I've never met any mysterious strangers on airplanes; on the contrary, my row-mates are invariably interesting and outspoken. One example is the woman who took the seat next to me for my first transatlantic flight. She was finishing her Ph.D. in linguistics, so I asked her the question that was uppermost in my mind: Why are the words for "new" and "nine" almost identical in all the Indo-European languages?
"Just coincidence", she said without hesitation.
A proper mysterious stranger, you see, would have dropped a dark hint or two, or asked if I knew the Ukrainian in seat F, rather than stopping my etymological search in its tracks.
I've only recently recovered from this setback and taken a closer look at the phenomenon. The parallel is really quite neat:
| English | new | nine |
| German | neu | neun |
| French | neuf | neuf |
| Spanish | nuevo | nueve |
| Italian | nuovo | nove |
| Latin | nova | novo |
| Sanskrit | nava | navas |
| Greek | ennea | neon |
Certainly more than a little consistent. One explanation is that the IE root from which all these sprang had similar-sounding words, and the similarity endured. This is the "just coincidence" theory, and it has the advantage of much explanation with few means. Still, such a minimal sound drift across two unrelated words over many millennia seems surprising. Similar meanings, though, would help reinforce the kinship in pronunciation.
So what do "new" and "nine" have in common? Well, nine begins a new pair of hands if you're counting on your fingers alone. This idea gets support from Karl Menninger, who wrote nothing less than a 400 page book on the origins of number names. There's a close linguistic parallel between the words for one to four, and those for five to eight. It argues for an early period of counting by fours that was later displaced by counting by fives.
And lo! Menninger comes to my rescue with this:
| The root of the [Ancient] Egyptian word for "nine" is also used to indicate the rising of the sun and the first appearance of the new moon. |
Ancient Egyptian is not an IE language, by the way, so those of you settling into your airline seats, about to mutter "just coincidence" had better think again.
I checked Basque as well. Basque is a language isolate, related to no other existing tongue. But:
| Basque | berri | bederatzi |
(-atzi is the suffix indicating number, so the essential root is beder-.)
Close enough to justify a flush of vindication.
I should add, for the sake of completion, a few words on "church". It's one of the many common words traveling in disguise due to a shift from hard to soft ch (cf shirt/skirt, ship/skip). That would have been a hard sound in earlier English and German, pronounced kurk, which is why you find it today in Dutch and Scottish as kirk.
Check out Menninger's "Number Words and Number Symbols"
There is a special mystery to ancient lost cities discovered, a surprise and delight akin to finding an unknown volume of an encyclopedia believed to be complete. The nineteenth century did a brisk trade in turning up fabled lost cities: Troy, the Maya, Babylon; so much so that it seemed there was little left to uncover.
Happily, some wonders remain for the 21st-century Victorian explorer. One is Kampyr-Tepe, a major establishment in the time of Alexander the Great, now a fortressed dig on the uncertain border of Afghanistan. Its discovery is not new, but access to it is, war and political clouds hiding it as well as the sands did for years. Gold, a great reclining Buddha, and the world's oldest chess set have been found there. This article from the BBC tells a little of its story.
It is becoming less a question of when and how life arose on Earth, and more of what could possibly prevent it. Bacteria have been detected in the stratosphere, in near-boiling deep-sea volcanic vents, and in near-freezing water pockets six feet under Arctic ice. Apparently stuff can live anywhere that we trouble to look, and that now includes 3.5 billion-year-old volcanic rock. Traces of organic material in tubules leave no explanation but that the organisms, whatever they were, took up residence in solid rock by eating their way through it only shortly after the Earth's surface cooled enough to be solid at all.
Irradiated, boiled, frozen, entombed, drowned, life goes on. Deep space could hardly be less hospitable than conditions like these. Everything the planet is made of was thrown out by stars, collected, and condensed from space itself. The more that discoveries like this come to light, the more reasonable it seems that bacteria could have made that long trip, too.
I didn't even know there was a Fine Structure Constant, but this number, said to be one of 25 essential constants in the physicists's description of the universe, has apparently been giving cosmologists trouble. Certain Theories of Everything depend on it being an unchanging value in all conditions and throughout all time, although nagging evidence seems to imply that it might not be. Yet those unflagging Chilean teloscopists have ridden to our rescue once again....
Original, black-and-white photography seems as unlikely as breaking new ground in charcoal sketching. These austere works by Michael Kenna are nevertheless striking and fresh to the eye.
I'm browsing through William Dunham's excellent book "Journey Through Genius", a uniquely successful attempt to turn a series of proofs into a readable and engaging book. As with any book of great proofs, it starts off with Euclid and lots of geometry.
Even though I cut my logico-mathematical teeth on plane geometry in school, it was so long ago that their propositions, diagrams and proofs are now like so much abstract art to me. But out of the confusion I came across two simple and beautiful kernels of geometric truth, the kind of thing that must have helped raise geometry's status far above that of arithmetic for so many centuries.
The first is out of Euclid, and concerns itself with right triangles. These are so familiar from trigonometry that I never thought there were any new facts to uncover. Here's one I missed, though, and it's elegant indeed:
In any right triangle, the midpoint of the hypotenuse is equidistant from all three vertices.
Which is to say, a circle centered halfway along the hypotenuse runs through all three points of the triangle. It's a surprising connection between the circle and the triangle, virtual opposites of one another, and entirely different from the way that trig usually relates them. With a little thought, it can be seen that this is equivalent to the well-known fact that any triangle inscribed in a semicircle is a right triangle; but the consequence of equidistance makes it a more rewarding and unexpected insight to me.
The second nugget of gold comes from Archimedes, the Newton of his day. It, too connects the circle and the triangle, this time by area. Circular area, of course, we learn early on as a formula, and move on quickly from there. But Archimedes, on his way to discovering that formula, found this beautiful relation along the way:
The area of a circle is exactly equal to the area of a right triangle with legs whose lengths are
the radius and circumference of the circle, respectively.
This is easy to work out algebraically once you know that the area is pi times the square of the radius, but it's a lovely and overlooked fact geometrically, a victim of the modern habit of writing out our numbers instead of making shapes of them.
My lamenting of the passing of the art of memory seems to have been premature. Not only is there a U.S. competition to memorize such things as the order of cards in a shuffled deck in under five minutes, but the eventual winner goes on to the World Memory Championship, full of even more unlikely and astonishing feats. Surely the mental equivalent of Olympic weightlifting.
Sonoluminescence has been around as a recognized physical phenomenon for a long time: bubbles formed by ultrsound in liquid collapse catastrophically, generating pulses of light. A Purdue team now claims to have produced bubbles that collapse with enough force to produce fusion in a deuterium-rich fluid -- tritium and gamma rays are the apparent byproducts, just as larger-scale fusion reactions do.
Beyond the surprise that bubbles of any kind can produce such tremendous (if brief) forces, this represents the first new approach to fusion in decades, and the only that you could build and run at home, so simple is the apparatus. One to watch!
I noticed on Friday a very small ad on page six of an eight-page weekly. Playing at Soulshine Pizza (adjoint to Hal & Mal's, your basic downtown bar), sandwiched between Friday's blues performances and Sunday's jazz, was "Matt Haimovitz, Classic Cello". Nine p.m., ten dollar cover.
This looked very wrong, yet tempting. The name was vaguely familiar -- a young, iconoclastic cellist, as I recalled, and something about starting his own record label -- but if it was who I had in mind, far too much of an artist to be taking to the scuffed stage of a scruffy pizza room downtown, even if their mushroom special was pretty good. He should be playing concert halls in European capitals.
Puzzled, I went to the web. Sure enough, same guy.
So I put on my best direct-from-my-brother-in-New York outfit, drove downtown at 8:45 to the crumbling warehouse/bar, went through its creaking, dim door, and handed over my ten dollars. They stamped my hand and waved me through.
What is the opposite of a "packed house"? There were exactly two people there besides the waitress who brought me my Heinekin. One was a twenty-something fellow sitting at the table next to me, dressed in just-arrived-from-New York clothes identical to mine. Perforce, we struck up a conversation. He turned out to be a music critic from the New York Times, on assignment to cover tonight's performance, and a sign, if it wasn't clear already, that this was not your ordinary pizza room cello performance. Quite an interesting conversationalist, as you might imagine, once you got over the note-taking.
The other occupant of the firetrap was on stage, unpacking his cello. He looked unassuming yet dedicated, just like his picture on the web. This was, indeed, Matt Haimovitz, and in a few minutes he joined us at our table.
Pause now, and let me paint this picture for you. Go to your typical world-class cello performance and you'll find yourself in a vast auditorium ninety feet from the performer, with an oil executive on your left and a woman who won't stop coughing on your right. The artist will eventually come on stage, play, speak a little (but not to you), play some more and then leave. You'll feel that your forty dollars was well paid, for all that.
Here I was, with a music writer on one side and the artist on the other, talking about Mississippi, travels, composing, cello playing and most everything else, for an hour while we waited for an audience to accumulate. From time to time Matt would move his chair back a little and warm up on his cello. This was a 1710 Gofriller (Casals played one; Starker does, too), just about five feet away from me, and the sound from it was nothing short of mind-boggling. For a while, it looked as though I was going to be the only audience there was, in which case, Matt said, he'd be playing "whatever I asked for".
Ten dollars. Plus a beer.
At 10.pm. a dozen people had taken up seats around the room. Some were clearly there for the music, and some, like the very large gentleman with the Ridgeland Fire Department T-shirt on, were there for pizza. Matt took the stage and started into an atonal 20-century piece. It got stranger from there, but for nearly an hour he held the entire room, including the Fire Department contingent, in rapt silence. And then he started into Bach.
Now there is music played on the cello, and music for the cello. Up to this point, it must be admitted that the music was all of the former kind. But the Bach was cello music, music that opened up the voice and power of the instrument. He played the second solo cello suite, and no one breathed for a quarter of an hour. It was, quite simply, the best performance of any music I've ever sat in front of.
The crowd, such as it was, went wild. Matt stepped down to chat -- all of us could fit around a good-sized table -- and Jeremy, the writer, started asking reporterly questions of those who looked as though they might get away sooner. My head was swimming from the music and the Heinekin.
And then the best part of the evening happened.
Two middle-aged ladies came wandering tentatively in. "Are we too late?" they asked. It was 11:30 at night, after all. Seems they had come earlier, seen no one, and left.
And Matt said "We were just finishing up, but I'll play a piece just for you". They sat down, and he pulled up a chair in front of them. The Gofriller came out of its case, and he played, just for them, the whole of the first Bach cello suite.
Everyone stopped where they stood. The bartender leaned over the bar on his elbows. The waitress clung to a barstool nearby. I was hunched forward in my chair, watching the bow hand, and the two women were transfixed. This was the absolute distillation of what Haimovitz had been trying to achieve with his 50-state tour of back rooms, bars and hangouts: putting extraordinary music into ordinary settings to bring it as directly to people as possible. And sitting there, hearing one person playing not to an crowd but to two particular people, I heard one of the best performances imaginable precisely because it was anything but a stranger playing to strangers.
Great music, great performer, great cello. You had to be there, really, to grasp it; listening to his Bach CDs that I bought afterwards, I hear the personality as well as the music, and that makes the idiosyncratic interpretation convincing. Happily, I was there. And he'll be in Asheville on March 10th, just in case you're interested.
The invention of writing "will cause forgetfulness in learners because they will no longer cultivate their memories; they will rely on writing rather than remember themselves. Your discovery fosters reminiscence, not memory", Socrates is reported to have said. A man was measured by what he could carry in his mind.
