But the astronomer I was with had some plates to expose --- classic plates, thin squares of glass more than a foot across, coated on one side with a silver halide emulsion. (The Kodak Corporation kindly kept making plates for the astronomical community for many years, as a charitable way to support research.) Our plates were baked in a gas chamber a day or two before we used them, to increase their sensitivity. We loaded them in pairs, back-to-back, into special holders that bent the glass slightly to an optimum shape for the focal plane.
SS had begged, proposed, cajoled, argued, and finally won two nights on a Schmidt telescope --- essentially a camera the size of a milk tanker truck. The Schmidt we were to use had a 48-inch mirror and cleverly-shaped correcting lenses to give it a large, sharp field of view. SS's goal was to take long exposures of several clusters of galaxies, measure the average colors of their stars, and thereby prepare for more detailed observations of galactic properties. Foundational work, in other words, but nothing earthshaking (though it was undoubtedly cosmic!).
For an observatory, good "seeing" --- a crisp, clear view of the stars --- is everything. Telescopes at high altitudes have less atmosphere above them, so stars twinkle less. Domes are unheated, to minimize air currents. Major astronomical facilities are often placed at middle latitudes on the western side of a land mass, so that prevailing winds come across an ocean and thus flow as smoothly and steadily as possible. Light pollution is the great enemy, and unshielded streetlights (especially ones that put out a broad spectrum of glare) make deep sky photography impossible.
Our first night began with light cloud cover, thin enough to give hope of clearing but thick enough to prevent any useful work. The kitchenette below the dome was well-stocked with junk food, so we drank coffee and snacked and talked with the technician in charge of the telescope. He wasn't an astronomer, but rather something of a mechanic and general expert on the instrument. Observers came and went; his job was to keep the machine running smoothly and, most importantly, prevent mistakes that might cause serious damage.
A bit before midnight the clouds blew away. We slipped the first plateholder into the Schmidt and confirmed coordinates. The tech swung the telescope and rotated the dome. Faint lights glowed, deep red to preserve night vision and avoid fogging film. Through the guide scope (a respectable-sized instrument for an amateur) the star that SS had chosen to track swam into view. For half an hour, the game was to punch buttons on a control paddle and keep that star centered on the crosshairs at high magnification, so that any irregularities in the big telescope's clock drive would not spoil the photograph. This was in fact a game, not something serious --- since we all knew that for the galactic measurements SS needed to take, minor tracking errors would make no difference whatsoever. But it kept us busy, each in turn. When an exposure time had elapsed we closed the shutter, removed and flipped the holder, and repeated the process for the other side's plate on a new field of stars. Then we put that holder away and inserted the next one. So the night passed.
Dawn came and (dog-star-tired?!) we walked to the observer's quarters on the mountain, a snug white farmhouse. After a light dinner at about 6am we retired to individual bedrooms, closed the blackout curtains, and napped until early afternoon. Then came the time to develop the previous night's plates, check their quality (all turned out well), and plan the schedule of observations to make during the night to come. Ominous clouds did not bode well. We walked to other domes and visited with the astronomers there.
At the 200-inch (5 meter) Hale telescope I climbed a ladder and sat for a few minutes in the prime focus cage, a small cylinder suspended in the middle of the instrument's tube above the huge mirror. It's a high and cozy perch even for a small person. As the big scope pivots to follow the stars, the observer's seat swivels in a circle around a boxy desk-like holder for photographic plates. Reflected starlight comes up inside a hollow cylindrical post; the human's legs are squeezed around either side of it. Control buttons adjust the telescope and rotate the dome. The hardwood railing feels like old furniture, smoothed by decades of use.
The 200-inch mirror gathers about a million times as much light as a naked human eye. A few percent gets lost at each reflection; the prime focus roost and other structures inside the tube waste a few percent more. The astronomer's job is to track the heavens, change plates, and be patient. By the 1970s the prime focus cage was rarely used: alternative light paths, better for electronic sensors, relied on arrangements of secondary mirrors to bring photons out the side or back of the telescope. It's more efficient --- but far less romantic than sitting quietly in a nest while starlight, from halfway across the universe, comes up between one's knees and strikes tiny crystals of silver salt.
SS and I walked back to his assigned dome. The afternoon clouds thickened and a light drizzle began to fall as the sun set; bad luck for observers. A bit after midnight we gave up and went to bed.
