EDGE 5 — February 10, 1997


A Talk with Reuben Hersh

What is mathematics? It's neither physical nor mental, it's social. It's part of culture, it's part of history. It's like law, like religion, like money, like all those other things which are very real, but only as part of collective human consciousness. That's what math is.


Charles Simonyi and Stanislas Dehaene on Reuben Hersh

Steven Pinker responds on Nicholas Humphrey & Richard Potts

Philip Leggiere on Nathan Myhrvold

(6,608 words)

John Brockman, Editor and Publisher | Kip Parent, Webmaster


A Talk With Reuben Hersh

For mathematician Reuben Hersh, mathematics has existence or reality only as part of human culture. Despite its seeming timelessness and infallibility, it is a social-cultural-historic phenomenon. He takes the long view. He thinks a lot about the ancient problems. What are numbers? What are triangles, squares and circles? What are infinite sets? What is the fourth dimension? What is the meaning and nature of mathematics?

In so doing he explains and criticizes current and past theories of the nature of mathematics. His main purpose is to confront philosophical problems: In what sense do mathematical objects exist? How can we have knowledge of them? Why do mathematicians think mathematical entities exist forever, independent of human action and knowledge? -


REUBEN HERSH is professor emeritus at the University of New Mexico, Albuquerque. He is the recipient (with Martin Davis) of the Chauvenet Prize and (with Edgar Lorch) the Ford Prize. Hersh is the author (with Philip J. Davis) of The Mathematical Experience, winner of the National Book Award in 1983. His new book, What is Mathematics, Really?, is forthcoming (Oxford).


JB: Reuben, got an interesting question?

HERSH: What is a number? Like, what is two? Or even three? This is sort of a kindergarten question, and of course a kindergarten kid would answer like this: (raising three fingers). Or two (raising two fingers). That's a good answer and a bad answer.

It's good enough for most purposes, actually. But if you get way beyond kindergarten, far enough to risk asking really deep questions, it becomes: what kind of a thing is a number?

Now, when you ask "What kind of a thing is a number?" you can think of two basic answers- either it's out there some place, like a rock or a ghost; or it's inside, a thought in somebody's mind. Philosophers have defended one or the other of those two answers. It's really pathetic, because anybody who pays any attention can see right away that they're both completely wrong.

A number isn't a thing out there; there isn't any place that it is, or any thing that it is. Neither is it just a thought, because after all, two and two is four, whether you know it or not.

Then you realize that the question is not so easy, so trivial as it sounds at first. One of the great philosophers of mathematics, Gottlob Frege, made quite an issue of the fact that mathematicians didn't know the meaning of One. What is One? Nobody could answer coherently. Of course Frege answered, but his answer was no better, or even worse, than the previous ones. And so it has continued to this very day, strange and incredible as it is. We know all about so much mathematics, but we don't know what it really is.

Of course when I say, "What is a number?" it applies just as well to a triangle, or a circle, or a differentiable function, or a self-adjoint operator. You know a lot about it, but what is it? What kind of a thing is it? Anyhow, that's my question. A long answer to your short question.

JB: And what's the answer to your question?

HERSH: Oh, you want the answer so quick? You have to work for the answer! I'll approach the answer by gradual degrees.

When you say that a mathematical thing, object, entity, is either completely external, independent of human thought or action, or else internal, a thought in your mind--you're not just saying something about numbers, but about existence--that there are only two kinds of existence. Everything is either internal or external. And given that choice, that polarity or dichotomy, numbers don't fit - that's why it's a puzzle. The question is made difficult by a false presupposition, that there are only two kinds of things around.

But if you pretend you're not being philosophical, just being real, and ask what there is around, well for instance there's the traffic ticket you have to pay, there's the news on the TV, there's a wedding you have to go to, there's a bill you have to pay--none of these things are just thoughts in your mind, and none of them is external to human thought or activity. They are a different kind of reality, That's the trouble. This kind of reality has been excluded from metaphysics and ontology, even though it's well-known--the sciences of anthropology and sociology deal with it. But when you become philosophical, somehow this third answer is overlooked or rejected.

Now that I've set it up for you, you know what the answer is. Mathematics is neither physical nor mental, it's social. It's part of culture, it's part of history, it's like law, like religion, like money, like all those very real things which are real only as part of collective human consciousness. Being part of society and culture, it's both internal and external. Internal to society and culture as a whole, external to the individual, who has to learn it from books and in school. That's what math is.

But for some Platonic mathematicians, that proposition is so outrageous that it takes a lot of effort even to begin to consider it.

