^zhurnal - v.0.09

This is Volume 0.09 of the ^zhurnal --- musings on mind, method, metaphor, and matters miscellaneous ... a rather cluttered set of sporadic Good Mistakes. What's it all about? Maybe "... to create moments of philosophy --- that is, to pass from opinion to thought ...." It's also the journal of ^z = Mark Zimmermann. See the ZhurnalyWiki on zhurnaly.com for a parallel "live" Wiki experiment. For back issues of the ^zhurnal see Volumes 0.01, 0.02, ... 0.41, 0.42, ... Current Volume. Send comments & suggestions to "z (at) his (dot) com". Thank you! (Copyright © 1999-2004 by Mark Zimmermann.)


Last week John W. Tukey died; he was 85 years old. Tukey was a Princeton professor, ostensibly a statistician, who coined the words "software" and "bit". He rediscovered and popularized the Fast Fourier Transform ("FFT"), a hack worth knowing both for its beauty and its utility.

Fourier Transforms (FTs) map information from one space to another. The best examples are from the world of music. Consider, for starters, a note --- a single pure tone. On the one hand, it's an oscillating pressure wave in the air, a wiggle on an oscilloscope or phonograph record groove, a sequence of numbers stored on a CD or in a computer's memory. That's the tone in the time domain. But the same information can also be represented as a note on the musical scale: a static description of the frequency and amplitude and phase, essentially timeless. "Play me an A440." That's the tone in the frequency domain.

FTs are magical mathematical transporters that take data back and forth between frequency and time universes. They work for complex chords and sequences, the same way that an orchestra can turn sheet music into a symphony (and, inversely, a Mozart can hear a performance and write it down). FTs also work on images (think holograms), on quantum mechanical particles (think wavefunctions), on interstellar signals (think radio astronomy), on voices (think digital cellphones), and on a host of other things. FTs are vital for signal processing, noise reduction, and efficient information transmission.

But FTs are also horrendously expensive to compute --- or rather, they used to be, pre-Tukey, pre-FFT. Take 1,000 numbers, perhaps representing 0.1 second of ordinary speech. To Fourier Transform them by the obvious method takes about 1,000 * 1,000 * 1,000 operations = a billion multiplications and additions. That's marginally possible, today, with fancy computers. But it's not cheap, it doesn't fit into a handset, and it doesn't scale. The computational cost gets worse like the cube of the number of samples that have to be processed.

But there's a better way. Mathematicians discovered that the FT process was full of regular patterns and could be decomposed into simpler sub-steps. The 1,000 by 1,000 FT matrix of a million numbers can be factored into 10 pieces --- 10 clever sparse matrices that multiply together to give the original FT, but that each are mostly full of zeroes. (Multiplying by zero is easy!) A billion operations collapse into only ~10,000. And the factoring trick scales up; it grows slowly, like N*log(N) instead of exploding like N cubed. A million numbers can be transformed in ~20 million operations instead of 1,000,000,000,000,000,000. Amazing savings!

That's the Fast Fourier Transform, aka FFT. Dedicated mathematicians figured it out, published it in their obscure journals, and moved on to prove other theorems. A few decades later Tukey and colleagues rediscovered the FFT and realized how valuable it might be --- with the newly-developed programmable digital computers to do the arithmetic. The rest, as they say, is history.

John Tukey did many things besides uncovering the FFT. I was lucky enough to meet him ca. 1990 and showed him some of my work on user interfaces for free text information retrieval --- key parts of which he had anticipated and implemented 30 years earlier! (See "KWICs & Chinks & Chunks", the ^zhurnal entry of 31 January 2000, for the story of the JWT-^z encounter. See also "FTIR Desiderata" and "FTIR Philosophy" for more about the subject, and consult the FreeText archive at http://www.his.com/~z/c/ for annotated C source code, compiled executables, and implementation examples.)

John W. Tukey --- creative, helpful person. Requiescat in Pace.

- Monday, July 31, 2000 at 05:55:32 (EDT)


"Developers are from Pluto, Users are from Mercury" describes the chasm between many programmers (especially those working on large-scale software projects) and the ultimate customers of their craft. So often the people writing code lack any clear mental image of what real users need to do, how they operate, and why they demand certain features. So often the people using computers lack any clear mental image of the challenges programmers face in designing algorithms, controlling complexity, and implementing reliable systems. So often the managers on both sides of the fence fail to communicate --- and so often software is late, over budget, and dysfunctional.

There are no simple solutions. The natural bureaucratic path --- building walls between the two worlds, insisting on rigidly-defined "requirements", and pushing projects to meet predefined milestones --- almost guarantees failure. Fine code has to evolve from a collaborative venture involving programmers and users in close communion. It takes time and money, creativity and perseverance, deep thought and mutual respect.

