by Edna St. Vincent Millay

Love is not all: it is not meat nor drink
Nor slumber nor a roof against the rain;
Nor yet a floating spar to men that sink
And rise and sink and rise and sink again;
Love can not fill the thickened lung with breath,
Nor clean the blood, nor set the fractured bone;
Yet many a man is making friends with death
Even as I speak, for lack of love alone.
It well may be that in a difficult hour,
Pinned down by pain and moaning for release,
Or nagged by want past resolution’s power,
I might be driven to sell your love for peace,
Or trade the memory of this night for food.
It well may be. I do not think I would.

• Love is Not All
• Love Is Not All: It Is Not Meat nor Drink
• Love is not all…

by William Shakespeare

How like a winter hath my absence been
From thee, the pleasure of the fleeting year!
What freezings have I felt, what dark days seen!
What old December’s bareness every where!
And yet this time remov’d was summer’s time;
The teeming autumn, big with rich increase,
Bearing the wanton burthen of the prime,
Like widowed wombs after their lords’ decease:
Yet this abundant issue seem’d to me
But hope of orphans and unfather’d fruit;
For summer and his pleasures wait on thee,
And, thou away, the very birds are mute;
Or, if they sing, ’tis with so dull a cheer
That leaves look pale, dreading the winter’s near.

• Sonnet 97: How like a winter hath my absence been
• Sonnet 97

Thank you very much. Please excuse me for sitting; I’m very old. (Laughter) Well, the topic I’m going to discuss is one which is, in a certain sense, very peculiar because it’s very old. Roughness is part of human life forever and forever, and ancient authors have written about it. It was very much uncontrollable, and in a certain sense, it seemed to be the extreme of complexity, just a mess, a mess and a mess. There are many different kinds of mess. Now, in fact, by a complete fluke, I got involved many years ago in a study of this form of complexity, and to my utter amazement, I found traces – very strong traces, I must say – of order in that roughness. And so today, I would like to present to you a few examples of what this represents. I prefer the word roughness to the word irregularity because irregularity – to someone who had Latin in my long-past youth – means the contrary of regularity. But it is not so. Regularity is the contrary of roughness because the basic aspect of the world is very rough.

So let me show you a few objects. Some of them are artificial. Others of them are very real, in a certain sense. Now this is the real. It’s a cauliflower. Now why do I show a cauliflower, a very ordinary and ancient vegetable? Because old and ancient as it may be, it’s very complicated and it’s very simple, both at the same time. If you try to weigh it – of course it’s very easy to weigh it, and when you eat it, the weight matters – but suppose you try to measure its surface. Well, it’s very interesting. If you cut, with a sharp knife, one of the florets of a cauliflower and look at it separately, you think of a whole cauliflower, but smaller. And then you cut again, again, again, again, again, again, again, again, again, and you still get small cauliflowers. So the experience of humanity has always been that there are some shapes which have this peculiar property, that each part is like the whole, but smaller. Now, what did humanity do with that? Very, very little. (Laughter)

So what I did actually is to study this problem, and I found something quite surprising. That one can measure roughness by a number, a number, 2.3, 1.2 and sometimes much more. One day, a friend of mine, to bug me, brought a picture and said, “What is the roughness of this curve?” I said, “Well, just short of 1.5.” It was 1.48. Now, it didn’t take me any time. I’ve been looking at these things for so long. So these numbers are the numbers which denote the roughness of these surfaces. I hasten to say that these surfaces are completely artificial. They were done on a computer, and the only input is a number, and that number is roughness. So on the left, I took the roughness copied from many landscapes. To the right, I took a higher roughness. So the eye, after a while, can distinguish these two very well.

Humanity had to learn about measuring roughness. This is very rough, and this is sort of smooth, and this perfectly smooth. Very few things are very smooth. So then if you try to ask questions: “What’s the surface of a cauliflower?” Well, you measure and measure and measure. Each time you’re closer, it gets bigger, down to very, very small distances. What’s the length of the coastline of these lakes? The closer you measure, the longer it is. The concept of length of coastline, which seems to be so natural because it’s given in many cases, is, in fact, complete fallacy; there’s no such thing. You must do it differently.

What good is that, to know these things? Well, surprisingly enough, it’s good in many ways. To begin with, artificial landscapes, which I invented sort of, are used in cinema all the time. We see mountains in the distance. They may be mountains, but they may be just formulae, just cranked on. Now it’s very easy to do. It used to be very time-consuming, but now it’s nothing. Now look at that. That’s a real lung. Now a lung is something very strange. If you take this thing, you know very well it weighs very little. The volume of a lung is very small, but what about the area of the lung? Anatomists were arguing very much about that. Some say that a normal male’s lung has an area of the inside of a basketball [court]. And the others say, no, five basketball [courts]. Enormous disagreements. Why so? Because, in fact, the area of the lung is something very ill-defined. The bronchi branch, branch, branch and they stop branching, not because of any matter of principle, but because of physical considerations: the mucus, which is in the lung. So what happens is that in a way you have a much bigger lung, but it branches and branches down to distances about the same for a whale, for a man and for a little rodent.

Now, what good is it to have that? Well, surprisingly enough, amazingly enough, the anatomists had a very poor idea of the structure of the lung until very recently. And I think that my mathematics, surprisingly enough, has been of great help to the surgeons studying lung illnesses and also kidney illnesses, all these branching systems, for which there was no geometry. So I found myself, in other words, constructing a geometry, a geometry of things which had no geometry. And a surprising aspect of it is that very often, the rules of this geometry are extremely short. You have formulas that long. And you crank it several times. Sometimes repeatedly: again, again, again, the same repetition. And at the end, you get things like that.

