- Monday, May 24, 1999 at 21:04:37 (EDT)
In better cases, the name to be remembered gets linked to something of long-term value such as learning. Other times, it's a label on something ephemeral, deservedly forgotten. But either way, it's just a name, a string of characters. "What's in a name? That which we call a rose, by any other name would smell as sweet..." Yet people, fearing oblivion, struggle to keep their character string "alive", whether or not any real connection remains to their personal life's story.
Wouldn't it be better to have one's name forgotten, and instead leave the world a better place as a result of what one did? George Eliot wrote, at the end of Middlemarch:
"But the effect of her being on those around her was incalculably diffusive: for the growing good of the world is partly dependent on unhistoric acts; and that things are not so ill with you and me as they might have been, is half owing to the number who lived faithfully a hidden life, and rest in unvisited tombs."
- Friday, May 21, 1999 at 22:09:11 (EDT)
Why? Perhaps we find altering our own behavior hard, or unpleasant much of the time. Perhaps we fantasize that changing others will be a high-leverage activity, with much good produced if we can only persuade many individuals to do as we tell them. (Somehow we rarely dream of placing ourself in the role of merely following instructions.) Perhaps we see ourself as powerless, without influence, so that modifying ourself will make no difference to the world.
In 1974, as a new arrival on campus I was browsing in the Astronomy Department's collection of books when a kindly librarian asked me who I was. "Just a grad student," I replied. She promptly scolded me soundly (and correctly) for using the word Just in that answer! Graduate students are important, like junior employees in a company, like children in a family, and like everyone else. The people who aren't significant are those who stop learning and changing (themselves!).
- Thursday, May 20, 1999 at 21:41:50 (EDT)
But nothing grows forever, and few things grow for long. Growth has side-effects, externalities that affect the neighborhood of a growing system. At some point, the negative spin-offs of growth trigger feedback loops that make the growth slow down and stop, or even reverse. If the feedback is highly nonlinear, growth beyond a certain limit leads to catastrophic collapse.
Growth über alles is the ideology of a carcinoma. In the short term, a cancer cell does splendidly. It takes in nourishment, cranks out copies of itself, and thrives. And for a while, it can say "I'm all right, Jack!" and apparently prosper. But in the longer run, it kills its host and itself.
A "Me first!" philosophy can't last. What's needed instead is understanding, balance, and a recognition of the need for quality rather than mere quantity.
- Wednesday, May 19, 1999 at 21:53:09 (EDT)
It's not just conspicuous consumption, though we do plenty of that. It's throwing food away, at home and at restaurants. It's piling up closets full of clothes that we wear a few times and then get tired of. It's buying books and not reading them, or tossing them out after one pass. It's taking classes in subjects that we don't care about and that aren't any use to us or anybody else. It's vacationing so we can say "been there, done that," and come back otherwise unchanged.
It's hoarding things and not sharing with others.
- Tuesday, May 18, 1999 at 21:48:29 (EDT)
A great hypothesis does more than just tie together disparate phenomena in a startling, beautiful, simple way. A great hypothesis also is vulnerable to disproof from a thousand directions. It makes specific predictions, in detail, without any wriggle-room to permit redefining failure as success.
General relativity, Einstein's theory of gravitation, is a good example. As Misner, Thorne, and Wheeler describe in their textbook Gravitation, relativity stands out from competing theories in that it has no free parameters, no knobs to adjust. It has just one chance to succeed. If it doesn't predict the right orbit for Mercury, the right amount of light-bending near the Sun, the right amount of time-delay for signals going to and from distant spacecraft, then relativity fails. (So far, it hasn't ... though it still could, and some unconfirmed experiments are always around to raise doubts!)
Non-scientists sometimes wonder why scientists seem so conservative. A new theory comes along, gets some coverage in the popular press, and sounds great --- why isn't it taken more seriously in Academia? Or, even more frequently, an individual amateur proposes something radically different in high-energy physics, or medicine, or cosmology --- why do all the "experts" ignore his or her letters?
The answer is multifaceted. To start with, most new theories are simply wrong. They disagree with well-understood evidence from observation and experiment. Many other novel proposals are expressed in too fuzzy a language to make specific predictions; they lack sharpness or specificity, and shouldn't even properly be called "theories".
Those few radical ideas that aren't in disagreement with the body of scientific evidence, and do predict something, usually don't offer anything new and testable. They don't make any different predictions that would expose them to refutation --- or if they do, they have a host of fudge-factors available to explain away disagreements. So they're just not "interesting" to an expert working in the field.
There are exceptions, new theories that come from outside the mainstream ... scribblings by a patent clerk in Zurich, for instance. But it takes time for such ideas to be accepted. They have to land on fertile ground, in circumstances where existing theories aren't entirely satisfactory. Then, scientists do take new ideas seriously --- until disagreeing evidence piles up and still newer ideas come along to push the previous revolutionary theory aside!
