The first source historically is simple: conversation with family, friends, and colleagues. Amongst the dull and repetitive daily drone, gems of insight surface and are shared around the dining room table or the (metaphorical!) office water cooler. Most of these gems are badly flawed. They're chuckled over and then quickly forgotten, deservedly so, as minor word play. But some fortuitous metaphors persist, and spread to other conversational circles. The total volume of global chit-chat is huge, while barriers to entry are low --- and so mere banter can be a major contributor to human metaphorical invention.
Listening to active and energetic conversation is also an infinite source of learning for children, to whom all is new and wonderful. Adults who open their minds, like children, to what's actually being said --- instead of tuning out based on what they expect to hear --- can find hidden jewels in mere gossip. And then there are those critical-mass conjunctions of ideas with people who, through simply talking together, trigger explosions of mutual creativity. Witness extraordinary artistic salons, scientific symposia, literary circles, and revolutionary political gatherings.
Conversation was surely the most productive vector for metaphoric creation and transmission until recent decades. But who has time to talk any more? Exhausted from work, we collapse on a couch, turn on a TV, turn off our critical faculties, and let words and images wash over us. Mass electronic media, for most people in the wealthier parts of the globe, have become the dominant source of language input every day. But television and radio are a one-way channel aimed at passive receivers. That's not a path to enhancing human creativity and critical thought. The media can only afford to offer what an audience will pay to hear --- and the costs of production, even for a local program, are high enough that with few exceptions only the least-common-denominator can make it to the air. Not much hope for new, powerful metaphors there. Movies are even more cost-constrained as idea sources. They're too few, too slow, too single-threaded.
But if conversation is localized and narrow, and mass media are unproductively broad and shallow, where should a prospector for rich metaphorical ore dig nowadays? There's an obvious mother lode --- so ubiquitous that, like air, it's often overlooked. Symbols for thought come alive in the mind, but they can be stored and retrieved as scratches on stones, impressions on clay tablets, pigment on canvas, ink on paper, magnetic domains on ferric coatings, charges on capacitors, and pits on optical surfaces (so we're back to scratches on stones again!).
Writing is the one best source for building and sharing serious, mature metaphors. Writing can be conversational --- as we correspond with kindred spirits, in a slower-paced and more reflective mode than hallway chatter, with time enough to find and arrange the beautiful words needed to express beautiful ideas. Writing can teach --- as we re-read and study difficult passages, struggle to understand, and succeed. And writing can endure --- as we hear today words echoing down the centuries from the great minds of the past.
- Tuesday, September 28, 1999 at 01:51:24 (EDT)
Infinitely more important, Stoics argue, are higher questions of virtue, "right living" writ large. How should we respond when someone wrongs us, when the challenges of the world become overwhelming, when evil is clearly about to triumph? What should we focus our life's energies on doing, and why? When do events, mere things, become meaningful? A classical Stoic tries to separate self from dependence on circumstances. The goal is to establish an "inner citadel" of the mind, free from passion about unworthy externalities: a rock against which waves break and are rebuffed.
But is this right? Maybe the idealized Stoic position is too extreme, too abstract and doctrinaire to be relevant in normal life. We have to survive in the real world, constantly making decisions both big and small. Other people do matter, to most of us, and some people matter a lot. Strictly cultivating one's own garden, taking no notice of outside events, seems selfish and inhumane. How about people who can't take care of themselves --- especially children? How about large-scale world events, war and peace, environmental destruction, liberty and justice? Is it wisdom to label everything outside the mind as "indifferent"?
The Inner Citadel is a powerful metaphor. Perhaps we each could use one, to retreat to in times of extreme crisis. There are moving stories of prisoners of war, of tortured slaves, of death-camp inmates who built such mental fortresses and survived. In more ordinary circumstances, we can individually find comfort in an inner study, a conservatory, a psychic room of one's own to relax within and regenerate. Having such a shelter from the storms of life can make it far easier to smile and be polite to one another.
Humans aren't by nature oysters; we don't normally live inside shells. We're extraordinary animals who thrive together, sharing and learning from each other, in ways that go far beyond the naive Stoic model. Part of growing up is learning to unify all those dimensions of our humanity --- internal and external --- intellectual, emotional, and social. Not easy!
- Sunday, September 26, 1999 at 14:06:51 (EDT)
But just as bad as being too slow, in chess and in life, is being too fast. Some threats are ephemeral; a good long-range approach shouldn't be abandoned in response to momentary distractions. More importantly, many plans take time to mature and will fail if rushed. Although certain situations are time-critical and demand instant attention, more often there's enough slack in real-world systems to permit a wide range of choice in response, paced more or less quickly. Speed is one factor, and not always the most important one.