We know that much more was routinely memorized in ancient times than today, but we have largely forgotten that there was once a science of memory that relied not on rare talent but sound methodology and practice. It thrived in classic times, was still preserved in Rome long enough for Cicero to refer to it as routine schooling for orators, and was given a whole book by Giordano Bruno as late as 1582. Memory was in something of a crisis by then, though, and its science needed writing down to avoid being forgotten altogether.
A graceful little article in an clever on-line magazine, Mappa Mundi, touches on the history of this vanished art and adds some well-chosen book suggestions. It's worth the brief, eclectic excursion to their site, and it may restore a sturdy metaphor for the workings of the mind.
I had a great Sunday. I got out my oils and painted a (sort of) picture; I finally figured out what was going on with Gaussian curvature (mostly); I wrote some good notes about an idea on complexity that has been bothering me for a while; and after all that I stepped out into the cold, clear night with a pipeful of Cornell & Diehl's Plantation Evening.
It took me a while to unearth my pipes, and my tobacco was dry as dust after being packed away for three years. I took the desperate measure of microwaving a damp paper towel and folding up the leaf in it, not really expecting much. But when I packed it into a pipe I had picked up on the spur of the moment in New Orleans, stepped out into the crisp, clear night, and lit it with a cheap Bic lighter, it burned perfectly and tasted like an autumn afternoon in the woods.
I had forgotten how indefinably enjoyable smoking is. It's the pure essence of indulgence -- nothing solid, liquid or otherwise tangible about it. Just the sudden creation of a private atmosphere, and the sense that you're wearing an invisible comfy robe and slippers everywhere you go. Cool air, a smooth blend, and a fine sky view.
The sky has been very kind to the telescope recently as well. Through it, Saturn is small but exquisitely detailed, like a jewel hung up in the sky. There is always a quiet gasp when you see it, three-dimensional and real instead of a flat picture, with its rings and moons flung around it. Jupiter, in another quarter of the sky, is almost as splendid, adorned with faint cloud bands and the pinpoint brightness of its moons. The Orion nebula is ghostly and beautiful, as if God stopped drawing with a pencil and picked up a brush. It's a patient pastimes, star-gazing, waiting for the earth to turn just right, and roving along the sky until your target settles in the eyepiece. It's a good companion to a slow pipe: two silent, delicious pursuits.
Just discovered on the web, this 1970s New York Times interview with sabre fencer George Santelli. Santelli pines for the days when satisfaction, not damages, settled a score; and the fencing master, not the attorney, was the aggrieved party's first recourse -- and who's to say he's altogether wrong?
The Fencing Master, by Robert Lipsyte
"Now take this country," said George Santelli. "I call you names. You
give me a good punch in the nose. I, being 72 years old, would have
no chance against you in a fist fight. So, I call a lawyer. I sue.
Ah. Childish."
He touched his nose, a beak of great power and majesty above a white
moustache, and waited for the traffic noise to subside on Sixth
Avenue, directly beneath the fourth-floor window of his famous
salle-d'armes.
"A duel would solve many problems," he continued. "We have insulted
each other. We have common friends who cannot invite us to the same
parties. It becomes very difficult. So, we have a duel with sabres."
"It is not very dangerous. We each bring a doctor, and two seconds.
The best fencer among them directs the duel, ready to leap in should
either of us become angry or lose control. We have a chance to show
courage, save face, derive satisfaction, gain new respect for each
other. We shed a little blood, earn a few stitches, throw our arms
about each other and drink champagne."
He stretched his tall, still supple body, and raised an arm that, in
its day, was said to have borne the strongest sabre in Europe. "Paul
Lukas, the actor, came to my father's salle in Budapest. He had
insulted his producer, and he had been challenged. We had a week to
prepare him for the duel, so I concentrated on teaching him to parry
the blow to the head and return it. Secretly, we blunted the sabers
so Lukas's face wouldn't be disfigured. The duel went well. They
hacked at each other and raised welts. The doctor squeezed a drop of
blood from one of the producer's welts, and everyone was very happy."
Salle Santelli
Santelli's father, Italo, ran one of Europe's most famous salles
d'armes, a training center for aristocrats and Olympic athletes in an
age and in a country that still admired the swordsman. The Hungarian
Government had brought Italo to Budapest in 1896 from his native Italy
and subsidized his school. In 1924, George was brought here by the New
York Athletic Club. He was fencing master there for 25 years.
Santelli has been the dominant figure in American fencing for many
yeaears, He coached the Olympic teams from 1928 through 1952,
revolutionized technique, and exerted an incomparable spiritual force
with his singleminded and selfless dedication to his sport.
Through Salle Santelli, which he opened after World War II, he broke
the racial and class restrictions of fencing by encouraging Negroes
and holding free classes for public high school students. Tonight, in
a rare tribute in this sport, Santelli will be honored at the Statler
Hotel.
Santelli admits to having fought only one duel himself, an affair of
great complexity. During the 1924 Olympics in Paris, a dispute arose
between an Italian fencer and an official. A witness was necessary and
Italo Santelli's testimony led to the disqualification of the
Italian fencer, and a scandal. The captain of the Italian team, Adolfo
Cotronei, wrote a newspaper article denouncing Italo as a renegade
and a liar. Italo, 61 years old, challenged Cotronei, who was about 30.
On a Barge Off Abazia
George, unearthing an obscure rule in the dueling code that allowed a
son to replace his father under certain circumstances, met Cotronei
on a barge in the waters off Abbazia, between Trieste and Fiume.
"We really fenced," said Santelli, staring out his salle window at the
Women's House of Detention. "We did not hack. It lasted perhaps
three and one-half minutes. He came down like this, so I parried and
riposted and struck him on the side of the head. He was temporarily
blinded, and so the duel was stopped. He required 12 stitches.
The men met again, at the 1932 Olympics in Los Angeles, and Cotronei
stood dinner and drinks, absurdly proud of his scar, the slight
squint in his left eye, and the monocle he wore.
"I do not believe," said Santelli, "that there should be dueling in
this country at this time. Americans think who won? who lost? and this
is not dueling, dueling is saving face and gaining satisfaction. It
grows from the culture."
His lips parted for large teeth. "But I must say that dueling was an
educational thing. It taught many people to behave properly. You have
to prepare for a duel, spend money on equipment, pay the fencing
master, pay the doctor, suffer the wounds. The next time you think
twice before you call a man an insulting name."
Couldn't resist this excerpt from January 21, 1600: "It is strange what weather we have had all this winter; no cold at all; but the ways are dusty, and the flyes fly up and down, and the rose-bushes are full of leaves, such a time of the year as was never known in this world before here."
Pepys's Diary (January 21, 2004)
One of the chief mysteries in the history of mankind is the transition from a world full of Neanderthals to one of modern Homo sapiens. Neanderthals were smart, tough, social and showed plenty of ability to survive; why they didn't has been often speculated, but never explained.
Elegant and simple evidence now points to climate -- the same force that drives many species into extinction or change. The same Greenland ice cores that have recently provided insights into global warming show a close correlation between increasingly cold weather and Neanderthals' southward retreat and eventual decline. It would appear that Cro-magnon man was simply a little better at keeping warm when it counted, a factor that can make all the difference over a few thousand years of ice age. Too, it explains why the most recent Neanderthal remains are in tropical climates: it's the best place to make a last stand against the ice.
Venus is a truly foreign place compared to Mars, with virtually no close-up surface images from that hot, clouded planet. Photos from the Soviet missions in the 1970s, though, have been reprocessed to reveal remarkable color and detail. Not up to current Martian photo standards, but more than enough to show a strange and rocky environment that until now has remained hidden.
One of my projects on long drives when the book-on-tape runs out is training myself to think with senses that aren't usually associated with the act of reasoning: evaluating a chess position by touch, for instance, or turning a mathematical abstraction into a picture. This concept is sharpened into a nice question over at the LanguageHat site: in what language do the deaf think? The question presumes that we think in words, an idea that's pretty well exploded, but the exploration of the answer is a fine short trip into the world of Sign, that language right around the corner from conventional ones.
A previously unknown manuscript of Archimedes has come to light, a thousand-year-old copy of a thousand-year-old work by the most inventive of the Greek mathematicians, and it's a major find.
Archimedes is the giant among the ancient geometer/mathematicians. His questions were fundamental and penetrating, and his methods were grounded in geometric analysis, often in surprising ways. He discovered the elegant formula for volume of a cylinder inscribed in a sphere; he derived results in buoyancy and centers of gravity in conic solids and the quadrature of the parabola by making ingenious analogies between leveraged weight and proportional volumes ("mechanical theorems", he called them); he dealt in pure math as well, devising a place-value number system and applying it to numeric problems, and he made his derivations of pi through the crucial insight that the limit of infinitely-sided polygons is the circle.
To this list, add the first study of combinatorics. It's no surprise that it has a geometric bent: it asks the question of how many ways 14 specified triangles can be assembled into a square -- a much more sophisticated question than how to do it, for the solutions run into the thousands and rely on the invention of techniques that simply didn't exist at the time. Even the kind of question is unique in its abstraction: I can't think of any other mathematician, western or asian, in the next few centuries, that dealt in the measurement of solution spaces.
The manuscript itself has a Maltese Falcon kind of history. From the New York Times:
. . . . .
Perhaps as remarkable as the discovery that Archimedes knew combinatorics is the story of a manuscript that dates to 975, written in Greek on parchment. It is one of three sets of copies of Archimedes' works that were available in the Middle Ages. (The others are lost, and neither contained the Stomachion.)
In the 13th century, Netz explained, Christian monks, needing vellum for a prayer book, ripped the manuscript apart, washed it, folded its pages in half and covered it with religious text. After centuries of use, the prayer book -- known as a palimpsest, because it contains text that is written over -- ended up in a monastery in Constantinople.
Johan Ludvig Heiberg, a Danish scholar, found it in 1906, in the library of the Church of the Holy Sepulcher in Istanbul. He noticed faint tracings of mathematics under the prayers. Using a magnifying glass, he transcribed what he could and photographed about two-thirds of the pages. Then the document disappeared, lost along with other precious manuscripts in the strife between the Greeks and the Turks.
It reappeared in the 1970s, in the hands of a French family that had bought it in Istanbul in the early 1920s and held it for five decades before trying to sell it. They had trouble finding a buyer, however, in part because there was some question of whether they legally owned it. But also, the manuscript looked terrible. It had been ravaged by mold during the years the family kept it.
In 1998, an anonymous billionaire bought it for US$2 million and lent it to the Walters Art Museum in Baltimore, where it still resides.
With the manuscript in hand, a small group of scholars set out to reconstruct the original Greek text. It was not easy. "You look with the naked eye and you see nothing, absolutely nothing," Netz said.
Ultraviolet light revealed faint traces of writing, but it included both the prayers and the mathematics. "The major problem is the combination of the fact that many characters are hidden with the fact that many are so faint that they are invisible," Netz said. Then there are the gaps where the pages were ripped or eaten away by mold.
Computer imaging helped. Roger Easton of the Rochester Institute of Technology, Keith Knox of the Boeing Corp. and William Christens-Barry of Johns Hopkins University managed to write programs to pick out writing from the "noise" around it, and in many places the Greek letters fairly pop off the computer screen.
"The product of the software is incredible," Netz said. But it too has limitations, especially near the tattered edges of the pages. To reconstruct the writings, Netz and Nigel Wilson, a classics professor at Oxford University, are using every tool available: ultraviolet light, the computer images, Heiberg's photographs and their own intimate knowledge of ancient Greek texts. Still, in some areas, "the text is likely to remain conjecture," Netz said.