- Monday, May 17, 1999 at 21:16:23 (EDT)
But "natural philosophy" has so much nicer a ring to it! "Natural" suggests Nature, the universe of phenomena --- but it also adds in nuances of innateness, normalcy, intrinsic quality (with echoes of R. Crumb's "Mr. Natural" if one grew up with underground comix in the '60s (^_^)!). "Philosophy" in turn means the love of wisdom, almost by definition the highest goal of human life. Putting them together, who wouldn't want to be a Natural Philosopher?
- Monday, May 17, 1999 at 21:13:21 (EDT)
A top-down style moves from general to specific. It begins with the big picture, overarching principles, wide-angle views, and then zooms in to reveal increasing levels of fine detail. When something is clearly feasible but demands a coordinated approach, with harmonizing contributions from multiple sources, top-down methods make a lot of sense.
A bottom-up style, on the other hand, goes from atomic scales toward the macroscopic world. It begins with fundamentals, first principles, infinitesimal slivers, and then puts those building blocks together to create the whole. When something depends utterly on getting every detail right, as in proving a mathematical theorem, and when the pieces are relatively independent modules which can be clicked together in a straightforward fashion, then bottom-up methods make a lot of sense.
Flexibility in applying both top-down and bottom-up approaches can offer extraordinary power. Consider the problem of optimizing a computer program. (It's analogous to doing just about anything in life more efficiently!) A bottom-up attack focuses on the key subroutines --- chokepoints on which the processor is spending most of its time. Those are high-leverage areas where software tweaks can pay off directly in big performance gains. A top-down view, in turn, explores the gestalt structure of the program. From that kind of perspective, often it's possible to spot opportunities for radical reorganizations that can save orders of magnitude of effort. Going back and forth, moving smoothly between general and specific, gives both bottom-up and top-down methods the chance to work together, each contributing what it does best.
The short movie Powers of Ten (by Charles and Ray Eames) offers a wonderful visualization of the universe, from sub-nuclear to galactic-supercluster scales. It's an example of moving among levels in a nonalgorithmic domain. Another example is captured in a proverb of John Archibald Wheeler, describing gravitation: "Matter tells space how to curve. Space tells matter how to move." The levels work back and forth, in mutual feedback loops, each guiding the other.
- Sunday, May 16, 1999 at 18:27:24 (EDT)
Who doesn't, just about every day, find and use a chance to blame another person for problems great and small? And what collective task, if it fails, doesn't provoke a flurry of "blamestorming" as groups work feverishly to figure out why punishment belongs elsewhere for the shortcoming?
But most of the time, once passions have cooled or time has passed, we see that "...the fault, dear Brutus, lies not in our stars but in ourselves...." It's an interesting and potentially high-payoff experiment to avoid blaming anyone else. Instead, one can try to change the default to immediately taking responsibility.
Arnold Bennett described it nicely: Pretend that you alone have free will, and everyone else is utterly predestined to do what they do. That sounds unfair --- but the result in daily life is an amazing liberation, like cutting a Gordian knot. Suddenly other people are no longer malign forces bent on blocking progress; they're more like natural phenomena, rocks, trees, winds. There's no need to get angry or frustrated with them. It's not the rock's fault for tripping me; I overlooked it. If someone causes me trouble, perhaps they were brought up badly, or they're physically ill, or they're basing their actions on incorrect information. I can offer them helpful advice, but I cannot make them take it.
In contrast to acts by others, if I choose unwisely and create (or contribute to) a bad situation, I have done wrong. I could have done otherwise. The fault is mine. I can and will do better.
Marcus Aurelius in his personal notebooks labeled "To Himself" (also known as Meditations) returns to this point again and again. Taking responsibility, completely and unconditionally, is a central tenet of Stoic philosophy. No one has ever succeeded in doing it, or even approaching it. But what a goal to strive for, every day!
- Saturday, May 15, 1999 at 20:17:44 (EDT)
Rational numbers are "dense" because no matter how tiny a neighborhood you pick around any number, there are still an infinite number of fractions that lie in that neighborhood. Simultaneously, the rationals are "nowhere dense" because however tiny a zone you pick around a rational number, there are infinitely many non-rational numbers (irrationals, numbers not expressible as fractions) in that zone too.
An important part of the game of mathematics involves thinking up pathological or perverse examples and seeing where they lead. For instance, take the decimal numbers that don't have any odd digits in their representation (please!). Or consider the set of numbers left when you start with the interval between 0 and 1 and cut out the middle third --- and then cut the middle third out from each of the pieces that remain, and on, and on ad infinitum. Or how about the function sin(1/x) and how it behaves near x=0, where it wiggles faster and faster? Or ponder x*sin(1/x) near x=0, where the wiggles are getting squeezed down by the overall multiplier "x"?
The magic of these weird and wacky cases is that they stress our everyday understanding, reveal gaps in our knowledge, and break down our prejudices. That's not a bad goal for the nonmathematical parts of life either, eh?
