Probability and Statistics

For [Luck] your science finds no measuring-rods; . . .
Her permutations never know truce nor pause

Dante, Commedia I: Inferno (transl. D. L. Sayers), Penguin, London, 1949. (Written early 14th century.)

In calculating entropy by molecular-theoretic methods, the word "probability" is often used in a sense differing from the way the word is defined in probability theory. In particular, "cases of equal probability" are often hypothetically stipulated when the theoretical methods employed are definite enough to permit a deduction rather than a stipulation.

A. Einstein, On a heuristic point of view concerning the production and transformation of light (1905).

. . . statistics is not a subset of mathematics, and calls for skills and judgement that are not exclusively mathematical. On the other hand, there is a large intersection between the two disciplines, statistical theory is serious mathematics, and most of the fundamental advances, even in applied statistics, have been made by mathematicians like R. A. Fisher.

Sir John Kingman, interview in the EMS Newsletter, March 2002.

The TV scientist who mutters sadly "The experiment is a failure: we have failed to achieve what we hoped for," is suffering mainly from a bad scriptwriter. An experiment is never a failure solely because it fails to achieve predicted results. An experiment is a failure only when it also fails adequately to test the hypothesis in question, when the data it produces don't prove anything one way or the other.

Robert M. Pirsig, Zen and the Art of Motorcycle Maintenance: An Inquiry into Values, Bodley Head, London, 1974.

Once Bose was teaching a class in which Somesh Das Gupta was the only Indian and all of a sudden, Bose said, "Only Hindus can understand Design of Experiments. You see, in Design of Experiments we work with the same structure in different forms: plots viewed as points, blocks viewed as lines, plot in a block as a point incident with a line and so on. The same thing the Hindus do, they worship the same God in different forms."

Bose memorial session, in Sankhya 54 (1992) (special issue devoted to the memory of Raj Chandra Bose), i-viii.

Codes and cryptography

(An early use of coding and cryptography)

When Lludd told his brother the purpose of his errand Llevelys said that he already knew why Lludd had come. Then they sought some different way to discuss the problem, so that the wind would not carry it off and the Corannyeid learn of their conversation. Llevelys ordered a long horn of bronze to be made, and they spoke through that, but whatever one said to the other came out as hateful and contrary. When Llevelys perceived there was a devil frustrating them and causing trouble he ordered wine to be poured through the horn to wash it out, and the power of the wine drove the devil out.

"Lludd and Llevelys", from The Mabinogion (earlier than 1325).

The code often used in the Arthurian Chancellery was the same which the Laconians had used in ancient Greece, known in their tongue as `skitale'. The Ephors had used it in their letters to ambassadors and generals. The method involved a rod of olive-wood about a span and a half in length, around which was obliquely wrapped a bit of skin; on this the message was written, from top to bottom, in such a way that when the skin was unrolled only detached letters appeared, and to read the message the recipient had to roll the skin again around a rod of the same dimensions.

Alvaro Cunqueiro, Merlin and Company (transl. Colin Smith), J. M. Dent, 1996.

I have written these words in code, made only for Your eyes.
Please take them, and read them right away!

Hafiz (transl. Thomas Rain Crowe)

 

The best way to win an online auction is to wait until the very last moment before making a bid in the hope no one else will have time to respond.

This strategy is already practised by many auction aficionados and is known as "sniping". Now a mathematical analysis by researchers from Seoul National University in Korea has confirmed that it gives the best chance of winning.

Byungnam Kahng and his colleague Inchang Yang analysed more than half a million auctions on the US and Korean versions of the auction site eBay in an effort to determine the best strategy for bidding. They saw a mathematical pattern in the bidding behaviour of bidders and derived a simple power-law equation to describe this.
Best probability

This power law reflects the fact that bids become more frequent as the end of an auction approaches. The researchers used this equation to determine the best time to make a winning bid.

They conclude that sniping is the best approach. "Bidding at the last moment is a rational and effective strategy to win in an eBay auction," the researchers write in the July edition of the journal Physical Review E.

The research builds on a 2002 paper in the American Economic Review by economists Al Roth from Harvard University in the US and Axel Ockenfels from the University of Cologne in Germany.
Time interval

"We noted that the way bids are distributed over the duration of an internet auction obeys what is known as a power law," Roth told New Scientist. This law remains describes the distribution of bids regardless of the time interval examined, Roth says.

Many eBay pundits already claim that sniping is the most efficient strategy: it gives others little time to respond with a higher bid and also lulls early bidders into a false sense of security about how much interest there is. The strategy only applies online, however. Real-life auctioneers always offer all bidders a final chance to make an offer.

