- Tuesday, May 02, 2000 at 20:45:38 (EDT)
Regular stars like the Sun generate energy by fusing hydrogen atoms. Giant and supergiant stars have exhausted their hydrogen and survive by fusing helium or heavier elements in their central regions. Those stellar cores are something like a white dwarf star, thousands of miles across, with atoms packed so closely together that the electrons are squeezed out of their normal orbits. Around the core are millions of miles of thinner gas, held up by the fierce pressure of radiation escaping from the center. One such star is Betelgeuse, a red supergiant in the constellation Orion.
But could there be stars with much denser cores? They would look almost the same as "normal" red supergiants from the outside. But in the center, instead of a white dwarf there might be a neutron star or even a black hole. Are such stars possible? To survive they would have to be incredibly hot towards the middle. Otherwise the gas would all fall down in a matter of a few years.
In the mid-1970s Kip Thorne and Anna Zytkow began an analysis of stars with neutron-star cores. They found that such objects could support themselves by slow, steady accretion onto the dense central body if the envelope was less than about 10 solar masses. More massive stars needed extra energy, from hydrogen-burning nuclear reactions, to hold themselves up. Thorne and Zytkow estimated this nucleosynthetic process, but they warned that a more detailed treatment might significantly change their results. I undertook such a calculation, building upon work by Michael J. Newman, my advisor Kip, and Anna.
Anna N. Zytkow (pronounced ZHIT-kov, more or less; there's a dot over the "Z" in the original) was a young astrophysicist from Poland. She was both brilliant and beautiful, with long black hair, dark eyes, a soft voice, and a striking profile. Anna made stars. More precisely, she created stellar models: sets of equations that specified the density, pressure, temperature, and composition of the materials that form a star. To get a a successful model, those parameters have to be self-consistent. They must obey the laws of nature and match up properly at the center and the edges of the star.
Self-consistency is tricky. I started with Anna's and Kip's work and put in nuclear reactions as contributed by Mike Newman, a Caltech nuclear physicist. Using simple but plausible approximations I wrote moderate-sized FORTRAN programs, punched holes in hundreds of computer cards, and fed my decks into the reader. The bytes flowed over leased lines to Berkeley where a CDC-7600, quite a supercomputer for its time, compiled and executed my instructions.
It sounds simple enough ... but before I could create any models there were months of learning numerical methods, tracking down algorithmic errors, suppressing computational instabilities, and puzzling over reams of cryptic line printer output. When I got things to "work", the real challenge began: understanding and explaining the features of my calculations.
While I was attacking the problems of stars with neutron-star centers a fellow grad student, Richard Flammang, worked on cracking an even tougher nut. Working with Kip Thorne, Rich sought to simulate stars with black-hole cores. With a neutron star, at least there's a solid foundation on which to build. A black hole is more like a bottomless pit! The only hope for such objects would be to generate insanely high temperatures before the gas goes down the drain --- hot enough that radiation pressure could counterbalance gravity. That's not trivial. If matter gets too hot it will give off not merely light (and X-rays and gamma rays) but also neutrinos ... which slip away so easily that they are almost worthless in the fight against collapse. Moreover, once gas starts to fall down rapidly it carries a lot of light with it, and there's no time to benefit from the radiation pressure.
But if it takes an unconventional grad student to make an unconventional stellar model, Rich Flammang was the man. He was almost as old as Kip, for starters --- not the usual student-teacher relationship. Rich had been a Caltech physics undergrad in the 1960s who then went to Harvard to pursue a graduate degree in economics. After several unhappy years of that he returned to his first love and came back to the Caltech physics department. He was a fun companion, a strong hiker, and a native southern Californian whose parents were rather well-to-do; they owned a lovely house in the hills overlooking the Los Angeles basin. Rich himself was (or played the rôle of) a child of the '60s who balanced work and play, with the scale tipping toward play much of the time.
In spite of the creative energy that he brought to his research, however, Rich never succeeded in crafting stable models of stars with black-hole cores. I saw the same outcome in my erstwhile models of stars with neutron-star centers. One can rarely "prove a negative" --- it's always conceivable that unanticipated phenomena could save the day --- but the results that I got strongly suggest that such models can't exist in the universe.
Soft or hard, crunchy or squishy inside, the type of stellar candy doesn't matter: gravity is too strong. The cakes I baked always fell down for three major reasons:
Can stars with neutron-star cores exist, or are they doomed to fall down and go "boom" on timescales of a few years or less? Perhaps escape is possible via bizarre nuclear reactions that my models didn't include. Or maybe a star could survive by a series of small collapses and explosions, something like an internal combustion engine. But those are long shots. My bet is that Nature doesn't hide neutron stars inside ordinary-looking stellar objects.