It was chance that led Netz to his first insight into the nature of the Stomachion. Last August, he says, just as he was about to start transcribing one of the manuscript pages, he got a gift in the mail, a blue cut-glass model of a Stomachion puzzle. It was made by a retired businessman from California who found Netz on the Internet as a renowned Archimedes scholar. Looking at the model, Netz realized that a diagram on the page he was transcribing was actually a rearrangement of the pieces of the Stomachion puzzle. Suddenly, he understood what Archimedes was getting at.
As he examined the manuscript pages, piecing together their text, he realized that what Archimedes was really asking seemed to be, "How many ways can you put the pieces together to make a square?" That question, Netz said, "has mathematical meaning."
"People assumed there wasn't any combinatorics in antiquity," he went on. "So it didn't trigger the observation when Archimedes says there are many arrangements and he will calculate them. But that's what Archimedes did; his introductions are always to the point."
. . . . .
There are even more of Archimedes' accomplishments in a Wikipedia article -- read and wonder.
An engaging article in Fortune magazine poses the daunting question of whether Ansel Adams, whose work was done as much in the darkroom as it was in the field with a lens, would have traded his hefty black-and-white plates for a digital camera. One Christopher Burkett, photographer at large, thinks Adams would have happily done so, but that answer is not so surprising as Burkett's own photography. Unapologetically analog, Burkett's large-format nature photos, exposed onto and printed directly from 8x10 negatives, are luminous wonders untouched by any software. This is art remarkably close to life: have a look.
"The late Samuel Mockbee, FAIA, has just joined Thomas Jefferson in an elite club of architects who have received AIA Gold Medals posthumously. The widely admired Mockbee was a practitioner and educator until his death in 2001. The American Institute of Architects announced on December 4, 2003 that they would confer on him their highest honor."
That via Architecture Week. Mockbee raised beautiful and unexpected structures from the most casual of materials, and while he was known most for his long tenure at Auburn, his last home was in Canton, Mississippi: a house of sheet metal, plywood and glass like a giant version of something you built when you were eight years old from bits found in the garage. Mockbee, though, made it all work and endure. Check out the links for examples of his work -- they're unmistakable and memorable.
Architecture Week, The Rural Studio
Six million digits (not yet available) and two years in the finding through distributed computing -- the Great Interent Mersenne Prime Search, to be exact, the equivalent of building Rome in a few hundred days in the spare time of ten thousand peasants.
Here's a remarkable gallery of trompe l'oeil art -- on sidewalks. Like classical murals, only horizontal, and perhaps all the more effective for that.
Many a language, including English, has polite terms of address in its vocabulary, but Japanese is one of the very few languages to integrate degrees of politeness into its grammar: nouns, verbs and adjectives change form for various poluteness levels, just as they do for number or gender in English. Western influence and changing social conditions in Japan have begun to erode this basic aspect of the language, though, after a millenium of existence. The result may be more convenient for the Japanese speaker, but it represents the loss of a unique linguistic trait.
The mailman has been busier than usual delivering books to my door recently, and as they pile higher next to my reading chair, it's time to pass along a few of the titles of interest.
"Chopin's Funeral" is a biography of the composer that starts at the wrong end, as it were, as it treats both Chopin and his music as a single story. If your impression of Chopin, or any composer for that matter, is of someone who arrives at the studio at nine sharp each day, rolls up his sleeves, and composes until quitting time, this book will clear that up nicely. Nothing sounds more carefully and quietly crafted than Chopin's work, but nothing was quiet about his life. He lived in a turmoil of his own making, a mixture of illness, passion and socializing mostly resembling a college freshman year that lasted two decades, with tuberculosis thrown in. The music is what happened in the brief respites from all this. It confers a completely new way of hearing these works once they've been embedded in the turbulence of his short life and career. The book is splendidly written; not a scholarly biography, thank goodness, but a real look at life and an informed voice on music.
"Wooden Boats", by Michael Ruhlman, is one of those rare books in the tradition of John McPhee that takes a long look at a captivating subject and delivers fresh perception and fine writing in equal parts. The craft of wooden boatbuilding, almost extinct after the 1960s, has been revived in a few Maine shipyards as the highest calling of the craftsman. Ruhlman follows the course of a few boats plank-by-plank, from the trips to South American rain forests to secure trees of correct size, shape and quality, through the careful transformation of that wood into the timeless curves of a boat, a "living creature" of wood that sails. It's a nautical book, of course, but also a book about character and quality that's hard to put down. It's for sale cheap at Daedalus Books; do yourself a favor and buy it.
Leonard Cohen is best known as singer/songwriter, with a voice somewhere between velvety and gravelly. He's also a poet and novelist, it seems, and I picked up his small book "The Favorite Game" after it was urged on me by a dark-eyed young woman. It only takes a few sentences to realize that this is prose of a very high order, more than a little colored by poetry, directed by a sure hand. Each sentence is sculpturally perfect, the kind of book that makes you want to stop people on the street and read sections out loud. There's a story, but the book hangs on characters and their inner lives, and the sheer literary pleasure of turning the page.
Nobel Laureate John Wheeler is the giant of physics in Austin, Texas who is the best candidate for Einstein's successor. The central concern of his career has been gravity and space, and his immense book "Gravitation", with Misner and Thorne, has been on my list for a long time, so I jumped at the chance to pick up a much shorter book, "Gravity and Inertia", when went on sale at Labyrinth Books. It's one of those rare books of mathematical physics that's actually useful and enjoyable. It teaches the whole gamut of modern relativity, from the utter basics forward, pulling no mathematical punches, and yet eminently readable. That's because it's part historical exposition, part mathematical text, combined by a gifted and literate teacher. I'm only six pages in, having sidetracked into the appendix to learn the basics of topology, but it's already clear that this is a mind-opening book.
Finally, "Cicero", a new biography of the Roman statesman and oratory Anthony Everitt, is on loan from Andy, and I'm not in a hurry to return it. This is a classic book in every sense: richly informed, masterfully written, and desperately needed to fill big gaps in my education. More than just the story of Cicero's life, it's a history of Rome in one of its most turbulent times, that saw the rise and fall of Caesar and the transformation of its social and political structure. It could all be dull if Everitt were not such an articulate and engaging writer. A book that actually makes you feel smarter for having read it.
Daedalus, Labyrinth (Quite a classical pair)
Objects in motion tend to stay in motion: Newton's first law, and one that has reliably held for just about everything we can imagine, from matter to electromagnetism. The universe, it seems, plays by different rules. It not only currently seems to be expanding at an ever-increasing rate, but stellar observations now strongly indicate that it hasn't always been so. Up until five billion years ago, it was contracting due to gravity. And then, apparently, it changed its mind. Outward expansion began and continued right through the present.
So just what intervened to stop the entire universe in its tracks and turn its contraction around? It's not completely unprecedented: the current physics mythology has the universe starting out infinitely contracted, and then spontaneously taking up expansion with gusto. Perhaps the five-billion-year event is an echo of that first reversal, a kind of elastic reverberation whose troughs give way to gravity and whose peaks escape it. In any event, it looks like big new cosmologies are called for, just when things seemed to be making sense.
You can now install a little piece of the early Jurassic in a corner of your house: a Wollemi pine tree. Flourishing 175 million years ago, and thought to be extinct for two million, a living example -- exactly one of them -- was discovered in remote Australia nine years ago. Research into breeding cuttings has been going on ever since, and now, it seems, they're ready for market.
The little Wollemi narrowly escaped oblivion, but it seems a good candidate for longevity. It's slow-growing; it prefers the shade; innocuous, it has kept quietly to itself, hoping the new phenomenon of mammals wouldn't notice it. And it took up residence in an untrammeled part of a pretty untrammeled country, Australia's Blue Mountains. It's hard not to think of the coelacanth, the fish that most looks like it just wants to be left alone.
Tree species of mighty age are not that rare. Apparently the dawn redwood, dating from the Jurassic as well, made its comeback when the first living specimens outside the fossil record was stumbled upon in China fifty years ago. And of course there's the magnolia, which has been going strong for the last 70 million years without a hitch. It took the high road to plant immortality: grow flowers, look good, and stay cultivated through the hard times. If only the coelacanth were prettier to look at, we might never have lost track of it.
Shades of Chitzen-Itza. It might be 1880 all over again, with the first reports of strange ruins found in the deep mesoamerican jungles. It seems that Amazon forests have yielded up the remains of highly organized towns and roads, implying a far more sophisticated civilization in the 100-square-mile area studied than has ever been suspected. The comparison to the Aztec empire may not yet be warranted, but it does come immediately to mind: settlements linked across the jungle by a vast system of roads, with a sprawling bureaucracy to match. That sound you hear is history books being rewritten.
CNN, Salon.com (September 24, 2003)
Aristotle's notion that men had more teeth than women stood unchallenged until someone thought to actually count them. The science of the perfectly obvious takes another curious step forward with this discovery: right-handers have hair that consistently whorls to the right; left-handers don't. Handedness is a long-standing mystery, nearly unique to humans, with no obvious evolutionary merit. It is strongly associated with the rise of language in early humans, though, which makes this discovery more than just a passing connection between a physical and motor traits.
Two examples of photographic techinques that escape the camera and darkroom and take place by natural light and shadow have drawn my attention. Both of them turn to media that respond to degrees of light so naturally that we've all but overlooked them.
Most elegant is the grass photographyof Ackroyd & Harvey. Like the chemical complexities of film, grass grows greener where light falls on it, and gradually less so as it lies in shadow. Anyone can make a one-to-one scale grass print by leaving an object on the lawn for a week. The graceful extension of this idea is to project a black-and-white negative onto grass: where light passes most, the surface becomes in time greenest. No moving parts, no special equipment. It is simply nature responding to light with permanence.
An even simpler idea drives the Wooden Mirror. Light being the absence of shadow, and darkness being degrees of it, it follows that shades of gray can be captured by the lesser and greater shadows cast by an array of variously raised wooden blocks. This technique requires mechanical intervention, since the elements, unlike grass, are not alive. It is still one of the purest and simplest methods of fixing an image to an unexpected surface, yet so naturally that it seems to been intended just for that ever since grass and wood were invented.
From almost out of nowhere (a New Zealand tutor's spare time, apparently) has come a fresh and fundamental observation on the nature of time, both physical and philosophical. As far as I can tell, the approach -- so obvious as to seem trivial at first -- is to observe that a system of moving bodies must obey the Heisenburg Principle just as individual ones do. The consequence is not only that where they are is ultimately uncertain, but also when: time, even when appplied to the purely relative motion of moving bodies with respect to one another, is indeterminate. This article is too garbled to make out many details, but apparently the paper is drawing more and more attention. If so, it may be the harbinger of the Next Big Idea in physics.
In what must surely be one of the most curious on-line revitalizations of the past, the entire corpus of the Proceedings of the Old Bailey -- London's chief court for centuries -- has become electronically available, spanning the years 1674 to 1834. It is the very diary of English crime, high and low, no detail omitted.
By and large the only way of getting something tangible and reasonably permanent named after yourself is to have a child. Even then the chances are only 50/50 that it will be the kind that your name applies to. Having a building, battleship, topological theorem or street with your own name on it is likely to be out of reach for us all.
But there was a time, only a few years ago, when any one of us could have staked a claim on our own name in an visible and valuable way: as an internet domain. There was a turning point in the mid-90's when domain names changed almost overnight into scarce and valuable property, and the shorter they were, the more quickly they were snapped up by speculators and registrars. But until that time domain names were the labels of large institutions and universities alone, and the idea of a first name, say, as the name of a domain was as improbable as someone starting the University of Jim. Certainly there was no way you could register harvard dot anything for yourself. But jim.com was just lying there, waiting for me and my $100 to come and claim it.