- Wednesday, May 12, 1999 at 21:10:14 (EDT)
Transients, by definition, will pass --- unless the input tweaks that provoked the transients are themselves repeatedly changed. If we see a short-term transient signal and respond aggressively to it, we can easily get into a vicious cycle of reacting to the reaction to our own actions --- and so cause instability where we were trying to cure it. This happens often, particularly when significant time delays are involved in a system.
Flying an airplane, when we see the ground approaching our natural tendency is to pull back on the stick, increasing the angle of attack of the wings. For a few seconds, that gives us a transient altitude gain. Then, the plane slows and resumes its descent. We pull back more and more, until we stall and crash. What we really should have done was the opposite: get the stick forward to gain airspeed while feeding more gas to the engine. This counterintuitive feedback loop --- with the throttle controlling altitude and the stick controlling speed, once transients have passed --- is beautifully described in Wolfgang Langewiesche's classic aviation book Stick and Rudder.
Similarly, in medicine many patients get sicker the more they are treated; they are prescribed drugs to counteract the side effects of earlier drugs they have been given, and then more drugs to remedy the problems caused by those drugs, in an accelerating cascade. In government, politicians get the blame (or credit) for the long-term consequences of their predecessors' actions, and in turn pursue short-term policies which result in worsening conditions when they have left office. In business, a vigorous new CEO comes in, "cleans house", declares victory, and then moves on before the corporate wreckage comes tumbling down.
How can we see through the veil of transient behavior to the ultimate consequences of our choices? One way is to develop mental models of systems, with explicit recognition of feedback loops and delays between cause and effect. Such "systems thinking" forms the core of Peter Senge's highly readable book The Fifth Discipline. Working with systems models can help us avoid foolish and self-defeating "decisiveness" and instead develop mature, productive decision-making skills.
- Tuesday, May 11, 1999 at 06:00:49 (EDT)
But more generally, the failure to put ourselves into others' shoes is a special case of a whole family of fallacies based on what astronomers call "selection effects". We do not observe a random sample of the universe; bright stars can be seen from farther away than dim ones. If we simplemindedly count stars, we may come to think that there is a growing surplus of bright stars the farther off we look. Apparently we are in a neighborhood of unusually faint objects compared to the rest of the universe. (The same holds for galaxies on cosmic scales.)
How obvious a fallacy, we may say --- but how often do we ourselves fall prey to this in our daily lives? We think that the people and events we read about in the newspaper are typical of society --- whereas they are in fact selected for their newsworthiness. So they are anything but representative! We commonly have an exaggerated fear of big, dramatic kinds of accidents --- airplane crashes, mass murders, explosions, etc. We hear about them because they're "news". We overestimate their probability far beyond their actual rate of occurrence; we conversely underestimate the chance of much more common but more isolated events such as household accidents, death or illness from smoking or overeating, and the like.
We remember extraordinary happenings, however rare, and tend to give them more weight than they deserve. A conscious appreciation of selection effects can help us avoid such fallacious thinking.
- Tuesday, May 11, 1999 at 05:56:55 (EDT)
But on the other hand, we share a vast amount of common experience with one another as we grow from infancy, learn language(s), perceive nature, interact with our fellow creatures, and develop mental models of how diverse people act and react. Different races, different sexes, different cultures all still have in common a huge base of mutually observed and experienced phenomena.
In the context of literature, Douglas Hofstadter writes (Le Ton Beau de Marot: In Praise of the Music of Language, 1998, p. 250):
"All readings are partial and approximate, and we must content ourselves with whatever joy and insight we can derive from deep ideas rendered clearly in beautiful language, knowing that our derivative response and the author's original version will never be perfectly aligned."The same holds throughout life: we can share ideas and emotions with one another, quite effectively, while acknowledging that absolute agreement between internal states is always out of reach. The moments when alignment is best, as in "... the marriage of true minds...", perhaps correspond to the times when we feel ourselves in the presence of love in its purest form.
- Sunday, May 09, 1999 at 20:36:34 (EDT)
But the taunt "Anything you can do, I can do meta!" has a lot more going for it than that. "Meta" in this context means "beyond" --- something that transcends the common level of things.
All real progress comes from transcending the ordinary, from rising above the usual state of affairs and thereby discovering new, higher-level structures. On an elevated plane, one can see how myriad special cases are unified into a single powerful pattern. One can capture complexity and control it. One can, with cleverness and hard work, self-transcend --- and come to understand a multi-level system by using it to talk about itself. That's the magic secret of Gödel's Theorem, and of consciousness and intelligence.
- Saturday, May 08, 1999 at 17:36:54 (EDT)
Why do we believe that the space program created Velcro (or Teflon, or Tang)? Why do we fall for tales of how A's discovery of B led C to find D which resulted in E, as if this causal chain had any true explanatory power? Most probably, because we haven't thought about all the other paths which could have given us those inventions, perhaps sooner and better. Such alternatives are more than invisible. They never happened; it takes a strong act of creative imagination to visualize them.