This cloud is completely, 100 percent artificial. Well, 99.9. And the only part which is natural is a number, the roughness of the cloud, which is taken from nature. Something so complicated like a cloud, so unstable, so varying, should have a simple rule behind it. Now this simple rule is not an explanation of clouds. The seer of clouds had to take account of it. I don’t know how much advanced these pictures are. They’re old. I was very much involved in it, but then turned my attention to other phenomena.

Now, here is another thing which is rather interesting. One of the shattering events in the history of mathematics, which is not appreciated by many people, occurred about 130 years ago, 145 years ago. Mathematicians began to create shapes that didn’t exist. Mathematicians got into self-praise to an extent which was absolutely amazing, that man can invent things that nature did not know. In particular, it could invent things like a curve which fills the plane. A curve’s a curve, a plane’s a plane, and the two won’t mix. Well, they do mix. A man named Peano did define such curves, and it became an object of extraordinary interest. It was very important, but mostly interesting because a kind of break, a separation between the mathematics coming from reality, on the one hand, and new mathematics coming from pure man’s mind. Well, I was very sorry to point out that the pure man’s mind has, in fact, seen at long last what had been seen for a long time. And so here I introduce something, the set of rivers of a plane-filling curve. And well, it’s a story unto itself. So it was in 1875 to 1925, an extraordinary period in which mathematics prepared itself to break out from the world. And the objects which were used as examples, when I was a child and a student, as examples of the break between mathematics and visible reality – those objects, I turned them completely around. I used them for describing some of the aspects of the complexity of nature.

Well, a man named Hausdorff in 1919 introduced a number which was just a mathematical joke, and I found that this number¹ was a good measurement of roughness. When I first told it to my friends in mathematics they said, “Don’t be silly. It’s just something [silly].” Well actually, I was not silly. The great painter Hokusai knew it very well. The things on the ground are algae. He did not know the mathematics; it didn’t yet exist. And he was Japanese who had no contact with the West. But painting for a long time had a fractal side. I could speak of that for a long time. The Eiffel Tower has a fractal aspect. I read the book that Mr. Eiffel wrote about his tower, and indeed it was astonishing how much he understood.

This is a mess, mess, mess, Brownian loop. One day I decided – halfway through my career, I was held by so many things in my work – I decided to test myself. Could I just look at something which everybody had been looking at for a long time and find something dramatically new? Well, so I looked at these things called Brownian motion – just goes around. I played with it for a while, and I made it return to the origin. Then I was telling my assistant, “I don’t see anything. Can you paint it?” So he painted it, which means he put inside everything. He said: “Well, this thing came out …” And I said, “Stop! Stop! Stop! I see; it’s an island.” And amazing. So Brownian motion, which happens to have a roughness number of two, goes around. I measured it, 1.33. Again, again, again. Long measurements, big Brownian motions, 1.33. Mathematical problem: how to prove it? It took my friends 20 years. Three of them were having incomplete proofs. They got together, and together they had the proof. So they got the big [Fields] medal in mathematics, one of the three medals that people have received for proving things which I’ve seen without being able to prove them.²

Now everybody asks me at one point or another, “How did it all start? What got you in that strange business?” What got you to be, at the same time, a mechanical engineer, a geographer and a mathematician and so on, a physicist? Well actually I started, oddly enough, studying stock market prices. And so here I had this theory, and I wrote books about it – financial prices increments. To the left you see data over a long period. To the right, on top, you see a theory which is very, very fashionable. It was very easy, and you can write many books very fast about it. (Laughter) There are thousands of books on that. Now compare that with real price increments. Where are real price increments? Well, these other lines include some real price increments and some forgery which I did. So the idea there was that one must be able to – how do you say? – model price variation. And it went really well 50 years ago. For 50 years, people were sort of pooh-poohing me because they could do it much, much easier. But I tell you, at this point, people listened to me. (Laughter) These two curves are averages: Standard & Poor, the blue one; and the red one is Standard & Poor’s from which the five biggest discontinuities are taken out. Now discontinuities are a nuisance, so in many studies of prices, one puts them aside. “Well, acts of God. And you have the little nonsense which is left. Acts of God.” In this picture, five acts of God are as important as everything else. In other words, it is not acts of God that we should put aside. That is the meat, the problem. If you master these, you master price, and if you don’t master these, you can master the little noise as well as you can, but it’s not important. Well, here are the curves for it.

Now, I get to the final thing, which is the set of which my name is attached. In a way, it’s the story of my life. My adolescence was spent during the German occupation of France. Since I thought that I might vanish within a day or a week, I had very big dreams. And after the war, I saw an uncle again. My uncle was a very prominent mathematician, and he told me, “Look, there’s a problem which I could not solve 25 years ago, and which nobody can solve. This is a construction of a man named [Gaston] Julia and [Pierre] Fatou. If you could find something new, anything, you will get your career made.” Very simple. So I looked, and like the thousands of people that had tried before, I found nothing.

But then the computer came, and I decided to apply the computer, not to new problems in mathematics – like this wiggle wiggle, that’s a new problem – but to old problems. And I went from what’s called real numbers, which are points on a line, to imaginary, complex numbers, which are points on a plane, which is what one should do there, and this shape came out. This shape is of an extraordinary complication. The equation is hidden there, z goes into z squared, plus c. It’s so simple, so dry. It’s so uninteresting. Now you turn the crank once, twice: twice, marvels come out. I mean this comes out. I don’t want to explain these things. This comes out. This comes out. Shapes which are of such complication, such harmony and such beauty. This comes out repeatedly, again, again, again. And that was one of my major discoveries, to find that these islands were the same as the whole big thing, more or less. And then you get these extraordinary baroque decorations all over the place. All that from this little formula, which has whatever, five symbols in it. And then this one. The color was added for two reasons. First of all, because these shapes are so complicated that one couldn’t make any sense of the numbers. And if you plot them, you must choose some system. And so my principle has been to always present the shapes with different colorings because some colorings emphasize that, and others it is that or that. It’s so complicated.