JB: Reuben, sounds like you're about to push some political agenda here, and it's not the Republican platform.

HERSH: You're saying my philosophy may be biased by my politics. Well, it's true! This is one of the many novel things in my book-- looking into the correlation between political belief and belief about the nature of mathematics.

JB: Do you have a name for this solution?

HERSH: I call it humanistic philosophy of mathematics. It's not really a school; no one else has jumped on the bandwagon with that name, but there are other people who think in a similar way, who gave it different names. I'm not completely a lone wolf here, I'm one of the mavericks, as we call them. The wolves baying outside the corral of philosophy.

Anyhow, back to your other question. The second half of my book is about the history of the philosophy of mathematics. I found that this was best explained by separating philosophers of mathematics into two groups. One group I call Mainstream and the other I call Humanists and Mavericks. The Humanists and Mavericks see mathematics as a human activity, and the Mainstream see it as inhuman or superhuman. By the way, there have been humanists way back; Aristotle was one. I wondered whether there was any connection with politics. So I tried to classify each of these guys as either right-wing or left-wing, in relation to their own times. Plato was far right; Aristotle was somewhat liberal. Spinoza was a revolutionary; Descartes was a royalist, and so on. These are well known facts. There are some guys that you can't classify. It came out just as you are intimating, The humanists are predominantly left-wing and the mainstream predominantly right wing. Any explanation would be speculative, but intuitively it makes sense. For instance, one main version of mainstream philosophy of mathematics is Platonism. It says that all mathematical objects, entities, or whatever, including the ones we haven't discovered yet and the ones we never will discover-all of have always existed. There's no change in the realm of mathematics. We discover things, so our knowledge increases, but the actual mathematical universe is completely static. Always was, always will be. Well that's kind of conservative, you know? Fits in with someone who thinks that social institutions mustn't change.

So this parallel exists. But there are exceptions. For instance, Bertrand Russell was a Platonist and a socialist. One of my favorite philosophers, Imre Lakatos, was a right-winger politically, but very radical philosophically. These correlations are loose and statistical, not binding. You can't tell somebody's philosophy from his politics, or vice versa.

I searched for a suitable label for my ideas. There were several others that had been used for similar points of view--social constructivism, fallibilism, quasi-empiricism, naturalism. I didn't want to take anybody else's label, because I was blazing my own trail, and I didn't want to label myself with someone else's school. The name that would have been most accurate was social conceptualism. Mathematics consists of concepts, but not individually held concepts; socially held concepts. Maybe I thought of humanism because I belong to a group called the Humanistic Mathematics Network. Humanism is appropriate, because it's saying that math is something human. There's no math without people. Many people think that ellipses and numbers and so on are there whether or not any people know about them; I think that's a confusion.

JB: Sounds like we're talking about an anthropic principle of mathematics here.

HERSH: Maybe so; I never thought of that. I had a serious argument with a friend of mine at the University of New Mexico, a philosopher of science. She said "There are nine planets; there were nine planets before there were any people. That means there was the number nine, before we had any people."

There is a difficulty that has to be clarified. We do see mathematical things, like small numbers, in physical reality. And that seems to contradict the idea that numbers are social entities. The way to straighten this out has been pointed out by others also. We use number words in two different ways: as nouns and adjectives. This is an important observation. We say nine apples, nine is an adjective. If it's an objective fact that there are nine apples on the table, that's just as objective as the fact that the apples are red, or that they're ripe, or anything else about them, that's a fact. And there's really no special difficulty about that. Things become difficult when we switch unconsciously, and carelessly, between this real-world adjective interpretation of math words like nine, and the pure abstraction that we talk about in math class.

That's not really the same nine. Although there's of course a correlation and a connection. But the number nine as an abstract object, as part of a number system, is a human possession, a human creation, it doesn't exist without us. The possible existence of collections of nine objects is a physical thing, which certainly exists without us. The two kinds of nine are different.

Like I can say a plate is round, an objective fact, but the conception of roundness, mathematical roundness, is something else.

Sad to say, philosophy is definitely an optional activity; most people, including mathematicians, don't even know if they have a philosophy, or what their philosophy is. Certainly what they do would not be affected by a philosophical controversy. This is true in many other fields. To be a practitioner is one thing; to be a philosopher is another. To justify philosophical activity one must go to a deeper level, for instance as in Socrates' remark about the unexamined life. It's pathetic to be a mathematician all your life and never worry, or think, or care, what that means. Many people do it. I compare this to a salmon swimming upstream. He knows how to swim upstream, but he doesn't know what he's doing or why.