There is some justice in the universe: vision, consistency, persistence, and focus do get their rewards. Even a second-best plan is often better than flitting from one great idea to another, not giving any of them enough time to work. "The fox knows many things, but the hedgehog knows one big thing" --- and although foxes win on occasion, a hedgehog usually has at least a fighting chance.
- Saturday, September 25, 1999 at 21:35:39 (EDT)
In essence a secret is simply a puzzle. Somebody else has the answer; they've just hidden it and won't tell us where to find it. Unveiling a secret gives a quick thrill, but there's no lasting compensation. Secrets can be cute, clever things, maybe even temporarily valuable things, but they're by nature finite. Governments and corporations and individuals expend vast resources to keep their own secrets, and to attempt to unravel others' secrets. So what?
In contrast, a mystery is a problem, a challenge that has depth, staying-power, mana. What governs the large-scale structure of spacetime? Where are the sources of values, of good and bad, right and wrong? What are the limits to computability? Whom should we trust, love, and obey? What forces drive history? Where do the fundamental particles of the universe come from? What's the meaning of life? Why?
Nobody knows the answer to a true mystery. Perhaps nobody will ever know; the best mysteries have wheels within wheels, never-ending levels of ever-changing complexity. But wrestling with a good mystery repays us with learning, partial solutions, maybe glimpses of a Holy Grail that we will never touch. Secrets can be useful as warm-up exercises --- but secrets only tease. Mysteries endure.
- Thursday, September 23, 1999 at 22:14:03 (EDT)
We can hope....
- Wednesday, September 22, 1999 at 20:12:23 (EDT)
'But this is terrible!' cried Frodo. 'Far worse than the worst that I imagined from your hints and warnings. O Gandalf, best of friends, what am I to do? For now I am really afraid. What am I to do? What a pity that Bilbo did not stab that vile creature, when he had a chance!'
'Pity? It was Pity that stayed his hand. Pity, and Mercy: not to strike without need. And he has been well rewarded, Frodo. Be sure that he took so little hurt from the evil, and escaped in the end, because he began his ownership of the Ring so. With Pity.'
'I am sorry,' said Frodo. 'But I am frightened; and I do not feel any pity for Gollum.'
'You have not seen him,' Gandalf broke in.
'No, and I don't want to,' said Frodo. 'I can't understand you. Do you mean to say that you, and the Elves, have let him live on after all those horrible deeds? Now at any rate he is as bad as an Orc, and just an enemy. He deserves death.'
'Deserves it! I daresay he does. Many that live deserve death. And some that die deserve life. Can you give it to them? Then do not be too eager to deal out death in judgement. For even the very wise cannot see all ends....'
Gandalf's speaks to us: "Many that live deserve death. And some that die deserve life. Can you give it to them?" No, we cannot. And every day, in far smaller things, we face the same question. People wrong us. They are guilty. They deserve punishment. We pass judgement and mete out justice. We do it to colleagues, friends, children, lovers ... via harsh words, raised eyebrows, turnings away, and silently held grudges. We do it to more distant people, who "deserve" their poverty, ignorance, and ill health; they (or their ancestors) should have worked harder; they should have been born into better circumstances.
When may we strive to forgive rather than punish, to choose mercy rather than fairness? The past is a frozen lake; every action we take is irrevocable. Retaliation echoes back and forth until it destroys a relationship; forgiveness echoes to build a relationship stronger. And one who can give the gift of forgiveness, meekly and selflessly, as a bonus grows thereby.
It's hard to forgive. Sometimes it doesn't work. But perhaps we can at least hesitate, and remember to try. And to have Pity. And Mercy.
- Monday, September 20, 1999 at 18:43:04 (EDT)
But once a week, every Friday at 7:45am, a few individuals gather at a round table in an almost-empty cafeteria. The corporate haze thins, imperceptibly ... a faint glow, like the earliest fingers of dawn, emerges ... the fog lifts slightly, and an elusive light begins to illuminate the entire organization --- though almost no one notices. A handful of people in the early morning have come together to think and talk about ... philosophy.