(Laughter)

In 1990, I was in Cambridge, U.K. to receive a prize from the university, and three days later, a pilot was flying over the landscape and found this thing. So where did this come from? Obviously, from extraterrestrials. (Laughter) Well, so the newspaper in Cambridge published an article about that “discovery” and received the next day 5,000 letters from people saying, “But that’s simply a Mandelbrot set very big.”

Well, let me finish. This shape here just came out of an exercise in pure mathematics. Bottomless wonders spring from simple rules, which are repeated without end.

Thank you very much.

(Applause)

1. Hausdorff dimension: In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was first introduced in 1918 by mathematician Felix Hausdorff.

2. In 1982, Benoit Mandelbrot conjectured that the fractal dimension of the outer boundary of the trajectory of a Brownian path is 4/3. Resolving this conjecture seemed out of reach of classical probabilistic techniques. Lawler, Schramm, and Werner proved this conjecture first by showing that the outer frontier of Brownian paths and the outer boundaries of the continuous percolation clusters are similar, and then by computing their common dimension using a dynamical construction of the continuous percolation clusters. Using the same strategy, they also derived the values of the closely related “intersection exponents” for Brownian motion and simple random walks that had been conjectured by physicists B. Duplantier and K. H. Kwon (one of these intersection exponents describes the probability that the paths of two long walkers remain disjoint up to some very large time). Further work of Werner exhibited additional symmetries of these outer boundaries of Brownian loops.

by Peter F. Drucker

The typical large business 20 years hence will have fewer than half the levels of management of its counterpart today, and no more than a third the managers. In its structure, and in its management problems and concerns, it will bear little resemblance to the typical manufacturing company, circa 1950, which our textbooks still consider the norm. Instead it is far more likely to resemble organizations that neither the practicing manager nor the management scholar pays much attention to today: the hospital, the university, the symphony orchestra. For like them, the typical business will be knowledge-based, an organization composed largely of specialists who direct and discipline their own performance through organized feedback from colleagues, customers, and headquarters. For this reason, it will be what I call an information-based organization.

The large business 20 years hence is more likely to resemble a hospital or a symphony than a typical manufacturing company.

Businesses, especially large ones, have little choice but to become information-based. Demographics, for one, demands the shift. The center of gravity in employment is moving fast from manual and clerical workers to knowledge workers who resist the command-and-control model that business took from the military 100 years ago. Economics also dictates change, especially the need for large businesses to innovate and to be entrepreneurs. But above all, information technology demands the shift.

Advanced data-processing technology isn’t necessary to create an information-based organization, of course. As we shall see, the British built just such an organization in India when “information technology” meant the quill pen, and barefoot runners were the “telecommunications” systems. But as advanced technology becomes more and more prevalent, we have to engage in analysis and diagnosis—that is, in “information”—even more intensively or risk being swamped by the data we generate.

So far most computer users still use the new technology only to do faster what they have always done before, crunch conventional numbers. But as soon as a company takes the first tentative steps from data to information, its decision processes, management structure, and even the way its work gets done begin to be transformed. In fact, this is already happening, quite fast, in a number of companies throughout the world.

We can readily see the first step in this transformation process when we consider the impact of computer technology on capital-investment decisions. We have known for a long time that there is no one right way to analyze a proposed capital investment. To understand it we need at least six analyses: the expected rate of return; the payout period and the investment’s expected productive life; the discounted present value of all returns through the productive lifetime of the investment; the risk in not making the investment or deferring it; the cost and risk in case of failure; and finally, the opportunity cost. Every accounting student is taught these concepts. But before the advent of data-processing capacity, the actual analyses would have taken man-years of clerical toil to complete. Now anyone with a spreadsheet should be able to do them in a few hours.

The availability of this information transforms the capital-investment analysis from opinion into diagnosis, that is, into the rational weighing of alternative assumptions. Then the information transforms the capital-investment decision from an opportunistic, financial decision governed by the numbers into a business decision based on the probability of alternative strategic assumptions. So the decision both presupposes a business strategy and challenges that strategy and its assumptions. What was once a budget exercise becomes an analysis of policy.

Information transforms a budget exercise into an analysis of policy.

The second area that is affected when a company focuses its data-processing capacity on producing information is its organization structure. Almost immediately, it becomes clear that both the number of management levels and the number of managers can be sharply cut. The reason is straightforward: it turns out that whole layers of management neither make decisions nor lead. Instead, their main, if not their only, function is to serve as “relays”—human boosters for the faint, unfocused signals that pass for communication in the traditional pre-information organization.

One of America’s largest defense contractors made this discovery when it asked what information its top corporate and operating managers needed to do their jobs. Where did it come from? What form was it in? How did it flow? The search for answers soon revealed that whole layers of management—perhaps as many as 6 out of a total of 14—existed only because these questions had not been asked before. The company had had data galore. But it had always used its copious data for control rather than for information.

Information is data endowed with relevance and purpose. Converting data into information thus requires knowledge. And knowledge, by definition, is specialized. (In fact, truly knowledgeable people tend toward overspecialization, whatever their field, precisely because there is always so much more to know.)

The information-based organization requires far more specialists overall than the command-and-control companies we are accustomed to. Moreover, the specialists are found in operations, not at corporate headquarters. Indeed, the operating organization tends to become an organization of specialists of all kinds.

Information-based organizations need central operating work such as legal counsel, public relations, and labor relations as much as ever. But the need for service staffs—that is, for people without operating responsibilities who only advise, counsel, or coordinate—shrinks drastically. In its central management, the information-based organization needs few, if any, specialists.

