Twelve Routes to Useless Computation

1. Start with nothing in mind

   How very Zen-sounding. How very useless. Even if the goal is only to explore a new tool or a new mathematical idea, there must be some goal to guide a computation.

2. Solve the wrong problem

   Also known as the build a swimming pool to avoid getting wet approach. This is a popular means for mathematicians to make themselves the butt of jokes ending with lines like consider a spherical cow.

3. Assume there exists a unique solution

   There is an old joke about a mathematician who wakes to see that his blanket is on fire, sees a bucket of water in the corner, exclaims A solution exists! and goes back to sleep. I know of no comparable joke about an engineer with thirty feet of rope with which to build a bridge across a forty-foot chasm, but there ought to be one.

4. Put the method before the problem

   You've done some work to reduce your problem to the solution of a large linear system, and you've decided to use dense Gaussian elimination with partial pivoting as your solution method. Your code runs slowly, so you buy a larger computer. After a month of painstaking work, you finally get an answer, which you proudly present to your boss. Your boss points out that while the equation 2x = b can indeed be solved using dense Gaussian elimination, dividing every element by two would have been much more economical, and fires you on the spot for gross incompetence.

5. Use the wrong level of abstraction

   One-dimensional calculations are often easier than calculations in two and three dimensions. That doesn't keep people from devising elaborate theorems about the behavior of an equation on an n-dimensional manifolds when all anybody really cares about is the behavior on the interval [0,1]. This error is a favorite of novice C++ and Java programmers who supplant a modicum of common sense with a ton of object-oriented jargon.

6. Avoid useful tools

   I'm not sure why people think it is more rigorous to write a half-assed code to solve a linear system (for example) rather than to use an existing library which is faster, more robust, better documented, and freely available. I'm also not sure why people solve medium-sized systems of linear equations by hand rather than use the computer. But there are people who do such things. May the Lord have mercy on their souls if they ever get between me and food in the process.

7. Insist on the wrong tools

   If you want to solve a 2-by-2 linear system, do it in MATLAB, or Octave, or on your calculator, or by hand. Do not write a C++ program with a class hierarchy that takes three pages to describe. This is, of course, situational -- a C++ program with a three-page class heirarchy may be the right approach if you're solving a variety of types of linear systems, all with special structure that you can use, and you want to organize your ideas into a coherent library.

8. Don't consult the literature

   It's good that you're a genius. We're all impressed that you managed to re-invent fire, the wheel, and the Edsel. Please be our competitor instead of our collaborator.

9. Blindly follow the literature

   The literature on computing contains a lot of very good ideas by very smart people. It also contains some ideas which were obviously written while the author was hallucinating, and subsequently were reviewed by three chimps and a hung-over undergrad. Even if you read with enough criticism to pass over papers in the latter category, you may be reading papers by very smart people who were solving a problem only superficially similar to your own. This error is often coupled with solving the wrong problem, putting the method before the problem, or insisting on useless tools.

10. Mis-understand the error sources

    If you model the Golden Gate bridge as a single degree of freedom system, fit your parameters very carefully, and use smart methods to figure out the resonant frequency of your model to a gazillion digits, that does not mean you know the resonant frequency of the Golden Gate to a gazillion digits. That doesn't keep people from claiming much higher accuracy than they really have -- and, upon later discovering that their answers don't match experiments, blaming the problem on roundoff error.

11. Fail to check the results

    You wrote down the equations, you did a lot of algebra, and you got a solution. Did you actually test the solution to see if it satisfied the equations? A computation that fails for want of a sanity check is like the five-thousand dollar computer that sacrifices itself to save a five cent fuse.

UPDATE: As Heidi trenchantly observes, a bout of temporary confusion led me to use base 9 for my title numbering.

A weekend in quotes

Rick and Sarah came to visit on Friday afternoon, and stayed until Saturday morning. We met with Winnie for dinner, and on Saturday morning, we walked her to her class, and then made one last pass about Berkeley before I took them to the BART station.