- Monday, May 01, 2000 at 05:46:11 (EDT)
In other words, there's no magic formula for making money. If there were, others would recognize it, exploit it, and thereby neutralize it. Generations past saw this with the printing press, steam-powered shipping, railroads, telegraphy, electrical power, and radio. In a smaller way, they saw it with new resource discoveries like gold rushes, oil booms, and the opening of new lands for settlement. We're seeing it now with the Internet and computing technologies. Capital, like water, flows toward an optimal distribution. When a new channel appears --- when a river finally erodes through a ridge, or when an idea finally comes to maturity --- then older paths dry up and more efficient routes take over. Change happens, and stability returns until the next shift.
So in spite of what some silly pundits say, we're not witnessing the biggest discovery since fire, not by a long shot! We're just seeing a marginal economic change. The really key inventions are social and organizational ones that we rarely think about and that nobody makes instant profits from. Things like universal access to education ... high social mobility ... limited government ... the shared culture of art, science, and literature --- those sorts of changes are what make us infinitely wealthier than our ancestors. That's the real fire, and it's a fire that all humans can warm themselves by.
- Saturday, April 29, 2000 at 18:49:52 (EDT)
Sorry --- it's not that easy. As human animals we're optimistic by nature, at least when we're healthy and things are going well for us. We love to hear stories of people who triumph over impossible odds, of pluck and grit and cleverness winning out against all adversity. Our newspapers and TV shows and inspirational books are full of such homilies. They make our spirits soar ... and they tell us that we deserve our good fortune. We smile.
But in reality most struggles end up in failure or at best partial recovery. People are crippled by disease, by injury, by cruelty, by poverty, by pernicious racism, and by a thousand outrageous accidents. When we ignore human suffering we make the situation worse. We implicitly blame the victim. Mee's fluid and thoughtful prose tells of his realization, forced upon him by polio, that luck is a huge force in our lives. Not the only force; there's still room to fight against fate, to push the clouds of probability back a bit. But let's be honest about the situation, and introduce a little justice and fairness into the world --- as a counterweight to the random factors that otherwise crush so many innocent creatures.
- Friday, April 28, 2000 at 21:58:09 (EDT)
Such a coincidence isn't unusual in science; open questions are often "in the air" and several people are likely to work on solving them at once. In this case the synchronicity was even less startling. "Victor" Ni had been a grad student of Kip's a few years earlier, and his research had been in this general area. It was good luck that we met before submitting our separate papers; both of us saved time and potential embarrassment by teaming up.
The topic we addressed was a simple one: imagine trying to do an experiment on a roller-coaster. You would see all sorts of weird effects, seemingly strange forces and accelerations, just because your apparatus is being twisted and pushed about. You would have to compensate carefully for those pseudoforces in order to actually measure something independent of your motions.
Well, in real life hardly anybody works in free fall. The Earth rotates on its axis and revolves around the Sun. So do we. The ground shakes and tides tug. Our laboratory equipment is turned and shoved around relative to the "fixed stars" --- and therefore experiments see pseudoforces, centrifugal/centripetal and Coriolis accelerations that wouldn't be there if we were floating in space.
Easy to say --- but it's nontrivial to compute the precise effects, accurately, taking into account special and general relativity. But that degree of precision is needed in order to analyze delicate gravitational-wave detectors, where sensors are striving to pick up signals of one part in a trillion trillion or less.
Wei-Tou Ni and I hacked through the algebra and found 14 different types of pseudoforces. There's the usual inertial acceleration plus the well-known Doppler (a.k.a. "gravitational") red-shift correction. (Physical processes "overhead" run more quickly than one would expect; light gains energy and oscillates faster as it falls downhill.) Then there are special-relativistic and red-shift corrections to those terms. Next the Coriolis acceleration appears; it's the same force that makes hurricanes swirl counter-clockwise in the Northern hemisphere. The centripetal (or centrifugal) force is in there too. Beyond that, we found "electric" and "magnetic" gravitational effects, analogous to those that work on charged particles but arising from inhomogeneous gravity fields (tides, based on the Riemann curvature of spacetime).
Quite a thicket of complexity, but reasonably straightforward to measure and neutralize in an experiment --- once one knows what to watch out for. Our paper appeared in the 15 March 1978 issue of Physical Review D. It was titled "Inertial and gravitational effects in the proper reference frame of an accelerated, rotating observer", by Wei-Tou Ni and Mark Zimmermann. Almost certainly, fewer people read it than have already read this ^zhurnal. Such are the laurels of science.
But more amusing, perhaps, was a mundane factor that arises in every joint publication: Whose name comes first on the paper?! Victor Ni was a bit shy about asking me, but via Kip he requested permission to be the lead author. I happily agreed. Ni was (slightly!) my elder, an established scholar but still struggling to get tenure and respect; I was already thinking about moving on to work outside of physics. It was an easy and collegial decision to appear last. (Besides, with the name "Zimmermann" I was used to it!)