Yes, philosophy. The Philosophy Breakfast is not a club; it has no rules and no admission requirements; people drop in and drop out, as they please. It began in early 1998, triggered by a New York Times piece on the French "philosophy cafe" movement. Some weeks, the group picks a reading to springboard from --- a book within Marcus Aurelius' Meditations, a chapter of Clausewitz's On War, a few dozen pages of Machiavelli's The Prince. Other times, there's no agenda whatsoever.
It matters not; within a few minutes, regardless of the starting point, dialogue moves to a topic of concern --- death, truth, respect for authority, sources of creativity, whether violence can ever be justified, how and when to tell children about evil ... or literally a thousand other things. One week a person who had just turned 50 years old came and talked about his angst. Another discussion centered on career frustrations and the nature of "rewards" worth seeking.
There are many questions but few answers, many beginnings but few conclusions. And after forty-five minutes of conversation, Philo B'fast participants thank each other, clear the table, and slip away. They vanish into the corporate sea --- but their thoughts echo and reverberate throughout the organization, enriching and energizing their lives and the lives of their colleagues. Quiet, invisible magic is happening, every week.
- Saturday, September 18, 1999 at 21:39:53 (EDT)
- Friday, September 17, 1999 at 20:37:56 (EDT)
- Wednesday, September 15, 1999 at 20:37:06 (EDT)
Why do good models fail? Sometimes the data we have are incomplete, and catastrophes actually have happened in the past --- but we don't know about them because they came too long ago or in out-of-the-way corners of the world. Sometimes our models have subtle "bugs" in them, logical errors that testing has failed to reveal.
But more often, our forecasts go awry because things change. New influences emerge; patterns of behavior evolve; systems are no longer what they once were. Things change in nature, as atmospheric gas levels wax and wane, as ocean currents shift, as volcanoes erupt, as continents drift. And more suddenly, things change as humans choose and act. Profits are momentarily high in an economic sector, so investors plunge in. A dramatic incident is widely reported, so people shy away from a mode of transportation, or a medical treatment, or a type of food. Not rational in the long run, perhaps ... but it happens.
Scientists have studied noise and fluctuations in physical systems of all sorts, and have found patterns that help explain and predict events. One particularly powerful technique analyzes changes by frequency. Some prices, for instance, go up and down on an annual basis, perhaps because they're tied to climate or holiday spending or vacation schedules. Other activities have prominent daily, weekly, or monthly cycles. Sunspots have an ~11 year period; cicadas emerge every 17 years; eclipses recur in an ~18.03 year saros pattern.
Plotting the size of fluctuations against their frequency, "f", gives a power spectrum, analogous to a spectrum of light. Peaks and valleys tell something about the likelihood of events on various timescales. A power spectrum that's flat, equal at all frequencies, is called "white noise". A random walk, on the other hand, has a lot of long-term drift, but its high-frequency components cancel out. Its power spectrum falls like one over frequency squared.
In between the total chaos of white noise and the predictable, lethargic meanderings of random walks, there's the extraordinarily important zone called "1/f". The power spectrum of 1/f noise describes a host of interesting systems, from the flooding of the Nile to the ticking of an atomic clock, from the insulin dose of a diabetic to the noise in an electronic circuit.
A 1/f spectrum is divergent at low frequencies. In other words, rare but huge fluctuations are gonna occur --- and the longer we wait, the bigger the spikes will be. There's no way to know when they're coming, but come they must. The bottom line: just because stocks (or anything else) have moved in such-and-such a pattern for years (or decades or centuries) doesn't mean that this pattern will persist.
Rather, the only certainty is change --- of a form and magnitude beyond all expectation. We'd best keep our powder dry!
- Tuesday, September 14, 1999 at 11:58:52 (EDT)
Judging by the experience of the last fifty years, it seems that major changes come roughly once in a decade. In this situation it makes an enormous difference whether we are able to react to change in three years or in twelve. An industry which is able to react in three years will find the game stimulating and enjoyable, and the people who do the work will experience the pleasant sensation of being able to cope. An industry which takes twelve years to react will be perpetually too late, and the people running the industry will experience sensations of paralysis and demoralization. It seems that the critical time for reaction is about five years. If you can react within five years, with a bit of luck you are in good shape. If you take longer than five years, with a bit of bad luck you are in bad trouble.The same applies to individual lives. People who expect their jobs and their relationships to persist unchanged for a decade are likely to be disappointed. People who are flexible enough to adapt to major new challenges are likely to be happy and productive.
