fast! One of the themes running through Patrick O'Brian's books, which are set in the British Navy early in the nineteenth century, is the sending and receiving of mail. A letter sent could take months to arrive at its destination, if it arrived at all. A correspondence in which there are months of delay between exchanges must be different from a correspondence in which the delay is a minute, an hour, even a day. Minutes are a matter of short term memory; months are not.

Have you noticed how much shorter pop music pieces are than classical or jazz pieces? Or how instantly identifiable BBC segments are by the relatively long periods of time the camera remains in one place? How differently people talk on cell phones than on land lines? How different conversations are when you have only a few minutes to talk over the phone rather than a couple hours to talk over food (or over books, as the case may be)?

Fill in the blank: the blank pace of modern life. Hectic, right? There's a very interesting discussion of American perceptions of leisure time in Bowling Alone by Robert Putnam (which came to my parent's home around the same time as Faster; the two books sit together on the shelf). It's not very original to say that Americans scurry a lot; nor is it original to observe that we actually have a lot of spare time, much more than we realize. Unoriginal hardly means unworthy, though. Old topics are good for chewing slowly; and time is a very old topic.

What's the most famous quote of Thoreau? I came to the woods to live deliberately. The word deliberately does not connote slowness so much as unhurried or careful. It's good to spend some time remembering to be deliberate.

I don't want to reject the fast or the slow. I just like being able to think about it, and make choices about what things I find useful and what things I'd rather not have:
Cell-phone? Not yet.
E-mail? Is great.
Long letters? Also great.
Staccato sentence fragments? Check.

• Currently drinking: Green tea

I am at my family's home, and have been here since last Wednesday. Winnie came along for the first week, and we trooped around College Park and DC and Annapolis. My siblings came along for some of the DC visits, and we went to Annapolis with my parents. We ate dinner with my friends on Saturday evening, and ate lunch with one of her college friends on Sunday afternoon, and had other meals with varying subsets of my family. The weather was mild and clear through Wednesday morning, when Winnie left. A thunderstorm blew past Wednesday afternoon, and today a more serious storm system started moving past. I'm listening to the sound of rain on the roof as I type. It's a nice sound.

College Park remains much the same as I remember, enough that it was no problem to navigate. There is a Ten Ren Tea House, new since I graduated (though that's five years past, now). I remember a quirky little coffee shop at that corner which no longer seems to be there. They used to have open mike nights periodically. I visited that cafe sometimes, though I always avoided the open mike nights; but I like the idea of a tea house, too. Not that it matters either way, I suppose.

Now I'm just enjoying the quiet of home. Our old grey cat, Misty, is the only survivor from when I still really lived here, but the other cats are willing to be around, even if they're cautious. There are books, of course, and I've been going through a novel or two each day, for the past couple days. They're mostly short, light, and forgettable. An exception, which I picked up in an idle moment in a Barnes and Noble in DC (you knew I would visit a book store some time, right?) is Don Knuth's Things a Computer Scientist Rarely Talks About. I particularly enjoyed lectures 3 and 4, but the whole book was interesting and entertaining, and I'm looking forward to taking it back to California to lend to friends there.

I'm in the middle of a few serial letters. I do enjoy writing to people, assuming that I remember their address and have some inkling that a letter might be welcome. I took home a fountain pen which is one of my favorites for letter-writing, and some pads of regular-sized paper. I like e-mail -- at least, I like it many days when the spam filter is working -- but there's something relaxing to writing a letter that isn't shared in writing an e-mail. Perhaps it's a lack of immediacy. Or maybe it's just that a pen or pencil and a piece of paper are such wonderfully engineered artifacts: simple to use, robust, unlikely to freeze up or lose a connection, unchanging in their fundamental design for a long time.

I've done a little work, sipped a little tea, and spent a lot of time staring into space. I've exchanged awful puns with Dad, and sung silly songs with Mom, and had unhurried conversations with my brothers, and played with the cats. And while I look forward to returning home to California on Monday, for now I'm just enjoying the old home.

Gen mai cha is green tea with toasted rice kernels. Adagio Tea makes a variant which they call gen mai cha pop, in which the rice kernels are toasted for long enough that they pop. The rice gives the tea a nutty flavor that I like. I keep a tin at the office in the top drawer of my desk.

The office is quiet in the evening these days. One of the advantages of being the only person here after hours is that I can listen to the radio -- via the Internet or from my clock radio -- without my earphones. It's like whistling while I work, but without the absent-minded off-key wandering periods when I concentrate.

The radio is nice during tea breaks, too.

• Currently drinking: gen mai cha

What the programming world really does not need is a debugging tool based on the antics of a troop of monkeys. It would be amusing, though -- give a whole new meaning to tree walk and dangling pointer.

• Currently drinking: Russian caravan blend

Surf the web and talk on the phone at the same time! says the announcer on the Comcast commercial. Does this seem rude to anybody else?