In other cases, alas, name-order is far more controversial an issue. I was a minor co-author on a paper (which shall remain otherwise unidentified) where the "natural" solution, alphabetical listing of the players by their surnames, would have hidden the magnitude of contribution by one of the authors. The person who came first alphabetically deserved the lion's share of credit for the work. How to signify that fact?
I was in a dead heat for last place among the co-authors, deservedly so given the minor nature of my involvement. The Solomonic solution: move "Zimmermann" up a notch --- making it obvious by the incongruity of that out-of-place "Z" that the author list was not alphabetized, but signified the proper share of glory. Silly-sounding, to be sure, but such subtle games keep blood from being shed in the groves of Academe every day. When ideas are the coin of the realm, getting proper credit is the only route to wealth.
- Thursday, April 27, 2000 at 17:53:17 (EDT)
Other "totality effects"? All the particles in the universe are pulling on each other, gravitationally, all the time --- and that just might add up to the inertia that every object has (Mach's principle). Each person in the world has an individual scale of preferences, and in the marketplace all those separate utility functions converge to make supply and demand, determine prices, and allocate resources in a global economy. Mathematically pure sine waves at all possible frequencies, when superposed, create every sound, every image, every shape. &Aelig;ons of reproductive competition, plus mutation and natural selection, give all the marvelous creatures of this Earth. And the totality of human thought and experience, shared via language and learning, create our civilization.
- Wednesday, April 26, 2000 at 19:15:55 (EDT)
A landscape is full of hills and valleys, ridges and clefts; so is a body, a face, a chart of the stock market, or a musical score for a concert. But that complexity is built from a flock of simple pieces: straight lines, smooth planes, intervals of constant motion. Study the easy parts and how they fit together. The large-scale messiness may go away or at least become manageable. Even if not, in many cases what really counts is getting the local patch right. The global situation is likely to be insoluble, unknowable, or subject to change by the action of other forces. Work on solving the immediate problem first.
- Monday, April 24, 2000 at 21:29:30 (EDT)
- Saturday, April 22, 2000 at 19:19:18 (EDT)
- Thursday, April 20, 2000 at 12:38:31 (EDT)
The astrophysical cherished beliefs we assumed are quite straightforward and relatively uncontroversial:
The final paper that explored all this was titled "The Gravitational Waves That Bathe the Earth: Upper Limits Based on Theorists' Cherished Beliefs". It was dedicated to Abraham H. Taub, on the occasion of his retirement from the University of California at Berkeley, and appeared in a festschrift in honor of him published in 1980. Taub is a towering figure in relativity theory, whose work on ideal models of the universe (e.g., "Taub-NUT Space") is reputed to provide a counterexample to just about every common prejudice about cosmology. Kip knew Abe Taub personally as a colleague; I didn't have the privilege, though we met once or twice at seminars.
Our essay provided bounds on how strong gravitational waves might be at various frequencies for extragalactic and galactic sources, and for discrete objects --- bursters, transient sources, and continuous-wave monochromatic emitters --- as well as for an unresolved stochastic background. Thus far, no gravitational waves have been seen in confirmed experiments (though likely side-effects of waves are apparent in such systems as the Taylor-Hulse binary pulsar). Detectors are now becoming sensitive enough to get below our "cherished belief" limits. Perhaps some day soon!
- Wednesday, April 19, 2000 at 06:11:35 (EDT)
- Tuesday, April 18, 2000 at 06:03:37 (EDT)
But there's a bright side. Our (all too commonplace) experience has convinced me that the scary picture painted by Bill Joy (in his recent Wired magazine article) is far, far less realistic than the author may think. Gray goo from replicants run amok --- the nightmare nanotech scenario --- presupposes near-perfect software. Not likely, mate!
Any contrivance that can copy itself has to be complicated. Yes, it's easy to clone if one's surroundings are ready-made to provide reliable duplicating machinery. That's how viruses work, by hijacking a cell's well-tuned biochemistry. Massive complexity is there, hidden outside the replicator. A nanotechnological mechanism, on the other hand, has to do all the dirty work itself. And its job is far trickier in a heterogeneous, diverse environment (like the real world) than inside a laboratory testtube or a computer simulation. Energy is tough to get and competition for resources is fierce. No free lunch, in other words.
How probable is it that a human-designed system, millions or billions of times more intricate than the largest computer programs yet built, will successfully take over the world? How likely is it to be bug-free in all the most vital routines? How plausible is it to imagine that it can adapt to the incredible range of conditions it will encounter within a journey of only a few meters on the surface of this planet?