On the other hand, there's a difference between quickness and flightiness! At the crest of an economic boom, jumping from job to job is rewarded with big raises. Genius appears to lie in starting a new business, hemorrhaging money, and flitting on ... leaving the wreckage for others to clean up. Students change their majors to the hot field of the year, and graduate with credentials that evaporate when the trend shifts and times get tight. Long-range thinking is ridiculed; the "next big thing" is worshiped.
This won't last, of course; it never has, and it never will. Fundamentals, flexibly applied, are the foundations of success. They don't change --- learning, thinking, understanding, creating, caring, sharing --- and their results will be remembered long after the go-go trend du jour has turned to dust.
- Sunday, September 12, 1999 at 14:41:32 (EDT)
But looking up, we see the rest of the universe moving millions of times faster! Our world is in a time machine, plunging into the future at a tremendous rate. We watch alien civilizations flower and die, stars evolve, and galaxies whirl. We do so through protective instrumentation, of course, since ordinary light is blueshifted into gamma ray wavelengths as it falls down upon us.
How to engineer this gargantuan artifact? Let mass density outside our central solar system fall off inversely with distance. Then the local acceleration is a constant; we can make it a comfortable one gee, a normal Earth gravity. (The inverse-square law of Newton is counterbalanced by a growing amount of mass.) To keep us from cooking we had better use mostly cold material ... dead neutron stars, small planets, stellar-mass black holes, whatever. We must take care to synchronize orbits so that objects don't collide, and we have to keep interstellar gas or dust away. Assembling our cluster will liberate huge amounts of gravitational binding energy, plenty to cover the costs of bringing the masses together.
The result is a cosmological observatory --- perfect for impatient astronomers who want to personally see the evolution of the universe to its ultimate end. And when the show's over we can fold our tent, collapse into a singularity, and leave behind only a tidy supermassive black hole a few light-minutes across. Neat!
- Saturday, September 11, 1999 at 19:29:21 (EDT)
- Friday, September 10, 1999 at 06:00:42 (EDT)
Most nontrivial programming tasks are wicked. So are most political and social issues, most interpersonal relationships, and most of the deep questions of life. We do the best we can, under the circumstances ... struggling against our shortcomings ... striving to recognize and concentrate on what's really important ... and, if we're lucky, accepting with good grace inevitable failures in the context of what limited success we may achieve.
- Wednesday, September 08, 1999 at 06:10:41 (EDT)
"He was gifted with the special capability of making many mistakes, mostly in the right direction. I envied him for this and tried in vain to imitate him, but found it quite difficult to make good mistakes."as quoted by Simon Singh in Fermat's Enigma. The challenge, as Shimura notes, is to make "good mistakes", and to learn to differentiate them from unproductive blunders.
In the same vein, Amir Azcel's Fermat's Last Theorem quotes Andrew Wiles:
"Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it's dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it's all illuminated and you can see exactly where you were. Then you enter the next dark room ..."That's life: a succession of dark chambers. Learning experiences, if taken rightly.
- Monday, September 06, 1999 at 21:09:39 (EDT)
Minimax has nice mathematical properties; a classic and entertaining discussion appears in John Williams' book The Compleat Strategyst. For practical purposes, minimax is like an insurance policy. It guarantees that nothing utterly horrible will happen, but leaves open the hope of doing a bit better than expected. It's independent of the opposition, so it can't be faked out, bluffed, or intimidated. And minimax is stable, in that if all sides pursue their respective plans things quickly settle down so that no further changes are profitable to anyone.
In life, minimax-style worst-case avoidance isn't a bad strategy either. Most of the time swinging for the fence results in a strike-out. For every lottery winner, there are millions of losers, and the total amount paid out is far less than the money put into the pot. Few people become movie stars, professional athletes, or celebrities of any sort. Much better to practice a bit of sensible risk aversion, and focus on maximizing realistic possibilities. A big win can still happen, but if so it's just a bonus; nobody should count on it for anything important.
- Sunday, September 05, 1999 at 20:36:05 (EDT)
How to preserve new notions, especially during those critical few minutes or hours before they solidify?
- Saturday, September 04, 1999 at 16:08:34 (EDT)
Stoics focus their passion on virtue, right living in harmony with the highest potentials of humanity --- and so they are and should be utterly indifferent in the face of most day-to-day distractions. Strong feelings are simply inappropriate reactions to irrelevant happenstance. Clinging to emotions is childish, or animal, behavior. People can do better.