Because of its flatter structure, the large, information-based organization will more closely resemble the businesses of a century ago than today’s big companies. Back then, however, all the knowledge, such as it was, lay with the very top people. The rest were helpers or hands, who mostly did the same work and did as they were told. In the information-based organization, the knowledge will be primarily at the bottom, in the minds of the specialists who do different work and direct themselves. So today’s typical organization in which knowledge tends to be concentrated in service staffs, perched rather insecurely between top management and the operating people, will likely be labeled a phase, an attempt to infuse knowledge from the top rather than obtain information from below.

Finally, a good deal of work will be done differently in the information-based organization. Traditional departments will serve as guardians of standards, as centers for training and the assignment of specialists; they won’t be where the work gets done. That will happen largely in task-focused teams.

Traditional departments won’t be where the work gets done.

This change is already under way in what used to be the most clearly defined of all departments—research. In pharmaceuticals, in telecommunications, in papermaking, the traditional sequence of research, development, manufacturing, and marketing is being replaced by synchrony: specialists from all these functions work together as a team, from the inception of research to a product’s establishment in the market.

How task forces will develop to tackle other business opportunities and problems remains to be seen. I suspect, however, that the need for a task force, its assignment, its composition, and its leadership will have to be decided on case by case. So the organization that will be developed will go beyond the matrix and may indeed be quite different from it. One thing is clear, though: it will require greater self-discipline and even greater emphasis on individual responsibility for relationships and for communications.• • •

To say that information technology is transforming business enterprises is simple. What this transformation will require of companies and top managements is much harder to decipher. That is why I find it helpful to look for clues in other kinds of information-based organizations, such as the hospital, the symphony orchestra, and the British administration in India.

A fair-sized hospital of about 400 beds will have a staff of several hundred physicians and 1,200 to 1,500 paramedics divided among some 60 medical and paramedical specialties. Each specialty has its own knowledge, its own training, its own language. In each specialty, especially the paramedical ones like the clinical lab and physical therapy, there is a head person who is a working specialist rather than a full-time manager. The head of each specialty reports directly to the top, and there is little middle management. A good deal of the work is done in ad hoc teams as required by an individual patient’s diagnosis and condition.

A large symphony orchestra is even more instructive, since for some works there may be a few hundred musicians on stage playing together. According to organization theory then, there should be several group vice president conductors and perhaps a half-dozen division VP conductors. But that’s not how it works. There is only the conductor-CEO—and every one of the musicians plays directly to that person without an intermediary. And each is a high-grade specialist, indeed an artist.

But the best example of a large and successful information-based organization, and one without any middle management at all, is the British civil administration in India.¹

The best example of a large and successful information-based organization had no middle management at all.

The British ran the Indian subcontinent for 200 years, from the middle of the eighteenth century through World War II, without making any fundamental changes in organization structure or administrative policy. The Indian civil service never had more than 1,000 members to administer the vast and densely populated subcontinent—a tiny fraction (at most 1%) of the legions of Confucian mandarins and palace eunuchs employed next door to administer a not-much-more populous China. Most of the Britishers were quite young; a 30-year-old was a survivor, especially in the early years. Most lived alone in isolated outposts with the nearest countryman a day or two of travel away, and for the first hundred years there was no telegraph or railroad.

The organization structure was totally flat. Each district officer reported directly to the “COO,” the provincial political secretary. And since there were nine provinces, each political secretary had at least 100 people reporting directly to him, many times what the doctrine of the span of control would allow. Nevertheless, the system worked remarkably well, in large part because it was designed to ensure that each of its members had the information he needed to do his job.

Each month the district officer spent a whole day writing a full report to the political secretary in the provincial capital. He discussed each of his principal tasks—there were only four, each clearly delineated. He put down in detail what he had expected would happen with respect to each of them, what actually did happen, and why, if there was a discrepancy, the two differed. Then he wrote down what he expected would happen in the ensuing month with respect to each key task and what he was going to do about it, asked questions about policy, and commented on long-term opportunities, threats, and needs. In turn, the political secretary “minuted” every one of those reports—that is, he wrote back a full comment.• • •

On the basis of these examples, what can we say about the requirements of the information-based organization? And what are its management problems likely to be? Let’s look first at the requirements. Several hundred musicians and their CEO, the conductor, can play together because they all have the same score. It tells both flutist and timpanist what to play and when. And it tells the conductor what to expect from each and when. Similarly, all the specialists in the hospital share a common mission: the care and cure of the sick. The diagnosis is their “score”; it dictates specific action for the X-ray lab, the dietitian, the physical therapist, and the rest of the medical team.

Information-based organizations, in other words, require clear, simple, common objectives that translate into particular actions. At the same time, however, as these examples indicate, information-based organizations also need concentration on one objective or, at most, on a few.

Because the “players” in an information-based organization are specialists, they cannot be told how to do their work. There are probably few orchestra conductors who could coax even one note out of a French horn, let alone show the horn player how to do it. But the conductor can focus the horn player’s skill and knowledge on the musicians’ joint performance. And this focus is what the leaders of an information-based business must be able to achieve.

Yet a business has no “score” to play by except the score it writes as it plays. And whereas neither a first-rate performance of a symphony nor a miserable one will change what the composer wrote, the performance of a business continually creates new and different scores against which its performance is assessed. So an information-based business must be structured around goals that clearly state management’s performance expectations for the enterprise and for each part and specialist and around organized feedback that compares results with these performance expectations so that every member can exercise self-control.

The other requirement of an information-based organization is that everyone take information responsibility. The bassoonist in the orchestra does so every time she plays a note. Doctors and paramedics work with an elaborate system of reports and an information center, the nurse’s station on the patient’s floor. The district officer in India acted on this responsibility every time he filed a report.