Uttered in an introductory programming class:

How do you eat an elephant? Anybody? You cannot eat an elephant all at once. Not even a tiny baby elephant. You must divide and conquer!

Seems like it could go for any number of disciplines. How much gnashing of teeth actually comes from some poor soul trying to gnaw through the skin of an elephant? Even a tiny baby elephant?

Some days I think I should have chosen a different career path. Like being a zookeeper.

I like paper. Part of this, of course, is because I love to read, but there's also the smell and the heft and the texture of it. Flipping through a book can be a wonderful experience even without the words on the pages, just because of the feel of paper on finger tips. Books smell good, too, whether they're new or old. So sometimes I flip through a book even if I don't feel like reading it, just for the feel of flipping through the book.

In a brief break this afternoon to rest my eyes from the monitor and let the world regain non-pixelated edges, I flipped through Desolation Island, the next of the Patrick O'Brian books in my queue (The Mauritius Command was fun, by the way). I wasn't paying a great deal of attention to the words, though I sometimes paused to sample a sentence. But an indented passage of text caught my eye, and I stopped to read

Before my bed, clear moonlight
Frost on the floor?
Raising head, I gaze at the moon
Bowing head, I think of my own country.

Winnie taught me that poem last weekend! At least, she tried to teach me; I remember how to say the first two lines in Cantonese, but when I was practicing I mistakenly said chicken head instead of raising head, and promptly forgot everything from there on. I laughed at the coincidence, and that broke the sour mood that I hadn't even realized I'd fallen into.

This morning, like so many other summer mornings, the sky over Berkeley was overcast. But the clouds broke in the afternoon to let the sun through, and so I extended my break to take a walk. I went to the office to pick up a book, then wandered through downtown Berkeley to Safeway to buy fruit. Jazz music, the smell of cheese, and a queue of customers wound their respective way out of Cheeseboard Pizza as I passed, and the smell of coffee and the sound of espresso machines wafted out of the cafes. I passed a seeing-eye dog leading a blind woman and a woman walking a blind dog with eyes clouded by cataracts. I heard conversations in Spanish and Mandarin and English, and perhaps in Russian and Greek as well. As I made my way home, the sound of the BART train passing through the tunnel mingled with traffic noise and shouts from a soccer game in the park. And I walked and looked and listened, and hummed Walking in Memphis under my breath, and was pleased with the world.

Cities and neighborhoods have personalities. Getting to know a place is a little like getting to know a person. There are first impressions, sometimes right and sometimes wrong; there are things the city shares with one person but not with another; there are shades and shifts and changes over time, and there are things that stay pretty much the same. And we get to like a place, or dislike it, or live with it happily, or ignore it, or treat it nobly or ignobly in many of the same ways we treat other people.

So I wandered, and I let my mind wander. I thought about how alien Berkeley felt when I first came, how it became more familiar over time, how it changed as friends arrived and left. When I stopped at the office to pick up one of my books on eigensolvers, I read an e-mail from a professor at College Park, who I hadn't heard from since I took his course on ODE theory as an undergrad; and so I was thinking about Maryland, too. The squirrels will be out in force on campus at this time of year, sporting around the end of McKeldin Mall like a particularly playful invading army. It's probably hot and humid, perhaps with a smell of rain in the air, quiet as campuses always are in the summer.

And then I came back and sat down and discovered that I didn't feel like returning to my strivings with Matlab. I picked up a fountain pen and thought for a moment about writing a letter; but after playing with it for a moment, much in the same spirit as I flipped through the book earlier in the afternoon, I put the pen down. I wasn't sure who I would write to. So here I write, and, it would seem, here you read.

And now I'm going to have some bread and water (a wonderful combination given an undeserved reputation by association with solitary confinement), and do some more work.

Something to ponder if you are interested in shock waves or phase transitions, or if you're just stuck in traffic -- could controlling a few cars stabilize the state of stable traffic flow when a jam would usually occur?

In college, we played the Vacuously True Statement Game. Example: Every time I've been abducted by space aliens, they've treated me well. The statement is true, since I've never been abducted by space aliens (at least to my knowledge). Related amusements include:

• The Alarmist Trivia Game -- Dihydrogen monoxide can be fatal when inhaled!
• The Escalating Exaggeration Game -- This pack must weight fifty pounds. What's that, fifty kilos? Yes, it's amazing that I'm not squashed under this fifty kiloton pack. This is one of Patxi's favorites.
• The New Constant Game -- Someday, I'll have an important class of numbers named after me. Like the set of all even primes. Like the Vacuously True Statement Game, this is Mike's invention.
• The Ridiculous Song Game -- Self-explanatory. Since this is one of my favorites, there are examples in the archives. Chopsticks, Edelweiss, and the Surprise Symphony are my favorite templates.
• The Flagstaff Game -- In which any geographical location you care to name is placed in relation to Flagstaff (usually within walking distance). This is also Patxi's contribution.
• The Ramsey Theory Bites Dance -- It doesn't, really. But after Mike and I got to prove the fifth or sixth variant, it did start to get old.
• The Spackle Convention -- If your friend told you he'd eat a gallon of spackle if he were shown wrong, would you, too, quickly change topics?
• X Wars -- How many sets of xeyes can your host support before it becomes unusable?
• Boardy -- This was a variable name from a chess program capable of bending the computer into pretzels, written in AP Computer Science by Will. Chant it over and over again, and it becomes fantastically funny. At least, it does if you're me. Or if you're Will, for that matter. I don't think it ever amused anyone else quite so much.