- Saturday, July 29, 2000 at 13:55:56 (EDT)

Round Table Musings

Philosophy Breakfast conversations to kick off a new year: Thanks as always to MK, DW, AP, JJ, JB, BW, BD, GdM, JC, et al. --- for their many gifts.

- Thursday, July 27, 2000 at 06:29:54 (EDT)

Life & Lies

A short month of Philosophy Breakfast table discussions: Thanks again to BW, JC, BD, GdM, AP, JB, JJ, et al.!

- Tuesday, July 25, 2000 at 20:56:21 (EDT)

Foam on the Ocean

Albert Schweitzer in his autobiography Out of My Life and Thought (translated by A. B. Lemke) writes (in Chap. 9, "I Resolve to Become a Jungle Doctor") about his decision:
"Long ago in my student days I had thought about it. It struck me as inconceivable that I should be allowed to lead such a happy life while I saw so many people around me struggling with sorrow and suffering. Even at school I had felt stirred whenever I caught a glimpse of the miserable home surroundings of some of my classmates and compared them with the ideal conditions in which we children of the parsonage at Günsbach had lived. At the university, enjoying the good fortune of studying and even getting some results in scholarship and the arts, I could not help but think continually of others who were denied that good fortune by their material circumstances or their health."
"One brilliant summer morning at Günsbach, during the Whitsuntide holidays --- it was in 1896 --- as I awoke, the thought came to me that I must not accept this good fortune as a matter of course, but must give something in return.
"While outside the birds sang I reflected on this thought, and before I had gotten up I came to the conclusion that until I was thirty I could consider myself justified in devoting myself to scholarship and the arts, but after that I would devote myself directly to serving humanity. ... What the character of my future activities would be was not yet clear to me. I left it to chance to guide me. Only one thing was certain, that it must be direct human service, however inconspicuous its sphere."

Schweitzer explored working with the homeless, with orphans or neglected children, and with former criminals --- but was frustrated by the impossibility of doing much outside official channels and existing organizations. He was driven by his personal religion (Christianity) and philosophy to serve as an individual. When he discovered the desperate need for medical care in the Congo, he told his friends and relatives that he was abandoning his career as a concert musician and theologian to become a physician. They were dumbfounded and tried to dissuade him. Schweitzer comments, tongue in cheek, that "The attitude of people who did not try to explore my feelings, but regarded me as a precocious young man not quite right in the head and treated me with correspondingly affectionate ridicule, represented a real kindness."

Albert Schweitzer then gets to the core of the matter: Who should make such personal sacrifices?

"As a man of independent action, I have since that time been approached for my opinion and advice by many people who wanted to risk a similar venture. Only in comparatively few cases have I taken the responsibility of giving them encouragement. I often had to recognize that the need 'to do something special' was born of a restless spirit. Such people wanted to dedicate themselves to larger tasks because those that lay nearest did not satisfy them. Often, too, it was evident that they were motivated by quite secondary considerations. Only a person who finds value in any kind of activity and who gives of himself with a full sense of service has the right to choose an exceptional task instead of following a common path. Only a person who feels his preference to be a matter of course, not something out of the ordinary, and who has no thought of heroism but only of a duty undertaken with sober enthusiasm, is capable of becoming the sort of spiritual pioneer the world needs. There are no heroes of action --- only heroes of renunciation and suffering. Of these there are plenty. But few of them are known, and even they not to the crowd, but to the few."
Schweitzer goes on to explain that not many people can afford to step away from their immediate responsibilities to perform independent personal service. Those who can "... must accept their good fortune in a spirit of humility. They must often think of those who, though equally willing and capable, were not in a position to do the same."

And for we who must stay behind? For us, he echoes and expands some of the thoughts voiced by George Elliot in the closing pages of her novel Middlemarch. Albert Schweitzer counsels:

"Of all the will toward the ideal in mankind only a small part can manifest itself in public action. All the rest of this force must be content with small and obscure deeds. The sum of these, however, is a thousand times stronger than the acts of those who receive wide public recognition. The latter, compared to the former, are like the foam on the waves of a deep ocean.
"The hidden forces of goodness are alive in those who serve humanity as a secondary pursuit, those who cannot devote their full life to it. The lot of most people is to have a job, to earn their living, and to assume for themselves a place in society through some kind of nonfulfilling labor. They can give little or nothing of their human qualities. The problems arising from progressive specialization and mechanization of labor can only be partly resolved through the concessions society is willing to make in its economic planning. It is always essential that the individuals themselves not suffer their fate passively, but expend all their energies in affirming their own humanity through some spiritual engagement, even if the conditions are unfavorable.
"One can save one's human life, along with one's professional existence, if one seizes every opportunity, however unassuming, to act humanely toward those who need another human being. In this way we serve both the spiritual and the good. Nothing can keep us from this second job of direct human service. So many opportunities are missed because we let them pass by.
"Everyone in his own environment must strive to practice true humanity toward others. The future of the world depends on it."