- Friday, January 14, 2000 at 06:00:50 (EST)
- Thursday, January 13, 2000 at 06:40:33 (EST)
The organizers (CMC, RF, et al.) chose a cloud-free night with a last quarter moon, which provided good post-midnight illumination. A dozen of us piled into cars late one spring evening and rode an hour-plus east to the trail base. Those who had brought flashlights found them unnecessary once everyone's eyes became dark-adapted. The walk up was straightforward, if a bit steep in places. Some helpful souls had installed steel cables between posts alongside the path in the trickier spots, and we clung to them.
Even with the moon in the sky, stars shone brilliantly. We must have been lucky (or have picked a night during a meteor shower) because we saw at least a dozen bright meteors streak by during the climb. The air was cool but exertion kept us warm --- until we reached the top. There, of course, the view was stunning, the wind blew unobstructed, and we shivered. A circle of boulders gave not even the illusion of shelter. We huddled and waited. Finally the sun rose, thawed our spirits, and we shuffled down to the cars and thence home to bed.
- Wednesday, January 12, 2000 at 08:48:43 (EST)
The acme of charity is to give an anonymous gift, and to be so selfless as to then forget the act. That's something a real mensch (of any sex) can strive to achieve --- though it's not something that any of us can ask of another.
- Tuesday, January 11, 2000 at 06:49:23 (EST)
A narrow corridor separated the east and west wings of the basement. Naked pipes for steam and water ran overhead. (Easy access to the (in)famous Caltech steam tunnels was via a side door.) The lights in this part of the building were usually off, to save electricity. After going to and from one's office a few hundred times, it hardly seemed necessary to turn them on for the journey. The path was familiar: a dozen steps, turn left, two dozen more, jog right, then left, and you reached the lighted alley where the student offices were.
One day the obvious happened. Thinking about something else, carrying books under each arm, I turned left a step too early ... and in the dark walked smack into a solid brick wall. Ker-whap! My forehead was in the lead. I can testify that "seeing stars" is a real phenomenon, not just a cartoon metaphor. Ouch! Luckily, no major damage ensued ... just ugly bruises to face and ego.
- Monday, January 10, 2000 at 05:49:44 (EST)
Social systems have layers too. On a component basis, we have individuals, families, neighborhoods, towns, counties, states, and nations. In the monetary sphere, we have transactions, property, owners, businesses, and major sectors of the economy. There are countless other layers in the doing of art and science, in the gathering and delivery of information, and in the functioning of social institutions such as religions, schools, etc. Each layer has interfaces to higher and lower layers; each is to some degree insulated from its neighbors.
What's the top layer of society? Perhaps it's the shared concept of justice --- fairness, honesty, rights, ....?
- Sunday, January 09, 2000 at 07:19:34 (EST)
On top of these not-always-intuitive techniques, there are some simple yet important tactics from classical chess wisdom:
Caissa, the (make-believe) goddess of chess, is watching....
- Saturday, January 08, 2000 at 06:35:37 (EST)
Software engineering similarly applies the same two strategies for dealing with complexity. A program can reveal internal routines to the outside world and, through documented interfaces, invite users to customize and extend the system to handle new tasks. A program can alternatively isolate internal functions and make it impossible to tinker with or modify them during normal operation. Real programs do both, to varying degrees under varying circumstances and depending on design philosophy.
Scientific hypotheses similarly use the same two techniques. A good theory exposes itself to refutation in a myriad ways. The more experimental tests that it passes and the more predictions that it makes which are verified by observation, then the stronger conviction we have that the theory is an accurate description of Nature. At the same time, good theories encapsulate information and put it into a "you don't need to worry about these details" box --- thereby simplifying, making precise yet compact explanations possible. We don't have to look at the detailed motions of subatomic particles to analyze a gas (in equilibrium, far from critical points in phase space, etc.); we don't have to know the detailed compositions of the planets to understand their motions around the Sun (when internal tidal forces are negligible, etc.); we don't have to worry about the state of mind of a person in order to treat an infection (though an optimistic attitude often helps recovery). Exposure and encapsulation: good theories do both.
- Friday, January 07, 2000 at 05:54:28 (EST)
An addition or multiplication problem can quickly be checked by casting out nines from the inputs and the answer: if the calculation was done right, then the single-digit version with nines taken out will also work. Thus, is 12345*67890 = 837102050 correct? Well, it transforms into 6*3 = 8, but we know 6*3 = 18 and 18 turns into 9 (or equivalently, 0), not 8. So there's something wrong with the original answer (maybe we forgot to carry properly?). To check subtractions and divisions, turn them into the associated additions and multiplications.