- Friday, September 03, 1999 at 20:38:28 (EDT)
We give different names to these transformations, but in some sense they're all forms of inversion. The mathematician Jacobi said "One must always invert!" Turning things around is an extraordinarily powerful tool for creative discovery. Looking from a new angle reveals unexpected truths. Swapping effect with cause, destination with source, or future with past sometimes shows new links among entities. Systems have subtle symmetries which we often overlook. Mirror-imaging, reflecting, trading places, can make those patterns visible.
- Thursday, September 02, 1999 at 20:24:38 (EDT)
Similarly, when a system of any sort changes over time, the point that represents it on a graph of its characteristics moves --- and that point may be attracted towards various places in a weird, non-physical phase space.
For instance, a nation's economy has a growth rate, inflation rate, unemployment rate, trade balance, and so forth. A cow has a daily feed consumption, weight, milk production, etc. Those parameters are interrelated: a cow that isn't fed will lose weight and won't produce milk for long. For any system, some combinations of characteristics are stable --- and when the system gets near enough, it falls into that happy place of stability. The cow has a natural weight. She feels hungry and eats more if below it, or is satiated and eats less if above it ... within limits, of course, and providing nothing else interferes. People are the same, as any dieter can testify. A stable configuration like that is a kind of "attractor".
But besides ordinary attractors, some complex systems have "strange attractors" --- regions of phase space which pull a body in, chew on it for a while, and then spit it out again, or which churn a body into a chaotic pseudorandom mess. In an ordinary situation, two systems which start out similar tend to stay similar. Twin cows grow up to resemble each other, other things being equal. But near a strange attractor infinitesimal differences are magnified, until the results are grossly divergent. That's why weather is so hard to forecast beyond a week or two, and perhaps why economics and other areas of human action seem so inscrutable. Tiny changes blossom into a world of difference.
- Wednesday, September 01, 1999 at 19:43:16 (EDT)
- Tuesday, August 31, 1999 at 17:13:47 (EDT)
- Sunday, August 29, 1999 at 07:47:41 (EDT)
- Saturday, August 28, 1999 at 08:35:06 (EDT)
- Thursday, August 26, 1999 at 17:20:59 (EDT)
The shape that this kind of graph assumes is called the envelope. Looking at it sometimes yields unexpected insight. Humans have great pattern-recognition abilities, and studying the envelope of a system can reveal subtle relationships, places where ordinary behavior breaks down. "Pushing the envelope" --- that is, exploring the edge of what is possible, and trying to go beyond it --- may also lead to new discoveries, as well as to better understanding of why things are the way they are.
- Wednesday, August 25, 1999 at 21:36:16 (EDT)
- Tuesday, August 24, 1999 at 20:06:50 (EDT)
Turning the sandglass on its side, mentally stopping time, stepping outside the flow of events --- these can reveal things in a different light. Physicists do it when they rearrange their equations to examine how things move in spacetime, minimizing various measures between two fixed endpoints. (See "Fermat's Principle" and "Lagrangian Mechanics" for examples.)
Mystics and philosophers (is there a difference?!) similarly think about time not as an inexorable current that carries us along, but rather as another dimension of life, something to transcend and observe from a universal perspective. Past and future coexist, simultaneously. Free will and predestination are only local issues, based on a limited viewpoint.
True, it's not easy to pop out of time while rushing to catch a bus, finish a project, fix dinner, comfort a hurt child ... but it may help to pause, at least momentarily, to take a breath --- envision past/present/future as a great tapestry woven of countless individual threads, existing in an eternal space beyond time --- and then get back to work!
- Monday, August 23, 1999 at 06:33:32 (EDT)
Individual _____ are often stared at, sometimes innocently as curiosities, in other cases with fear or hostility. Their presence in many contexts is viewed as a surprise; people comment when one of them is seen doing advanced or sophisticated tasks. A ______ when noticed tends to be seen as an object, "one of them", not a person with a name and a history. But surprisingly, in many circumstances ______ are virtually invisible, except to each other. People treat _____ as part of the landscape, look right through them, and talk as though they aren't there.
______ until quite recently had limited legal and voting rights in most countries. They still are subject to state-sponsored restrictions in some parts of the world. Their special socioeconomic status (or lack thereof) has often limited their opportunities to get good educations, and so they are noteworthy for their absence in many fields of letters, science, and the fine arts. Attempts to increase their numbers in those fields appear likely to take generations to succeed, and in the meantime have aroused stiff opposition from some non-______ who feel threatened or see such remedies for past discrimination as unfair.