Jim, this is my brother Rick and his girlfriend Sarah. Rick, Sarah, this is my advisor.
I see the family resemblance. How long are you here?
We just came to vacation this week. We leave tomorrow.
Jim to me: Some day, you'll be able to do such things, too.

And we've been here before.
Dave, you could have made up a completely different story about the gate this time, and we probably would have believed you.

It's milk tea with tapioca balls.
Oh?
I think it's originally Taiwanese.
Huh.

And here's Zachary's Pizza -- right between two of my favorite book stores
Do you want to go in?
No, I'm hungry, let's just get pizza.

You spell out words when you don't understand each other? And give dictionary definitions! Ha!
Yes...
Rick and I usually just exaggerate our pronunciations when we don't understand.

What would you like for breakfast?
Schweze!
Ham? Eggs? Chai? Cocoa?
Just schweze. And some milk.

---

After Rick and Sarah left, I went to the office until Winnie got out of class. As I walked down the hill to meet her, I ran into my flatmate Jim and one of his buddies.

Anyhow, as I was saying, humor works in threes. You would realize this if you watched as much stand-up comedy as I do.
Wait, let me see if I have this straight. One of us is developing a mathematical theory of humor, and it's not me?
He has you there, Jim. And he only had to say it once to be funny.

Jim was pretty tipsy, and was loudly declaiming his theory of humor to us all, when we ran into a pair of Mormon missionaries walking in the opposite direction. Jim was insulting, the missionaries were earnest and condescending, and the whole situation was amusing.

---

Winnie took off for dinner with friends in the south bay, and I had dinner with my former neighbors and crazy Basque former roommate. After dinner, we saw Patxi's pictures from his trip, and then watched Real Genius.

One million dollars! Why are you laughing, Dave?
That didn't sound evil. In fact, rather the opposite.
What?
It sounded sultry, really.
No! It was evil! Back me up, Mike.
I think I have to agree with Dave on this one. That did sound sultry.

---

Sunday, I went to the south bay, and Winnie and I spent the day on pancakes, walking around the lake, tea, miniature golf, air hockey, and sushi. And trying to see what benefits we could get for Winnie's birthday.

It's my birthday!
Happy birthday! I'd have put a candle in your Swedish pancakes, but it would have just fallen over anyhow.

Do you mind if we go ahead? It's his birthday.
That's fine, we're in no rush.
But it's my birthday, too!
We're slow, though. Do you really want those hellions to follow us through every hole in the course?
Okay...
Thank you. You know, he was probably just as rowdy when he was that age.
Not David!

It's my birthday!
Happy birthday! It'll be about twenty minutes.
I guess they don't have birthday specials here.

Hebetudinous

From A.Word.A.Day today:

hebetudinous (heb-i-TOOD-n-uhs) adj: Dull or lethargic, especially relating to the mind.

Schweze

Rick and Sarah (my younger brother and his girlfriend) came to visit the Bay Area this week. They toured around SF on Monday and Tuesday, camped in the redwoods Wednesday and Thursday, and came to visit me in Berkeley yesterday. It was a good visit, and I may write more later, but first I want to write a recipe that I finally got from Sarah after forgetting several times to ask. This is a Burmese dessert. I've probably bungled the spelling of the name, but however it is spelled, it tastes great.

1. 1 cup cream of wheat
2. 1 cup sugar
3. 1/4 tsp salt
4. 2 can light coconut milk
5. 2 tbsp butter
6. 2 eggs
7. 3/4 cup raisins
8. 1/4 cup poppy seeds (or a bit less -- a palmful)

Separate the egg yolks from the whites. Mix together the cream of wheat, sugar, salt, coconut milk, butter, and beaten egg yolks in a sauce pot; stir and allow to cook for 15-20 minutes. Meanwhile, whisk the egg whites until they form peaks. Fold the egg whites, raisins, and poppy seeds into the mixture in the pot. Pour the mix into an 8 in square baking pan and bake at 350-400 Farenheit for 40-60 minutes, until the top is a light golden brown.