Casting out nines works because the process in base ten (decimal system) gives the remainder left over when a number is divided by nine --- and we can deal with the remainders to verify the full computation. It's just like knowing that the sum of two even numbers, or two odd numbers, had better come out even.
The deep idea behind casting out nines is projection: shining a light on something and studying the shadow. Howsoever an object moves, its shadow must follow --- and if we know the laws governing the shadow world, we can check the situation there and detect illegal activity going on in the real universe. If the shadow world is simple (say, single-digit arithmetic versus hairy multiple-precision math) then working there can be quick and efficient. We may not catch all mistakes --- two objects might cast the same shadow --- but by making projections into different subspaces we can improve the odds, maybe even to the point of certainty. Projection is a powerful kludge, with lots of applications in unexpected places.
- Thursday, January 06, 2000 at 05:48:24 (EST)
- Wednesday, January 05, 2000 at 06:49:20 (EST)
Error correction is like holography but with an extra twist. Holograms encode an image and spread it out over a surface. The non-locality of the data means that if part of the hologram is destroyed, the whole picture is still there, only somewhat fuzzier. (Footnote for quibblers: we're talking about classic Fourier-transform-style holography, not white-light or other variants which put image information into narrow strips or patches.) Digital error correction similarly takes data and spreads it out, but with a little extra redundancy. That way if some bits are lost, they can be reconstructed. A trivial form of error correction is to repeat the data three times ("What I tell you three times is true!") and then when reading it out take a "majority rules" approach if parts of the record differ. That's simple but wasteful, and it can only fix a single error for each triplet of information. More sophisticated math permits the detection and correction of many mistakes with only a slight overhead in extra storage.
In fact, though they often don't realize it, when people use words in any form they're dealing with a digital bitstream --- whether the text is printed on paper, handwritten as calligraphy, or spoken into a recorder. Words are made of letters, and letters are chosen from a finite set of symbols. The same holds for spoken language, which is built of phonemes. Alphabets typically encode four to eight bits per symbol; a language like Chinese may have up to 20 bits per ideogram. And there's redundancy galore: "Q" in English is almost always followed by "U", the letter "E" is commonest, followed by "T", and so forth. A slightly garbled or faded message can be recovered quite reliably, and vn txts wrttn wtht ny vwls cn b rd strghtfrwrdly n mny crcmstncs. That's natural error correction for a digital medium. It's used by cryptographers to break codes, and by linguists to reconstruct lost languages from fragmentary inscriptions. In a manner of speaking, redundancy and error correction supply a built-in Rosetta Stone for digital media --- a safety net that analog systems lack.
- Tuesday, January 04, 2000 at 05:49:05 (EST)
Why fear a Ph.D. (or any other mark of distinction)? A doctorate from a decent school is one piece of evidence about a person. It suggests that its holder is at least somewhat persistent, reasonably intelligent, and can finish a moderately large project, but says relatively little about all the other crucial characteristics that a good person needs to have --- for instance, articulateness, breadth and depth of knowledge, collegiality, ability to learn, good humor, stability under pressure, sound judgment, and a host of interpersonal skills.
"Ph.D. envy unnecessary? Easy for you to say," some may reply. No, not really. Until I was well into grad school, my mental models of professors scarcely included any human elements. Faculty members were on pedestals, or some higher planes of existence. They suffered from no petty weaknesses, they made no mistakes, and they knew (or could find) all the answers. It wasn't until I saw brilliant academics making fools of themselves as persons --- jilting their spouses, fighting over money and perquisites, playing departmental politics --- that I began to understand that they were mortals too. And in the "real world" it took me another decade to begin to perceive that my bosses (and their bosses all the way up the pyramid) were the same. (OK, so I'm slow to notice.)
Hitherto I always assumed that somebody up there knew what was going on. Sorry, but I was wrong. The most senior managers may have responsibility and authority, but they don't necessarily have supernatural vision. And getting back to credentials: fancy degrees don't make a person any different, not in the long run. A title, an award, a medal, a laurel wreath? They're clues, and they may signify something about a person, something to check out --- but they're not worth worrying about, and certainly aren't appropriate objects of awe, fear, or jealousy.
- Monday, January 03, 2000 at 05:55:57 (EST)
Answer: when working in different number systems, "Oct" means octal, base-8, and thus "31 Oct" is 3 in the eight's place plus 1 = 3*8+1 = 25 --- and "Dec" means decimal, usual base-10 arithmetic, so of course "25 Dec" is 2 in the ten's place plus 5 = 2*10+5 = 25. So 31 Oct = 25 Dec, eh? (Maybe you have to be a programmer to smile at that one....)