I think it's time to eat now.

From the farmer's market: fresh salmon and heirloom tomatoes
From the Cheeseboard: asiago bread and tomato salsa
From things around the kitchen: spices and peppers and onions
From Winnie: sweet corn on the cob

I'm really looking forward to dinner this evening.

There are days when editing, for me at least, is a way to slack off.

Now, in college I had a friendly argument with friends which went on intermittently for a month or so before we all dropped it. I claimed that vacuuming, washing dishes, cleaning the bathroom, and eating meals are all -- potentially, at least -- ways of slacking off. I like to eat, and I like to clean -- eat something messy, wipe a dish off, and admire the sparkle. It takes little effort, and the results are immediate. Now, these activities are necessary, and I would probably do them even if I didn't enjoy them. But I do enjoy them, and I figure that if I eat and clean when I have other, more urgent, and perhaps less enjoyable tasks pending, then the eating-and-cleaning time counts as goofing off. My friends disagreed, but they never really convinced me.

Therefore, I feel vaguely guilty for spending the afternoon editing when I should probably have been writing code or running experiments. I'm fond of my red pen, probably because very few other things in my life involve such a vivid primary color. Sit me down with a red pen, a cup of something warm, and a manuscript in progress, and I'll be happy as a clam. Writing new text is hard work, but revising existing text is fun. Maybe I enjoy editing for the same reasons that I enjoy cleaning: it's easy, and the results are immediate. Still, while I don't feel guilty about my editing time (certainly not as if I should be chastised with scorpions as one high-school teacher put it), I also think it's fair to say that I was slacking off. At least a little.

I also goof off in other ways, of course. I read books, and I've taken to watching television sometimes. I make up bad puns (does anyone else think about legally changing their name to Bic Pentameter?); I go for walks; I people-watch; I hang out with friends; I surf the web. Sometimes I just stare into space, though I can't imagine how I look any different when daydreaming than I do when proving a theorem or thinking out how to design a program. Apart from some extra enthusiasm about things mathematical and a tendency toward speech patterns more commonplace in the nineteenth century than in the twenty-first, my distractions and my habits of work and play are in the normal range for a modern-day male American in his mid-twenties. And so I'd guess that there are plenty of other folks out there who, like me, sometimes engage in goofing off of the necessary sort, whether by fixing a car, cleaning, or doing some other enjoyable chore in place of something more onerous.

Pete, feel free to disagree with me the next time you feel like goofing off.

• Currently drinking: Osymanthus fancy black tea

From Patrick O'Brian's The Mauritius Command:

   Certainly, said Stephen. To the ultimate crosstrees if you choose: I too am nimble as an ape.
   Jack was moved to ask whether there were earthbound apes, as compact as lead, afflicted with vertigo, possessed of two left hands and no sense of balance; but he had seen the startling effect of a challenge upon his friend, and apart from grunting as he thrust Stephen up through the lubber's hole, he remained silent until they were comfortably installed along the studding-sails, with their glasses trained upon the town.

What a wonderful sentence!

• Currently drinking: Black coffee

A cup of tea or a glass of lemonade, sipped in solitary quiet, is a wonderful thing. Eating alone is usually not as fun. But there are exceptions.

I eat fast. I often make cold meals of fruit, bread, and cheese, and when I do, it usually takes me more time to cut things up and wipe away the crumbs than it does to actually eat. Cold leftovers disappear go just as quickly. But I also like to cook, and it's a good thing. Cooking can be almost as meditative an activity as preparing tea (not quite, but almost); and I find it easier to take my time enjoying hot food. Also, while I enjoy fresh fruits and vegetables and bread, not all the food in the kitchen is fresh. I've eaten stale bread with molding cheese and wilting spinach. I've also used stale bread, Cheese of Ages, and wilted veggies to make french onion soup and omelette fillings. The soup and omelette were good; the sandwich was miserable.

This evening, I split the difference. I had fresh olive bread and good black cherries (on sale at Safeway), and I also made an omelette filled with the last of the munster cheese (which wasn't exactly bad, but needed to be used), the last of the zucchini (in about the same state as the munster), some tomato, and an excellent jalapeno. I cooked the vegetables for the omelette filling in olive oil with a little black pepper, and added them after the cheese melted. It was good, and it was hot, and I ate with gusto tempered by caution against burning my mouth.

What better way to end than with a hot beverage of choice?