Crossed wires

I decided to have a cup of coffee, sit in the sun, and read another chapter of Rapid Development after lunch. So I walked to the Free Speech Movement Cafe in the center of campus, sat, and spent a pleasant 45 minutes or so sipping and reading and thinking.

As I walked to the cafe, though, the Campanille played one of its usual lunch songs, and something in the back of my head insisted the tune was familiar. It took a minute or two, but as I came near the cafe, I realized that it sounded an awful lot like one of the theme songs from Tetris Attack, a game which was often played in the dorm where I lived for my last two years as an undergraduate. One of my flat mates at the time made up words for the tune, which went something like:

Killer crabs are coming to get you.
They do not like you.
They want to eat you.
They are the killer crabs.

If the words sound inane, consider that at the time, most of the composer's attention was directed toward not getting squashed.

While I stood in line, I thought about how often this type of mental criss-crossing happens to me. The first few times I heard FSM Cafe I thought of Finite State Machines rather than the Free Speech Movement; I still sometimes get confused when someone says NDA and means Non-Disclosure Agreement instead of Non-Deterministic Automata; depending on the conversation, ROM can mean Reduced Order Model or Read-Only Memory; and when looking through the Springer sale books earlier in the week, I confused myself immensely -- not for the first time -- by reading DFT as Discrete Fourier Transform where the author meant Density Functional Theory.

I wonder how confused I'd get if I worked for the government?

The Yellow Catalog

The Springer Yellow Sale on mathematical books is here. I made the mistake of stopping by the book store in the student union (for a completely non-book-related errand), saw the sale signs, and walked away an hour later with Brenner and Scott's The Mathematical Theory of Finite Element Methods and a big smile. I almost got Marsden and Ratiu's book on symmetry in mechanics, too, or Osher and Fedkiw's level set book. But I resisted temptation.

Hooray for books!

The Progress Pen Diary

I love my fountain pen, and I love LaTeX, but I think it's as well that I haven't found a way to combine them...

Day 1:
Just bought a new Progress Pen. Here's what the advertising brochure says:

Congratulations on your purchase of the Millennium Progress Pen. This state-of-the-art fountain pen has a built-in typesetting engine based on the popular and powerful LaTeX program. Bring the typeset beauty of LaTeX to your handwritten documents!

How exciting!

Day 2:
Just booted my new pen. Waited an hour while it dialed up and downloaded all the latest security patches. By that time, I forgot what I was going to write.

Day 3:
I've decided to install Linux on the pen. Hope it goes well.

Day 4:
It didn't go well. Turns out that my pen nib is only supported by an experimental kernel version, and it took some time to cross-compile the kernel on my desktop (I didn't want to install the Pen version of gcc). I'm going to try again this evening.

Day 5:
I wrote Hello World! It took me a while to figure out that I had to specify the document class before I could actually start typing, though. Also, my pen kept complaining about a runaway argument the first time I tried to make my document.

Day 6:
Today, I wrote a Makefile for my pen, so that I don't have to remember as long a sequence of Morse code to be tapped into the button at the top of the barrel in order to get the ink to start flowing.

Day 7:
With the help of The LaTeX companion, I figured out how to adjust the margins when I write lists with my pen. I still haven't figured out how to place figures, though.

Day 8:
I wrote a letter to a friend today. Won't she be surprised at how clear my handwriting has become! I can produce neat documents so much more quickly with my Progress Pen!

• Currently drinking: Coffee

Yee-haw

Yee-haw is not a foreign policy
-- seen on a Berkeley shop window

Yesterday mid-afternoon, after Winnie finished her class and I finished writing some documentation, we took a walk toward the Berkeley Marina. We did not, however, actually make it to the Berkeley Marina. Instead, we ended up wandering around Fifth Street, which resembles nothing so much as an outdoor mall. There were a variety of shops that sold clothing and furniture -- or perhaps they sold image, since it seemed that the less fabric was involved in a piece of clothing, the higher the price tag was likely to be. Fifth Street is also home to a branch of Cody's Books, and a branch of Peet's Coffee and Tea, too, and I approve of them, whatever I may think of clothing stores.