- Sunday, January 02, 2000 at 07:34:30 (EST)
Art and language work via conventions, arbitrary mappings between patterns and meaning. Many conventions start out instinctive, firmware coded into the brain as an inheritance from thousands of naturally-selected generations: the diverse forms of physical attractiveness, the tastes of good food, the comforts of familiar surroundings, and the appeals (within safe limits) of novelty. As babies grow up they adjust and modify their perceptual processes, and learn (consciously or unconsciously) new conventions. Sounds and shapes are made into symbols for ideas. Scraps of cloth turn into scarves, swimsuits, uniforms, or flags, each with its own set of associations. A scent brings back old memories; a melody calls tears to the eyes.
Some conventions are private, or are shared only between lovers, within a family, or among clan members. Other symbol systems spread like wildfire, and then die out just as quickly: slang catch-phrases, æsthetic fashions du jour, best-sellers, must-see shows, and the like. Still other conventions grow imperceptibly over time, but have profound effects --- such as our evolving conceptions of justice, equality, peace, and freedom. How much farther can such good conventions go, and what new "conventional wisdom" can we hope to see emergent in our future?
- Saturday, January 01, 2000 at 07:12:07 (EST)
- Friday, December 31, 1999 at 07:06:50 (EST)
In the chaotic buzz of events, you need a theory to interpret what's going on. We all begin with naïve theories, based on experiences in infancy with ordinary objects like balls, blocks, breasts, and bells. We've evolved so that we're born with (or quickly develop) simple models of the world. Push on something and it moves; push harder and it moves more; let it go and it may slide along or roll away or swing back or make a sound.
The game of science is to extend primitive notions into more precise or general hypotheses --- and then to ask questions and compare the answers with what Nature exhibits. With a theory to guide the process, answers can start making sense and lead to better questions, better theories, and better models of the universe. Without a theory, Nature stands mute.
- Thursday, December 30, 1999 at 05:54:09 (EST)
Most pioneers are losers. They waste their lives exploring empty corners in a huge multidimensional maze. One in a thousand wins the lottery --- and everybody who didn't gamble also gets a prize. What a scam! Is there some way to run things more fairly, so that fewer lives are thrown away in vain? A more explicit social "insurance policy" to spread, and thereby reduce, individual risk and loss?
- Wednesday, December 29, 1999 at 05:48:02 (EST)
- Tuesday, December 28, 1999 at 06:03:38 (EST)
True (no quote-marks!) leaders, celebrities, and authorities do exist. They differ from their fake "kin" in that real ones are recognized by others, not annointed by themselves. Good leadership is chosen by its followers, based not on platitudes but on deeds, honesty, and mutual respect. Worthy celebrities shine by their modesty, charity, and the substance of their work. Genuine authorities are sought out for their advice --- which rarely comes neatly packaged as bumper sticker slogans. Honest counsel is framed with caveats and disclaimers. Real expertise, in all domains, recognizes its own limitations.
- Monday, December 27, 1999 at 05:48:36 (EST)
"The character of the tribunes was, in every respect, different from that of the consuls. The appearance of the former was modest and humble; but their persons were sacred and inviolable. Their force was suited rather for opposition than for action. They were instituted to defend the oppressed, to pardon offences, to arraign the enemies of the people, and, when they judged it necessary, to stop, by a single word, the whole machine of government."
Negative power is critical, particularly where great engines have the potential to run amok. The Framers of the U.S. Constitution showed genius not in what they built government to do, but rather in what they forbade it to do. On an individual level, physicians learn to "First, do no harm" --- that is, when to refrain from active measures. Natural systems are amazingly resilient; they evolved to heal themselves. Designed systems are fragile, in a multitude of ways. Any complex artifact --- a computer program, an aircraft, a power grid, a State --- is guaranteed to fail, again and again, as it goes through testing. Engineers fix the problems that appear, and during ordinary operation things work fine. Extraordinary circumstances, however, unveil new problems. Smart designs are crafted to fail gracefully, to degrade rather than collapse, and to allow an emergency override when unanticipated stress threatens to drive things out of control. Good systems build in a tribunician veto, a panic button.
- Sunday, December 26, 1999 at 16:27:12 (EST)
Those who are wealthy can try to share with those who are poor; those who have little can try to take joy in the success of others, without envy or hatred. All can strive to live with grace and good humor, with patience and hope, and with caring and love for one another.