JB: How does having a philosophy of mathematics affect its teaching?

HERSH: The philosophy of mathematics is very pertinent to the teaching of mathematics. What's wrong with mathematics teaching is not particular to this country. People are very critical about math teaching in the United States nowadays, as if it was just an American problem. But even though some other countries get higher test scores, the fundamental mis-teaching and bad teaching of mathematics is international, it's standard. In some ways we're not as bad as some other countries. But I don't want to get into that right now.

Let me state three possible philosophical attitudes towards mathematics.

Platonism says mathematics is about some abstract entities which are independent of humanity.

Formalism says mathematics is nothing but calculations. There's no meaning to it at all. You just come out with the right answer by following the rules.

Humanism sees mathematics as part of human culture and human history.

It's hard to come to rigorous conclusions about this kind of thing, but I feel it's almost obvious that Platonism and Formalism are anti-educational, and interfere with understanding, and Humanism at least doesn't hurt and could be beneficial.

Formalism is connected with rote, the traditional method which is still common in many parts of the world. Here's an algorithm; practice it for a while; now here's another one. That's certainly what makes a lot of people hate mathematics. (I don't mean that mathematicians who are formalists advocate teaching by rote. But the formalist conception of mathematics fits naturally with the rote method of instruction.)

There are various kinds of Platonists. Some are good teachers, some are bad. But the Platonist idea, that, as my friend Phil Davis puts it, Pi is in the sky, helps to make mathematics intimidating and remote. It can be an excuse for a pupil's failure to learn, or for a teacher's saying, "Some people just don't get it."

The humanistic philosophy brings mathematics down to earth, makes it accessible psychologically, and increases the likelihood that someone can learn it, because it's just one of the things that people do. This is a matter of opinion; there's no data, no tests. But I'm convinced it is the case.

JB: How do you teach humanistic math?

HERSH: I'm going to sidestep that slightly, I'll tell you my conception of good math teaching. How this connects with the philosophy may be more tenuous.

The essential thing is interaction, communication. Only in math do you have this typical figure who was supposedly exemplified by Norbert Wiener. He walks into the classroom, doesn't look at the class, starts writing on the board, keeps writing until the hour is over and then departs, still without looking at the class.

A good math teacher starts with examples. He first asks the question and then gives the answer, instead of giving the answer without mentioning what the question was. He is alert to the body language and eye movements of the class. If they start rolling their eyes or leaning back, he will stop his proof or his calculation and force them somehow to respond, even to say "I don't get it." No math class is totally bad if the students are speaking up. And no math lecture is really good, no matter how beautiful, if it lets the audience become simply passive. Some of this applies to any kind of teaching, but math unfortunately is conducive to bad teaching.

It's so strange. Mathematical theorems may really be very useful. But nobody knows it. The teacher doesn't mention it, the students don't know it. All they know is it's part of the course. That's inhuman, isn't it?

Here's an anecdote. I teach a class, which I invented myself, called Problem Solving for High School and Junior High School Teachers and Future Teachers. The idea is to get them into problem solving, having fun at it, feeling confident at it, in the hope that when they become teachers they will impart some of that to their class The students had assignments; they were supposed to work on something and then come talk about it in class. One day I called for volunteers. No volunteers. I waited. Waited. Then, feeling very brave, I went to the back of the room and sat down and said nothing. For a while. And another while. Then a student went to the blackboard, and then another one.

It turned out to be a very good class. The key was that I was willing to shut up. The easy thing, which I had done hundreds of times, would have been to say, "Okay, I'll show it to you." That's perhaps the biggest difficulty for most, nearly all, teachers-not to talk so much. Be quiet. Don't think the world's coming to an end if there's silence for two or three minutes.

JB: Earlier you mentioned the word beauty. What's with beauty?

HERSH: Fortunately, I have an answer to that. My friend, Gian-Carlo Rota, dealt with that issue in his new book, "Indiscrete Thoughts." He said the desire to say "How beautiful!" is associated with an insight. When something unclear or confusing suddenly fits together, that's beautiful. Maybe there are other situations that you would say are beautiful besides that, but I felt when I read that that he really had something. Because we talk about beauty all the time without being clear what we mean by it; it's purely subjective. But Rota came very close to it. Order out of confusion; simplicity out of complexity; understanding out of misunderstanding; that's mathematical beauty.