Henry Hazlitt in his book Economics in One Lesson retells the parable "That Which is Seen and That Which is Not Seen" from an 18th Century essay by the French writer Frederic Bastiat. The key to good economic thinking, Hazlitt suggests, consists in analyzing not just the immediate visible effects of human actions, but also the long-range subtle cascade of consequences. The same applies to history.
History is not a chain that breaks when a single link is cut. History is a web, a supremely resilient fabric of events, where multitudes of paths connect every pair of points. To escape from the simplistic celebrity-history trap, we can think about those paths, about alternative might-have-been universes, and about the contributions of unseen, "unhistoric", forgotten individuals. Such an appreciation of the richness of history also reveals the value of our own personal acts, great and small, as we help each other learn and grow.
- Saturday, May 08, 1999 at 10:18:45 (EDT)
We few, we happy few, we band of brothers,
For he that sheds his blood with me today shall be my brother;
Be he ne'er so vile, this day will gentle his condition....
Traffic engineers can gentle the flow of cars on a busy street by adding curves, removing chokepoints, and tricking drivers via optical illusions into moderating their pace. We have all experienced the opposite phenomenon to gentling: the disruptive wrench-in-the-works person who adds to stress, who exacerbates a situation.
Cardinal Newman in his Definition of a Gentleman (1852) discusses how a graceful human may remove barriers to the free action of others, how such a person may give aid invisibly where needed, and how a "gentleman" may respect and honor institutions (such as religions) even while not sharing in them. That spirit of gentleness, of actively gentling one's environment, is worth pondering.
When trapped on a highway at rush hour, try an experiment: instead of mindlessly tracking the motions of the car ahead, deliberately gentle its accelerations. Speed up a bit more slowly, letting the gap in front grow like money in a bank. Decelerate more slowly, applying the brakes delicately. One's own trip time may be unchanged --- but consider what happens to the cars behind. They see a smoother traffic pattern, with less stop-and-go and more continuous motion. If enough other drivers follow suit, the gentling effect propagates --- and a traffic jam changes phase to become a fast, efficient flow again.
Now, ask the important questions:
- Friday, May 07, 1999 at 22:15:34 (EDT)
- Thursday, May 06, 1999 at 21:11:51 (EDT)
One character says, "Maybe you're just looking for simple answers. Maybe there are no simple answers. Problems require thought and dedication."
The other character replies, "But there are simple answers. There are just no good answers. --- Although that one was pretty good."
We constantly seek "simple answers". We can't help it. Simple answers are triumphs of thought --- brilliant insights that unify whole realms of the cosmos. Newton's Laws are a simple answer to the problem of force and mass and motion. Maxwell's Equations are a simple answer to the problem of electricity and magnetism.
But Newton's Laws fail when things move fast; Maxwell's Equations break when things are tiny. And when complex systems are involved --- like economies, like ecologies, like minds --- simple answers don't even come close.
Our challenge is to recognize both the strengths and weaknesses of simple answers. Then we can simplify when appropriate, and contrariwise demand complexity when it is needed. We can distinguish between cases in which the future is unknown, and cases in which it is unknowable. We can applaud a brilliant analysis of the key factors in a situation, yet reject attempts to prescribe quack nostrums to cure complicated interlocking challenges.
We can, in short, learn to differentiate between the simple and the simplistic.
- Tuesday, May 04, 1999 at 21:54:15 (EDT)
A good answer for the "bit rate" of cognition is of the order of speech or internal narration rates, as suggested by Daniel Dennett's model of mind as the "narrative center of gravity" (in Consciousness Explained). That's arguably how we really think. A rough but reasonable upper-bound value for that is ~1 kb/s --- about 100 bytes per second. And that may be rather generous; 1% to 10% of that could be more likely, most of the time. Multiply that by a few decades of active waking life, roughly a billion seconds, and the output is ~100 GB, a tenth of a Terabyte.
That's big, but not impossibly huge to store inside a cranium. A CD-ROM holds several hundred MB, so our estimate comes to a thousand or so CDs. But note that the data of life may compress rather well --- most memories are of sequences of events, reasonably continuous and predictable --- so nobody is suggesting that a lifetime fits onto a bookshelf of music albums!
But it is more than a little humbling to think that all the events of a life, or at least all the events that one can possibly remember and think about, are expressible in under a trillion bits....
- Monday, May 03, 1999 at 22:14:38 (EDT)
Interlocking pairs of opposites, or conjugate quantities, seem to be singularly fruitful sources of creative thought. Some candidate pairs to ponder are:
mercy {-} justice
solitude {-} friendship
independence {-} collaboration
electricity {-} magnetism
innovation {-} recycling
position {-} momentum
limited {-} infinite
depth {-} breadth
time {-} space
yin {-} yang
0 {-} 1
Marion Tinsley, the late world checkers champion, reportedly noted "Chess is like looking over a vast, open plain; checkers is like peering down a deep, dark well." Numerous other aphorisms arise from the juxtaposition of duals. Einstein's advice, "Make things as simple as possible, but no simpler.", is an example. Meditation on paired concepts may be worthwhile. (Then again, maybe not!)