Even in online auctions, Roth points out that sniping takes extra effort, and may not always be worth it. "If you're sitting at your computer and have time to be a sniper, then do that," he says. "But if you have to be at work, or the auction ends after your bedtime, just put in a sensible bid and sleep the sleep of the just."

Journal references: Physical Review E (vol 73, p 067101), American Economic Review (vol 92, p 1093)

From NBER

 

"Countries with successful stock markets mandate that shareholders receive the information they need and the power to act - including both voting and litigation - on this information? The empirical results further suggest that an effective strategy of regulating large self-dealing transactions is to combine full disclosure of such transactions with the requirement of approval by disinterested shareholders."

Investor expropriation -- also known as self-dealing or tunneling -- takes such forms as excessive executive compensation and perquisites, transfer pricing, insider trading, self-serving transactions, and outright theft. In The Law and Economics of Self-Dealing (NBER Working Paper No. 11883) by Simeon Djankov, Rafael LaPorta, Florencio Lopez-de-Silanes, and Andrei Shleifer, the focus is on the kinds of cases in which controllers of companies make deals that may benefit them at the expense of other investors, but in which -- unlike in the Enron and Parmalat scandals -- the controllers observe the laws regarding disclosure and approval procedures. One of the primary questions the researchers ask is: if a controlling shareholder wants to enrich himself without breaking the law, how difficult is it for minority shareholders either to thwart the deal or, if it is carried out, to recover damages?

In order to determine which nations best protect minority shareholders from such abuses - and to ascertain how those protections affect a nation's financial development - the researchers create a hypothetical scenario in which a corporate officer who owns large portions of two companies engages in a self-dealing sales transaction between the firms that benefits the officer via an inflated payment. They presented this scenario to members of Lex Mundi, an association of international law firms that operates in 108 countries. The lawyers were asked to describe the legal barriers in their countries to getting away with such a transaction.

Lawyers from 102 countries provided complete answers to the researchers' questionnaire. The researchers conducted follow-up inquiries, and the sample they used for this paper was based on the responses of 72 lawyers who confirmed the validity of the aggregate data.

The lawyers were asked to describe the minimum legal requirements in force in May 2003 regarding who approves a transaction such as described in the hypothetical scenario; what needs to be disclosed to the board of directors, the stock exchange, and the regulators; the duties of corporate officers, directors, and controlling shareholders; how the transaction's validity could be challenged; what plaintiffs would need to prove to recover damages; access to information; fines and other penalties, and the like. Based on the data, the authors reached several conclusions. Primary among these is that the index for minority shareholder protection is sharply higher in common law countries, such as the United Kingdom (which ranks fifth on the anti-self-dealing index), than in civil law countries, such as Italy (forty-second on the index). This is consistent with earlier studies that concluded that investor protection is higher in common law countries than in civil law ones.

The researchers also were interested in how the regulation of self-dealing might relate to the development of a nation's stock market. It was also clear that the index is a statistically significant and economically strong predictor of a variety of measures of stock market development across countries. Foremost among these measures is the ratio of stock market capitalization to GDP. The index results support earlier findings that demonstrated that common law countries have much more valuable stock markets relative to their GDPs than do civil law countries. The results also show that theoretical measures of investor protection are closely linked to financial development.

The researchers could not isolate a single "best" measure of shareholder protection, but concluded that measures of shareholder protection from securities laws appear to work best in terms of predicting stock market outcomes; the data for this, however, was available for only 49 countries. These measures moreover are particularly appropriate for studies of protection of investors buying securities, as opposed to corporate governance per se.

The researchers say that perhaps the most basic conclusion from their data is that laissez-faire - having no public regulation or oversight at all - is certainly not conducive to developing financial markets. Countries with successful stock markets mandate that shareholders receive the information they need and the power to act - including both voting and litigation - on this information.

The empirical results further suggest that an effective strategy of regulating large self-dealing transactions is to combine full disclosure of such transactions with the requirement of approval by disinterested shareholders. Similarly, the results suggest that ongoing disclosure of self-dealing transactions, combined with a relatively easy burden of litigation placed on the aggrieved shareholders, also benefits stock market development.

Finally, the evidence suggests that the government's power to impose fines and imprisonment for self-dealing transactions that meet disclosure and approval requirements does not benefit stock market development. The authors stress that this is a narrow conclusion, since it does not address the importance of public enforcement in situations where self-dealing transactions are concealed, as in the cases of Enron and Parmalat. To avoid self-dealing, however, it appears best to rely on extensive disclosure, approval by disinterested shareholders and private enforcement.