- Sunday, July 23, 2000 at 16:06:38 (EDT)

Ideas & Arguments

More scraps from the Philo B'fast table of early 2000: Thanks again to JB, AP, JJ, GdM, JC, BW, BD, et al. --- for thoughts and encouragement.

- Saturday, July 22, 2000 at 06:28:13 (EDT)


If you know everything about a simple system, it's easy to predict what it will do. Given the order of cards in a deck, you can "forecast" the next card to appear --- as long as the deck remains unshuffled. Given the quantum-mechanical state of an atom, you can "forecast" the future evolution of its wavefunction --- as long as no outside perturbations induce transitions. Prediction works only for a decoupled system, isolated from the rest of the universe.

But it's a huge leap from a toy problem to even the tiniest real-world situation. Knowing the configuration of a single-cell organism isn't enough to foresee what it will do. Uncertainties cascade; infinitesimal disturbances ripple and grow. External forces like the absorption and emission of infrared photons (heat!) randomize the details of the system. Gross properties remain unchanged, but critical fine structures shift and flow ... and forecasts fail.

- Thursday, July 20, 2000 at 17:14:19 (EDT)

Questions & Quotations

Philo B'fast round-table fragments from Spring 2000: Thanks to the usual crew --- GdM, AP, JJ, JC, BW, BD, JB, et al. --- for countless ideas and commentary.

- Tuesday, July 18, 2000 at 21:56:45 (EDT)

Afterlife Grosses

Here's an idea for folks who focus their lives on money and fame: when you die, your full biography is made into a movie and gets shown throughout the Next World --- and depending on the per-screen cash flow and the first weekend's box office grosses, you get sent to Heaven ... or Elsewhere. (Alternatively, if you prefer, your next incarnation is up or down a notch in the rankings.) Sounds fair enough, if that's what's really important in life!

- Monday, July 17, 2000 at 10:49:04 (EDT)


What's the most important thing to learn on the job? What makes somebody a valuable employee, a leader, a prime contributor, somebody worth fighting for, a first-round draft choice?

Metaknowledge --- the ability to understand problems, to know:

... and so forth. Specific answers are helpful; metaknowledge is critical.

- Saturday, July 15, 2000 at 16:25:57 (EDT)

Proverbs & Rules & Bureaucracy (Oh My!)

The Philosophy Breakfast table in May 2000 free-associated long and hard. Here are some of the questions we discussed; grateful acknowledgements to JB, JC, BD, GdM, JJ, AP, BW, and others.

- Wednesday, July 12, 2000 at 21:59:54 (EDT)

Month of Questions

The "Philosophy Breakfast Table" random-walked through a host of issues during four recent Friday morning get-togethers. (Many thanks to BD, BW, GdM, JC, JJ, and everybody else for their thoughtful comments, suggestions, and above all questions!)

- Tuesday, July 11, 2000 at 06:01:37 (EDT)

Diagnosis: Mortality

A person is told s/he has an incurable disease and will soon die. Abruptly, life changes! Some items become trivial, unworthy of a human's time; other things take on utmost importance. Family and friends, formerly ignored, are now precious jewels. Reputation moves to center stage. The edge of the universe jumps closer ... perspective shifts ... lights go out ... the fog thickens ... and every moment sparkles.

Should such an attitude apply to life before a doctor pronounces the death sentence?

- Sunday, July 09, 2000 at 09:26:09 (EDT)


Life's a big circle --- but most of the time we only think about a small arc ... sometimes, only a few arc-seconds of the whole!

- Saturday, July 08, 2000 at 08:25:08 (EDT)

Irreducibility & Pseudoscience

It's a human tendency to push farther than is justified --- to take a good concept and run with it beyond the limits of its known validity. Such leaps of faith have paid big dividends, time and again, especially in studying the laws of nature. But it's important, when leaping, to respect those already on the other side of the chasm.

Good explanations of fundamental phenomena don't answer all questions on larger scales. People and their activities aren't simply reducible to their genes, for instance. Contemptuous claims that we're just big lumbering robots, puppets dancing to the strings pulled by our DNA, don't hold water ... any more than the opposite arguments that our minds are transcendent entities, independent of physical bodies and their underlying chemistry. Life's more complex than that, both ways.