- Saturday, December 25, 1999 at 09:14:48 (EST)
This is an important point, often overlooked in intellectual circles: we're all creatures of the flesh. Rational as we may (like to) think of ourselves, our judgments are constantly colored by our health, our environment, and our interactions with other people. Often the shading is quite subtle: a slight crankiness one day, a cheerful mood another, a propensity to get bored on a third. Should this be of concern? Or is it just part of the spice of life, an emotional MSG that enhances the flavor of a nourishing meal?
Few of us would want to give up the pleasures of the body, the raptures of love, the beauties of the arts, and the thrills of intellectual discovery. But are these joys mere aberrations of brain and body chemistry, the flip sides of depression, irritation, or indigestion? Do positive feelings justify themselves? Or could they be misdirected --- perhaps, most arguably, when they come from drugs, from dalliances, from time-wasting distractions, or from other activities far below our potential as sentient beings?
Human emotions, a Stoic Sage might contend, can be useful indicators and pleasant rewards, but should not be mistaken for ends in themselves. Emotions below the threshold of conscious perception are singularly treacherous in that they can lead us to act in ways we will regret later. True? Can it ever be wise to hand oneself over to passion? Or should one always retain some level of detachment, some ability to step back from the brink of total emotional commitment? Is such an internal monitor analogous to a computer's Operating System: the highest-priority set of supervisory routines which maintain control over all executing programs?
- Friday, December 24, 1999 at 18:49:35 (EST)
A couple of years ago, much to the amusement of my friends, I claimed that one of my New-Year's Resolutions was to drink more coffee --- a vow that was relatively easy to keep. Recently I quit for a month, got through the headaches of withdrawal, and found myself in a happy but somewhat less creative state (at least, it felt that way). Was the artificial boost from caffeine an unæsthetic trick, or a legitimate tune-up for the system? Are eyeglasses (or any other visual correction technology) to be scorned or embraced? How about antibiotics to fight infection, or insulin for a diabetic? Where are the lines to be drawn in modifying the body? The mind?
- Thursday, December 23, 1999 at 06:39:16 (EST)
When a signal goes from one medium to another, like light going from air into glass, part of the wave makes it and part gets reflected. The relative impedance of the two media govern that process. If we're clever, we can match impedances and avoid reflective losses at the interface. For light, thin coatings on a surface can do the trick (e.g., look closely at the lenses on a good camera). For electrical signals, transformers match impedances between circuits.
For people and their conversations, impedance is a useful concept too! Some folks are quick in one subject but slow in another. They don't communicate well with somebody who has a different set of abilities. A conscious impedance-matcher --- a person who can translate from, say, the language of art to that of science --- can help a message get through. (But when there's enough resistance, alas, no amount of transformation can prevent serious loss of signal!)
- Wednesday, December 22, 1999 at 06:34:48 (EST)
- Tuesday, December 21, 1999 at 06:37:26 (EST)
Nature may not be so wasteful after all. Mathematicians have studied "cellular automata": idealized simulations on a grid of pseudo-cells, with fixed rules for how patterns change from one generation to the next. It's not easy to make a general self-reproducing system. Typical configurations that can replicate need huge sprawling arrays of cells, delicately arranged. (Or they need comparably complex underlying rule sets.) If there's any sort of threat to stability and growth --- such as competition by other "creatures" or stressful changes in the background "environment" --- then patterns have to be even larger in order to succeed in copying themselves and correcting errors, accidental or induced. And if there's to be growth into new ecological niches, then more individuals are needed so that they can experiment and evolve in myriad directions. Most such experiments fail, but the few that survive offer hope of additional progress.
The breathtaking diversity of Nature is necessary, not arbitrary. When numbers of units shrink, a subsystem tends to get less robust, more vulnerable to bad luck --- and species go extinct, as biologists have documented.
- Monday, December 20, 1999 at 06:38:00 (EST)
Such boons to others, and to the future, are called "supererogatory". Simple kindness is supererogation. So is charity, particularly the anonymous sort. (Many parents, in retrospect, are prime examples; children rarely recognize it at the time.) Sharing ideas, offering a sympathetic ear to someone with a problem, and doing the honorable thing when it hurts are all supererogatory. Nobody can demand that a person do these; it's perfectly legal to say "No!". But going beyond what's required is a partial payment we can make to our predecessors who did so, and who thereby helped us get where we are today. And giving a little gift is a big step toward becoming a mature adult, a contributor to the world and its improvement.