- Monday, May 03, 1999 at 22:11:57 (EDT)
The ideas of modern physics help us see that our daily lives only sample an infinitesimal corner of the vast universe, and that our prejudices --- built from experience with largish objects moving at slow speeds in weak gravitational fields --- are not good indications of what is possible. Thinking about how little we know of the physical world, perhaps, can lead us also to think about how limited our experience is with kinds of minds, and relationships among minds. How little do we really know about life?
- Sunday, May 02, 1999 at 21:43:45 (EDT)
The book Structure and Interpretation of Computer Programs by Abelson and Sussman explores this dichotomy in its discussion of the "eval" and "apply" functions. To do anything, the computer must evaluate the quantities that are to be worked with, and then apply the chosen transformations to the resulting data.
In the same way, when we think, we need to take hold of our problems, evaluate the facts that are at hand in our particular circumstances, and then apply the appropriate methods to what we know, to move toward a solution. There are a host of methods that have proved to work on problems in the past. If we build up our mental arsenal of methods, we will have a better chance of having the right tool close at hand to solve new problems as they occur.
- Saturday, May 01, 1999 at 07:27:50 (EDT)
Human lives begin as diamonds do,
Dull and rough like common pebbles.
Some are large, blue-white, and perfect underneath;
Most are small, off-colored, flawed.
But all are precious, latent with a dazzling beauty.
What is my life?
It's taking my rough pebble, large or small,
And working on it, year by year,
Cleaving off this flaw and that,
Polishing facets, one by one,
Until, naked before the world,
My true self stands revealed,
Calm but proud,
And adds its small but radiant brilliance
To the smoldering fire of Man's emergence
From his savage past.
Richard L. Ropiquet's poem was published in The Freeman, a journal of libertarian ideas published by Leonard Read's Foundation for Economic Education ("FEE"). The above rendering is from memory and may differ in minor details from the original; some of the scansion is flawed (and the language in the final lines is arguably marred by sexism), but the overall spirit of hope and love shines through.
- Friday, April 30, 1999 at 19:57:54 (EDT)
Leonard Read also felt that "education" (in its usual sense of teaching, training, schooling, or rearing) was not the right word to use for spreading important ideas. He suggested instead the term "eduction" --- meaning drawing forth, revealing what is hidden, leading out from the darkness. Read's immediate interest was free markets, private property, limited government, and libertarian (or "classical liberal") economics.
But Leonard Read's gentle philosophy applies far more widely, to every critical concept in life and mind. If a thought is truly good, it cannot be imposed on others by force or fraud without losing whatever goodness it may have had. Rather, it must be offered, diffidently, to those who seek it and are prepared to grasp it. The only real way to share such ideas is by example.
- Friday, April 30, 1999 at 19:54:09 (EDT)
From Chapter VII of How to Live on Twenty-Four Hours a Day (1907)
"I do not care what you concentrate on, so long as you concentrate. It is the mere disciplining of the thinking machine that counts. But still, you may as well kill two birds with one stone, and concentrate on something useful. I suggest --- it is only a suggestion --- a little chapter of Marcus Aurelius or Epictetus.
"Do not, I beg, shy at their names. For myself, I know nothing more 'actual,' more bursting with plain common-sense, applicable to the daily life of plain persons like you and me (who hate airs, pose, and nonsense) than Marcus Aurelius or Epictetus. Read a chapter --- and so short they are, the chapters! --- in the evening and concentrate on it the next morning. You will see.
"Yes, my friend, it is useless for you to try to disguise the fact. I can hear your brain like a telephone at my ear. You are saying to yourself: 'This fellow was doing pretty well up to his seventh chapter. He had begun to interest me faintly. But what he says about thinking in trains, and concentration, and so on, is not for me. It may be well enough for some folks, but it isn't in my line.'
"It is for you, I passionately repeat; it is for you. Indeed, you are the very man I am aiming at.
"Throw away the suggestion, and you throw away the most precious suggestion that was ever offered to you. It is not my suggestion. It is the suggestion of the most sensible, practical, hard-headed men that have ever walked the earth. I only give it to you at second-hand. Try it. Get your mind in hand. And see how the process cures half the evils of life --- especially worry, that miserable, avoidable, shameful disease --- worry!"
From Chapter XIII of The Human Machine (1908)
"I suppose there are some thousands of authors who have written with more or less sincerity on the management of the human machine. But the two which, for me, stand out easily above all the rest are Marcus Aurelius Antoninus and Epictetus. Not much has been discovered since their time. 'The perfecting of life is a power residing in the soul,' wrote Marcus Aurelius in the ninth book of 'To Himself,' over seventeen hundred years ago. Marcus Aurelius is assuredly regarded as the greatest of writers in the human machine school, and not to read him daily is considered by many to be a bad habit. As a confession his work stands alone. But as a practical 'Bradshaw' of existence, I would put the discourses of Epictetus before M. Aurelius. Epictetus is grosser; he will call you a blockhead as soon as look at you; he is witty, he is even humorous, and he never wanders far away from the incidents of daily life. He is brimming over with actuality for readers of the year 1908. He was a freed slave. M. Aurelius was an Emperor, and he had the morbidity from which all emperors must suffer. A finer soul than Epictetus, he is not, in my view, so useful a companion. Not all of us can breathe freely in his atmosphere. Nevertheless, he is of course to be read, and re-read continually. When you have gone through Epictetus --- a single page or paragraph per day, well masticated and digested, suffices --- you can go through M. Aurelius, and then you can return to Epictetus, and so on, morning by morning, or night by night, till your life's end."