The key to such a system is that everyone asks: Who in this organization depends on me for what information? And on whom, in turn, do I depend? Each person’s list will always include superiors and subordinates. But the most important names on it will be those of colleagues, people with whom one’s primary relationship is coordination. The relationship of the internist, the surgeon, and the anesthesiologist is one example. But the relationship of a biochemist, a pharmacologist, the medical director in charge of clinical testing, and a marketing specialist in a pharmaceutical company is no different. It, too, requires each party to take the fullest information responsibility.

Who depends on me for information? And on whom do I depend?

Information responsibility to others is increasingly understood, especially in middle-sized companies. But information responsibility to oneself is still largely neglected. That is, everyone in an organization should constantly be thinking through what information he or she needs to do the job and to make a contribution.

This may well be the most radical break with the way even the most highly computerized businesses are still being run today. There, people either assume the more data, the more information—which was a perfectly valid assumption yesterday when data were scarce, but leads to data overload and information blackout now that they are plentiful. Or they believe that information specialists know what data executives and professionals need in order to have information. But information specialists are tool makers. They can tell us what tool to use to hammer upholstery nails into a chair. We need to decide whether we should be upholstering a chair at all.

Executives and professional specialists need to think through what information is for them, what data they need: first, to know what they are doing; then, to be able to decide what they should be doing; and finally, to appraise how well they are doing. Until this happens MIS departments are likely to remain cost centers rather than become the result centers they could be.• • •

Most large businesses have little in common with the examples we have been looking at. Yet to remain competitive—maybe even to survive—they will have to convert themselves into information-based organizations, and fairly quickly. They will have to change old habits and acquire new ones. And the more successful a company has been, the more difficult and painful this process is apt to be. It will threaten the jobs, status, and opportunities of a good many people in the organization, especially the long-serving, middle-aged people in middle management who tend to be the least mobile and to feel most secure in their work, their positions, their relationships, and their behavior.

To remain competitive—maybe even to survive—businesses will have to convert themselves into organizations of knowledgeable specialists.

The information-based organization will also pose its own special management problems. I see as particularly critical:

1. Developing rewards, recognition, and career opportunities for specialists.

2. Creating unified vision in an organization of specialists.

3. Devising the management structure for an organization of task forces.

4. Ensuring the supply, preparation, and testing of top management people.

Bassoonists presumably neither want nor expect to be anything but bassoonists. Their career opportunities consist of moving from second bassoon to first bassoon and perhaps of moving from a second-rank orchestra to a better, more prestigious one. Similarly, many medical technologists neither expect nor want to be anything but medical technologists. Their career opportunities consist of a fairly good chance of moving up to senior technician, and a very slim chance of becoming lab director. For those who make it to lab director, about 1 out of every 25 or 30 technicians, there is also the opportunity to move to a bigger, richer hospital. The district officer in India had practically no chance for professional growth except possibly to be relocated, after a three-year stint, to a bigger district.

Opportunities for specialists in an information-based business organization should be more plentiful than they are in an orchestra or hospital, let alone in the Indian civil service. But as in these organizations, they will primarily be opportunities for advancement within the specialty, and for limited advancement at that. Advancement into “management” will be the exception, for the simple reason that there will be far fewer middle-management positions to move into. This contrasts sharply with the traditional organization where, except in the research lab, the main line of advancement in rank is out of the specialty and into general management.

More than 30 years ago General Electric tackled this problem by creating “parallel opportunities” for “individual professional contributors.” Many companies have followed this example. But professional specialists themselves have largely rejected it as a solution. To them—and to their management colleagues—the only meaningful opportunities are promotions into management. And the prevailing compensation structure in practically all businesses reinforces this attitude because it is heavily biased towards managerial positions and titles.

There are no easy answers to this problem. Some help may come from looking at large law and consulting firms, where even the most senior partners tend to be specialists, and associates who will not make partner are outplaced fairly early on. But whatever scheme is eventually developed will work only if the values and compensation structure of business are drastically changed.

The second challenge that management faces is giving its organization of specialists a common vision, a view of the whole.

In the Indian civil service, the district officer was expected to see the “whole” of his district. But to enable him to concentrate on it, the government services that arose one after the other in the nineteenth century (forestry, irrigation, the archaeological survey, public health and sanitation, roads) were organized outside the administrative structure, and had virtually no contact with the district officer. This meant that the district officer became increasingly isolated from the activities that often had the greatest impact on—and the greatest importance for—his district. In the end, only the provincial government or the central government in Delhi had a view of the “whole,” and it was an increasingly abstract one at that.

A business simply cannot function this way. It needs a view of the whole and a focus on the whole to be shared among a great many of its professional specialists, certainly among the senior ones. And yet it will have to accept, indeed will have to foster, the pride and professionalism of its specialists—if only because, in the absence of opportunities to move into middle management, their motivation must come from that pride and professionalism.

One way to foster professionalism, of course, is through assignments to task forces. And the information-based business will use more and more smaller self-governing units, assigning them tasks tidy enough for “a good man to get his arms around,” as the old phrase has it. But to what extent should information-based businesses rotate performing specialists out of their specialties and into new ones? And to what extent will top management have to accept as its top priority making and maintaining a common vision across professional specialties?

Heavy reliance on task-force teams assuages one problem. But it aggravates another: the management structure of the information-based organization. Who will the business’s managers be? Will they be task-force leaders? Or will there be a two-headed monster—a specialist structure, comparable, perhaps, to the way attending physicians function in a hospital, and an administrative structure of task-force leaders?

Who will the business’s managers be?