- Saturday, December 18, 1999 at 18:45:34 (EST)
Go deeper, down to the simplest of shapes: paths in space, lines that twist and bend. The slope of a line is no good as an intrinsic quantity. It's not self-contained; it changes depending on how one rotates coordinate axes. What counts? Curvature --- the rate of bending for the path. A flat arc of constant curvature closes on itself and makes a perfect circle. In three dimensions, constant curvature escapes into a helix, a barber-pole spiral along the surface of a cylinder, a strand of DNA, the path of an electron in a magnetic field. Let the tightness of the curl vary, and generate the lovely lines of Nature, from vine to flower to seashell to human body. Take the curvature into higher dimensional spacetime, link it to the distribution of matter, and find the laws of gravitation and motion. Awesome curves....
- Friday, December 17, 1999 at 05:52:37 (EST)
- Thursday, December 16, 1999 at 06:21:37 (EST)
Analysis feels like space, flowing across the universe without bounds, smooth, calm, peaceful. Algebra feels gritty, rough, with pits and walls, jumps and sharp corners. Yet the two are united by some of the deepest results of modern mathematics.
- Wednesday, December 15, 1999 at 06:22:05 (EST)
A library is an idea --- the idea of preserving and sharing knowledge. Libraries offer a quiet place for serious thought, deep meditation on important problems. Libraries offer selected resources to nourish the thinker, and leisurely access to the learning of the world. Speed is of minimal relevance. A screen of flashy images fetched in a second has little to contribute for a subject that demands months or years of study.
In modern society, libraries have become invisible, like air; and like air, libraries are seldom noticed except in their absence. A library is a luxury in the short term --- just as the Research Department is for a corporation that doesn't look past the next quarter's sales figures, or as education is for a country that focuses its creative energies on entertainment. Libraries are superfluous; we can do without them. We can also do without wisdom and meaning in our lives. For a while, anyway.
- Tuesday, December 14, 1999 at 06:06:53 (EST)
To do better than simple hill-climbing takes a willingness to go down once in a while, that is, to give up immediate gain for long-range profit. One approach that works is to sample the terrain on a grid, say every 1000 meters in a north-south and east-west direction. The altitude data from those samples can then be used to model the entire mountain, assuming that the surface is reasonably smooth. (There's no guarantee that it is, but one can hope ... and measurements give evidence for or against the smoothness of the land.) A model that fits the samples then can guide an explorer to home in on the likeliest zones, where more readings taken on a finer grid, perhaps every 100 meters, may lead to the true peak.
Another way to seek the mountaintop comes from the physics of solids; it's called "simulated annealing". When crystals grow quickly, layers of atoms are laid down with lots of defects. To get rid of those faults, a blacksmith heats an ingot and then gradually cools it. The heat lets atoms bounce around and get into their proper places, and then the cooling locks them in where they belong. In the same way, a simulated hill-climber is started at a high "temperature", racing off in a random direction with only a slight bias toward going up. The ersatz climber's temperature is then lowered slowly, increasing the tendency to climb and making it less likely (but not impossible) to go down. This method keeps the climber from always getting trapped on a local maximum, and when done many times can lead to a good (though maybe not the best) solution.
The real challenge comes when trying to optimize not over two quantities, but over hundreds or more. Imagine the trek up a thousand-dimensional mountain! At each point along the trail there are so many directions to turn that one is almost certain to waste time heading the wrong way. But such high dimensionality problems are precisely what must be solved when dealing with complex real-world situations --- scheduling an airline's flights, running a factory, or tweaking a telecommunications network. Tough or impossible to do perfectly, especially under time constraints, but with mathematical help feasible to do "good enough".
- Monday, December 13, 1999 at 22:21:13 (EST)
- Sunday, December 12, 1999 at 20:57:05 (EST)
- Saturday, December 11, 1999 at 07:50:35 (EST)
Broken symmetries are patterns that begin by working but then slip. A pencil balances on its point --- but falls upon the slightest disturbance. The electrons in a hot crystal of iron are randomly oriented, with no preferred direction --- but cool the metal below its Curie temperature and the electron spins lock with each other and point the same way, giving a strong magnetic field. Make a cylindrical soap film, a tube between two parallel rings --- but pull the rings apart and beyond a certain limit the cylinder pinches off and snaps into two separate disks.
More exciting: stand on an empty aluminum soda can. If you're light enough it carries your weight, just as a girder compresses slightly but remains symmetric and supports its burden. But go past its load-bearing capability and the can suddenly buckles. The fourth-order differential equations that govern it develop new solutions that grow exponentially. Ka-pow!