And face it, much as you might like the domain name you have now, and proud as you may be of the work that went into discovering a string of letters to call your own, there is no substitute for the site that's purely and simply you. But me.com, you.com, jim.com and the rest are all long claimed.
Where did they go? Let's fire up whois and see.
Try visiting www.jim.com and you'll actually get a live site. One James Donald was alert enough in 1995 to spend a few dollars to become the envy of Jims around the globe. What was jim.com good for in 1995? Recall that the web and HTTP was a very new thing, and a simple page with text, links and even a picture(!) was a high-tech approach to listing your hobbies. That's what the page is now. Black text. White background. Black and white picture. A little piece of 1995 frozen in cyberspace.
Jim's registration of jim.com expires next year. I must just drop him a note. But like a man living a trailer home right where you'd like to dig an oil well, he's probably grown to accustomed to the place to move for any amount of money.
Ken.com is quite another matter. It didn't go to a quick-thinking techie named Ken with a few extra dollars to spend. No, today ken.com is owned by -- Mattel. That's right, the same folks who own barbie.com. No web page yet, but then they only took ownership last September. Perhaps there is a quick-thinking techie named Ken out there after all, who finally parted with his own name for more than a few extra dollars.
Happily, Brad was truer to himself than Andy. Back in 1995 he took the trouble to set up housekeeping under his own name, and he's been at the same address on the web ever since, happily living there as well as in the more physical locale of Utah. While he proudly lists himself as "Brad McCall, Designer" in his registration, I can't say much for what he's done with www.brad.com. It's a generic name-registration spot, nothing personal. Nice graphics, though. Perhaps Brad has rented his name away instead of selling it, like Ken.
But the prize for forward thinking goes to Andy Palmer of California. Back in '94 he staked a claim to andy.com, and by golly it's going to be his until 2011. Moreover, he's the only one of the bunch who gets mail under his own name. His address is listed as "palmer" at andy.com, but I'll bet that pretty much any mail that goes to andy.com finds its way to Andy.
Is there any hope left for the rest of us? You'll have to speak to John Donald (donald.com, 2002), John Charles (charles.com, 2002), John Thalacker (mechelle.com, 2001), or Stephen Perillo (steve.com, 2002) about that. But I see that jimnewkirk.com is still up there for the taking. It's not a lecture hall or a stadium, but it's a start.
Fine manipulation of electric current by capacitors, resistors and amplifiers is long-established, and has evolved to an exquisite degree of finesse. Not so with light. It can be transmitted and received in a variety of ways, and redirected along the way by reflection and refraction, but the state of light control really stands pretty much where electrical control did a century ago: we can make it, and send it down a wire, and that's about it.
This seems about to change, and radically. In an announcement from MIT comes a claim that borders on the miraculous: the ability to arbitrarily tune the frequency of light, not as it is emitted, but at any point as it travels through a crystal. That's an unprecedented measure of control, like adjusting the caliber of a bullet in flight. And because frequency equates to energy, and affects a multitude of other properties, it means that much of light's fundamental behavior can now be adjusted as we please. For the first time, light has acquired not just a physics, but a chemistry -- perhaps the first real 21st-century accomplishment of science.
There's something touching about the fact that even on distant Neptune some kind of change of seasons occurs amid the methane and frozen hydrocarbons. A little Earthness, it seems, survives at four billion kilometers from the sun.
This is something like procuring the New York Philharmonic to play your wedding. In Biloxi. Gehry is not the world's greatest architect, but is the most renowned architect living. He's hot off the construction of the Guggenheim Museum in Bilbao, the building that put an otherwise overlooked town on the northern coast of Spain into the center of the art world's eye. Spuring the trend of museums that look like alien space vehicles, his monumental metallic effort looks like an alien space vehicle that has crash-landed, very beautifully and sculpturally, onto several hundred paintings. The new Biloxi museum (model photos are on the site) won't be quite as extreme or grand, but it will have the stamp of the genuine article about it, and probably change the face of tourism on the coast as we know it.
It's an eerily appropriate choice of architects. Ohr was an arch-individualist, rebelling against all previous notions of form, creating pottery that you'd expect from a madman in an attic with a direct but noisy line to God. His potery looks like nothing else in clay, and it's safe to say that Gehry's gloriously weird architectural manifestations look like nothing else in the waking world either. Someone of peculiar genius must have realized that the two belonged together and somehow struck sparks between them. After all, the New York Philharmonic doens't come to Mississippi just for the catfish.
Here is a criterion of great beauty: surface simplicity that rewards deeper examination with ever more complexity. That's why so many math problems and their solutions are attractive -- they uncover the unsuspected in the trivial. The twin-primes conjecture is one of those very simple questions (about primes, like 3 and 5, that differ by exactly two) made beautifully complex by generalization (are there finitely or infinitely many?). The question has stood open since formal study of primes began, but now a significant step has been made toward bounding the problem. The answer, as has been suspected, is "yes"; but it's the manner of arriving at the answer that should be lovely indeed.
Science News, SiliconValley.com
Lovely and unexpected: plotting a second-order property of the sequence of primes -- the difference between the intervals between them -- yields a dynamic property, a cycle of three. It is not exact, but it is probable, the result of a simple statistical analysis undertaken merely as a test. The result may not be revolutionary, but it is a reminder that the primes can be treated as a dynamic system rather just a sequence, with all the tools and concepts that apply in that domain.
They're deep imprints in volcanic ash in Italy, 325,000 years old. There are far older hominid prints (in the millions of years), but these are the oldest that are distinctly human, dating from pre-Neanderthal man. They run zigzag up and down the slope of a volcano, punctuated with the occasional palmprint where someone has had to catch themselves; a few animal prints are nearby. The stride is short, suggesting a stature of about four feet, too small for the adults of that time. But who else would take their pets and go cavorting on the side of a recently active volcano but children, even a few hundred thousand years ago?
At the risk of becoming known as the guy who only posts gambling related material, here's a well-written article that I just discovered online. I'm familiar with the author, and more familiar yet with his character "X", whose team I have occasionally considering joining.
The last time I saw "X" in person was in October 1999, when a group of about 8 "advantage players" converged on a casino in north Mississippi, to play a promotion that started at 2 AM and was to run 24 hours. Our advantage during the promotion was about 1.75% of our bets. I played 13 hours, not stopping to even eat. I decided I had done all I could, and left to get some sleep. It turns out that was a good thing. An hour after I left the table, the remaining players were told that the promotion had been cancelled. The net win for the 8 players was $43,000. My win was a mere $2900, down from about $4000 an hour before I quit.
For an interesting view into the world of advantage play, check out the link to the four-part article.
The great Library of Alexandria, the legendary Egyptian manuscript collection that put the city founded by Alexander the Great on the map, was already going great guns a couple of centuries before Christ. Its avowed purpose was to collect all the knowledge of mankind, doing so for seven hundred years and giving Eratosthenes a job as Librarian along the way before being dispersed under Roman occupation.
It has endured as a legend, but not as a building, until now. The architectural exercise of creating a new house of knowledge has been undertaken by a Norwegian group with results that are both very modern and very Egyptian. The links lead to an exposition of it, and to the Library's own site, refreshing presented in Arabic. The site has its own architectural novelty: all the design is from right to left. Also below is a link to a fine short history of the Library from the ever-handy Perseus classics site.
From the thicket of prospects for a new building on the site of the World Trade Center, a most unlikely candidate has recently emerged. It's not a new design, nor even a new architect: it's a hotel, proposed for New York in 1908 but never built, by Antonio Gaudi.
Don't imagine that it's an old-fashioned design just because it's a century old. Tall as the Empire State Building, this looks like an upended zeppelin crownded with starry spikes and a cluster of tubular coral reefs at its base. It's as weirdly massive and organic as his most famous work, the Barcelona cathedral of Sagrada Familia (still under construction). More about concrete and surface detail than steel and smooth transparent glass, it's unearthly, European, and as far from a contemporary downtown Manhattan design as you can possibly imagine. It has even less chance of being built, I'd say, than Wright's Mile-High tower, to pick another retro-design: no one in New York would know what to make of such a structure, a building that refuses to mind its own business, a transatlantic emigree with no chance of blending into the architectural melting pot. Still, it's an exceptionally imaginative gesture just to propose it, and a welcome chance to take a first look at a building and a second at its architect who has had to wait decades after his death for recognition. His building won't be revived, but Gaudi may get a new lease on life for a while.
China, of all nations, is going to the moon. An unmanned capsule is in orbit now, and an manned flight is planned next. The ultimate destination is the Moon, and after that, Mars. The effort couldn't be coming from an unlikelier source.
China is a high-technology nation, of course. But space exploration has a uniquely American stamp to it, and it seems out of character when a very foreign nation -- like Japan's upcoming space shuttle -- steps into this very familiar territory. (The Soviet Union was never more Western than when it was profoundly anti-Western, and launched the first satellite.) The reason is not ethnological, but one of long-standing history. Of all the nations in the world that aspire to technological greatness, only Britain and America have a background rooted in exploration and discovery. America was found; Europe, Russia, Asia, and Japan have almost always just been there. Our space program is in a very real sense a direct extension of the Columbus's voyage: it's European and British exploration taken across the ocean, across the continent, and then straight up, pretty much without a pause since 1492.
China, on the other hand, has been profoundly insular for several millennia; it's part of the national consciousness in the same way that the wide open West is part of ours. There was a brief flurry of overseas travel in the fifteenth century, a remarkable exception, in which a fleet was built that traveled east into the Philippines and beyond -- perhaps even to the New World -- but it was a strange diplomatic gesture, not a voyage of discovery. Local governments were duly intimidated, but nothing was discovered, nothing researched, nothing brought back by the voyage; nor was it ever repeated. It never became an element of the culture. Appearing, dazzling, disappearing -- metaphorically right for the civilization that invented the rocket centuries ago and used it just for fireworks.
China, of all nations, should be a spacefaring one. With a billion people, its needs the lebensraum; with an isolationist sensibility, it can appreciate the greatest Wall of all, the moat of deep space. But it will be fascinating to see if its space program will be more than just fireworks, abandoned after it accomplishes an eye-catching goal, or whether it becomes a second open door, and the first exodus, in Chinese history.
Article (January 14, 2003)
The latest results from the Kamioka detector, buried deep under ground in Japan, firmly establish that neutrinos have a definite mass that enables them to transform their type. This breaks the Standard Model of physics, in which neutrinos are affected by nothing but the weak force. Now it seems that gravity must be included as well.
Shell sort is the forgotten hero of many a memory-limited program, long upstaged by its recursive big brother, Quicksort. But back when machines had 64K to work in (if they were lucky) and entire applications were written in tediously optimized BASIC and Pascal, Shell sorting's simplicity and relative efficiency made it a surprisingly good choice.
In spite of Shell sort's long existence, and the application of GAs to other sorting problems, no one has tried to improve on Shell's basic parameters by an evolutionary search. Until now. The efficiency gain is small, but it's still enough to make you wonder why you didn't think of it first.
Yasumasa Kanada of Tokyo University has just broken his own record for calculation of digits of pi, extending it from 200 billion (an unbelievable number itself) to 1.2411 trillion (a thoroughly incomprehensible number). The last I looked, in the late 80s, the record had just crossed an astonishing billion digits by the use of dedicated hardware rather than mere computer progamming. Japanese teams have, since then, been making ever-increasing strides into digit calculations, most recently with a Hitachi supercomputer (and you thought they only made TVs).
All this suggests the immediate adoption of a new performance standard for computers. Instead of the outmoded gigaflop (billions of floating-point operations per second), I propose the much more relevant, yet esoteric, megapips (millions of pi digits per second). Kanada's calculation in 400 hours clocks in at 833,000 digits per second: .833 megapips.