The decisions we face on the role and function of the task-force leaders are risky and controversial. Is theirs a permanent assignment, analogous to the job of the supervisory nurse in the hospital? Or is it a function of the task that changes as the task does? Is it an assignment or a position? Does it carry any rank at all? And if it does, will the task-force leaders become in time what the product managers have been at Procter & Gamble: the basic units of management and the company’s field officers? Might the task-force leaders eventually replace department heads and vice presidents?

Signs of every one of these developments exist, but there is neither a clear trend nor much understanding as to what each entails. Yet each would give rise to a different organizational structure from any we are familiar with.

Finally, the toughest problem will probably be to ensure the supply, preparation, and testing of top management people. This is, of course, an old and central dilemma as well as a major reason for the general acceptance of decentralization in large businesses in the last 40 years. But the existing business organization has a great many middle-management positions that are supposed to prepare and test a person. As a result, there are usually a good many people to choose from when filling a senior management slot. With the number of middle-management positions sharply cut, where will the information-based organization’s top executives come from? What will be their preparation? How will they have been tested?

With middle management sharply cut, where will the top executives come from?

Decentralization into autonomous units will surely be even more critical than it is now. Perhaps we will even copy the German Gruppe in which the decentralized units are set up as separate companies with their own top managements. The Germans use this model precisely because of their tradition of promoting people in their specialties, especially in research and engineering; if they did not have available commands in near-independent subsidiaries to put people in, they would have little opportunity to train and test their most promising professionals. These subsidiaries are thus somewhat like the farm teams of a major-league baseball club.

We may also find that more and more top management jobs in big companies are filled by hiring people away from smaller companies. This is the way that major orchestras get their conductors—a young conductor earns his or her spurs in a small orchestra or opera house, only to be hired away by a larger one. And the heads of a good many large hospitals have had similar careers.

Can business follow the example of the orchestra and hospital where top management has become a separate career? Conductors and hospital administrators come out of courses in conducting or schools of hospital administration respectively. We see something of this sort in France, where large companies are often run by men who have spent their entire previous careers in government service. But in most countries this would be unacceptable to the organization (only France has the mystique of the grandes écoles). And even in France, businesses, especially large ones, are becoming too demanding to be run by people without firsthand experience and a proven success record.

Thus the entire top management process—preparation, testing, succession—will become even more problematic than it already is. There will be a growing need for experienced businesspeople to go back to school. And business schools will surely need to work out what successful professional specialists must know to prepare themselves for high-level positions as business executives and business leaders.• • •

Since modern business enterprise first arose, after the Civil War in the United States and the Franco-Prussian War in Europe, there have been two major evolutions in the concept and structure of organizations. The first took place in the ten years between 1895 and 1905. It distinguished management from ownership and established management as work and task in its own right. This happened first in Germany, when Georg Siemens, the founder and head of Germany’s premier bank, Deutsche Bank, saved the electrical apparatus company his cousin Werner had founded after Werner’s sons and heirs had mismanaged it into near collapse. By threatening to cut off the bank’s loans, he forced his cousins to turn the company’s management over to professionals. A little later, J.P. Morgan, Andrew Carnegie, and John D. Rockefeller, Sr. followed suit in their massive restructurings of U.S. railroads and industries.

The second evolutionary change took place 20 years later. The development of what we still see as the modern corporation began with Pierre S. du Pont’s restructuring of his family company in the early twenties and continued with Alfred P. Sloan’s redesign of General Motors a few years later. This introduced the command-and-control organization of today, with its emphasis on decentralization, central service staffs, personnel management, the whole apparatus of budgets and controls, and the important distinction between policy and operations. This stage culminated in the massive reorganization of General Electric in the early 1950s, an action that perfected the model most big businesses around the world (including Japanese organizations) still follow.²

We can identify requirements and point to problems; the job of building is still ahead.

Now we are entering a third period of change: the shift from the command-and-control organization, the organization of departments and divisions, to the information-based organization, the organization of knowledge specialists. We can perceive, though perhaps only dimly, what this organization will look like. We can identify some of its main characteristics and requirements. We can point to central problems of values, structure, and behavior. But the job of actually building the information-based organization is still ahead of us—it is the managerial challenge of the future.

1. The standard account is Philip Woodruff, The Men Who Ruled India, especially the first volume, The Founders of Modern India (New York: St. Martin’s, 1954). How the system worked day by day is charmingly told in Sowing (New York: Harcourt Brace Jovanovich, 1962), volume one of the autobiography of Leonard Woolf (Virginia Woolf’s husband).

2. Alfred D. Chandler, Jr. has masterfully chronicled the process in his two books Strategy and Structure (Cambridge: MIT Press, 1962) and The Visible Hand (Cambridge: Harvard University Press, 1977)—surely the best studies of the administrative history of any major institution. The process itself and its results were presented and analyzed in two of my books: The Concept of the Corporation (New York: John Day, 1946) and The Practice of Management (New York: Harper Brothers, 1954).

A version of this article appeared in the January 1988 issue of Harvard Business Review.

Peter F. Drucker (November 19, 1909 – November 11, 2005) was an Austrian-born American management consultant, educator, and author whose writings contributed to the philosophical and practical foundations of the modern business corporation. He was also a leader in the development of management education, he invented the concept known as management by objectives, and he has been described as “the founder of modern management.”

© The Coming of the New Organization - Harvard Business Review - From the January 1988 Issue

Abraham Lincoln

Four score and seven years ago our fathers brought forth on this continent, a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal.

Now we are engaged in a great civil war, testing whether that nation, or any nation so conceived and so dedicated, can long endure. We are met on a great battle-field of that war. We have come to dedicate a portion of that field, as a final resting place for those who here gave their lives that that nation might live. It is altogether fitting and proper that we should do this.