Mary Midgley makes some balanced and insightful insightful comments on this topic in Chapter 4 of Beast and Man: the Roots of Human Nature:

"... Anyone who speaks of a small part as doing something that can only intelligibly be done by the whole grinds his logical gears, producing a frightful noise that obscures all the implications of what he is trying to say. (Very few scientists treat their cars as badly as they treat their conceptual schemes.) If I claim that this carburetor won the Monte Carlo Rally, or that Eclipse's left hock won the Derby; if I say that my small intestine has digested my lunch; if the boy soprano's family remark that he has just sung the Messiah --- we speak confusedly. It was Cæsar, not just Cæsar's brain, that crossed the Rubicon. And what took the decision to do it was again Cæsar, not his HLC [hypothalamic-limbic complex] or his cerebral cortex.
"People find it hard to grasp this point because they see it as antiscientific. Must not the real account of what is happening, they say, be the physical one? Are we not speaking only indirectly or superficially, if not superstitiously, whenever we describe an event in any other term than as the movement of electrons? Is not everything else in some way unreal?
"Asking different kinds of questions produces quite different kinds of answers; they are usually not reducible to one another, though they must be compatible. Slicing the world in different directions reveals different patterns. Jelly rolls, sliced downward, have a spiral structure. Sliced across, they have stripes. Stripes are not reducible to spirals, nor vice versa, and will not become so by further analysis. Both are real, and the two patterns can be related if we understand the relation between the two slicing angles. In just the same way, other things are real as well as electrons. Brains are also real --- but so are the colors we see and the pains we feel, though they could never figure in books on physics or neurology. And someone with a moral conflict has a real conflict --- granted that it is not unreal in the way that conflicts can be so (that is, fictitious, imaginary, or self-induced). All real features of the world can be studied directly, on their own terms. They do not have to be approached indirectly, by finding their mirror images in a pattern studied by physicists."

Midgley goes on to explain how the DNA of living creatures can be both worthy of reverence (as part of an awesome, wonderfully complex system) and yet not any more worthy of reverence than the beings whom we interact with on a macroscopic scale. She concludes by critiquing the logic of those who try to use an ersatz "scientific" viewpoint (e.g., "a chicken is only the egg's way of making another egg" applied to genetics), in a game of intellectual one-upmanship, to cast scorn on real-world thinking:

"... It can lead, with startling ease, to a confident belief that all the concerns of daily life are somehow "unscientific," that the scientific thing to do is always to find some extremely remote standpoint and insist that only what is seen from it shall count as reality. Middle-sized phenomena, such as we must always deal with in our lives, are dismissed as beneath explanation, while the scientist makes off with the speed of light, either to use his electron microscope on ultimate particles, or to gaze through his telescope at remote perspectives, in terms of which indeed the individual counts for almost nothing. Now both these things must be done, but they are no more scientific than working on patterns seen in the phenomena immediately before us. The scientific temper is one that looks for the appropriate method in each field, that carefully distinguishes different sorts of questions for differing treatment. To become obsessed with a method for its own sake and try to use it where it is unsuitable is thoroughly unscientific.* And the purpose of all explanation must be, ultimately, to illuminate the chaotic world with which we are actually surrounded. That is what we have to explain."
* "It is the mark of an educated man to look for just as much precision in each enquiry as the nature of the subject allows" (Aristotle, Ethics 1.3).

For additional Mary Midgley comments see the ^zhurnal entries of 1 June 2000 and 10 May 2000.

- Thursday, July 06, 2000 at 04:52:47 (EDT)

Art, Courage, Life: Fésole II

One more quotation from John Ruskin's The Laws of Fésole: A Familiar Treatise on the Elementary Principles and Practice of Drawing and Painting as Determined by the Tuscan Masters (1877-1879), Chapter VIII:
"The best practice, and the most rapid appreciation of [J. M. W.] Turner, will be obtained by accurately copying those [drawings] in body-colour on grey paper; and when once the method is understood, and the resolution made to hold by it, the student will soon find that the advantage gained is in more directions than one. For the sum of work which he can do will be as much greater, in proportion to his decision, as it will be in each case better, and, after the first efforts, more easily, done. He may have been appalled by the quantity which he sees that Turner accomplished; but he will be encouraged when he finds how much any one may accomplish, who does not hesitate, nor repent. An artist's time and power of mind are lost chiefly in deciding what to do, and in effacing what he has done: it is anxiety that fatigues him, not labour; and vacillation that hinders him, not difficulty. And if the student feels doubt respecting his own decision of mind, and questions the possibility of gaining the habit of it, let him be assured that in art, as in life, it depends mainly on simplicity of purpose. Turner's decision came chiefly of his truthfulness; it was because he meant always to be true, that he was able always to be bold. And you will find that you may gain his courage, if you will maintain his fidelity. If you want only to make your drawing fine or attractive, you may hesitate indeed, long and often, to consider whether your faults will be forgiven or your fineries perceived. But if you want to put fair fact into it, you will find the fact shape it fairly for you; and that in pictures, no less than in human life, they who have once made up their minds to do right will have little place for hesitation, and little cause for repentance."
See the 25 June 2000 ^zhurnal entry for other Ruskin thoughts.