Technical details of past efforts are on Kanada's web page, and more amazing facts and record can be found on the last link, The Pi Pages.
For the truly determined, you can get in on the pi-calculation action yourself with a version of Kanada's own program. I quote:
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Title: Super PI Ver1.1e (calculation of pi up to 33.55 million digits)
Keywords: PI MATH WINDOWS
In August 1995, the calculation of pi up to 4,294,960,000 decimal digits was succeeded by using a supercomputer at the University of Tokyo. The program was written by D.Takahashi and he collaborated with Dr. Y.Kanada at the computer center, the University of Tokyo. This record should be the current world record. ( Details is shown in the windows help. ) This record-breaking program was ported to personal computer environment such as Windows NT and Windows 95. In order to calculate 33.55 million digits, it takes within 3 days with Pentium 90MHz, 40MB main memory and 340MB available storage.
The software is free and the circulation of program is also free!
Kanada's site, Get the program
One of John Brunner's futuristic novels gives us the concept of a world computer, Delphi, that both reflects the present and predicts the future by virtue of being connected to everyone at all times. It's a continuous opinion poll, the sum of which is the mental state of humanity. Google has, quite casually, stumbled on something similar: at their California headquarters a scrolling display reels off a sampling of the topmost search phrases from everyone, everywhere. It's a stream-of-consciousness take on the planet itself, or to put it another way, a chance to read the world mind.
Another compnay, ComScore, is tracking more than just ideas. By capturing the on-line activity of its large subscriber base, it's forming a picture of national behavior: not just what we search for, but what's being bought and sold, and who's doing it. It's group psychology by finance, and the group is everybody.
It's all a sign of a new phenomenon, real-time statistics, that's made possible only by the constantly-connected nature of the Web. More importantly, it's a kind of statistical information that goes beyond objective facts, extending to ideas themselves. You might even say it's another kind of Internet, a meta-Web made possible by searching not content, but what people do with it. Today it's in the hands of a few. But if it finds its way to the level of a free and speedy tool, it stands to become the next indispensible information commodity: the satellite photography of the mind.
- - -
From a Chicago Tribune article on ComScore:
Investors are always scavenging for data that could indicate the market's direction. Changes in everything from cardboard box orders to hemline lengths have led to stock market bets. Now upstart ComScore Networks Inc. is claiming it can predict major economic trends by tracking the online activity of 1.5 million people.
"It's a heck of a lot easier to watch somebody's online behavior than to follow everyone around in their daily lives," said Brian Wesbury, chief economist with Griffin, Kubik, Stephens & Thompson Inc. in Chicago. "So the more things we do online, the easier it is".
ComScore gains access to people's Internet travels by giving them free security software and programs that speed up their Internet connections. With its capacity to download 18 billion Web page views annually, ComScore expects this year to capture 800 million Internet searches and 5 million online transactions.
Now the company is launching its boldest initiative, betting it can extrapolate what is happening online to the offline world. ComScore says it can determine spending, employment, automobile sales and other economic measures by comparing prior government data to levels of Internet spending and traffic on certain sites during the same period.
As a second gauge of spending, ComScore also looks for trends in the credit card statements that about 30,000 of its panelists view online.
David Nuelle, a founder of the Arcanum Fund, said he will use ComScore's data to make investment decisions in e-commerce companies and offline firms, such as Southwest Airlines, where customers often place orders via the Internet.
Though it's only just coming to my attention, Water is a fairly well developed new language out of MIT that's intended to span all the features of presentation and markup, data representation, and client and server logic. To do so it takes the form of HTML/XML, but adds the ability to create objects, functions and logic as Javascript would. It's gruesome to look at, but conceptually simple, and as its name suggests, heroically flexible. Like Lisp and its descendants, it's a dynamic language to the utmost, with the ability to modify anything at run time -- even the parent of an instance. And like Lisp, it brings to the programming of today the fossil relic of the past: dynamic scope. They're called "fluid variables" now, and while they're made a little more relevant because of their kinship to class variables, they're a bit like an univited guest at programmer's party. Water may be the next big thing, giving .NET a run for its money as an all-in-one environment; or it may be the harbinger of the next kind of programming to come.
The Nasca desert in Peru turns out to be one of the best places in the world, if not the only, to draw long straight lines that will stay there for centuries: it's miles of dark volcanic rock over a substrate of light-colored sand, devoid of rain and wind. The immense lines and figures that indeed have been drawn there centuroes ago have attracted either fabulous explanations or none at all. This article takes a refreshingly level-headed look at the artifacts, and draws some new and eminently sensible conclusions. Plus, there's a report on building an ancient hot-air balloon. It's all archaeology as it should be, a good mix of explanation and fascination.
Courtesy of Victoria TangoMan from the Space Settlers discussion group:
When we see a space shuttle sitting on the launch pad, there are two big booster rockets attached to the sides of the main fuel tank. These are the solid rocket boosters, or SRB's. The SRB's are made by Thiokol at a factory in Utah. The engineers who designed the SRB's might have preferred to make them a bit fatter, but the SRB's had to be shipped by train from the factory to the launch site.
The railroad line to the factory runs through a tunnel in the mountains. The SRB's had to fit through that tunnel. The tunnel is slightly wider than a railroad track, and the US standard railroad gauge (the distance between the rails) is 4 feet, 8.5 inches. That's an exceedingly odd number.
Why was that gauge used? Because that's the way they built them in England, and the US railroads were built by English expatriates. Why did the English people build them like that? Because the first rail lines were built by the same people who built the pre-railroad tramways, and that's the gauge they used.
Why did "they" use that gauge then? Because the people who built the tramways used the same jigs and tools that they used for building wagons, which used that wheel spacing.
Okay! Why did the wagons use that odd wheel spacing? Well, if they tried to use any other spacing, the wagons would break on some of the old, long distance roads, because that's the spacing of the old wheel ruts.
So who built these old rutted roads? The first long distance roads in Europe were built by Imperial Rome for the benefit of their legions. The roads have been used ever since.
And the ruts? The initial ruts, which everyone else had to match for fear of destroying their wagons, were first made by Roman war chariots. Since the chariots were made for or by Imperial Rome they were all alike in the matter of wheel spacing, thus, we have the answer to the original question.
The United States standard railroad gauge of 4 feet, 8.5 inches derives from the original specification for an Imperial Roman army war chariot. Specs and bureaucracies live forever. So, the next time you are handed a specification and wonder what horse's ass came up with it, you may be exactly right, because the Imperial Roman chariots were made to be just wide enough to accommodate the back-ends of two war horses.
So a major design feature of the shuttle, which is arguably the world's most advanced transportation system, was determined by the width of a horse's ass.
Once upon a time all computers were big, and the best computer was the biggest. In the 1970s, just before the personal computer stole the thunder from mainframes, the giants of computing power were the IBM 7000 series (roomful of tape drives like dominoes) and the unearthly Cray XMP, eight parallel processors strong, cooled by liquid nitrogen, its eight black towers looking like they had just landed from space, and might take off again at any time. It was the stuff of dreams, and it was all big stuff.
Then came minicomputers and the revolution of microcomputers. The big machines stopped selling, and soon they stopped existing; it was cheaper to buy a thousand microcomputers than one computer a thousand times as powerful to serve the same number of people. Cray closed its doors, and IBM made headlines with its little PC. Today when thousandfold computing power is needed the trend is to yoke that many machines together on the Internet and do by teamwork what was once done by solitary brute strength.
So it was a surprise to see recently that the supercomputers, the biggest and fastest machines on the planet, have not only survived but are thriving in new ways. At the top of the heap is the unprecendented 8,192 processor system from NEC, named -- a little ominously -- the Earth Simulator. This is not your father's supercomputer. The old Crays took up a whole room; the Earth Simulator consumes an entire building. Indeed, it is an entire building, a piece of raw architecture as well as computer. If you follow the link to its page you can find pictures from inside the Simulator's building, but it's only the last -- a 360 degree Flash movie -- that gives a sense of the whole thing. Its lucky users are running experiments in rocket exhaust flow and the wind and waters, naturally, of the Earth. The Simulator's 640 units -- each a supercomputer in its own right -- clocks in at 35 trillion operations per second, dwarfing its nearest competitor.
But the fastest computer might not be in the smallest country for long. Cray is makinga comeback, promising the 50 teraflop X1 for delivery this year and -- hold on -- a goal of a one petaflop machine by 2010. That's a quadrillion operations per second, a number I honestly can't even imagine. The stuff of dreams is in good hands.
Here's a site -- and a nicely-designed one, at that -- that takes the simple idea of the road trip and elevates it to an art. Before America was turned into one giant nation by the interstate highway system, it was a patchwork of individual territories stitched together by two- and four-lane roads whose character today has faded, but is not quite gone. This site, run by a two-person team of photographer and trip planner, showcases these old highways and the sights along them. It's only a short step from this to a whole new socio-economic trend of retro-vacations; remember you saw it here first.
The endless recycling of documentaries on cable channels leaves me uncertain just how old-hat this is, but I was startled to learn that archaelogists have unearthed the site of Varus's terrible defeat in A.D. 9 at the hands of Arminius and his Germans. The German-language link below provides photographs of the site and of items recovered (click on 7a, 7b, and 7c); the English link is to a site devoted to the battle. For some reason, this battle has always stayed in my mind: the horrible sound of the Germans in the forest, hooting and calling from all directions, as the Romans realized they were trapped, and the immense slaughter---few survivors made it back to Rome.
Tacitus gave a haunting description of the site as it appeared 6 years later, where 20,000 or more Roman troops' bones lay unburied:
The scene lived up to its horrible associations. Varus' extensive first camp, with its broad extent and headquarters marked out, testified to the whole army's labors. Then a half-ruined breastwork and shallow ditch showed where the last pathetic remnant had gathered. On the open ground were whitening bones, scattered where men had fled, heaped up where they had stood and fought back. Fragments of spears and of horses' limbs lay there---also human heads, fastened to tree trunks. In groves nearby were the outlandish altars at which the Germans had massacred the Roman officers.
Brrrrr! The remnants of the Roman earthworks have been found.
University of Osnabrueck, background
Here is a magnificent collection of fifties-era photographs of fifties-era computing equipment. It's not only a reminder that computers should rightfully be the size of a refrigerator and communicate by blinking lights and teletype, that real programmers wear suits and narrow black ties; it reminds us that that the silicon chip has made invisible all the machinery of computing machines, a lost aspect and a beautiful one under the photographer's eye. Well worth it for a trip into the past and into the archaeology of your own machine.
Hands down, the most beautiful equation in mathematics is Euler's formula. It welds the fundamental constants of all mathematics -- e, i, pi and 1 -- into a single relation of almost impossible simplicity. It is the E = mc^2 of mathematics, as famous, classic and profound as Einstein's equation. And as revolutionary: just as Einstein showed that matter and energy, utterly different from one another, were really aspects of the same thing, so Euler's formula revealed unsuspected connections between exponential functions, trigonometry and imaginary numbers. That it does so with just five symbols is what grants it immortality and surpassing elegance.
That elegance has always been completely opaque to me. I've always admired this equation, with only a little understanding of its parts, and nothing of how they are put together. Recently, though, I decided it had been out of reach for too long, and that a pursuit of this abstruse beauty was long overdue.
Here's the cast of characters.
e = 2.71828...
Base of the natural logarithms. Major player in the calculation of rates of growth and decay. Practically everywhere in serious calculus.
pi = 3.1415926...
Fundamental constant of the circle. Holds a monopoly in the mathematics of practically everything curved. Has its own key on calculators, the equivalent of the Hall of Fame for numbers.
i = sqrt (-1)
The imaginary number: the square root of negative one. The place where math really stops making sense.