Charles Simonyi and Stanislas Dehaene on Reuben Hersh

From: Charles Simonyi
Submitted: 2/8/97

I feel like the Kinks who reported in one of their songs that after their single "You Really Got Me" had become Number One people started ask them about their "politics and theories of religion" ("Lola vs. Powermen" album).

But since you asked, I found the Hersh interview fascinating. I will certainly look up Imre Lakatos on the net. I have some disjointed observations.

As to Math education, why is it so difficult to divorce the problem of teaching Math (or anything else) from the subject matter? To be sure, I feel I am in agreement with Hersh but I'd like to state this a bit more forcefully, because education is so important for society and because it is not a philosophical question. In fact it should be pure engineering, albeit social engineering. Try X, measure result, measure sensitivity to variations, vary in promising direction, repeat. We should be willing to teach even the "wrong" things (for example that there is no difference between numbers and numerals, or that numbers are necessarily base 10) if we get the desired result: happy customers, enjoying and skilled at useful math, many of them will explore deeper levels where the "wrong" things are easily "righted". My point is that the philosophy of Math, even a "true" one, is just a heuristic when used for pedagogical purposes, sozusagen outside its domain, and then not necessarily even a useful one. (I might argue that it is, in fact, pernicious).

It always fun to see old dichotomies being shown as empty puns, verbal crutches: internal/external, real/abstract. My feeling is that the current distinction between real (tangible) and abstract will slowly fade into a single concept (call it "necessity" for example) as we continue probe the depths of physics. At that point maybe we will identify in Math a "necessary" or Platonic part (also explaining why Math is so good at describing physics i.e. reality) and the social, Hershian part. I mean, the Platonic world would no be populated by arbitrary human constructs such as triangles, sines, Lie groups any more than physics needs "feet" as the measure of length or "red" as the measure of frequency any more - to be sure these were useful for a long time and are still useful in engineering. One-half and sine of pi over six are social games, but why not games rooted in some basic necessity just as our social existence is rooted in physical existence, especially if the physical and abstract existence will become to be known as the same thing?

I am contributing this in the spirit of brainstorming only. I do not necessarily believe a word of it.I apologise for not using the standard nomenclature — this is just a consequence of my ignorance.-

Charles Simonyi

CHARLES SIMONYI, Chief Architect, Microsoft Corporation, joined Microsoft in 1981 to start the development of microcomputer application programs. He hired and managed teams who developed Microsoft Excel, Multiplan, Word, and other applications. In 1991, he moved on to Microsoft Research where he focused on Intentional Programming, an "ecology for abstractions" which strives for maximal reuse of components by separating high level intentions from implementation detail.

From: Stanislas Dehaene
Submitted: 2/8/97

Stanislas Dehaene

What is a number? As a neuropsychologist studying how the human brain wires itself to do mathematics, I'd answer that number is a parameter of our physical environment which is extracted and processed by dedicated cerebral networks—just like color, which is a subjective property entirely made up by brain area V4. Indeed, in my forthcoming book "The Number Sense", to appear in September, I show how animals and infants have a largely innate intuition about numerical quantities and their properties. Recent experimental evidence suggest:-

That the human baby is born with innate mechanisms for individuating objects and for extracting the numerosity of small sets. -

That this “number sense” is also present in animals, and hence that it is independent of language and has a long evolutionary past.-

That in children, numerical estimation, comparison, counting, simple addition and subtraction all emerge spontaneously without much explicit instruction.-

That the inferior parietal region of both cerebral hemispheres hosts neuronal circuits dedicated to the mental manipulation of numerical quantities, and that a lesion to that area leads to a loss of "number sense", including not knowing what is 3-1, or what number falls between 2 and 4.

I think that this inner feeling of quantity serves as a foundation for the later "construction of number" through mathematical axiomatizations. Yet as a basic category of experience provided by a dedicated brain circuit, number is as undefinable as color, space, movement, happiness, or beauty.

I thus agree with Reuben Hersh that Platonism, or the view that mathematical facts are abstract and independent of human existence and knowledge, is not a tenable position. (My own neurobiological interpretation is that Platonism is a cognitive illusion that imposes itself upon so many great mathematicians because with training, their brains develop a vivid, seemingly real, internal image of mathematical objects. Presumably, one can only become a mathematical genius if one has an outstanding capacity for forming vivid mental representations of abstract mathematical concepts - mental images that soon turn into an illusion, eclipsing the human origins of mathematical objects and endowing them with the semblance of an independent existence.)