The Paper that Will Not Die is in the hands of my co-authors. I've written about ten pages of draft documentation for HiQLab (a finite element code I'm developing which I've mentioned before, if not by that name). I finished reading Count Zero (Gibson) and Joel on Software (Spolsky), and I've started reading The Surgeon's Mate (O'Brian) and re-reading Rapid Development (McConnell). I made curry on Friday night, filled up on bread yesterday afternoon, and have no idea what I'll have for dinner tonight -- except that I'll have masala chai with whatever it is. I took lunch breaks longer than ten minutes yesterday and today: yesterday, Christof and I had burritos at a place around the corner, and today we ate at a Japanese place on the south side of campus (I had veggie udon). And so a weekend is spent.

Special K: Take 2

Upon my arrival home last night:

D: You should help finish the vat o' noodles in the fridge.
J: I'll do that. By the way, what are you going to do about that milk?
D: Milk?
J: Yeah, the bad stuff that's a week past the expiration date. Elena had her coffee before I had cereal yesterday, so I got a heads-up.
D: Oh! I'd never had Special K before, and I just thought that was what tasted terrible.
J: And you bought two boxes!

Around this time, Jim began to laugh, and ceased to communicate effectively for a minute or two. After that, we established that I'd bought the milk at Long's just a day ago; that there was a sale on Special K; and that Jim had bought a replacement gallon which was sitting in the fridge beside the sour milk.

I ate a bowl of Special K this morning. Guess what? It tasted pretty good.

• Currently drinking: Black coffee

Editing fool

I am revising a paper, and I'm in the middle of a particularly thorny section. In an earlier round of editing, I scribbled in the margin that I would like a cleaner presentation of this section; now, I've decided to quit procrastinating and actually clean it. In the process, I've gone from thinking the author is a lot smarter than I am to thinking what was this idiot author thinking? Of course, I'm the author who is the target of this alternate admiration and accusation.

My current method of revising papers involves a fountain pen, a legal pad, and a lot of time writing longhand from a printed page. One advantage of this method is that it's impossible for me to skim, no matter how familiar I am with the contents of the formula; consequently, I catch a lot of punctuation errors, notational inconsistencies, and similar types of mistakes. When I re-write my theorems longhand, I also more easily find places where I've been too loquacious (and my fingers start to ache) or too curt (so that I can hardly decipher what that fool author wrote).

The main disadvantage of this editing method is that I go through ink cartridges quickly. I suppose I'll visit the stationery store when I walk to Soda tomorrow.

Special K

When I went shopping for milk and cereal and machine oil yesterday, I picked up two boxes of Special K. I hadn't had Special K before, but it was on sale, and I'm not a picky eater, so I figured I would give it a try. So this morning, I poured myself a bowl of Special K -- and it was awful.

Have you ever had a multivitamin that makes you feel sick? I have a bottle of them at home, which I bought some time ago with good intentions of taking one a day. It's probably just the brand, but on no fewer than four occasions, I've tried taking them, only to discover that if I have a vitamin pill with my breakfast bowl, the back of my mouth fills with an awful metallic taste and neither vitamin nor cereal will stay down. Special K delivers that same special taste at the back of my tongue, the sort of flavor you might expect to get if you took light corn syrup and dissolved a lot of copper and sulfur and iron into it. It doesn't make me very nauseous, though, so I'll probably finish the box and rinse with mouthwash after each bowl, and never buy Special K again.

Well-intentioned advice can leave an awful taste in the throat, too. I got a dose of Special K advice today (mixed with some pretty good advice). Afterward, I spent a few hours wanting to avoid the world, and so I took my work home. Actually, that's overly dramatic -- I went home because my lunch was there, and because I wanted to sit away from my books and computer resources while I worked on a writing task. But I did leave the office in a markedly anti-social mood, which has fortunately now passed.