• Currently drinking: Hot water with lime

• According to StarDate, the navy bounced the first voice transmission off the moon fifty years ago today.
• The CBC has an entertaining and informative brief history of beer.
• Smithsonian Magazine has an interesting article on the legend -- perhaps apocraphyl? -- of William Tell.
• In the July issue of The New York Review of Books there is a review entitled The Lost Art of Eating. It is inspired by Roy Strong's Feast: A Grand History of Eating, which I think I must add to my to-read list; but like most NYRB reviews, it wanders entertainingly far afield from the topic of the book.
• I've mentioned Mark Kurlansky's Salt: A World History before. It's a fascinating book. So is The Basque History of the World by the same author (who also wrote Cod: The Fish that Changed the World -- do I see a pattern?). I stumbled across a rather shorter history of salt online, but the book is more entertaining.

I think now is a good time to close the computer and take a walk.

This morning, I read an amusing revision of Asimov's three laws of robotics written by Mark Zimmermann after watching I, Robot. There was also an NPR segment on the same film earlier this week, and a review by Gary Westfahl at Locus Magazine. The review confirm what I'd guessed from the trailer: that I, Robot is an action movie more influenced by Will Smith than by Isaac Asimov. It seems a pity. But then, I enjoyed Independence Day; why should I be disappointed to hear that I, Robot is another movie in the same style?

In a talk given at BookExpo America, Ursala Le Guin commented on some assumptions about fantasy. Though none of her examples are drawn from science fiction, her points apply more generally. The third point she makes seems particularly apropos:

Assumption 3: Fantasy by definition concerns a Battle Between Good and Evil. This is the one where the cover copywriters shine. There are lots of fantasies about the Battle Between Good and Evil, the BBGE, sure. In them, you can tell the good guys from the evil guys by their white hats, or their white teeth, but not by what they do. They all behave exactly alike, with mindless and incessant violence, until the Problem of Evil is solved in a final orgy of savagery and a win for the good team.

Westfahl echoes Le Guin's sentiment in the first paragraph of his review:

Contrary to some published reports, the film I, Robot does in one respect powerfully recall the thoughts and writings of Isaac Asimov. Unfortunately, what came to my mind while watching the film had nothing to do with Asimov's robots, but was rather the statement that echoes through his early Foundation stories Violence ... is the last refuge of the incompetent which explains why Asimov's fans will regard this film as an appalling travesty.

Violence need not be the anathema of plot and character development; just look at the death toll in Hamlet, in which Shakespeare gives the final soliloquy to a secondary character for lack of any main characters left alive! And while Asimov created the character of Salvor Hardin, whose motto about violence is the source of Westfahl's quote, he also made Hari Seldon proficient in a judo-like martial art (twisting). Still, the point is made: a shoot-em-up cannot be fairly said to be based on Asimov's ideas if those ideas are displaced by mayhem.

A good screenplay based on an Asimov book could not be the same as the book. Books contain details which don't fit easily into the dialogue and scenery; and book authors can deliberately omit details in a way that would be hard for a screenwriter to manage. Peter Jackson's adaptation of The Lord of the Rings was successful in part because of the beauty of New Zealand's landscape and the power of Howard Shore's score, elements which were clearly not part of the books. Jackson paid respect to Tolkien's ideas and intentions where it was appropriate, and he interpreted, added, and elided elements as needed to craft a film. The result was a grand success, and, I think, faithful to the spirit of the book.

I think many of my favorite science fiction and fantasy books would be very difficult to adapt to the screen. Jackson managed better with Tolkien than I would have imagined, but attempts to interpret Frank Herbert, Robert Heinlein, and Isaac Asimov have all fallen flat. I think the thing that separates the successful from the luckless is the skill with which the filmmaker sifts out the character, plot, and high-level ideas and makes them independent of the author's crafting of details. Tolkien was a linguist; Heinlein was an engineer; Asimov was trained in the physical sciences. Vernor Vinge was a professor of computer science for a time; Kim Stanley Robinson received a doctorate in English; Jerry Pournelle studied a variety of things before he turned to writing (and picked up two doctoral degrees along the way). Mary Doria Russell, whose books I enjoyed recently, has a day job as a researcher in paleoanthropology. Not all my favorite science fiction authors hold advanced degrees, but almost all of them have some area of intense interest and long study, and it shows in the way they write. Tolkien wouldn't be Tolkien without the created languages. Heinlein wouldn't have been nearly such fun if he didn't tell the details of the control systems on his rocket ships. Part of the fun of Vinge is reading about his interstellar version of Usenet, or about his vision of programming turning into archaeology as computer systems become too complicated and baroque for anyone to truly understand. David Weber's battle scenes would fall flat without his interest in military history and his thoughtful analysis of the ways in which different technologies would necessarily change tactics and strategy. But none of these detailed interests would translate well into a movie.

I'd say that's a good reason to keep reading... as if I needed an excuse.