1
The most real number of all; the opposite of i. Basis of all arithmetic. Also has its own key on calculators.
And here's Euler's formula: e ^ (i pi) = -1. That's e, raised to the power i times pi, equals (somehow) minus 1.
To put these all together, I began by hitting the Web. I found plenty of explanations of Euler's formula, but they didn't really dispel the mystery or reveal its inner workings. Mostly they presented a few definitions without elucidating them, waved the magic wand of proof, and left you with the result, but no illumination.
So I decided that the only way to get to the heart of the matter was to derive this formula for myself from first principles. My goal was to find my way there, trace the marvels along the way, and bring back an explanation that was complete, comprehensible and satisfying. I took a clean sheet of paper, a double latté, the definition of the number 1 and, having no day job, set to work. A week, some sleepless nights and a lot more ingredients later, I nailed it down. And despite the torturous path, the goal was worth it: it really is one of the most beautiful things I've ever seen.
I've condensed that winding path into a series of Web pages that set forth the whole route. I've tried to strike a balance between detail and conciseness, mathematics and intuition. The result is an uneasy compromise, long-winded in many simple places and mighty brief in some complex ones -- but it does work. With a little patience and mathematical daring (you'll need to recall a dash of basic calculus to get a grip on e) you can find your way through it, appreciate the things to be found on the way, and put the understanding of a piece of immortal mathematics into your aesthetic portfolio. All in under an hour if you put your mind to it.
So cancel that lunch appointment, close the office door, and go for it. It should be accessible to the mathematically wary, and rewarding for the mathematically supple. A pearl of advice: follow the examples closely; they'll steer you right when my verbiage may not. Good luck, and don't forget the latte.
Apart from the obvious appeal of someone's trying to present computing to humanities students---C ++ for Poets, say---I'm for some reason struck by the idea that, perhaps for the first time in history, the understanding of a particular machine and its nature is considered something of humane and even philosophical interest on such a broad level. (Fishing for counterexamples.)
Why should this be, exactly? Why should the English major care how his glorified typewriter works? The argument may be, I guess, that computing exemplifies a way of thinking that is important in its own right, and that is somehow not covered by Logic 101 or other such courses. There may also be a whiff of cybernetics in the air: has computing become such a part of who we are that we can't understand ourselves without understanding our machines? I don't think this is broadly true even of Americans, but I can see the argument that the upper classes are moving in that direction.
Any thoughts on how computing fits into a broader story, a grand narrative, of Western intellectual development?
Archaeology has been headed underwater for a while, what with major new settlements discovered on the floor of the Black Sea and most of the best parts of ancient Alexandria turning up, quite intact, beneath its own harbor. But even stranger are deep-sunken megalithic structures, the most famous being just off Okinawa: a parade of giant dark rectilinear forms that look man-made, but must date, by reason of being submerged, from an ice-age period long before anyone shoul dhave been around to build more than a fire with two sticks.
Now another such structure has been found near Cuba, an unmanned vessel photographing "massive stones in oddly symmetrical square and pyramid shapes" almost half a mile down. No one's offering a reasonable explanation yet, but it's sure to involve a new look at current archaeology or current geology. The rocks had to get there somehow.
I purloined the following from the "Volokh Conspiracy" weblog:
ECONOMICS AND THE ENGLISH LANGUAGE: Here's a nice quote from Alfred Marshall (February 27, 1906):
I had a growing feeling in the later years of my work at the subject [economics] that a good mathematical theorem dealing with economic hypotheses was very unlikely to be good economics: and I went more and more on the rules -- (1) Use mathematics as a shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life. (5) Burn the mathematics. (6) If you can't succeed in 4, burn 3. This last I did often.
(Robert B. Ekelund, Jr. & Robert F. Hebert, A History of Economic Theory and Method 377 (3d ed. 1990) (quoting Memorials of Alfred Marshall 427 (A.C. Pigou ed., 1925).)
I've always thought of the Space Shuttle as something uniquely American, like the station wagon. But here is Japan's version: smaller and unmanned, but as you might expect, working just fine and cool-looking to boot.
At the University of Kansas, a sandwich of carbon nanotubes and polymer had made the first large-scale, cheap nanotube composite, many times stronger than carbon fiber. It's a reminder that as the Information Age has been coming in, the Iron Age has been quietly fading away. Over the last fifty years steel has replaced wood in countless commonplace items, and plastics are rapidly displacing all things metal. If your food still comes in tin cans or cardboard boxes, you're behind the times: even grocery shelves are starting to fill with metal-film mylar envelopes and designer plastics. Synthetic fabrics have moved from exotic high-performance tents to the ten-dollar outerwear racks at Wal-Mart, and for the same reson -- they're lighter, cheaper, more durable, and don't require a herd of sheep to produce. It's a Materials Age that we're really caught up in, and even the Information Age is just its spin-off, a footnote to the synthetic silicon crystal industry, with a little math thrown in.
(Popular history note: both shampoo and dishwashing liquid -- the two slipperiest substances known to man -- were sold in glass bottles right through the mid-sixties. If that almost unimaginable fact doesn't impress you with how radically the world is advancing, nothing will.)
It's like a window straight back to the late Cretaceous: the preserved remains of a Brachylophosaurus -- a 22-foot youngster -- have been unearthed in Montana. The actual appearance of dinosaurs has been the sole province of artists, more and less scientific, until now. Time has bleached this one a bit, but its skin texture is clearly visible, the musculature is intact, and even the magnolia leaves it last dined on remain within. Besides resolving artistic conjectures, this find answers an ontological issue as well. Up to now dinosaurs have not been quite as real as, say, cocker spaniels. We inferred a creature from its bones, but its absolute existence was only in our imagination. The discovery of a real, dead dinosaur is a big step up the philosophical ladder for real live dinosaurs.
The links here include a great page of photos from the institute sponsoring the dig, as well as a visit to a dinosaur park where you can see the current state of the art in guessing what this duck-billed dinosaur must have looked like.
National Geographic
Photos
Montana Dino Digs
This is an excellent survey of the approaches to super-Turing computation, written with great clarity by Toby Ord at the University of Melbourne. Since ordinary Turing machines have achieved great popularity (I'm writing this on one), more powerful formulations of computation have received relatively little attention. Despite the fact they they're all impossible to build, super-Turing designs (such as the replacement of discrete tape symbols with real numbers) permit some otherwise impossible solutions: the Halting Problem, for instance, is no problem at all. The greatest asset of this work, though, is the background material it provides: a perfect capsule exposition of computation theory and classical Turing machines from the ground up, and a nice introduction to the arithmetic hierarchy together bracket the main topic. Both are worth a look for their own sake, especially if you haven't thought your two impossible things before breakfast yet.
Don't miss this one: it's a half-hour movie (Real format) on Claude Shannon, founder of just about everything digital. If you don't know the man, this is an essential introduction; if you think you do know him, you'll be surprised all over again by the scope of his ideas, from cryptography to -- yes -- blackjack.
The cathedral is the perfection of the arch; the arch is the heart of all architecture. Two remarkable buildings have caught my eye recently, each a church, and each with something new to say about arches.
From a supermarket parking lot in Dallas springs up a sixty-foot hill surmounted by a chapel of arresting design. Shoppers didn't seem to notice it when I was there, but I couldn't take my eyes off it. A steep, wood-clad roof rises up from the trees around it, giving glimpses of geometric beams and masonry beneath its eaves. There's not an arch in it, nor any curve: it's stitched out of extended lines and planes in the most modern way, but at the same time looks exactly as a church should. It accomplishes this paradoxical feat by extracting the essence of the gothic cathedral and discarding the rest. Its interior is composed of the same lines of light coming in from high windows; and the prevailing angle, in the roof and in the rest of the structure, is exactly that of the narrow gothic arch where its rising curves meet at a culminating point. The whole is the work a Fay Jones, a Wright apprentice, out of Arkansas, who seems to have devoted his career to building things exactly as he thinks they should be, and no other way.
The chapel of Santa Maria degli Angeli by Mario Botta is another modern building with an old soul. It's a chapel as well, but perched on an isolated Swiss mountain -- about as far from a Texas parking lot as you can get. It's a passionately geometric building that somehow captures the feel of a medieval monastery, as if Le Corbusier had visited the fourteenth century. Everything about it looks startling and yet feels right. The great secret of its design, I think, is that the characteristic cathedral curves of the flying buttress, Roman arch and gothic window have been lifted whole and then refitted to one another, so that everything is familiar yet new. It's a remarkable building, and the truest example of real architecture.
Besides the Lena Pope Home chapel, check out:
this Czech site
www.galinsky.com
The closest thing to speaking to a native of the year 2300 B.C. is laying eyes on a manuscript from a past civilization. Cuneiform laws engraved on clay, Greek poetry rescued from mummy wrappings -- it's all here at the Schoyen Collection site, gloriously illustrated. Check out their Picture Index, and the exuberant calligraphy of Aristotle's Nicomachean Ethics (Special Collection 5.5). Wonders abound.
On the top floor of the Metropolitan Museum, between Chinese Arts and Near Eastern Antiquities, is a small side entrance that takes you two steps down to a quiet, narrow room. This is the Musical Instruments collection, where a handful of old and famous instruments sit in dim light and plush-carpet silence, waiting to be discovered by the passerby. A Chopin-era Erard piano is the first thing you notice, looking at once grand and a little worse for wear; not far away is one of the first pianos ever made, a spindly Christofori from 1720. Past them, past a wall of ornate Middle Eastern woodwind instruments and a perfect, unplayed Stradivari violin, is a plexiglass case where they keep Segovia's Hauser.
The first thing that strikes you is how small it is. All the instruments here, separated from their players, have a strange, out-of-scale look to them, as if they've shrunk waiting for their owners to return. But the Hauser really is a bit smaller than the usual Spanish guitar, if only by a little. Hauser's workshop was in Munich, and he turned out instruments, as his father did, based on the German tradition. The curve of the bouts is slightly exaggerated, almost elliptical; there seems to be more neck than body. Hauser saw his first great Spanish guitar in 1925 when Segovia played a concert in Munich, and took down its dimensions when Segovia visited his shop later. A dozen years after that he finally created an instrument he thought was better. Segovia agreed, put aside the Ramirez given to him in 1912, and played the Hauser exclusively in concert and on recordings for the next twenty years.
Those who heard it never forgot it. Sharon Isbin called it "the guitar of the century", and in Segovia's hands, it was. It was a punchy guitar, strung with gut and full of power and color; it wanted to be played by big hands. It not only put its maker on the map, it fixed him among the constellations, and more orders were placed for his guitars than he could fill in a lifetime. That instrument became only a little less famous than its player, referred to in hushed tones and known the world over simply as The Hauser.
For all this, it's now unplayed, under glass. Like the Erard, it looks rather worse for the wear. The face at the sound hole has the varnish worn away from decades of daily playing. This isn't the rapid wear of a hard-strumming guitarist; the classical player's right hand never touches the wood. It's an accumulation of chance brushes of the little finger and the occasional pass of the fingertips when the thumb plays the top strings for effect. It's the same wear that river water makes on rock over centuries, and took about as long. The guitar looks tired, too, and played out, as if it's not just on display, but out to pasture. It needs a good restoration, and like the other untenanted instruments here, it wants a player. It won't be getting one. Its fame has locked it in a museum, but even with a less celebrated background, we can be sure of one thing: it won't be coveted by the guitar superstars of today; it won't pack an auction house with expectant buyers; it won't set any sales records. No guitar from 1937 would.