We're safe, for quite a long time to come. Destruction on a global scale isn't as trivial as one might fear. The complexity required for self-reproduction is our safety net. The large-scale risks, if any, come from rapid evolution of mechanisms that can improve themselves. But to get to a jumping-off point will take a lot of hard work and brute cleverness, not just technological fantasy-weaving. Somebody's gotta write the software, the critical code --- or more precisely, write the code to write the code to write the code to ....
- Saturday, April 15, 2000 at 08:04:14 (EDT)
- Friday, April 14, 2000 at 05:44:13 (EDT)
Roger gently pointed out to me that, contrary to my naïve mental model, a spinning mass might not merely give off gravitational radiation at twice its rotation frequency. Rather, Roger suggested, there could be emissions at lower frequencies, and maybe even more complicated signals that would give valuable information about the system to a distant observer. He argued by analogy with the electromagnetic case, for which he had strong classical instincts.
Roger was right! Free rotation in empty space is simple only for a simple body like a dumbbell twirling about one of its principal axes. Off-axis motion --- especially for an asymmetric object --- causes precession, nutation, and other messy phenomena (involving in the general case elliptic functions, about which I knew next to nothing). Such might well be the case for a rapidly spinning neutron star.
The calculations to prove this were quite ugly and stressful to perform; they took me a few months of steady work. I used a symbolic math program called MACSYMA to simplify the equations and check my algebra. The MACSYMA software at that time only ran on a weird computer at MIT, and so to access it I learned to use the ARPAnet --- an early experience on the Internet's ancestor.
Eugene Szedenits, Jr. helped me with much of the analysis. Gene was a good-naturedly eccentric grad student who came to Caltech in 1975 and stayed for only a couple of years before moving to Michigan to write compilers for computer-controlled numerical machine tools. He was born in Hungary and grew up in Cleveland, where he attended Case-Western Reserve University. His uniform was a white shirt, black pants, and a scarlet sports coat --- which could be seen at great distances as he scooted around campus, and which helped him become invisible when he uncharacteristically failed to wear it. Gene's wicked sense of humor made him a great late-night studying companion. He was honest, hard-working, a bit shy, and earnest in his insistence on the "Junior" suffix to his name.
I wrote up our results as the paper "Gravitational waves from rotating and precessing rigid bodies: Simple models and applications to pulsars", with Eugene Szedenits, Jr. as co-author. (Gene derived the major equations independently of me, checked my results, and kindly and continuously prodded me to get the research finished, written, and published. Thanks, fellow!) The article appeared in Physical Review, part D, the section subtitled "Particles and Fields". Phys Rev didn't allow me to call it "Part I", probably because the journal had already been burned too often by authors who meant well but never got around to writing their promised "Part II". In the original draft of the paper I used feminine pronouns throughout, as a tiny blow against English's default gender discrimination. Alas, an anonymous referee objected --- he (you can bet it was he!) found the usage distracting, and the editors agreed. Kip Thorne (my thesis advisor) was willing to fight, bless him, but I was conflict-averse and gave in to speed publication. Too bad....
My paper with Eugene appeared in mid-1979. As far as we were able to determine, all previous work assumed that gravitational waves from mechanical systems came at twice the spin frequency. Roger Blandford's insight (plus a lot of hard work!) proved that assumption wrong. Our weak-field, slow-motion, small-stress, quadrupole-moment analysis derived the explicit waveforms radiated by two special cases of freely precessing rigid bodies. The first case was that of an axisymmetric object; the second was that of an arbitrarily-shaped body with a very small wobble angle.
Three new, important, unexpected ideas emerged:
I did eventually write the "Part II" paper, titled "Gravitational waves from rotating and precessing rigid bodies: General solutions and computationally useful formulæ". It was published in Phys Rev D in 1980 (and as Chapter III of my dissertation). In the article, I dotted the i's and crossed the t's of the earlier piece by extending the analysis to the case of an object with arbitrary moment-of-inertia tensor (arbitrarily great deviations from axisymmetry). I gave plug-in-and-grind algorithms for computing the gravitational power radiated and waveforms produced by an arbitrary source. Those exact results confirmed the approximations and special cases calculated in Part I.
It was rather a dull paper in my opinion, without any fundamental or exciting new insights. Boring work, but somebody had to do it. Science is like that sometimes. So is life.
- Tuesday, April 11, 2000 at 06:10:53 (EDT)
Obviously, one needs both. Making a hole-in-one isn't the only proper criterion; neither is a lovely swing and follow-through. Somebody who wins the race may yet deserve a reprimand for cheating. Somebody who obeys the rules but gets the wrong result may still deserve to be rewarded. Being right is evidence, not proof, of excellence.