• Currently drinking: Oolong (which I now know means absent-minded in Cantonese)

I think the extended complex scaling technique sometimes used in quantum mechanics computations is extremely similar to the perfectly matched layer methods used for acoustics, Maxwell's equations, and (most recently) elastodynamics. Sadly, while I understand the notion of a PML at this point, I don't know enough about quantum mechanics to decipher much of the available literature on ECS.

One day I'll have to learn some quantum. And some statistical mechanics. And some economics. And some more topology. And some Mandarin. And...

To the tune of My Favorite Things:

I take my car to a quantum mechanic.
He's a little bit strange, and perhaps a bit manic.
He strokes Schrodinger's cat, and uncertainly sings:
What are a few of my favorite things?

My position! My momentum! All that folderol.
I can know one of two of my favorite things,
So why can't I know them all?

(The answer to that last why question has something to do with non-commutativity of certain operators -- as I understand it, that's really what the uncertainty principle is about. I might be able to say something more if I actually understood something about quantum mechanics; alas, knowing something about spectral theory for continuous self-adjoint operators is not quite the same.)

• Currently drinking: to the confusion of my foes?

I was at the SIAM Annual Meeting in Portland from Tuesday through today (Friday). However, I've had relatively little time accessing, and I've spent more time on the human sort of networking than on the computer sort. I'll catch up on e-mail and such over the next few days.

The technical program was interesting. Topics that I found particularly exciting included:

• Shear wave imaging

  When a doctor feels for lumps, she moves her fingers back and forth. A lump is a place where the subsurface tissue is more resistant to the shearing force that comes from rubbing across the surface. We already use ultrasound imaging, which involves compression waves traveling through tissue. Why not use the much more slowly-traveling shear waves, too?

• Splines and Boeing

  There was a keynote talk about computations done at Boeing using spline. The talk involved a lot of pretty pictures, and also a back of the envelope calculation in which the speaker estimated that there were probably about half a billion spline calculations done in Boeing systems every day.

  A half billion is a lot.

• Equation-free and multiscale models

  Mathematical modeling usually involves creatively fuzzy vision. If you want to model a weight hanging on a spring, you can try to model every atom in the system, and go nuts; you can do some averaging and model the spring by a set of partial differential equations, and keep people like me employed; or you can assume that the amount that the string stretches is roughly proportional to the amount of weight you hand on an end, do one experiment to find the constant of proportionality, and go for a walk.

  We have a lot of tools, both analytical and numerical, that work well for systems described by partial differential equations. But what about systems of particle interactions in which we're not smart enough to write down a continuous approximation? It turns out that it's sometimes enough to posit such an equation exists (and is continuous) -- without writing it down. You use your microscopic model to fill in what's happening in a few places, and then use the data at those points to fill in everywhere else. The idea is simple, the details are hard, and the whole effort is immensely interesting.

  It's also sort of astounding. How do you solve an equation without the equation? Equation-free modeling sounds like it ought to be the title of a Zen koan -- if Zen koans had titles and a flair for the technical -- but it was actually the title for one of the keynotes.

  A related area, less magical-sounding but equally profound, is multi-scale modeling. It's exactly what it sounds like: there are some things that happen very quickly and some things very fast, or there are some things that happen over a large area and some over a small area. If you looked at everything finely enough, you'd see the whole picture, but that's unbearably expensive. So you selectively put on glasses, and build some machinery to connect the very small to the very large.

• Implicit codes and software engineering

  We didn't want to tell the scientists they would have to change their codes a lot. The scientists hate that.

  Very true. I'm glad to see it recognized.

• Google

  We'll take Google as an example. Nobody knows quite what Google does, but we think it might be this.

  Web searching is a hard technical problem involving some very interesting ideas from numerical linear algebra. Marveling at the math is almost as much fun as marveling at Google.

• Eigenvalue problems

  I talked about one type of eigenvalue problem. Other people talked about different types of eigenvalue problems. I enjoyed the talks and the conversations.

More generally:

• Portland is impressive. There is a book store here that covers an entire city block, and a companion technical book store which is also extensive. Several of us went there this afternoon; we met others with the same idea. We should have just held the last session here.
• There are other impressive things about Portland, too, like the train system and the people. And did I mention the book store?
• Through Thursday, there were vendor booths with several major technical publishers and a handful of people selling software. I bought two books, a little monograph on Lanczos algorithms and Matrix Algorithms, Volume II: Eigensystems by Pete Stewart. I've intended to buy the latter since it came out -- a year ago? two? -- and I haven't finished gloating over it yet.
• I still find it astounding to watch human networks at work. I met a lot of people at the meeting -- that's much of the point, after all. Some of them I knew from reputation, some of them I didn't. In any case it usually took all of fifteen seconds of conversations to find someone we knew in common, and often a common research interest. Also, I'm always impressed by how friendly and approachable the people at these meetings are.
• I'm so glad that I took classes on fluid mechanics and finite element analysis. I cannot imagine enjoying this meeting half as much as I did if I knew nothing about those topics.
• My talk went well. I'm glad it's done.

While I'm finishing my coffee and waiting for clean socks from the drier, some notes on recent and moderately-recent reading.