Stringed instruments age; guitars just get old. There's scarcely any difference between the two in terms of quality of materials or construction; there are as many reasons for the old to be at least as desirable as the new. But drop by the site of Chicago's Bein and Fushi, or Tarisio, and you'll find a 1713 Stradivari violin, a 1717 Tecchler cello; both look like they've been dragged behind an oxcart and given up for dead. Christie's home page proudly displays a Strad that recently sold for $1.3 million -- alongside a 1947 Hauser that commanded less than $50,000. The violin is destined for the concert hall; the guitar is not. Concert guitarists want new guitars.
Perhaps the mystique of age takes longer to acquire than fifty years, or seventy-five. Maybe those old guitars will come out of attics and museums in 2137, if there are any left. But meanwhile a unique sound world is disappearing behind protective glass in dim rooms, and the only way you'll hear any guitar made in the thirties or forties is to pick the right Segovia recording and listen to The Hauser, or stage a daring raid on the Met and play it yourself.
If there's hope for old guitars becoming the next new thing, it will come from exceptional places like The Guitar Salon in New York, not all that far away from the Metropolitan Museum itself. They have mint-new guitars like the Bernabe Especial that put a gleam in my eye; but they also have a 1929 instrument by Santos Hernandez, and an 1875 Torres; you can see both by following this article's link. Better, check out their west coast sister at www.guitarsalon.com. There you'll find another 1937 Hauser. Like the one in the Met, it's waiting for a player, too.
I've been relativity-shopping lately in a long-standing attempt to comprehend the whole space-time-gravity thing. There's a lot out there. Einstein has his own streamlined explanations, and everyone else since then has a book, some technical, some not, that purports to set the story straight on curved space. After quite a bit of in-store perusal, I took home "Einstein's Theory of Relativity" by Max Born. It has turned out to be a masterly exposition of the physics that culminates in relativity, with enough mathematics to illuminate without confounding.
But there's another way to take your Einstein: straight up. Two books -- one older, one soon available -- give you Einstein and nothing but. "Einstein's 1912 Manuscript on the Special Theory of Relativity: A Facsimile" is a couple of hundred dollars' worth of relativity in Einstein's own handwriting as well as words. It's seventy-two pages of scratched-out ideas, false starts and changes of mind -- a great glimpse behind the curtain of revolutionary thought in the making. I've wanted this one on my coffee table for some time.
In something of the same spirit, a new book coming in November is "The Einstein Scrapbook" by Rosenkranz. It's a collection of unpublished notes; call it all the envelopes from a lifetime of back-of-the-envelope calculations. I haven't seen it yet, but the notion of a collection of ideas that didn't quite make it has the potential to be as fascinating as Leonardo's notebooks, with the ability to bring you just as close to the inner workings of an original mind.
project at the murky crossroads of mathematics and modern culture; all I can say is that I wish I had thought of it myself, and to quote from the site:
"The authors conducted an exhaustive empirical study, with the aid of custom software, public search engines and powerful statistical techniques, in order to determine the relative popularity of every integer between 0 and one million. The resulting information exhibits an extraordinary variety of patterns which reflect and refract our culture, our minds, and our bodies."
The results are winningly graphed, with the universal propensities for repeated digits and round numbers clearly evident in their neat geometries. And there are inexplicable standouts from the expected pattern, too: the baffling popularity of 11042, for example, and the twins 14850 and 14853. Taken together, it's a unique species of cultural map.
This John Mcphee book is a compendium of no less than four other books of ordinary size, under one cover and thick as a Manhattan phone directory. The theme through all four volumes is, surprisingly, geology: geology with no hold barred. The endpapers chart the epochs of the last two billion years as a textbook would, and nary a page is without a barrage of technical terms and complex ideas about rocks and how they got that way. The other surprise in all this is that it works. Rocks are the earth, and their plate-tectonic history is our history on a different stage. I finished this opus a little winded intellectually, but I'll also never look at a map the same again now that the surface tells so much more of what lies beneath, and came before.
The book is also a celebration of good writing. McPhee's strength is metaphor, and when the abstractions of an unfamiliar science call heavily upon his talents, he answers. I picked up my copy for but five dollars at the local Barnes & Noble; you should do the same.
The article at the link below describes a French skydiver's plans to set a new record for high altitude skydiving. The previous (unofficial) record of 102,000 ft. was set way back in 1960, and a number of divers have died trying to surpass it. The French army skydiver expects to actually break the sound barrier during his 6-minute fall over the Canadian plains.
TransOrbital, Inc., of California, has received permission from the State Department and NOAA to launch and land a commercial vehicle on the moon. "The moon is ripe for commercial developement", TransOrbital says. The approval process itself is interesting, having been under way for the last two years. The goal seems to be mapping the lunar and terrestrial surfaces for profit.
This is a surprising development (to me, anyway), and it more than a little recalls the Internet of seven or eight years ago: like the moon, it was everywhere visible and little occupied, and completely free of commercial interests. Indeed, the very existence of advertising or business was hotly debated and widely rejected. Business had other ideas, though, and untimately drove most of the expansion of the Web. Tip of the iceberg all over again?
Nature (September 9, 2002)
Nash is an elegant game that you can play on-line, and also its co-inventing mathematician who made his name in game theory and pure mathematics. I ran across both while re-reading Sylvia Nasar's biography of John Nash, surely the only such bio ever to become a film.
It's a fine book, deeply researched and well written. It's a delving biography, meaning that there's plenty of history of the times and places involved (chapter histories of Princeton University, early computing, the Riemann hypothesis) as well as an unflinchingly detailed life story. It's a moving story, but also a disturbing one: Nash is the mathematician who descended into deep schizophrenia in the middle of his career, and then gradually -- and unexpectedly -- emerged from it decades later.
That makes this a remarkable biography by reason of structure alone. All biographies have the same plot: in the end, after many adventures, the hero always dies. One never finishes a biography with a sense of cheer. Nash's story has a completely different shape: he is born, rises to fame very early, and -- intellectually, at least -- dies. Many chapters later, he comes back to life, and at the end of the book, he stays that way. He's still alive today, living with his family in Princeton. It all feels strikingly different from a traditional life-and-death story, and like any story that centers on resurrection, more than a little mystical.
As a new student at Princeton, Nash invented a board game that was promptly named after him. Quite separately, the famous Piet Hein invented the same game in Denmark. It's played on hexagonal tiles arranged in a four-sided diamond, with two players who alternate placing pieces. The goal is exquisitely simple: to create a connected path of your pieces from one side to the other. It sounds reminiscent of Go; it feels a little like Tic-Tac-Toe in play, but much richer.
Creating a new board game, especially within the tradition of symmetrical field, regular subdivisions, and uniform pieces, is almost impossible to do successfully. I've tried more than once, and it soon becomes clear that the canonical forms that meet these criteria have all been taken: chess is the game of mobile, diverse pieces; checkers of mobile uniform pieces; and Go of static uniform pieces. Nash's game (Hein called it Hex) is suprisingly successful, achieving considerable complexity from almost no rules at all (the recommended board size of 14x14 is even more challenging). You can give it a try by follow the link.
Paintings are flat imitations of three dimensions; photographs are genuine three dimensions flattened onto two. A New York artist, Katinka Matson, is making images that hang eerily between the flat and the solid, by using neither camera nor canvas, but a flatbed scanner. The results are remarkable for the beauty produced by composition under such constraints: a scanner has terrific color resolution and detail, but can only see a short way into the third dimension. Check out the article, and look for the links to images at the end of it.
I happened to see the SETI@Home project screen saver some up on a friend's computer recently; like countless other home machines, it was diligently searching for signals in the extraterrestrial noise. Being a hardened skeptic, I could only sigh at the fruitless use of all those cycles of computing power.
But what better use is there for the spare time of a few hundred thousand computers? The Great Mersenne Prime search runs on a similarly distributed basis, going where no single computer has gone before. But -- while admitting the exquisite attraction to primes of any sort -- one Mersenne prime is starting to look much like another.
The digits of pi? Done to a turn already, and after a billion digits, it's hard to yearn for more. Verifying the Goldbach conjecture is a nice idea -- we only have to check all even numbers up to 10^43000, the conjecture having been proved true beyond that -- but those kinds of magnitudes will need another century of technological development, or an as-yet-undiscovered way to link together all those PlayStation 2's out there. Climate modeling came to mind; it would be both worthy and cool to have a weather model that ran in real time, and the structure of the problem should be reasonably amenable to parallelization.
I dropped by Entropia.com, a company dedicated to this sort of application, for a look at what they had to offer. The scope is wide: pharmaceuticals (ligand-receptor complex modeling, anyone?), finance (believe it or not, portfolio modeling) and aerodynamic simulation. They're neat, but they don't really capture the imagination, and when your computing power relies on the voluntary contributions of time from individual computer owners, imagination is the only currency you have.
The Aspenleaf site (follow the link) is the gold mine of imaginative applications. Climate modeling is there, as is protein folding, twin primes, and verification of the Riemann zeta function. The zeta function and the distributed drug design project get my vote so far as the best and most interesting way to invest my scant few idle cycles.
But is there something better? If you know, let me know. Or if there should be something better, but isn't yet, tell me what it would be. Rememer, while you're sitting there thinking your machine (and mine) could be working away.
What Mandelbrot's classic function, Lychrel numbers and values in the hailstone series all have in common is the form their function output takes: a series of values that either diverges from or converges upon a constant. Graphs of the Mandelbrot set capture this information beautifully by color-coding the number of iterations that lead to divergence. Though it's not a complex function with a natural two-dimensional graph, I've tried to do the same with the Collatz function.
Wolfram's Mathworld site will tell you that this function goes by a bewildering number of names: hailstone numbers, Ulam's problem, Hasse's algorithm, the Collatz problem. It's simple: take any number, halve it if it's even, triple it and add 1 if it's odd. Repeat with the new result until it reaches 1. Each number breeds a series of values, long or short, before it finally finds its way to 1. Like its sister functions, it feeds upon its own results, thus giving rise to its complexity.
The same graphing scheme use in the Mandelbrot set -- coloring each point by sequence length -- could be used here one-dimensionally, but I've chosen a couple of different routes to visualization in two dimensions. In the first, I plot the initial values on the x-axis, and all the function values it gives rise to directly above it on the y-axis. This doesn't preserve their order, but it does reveal the overall pattern of their distribution. The result is a remarkable graph in two ways: it clearly shows a self-similar scaling structure vertically, with strong attractors along various horizontal bands, and just as clearly shows a distinct series of values that fall into an entirely different and quite unexpected pattern. I don't have an explanation for this yet, but I'm looking.
The second graph plots function values vertically, but against their position in the result sequence horizontally. The sequences for the first several hundred initial values are overlaid, emphasizing common values. This graph is narrower, since it is only as wide as the longest sequence encountered. It's a pretty thing, but less startling than the first.
There's more to be discovered here, I imagine, from other visualizations of this data. I have plenty to interpret as it is, though, in the mystery of the nonconformist lines. Explanations are welcome!
A Seattle company is confidently claiming that their space elevator design is only one technological hurdle away from sending you and your family into orbit, cheap, in the next 15 years. NASA agrees, at least to the point of extending them half a million in funding. This is a breathtaking re-evaluation for me of the feasibility of such a device; NASA's own writeups cited more technical challenges than you could shake a carbon nanotube at. We've seen just-around-the-corner promises for technology before (fusion has seen that corner recede more times than most). Will a wire into orbit escape the same fate?
We forget just how recent computers and computer science are. The great names that invented the hardware have passed away, but we are still living on the cusp of the age of the Olympians of software. The creators of COBOL, Unix, DOS, BASIC, Pascal, LISP, and object-oriented programming are all still with us. Only John Backus, the author of the first FORTRAN compiler, died in 1988. Now Edsger Dijkstra has joined him.