- Monday, July 03, 2000 at 21:44:54 (EDT)

Human Genomania

An astronomer develops the final photographic plate of an all-sky survey and declares "Now we understand the universe!" A lexicographer finishes defining the ultimate word in the Z's of a dictionary and announces "All problems of language have been solved!" A census-taker records the name of the last citizen and boasts "Our society is complete!" The Human Genome Project computes a DNA sequence and holds a press conference to proclaim "The Book of Life lies open to us!"

Well, it's a wee bit more complex than that....

- Saturday, July 01, 2000 at 20:24:59 (EDT)


How to keep large numbers of people poor and unhappy in an otherwise prosperous nation? How to aim humans into lives of violence, crime, prison, teenage motherhood, mutual abuse, and generally meaningless existence?

One part of the answer: while folks are young, encourage them to minimize their education. Let them form cliques which fight against personal growth, self-defined groups to tease those who study hard. Tell them not to struggle against difficulties. Push them toward the easiest classes, toward just getting by. Make their schools inferior: don't pay for good teachers, adequate facilities and equipment, modern textbooks, or decent learning environments. Let it be clear to these erstwhile students that they are second-class, that most of them are not going to do well, and that they've just got to serve their time before they can escape.

The antilearning subculture that develops is a key driver in a larger social system of unemployment or low-paying jobs (no qualifications for anything better) and personal discrimination ("justified" by retrospective statistics). Once the feedback loops and disincentives get well-established, only a few individuals will break out via exceptional strength of will and herculean effort.

In contrast, imagine what would happen if, for a single generation, huge investments could be made to demolish the antilearning box on the flowchart. How would a society react to millions of smart, eager, highly-educated young people --- utter stereotype-breakers --- when they began appearing in the workforce and moving up in their organizations? Jails would begin to empty, neighborhoods would begin to improve, and countless positive experiences would begin to smash negative prejudices.

Economically, what's the payback time for such a space-program-scale investment? (I estimate less than 50 years, counting productivity enhancements and savings on welfare.) Morally, what excuse is there for not making it? And in the meantime, personally, individual acts and choices by every one of us can push the system toward greater justice for all, bit by bit, day by day.

- Friday, June 30, 2000 at 19:48:58 (EDT)


Imagine a cavern: darkness and silence,
Broken betimes by the faintest of glows,
  Trickle of water in rock.

Then for an instant a sliver of sunbeam
Slips through a rift and reflects from a pool,
  Scatters off facets of gold.

Light breathes on a mirror of ice and then focuses
Down to a point, at a droplet that hangs
  Poised on the never-yet-seen.

Two ponderous, pendulous, crystal stalactites
Touch, clasp, and fuse --- and the pattern is changed.
  New threads appear in the stone.

As neurotransmitters bridge gaps in a cortex,
Water's course shifts; pathways open and close.
  So thinks the mind of the cave.

- Wednesday, June 28, 2000 at 12:11:05 (EDT)


In The Laws of Fésole: A Familiar Treatise on the Elementary Principles and Practice of Drawing and Painting as Determined by the Tuscan Masters (published 1877-1879) John Ruskin offers charmingly idiosyncratic suggestions to students of art and life. Chapter I ("All Great Art Is Praise") advises:
"Fix, then, this in your mind as the guiding principle of all right practical labour, and source of all healthful life energy, --- that your art is to be the praise of something that you love. It may be only the praise of a shell or a stone; it may be the praise of a hero; it may be the praise of God: --- your rank as a living creature is determined by the height and breadth of your love; but, be you small or great, what healthy art is possible to you must be the expression of your true delight in a real thing, better than the art. You may think, perhaps, that a bird's nest by William Hunt is better than a real bird's nest. We indeed pay a large sum for the one, and scarcely care to look for, or save, the other. But it would be better for us that all the pictures in the world perished, than that the birds should cease to build nests."
And in Chapter VIII ("Relation of Colour to Outline"), on the complex and multitudinous faces of reality:
"Now, there are many truths respecting art which cannot be rightly stated without involving an appearance of contradiction, and those truths are commonly the most important. There are, indeed, very few truths in any science which can be fully stated without, such an expression of their opposite sides, as looks, to a person who has not grasp of the subject enough to take in both the sides at once, like contradiction. This law holds down even to very small minutiæ in the physical sciences. For instance, a person ignorant of chemistry hearing it stated, perhaps consecutively of hydrogen gas, that it was 'in a high degree combustible, and a non-supporter of combustion,' would probably think the lecturer or writer was a fool; and when the statement thus made embraces wide fields of difficult investigation on both sides, its final terms invariably appear contradictory to a person who has but a narrow acquaintance with the matter in hand."