Jul 20th 2006
From The Economist print edition

Evolutionary economics is surviving, but not thriving

     BEFORE he turned to the bigger fish that occupy the White House, Paul Krugman, an economist at Princeton University and a polemicist for the New York Times, enjoyed nothing more than frying the cranks, impostors and other forms of pondlife he found outside the mainstream of economics. In 1997 he singled out the purveyors of so-called “bionomics”. Bionomics argued that economics was hopelessly wedded to the principles of mechanics, and should instead borrow ideas from evolutionary biology. After all, it declared, “a modern market economy is like a tropical rainforest”.

      Such heresy was not new. In the preface to his “Principles of Economics”, Alfred Marshall, one of the founders of neoclassical economics, declared that “The Mecca of the economist lies in economic biology”. But Mr Krugman showed little mercy. Arguing that his victims knew little about either economics or evolution, he dismissed their work as “biobabble”.

        Undeterred, Eric Beinhocker, of the McKinsey Global Institute, has undertaken his own 500-page haj, entitled “The Origin of Wealth: Evolution, Complexity, and the Radical Remaking of Economics”. In places (such as its headline call for a “paradigm shift” in economics) the book may irk Mr Krugman and other gatekeepers of the profession. But it is good enough, and scholarly enough, to warrant their attention rather than their scorn.

        Indeed, Mr Beinhocker is himself critical of “loose analogising” between biology and economics. The economy, Mr Beinhocker says, is not “like” a rainforest. Rather, economies and ecosystems are both evolutionary systems in their own right. The evolutionary formula—variation, selection and replication—is a formal, “all-purpose” principle, which can perform its magic equally well in either domain.

       How, then, does the principle go to work on the stuff of economics? The business plan is the economic equivalent of DNA, and the enterprise its host in the world. Mr Beinhocker envisages a Borgesian library of every conceivable plan, from farming wheat in Lebanon in 8500BC to manufacturing “supernano neural-blastule tubes” that have yet to be invented. Evolution provides a remarkably effective way for the economy as a whole to scour this vast library for viable strategies, finding “needles of good design in haystacks of possibility,” as Daniel Dennett, a philosopher, has put it.

        Countless firms, busily tinkering with their business models, provide a source of variation. The market itself—what gets bought and what gets left on the shelf—imposes a powerful form of selection. And although business plans cannot reproduce, successful ones do command a growing share of the economy's resources, as companies expand on the back of them and rivals copy them.

       Such a process succeeds at the level of the economy as a whole, while remaining coldly indifferent to the fate of individual firms within it. Indeed, Mr Beinhocker cites research showing that progress owes more to new firms replacing old than to incumbent firms renewing themselves. This is not a comfortable conclusion for businessmen who might buy this book. But as a McKinsey man, Mr Beinhocker cannot resist offering a few tips to executives who are not content to be “experimental grist for the evolutionary mill”.

         Such ideas are less threatening to economists: Milton Friedman evoked the notion of market selection over 50 years ago. But more unsettling than the ideas are the techniques and tools Mr Beinhocker advocates. He argues that economists should abandon blackboard deduction in favour of computer simulation. The economists he likes do not “solve” models of the economy—deducing the prices and quantities that will prevail in equilibrium—rather they grow them “in silico”, as he puts it.

      An early example is the sugarscape simulation done in 1995 by Joshua Epstein and Robert Axtell, of the Brookings Institution. On a computer-generated landscape, studded with “sugar” mountains, they scattered a variety of simple, sugar-eating creatures, which compete for this precious commodity. Some creatures move faster than others, some see farther, and some burn sugar at a higher metabolic rate than their rivals.     

 The pandas of economics

        Surprisingly, the results of their myopic lives can be gripping. Even simple rules of behaviour result in collective patterns that are impossible to foresee yet easy to recognise. The sugarscape, for example, is quickly beset by a division between haves and have-nots, which bears a strong statistical resemblance to the distribution of income in real economies. These macro-results cannot be deduced from the micro-rules simulators write. Rather, they emerge from the interactions of the creatures in the model, just as “wetness” emerges from the interaction of water molecules, rather than being a property of the molecule itself.

       Such simulations may be unpredictable, but they are nonetheless understandable, Mr Beinhocker insists. By toying with different parameters, such as metabolic rates or the height of the sugar mountains, analysts can learn how to “tune” their model to generate different results. This understanding may be more valuable than a forecast, he argues. But whatever such enlightenment is worth, it is not easy to communicate to others. The revelations contained in a deductive proof or theorem are easy to pass on: they leave a set of footprints for other people to follow, making it easy for a theory to persuade and convert. For simulations, by contrast, “the only way to see what happens is to run the model and evolve it—there is no shortcut.”