But, in a larger sense, we can not dedicate—we can not consecrate—we can not hallow—this ground. The brave men, living and dead, who struggled here, have consecrated it, far above our poor power to add or detract. The world will little note, nor long remember what we say here, but it can never forget what they did here. It is for us the living, rather, to be dedicated here to the unfinished work which they who fought here have thus far so nobly advanced. It is rather for us to be here dedicated to the great task remaining before us—that from these honored dead we take increased devotion to that cause for which they gave the last full measure of devotion—that we here highly resolve that these dead shall not have died in vain—that this nation, under God, shall have a new birth of freedom—and that government of the people, by the people, for the people, shall not perish from the earth.

• Gettysburg Address
• The Gettysburg Address

by Carl Sandburg

A father sees his son nearing manhood.
What shall he tell that son?
“Life is hard; be steel; be a rock.”
And this might stand him for the storms
and serve him for humdrum monotony
and guide him among sudden betrayals
and tighten him for slack moments.
“Life is a soft loam; be gentle; go easy.”
And this too might serve him.
Brutes have been gentled where lashes failed.
The growth of a frail flower in a path up
has sometimes shattered and split a rock.
A tough will counts. So does desire.
So does a rich soft wanting.
Without rich wanting nothing arrives.
Tell him too much money has killed men
and left them dead years before burial:
the quest of lucre beyond a few easy needs
has twisted good enough men
sometimes into dry thwarted worms.
Tell him time as a stuff can be wasted.
Tell him to be a fool every so often
and to have no shame over having been a fool
yet learning something out of every folly
hoping to repeat none of the cheap follies
thus arriving at intimate understanding
of a world numbering many fools.
Tell him to be alone often and get at himself
and above all tell himself no lies about himself
whatever the white lies and protective fronts
he may use against other people.
Tell him solitude is creative if he is strong
and the final decisions are made in silent rooms.
Tell him to be different from other people
if it comes natural and easy being different.
Let him have lazy days seeking his deeper motives.
Let him seek deep for where he is born natural.
Then he may understand Shakespeare
and the Wright brothers, Pasteur, Pavlov,
Michael Faraday and free imaginations
Bringing changes into a world resenting change.
He will be lonely enough
to have time for the work
he knows as his own.

• A Father To His Son
• What is the theme of the poem father to his son by Carl Sandburg?

作者：陶淵明

有生必有死，早終非命促。
昨暮同為人，今旦在鬼錄。
魂氣散何之？枯形寄空木。
嬌兒索父啼，良友撫我哭。
得失不復知，是非安能覺？
千秋萬歲後，誰知榮與辱！
但恨在世時，飲酒不得足。

在昔無酒飲，今但湛空觴。
春醪生浮蟻，何時更能嘗？
餚案盈我前，親舊哭我傍。
欲語口無音，欲視眼無光。
昔在高堂寢，今宿荒草鄉。
荒草無人眠，極視正茫茫。
一朝出門去，歸來良未央。

荒草何茫茫，白楊亦蕭蕭！
嚴霜九月中，送我出遠郊。
四面無人居，高墳正嶕嶢。
馬為仰天鳴，風為自蕭條。
幽室一已閉，千年不復朝。
千年不復朝，賢達無奈何！
向來相送人，各自還其家。
親戚或餘悲，他人亦已歌。
死去何所道，托體同山阿。

Problem

4. Median of Two Sorted Arrays

Follow up

The overall run time complexity should be O(log (m+n)).

Java

extra space

On the basis of 88. Merge Sorted Array, this is not preferable method, just better than nothing.

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class Solution {
    public double findMedianSortedArrays(int[] nums1, int[] nums2) {
        final int m = nums1.length;
        final int n = nums2.length;
        if (m == 0)
            return (n & 1) == 1 ? nums2[n / 2] : (nums2[n / 2 - 1] + nums2[n / 2]) / 2.0;
        if (n == 0)
            return (m & 1) == 1 ? nums1[m / 2] : (nums1[m / 2 - 1] + nums1[m / 2]) / 2.0;
        int[] aux = merge(nums1, m, nums2, n);
        double median = ((m + n) & 1) == 1 ? aux[(m + n) / 2] : (aux[(m + n) / 2 - 1] + aux[(m + n) / 2]) / 2.0;
        return median;
    }

    private int[] merge(int[] nums1, int m, int[] nums2, int n) {
        int[] aux = new int[m + n];
        if (m == 0) {
            for (int i = 0; i < n; i++)
                aux[i] = nums2[i];
            return aux;
        } else {
            for (int i = 0; i < m; i++)
                aux[i] = nums1[i];
        }
        int idx = m + n - 1;
        m--;
        n--;
        for (; m >= 0 && n >= 0; ) {
            if (nums1[m] < nums2[n]) {
                aux[idx--] = nums2[n];
                n--;
            } else {
                aux[idx--] = nums1[m];
                m--;
            }
        }
        if (n >= 0) {
            for (int i = 0; i <= n; i++)
                aux[i] = nums2[i];
        }
        return aux;
    }
}

Submission Detail

• 2091 / 2091 test cases passed.
• Runtime: 2 ms, faster than 99.73% of Java online submissions for Median of Two Sorted Arrays.
• Memory Usage: 40.1 MB, less than 10.39% of Java online submissions for Median of Two Sorted Arrays.