- Monday, April 10, 2000 at 05:55:09 (EDT)
There's a mathematical concept, the correlation, that quantifies the linkage between two variables. A correlation of 0 means that knowing one thing tells you absolutely nothing about the other. If a (fair) coin comes up "heads" that doesn't imply anything about the result of the next toss; the two events are totally independent. A correlation of 1, on the other hand, means that a pair of quantities are rigidly linked. Knowing one of them gives you absolute predictive power over the other. When a (normal) coin has come up heads, then the bottom side is sure to be tails. In between 0 and 1, the correlation identifies the fraction of the story that one variable tells about the other.
But being correlated doesn't imply a cause-and-effect relationship among variables. Both may be moved in parallel by an outside force. Or the correlation may be only a statistical artifact, the result of analyzing an incomplete data set. If you take enough observations, and try out enough hypotheses, then some of them will appear to fit ... until you do further measurements, when the effect fades away. Correlations are clues --- leads to pursue, not proofs.
- Sunday, April 09, 2000 at 06:44:23 (EDT)
The big ruckus of the past few years boils down to movements of capital. Folks have decided, rightly or wrongly, that the Internet and other information technology developments will let them meet human consumer needs more efficiently. Investors thus have chosen to let many capital goods deteriorate (or depreciate, or wear out). They have channeled resources into laying new fiber optics lines, building TCP/IP packet routers, installing file servers, launching satellite relays, and gathering "content" to sell. Some of these investments will pay off, and others will turn out to have been huge mistakes.
This is nothing new. Similar shifts in capital investment occur every few generations, as populations grow and move, as natural resources are discovered (remember the Gold Rush?), and as practical ideas (technologies) are tested and implemented. No big deal.
- Saturday, April 08, 2000 at 10:29:29 (EDT)
Quick technical background: gravitational waves are ripples in spacetime made by accelerating matter, much as electromagnetic waves (radio, light, etc.) are self-propagating ripples made by accelerating electrical charges. The more mass you take and the harder you shake it, the more gravitational waves you get. A neutron star, the remnant of a stellar collapse, is a dense ball several miles across with something close to the mass of the Sun. It can spin many times every second. (The rotation rate goes up as the star shrinks, just as an ice-skater whirls faster in the now-clichéd analogy.) Strong magnetic fields make some neutron stars give off radio waves, which we see once per turn as pulses --- hence, "pulsars" --- and the magnetism plus the stiffness of the neutron star's crystalline crust can make the body asymmetric. So, it spins off-axis, wobbles, precesses, nutates, quakes, shakes, rattles, rolls, and bottom-line wiggles enough to give off a goodly amount of gravitational radiation.
A major point made by my 1978 letter to Nature is that the fastest pulsars are not necessarily the strongest sources of waves. A more slowly rotating neutron star may be closer or may have a larger non-axisymmetry, for example. More specifically, my best estimates suggested that the Vela pulsar (with a period of 0.089 seconds) is likely to produce waves with amplitudes one or two orders of magnitude larger than the more-famous Crab Nebula pulsar (period 0.033 s). Although this possibility is rather obvious, it was apparently overlooked or discounted in earlier investigations. ^z's tiny contribution to the edifice of astrophysics! (^_^)
Gravitational waves from pulsars are unlikely to be much stronger than one part in a billion billion billion (10 to the -27th power). But such tiny signals, since they come at a predictable and stable frequency, might (barely!) be detectable in the laboratory using massive, supercooled, ultra-pure crystals, perhaps made of silicon or sapphire. Measurements of these waves could give new information about the structure of neutron stars.
As for me: gathering data to set up the problem, working through the equations, and coming to understand the results was a marvelous lesson in what it means to be a scientist. Even more important was the struggle to write up the results in a clear, compact, comprehensible form. I needed a lot of help, and I got it --- from Carl Caves, Peter Goldreich, Kip Thorne, and David Douglass. Thanks, folks!
- Thursday, April 06, 2000 at 05:46:45 (EDT)
- Wednesday, April 05, 2000 at 19:31:46 (EDT)
- Tuesday, April 04, 2000 at 18:36:45 (EDT)
But what is free action? The phrase in real life means choice, will, the ability to do (within limits) something not predestined. Daniel Dennett in Elbow Room: The Varieties of Free Will Worth Wanting wrestles with this issue for a few hundred pages. (It's not a topic to be solved in an anecdote!) Dennett argues that most of our problems in thinking about free will come from bugbears, boogey men, and other imaginary horrors that we impose upon ourselves. These free-will-devouring monsters arise from misapplied analogies, from incompletely analyzed stories, and from fuzzy wishing for things that we wouldn't really want to have, if we thought about them in detail. DD concludes that free will is in fact compatible with a belief in determinism, the idea that Nature is governed by physical laws ... and that we needn't seek an escape hatch via mystical means, whether supernatural or otherwise (e.g., bizarre interpretations of quantum mechanics).