       For the moment, then, evolutionary economics remains a niche pursuit, not the intellectual revolution Mr Beinhocker predicts and hopes for. It is ironic that evolutionists, of all people, should have such trouble reproducing themselves.

 

Algebra

You also get dramatic advances when you spot that you can leave out part of the problem. Algebra, for instance (and hence the whole of computer programming), derives from the realisation that you can leave out all the messy, intractable numbers.

Douglas Adams, The Salmon of Doubt, Macmillan, London, 2002.

Whatever you have to do with a structure-endowed entity Sigma try to determine its group of automorphisms . . . You can expect to gain a deep insight into the constitution of Sigma in this way.

H. Weyl, Symmetry, Princeton U. P. 1952.

Curiously enough, the twelve-tone system has no zero in it. Given a series: 3, 5, 2, 7, 10, 8, 11, 9, 1, 6, 4, 12 and the plan of obtaining its inversion by numbers which when added to the corresponding ones of the original series will give 12, one obtains 9, 7, 10, 5, 2, 4, 1, 3, 11, 6, 8 and 12. For in this system 12 plus 12 equals 12. There is not enough of zero in it.

John Cage, Eric Satie, from Silence: Lectures and Writings, Calder and Boyars, 1968.

There is a very famous joke about Bose's work in Giridh. Professor Mahalanobis wanted Bose to visit the paddy fields and advise him on sampling problems for the estimation of yield of paddy. Bose did not very much like the idea, and he used to spend most of the time at home working on combinatorial problems using Galois fields. The workers of the ISI used to make a joke about this. Whenever Professor Mahalanobis asked about Bose, his secretary would say that Bose is working in fields, which kept the Professor happy.

Bose memorial session, in Sankhya 54 (1992) (special issue devoted to the memory of Raj Chandra Bose), i-viii.

Langvetningur: . . . There are special spots here where the All-thought is manifest in the elements themselves, places where fire has become earth, earth become water, water become air, and air become spirit.
Embi: I thought it was the other way round.
The Langvetningur is of the old Teachers' College and learned algebra from the Danish book by Pedersen: The order of the factors is immaterial.

Halldór Laxness, Under the Glacier (1968) (transl. Magnus Magnusson 1972).

Geometry

"It's a fact I've continually observed in the witness box," he said abstractedly, "that nine people out of ten, off their own subject, are incapable of lucidity, whereas on their own subject they can be as direct as a straight line before Einstein . . ."

--oo--

". . . I think in a line -- but there is the potentiality of the plane." This perhaps was what great art was -- a momentary apprehension of the plane at a point in the line.

Charles Williams, Many Dimensions, 1931.

"One of the virtues of this simple but at the same time complex design", said Bembel Rudzak, "this design in which we see the continually reciprocating action of unity and multiplicity, is that it suits the apparent action to the mind of the viewer: those who look outward see the outward pre-eminent; those who look inward see the inward."

--oo--

"There is transitive motion and there is intransitive motion: the motion of a galloping horse is transitive, it passes through our field of vision and continues on to where it is going; the motion in a tile pattern is intransitive, it does not pass, it moves but it stays in our field of vision. It arises from stillness, and I should like to think about the point at which stillness becomes motion. Another thing I should like to think about is the point at which pattern becomes consciousness."

--oo--

"When a pattern shows itself in tiles or on paper or in your mind and says, 'This is the mode of my repetition; in this manner I extend myself to infinity', it has already done so, it has already been infinite from the very first moment of its being; the potentiality and the actuality are one thing. If two and two can be four then they actually are four, you can only perceive it, you have no part in making it happen by writing it down in numbers or telling it out in pebbles."

Russell Hoban, Pilgermann, Pan, London, 1984.

In Plane Geometry that afternoon, I got into an argument with Mr Shull, the teacher, about parallel lines. I say they have to meet. I'm beginning to think everything comes together somewhere.

William Wharton, Birdy, Alfred A. Knopf, New York, 1979.

Voyez-vous cet oeuf. C'est avec cela qu'on renverse toutes les écoles de théologie, et tous les temples de la terre.

Denis Diderot, Le rêve de d'Alembert

What? Will the line stretch out to the crack of doom?

William Shakespeare, Macbeth

An active line on a walk moving freely, without goal. A walk for a walk's sake.

Paul Klee, Pedagogical Sketchbook (1925)

 

Combinatorics

Journalists say that when a dog bites a man, that is not news, but when a man bites a dog, that is news . . . Thanks to the mathematics of combinatorics, we will never run out of news.