Mathematics is indeed a product of the human mind and brain, and as such it is indeed a very human enterprise, fallible, revisable, and highly dependent on the limits and abilities of our cerebral equipment. Does that mean, however, that mathematics is a purely social activity? The trouble with labelling mathematics as "social" or "humanistic", and with comparing it to art and religion, is that this view completely fails to capture what is so special about mathematic s—first, its universality, and second, its effectiveness. If the Pope is invited to give a lecture in Tokyo and attempts to convert the locals to the Christian concept of God as Trinity, I doubt that he'll convince the audience—Trinity just can't be "proven" from first principles. But as a mathematician you can go to any place in the world and, given enough time, you can convince anyone that 3 is a prime number, or that the 3rd decimal of Pi is a 1, or that Fermat's last theorem is true. The point is, universal agreement is often easily reached about what constitutes a mathematical fact. This makes a unqualified relativistic, social, Lakatosian, or post-modernist view of mathematics totally untenable (it is unclear to me whether Reuben Hersh himself adheres to such an extreme relativistic point of view). The ridicule of this position has been recently pointed out by Sokal in "transgressing the limits...". Relativists notwithstanding, the value of Pi does not vary from culture to culture, nor does each culture have its own different "mathematical universality", as I recently heard in a post-modernist talk last week in Paris!

The other key difference between math and other cultural objects such as religions is its effectiveness. This was, and still is, a subject of awe and wonder for physicists like Wigner and Einstein. "How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of physical reality?" Einstein asked in 1921. This is bound to remain forever a mystery as long as you adhere to a strong relativistic position, which asserts that mathematics is the result of the arbitrary cultural choices of mathematical "churches". For that matter, indeed, the effectiveness of mathematics is also not easy to explain if you believe, as Hersh seems, that mathematicians pursue their work for the sole purpose of its abstract beauty.

My tentative solution to both of these riddles appeals to evolution—of the brain and of mathematics. In my opinion, mathematical objects are universal and effective, first, because our biological brains have evolved to progressive internalize universal regularities of the external world (such as the fact that one object plus another object usually makes two objects), and second, because our cultural mathematical constructions have also evolved to fit the physical world. If mathematicians throughout the world converge on the same set of mathematical truths, it is because they all have a similar cerebral organization that (1) lets them categorize the world into similar objects (numbers, sets, functions, projections, etc.), and (2) forces to find over and over again the same solutions to the same problems (I am reminded of the reinvention of place-value number notation in 4 different cultures widely separated in space and time—chinese, babylonian, maya and indian). The common structure of our brains can explain why there is trans-cultural convergence in mathematics despite different social perspectives. In that respect, mathematical objects, while they are human constructions, are radically different from other cultural constructions of Western societies such as Christianism, Nouveau roman, symphony orchestras or French cuisine. Pies come in all sorts, American, French or Vietnamese; but hopefully there'll always be only one number pi!-

Stanislas Dehaene

STANISLAS DEHAENE, a researcher at the Institut National de la Santé, studies cognitive neuropsychology of language and number processing in the human brain. He was awarded a masters degree in applied mathematics and computer science from the University of Paris in 1985 and then earned a doctoral degree in cognitive psychology in 1989 at the Ecole des Hautes Etudes en Sciences Sociales in Paris. He is the author of The Number Sense: How Mathematical Knowledge is Embedded in Our Brains, forthcoming (Oxford).

Steven Pinker on Nicholas Humphrey & Richard Potts

From: Steve Pinker
Submitted: 2/7/97

While I see the value in John and Nick's invitation to open up the discussion to a wider circle, that could lead to an exponential series of answers to replies to remarks on comments, which I could not possibly keep up with. Regrettably, I have to make the following contribution to this discussion my last.-

Steven Pinker

PINKER ON HUMPHREY: I should make it clear that the theory in question here is not specifically about men killing their wives, but about acts of passion in general, by both sexes, of which revenge killing is just an extreme example.

Nick Humphrey asks, "How could a wife possibly get to know that her husband is so crazy? ... The best she can do is to infer it on the basis of indirect clues. But what could these clues possibly be, except either (i) evidence of this individual male having gone crazy in the past and killed a previous wife, or (ii) evidence of other males having killed their wives in the past."