Many ______ are quietly bitter about how they are treated each day. Many others are simply resigned to their station in life, and notice it as little as we all notice the air we breathe. A few lash out. Those _____ tend to be scorned as freaks, or boxed up and set aside as threats. Arguably the wisest ______ over the years have channeled their frustrations into teaching, learning, and consciousness-raising --- and have done wonders, long-term, in improving the lot of their group and of humanity as a whole. Their love for all, ______ or not, is a powerful miracle.
There is a final shocking truth, which many people try to avoid thinking about. Everybody's ancestry is literally full of ______, directly or collaterally. And, if one is blessed with descendants, they're eventually certain to include ______ as well. Maybe that's a reason for hope!
- Saturday, August 21, 1999 at 17:04:42 (EDT)
It doesn't "decide", of course; our model of the situation was sadly incomplete. The pencil is made of atoms, vibrating in interlocking structures; it's balanced on a table that trembles slightly; the air has subtle eddies and currents that push against it; and even if we eliminate all those disturbances, electromagnetic and gravitational influences from stars far away still tug the pencil off balance. When the slightest perturbation makes for growing error, in an amplified feedback loop, a simple symmetric picture of the situation can't work.
The pencil's precarious posture is intuitively obvious. But many other real-world systems can seem straightforward, yet hide subtle instabilities. If we try to describe them with simple models, it's critical for us to verify those models by putting in a touch of artificial "noise", tiny variations in the inputs to our calculations. If the results differ wildly, that's a sure sign that our model is broken, that we're leaving out something important --- or that reality is itself at a cusp, delicately poised, teetering on a brink.
If so, then we cannot simulate with any hope of success. We already know some limits of predictability in nature, for turbulent fluid flows and for planetary orbits. We may suspect similar instabilities in biological neural networks (minds!), in political and economic systems, or in the webs of interpersonal and social relationships. Perhaps history itself is unstable. Perhaps the best we can ever do, then, is to scorn false prophets who purport to predict the unpredictable, and settle instead for estimating the limits of our uncertainty --- error bars, plausible guidelines rather than rigid forecasts of the future.
- Friday, August 20, 1999 at 20:04:55 (EDT)
Mere transcendence doesn't make something worthy of worship. Transcendental items come in a hierarchy of types, like mathematical infinities beyond infinities, wheels encompassing wheels, levels of reality not only more, but different and qualitatively new. The attempt to capture and then leap beyond named objects is a tricky one. Simply saying "the thing bigger than anything you can name" often leads to paradoxes or meaningless word games. If we want to escape the known, the name-able, we had best move cautiously, mapping our path into the wilderness step by step. Jumping into a void doesn't make it easy to find home again.
- Thursday, August 19, 1999 at 21:00:15 (EDT)
Two reasons: effectiveness and æsthetics. Poetry is efficient communication, designed to capture and condense meaning into the smallest possible volume. Each well-chosen phrase carries more than its own weight; each syllable conveys a multidimensional message. But good poetry is also beautiful, with polished facets, well-rounded curves, and flares of brilliance. Poetry joins function and form, and when it works well, startles us into a new awareness of ourselves and our world.
- Wednesday, August 18, 1999 at 05:08:41 (EDT)
Dropping from a great height is a deeply ingrained source of terror, fun, and thought. Infants have an "instinctive" reaction to falling --- though it's unclear what evolutionary purpose that serves nowadays, other than providing a basis for mock-scary play by adults who toss babies into the air and catch them. Then there's the classic joke about the optimist plummeting from a high building, who passes the fiftieth floor and says, "So far, so good." A person falls in love; an economy goes into free fall; we skydive and bungee-cord jump for the thrill of the plunge. Buddhism uses the image of falling in some of its meditative stories, as do many other religions.
The state of falling is a splendid and powerful metaphor for life. We all face certain death. But is our purpose just to hit the ground last? Or worse, to act as though whoever dies with the most toys, wins? Can't we figure out something useful to do on the way down?
- Monday, August 16, 1999 at 20:27:00 (EDT)
But friction is universal, not just a wartime phenomenon. We almost always know what we should do: be kind to each other, take care of ourselves, strive for wisdom, and so forth. More often than not we try, or at least intend, to do the right thing. But actually doing it is another matter. Nothing goes as planned; people or events get in our way; we run out of time, or money, or energy; and we lose our temper, act hastily, and fall short of our goals.
Physical friction happens when objects rub together or push through a fluid. Friction takes motion and turns it into heat, the random vibrations of particles and fields. Energy cascades down from large-scale organized activity into smaller and ever more chaotic jitterings. Precisely the same thing happens in life --- our important plans dissolve into a series of tiny distractions, local events that knock us off course and wear us out.