The same thing happens to societies ... and to individuals. We're in a balanced mode, able to handle the usual day-to-day perturbations that come along --- and then a little extra stimulus or stress pushes us over the edge of instability. Wisdom consists in recognizing the approach of danger and turning back before we cross the line into catastrophe. After the point of no return, free will goes out the window. (Think teenagers in "love"!) The system evolves to another stable state, regardless of our wishes. Eventually control returns, but often there's no going back to the pre-crisis situation. Stiff systems are particularly vulnerable to such sudden transitions; flexible ones bend before breaking. Rigidity is risky.
- Friday, December 10, 1999 at 06:26:27 (EST)
- Wednesday, December 08, 1999 at 20:39:04 (EST)
Wouldn't it be better to be utterly forgotten, but to have done some immediate good that helped real living creatures? ... to have been a friend to the lonely? ... to have shared kindness with the fearful? ... to have made life better for individuals suffering from illness, hunger, poverty, or ignorance?
Rewards come not from labels, but from deeds --- quiet, anonymous deeds done in the here and now. Those deeds echo, through time and across space. They add to the only wealth that we have: the lights of knowledge, peace, love, and hope for all ... quickening and dawning around the world.
- Tuesday, December 07, 1999 at 20:59:11 (EST)
- Monday, December 06, 1999 at 06:04:25 (EST)
"Is human nature the same now as in the days of Babylonian civilisation, when the social machine was oiled by drenchings of blood? Is it the same now as in the days of Greek civilisation, when there was no such thing as romantic love between the sexes? Is it the same now as it was during the centuries when constant friction had to provide its own cure in the shape of constant war? Is it the same now as it was on March 2nd, 1819, when the British Government officially opposed a motion to consider the severity of the criminal laws (which included capital punishment for cutting down a tree, and other sensible dodges against friction), and were defeated by a majority of only nineteen votes? Is it the same now as in the year 1883, when the first S.P.C.C. was formed in England?
"If you consider that human nature is still the same, you should instantly go out and make a bonfire of the works of Spencer, Darwin, and Wallace, and then return to enjoy the purely jocular side of the present volume. If you admit that it has changed, let me ask you how it has changed, unless by the continual infinitesimal efforts, upon themselves, of individual men, like you and me. Did you suppose it was changed by magic, or by acts of parliament, or by the action of groups on persons, and not of persons on groups? Let me tell you that human nature has changed since yesterday. Let me tell you that to-day the friction of the machines is less screechy and grinding than it was yesterday."
... from The Human Machine, Chap. XI
- Sunday, December 05, 1999 at 20:49:04 (EST)
When it's time to buy the farm, not many of us want to say, "Gee, I'm glad that I made all that extra money working on a stupid, pointless job!" Somewhat nicer to think that one's life contributed to peace, freedom, prosperity, a better chance for people to achieve enlightenment, and all that....
And if making a difference isn't enough, there's a factor that seems irrelevant when one's attention is only focused on good times (i.e., roughly the past decade) --- namely, job security. Not many companies have been in business for 200+ years; maybe the Framers of the Constitution did something right. Take a look at the Japanese economy, and/or remember some of the down years that commerce in this country has experienced. I fearlessly predict that we will have serious Bad News within the next decade (maybe sooner), and that most of the current fluff will come drifting (or plummeting) down to earth. Be prepared to invite grasshoppers in the dot-com world to eat dinner, and to sleep on the couch, when they're suddenly unemployed....
Plus IMHO the quality of the people here is simply higher than any place else I've seen --- both intellectually and spiritually.
I'm pretty happy that I took a ~10% pay cut to join this place in 1981!
- Saturday, December 04, 1999 at 20:14:37 (EST)
What if many other people you know play the game and prosper --- does that make the right decision different? What if the last time anybody failed to win was generations ago? What if articulate individuals present clever arguments that things are different now, that the wheel has been fixed and nobody need lose any more? What if people who win do so without performing any real work or adding any perceptible value to the world --- that is, their riches flow from non-players who are laboring unrecognized day after day?
Logic tells you that this can't last --- it's a Ponzi scheme, a pyramid racket, a chain letter which only moves resources from pocket to pocket. But it hasn't collapsed yet, and there probably are enough suckers to keep it going until you escape with your profits. Talk about temptation!
So what do you choose?
- Friday, December 03, 1999 at 21:16:24 (EST)
But there's a deep complementarity between the dynamic and the static, between algorithm and data structure --- just as there is between time and space, energy and matter, momentum and position, current and charge, or magnetism and electricity. Depending on one's frame of reference, dynamic and static components can be transformed into each other. Clever data structures make algorithms simple, even trivial (e.g., precomputed look-up tables --- analogous to precooked food from vending machines?). Clever algorithms make data structures simple (imagine food preparation starting with the elements of the periodic table!).