Much ado about nothing? Maybe not. If we have freedom to choose, then we have a chance to create meaning --- not just plummet inexorably toward our fates. Through free action, we also gain responsibility. We are, when we so choose, agents rather than objects. Life becomes an enterprise both infinitely rich and infinitely dangerous ... since we can now make mistakes as well as move wisely. Risky business, this free action!
- Monday, April 03, 2000 at 05:49:41 (EDT)
Class 0 is most folks; they get by with a Gentleman's C, maybe doing a bit better (or worse) depending on context and mood. "Good enough" is their motto. In Class 1 are the teacher's pets with a mild flair for the subject, the one-in-ten who do pretty well without breaking into a sweat, the natural leaders of a small team working together. Class 2 is composed of the 1% who have real talent or (more likely) who simply enjoy a topic and have begun to work hard at it, studying and practicing without being nagged to do so. In Class 3 are the wiz kids, valedictorians, local heroes, supermoms; they make the community newspapers once in a while as rôle models or marginal curiosities.
On to Class 4, one in 10,000 --- winners of city or state competitions, graduates of the best universities, expert enough to write a book on the subject, maybe teach it to up-and-coming potential aces of the next generation. Then there's Class 5, the masters: roughly a few hundred per major country for many topics. A master makes a living performing, can pick and choose students, gets good press coverage, has a small book written about her, maybe even becomes the focal point for a clan of admirers or wanna-bees ... a mini-cult idol, for a decade or so.
Class 6 members are grandmasters --- one-in-a-million geniuses in their field. They all know each other, or could if they felt like looking up from their work. They're magazine cover subjects, celebrities with their own fan clubs. They make top-ten lists and win their shares of annual big-money prizes. When one dies, the obituary is front-page news.
Now the scale breaks down. Class 7+ are world champions, super-grandmasters, phenomenal talents who are saluted by even the most self-centered of their competitors. They come along every few generations in some specialties, less often in others. Their names become household words, part of the shared culture. They define their topics, rather than vice versa. Off the scale....
- Saturday, April 01, 2000 at 06:34:08 (EST)
Alas, the term "geek" has been depreciating in recent years (like the word "hacker") ... far too many folks are calling themselves geeks without having paid their dues in all-nighters and against-all-odds term projects. Perhaps it's almost time to replace "geek" with another moniker --- "tweet" or "dweeb" or "beezo" or "weenie" or ...?
Whatever it is, it's gotta have double-E!
- Thursday, March 30, 2000 at 19:56:42 (EST)
On a larger scale, the same phenomenon has occurred in modern astronomy. Our understanding of the universe has been enriched by an influx of ideas from general relativity, especially as those ideas were applied to "violent" events such as quasars, collapses to form black holes, and the birth of the universe itself. Theoretical relativity has its very raison d'être grounded in astronomically-observed fact, and much of the development of the field was guided and nurtured through problems posed by astrophysics. More cross-fertilization between these two subjects will certainly follow the first confirmed observations of gravitational radiation.
So the partnership between astrophysics and relativity in my thesis is not a new one. The specific object that has frequently embodied that partnership, the neutron star, is also not new. Speculation about and theoretical work on the structure of neutron stars dates back to the 1930s, and evidence accumulated from pulsar observations beginning in the 1960s has both solidified and extended the theoretically-acquired knowledge. The human mind, however, always seems to retain a fascination with extremes: the highest, the hottest, the smallest, the fastest, etc. As (probably) the densest material objects in the universe, neutron stars have a natural attraction (^_^) --- and they have repaid the attention given them by yielding a stream of discoveries. As central as neutron stars have been to a variety of fields in modern astrophysics, it was fitting that they should supply a central core for several of the projects I undertook in grad school.
As I wrote in 1979 when concluding the introductory essay to my minimum opus:
"The universe is an exciting place! In particular, the hot or fast or dense objects which bring relativistic effects into prominent display are interesting and rewarding subjects for investigation. Most of the work included in this dissertation has its ultimate roots in my personal fascination with astronomy, which began about the time I was six years old and first looked through a small telescope, and which developed during years of reading and asking stupid questions. I've finally understood a few things, at least in part, and have had some fun describing them in the chapters of this thesis. If I am required to give reasons or motivations for all that I've written herein, I must eventually fall back upon the enjoyment that it has given me. I suspect that the joy of discovering and of explaining one's discoveries is fundamental to a lot of people. If what I've done adds to anyone else's pleasure, or suggests something new and amusing for them to ponder, that's an unexpected bonus."Two decades later, I agree.