• Currently drinking: Rooibos

Free food

Last night when I left Soda, I took with me a tray of fried noodles with chicken and shrimp that was left over from an IBM recruiting event. Huzzah for free food! Several meals worth of free food, actually.

I think I should go home and eat some of that food now.

Mental models

I spent an hour or two yesterday evening correcting a problem in the error-handling code for one of the finite element programs I develop. Today, I spent some hours tracking down a problem in the eigs routine in MATLAB R14. There were two issues, one of them subtle and the other obvious but hard to locate (it resulted in a negative value which would be theoretically impossible -- even in floating point -- if things were working right). This evening, I walked to Long's to buy machine oil so that I could fix the office door lock, which had become nearly impossible to open.

In total, I've spent about half the productive hours since this time yesterday working on fixing problems with one thing or the other. But it's easy to see how those few hours could have become an entire week. So why didn't they?

The reason I'm spending this evening trying to clarify several pages of tedious algebra that I wrote a year ago rather than trying to diagnose problems with eigs and locks and sealing wax is that I have a set of mental models -- of all sorts of things -- that I can employ to find likely problem causes and solutions. My mental model of a lock is pretty crude -- you push in the key and it lifts the pins -- but it's sufficient to tell me that a little oil will probably help things along. My mental model of what goes on inside of eigs is a good bit more sophisticated, and includes a general mathematical component (which is what told me something was very wrong when I got negative numbers for this particular problem), a software architecture component (which told me where to start looking in a thousand line mass of MATLAB code), and a numerical analysis component (which told me why one of the bugs has probably remained undiagnosed for the past several years, and has made little difference to many users). My mental model of my own code is even more sophisticated, since I wrote the thing, and since I've been writing similar codes -- and thinking about how they should be written -- for a few years now.

Now, this collection of mental models is pretty handy for me. Some of those models contain a lot of details that few other people know about, which is probably why people knock on my office doors and ask me questions and then get excited by the simple (sometimes) answers and go off to do cool things (this is how most of my current collaborations got started). But I have not yet figured out how to do a telepathic brain dump to instantly teach another person everything I know about computer arithmetic or real analysis or mixed-language software engineering. I've been tuning some of those skills for over a decade, and while it takes me less time to teach them than it did for me to learn them, it's not an instantaneous thing. But I have more ideas than time, and I would dearly love to give someone enough of my mental models to make some headway on the ideas I end up neglecting.

I suppose I ought to finish being a graduate student before I start aspiring to take on students of my own.

• Currently drinking: Jasmine tea

Microsoft

Bill Gates is coming to speak at the Berkeley campus this Friday, and the CS graduate student mailing list is full of chatter. There have been several announcements for tickets; and a few mailings about organizing a possible protest, mostly from people who think it is a good idea, but also from at least one person who thinks a protest would be disrespectful to a guest. I have enough on my plate that I don't plan to go to either talk -- I'll go to talks with more information density if I go to any this week -- but all the sound and fury has set me to thinking: why do so many people hate Microsoft?

I do most of my work on Linux boxes, and split the remainder of the time using either Windows or some other UNIX variant (usually Solaris, sometimes HPUX). The tools I use -- LaTeX, gcc (and g77 and g++), emacs, Matlab, and a host of numerical libraries -- play reasonably nicely together under Linux, and I know how to fix things when they don't. My desktop environment is sufficiently transparent by now that I can concentrate on doing work rather than on working around glitches. And I'm happy to be in a situation where I'm encouraged to distribute my software freely, since academic CS departments produce ideas as their primary artifact, and code is just one means of distribution.

Now, suppose I were to change any of the variables involved. What if I hadn't learned a lot about UNIX and related systems through exposure as an undergraduate and through long-time use? What if I didn't spend so much time working with numerical software where the ability to mix languages is so critical? What if I spent less time writing mathematics and wanted to spend more time writing leaflets? What if my presentations included fewer equations and more media clips? What if I was trying to write programs for a mass market? Or -- heavens help me -- what if my favorite game were something other than Tetris?