And finally, an entry from Arnold Bennett's personal journal, dated Friday April 3, 1908
"Every morning just now I say to myself: Today, not tomorrow, is the day you have to live, to be happy in. Just as complete materials for being happy today as you ever will have. Live as though this day your last of joy. 'How obvious, if thought about' --- yet it is just what we forget. Sheer M. Aurelius, of course."
- Thursday, April 29, 1999 at 18:01:45 (EDT)
- Wednesday, April 28, 1999 at 06:09:48 (EDT)
Paradoxically, one thing that we can be certain of is the need for doubt. Among the few obvious truths of life (to all but the megalomaniac) is the incompleteness of our understanding. The more we learn, the more we realize our ignorance, and the more we see still remains to be learned.
Even the subjects which seem to promise us the most rock-solid and incontrovertible knowledge --- mathematics and physics --- present gaping chasms of uncertainty and incompleteness. We stand by the abyss of the unknown. The best we can do is recognize the limits of our knowledge, the bounds on what we can prove, the unavoidable errors in our measurements and predictions. We maintain a precarious balance on the edge of oblivion only through profound doubt. We do not know all. We cannot know all. But we can know that.
- Tuesday, April 27, 1999 at 16:56:39 (EDT)
Many religious theories (of reincarnation or rebirth or other forms of spiritual continuation) attempt to respond to our fear of death, but few religions seem to worry about or struggle with the symmetrical side of pre-existence. It's not a question that we tend to fret about. Perhaps we should. Perhaps thinking about the universe before our personally patterned piece came into being can help counterbalance the naive, natural tendency to flinch from the thought of our demise.
- Tuesday, April 27, 1999 at 16:55:03 (EDT)
How can a company, or a family, or an individual, stay fresh? Only through investing in learning. Probably about 10% of the time budget, at a minimum, needs to be devoted to learning; that's only ~4 hours of a 40-hour working week. There are many possible routes: taking classes, reading books, forming small study/discussion groups. A weekly "philosophy breakfast" club is a start, as are sack lunch seminars on off-the-wall topics. Escape the box!
- Tuesday, April 27, 1999 at 16:53:15 (EDT)
It's tough to take a long-term view and work to provide tools for better thinking. Tough, but essential if one hopes to give honest advice. Sometimes there's only room to present a single "if", as in "... if X continues, then Y ...". But then at least the audience can begin to look at cause-effect relationships, systemic factors, and the root sources of uncertainty.
- Tuesday, April 27, 1999 at 16:51:06 (EDT)
But though he vanished without a trace during a solo sailing expedition around the world, and though he left behind no major body of work, Jon Mathews still has a monument: the enthusiasm and creative fire that he gave his students, and the patterns of thought that he showed them. That invisible influence, incredibly diffuse, is his gift to us.
Thank you, Jon.
- Sunday, April 25, 1999 at 20:42:19 (EDT)
- Friday, April 23, 1999 at 06:40:07 (EDT)
Bluffing works for a while, sometimes, especially when used in an environment of ignorance or transience. Maybe a few can make a career of it, moving along to other jobs before the facade is penetrated. But what's the point? Have they actually accomplished anything by this deception? How much nicer to do good, even without recognition or credit, and leave the world a better place.
- Thursday, April 22, 1999 at 08:02:28 (EDT)
- Tuesday, April 20, 1999 at 22:00:42 (EDT)
There is truth in both the crystal and the ball of mud. Real life is messy and complex, but reveals a naked symmetric beauty in moments of profoundest insight.
- Monday, April 19, 1999 at 21:03:54 (EDT)
"... How much better is the man who does any thing that is innocent, than he who does nothing. Besides, I love anecdotes. I fancy mankind may come, in time, to write all aphoristically, except in narrative; grow weary of preparation, and connection, and illustration, and all those arts by which a big book is made. --- If a man is to wait till he weaves anecdotes into a system, we may be long in getting them, and get but few, in comparison of what we might get."
- Monday, April 19, 1999 at 20:59:27 (EDT)
- Sunday, April 18, 1999 at 15:55:57 (EDT)
- Friday, April 16, 1999 at 15:51:09 (EDT)
Other important books:
- Friday, April 16, 1999 at 06:27:39 (EDT)
And when one is done, even if hardly anybody elsecomes to look, the happy feeling of having done things "right" remains.