- Wednesday, March 29, 2000 at 18:19:21 (EST)
Amazingly enough, one can "hear" a lot: the total surface area, the circumference, and the number of holes in the drumhead, for starters. (To a mathematician the drum needn't be circular, or even a solid sheet of material.) The various normal modes of oscillation for a thin film under tension somehow encode a host of detail about the object.
Why was this such an exciting idea that a kid would remember it over a quarter century later? Maybe the magical spell came from seeing an unexpected partnership between numbers and the world, a surprise marriage of theory and reality. Applied math, of which Kac was a master, is that sort of enterprise: a game of deep patterns and startling connections. Similar magic comes in other areas of human knowledge, ranging from history to psychology, from economics to anatomy. Suddenly, one sees a why --- a reason for what at first seemed arbitrary --- a meaning behind an apparently random structure. A lovely idea, unveiled. Lightning strikes, sha-zap!
- Tuesday, March 28, 2000 at 19:37:22 (EST)
One good vaccination is to be near some big wheels for a few years, to see them with all their warts ... Nobel laureates, the rich, the smart set ... gracious to their juniors but fighting with their peers ... laughing over lunch and mugging to entertain any audience ... leaving spouses for younger companions, flatterers, hero-worshipers ... remembering incidents selectively, putting themselves at the center of the universe ... pouting over slights, imagined or real.
Even better to pump up the celeb-immune system: nothing helps more than exposure to near-misses. Study brilliant people --- who are just as (or more) deserving, but who weren't in the right place at the right time, who didn't get the publicity, whose work was co-opted and made famous by greedier sorts. Those in the shadows are far more numerous than the phenoms, and are often far better human individuals. (Some are bitter; the best have passed through or around that illness.) Seek them in diverse fields --- letters, science, the arts --- and talk with them, write to them, read them, watch them, listen to their voices.
The bottom line, of course, is that celebrities are human beings. Some deserve glory; some get it by luck. A big hit in one endeavor doesn't imply wisdom in another. Many who are forgotten by the masses are more worthy. Give them the gift of attention. Learn from them.
- Sunday, March 26, 2000 at 20:10:26 (EST)
Apart from my intellectual debt to Professor Kip S. Thorne, I can never fully express my personal debt. His wisdom, insight, kindness, enthusiasm, and unflagging encouragement of even the slightest signs of productivity among his students have been a continuous inspiration to all who know him. He is one of the great teachers of physics, as well as one of the great physicists, and I am grateful to have had the opportunity of studying for many years in his theoretical astrophysics and relativity group at the California Institute of Technology.These words were adapted from Murray Rothbard's preface to his treatise on economic principles, Man, Economy, and State (1970), in which Dr. Rothbard spoke of his advisor, Ludwig von Mises.
Kip insisted on being addressed by his first name. The only exceptions he allowed were in the case of Asian students whose upbringing made it impossible for them to speak to him in so familiar a way. I remember Kip as a dragon, fire-red hair and beard streaming as he raced across campus, full of creative energy, combining meticulous attention to detail with cosmic vision. In this Year of the Dragon he turns 60. Happy Birthday, Kip!
- Saturday, March 25, 2000 at 21:35:23 (EST)
So how can tasks too big for a handful of individuals ever get accomplished? We have to either pay the overhead --- huge inefficiency --- or figure out how to leverage the few genuine experts that exist. Maybe Frederic Brooks's "surgical team" proposal (see The Mythical Man-Month) is a good metaphor. A surgeon doesn't usually divvy up the cutting-edge work on a patient. But she does have assistants and specialized colleagues who help on parts of the job, who handle the paperwork before and after, and who let her focus on her special expertise. That maximizes productivity. Brooks suggests a similar approach to software engineering. Analogous applications in other fields could be equally wise.
- Thursday, March 23, 2000 at 19:20:48 (EST)
- Wednesday, March 22, 2000 at 21:07:22 (EST)
- Tuesday, March 21, 2000 at 20:36:04 (EST)
Suppose I only save five cents of every dollar I get. Give me a dollar and I'll spend 95 cents. If that ratio is typical, then when I spend $0.95 the recipient will save 5% and spend $0.95*0.95 = $0.9025, of which the person who stands next in line will spend 0.95 cubed (about $0.86), etc., etc. The sum of the series is $20 (counting the initial dollar I got to start with). Apparently there's a 20:1 multiplier effect. If the average savings rate is lower, the multiplier is (reciprocally) higher.
So a silly person who only thought about one side of the equation might deduce that a little "pump-priming" would "ripple through the economy" and "create jobs". And if only people would stop saving entirely, the magic multiplier would go to infinity and we'd all be infinitely rich without further effort. Forget about hard work, capital investment, human creativity, or anything else!