For me, it takes very little time using a Windows system -- even if something like Cygwin is installed -- before I realize that it doesn't have all the facilities of a well-configured Linux box. I remember this every time I try to recompile and debug my numerical codes for Windows, and find myself missing some favorite tool. There is no valgrind for Windows, and compiling MEX files that combine Fortran and C++ is a lot harder there. On the other hand, if I want to play video games with snazzy graphics, I'm going to use Windows. And as frustrated as I can get during those rare times when I have to use Word or PowerPoint, trying to use OpenOffice is still worse.

Linux is not worse than Windows. Windows is not worse than Linux. If I had to choose, I would probably rather have Linux, since it personally supports more of the tools I use (at least, tools that I use now -- I wrote closed-source Windows code part-time as a high school student and an undergrad, and tools like Borland C++ and Delphi were awesome for the type of work that I did then). I'm also a graduate student in computer science, which means both that I like to read source code sometimes and that I'm fully aware when I pay for software that I might rather be buying food or books or burlap sacks full of Lithuanian gerbil food. Okay, perhaps not the gerbil food, but you get the point. In my present circumstances, using Linux makes a lot of sense. But in other circumstances, it doesn't make so much sense, and I'm not so biased that I'm going to shun all Micro$oft software to make some sort of statement.

Bill Gates is a businessman whose name lends itself to bad puns (of course, I think it's hilarious that Richard M. Stallman is always referred to as rms -- the same initials used for root mean square -- so perhaps I'm a bad judge of name pun-ability). Microsoft is a business, and while I think some of the strategies they use are questionable, I don't think it's a Blood-Sucking Vampire Company (suck you dry in ten minutes or the next death is free!). If you want to be outraged, be outraged at a tobacco company. If you want to ponder questionable business ethics, look at medical insurance operations. For that matter, look at Haliburton. There are bigger fish to fry than Microsoft.

Besides, oh ye open source advocates, Microsoft is good for Linux. Yes, they break standards, and make interoperation a pain in the ass. They also have user interface people who don't think ps -a | awk '/matlab/ { print $1 }' | kill -9 is an intuitive way to stop an errant process. Most of Linux's office software uses interfaces similar to Office products, and in the areas where the two diverge, it's not always the open source version that's doing it right. And LISP may beat VBA hands-down as a scripting language -- it's certainly more elegant -- but do you really want to have to teach recursive thinking to a business major who dropped an introductory CS class after two weeks out of utter frustration (and out of the clever realization that MIS majors might have more time to pursue members of the opposite sex, get drunk, and scope out the Lithuanian gerbil food black market)?

Write useful software that runs on more than one platform. Analyze Microsoft's flaws and tell the world in a way that forces Microsoft to fix the problem or be punished in the market. And when in Berkeley, perhaps, protest, if only so you can tell your grandchildren about it when they start asking embarrassing questions about your past history dealing Lithuanian gerbil food. But really hating Microsoft is probably a waste of moral outrage, and certainly a waste of time.

• Currently drinking: More rooibos

For Dummies

Who first said something or someone was too stupid for words? It's an unfortunate phrase, since as English speakers we have a lot of words at our disposal to say how stupid something might be. Whether it was coined out of a (misplaced) surplus of diplomacy or a deficit of creativity, it is hardly as cutting a comment as it might once have been. That is because we are entering The Age of Aquarius for Dummies!

I did not see The Age of Aquarius for Dummies in Barnes and Noble. I did see Chihuahuas for Dummies, and Hockey for Dummies, and RF Engineering for Dummies. If I spent a little more time browsing in Barnes and Noble and a little less time staring at the shelves in the math library or the shelves in my office, I might start to automatically associate yellow covers with the phrase For Dummies; but I have too many Springer math books with bright yellow covers, and a title like Perturbation Theory of Linear Operators for Dummies seems unlikely to yield much profit. I also flipped through an essay in The Philosophy of the Simpsons about Lisa Simpson and American Anti-Intellectualism (it was after the chapter on Homer and Aristotle).