Context: Fésole (or Fiesole) is mentioned in Milton's Paradise Lost; it's a hill above Florence, Italy. Bill Beckley's introduction to a recent edition of the book notes that Galileo observed the moon from Fésole itself, and in Florence lived Giotto, Botticelli, and various other important Renaissance artists of Tuscany. John Ruskin's romantic mysticism associated that region with beauty and creativity.

- Sunday, June 25, 2000 at 08:28:16 (EDT)


An "artist" (who shall remain nameless, both because I can't remember a name and because s/he doesn't deserve to be remembered) recently exhibited goldfish swimming around in a set of blenders, those electrical mixers with blades at the bottom of a pitcher. Viewers were offered the opportunity to turn a blender on, thereby liquifying a living creature --- rending a carp into instant fish frappé. A few people pressed the button and did it. (Carpe mori?)

This "art" was mainly grandstanding cruelty-for-publicity, sure, and it semi-succeeded ... as so many scandalous acts have always done. But the experiment was woefully incomplete. A real artistic statement about the value of animal life could have been made by a simple extension: electrify one in every N blenders, so that instead of the fish being pureed, the human who clicks the switch gets fried. Zzzaapppp!

What value of N would make the situation a toss-up for the button-pusher? Is the thrill of whipping a fish worth a one-in-a-billion chance of electrocution? And extending art to everyday life, how does the joy of eating cooked beast-flesh compare to the risk of catching mad-cow disease, or salmonella, or a host of other parasites? And that's just looking at the human side of the equation. Does suffering of an animal count for anything compared to pleasure of a person? Where's the balance point?

- Saturday, June 24, 2000 at 10:16:17 (EDT)


A clever hack that sometimes saves lots of time: when a computation has to be updated, hang on to certain internal parameters that go into calculating the answer --- and then, rather than recomputing the whole shebang, as new information comes in you can simply revise those parameters and quickly get the new result. This is the key concept behind Kalman Filtering, the famous trick that solves many real-time aerospace control problems (and loads of other signal processing challenges).

A couple of examples may add light. For starters, suppose you need to figure out the average over the past 365 days of something like a temperature or a stock's price. You add up 365 numbers and divide by 365; boring but feasible. To find the answer tomorrow, however, instead of adding up the latest 365 values you can save work by taking the previous total, subtracting out the initial number from a year and a day ago, and adding in the current value before doing the division. (Ignore leap-year issues!)

Another, more subtle demonstration of the same kludge: "continued fractions" are infinite quotients of the form 1+1/(2+1/(2+1/(2+ ...))) --- fractions that crawl down forever. (They look prettier when written out as a big fraction with ever-shrinking horizontal bars, but you get the picture.) Lots of important numbers have brilliantly simple continued fraction representations. The one above, for instance, is just the square root of two ( = 1.41421356...). The base of the natural logarithms, e ( = 2.718281828...), has the continued fraction series 2+1/(1+1/(2+1/(1+1/(1+1/(4+1/(1+1/(1+1/(6+ ...)))))))). Continued fractions are superb for finding the best ratios to represent complicated numbers, like 22/7 for pi (or better yet, 355/113). They've got lots of other important uses too. (Enough motivation --- cut to the chase!)

But actually evaluating a continued fraction looks ugly. It seems to require picking some point in the nested parenthetical hierarchy to cut off the series, and then crawling up from there, converting denominators, taking reciprocals, adding terms, etc. Plentch! Doing it bottom-up is not only slow. It also means that you have to recompute the whole mess just to add a single new term. But there's an alternative: the subbookkeeping trick works magic to let you evaluate top-down, as far as you like. You just keep track of a couple of subtotals that combine to make the fraction at each stage.

There's a generic moral to this story (and it's not just the fact that "subbookkeeping" has more double letters in a row than any other common English word!). When a job gets unæsthetic and repetitive, look for a way to factor it into sub-jobs. Then seek covert components --- hidden variables --- that can carry along the information you need to axe the redundant effort. Sometimes, given luck and cleverness, there's a pleasant surprise.

- Wednesday, June 21, 2000 at 16:34:51 (EDT)

Science v. Stamp Collecting

Identifying and describing critical factors is a key step toward problem-solving, but it's only the first step. Next, one has to link those factors together and gingerly start to hook some numbers to them --- relative weights, speeds, probabilities, and so forth. That's how to turn a handwaving exercise into a testable theory.

Malcolm Gladwell's recent book The Tipping Point: Why Small Changes Can Make a Big Difference is a good example. It's an engagingly fast read, smoothly-written, full of striking metaphors and case studies. (Some pieces of the book were published earlier as essays in the New Yorker.) In brief, Gladwell argues that many social phenomena --- crime waves, fashion fads, teen suicides, success and failure of businesses --- are (like the spread of disease) governed by nonlinear relationships, and so they can be profoundly affected by slight shifts in a few parameters. (Hard to disagree with that!) The book describes several elements which may be key to understanding social epidemics:

Good concepts, all.