But of course, all those factors and more are critical. The flaw is not in the math but in the initial step: focusing on only one factor and treating it in isolation. A real system has feedback loops, internal delays, counterbalancing forces, and more. Good analysis is the art of seeing the whole system.
- Tuesday, March 21, 2000 at 06:48:51 (EST)
- Sunday, March 19, 2000 at 18:36:23 (EST)
Part of the difficulty originates with the user, in the form of ill-posed queries. One can scarcely expect an information retrieval (IR) system to be a mind reader! Yet the majority of searches are for single words or short ambiguous phrases. A human expert with decades of real-world experience could not parse and respond to such a question. It's unfair to expect a machine to do better.
But even sophisticated search patterns are too often unsuccessful. Most relevance-ranking algorithms do a poor job of identifying the documents (or web pages) that best answer a request. Weakness seems to be associated with several factors:
But there is hope for improvement. One tiny example: my work in the first TREC (Text REtrieval Conference of 1992, sponsored by the US National Institute of Standards and Technology) led me to write a prototype document ranking program that did surprisingly well in an impartial refereed fly-off competition. The results are included in the conference proceedings (edited and with commentary by Dr. Donna Harmon). In brief, I began with the simpleminded and subjective observation that the documents which people like most tend to have strong local clustering of "interesting" words.
So, I took the 50 TREC benchmark questions and constructed obvious regular expressions ("regexps") for each of the key terms in them. Thus for topic #001, a search for "pending antitrust cases", I built the pattern /ANTITRUST/ & /CASE/ & /PEND/. For topic #002, "acquisitions or mergers involving US and foreign companies", I came up with /ACQUISITION|BUYOUT|MERGER|TAKEOVER/ & /US|U.S.|AMERICAN/ & /FOREIGN/. For equivalent terms I wrote a regexp with "|" (the "OR" symbol) joining the words. I spent at most two minutes writing these patterns per query --- not a lot of deep thought. I converted all documents to upper-case before processing them, so my program was able to ignore capitalization issues.
To handle fuzzy proximity relationships among separate terms (the "&" symbol used above) and to generate relevance measures, I invented a quick and dirty point count system. Each search expression started out with 0 points. Every time a line in a document matched a search regexp I added an arbitrary 5 points to that regexp's score. A line in the document then received a net interest rating equal to the product of the separate pattern scores for that query. ("&" thus became a multiplication.) When moving on to the next line of a document, I multiplied all regexp point counts by 0.9, to make them fade away with a characteristic length scale of 10 lines.
The estimated relevance of a document as a whole was then just the maximum relevance of any line in that document. If a term needed to get a negative weight (boolean-NOT-like), instead of multiplying in the pattern's point score I used 5 minus that score. I experimented with different weights and relevance-length-scales for different terms, but it made little difference to overall rankings.
The bottom line of this almost-trivial algorithm is that high point scores go to documents which have many relevant words within a few lines of each other. The user has total control over thesaurus (synonym) expansion of terms, and can change relative weights and scoring ad lib. Long documents are neither penalized nor rewarded.
And it worked! With minimal effort this system came in among the top three of the TREC competition. My prototype implementation was slow as molasses: it took about a third of a second to rank each document against each query, so total run time was a couple of weeks(!). But of course the process ran politely in background and did not interfere with other activities on the workstation. If it were rewritten in a compiled language (I used gawk, the GNU project's free version of Awk) and executed on faster hardware (I had an original NeXT machine, the famously lethargic black cube) then it could easily run many orders of magnitude faster.
No magic elixIR (an Information Retrieval joke ... get it(^_^)?!) --- just recognition of the fact that "good" documents tend to have "good" words near each other. Fuzzy proximity search and a straightforward point-count system did the rest.
- Saturday, March 18, 2000 at 08:22:49 (EST)
But look back at the ancient Greeks and you'll see precisely the same divergent modes of thought. In particular, the Skeptic School of philosophy sought, through contradiction, to escape all attachment to beliefs. Their approach corresponds closely to what we now think of as "Zen": removal of reason, avoidance of dogma, and escape from emotion. The Skeptics sought first to neutralize logic, and then transcend it, thereby achieving a state of calm tolerance, and gentleness. (See the description in Chapter 8 of The Therapy of Desire by Martha Nussbaum.)
So really, nothing changes ... old is new ... East is West ... and people everywhere are pretty much alike. They grow and learn through conflict and resolution.
- Thursday, March 16, 2000 at 18:23:47 (EST)
What started out as a short-cut turned into a waste of time and energy. Nobody was fooled by the effort, at least not for long.
Now think of all the political advertisements, all the election slogans, all the bumper stickers and lawn signs. How much wisdom do they convey? How much closer do they move us toward understanding and solving complex problems?
- Tuesday, March 14, 2000 at 18:43:02 (EST)