- Thursday, April 15, 1999 at 14:08:37 (EDT)
T his method of bypasses appears constantly in problem solving. To reorder a scrambled Rubik's cube is tricky, because the moves that we can make all do complicated things and tend to mess up the parts of the cube that we have already gotten into place. But an approach based on the bypass method can help. We make a transformation that scrambles the cube but leaves one slice of it mostly unchanged - call this "M". We then do a simple change to that slice, and then undo (invert) the original transformation (performing 1/M). We can thereby control the complexity of the whole operation so that it does something manageable - such as swap two cubelets, or flip a pair of faces of edge cubelets, or twist two corners in opposite directions.
Similarly, bypasses can apply to many ordinary problems. We have to work with a difficult person to get a job done - perhaps we can instead get an intermediary to translate between us, someone who is comfortable on both sides; or perhaps we can divide the task so that each of us only has to do a minimal amount together.
- Wednesday, April 14, 1999 at 06:22:39 (EDT)
- Sunday, April 11, 1999 at 20:20:35 (EDT)
But even one who believes in thorough-going materialism, in rigid cause and effect at the particle physics level, can hold that we do have free will --- that treating our own selves and the selves of others as responding to choices made without total restraint is a reasonable metaphor in real life. And perhaps, via strange loops between levels of meaning (as Douglas Hofstadter alludes to in his preface to the 1999 edition of Gödel, Escher, Bach) mental patterns can break "free" of microscopic causality? Worth pondering....
- Sunday, April 11, 1999 at 14:28:56 (EDT)
Grace, of course, also means forgiveness --- a gift from another which can unexpectedly bless us when we need it most. We can live gracefully, moment to moment, by applying what we know to be highest and best to the current situation --- even when pressures of expediency and frustration tempt us to take short cuts.
- Saturday, April 10, 1999 at 11:30:12 (EDT)
In the preface to their textbook Simply Scheme, Brian Harvey and Matthew Wright of Berkeley begin:
There are two schools of thought about teaching computer science. We might caricature the two views this way:Thinking tools follow the second, radical, path. Their goal is not to divide problems into tiny bite-sized morsels, but rather to empower the individual analysts so that they can attack the huge, complex enigmas that we face today. Moreover, thinking tools aim to enable analysts to work together better, bridging gaps in space and time, so that the organization as a whole can learn and grow.
- The conservative view: Computer programs have become too large and complex to encompass in a human mind. Therefore, the job of computer science education is to teach people how to discipline their work in such a way that 500 mediocre programmers can join together and produce a program that correctly meets its specification.
- The radical view: Computer programs have become too large and complex to encompass in a human mind. Therefore, the job of computer science education is to teach people how to expand their minds so that the programs can fit, by learning to think in a vocabulary of larger, more powerful, more flexible ideas than the obvious ones. Each unit of programming thought must have a big payoff in the capabilities of the program.
- Friday, April 09, 1999 at 22:29:55 (EDT)
Many years ago at Cornell, Richard Feynman taught a course called Mathematical Methods of Physics. Notes from those lectures grew into a book of the same title by Jon Mathews and Robert Walker at Caltech. That book is a starter toolkit for graduate students and journeyman physicists. It covers differential and integral equations, probability and statistics, matrix and tensor algebra, series expansions, and a host of other topics. The subject is mathematics, but very much aimed at real day-to-day problems, without a lot of arcane derivations or unnecessary footnotes. As Mathews once said when teaching from the book, "My goal is to show you a lot of tricks, so that when we're done you'll be a tricky person!" Those "tricks" were really a repertoire of thinking tools for physicists.
In a similar fashion, Z. A. Melzak of the University of British Columbia has written several splendid books that explore the connections and interactions among various techniques from more pure mathematics, but with a concrete focus on potential applications to engineering and science. Melzak also has a more general and philosophical book, Bypasses, concentrating on ideas that radiate out from the concept of similarity transformations. In practical terms, one doesn't have to crash through a brick wall; one can tunnel down, move forward, and then come back up in order to get to the other side. The same concept applies to solving Rubik's Cube, or coordinate changes, or quantum mechanical measurements. If a problem is too hard when viewed from one aspect, think about transforming it into a universe where it becomes simple, solving it there, and then inverting the original transformation to get back to the real world. Melzak's musings about the implications of such "bypasses" may point the direction to new thinking tools.
Polya long ago wrote How To Solve It, a road map of tools for thinking through mathematical problems. Tufte of Yale is famous for The Visual Display of Quantitative Information and its sequels, which collect and analyze a multitude of ways to think with data, all designed to make the patterns in those data emerge with stunning clarity. Abelson and Sussman wrote the freshman MIT computer science text Structure and Interpretation of Computer Programs. Their book aims to provide students with an arsenal of tools for thinking about managing complexity, creating interfaces, isolating unknowns, and designing computational systems.