Using the trade-off between the dynamic and the static is a powerful mental tool for problem-solving. And more generally, dualism --- recognition of the pairs of related, complementary entities, like yang and yin --- is an even more powerful tool for understanding the world.
- Thursday, December 02, 1999 at 06:09:54 (EST)
Why are certain images of perverse torture so attractive to (apparently) healthy human beings? Horror movies, novels, short stories, and poems often revolve around moments of torment and pain. Why? Is it simply satisfying to be scared and yet safe? Is the brain taking advantage of a vicarious learning situation, encouraging the accumulation of data about trouble so as to avoid it in the future? Or are we just experiencing cross-talk between mental circuits? --- that is, getting excited by one set of stimuli because of their accidental linkage to completely different functions, e.g. food, shelter, reproduction, etc.? (And is that the basis of much commercial advertising? "Sex sells" and so forth?)
How should one respond to reports of individual or state-sponsored brutality and terrorism? ... to graphic descriptions of genocide? ... to news of ritual mutilation of young girls and boys, tribal "customs" which result in life-long suffering? Should one be ashamed of a fascination with horrible imagery? Or can this visceral emotion be recognized and harnessed --- or in appropriate circumstances even enjoyed?
And besides the fascination with evil that normal folk feel, how can one understand those individuals who actually perform grim things to other living creatures? What goes on in such people's minds? Do they have no empathy for their victims? Or is there a continuous spectrum of behavior from the saintly to the demonic?
- Tuesday, November 30, 1999 at 21:35:21 (EST)
Perhaps we need to get away from the linear or additive utility notion and consider a multiplicative utility --- not the sum, but the product of each person's feelings? Then when any individual's utility is zeroed out, the global product goes to zero. Utility monsters like Lola can't take control any more (short of going to infinity, which spoils the game). Another escape route might be to change the method of combining individual numbers to use the median, the mode, or maybe just the minimum of all values. That would a premium on risk-avoidance, and make the goal one of maximizing outcomes for the least fortunate. (John Rawls's "Theory of Justice" takes something like this approach at a societal level.)
The overall question is fairness --- what is it? How can it be measured? If a choice turns out splendidly for multitudes, but causes horrible pain to one human being, can it be right? Contrariwise, can one person block an action that everyone else urgently desires? How can people work together to make things turn out as well as possible for us all?
- Sunday, November 28, 1999 at 19:25:04 (EST)
I helped ALoT in a tiny way by working in my spare time on a couple of projects, the results of which are available from online archives:
Thanks ALoT, for encouraging these and other information sharing projects!
- Saturday, November 27, 1999 at 18:43:08 (EST)
The problem is that it's impossible to tell in advance what's important. That doesn't mean that we should write less --- rather, the opposite! A brilliant idea flashes across the mind like a meteor across the sky; its trail fades quickly unless recorded. Dozens of pages may have to be typed before the right metaphor surfaces. The trick, then, is to net the good fish and throw the minnows back into the ocean ... so they can swim away, grow fat, and be worth catching later ... or if not, serve as food for worthier creatures.
Write, write, write, throughout the day; then look back and transcribe a fraction (alas, most of the time for most of us a tiny fraction) into a journal or other archival storage; and finally focus on the gems from that enhanced ore for further cleaning and polishing. It's like isotope separation: careful and meticulous, with a huge energy expenditure before the concentration of product is high enough to serve. There's a whole physical theory of "separative work units", the basis of uranium gaseous diffusion plant design. Can it apply to idea-enrichment too? What other tactics promote better creative thought? And given an inspiration, how to help it grow from conception to maturity, from tiniest spark to bonfire?
- Thursday, November 25, 1999 at 21:05:04 (EST)
Why? Do we worship complexity, or mutability, or potentiality, or just similarity to ourselves? Do things count only as they stand in relationship to people? And what are the sources of debate on various levels of the hierarchy? That is, what are "persons": infants? the sleeping? the senile? the unborn? the dead? those not yet conceived? corporations? fictional characters in stories? ....
Over recent millennia, the trend seems to be toward greater inclusiveness. "Personhood" has been conferred on those who aren't of the same social class, sex, race, etc. of the ruling clique, at least in many nations. Is this a trend, or a fluctuation? Does it have room to continue? In the long run, what counts?
- Wednesday, November 24, 1999 at 06:22:49 (EST)