Dijkstra invented more things that I always used but never noticed -- semaphores (whose names, P and V, made perfect sense in Dutch), structured programming, and his eponymous shortest-path algorithm -- and reading over his list of accomplishments will keep your eyes constantly raised. He seems to have single-handedly hauled software out of its first generation and into its long-lived second.
Back in the days when there was only one computer magazine (Byte) and two word processors (WordStar and Spellbinder, glorified word processors both), Byte interviewed Dijkstra and asked him what software he used to produce his famous papers. "I write them all out in longhand", replied a horrified Dijkstra, "with a fountain pen".
I have no time to pursue this at the moment, but I thought somebody should take a look. Hint, hint, Jim.
It at least sounds important.
Read all about it (September 3, 2002)
From the first airplane flight to the first fleet of planes, hardly 20 years passed; from a computer on paper to a roomful of vacuum tubes was even less. Fusion power has had 50 years to come to fruition, but we're still burning coal and oil to fly our planes and power our microprocessors. Fusion is the runt of the 20th century technological litter.
Plasma confinement for fusion power has been quietly and steadily improving in miilisecond leaps over the last two decades, though, and now the Tore Supra reactor in France reports a remarkable new record of 210 seconds -- not milliseconds, real seconds. That's three and a half minutes, a remarkably long time compared to just the recent past. How much closer that puts us to a sustainable power source I can't say; the issues of efficiency, durability, and plasma creation are left untouched by this New Scientist article. But as it doubles the previous record, it definitely qualifies as a leap, not a step.
Why is fusion so hard compared with its sister technologies of flight and computation? It didn't have a war to spur it on, for one thing; the others had a World War each driving research and development. But certainly fusion experiments have a vast factor of scale that separates them from other endeavors: you could build a plane by dropping in an off-the-shelf piston engine, or power an early computer with no more difficulty than the factory next door, but it takes, literally, a city's worth of electric power to fire up a fusion reactor, even if it's only for three minutes. The scale of forces, and therefore the scale of construction, complexity and expense is orders of magnitude greater than in any other form of science; only particle accelerators come close. That problem of scale is at the heart of the matter. Instead of hundreds of academic and backyard experimenters at work at once on the problem -- the engine of multiplicity that basic science relies upon -- we have only one or two international teams. We think of evolution as blind and science as aware, but in fact they both depend on as large a pool of agents with as great a diversity as possible to make headway. In evolutionary terms, fusion research is an endangered species: low in population, low in reproduction, and depending on a scarce handful of distinct genomes. Under those difficult conditions, it's a long way to optimum.
I have a theory that when the first cave painting was first unveiled, it was hailed as cutting edge technology. A public, permanent display of information: who could ask for more? The Google archives of Usenet make another kind of archaeology possible, that of the nascent electronic society of fifteen years ago, what it thought of the world, and of itself.
The link here is to the very first mention on record, back in 1985, of the Year 2000 problem. A fascinating throwback in itself, and full of conceptual nuances; ourselves looking back at the past looking forward. One Spencer L. Bolles holds the honor of first putting his misgivings on this topic into print -- or onto the cave wall, if you will. Because if you look closer at the postings here, they have a primitive, small-culture aura to them. People use their real names. The addresses aren't from .com's or .edu's, but are UUCP routes. The signatures are full of information on other ways to get in touch, as though this newfound machinery for communication might break down at any moment and leave everyone in the dark. There's a telling human stratum overlaid on the mere information here that is as much of historical interest as the actual messages, and I don't think it's going too far to call it a kind of electronic archaeology accomplished from the armchair. It's too early to call it a field in itself, but as each year deposits another layer of change onto the digital past, there is more and more to be gained from looking back.
The August 5th, 2002 issue of the New Yorker magazine (not online, but which you should be subscribing to anyway as intelligent citizens of the 21st Century) has a long and fascinating article about the remarkable ability of a few talented individuals and an increasing number of academic specialists who are able to distinguish truth from lying solely by watching a person's face. The range of topics this touches on is rewardingly wide: anatomy and anthropology, relentless academic analysis, and the workings, volutary and otherwise, of the human mind. Of the many memorable people and events in this article, I'll cite just one: hearing of one scholar's self-trained ability to read personality in the actions of muscle groups of the face, a field anthropologist decided to test him by finding two jungle societies that had never been exposed to human contact (or facial expressions) outside their own, filming conversations between members of the two, editing the film so that only the conversants' faces were visible -- not their hands, tools or weapons -- and then playing the result before the famed reader of faces. After watching these interactions in a language unknown to him, he announced that one tribe was peaceful and cooperative, and that the other tibe was violent, warlike and probably cannabilistic. All of which was exactly right.
At NIAC you'll find over 100 reports on topics NASA considers promising enough to spend a little cash on. The Advanced Concepts section lists analyses NASA has hired consultants or experts to research and report on. Many are carefully considered engineering feasibility studies, and almost all are fascinating and enlightening. See what they'll think of next!
Here's an interesting item reported back in February: an anthropologist from the University of California created a software model to determine the necessary minimum population that, in initial isolation, could thrive not only biologically but socially, providing a reasonable diversity of, for instance, possible marriage partners. It's the first I've heard of quantitative thought being given to this intuitive notion, and it also raises the interesting questions of how such specialized populations might have their social parameters adjusted, initially or over time, to alter this minimum. Or to put it another way, are space travellers really like you and me?
Imagine that one of Antartica's dry valleys becomes a site of some industrial importance. The unique physical properties--maybe it's consistent low temperature and humidity--make it the ideal place for some kind of manufacturing--some hypothetical large-scale structural work that can only be done in -50 Celsius, with next to no humidity, and for which end users will pay gajillions.
When first it's proposed that a factory should be built down there, major corporations scoff. Too costly to keep the place supplied, they say, and how are you going to get the finished product the 400 snow-covered miles to the ocean--dogsled? But advances in lighter-than-air craft (tougher dirigibles) are theoretically possible, and it's not long before they're being built in quantity to support to burgeoning Antartic manufacturing industry. Whole cities for workers are built underground there, and mankind has crossed another threshold. The potential profit to be had led the innovation.
Exactly analogous to the India-pepper-sailing analogy mentioned in the Apollo 11 posting, right? Does the Moon have no pepper if its physical properties (low gravity, unoxidized raw materials, no atmosphere to inhibit astronomy or solar energy collection and beaming) can be taken advantage of? Isn't it just a question of having the right technology to make the cost equation balance?
Imagine that one of Antartica's dry valleys becomes a site of some industrial importance. The unique physical properties--maybe it's consistent low temperature and humidity--make it the ideal place for some kind of manufacturing--some hypothetical large-scale structural work that can only be done in -50 Celsius, with next to no humidity, and for which end users will pay gajillions.
When first it's proposed that a factory should be built down there, major corporations scoff. Too costly to keep the place supplied, they say, and how are you going to get the finished product the 400 snow-covered miles to the ocean--dogsled? But advances in lighter-than-air craft (tougher dirigibles) are theoretically possible, and it's not long before they're being built in quantity to support to burgeoning Antartic manufacturing industry. Whole cities for workers are built underground there, and mankind has crossed another threshold. The potential profit to be had led the innovation.
Exactly analogous to the India-pepper-sailing analogy mentioned in the Apollo 11 posting, right? Does the Moon have no pepper if its physical properties (low gravity, unoxidized raw materials, no atmosphere to inhibit astronomy or solar energy collection and beaming) can be taken advantage of? Isn't it just a question of having the right technology to make the cost equation balance?
(July 31, 2002)
Let's face it, when your whole country is a rocky volcanic island, there's going to be an inevitable bias toward seafood, and away from such exotic flavors as chocolate, vanillla, and strawberry. Check the link for the latest offerings in -- yes -- Japanese ice cream.
You still have your Collected Works of M.C. Escher from high school, right? Time to pull it out. This article from the New York TImes describes a mathematician's encounter with The Print Gallery, a surprisingly Mandelbrot-like image that spirals inward on itself, reducing in scale as it goes. Such a fractal convergence never ends, simply growing in complexity as it shrinks, but Escher's picture dissolves into a pristine white center where the artist has embedded his signature. Hendrik Lenstra set forth to uncover the mathematical structure behind the image and extend it to find out what, if anything, was at the missing center of Escher's enigmatic etching. The answer is just as interesting as the picture.
They're still in business. And they're still making front-panel units. It's a little hard to believe, but you can apparently go to the Imsai web site and order up that same red-and-blue switch-bedangled 8080 front panel that looks as good today as it did in 1975. Almost as good, scroll down a bit and look for their downloadable emulators. You still have your 88080 assembly langauge handbook, right?
The Titanic, a marvel of construction, an innovation in design, never served maritime science so much as when she sank. The improvements in ship building and sailing that she inspired affected big ship design for years to come; but this was nothing compared to the decades of research into exploration of the unearthly and hostile environment of the sea that eventually culminated in a return visit to her remains. When Ballard's team located the wreck in 1985 it was not scientific venture, even though it used science to accomplish its aims; nor a business venture despite the potential for profit. It was a gesture of consummate tourism.
I have always held that the great age of space exploration would open in the same way that the great age of sea exploration did, by commercial forces seeking over the waters what could not be found at home. There was pepper in India, profit in bringing it westward, and wealth in doing so faster than travelers on land. From that stark economic fact sprang the shipbuilding, navigation and cartography to make it possible. And once opened for trade, the seas became home to ships and sailors of all kinds.
Apollo 11 was supposed to have opened that great age; instead, we are still sitting on the shore. The reason is simple: the Moon has no pepper. There is desire to go into space, but value only in bringing something back from it, and unlike the Indies in the fifteenth century, there is simply nothing on the moon that we do not have on earth.
Except for one thing: Apollo 11. Like the Titanic, it may turn out that Apollo's greatest contribution was not landing on the moon, but leaving something behind when it left. Part of what's left is its own legend, but the other part is entirely physical, and these leftover landers, historic footprints, and vehicles for the taking have turned the moon into a tourist's dream, the perfect space museum; less accessible than the ocean floor, but not by much. The only disadvantage is that we know exactly where it is. If it were lost, like the Titanic, I suspect we would have already gone in search of it. Instead, it it just misplaced.
Still, the moon is a much more interesting place for the tourist than the bottom of the North Atlantic, and the prizes there just as fine. Instead of a second great age of sail inspired by profit, we may see for the first time, as some are now maintaining, new technology driven by the curious visitor and the desires for both novelty and rediscovery. And if these wear thin, one-sixth gravity is a great place to build a casino in.
There's a lot to like in this article: a worthy goal, a clever evaluation function, and surpising results. But what struck me most was the simple perceptiveness involved: someone bothered to notice what's beneath our fingers all the time, and to think long and hard about it in new ways. A good article for typists, coders and thinkers alike.
Here's a really surprising take on ice age causes: galactic rotation. Like me, you've probably figured that the angular velocity of the galaxy was something that you could safely leave out of your daily life; well, maybe not. The link has a review of the study, and a further link to the full article.
I know they made it into a movie. I know I should really have read the book, and not listened to it. Still, this two-cassette book was a terrific listen on the drive from Dallas to Jackson recently. It's a well-narrated tale full of the unexpected: the point of view is a German prisoner of war's who bounces around the Himalaya countryside on the run from the law, escaping into Tibet because it's the only place left, then befriending the family of the Dalai Lama because it's their house he stumbles into on a rainy night looking for shelter. The book is probably a good read (the link leads to the paperback), but it's probably a better listen; a traveler's tale spoken, as it should be.