There are many more cues to a person's likely future behavior than their having committed an identical act in the past and their belonging to a huge reference group, such as an entire sex, that statistically performs that act. Much of our everyday thought goes into interpreting a person's actions, words, and emotional reactions to predict what he or she is likely to do. In this case, a man who flies into rages, intimidates or assaults the woman, and shows a willingness to engage in reckless threats and displays, such as making noise and destroying property even if it attracts the attention of neighbors or the police, is giving ample evidence that he is crazy enough to punish desertion even at high costs to himself. Battered women frequently say "I'm afraid he's going to kill me," and they are often correct -- though judges and the police all too often criminally ignore their predictions. Nicole Brown Simpson, to take one example, predicted, probably correctly, that O.J. Simpson would murder her, based on his rages, assaults, and conspicuous vandalism.

Humphreys raises an excellent point when he says "Deterrence in general can only work when there actually are public guarantees that revenge will follow automatically, come what may. ...The problem is that this kind of guarantee can never be provided when the mechanism is hidden inside the brain and cannot in principle be open to inspection from outside." My own proposal is that this very consideration explains the age-old problem of why emotions are involuntarily expressed on the face and the body: in facial expressions, sweating, blanching, flushing, trembling, quavering, and so on. One signals that one's current course of action is under the control of the involuntary subdivisions of the nervous system, the parts tied in to regulation of the physical plant of the body, rather than under the control of the more conscious, rational, deliberative, voluntary subdivisions. These signs are a way of externalizing the fact that the reaction is automatic and uncontrollable, and serves as kind of guarantor of one's threats, promises, and bargains against suspicions that they are bluffs, double-crosses, or lowballs.

PINKER ON POTTS: Rick Potts seems to assume that reverse-engineering the mind requires that one ignore evidence from other species and the fossil and archeological record. I certainly do not subscribe to this mad view and neither does any evolutionary psychologist I know of. Paleoanthropological data clearly have limits -- reconstructing ancient minds is like trying to resolve current controversies in cognitive psychology by looking in graveyards and landfills -- but I certainly agree with Potts that we should squeeze every last drop of information that we can out of that kind of evidence (and of course comparative data as well). How the Mind Works discusses both comparative and paleoanthropological evidence in reasonable detail.

Don Symons' "Environment of Evolutionary Adaptedness" is not a specific time and place, but a composite: a weighted average of all the environments in which our ancestors were shaped by selection. Of course it is difficult to characterize the EEA in any kind of detail, but even characterizing it coarsely has radical implications for psychology that are seldom taken into account. It is not controversial that the vast majority of the span of human evolution, regardless of how far back you want to go, took place in an environment that lacked written language, institutionalized science and mathematics, police, a court system, contraception, substitutes for mother's milk, packaged food, money, and dozens of other features of modern life we take for granted. Contemporary psychology pays no attention to that fact, and proposes theories of human nature that are appropriate for survival in modern Western civilization. Even the crudest facts about the EEA go a long way in constraining psychological theories.

STEVEN PINKER is professor in the Department of Brain and Cognitive Sciences at MIT; director of the McDonnell-Pew Center for Cognitive Neuroscience at MIT; author of Language Learnability and Language Development, Learnability and Cognition, The Language Instinct, and the forthcoming How the Mind Works (Norton).

Philip Leggiere on Nathan Myhrvold

From: Philip Leggiere
Submitted: 2/7/97

Nathan Myhrvold's clear-headed and long term perspective on the economics of the web is a refreshing antidote to the all or nothing, instant boom or total bust mind set the topic's usually approached with. His description of the Web as a realm of content blindly chasing elusive customers with no evident profit formula ( the build it and they will come fallacy) accurately dramatizes one powerful dynamic.

I think there's been another, subtler, ultimately just as important process at work over the Web's first 18-24 months of pop cultural life, however, that of "customers" ( not the mass market those looking for blockbuster internet broadcasting success expect(ed), but a steadily increasing critical mass of regular Web users)in search of steady, reliable Web sites to integrate into their overall daily media mix. I know from my own experience and that of most veteran Web users I know that once the novelty of random surfing and the cornucopian glut of information wears off the next step is to critically and selectively organize one's limited Web time, choosing the few sites in each area of interest that really "pay off" from a consumer's point of view and reward regular visits.

The shake- out that'll probably prove more important than the mood swings of Wall St. will be the one in which the first wave of two or three dozen serious pioneer sites firmly establish themselves via critical reputation as a grade apart from the scads of ephemeral, coterie and vanity sites. I think this process of establishing widely accepted hierarchies of popularity and proven quality, though far slower than the other curves Myhrvold discusses, is actually moving along more quickly than we may think.-

Phil Leggiere

PHIL LEGGIERE is a journalist and cultural critic whose work appears in Salon, The Village Voice, Boston Review, Wired and other periodicals.

Copyright ©1997 by Edge Foundation, Inc.


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