• Henri Poincare. The Value of Science --

  Poincare was a luminary of mathematics and physics who contributed, among other things, to the study of dynamical systems (he won a prize for his work on the three-body problem) and topology (analysis situ, as it was known at the time). E.T. Bell called him the Last Univeralist for the breadth of his work. In addition to being a leading scientist, Poincare was a science writer, and The Value of Science is a translation of several of his popular science works from the end of his life, near the turn of the twentieth century.

  I've read some of The Value of Science, but I haven't exactly made rapid progress. I expect I would enjoy it more if I read French; while the translation is competent, it still has the odor of a translation about it. Also, while interesting, the topics covered are mostly familiar. The familiar topics and the slightly stilted translation together make my reading leisurely and sometimes drowsy.

• Patrick O'Brian. Post Captain and H.M.S. Surprise --

  I wish I read more books with lines in which one main character cries to the other You have debauched my sloth! The books are fun and easy to read, despite -- or perhaps even because of -- the frequent nautical jargon. The next two O'Brian books are in queue.

• Roger Zelazny. The Great Book of Amber --

  I bought this collection a while back while on a let's buy classic fantasy I haven't read kick. The Amber books are regarded as classic for a reason. There are some interesting premises, and the books move along smartly. I was glad to see the end of the last one, though. For all the plot twists -- and all the plotting -- the books seem to have an endlessly inconclusive quality to them, reminiscent of Neil Stephenson (but with a better editor).

• William Gibson. Pattern Recognition --

  One of my friends has commented that Stephenson's writing changes meaning completely if you don't pay attention to every word. I only half agree with him, but Pattern Recognition makes a persuasive argument for his case. Looking back, the plot seems a little off, but the writing is wry, witty, and dense in a way that makes it difficult to read some paragraphs only once. There are no cyber-cowboys or vat-grown ninjas, but the imagery is fully as developed and surrealistic as anything in Neuromancer and its successors.

• Bill Bryson. A Walk in the Woods --

  I'm only half done, but it's funny and fast-reading so far. If I like the second half as much as I liked the first, I'll probably check out some other things Bryson has written.

When Jim left last Tuesday for a week at home, he left behind a bag of donated zucchini. Eat it! I don't want to see it when I come back, he said.

So here are 2.5 ways to prepare zucchini if you're not the greatest zucchini fan. All were shared with and approved by Winnie, so there is at least one other person who thinks they're good ideas.

Zucchini stir fry:
I used baby bok choy, a green pepper, snap peas, and zucchini. It was seasoned with soy and served with a little beef (cooked separately).

Zucchini with eggs (1):
I used a small zucchini and a tomato, pan-cooked together with a little olive oil, black pepper, and salt. Then I added eggs, scrambled everything together, and added some cheese at the last minute.

Zucchini omelette (2):
This is a variant on zucchini and eggs. I pan-cooked zucchini, tomato, red onion, and green pepper in olive oil for the filling, with basil, black pepper, and salt for seasoning. The omelette was an ordinary omelette, with the some mozarella and some Munster added just before putting in the veggies and folding the entire thing.

Zucchini salsa:
I finely diced a small zucchini, lots of garlic, some tomatoes, some red onion, and some green pepper. I sauteed the zucchini and garlic in olive oil, which I used more generously than I sometimes do, and added black pepper and salt. Then I added the red onion, green pepper, and tomato, and cooked it all a little more. I think it would taste good without the second cooking, too. I mixed in a healthy dose of lime juice and served with the end of a two-day old baguette, which I sliced into thin rounds and toasted. I put the salsa in a bowl and arranged the toast in a double ring around the outside. It looked colorful and elegant -- at least to my eye -- and surely was one of the more appealing ways I've used up a zucchini, a fading pepper, and a slightly stale baguette end.

• Currently drinking: Hot water with lime and honey

Two minutes before completion, I lost the network connection to my machine on campus. Since I foolishly ran my hour-and-a-half simulation in the foreground, it was terminated when my secure shell session was terminated.

Joy.

Let's try something different for the moment: a mostly-unrewritten entry.

Usually, I write with great pauses between sentences. Sometimes the pauses last so long that I forget what I was writing in the previous sentence, or that I abandon a paragraph -- or an entry -- entirely. At other times, I write the same sentence four or five times, and constantly delete and re-type. I'm picky, and half the time I can't even form something grammatically correct the first time it comes out. Or if I can form something grammatically correct, it's technically incorrect, which is nearly as bad.

I am procrastinating now, though, from -- what else? -- writing. So this seems like a good experiment.

I write here for three reasons, really. The first is the reason that has kept me writing to myself for many years: I forget things. More specifically, I forget the chronological order in which things occur. Well, I sometimes forget other things, too -- like birthdays and people's names and where I put my glasses. But in terms of remembering events, I'm pretty good at keeping odd little details in my memory. I just forget the matrix in which those details should be embedded. And so I have a few notebooks of terse recounts of my days and weeks, which I doubt would be of much use or interest to anyone but me.