The For Dummies series doesn't particularly bother me -- no more than the woman with the worn pump sneakers making asthmatic-pug-dog noises who dawdled up the hill in front of me this morning. It's more like mushrooms growing after a rain storm, paper mushrooms with virulent yellow covers which are fascinating to observe and perhaps, with some expert guidance to help avoid unfortunate side effects like hallucination and death, good to eat.

I passed the Dummies books by on general principle, but I did buy something from Barnes and Noble this weekend. Actually, I bought two somethings. First, I got the next book in O'Brian's Aubrey and Maturin series, which I will probably put info my fiction reading queue immediately after Count Zero. Second, I bought Joel on Software, a collection of essays much like those on the web site www.joelonsoftware.com, which is amusing for many of the same reasons most things written by Eric S. Raymond are amusing. The essays are insightful, and possibly relevant to me as a software worker... but who am I kidding? I got it because of lines about carpenters who are only allowed to use nails and they stamp them into the wood with tap-dancing shoes because nobody told them about hammers. The book is funny.

Of course, this may be the same sort of humor that led to Dave, Patxi, and I gasping with laughter over our idea of putting a T-Rex skeleton on a shake table fitting it with sensors, hiring undergrads to wrap wet towels around the joints, and trying to use this to build an experimentally verified single degree-of-freedom model for a running dinosaur. We thought it was hilarious; Winnie and Esther were mildly amused, and most of that amusement probably came from watching us laugh. But while ridiculous jokes, bad puns, and poetry about branch predictors may not be the best way to win friends and influence people, they're still a lot of fun for me and thee (assuming thou hast as quirky a sense of humor as I have).

On an unrelated note: Winnie and I walked to the Pacific East Mall in El Cerrito on Saturday in order to have some pho and look at Chinese language books (I found a book with color pictures of espresso drinks which was pretty, if incomprehensible). There I learned a valuable life lesson: soda drink with preserved plums should properly be translated as carbonated brine with brown lumps. Exploration is good, but perhaps next time we'll stick to lemonade or Thai iced tea.

Fallacies, fallacies

My office mate sent me this classification of various fallacies from 1962. How many of them have you seen used this week?

Gardening at night

I'm alone in the office now. Perhaps not so surprising, given that it's 11:30 on a Sunday. I finished what I needed to finish this weekend, if not all that I wanted to finish; and so now I'm taking a few minutes to just enjoy the quiet.

When it's just me here, I can listen to the radio on speakers rather than on earphones (the program right now is World Cafe, a PRI program). I can take breaks to stretch or practice kicks without unnerving anyone. I can pace, or hum absent-mindedly, or gaze into space without unintenionally staring at someone (I'm told this can be unnerving).

I appreciate my time alone, whether it's spent working or playing or just thinking. I think I appreciate it more late in the evening; social graces take some effort for me, and when I start to wind down for the day, I become even more reticent than usual. I'll smile; I'll listen, and even listen actively; but I won't feel like saying anything for myself. So ask early if you want to know what I thought about that REM song, or about the two gentlemen practicing in the park this morning. (A word to the wise: guard your head, particularly if you favor a stance with your weight balanced forward -- and if you're going to use that style of leg block, put some thought into covering your groin, too.)

Mathematical book reviews

In the most recent SIAM News, there is an article on mathematical fiction. I read it and added several more books to my reading list. I was pleased to see that Kasman's list included Clifton Fadiman's Mathematical Magpie, which was one of the books I enjoyed from the Bel Air library when I was in high school.

Actually, most of the SIAM News book reviews make interesting reading. I should add that the books are usually accessible to a non-specialist audience. Quickly browsing through recent issues, I was also reminded of Philip Davis's review of a book of scientist's diaries. And now my reading list is even longer.

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.