But The Tipping Point never quite gets past storytelling to the essential next stage of knowledge. To build a theory, one must:

This process doesn't have to be arcane or even very mathematical. But it does need to be done if there's going to be progress in understanding a situation. That's the difference between natural philosophy and philately.

- Tuesday, June 20, 2000 at 20:36:35 (EDT)

Color Chains

Dawn blushes pink
  Pink skies fade blue
Blue winters chill
  Icicles glue

Flame tongues lick red
  Red coals die black
Black ashes blow
  Foundations crack

Green leaves dry brown
  Brown hairs go gray
Gray hills erode
  Sands sift away

- Sunday, June 18, 2000 at 20:11:01 (EDT)


The kids in my family have been Buick automobile spotters for many years now. It began over a decade ago when General Motors (Buick Division) gave away floppy disks with cute advertising animations to promote their cars. We all started watching for Buicks on the road and crying out "Buick!" whenever one came into sight. Buicks were ideal for this enterprise. They were neither too common nor too rare. They also had a distinctive profile, grill design, and logo that made them readily, but not trivially, identifiable.

The Game evolved from that. The first to call "Buick!" gets 5 points, and whoever then confirms the observation gets 2 points, with an additional bonus point going back to the initial spotter. (Wags then try to confirm the confirmation and argue that they deserve half a point for that; they are ignored.) A false call incurs a -5 penalty, with +5 awarded to the one who catches the mistake. A blue Buick, aka a "Bluick", is worth double. No score for parked cars. Special credit for naming the model ("LeSabre", "Skylark", etc.).

In actuality, the Game has always been more conceptual than real. Nobody keeps track of points beyond a single trip, if that long. It's the silly fun of the play, not the outcome, that matters.

- Saturday, June 17, 2000 at 14:04:02 (EDT)

Out of Sync

My dear Aunt "Froggie" (a nickname since her infancy ~70 years ago; she was a frog-like baby!) broke some bones recently. She described the discombobulating effect of the painkillers that her doctor prescribed: "You know how sometimes when you button a shirt, and get all the way to the end, you discover that you're off by one in lining up the buttons and the buttonholes? It feels like that!"

- Wednesday, June 14, 2000 at 06:08:21 (EDT)

Big Names

What do you get when you hire a famous person as a spokesman, or an advisor, or a member of your Board of Directors? That's tough to say. Maybe an insurance policy against blame? ("Don't accuse me; I was relying on Dr. X's judgment.") Or sometimes a gateway to other interesting people? (Let's ask Dr. X to invite Professor Y --- they shared a Nobel Prize, you know.) Or perhaps a bit of the aura that might rub off on the business? (We're a first-class enterprise; we have Dr. X on retainer.)

But most of the time, alas, celebrities can't pull their own weight. Creative energy and insight in one field don't transfer to another. Fame fades over time, though the bearer may not realize it. Worst of all, overconfidence after one success leads to misjudgment and underestimation of risk in a host of new areas.

A company can pay a lot for a few hours of big-name time --- and the recipient of such cash faces a strong natural pressure to say something, regardless of ignorance about a particular problem. It all adds up to danger. Better to get the real scoop from those who know, the insiders, the low-profile but savvy people who have the respect of their peers ... not the ones who give the best sound bites to network news mikes.

- Tuesday, June 13, 2000 at 06:32:32 (EDT)

Suffer the Animals

In 1789, Jeremy Bentham wrote:
The day may come when the rest of the animal creation may acquire those rights which never could have been withholden from them but by the hand of tyranny. The French have already discovered that the blackness of the skin is no reason why a human being should be abandoned without redress to the caprice of a tormentor. It may one day come to be recognized that the number of the legs, the villosity of the skin, or the termination of the os sacrum are reasons equally insufficient for abandoning a sensitive being to the same fate. What else is it that should trace the insuperable line? Is it the faculty of reason, or perhaps the faculty of discourse? But a full-grown horse or dog is beyond comparison a more rational, as well as a more conversable animal, than an infant of a day or a week, or even of a month, old. But suppose they were otherwise, what would it avail? The question is not, Can they reason? nor Can they talk? but Can they suffer?
From Introduction to the Principles of Morals and Legislation, Chapter 17, as quoted in Mary Midgley's Animals and Why They Matter (1983), Chapter 8.

- Sunday, June 11, 2000 at 17:12:03 (EDT)


Here's the business model: we network everybody's refrigerators together, wireless, so that your icebox knows what's in the neighbors' and vice versa. Then when you get a craving for something exotic, if you don't have it your 'fridge tells you who does --- and you just sneak over there and grab it!