Moving from books to the computer software world, a number of candidate thinking environments have emerged within the past few decades. Among the more noteworthy are:
Numerous other candidate thinking tools exist. Jeff Conklin of GDSS (formerly at MCC) has long worked on argumentation theory and has developed tools to structure and facilitate group decisionmaking (using computers, whiteboards, paper, or other media). Simulation and modeling can provide great insight, especially when used to generate alternative futures scenarios to explore and provoke thought. Game theory may often feature prominently in studies of situations where actors have competing goals and must resolve their conflicts. Computer tools for the analysis of linkages among discrete events can reveal patterns of large-scale order which are invisible to the unaided observer, as can statistical tools that work to cluster and correlate data sets.
On a broader conceptual level, thinking tools are needed to capture the process of cognition --- the Why of a conclusion, and the How it was reached, not just the What of a proposed "answer" --- so that researchers can collaborate more effectively on complex tasks and can create a "corporate memory" for their successors to build upon. Thinking tools work on the boundary between knowledge and wisdom; they aim to help reveal meaning in mountains of information.
- Thursday, April 08, 1999 at 21:46:30 (EDT)
Individual thinking tools, however, are of limited value if each lives in its own isolated universe. The most productive and significant tools must exist together in thinking environments --- societies within which many tools can work harmoniously, sharing information and multiplying each other's effectiveness. Another way to describe the ideal situation is that we want to have thinking toolkits --- portfolios of techniques and systems that can be applied as needed during our work.
What are the common characteristics of the best thinking tools and environments? Doubtless there are many; some strong possibilities include:
A winning environment for thinking tools will tend to be:
- Wednesday, April 07, 1999 at 06:12:19 (EDT)
A thinking tool need not be computer-based. Sir Karl Popper quotes Albert Einstein, "My pencil is smarter than I am!". Popper suggests this means that, with a pencil as a tool, one can be more than twice as effective in grappling with tough problems. But perhaps the pencil is only an interface to deeper thinking tools: language (both "natural" and mathematical), visual media for arraying and displaying information in space, and a persistent storage to bind concepts over time. Encouraging the better understanding and use of such fundamental tools falls within the scope of the thinking tools theme.
- Tuesday, April 06, 1999 at 17:59:02 (EDT)
What is the purpose of thought? To ask that is to ask for the purpose of life. Perhaps the answer is the question itself? The purpose of thought may be to ask --- and to learn how to pose better and more appropriate questions --- to help others ask their questions and to solve their problems --- to share ideas, to strive against barriers --- and to "be excellent to each other".
These notes are written with extreme diffidence. One could not share ideas without a certain minimum amount of hubris or without some other driving force to keep one scribbling away at the pages, tapping along on the keys, or whatever. The very selection effect associated with writing (no one who is illiterate can do it; no one who is not wealthy enough in time and resources can either) means that books, notes, and the like will tend to be crafted by those who have a special drive, and perhaps also a special axe to grind. The big risk is that the author wants to impose a world view, a set of ideas, a way of thinking, upon the reader. This asymmetry should be avoided --- hence, the hesitancy associated with these notes. "I" do not wish to impose anything upon "you". Rather, the theme of this work is conversation, mutual growth, and exploration. "We" are learning together.
In fact, we are always talking to ourselves in the adventure of the mind. The words here have evolved from countless conversations over the past several decades of life --- personal conversations, and one-way "conversations" that took place while reading books and thinking about what they meant. These words are a product of millennia of human cultural evolution, as individuals coined terms and patterns of usage to convey their thoughts to each other and to permit them to express internal mental states and relationships.
A large-scale goal of these notes is to provide the reader (and the author!) with a broad and deep arsenal of tools, based on the concepts of physics and the universe as we now understand it. Many of the facts and methods of the sciences --- especially those of modern physics --- help to pull one out of the boxes that ordinary existence tends to confine one inside.
What's worth remembering? Most of our conversations are best forgotten --- but there are a few that deserve to be kept in mind. How can we recognize them and increase their rate of occurrence? That is one topic that these notes will wrestle with.
Imagine the cacophony if, every time someone said "Good Morning" to us, all the thousands of previous instances of "Good Morning" came crowding into our mind?
But on the other hand, imagine the poverty of life if some words, sounds, tastes, smells, etc. did not have the power to strike resonant chords in our thinking. When someone says "Summer's Lease", we may get echoes of the rhythms of Shakespeare's sonnets; when we hear a piece of music, we remember how we felt when we heard it long ago with a loved one; when we taste a cookie we think of a madeline, and Proust, and perhaps then Ludwig Bemelmans and his children's books --- a chain of associations.
Such memories add great richness, both to our lives and to the creators of stories and other works of art by permitting great compactness of representation for complex ideas. This extensibility of language into the personal, but shared, allusive domain is what gives metaphors their power and makes them worthy of study.
These notes are not intended for people doing easy jobs in clean, ideal environments; rather, they are for people under pressure attempting to do impossible jobs in the worst of circumstances. The emphasis here is on hard-headed, intensely practical thinking.
- Monday, April 05, 1999 at 13:14:26 (EDT)
- Saturday, June 03, 2000 at 11:02:13 (EDT)