The second reason is to communicate with friends and family, which is really most of the set of people reading, I think. If someone else finds it amusing, that's fine, too. And for those arriving at these pages through a search engine: the proper spelling is teetotal, the conventional definition is to abstain completely from alcoholic beverages, and dictionary sites will probably serve you better than this search.

The third reason is to think. I do mathematics with pen or pencil in hand, and the pen is often moving, even when I'm staring into space. I take notes in classes that I find particularly difficult, even if I never look at the notes later. I write summaries of problems that I work on, even if I have no intention of sharing the summaries with anyone else. The act of writing forces ideas into a more concrete form, filters the mental fuzz, and enhances the memory. I can write some pretty incomprehensible garbage when I'm not thinking straight, but it's easy to recognize it as garbage once it's on paper.

This is not to say that I'm deliberately spending my time filling this page full of garbage. It is to say that some of the things I write have more to do with me writing than with you reading.

Even if there are no real meaty thoughts behind them, it's a joy to run fingers over the keyboard. It's almost as much fun as writing with a pen, though the two activities are different and suit different moods. I imagine I might get the same joy from playing a musical instrument, if there were any musical instruments that I played competently.

I'm listening to the radio. I'm waiting for a simulation to finish; it has about forty minutes left, which means that it's more than half finished. Sitting beside me is A Walk in the Woods, with the cover picture of a green forest and a bear's head peeking up over the subtitle bar at the bottom. On the other side is a pile of pages of scrap, intermixed with the marked-up pages of an old draft of the report I'm currently working on -- or avoiding working on, as the case may be. There are so many marks on the borders of the draft that it is hard to tell those pages from the pages of scrap paper. The pile is relatively neat, but I doubt the pages are in the right order, and I'm sure that the pages of the draft are mixed together with the pages of notes. And since I've processed most of the comments in the draft that actually meant anything for more than a minute after I wrote them, the state of disarray is just fine.

I don't think I had a face-to-face conversation for all of the day, unless you count the interaction with the clerk at Barnes and Noble. I talked to Winnie on the phone, of course, but beyond that, I don't think I had any conversations today. For that matter, I haven't had many conversations since the start of the past week. People are out of town, at home and at the office, and so days have been quiet. Suits my mood, it does. Still, I'm glad Winnie visited on Friday, and I'm looking forward to having dinner with her again tomorrow night.

And I'm actually really looking forward to my trip this coming week, even if it's a little bewildering to travel again so soon after I returned from Copenhagen. Well, perhaps it isn't that short a break.

Tap, tip, tap. Perhaps I should return to reading. Or perhaps I should return to editing.

I felt like a walk this afternoon. So I went to Barnes and Noble, where I got the next two Patrick O'Brian books and Bill Bryson's Walk in the Woods. After laughing so hard at the inebriated sloth in O'Brian's H.M.S. Surprise, I thought I would probably read the next in that series first. Instead, I read about the Applachian Trail for a while.

I opened all the windows and both the doors when I returned. It's a fine day, and the breeze passing through feels good.

• Currently drinking: Osymanthus black tea

During a break a little while ago, I found this article on the Bookshelf as Identity. I was reminded of an article a friend sent a while back, entitled The Library of Congress Comes Home. Both articles are about bookshelf organization, though from very different takes. And both concentrate on the topics of the books.

My bookshelves are topically organized only in very broad strokes. Books that have something to do with religion or philosophy mostly go on one shelf -- though that shelf also has my copy of The Smithsonian Book of Books and The Complete Guide to Calligraphy. I would say that this indicates something about my personal pantheon, except that the same shelf has Fermat's Enigma, Stairway Walks in San Francisco, The Pig Who Sang to the Moon, and Worms Eat My Garbage. Further down is a shelf which houses a few history books: From Dawn to Decadence, Africa in History, and The Soong Dynasty are there. So is Autumn Lightning, which is half history (the other half is autobiography). But wedged right next to those books are Kay's Tigana (fantasy), Zinnser's On Writing Well (what it sounds like), Brooks' The Mythical Man Month (software project management), Icke's Force of Symmetry (physics), Asimov's Azazel (humor), and an odd copy of SIAM Review (an applied math journal). Furthermore, Churchill's History of the English Speaking Peoples and Lewis's The Middle East are a couple shelves down; and Herotodus is again on the shelf with philosophy and religion, two books down from the Tao Te Ching and three from Marcus Aurelius.

So what's the correlation? Well, if you took all the books from one of my shelf and put them into a cardboard box, you'd probably find that they packed together pretty well. The philosophy shelf also happens to have a lot of books that are shaped oddly, and didn't fit that well with anything else -- the Book of Books in particular is very tall, and doesn't fit at all onto some shelves. Most of my science fiction fits neatly on the bookshelf by my bed, simply because those books are all paperbacks of roughly the same height, and taller books don't fit well on those shelves.