Problem

125. Valid Palindrome

Java

Two pointers

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class Solution {
    public boolean isPalindrome(String s) {
        final int N = s.length();
        char c1, c2;
        for (int i = 0, j = N - 1; i < j; ) {
            c1 = s.charAt(i);
            c2 = s.charAt(j);
            if (!Character.isLetterOrDigit(c1))
                i++;
            else if (!Character.isLetterOrDigit(c2))
                j--;
            else if (Character.toLowerCase(c1) != Character.toLowerCase(c2)) {
                return false;
            } else {
                i++;
                j--;
            }
        }
        return true;
    }
}

Submission Detail

• 481 / 481 test cases passed.
• Runtime: 2 ms, faster than 98.05% of Java online submissions for Valid Palindrome.
• Memory Usage: 39 MB, less than 5.64% of Java online submissions for Valid Palindrome.

alphanumeric and binary

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class Solution {
    public boolean isPalindrome(String s) {
        s = s.replaceAll("[^A-Za-z0-9]", "").toLowerCase();
        int N = s.length();
        for (int i = 0; i < N / 2; i++)
            if (s.charAt(i) != s.charAt(N - 1 - i))
                return false;
        return true;        
    }
}

Submission Detail

• 480 / 480 test cases passed.
• Runtime: 883 ms, faster than 12.58% of Java online submissions for Valid Palindrome.
• Memory Usage: 47.3 MB, less than 18.43% of Java online submissions for Valid Palindrome.

JavaScript

Algorithms, 4th Edition

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/**
 * @param {string} s
 * @return {boolean}
 */
var isPalindrome = function(s) {
    let str = s.toLowerCase().replace(/[^a-zA-Z0-9]/g, "");
    const N = str.length;
    for (let i = 0; i < N / 2; i++) {
        if (str.charAt(i) != str.charAt(N - 1 - i))
            return false;
    }
    return true;    
};

Submission Detail

• 480 / 480 test cases passed.
• Runtime: 67 ms, faster than 96.43% of JavaScript online submissions for Valid Palindrome.
• Memory Usage: 44.2 MB, less than 82.85% of JavaScript online submissions for Valid Palindrome.

Two pointers

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/**
 * @param {string} s
 * @return {boolean}
 */
var isPalindrome = function(s) {
    const N = s.length;
    const ALPHANUMERIC = /^[a-z0-9]+$/i;
    let c1, c2;
    for (let i = 0, j = N - 1; i < j; ) {
        c1 = s.charAt(i);
        c2 = s.charAt(j);
        if (!ALPHANUMERIC.test(c1))
            i++;
        else if (!ALPHANUMERIC.test(c2))
            j--;
        else if (c1.toLowerCase() != c2.toLowerCase()) {
            return false;
        } else {
            i++;
            j--;
        }
    }
    return true;    
};

Submission Detail

• 480 / 480 test cases passed.
• Runtime: 102 ms, faster than 45.96% of JavaScript online submissions for Valid Palindrome.
• Memory Usage: 44.9 MB, less than 61.23% of JavaScript online submissions for Valid Palindrome.

Problem

234. Palindrome Linked List

Follow up

Could you do it in O(n) time and O(1) space?

Java

Break and reverse second half

© LeetCode – Palindrome Linked List (Java) - Java Solution 2 - Break and reverse second half

We can use a fast and slow pointer to get the center of the list, then reverse the second list and compare two sublists. The time is O(n) and space is O(1).

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/**
 * Definition for singly-linked list.
 * public class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode(int x) { val = x; }
 * }
 */
class Solution {
    public boolean isPalindrome(ListNode head) {
        if (head == null || head.next == null)
            return true;

        //find list center
        ListNode fast = head;
        ListNode slow = head;
        while (fast.next != null && fast.next.next != null) {
            fast = fast.next.next;
            slow = slow.next;
        }
        ListNode secondHead = slow.next;
        slow.next = null;

        //reverse second part of the list
        ListNode p1 = secondHead;
        ListNode p2 = p1.next;
        while (p1 != null && p2 != null) {
            ListNode temp = p2.next;
            p2.next = p1;
            p1 = p2;
            p2 = temp;
        }
        secondHead.next = null;

        //compare two sublists now
        ListNode p = (p2 == null ? p1 : p2);
        ListNode q = head;
        while (p != null) {
            if (p.val != q.val)
                return false;
            p = p.next;
            q = q.next;
        }
        return true;
    }
}

Submission Detail

• 26 / 26 test cases passed.
• Runtime: 1 ms, faster than 95.13% of Java online submissions for Palindrome Linked List.
• Memory Usage: 41.7 MB, less than 5.11% of Java online submissions for Palindrome Linked List.

extrap space

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/**
 * Definition for singly-linked list.
 * public class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode(int x) { val = x; }
 * }
 */
class Solution {
    public boolean isPalindrome(ListNode head) {
        List<ListNode> list = new ArrayList<ListNode>();
        while (head != null) {
            list.add(head);
            head = head.next;
        }
        int n = list.size();
        for (int i = 0; i < n / 2; i++) {
            if (list.get(i).val != list.get(n - 1 - i).val)
                return false;
        }
        return true;
    }
}

Submission Detail

• 26 / 26 test cases passed.
• Runtime: 2 ms, faster than 39.06% of Java online submissions for Palindrome Linked List.
• Memory Usage: 42.8 MB, less than 5.11% of Java online submissions for Palindrome Linked List.

Recursion

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/**
 * Definition for singly-linked list.
 * public class ListNode {
 *     int val;
 *     ListNode next;
 *     ListNode(int x) { val = x; }
 * }
 */
class Solution {
    public boolean isPalindrome(ListNode head) {
        if (head == null)
            return true;
        if (head.next == null)
            return true;
        ListNode secondLast = head;
        while (secondLast.next.next != null) {
            secondLast = secondLast.next;
        }
        if (head.val == secondLast.next.val) {
            secondLast.next = null;
            return isPalindrome(head.next);
        } else {
            return false;
        }
    }
}

Submission Detail

• 26 / 26 test cases passed.
• Runtime: 1406 ms, faster than 5.02% of Java online submissions for Palindrome Linked List.
• Memory Usage: 42.7 MB, less than 5.11% of Java online submissions for Palindrome Linked List.