Sure, it sounds stupid ... nobody would have any reason to stock their own refrigerator, everybody would have to leave their house unlocked, naughty people could near-trivially spoof the system by modifying sensor code and broadcasting false data, and it's utterly vulnerable to denial-of-service attack by a few clowns. Pfluhghkh! But this is precisely the silliness that passes for reality in so many starry-eyed newspaper puff pieces for so many erstwhile high-tech start-ups.

Reporters haven't learned to ask for a even simple systems-analysis of what's proposed. Instead, it's all hype ... so any articulate shyster who can spin a cute yarn and grab an eager writer's attention gets coverage on the front page of the business section. No equations needed, or wanted. Hardly any code to write either. A demo can be faked up or patched together out of scripts and existing software modules. What tomfoolery! And yet many people fall for it, time and again.

It's the "tell me a story" syndrome that we humans are, by nature, so susceptible to. We don't think about:

New bogus schemes appear in every day's news. By the time one collapses, the techno-salesman will have cashed the checks and moved on to something else; the reporter will be chasing another chimera; the customers and the stockholders will be left with the wreckage. Oops....

- Friday, June 09, 2000 at 19:12:51 (EDT)


In exchange for silence --- conversation,
  At the cost of solitude --- a friend;
Give up certainty --- discover freedom,
  Cast off inhibition --- put on love.

- Thursday, June 08, 2000 at 17:25:55 (EDT)

Severe Privilege

How can those born (or dropped) into a state of great wealth learn to understand the less fortunate? Virtually everyone who encounters these words has a decent education (at least enough to be able to read), access to computer and network facilities, work to do, clothes to wear, friendly neighbors and acquaintances, reasonably good health, plenty to eat, and a relatively safe place to live. How often do we think about the many who lack all or most of those comforts --- who struggle amidst pain, poverty, hunger, and war?

And those of us near the top of the priviligentsia pyramid? Pick a few arguable gifts: rich, white, male, urban, English-speaking, heterosexual, powerful, well-connected, sleek, smart, sophisticated ... --- what obligations accompany such luck? Is one's chief duty to maximize personal utility? To acquire control over more resources? To grow in fame? To build memorials? Or are there other proper ends in life?

- Wednesday, June 07, 2000 at 06:05:57 (EDT)

1852 Trivia

The year 1852, a century before my birth, has become a tiny gateway into history for me ... a benign fixation, because of that personal (if distant) connection. Many interesting things happened in 1852: For images of some coins in my 1852 collection, see 1852! and the Gallery of 1852 Coins. (Thanks to Rudy Vonk for kind contributions of historical facts concerning my favorite year.)

- Sunday, June 04, 2000 at 21:51:05 (EDT)

Party Lines

Professor Plum, in the Kitchen, with the Lead Pipe. We all belong to multiple categories; we're members of many groups at once, divided and joined by age, sex, race, wealth, language, location, religion, occupation, avocation, .... The strong temptation is to pick one dimension and focus on it --- use it to form a club, a gang to fight in the war for power against other gangs. That's the political system, stripped down to its essentials, much of the time. Are there better ways to work together? Can we cut across the cliques and find common ends, and agree on means to pursue them?

- Saturday, June 03, 2000 at 10:59:02 (EDT)

This is Volume 0.09 of the journal of ^z = Mark Zimmermann ... musings on mind, matter, method, and metaphor ... new posts every few days, since April 1999. See ZhurnalyWiki on zhurnaly.com for a parallel "live" Wiki experiment in shared thought. For back issues of the ^zhurnal see Volumes v.01 (April-May 1999), v.02 (May-July 1999), v.03 (July-September 1999), v.04 (September-November 1999), v.05 (November 1999 - January 2000), v.06 (January-March 2000), v.07 (March-May 2000), v.08 (May-June 2000), v.09 (June-July 2000), v.10 (August-October 2000), v.11 (October-December 2000), v.12 (December 2000 - February 2001), v.13 (February-April 2001), v.14 (April-June 2001), 0.15 (June-August 2001), 0.16 (August-September 2001), 0.17 (September-November 2001), 0.18 (November-December 2001), 0.19 (December 2001 - February 2002), 0.20 (February-April 2002), 0.21 (April-May 2002), 0.22 (May-July 2002), 0.23 (July-September 2002), 0.24 (September-October 2002), 0.25 (October-November 2002), 0.26 (November 2002 - January 2003), 0.27 (January-February 2003), 0.28 (February-April 2003), 0.29 (April-June 2003), 0.30 (June-July 2003), 0.31 (July-September 2003), 0.32 (September-October 2003), 0.33 (October-November 2003), 0.34 (November 2003 - January 2004), 0.35 (January-February 2004), 0.36 (February-March 2004), 0.37 (March-April 2004), 0.38 (April-June 2004), 0.39 (June-July 2004), 0.40 (July-August 2004), 0.41 (August-September 2004), 0.42 (September-November 2004), ... Current Volume.Send comments and suggestions to z (at) his.com. Thank you!