There's some shuffling over time, of course, as I take a book down for reading or simply for reference, and as I put back books that begin to clutter my desk. And the books in my office are a little more topically organized: mathematical analysis in one place, computer systems in another, mechanics in another, and linear algebra -- well, linear algebra moves about the shelves and about the office, but there's some sort of concentration between the books on technical writing and the books on analysis. Even there, though, I organize by physical shape and by the frequency with which I refer to things before I organize by topic. And it shows: there is no topical reason for the top-shelf mixture of books on statistics, asymptotics, special functions, and other amusements, except that a lot of them are Dover paperbacks with sort of similar shapes.

It's fortunate that my spatial memory is better than my temporal memory, or I'd lose all sense of where my books live. But if you spoke no English and were somehow tasked with finding a place for a stray tome from my collection, I suspect you would manage to find a good place for it. Just be careful if that place is the shelf o' philosophy. You might knock over the origami cat.

Still looking for an old bookmark to a technical paper, I found a bookmark to Nature's debate on open access. Alas, my opinions on the topic are not sufficiently well formulated that I care to write anything about them.

Going through my bookmarks in search of something else, I stumbled across this page of photos of skills found only in China. I think I might be able to sleep atop a chain link fence, too, if sufficiently motivated.

• Currently drinking: Black coffee

As a youngster, I often responded to inquiries about my day with I ate lunch; I had recess; and... um... I've changed in many ways, but my response to such pleasantries has changed little. I know people who can reply smoothly and quickly to such inquiries, and to other social pleasantries; I have not decided if the smoothness of their response comes from some quickness of thought that I lack, or whether some habit or reflex allows these people to handle such routine interactions without any thought.

When I spend a day writing and revising, re-reading papers I've cited, and generally chewing over the presentation of a few technical ideas, I have an even harder time answering social questions. Writing code, sketching calculations, and related pursuits can be wordless things, difficult to express even to someone who asks about them with more than a perfunctory social curiosity. But a day of wordsmithing, perhaps, engenders the opposite problem. It's all too easy to express the words I've been thinking about all day. Do you want to hear why local moment-matching approximations are so attractive for producing reduced models of RF resonators with anchor losses taken into account? Or would you like to hear how to formulate the analogue of Sommerfeld's radiation condition for linear time-harmonic elasticity problems? The answer, of course, is likely a resounding no: the question what's up? is an invitation to a smile and a nod, perhaps, but not to an impromptu lecture, let alone an impromptu research presentation. So I smile, I nod, and these days -- usually -- I keep my impulses in check and stick to safe topics of conversation, like what I had for lunch; at least, that's what I'll do until my mind has had time to warm to some more mutually entertaining topic.

I had New England clam chowder for lunch, and a cup of Russian Caravan tea afterward. And dinner was a scramble of leftovers, combined in a way that called for no particular culinary skill, with some spiced black tea later. Oh, and I spent some time writing, and some time managing my recipes. Or managing my references. Um...

• Currently drinking: Hot water with lime

On my way to a meeting on Thursday afternoon, I was caught in a river of capoieristas walking along Shattuck. I was late, and in a grim temper, and I was not well pleased by the slowness of the crowd. But two women in front of me were practicing samba as they walked, and when one of them stopped so suddenly that I nearly ran into her, she grinned such a cheerful apology that I couldn't help but grin back. I was tempted to skip the meeting altogether, and walk with the crowd to their final destination, to hear the merimbau played and perhaps to see a roda. But I resisted the temptation, and went to my meeting.

On Friday, I walked to school to receive a call from a collaborator. As I walked by the park near my home, I saw two men practicing forms. More specifically, they were practicing one of the forms of a style from southern China which a college acquaintance of mine practiced. I slowed for a moment, watching. The Chinese martial arts can be very graceful, and one of the men was quite smooth; the other had problems with his elbow. While I watched, the more experienced man turned to his neighbor and corrected the position of his elbow, showing how to set it up to cover against a strike to the ribs even as the hand parried a strike toward the head.

Last night, I was deep in H.M.S. Surprise by Patrick O'Brian, and came to a passage involving an inebriated sloth. I laughed until I had to put the book down to catch my breath. In time I recovered, and as I reached to pick up the book, I thought Wouldn't a drunken sloth school of martial arts be grand? Practitioners would learn how to plod slowly along tree branches for a few feet, then fall asleep with one arm and one leg wrapped around a branch, half-dangling from their perch. Advanced exponents would learn to miss their footing and fall artfully in a way that squashed opponents passing below.

I think that the Drunken Sloth style, along with the style of Bread Do, would be a wonderful addition to the mix of Hong Kong action movies. But for longer lasting interest, I'll keep watching the parks and the streets on my way to work.

Death is a conservative sort of fellow. He still rides a pale horse, and does his work with an old-fashioned hand scythe. But with the world as crowded as it is, Death needs some assistance with his busy rounds. Something so that he can quickly be reached if needed, wherever he may be.

Thus, the Grim Beeper.