How to reduce friction? Move slowly but purposefully. Seek paths where resistance is least. Smooth interfaces where clashing may occur. Lubricate interactions by sharing information, so individuals can find a common vision and go forward together. When conflicts block progress, relax, regroup, remember the ultimate goal, and return to work with hope and good cheer.
- Saturday, August 14, 1999 at 20:50:40 (EDT)
Some people like situations. They want to "go with the flow", to "hang loose", to be ready to respond appropriately to new circumstances as they emerge. These people are comfortable with uncertainty.
Plans are great --- but not when taken to excess. Nothing is more deadly than a rigid plan that doesn't take into account new information, as countless military and economic disasters demonstrate. Over-planning is a strait jacket that kills creativity and initiative.
Situations are great --- but not when taken to excess. Nothing is more deadly than drifting without a compass, changing course with every shift of the wind, lost at sea. Without a target, it's impossible to measure success. Over-situationalism is a random walk.
What's needed is balance: flexible planning, a goal-oriented responsiveness to reality. It's the same balance that we must maintain between long-term and short-term, justice and mercy, reason and feeling, experience and innocence.
- Friday, August 13, 1999 at 19:28:53 (EDT)
Plus Ultra is a symbol of transcendence. Closed systems contain their own boundaries; open sets point past themselves, toward a greater universe. Beyond the finite, there is the infinite; beyond the known, the unknown; beyond matter, mind and meaning.
- Thursday, August 12, 1999 at 06:34:35 (EDT)
- Tuesday, August 10, 1999 at 16:20:43 (EDT)
Personal effective writing is also easy and fun to learn. By applying a few straightforward techniques, within hours you can gain 20% or more. Additional experience adds speed and comfort. The approach I suggest here has evolved from my experience, over the past few years, starting with Laurence F. Hawkins' excellent Notescript (Barnes & Noble, 1964; later editions are titled Quickscript).
- Monday, August 09, 1999 at 07:00:36 (EDT)
Prsnl efctv wrtg is also esy / fn to lrn. By aplyg a fw strghtfrwrd tchnqs, wthn hrs yu cn gn 20% or mr. Adtnl exprnc ads spd / cmfrt.That example (not concocted to show off the system!) is easy for anyone to read and has only about two-thirds as many letters to write as did the original. There are some ambiguities, but none serious enough to cause trouble. If you are concerned about possible misinterpretation of a word (e.g., if you fear that "gn" could be read as "gun" or "gin" or "gene" instead of "gain") then just write the word out in full.
After the rules here become second nature, it's time to begin building upon them. You may find some words are exceptionally common in your writing and deserve special abbreviations. (For instance, "data" appears frequently enough for me that I have made up my own "crossed-d" symbol for it.) You may wish to customize your handwriting to make single strokes stand for "th" or other letter combinations. You may choose to define short tokens for whole phrases that recur in a particular set of notes. You may drop silent letters, or keep them.
But always remember the first principle: your shorthand is your own. You control the laws; you're writing for yourself. If any aspect of your system becomes a burden or a distraction, then it's broken and needs to be fixed, or dropped. You're in charge. Write well!
- Monday, August 09, 1999 at 06:53:55 (EDT)
But they're thinking. We all are. We think about small things, moment to moment --- what somebody is saying, where we need to go next, who just came around the corner. We make choices every second, tiny ones, local micro-decisions, like what step to take right now, which rock to put our foot on. Sporadically we look ahead and think about how we can get to larger goals. We're trying to reach the other side of a river, so we seek a chain of stepping stones that are close enough together for us to cross. We want to finish this immediate task so we can move on to something else, get to the next break, and go home for the day.
Rarely, we look farther down the trail and think about important things. What are we doing here? Why choose the goals that we have? What makes them worthwhile? What happens after we get to them, and their successors? What are the trajectories of our lives --- where are we headed? Are we going in the right directions? When we get to our ends --- which could happen at any moment --- will we be able to look back and feel good about our paths?
We could ask those questions, much more often. Why don't we? We are all members of an invisible college, the tenured faculty of an unseen university --- and we spend our time scurrying from lecture hall to library, from laboratory to staff meeting, too busy with trivia to do our real jobs. What are those jobs? To apply for grants, recruit grad students, lobby for more office space, and fight with each other over departmental budgets? Or to ask, and attempt to answer, the big questions about life ... and to share the answers we find?
- Saturday, August 07, 1999 at 08:50:31 (EDT)
More æsthetic systems, in contrast, are built from simple rules but with components that interact in delicate feedback loops. The game of go is a stellar example. So is mathematics, where basic ideas of number and form lead quickly into infinite depths of conjecture, proof, and refutation. The physical universe itself seems to be governed, at its most fundamental level, by subtle yet straightforward laws.
The story of science --- of progress in our understanding of nature --- is one of moving from complex rules to simple ones. Epicycles, wheels revolving within wheels, aren't needed to explain the orbits of the planets; inverse-square gravity does the trick quite nicely, thank you. The colors that things give off when they burn, which is to say the spectral lines emitted by excited atoms, come out of a few quantum-mechanical equations. (Relativistic laws extend these solutions to even greater precision.) All the rich natural phenomena that we see in the world, all the wonders of life, all the joys and sorrows we experience, arise from the interplay of utterly simple rules. There's no need for ugly ad hoc regulations, riddled with exceptions and special cases. Real magic creates complexity from simplicity --- much from little.
- Thursday, August 05, 1999 at 21:48:44 (EDT)
And most singularly of all, we each have just one life. We assume that our experience is typical, the norm, and that others think and choose and act the way we do. Extremely skimpy data on which to base our judgments....
- Wednesday, August 04, 1999 at 06:45:07 (EDT)
Other people abhor mysteries. Their prejudice, upon meeting a new puzzle, is to declare with confidence that it will someday be figured out. They argue, by analogy with the vast progress of science, that there is no ignorabimus ... no "we shall remain ignorant" ... no ultimate limits to our understanding.
A third position that some people adopt is to select distinct mysteries and declare that, in a deep but unspecified way, they must be related to one another. Past experience sometimes justifies these hunches. Electricity and magnetism, apparently separate forces, are now understood to be complementary aspects of a single field.
How should we approach mysteries? That depends on the problem, on the state of our knowledge, and on our goal. Some questions are not important enough to be worth demystifying. Others, after investigation, seem so far beyond our capabilities that we may cheerfully suspend judgment and leave them for future generations to think about. Still other problems are so critical that we must grapple with them. We can take heart in the thought that even if we don't successfully solve the immediate challenge, we are likely to learn enough in the process to make the effort worthwhile. In rare but fortunate circumstances, our instincts may guide us to connect hitherto disjoint domains --- a leap of creative faith that lands on solid ground, from which we can build bridges and move forward.
But the extreme "Mysterian" position, that there are vital issues forever beyond our reach, is in many ways deeply unsatisfying. Yes, the stars at night are awesome to observe. But they become infinitely more awe-inspiring and worthy of wonder when we know that they are suns like ours, billions of years old, shining by the fusion of hydrogen atoms, visible to us through photons of electromagnetic radiation interacting with chemicals in our eyes. How marvelous!
- Monday, August 02, 1999 at 17:36:23 (EDT)
- Sunday, August 01, 1999 at 19:33:37 (EDT)
The realm of the infinite is another universe, one in which our basic instincts fail utterly. Parts are no longer smaller than the whole; sequences become ambiguous. The most elementary operations, such as adding up lists of numbers, give wildly varying results depending on the order in which they are executed.
Truth itself slips away. Statements are no longer verifiable; they begin to talk about themselves, and to generate paradoxical contradictions. A computer with any finite amount of memory, however large, is a well-defined and predictable entity. There's no problem (in principle) determining which programs run forever and which ones halt. Give the computer an infinite amount of memory, a boundless Turing machine tape, and it suddenly escapes comprehension. The same applies to logic.
Infinity is where the ghost of meaning sneaks its camel's nose into the tent of the mechanical universe.
- Saturday, July 31, 1999 at 07:46:52 (EDT)
Are some lists better than others? Can we look at the changes that "civilized" societies have undergone during the past few centuries, and by studying them extrapolate to the future? What sorts of trends represent real advances in the human condition, as opposed to chance, meaningless fluctuations? What does "progress" mean, anyway?
- Thursday, July 29, 1999 at 21:27:24 (EDT)
But it's possible to be different. One can seek solitude, not race to escape it. One can read and think. One can draw, or write code, or just listen to the sounds of the world. One can look at the stars, make music, or do a thousand other things --- slowly, quietly, by oneself.
And being alone isn't so scary any more.
- Wednesday, July 28, 1999 at 22:23:16 (EDT)
- Tuesday, July 27, 1999 at 21:50:07 (EDT)