Steven Pinker, How the Mind Works, W. W. Norton, 1997.

Net. Anything reticulated, or decussated at equal distances, with interstices between the intersections.

Samuel Johnson, Dictionary of the English Language (1775)

. . . nets, grids, and other types of calculus . . .

Alan Watts, The Book (1972)

This method of deduction . . . is often called "combinatory". Its usefulness is not exhausted at this stage, but it does even at the outset lead to some valuable conclusions . . .

John Chadwick, The Decipherment of Linear B, CUP, Cambridge, 1958.

These results, which are partly combinatorial and partly real mathematics . . .

A. Joseph, lecture to the London Mathematical Society, Oxford, 22 February 1997.

At the end of the thirteenth century, Raymond Lully was prepared to solve all arcana by means of an apparatus of concentric, revolving disks of different sizes, divided into sectors with Latin words; John Stuart Mill, at the beginning of the nineteenth, feared that some day the number of musical combinations would be exhausted and there would be no place in the future for indefinite Webers and Mozarts; Kurd Lasswitz, at the end of the nineteenth, toyed with the staggering fantasy of a universal library which would register all he variations of the twenty-odd orthographical symbols, in other words, all that it is given to express in all languages. Lully's machine, Mill's fear and Lasswitz's chaotic library can be the subject of jokes, but they exaggerate a propensity which is common: making metaphysics and the arts into a kind of play with combinations.

Jorge Luis Borges, Labyrinths, New Directions, New York, 1964.

. . . combinatorics, a sort of glorified dice-throwing . . .

Robert Kanigel, The Man who Knew Infinity: A Life of The Genius Ramanujan, Scribner, New York, 1991.

. . . the branch of topology we now call "graph theory" . . .

Stuart Hollingdale, Makers of Mathematics, Penguin, London, 1989.

More and more I'm aware that the permutations are not unlimited.

Russell Hoban, Turtle Diary, Jonathan Cape, London, 1975.

We have not begun to understand the relationship between combinatorics and conceptual mathematics.

Jean Dieudonné, A Panorama of Pure Mathematics: As seen by N. Bourbaki, Academic Press, New York, 1982.

The emphasis on mathematical methods seems to be shifted more towards combinatorics and set theory - and away from the algorithm of differential equations which dominates mathematical physics.

J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, 1944.

The process is directed always towards analysing and separating the material into a collection of discrete counters, with which the detached intellect can make, observe and enjoy a series of abstract, detailed, artificial patterns of words and images (you may be reminded of the New Criticism) . . .

Elizabeth Sewell, Lewis Carroll and T. S. Eliot as Nonsense Poets, in Neville Braybrooke (ed.), T. S. Eliot: A Symposium for his Seventieth Birthday, Hart-Davies, London, 1958.

Some of the particulars recommended by Abulafia contributed to the aura of magic surrounding Kabbalah: the best hour for meditative permutations (known as tzeruf) was midnight. The meditator was to light many candles, wear phylacteries and a prayer shawl, and write out the permutations of the alphabet with ever increasing speed. The resulting ecstatic state accompanied by the desire of the soul to leave the body could be so powerful that there was even the possibility of death. At the peak of ecstatic experience there would be a rush of unintelligible language and the kabbalist had to envision a surrounding circle of angels who could help to decipher the divine message. It was the sheer force of the letters themselves which brought forth the meaning, since the only link between the Sephirot of non-verbal Wisdom and verbal Intelligence was through the letters of the alphabet.

Johanna Drucker, The Alphabetic Labyrinth: The Letters in History and Imagination, Thames and Hudson, London, 1995.

Lord of sequence and design

Richard G. Jones, "The Earth is the Lord's", Hymns for Today 33.

Television? The word is half Latin and half Greek. No good can come of it.

C. P. Scott (attr.)

There is no problem in all mathematics that cannot be solved by direct counting.

Ernst Mach, quoted by A. T. Benjamin, G. M. Levin, K. Mahlburg and J. J. Quinn, Random approaches to Fibonacci identities, Amer. Math. Monthly 107 (2000), p.511.

While [Maynard Smith] believed that a Marxist in science could take a lot of different positions, he saw the need for "some kind of substitute for Hegelian dialectics . . . some kind of concept that in dynamical systems there are going to be sudden breaks and thresholds and transformations, and so on". He added that, in his opinion, "today we really do have a mathematics for thinking about complex systems and things which undergo transformations from quantity into quality". Here he saw Hopf bifurcations and catastrophe theory as really nothing other than a change of quantity into quality in a dialectical sense.

Ullica Segerstrale, Defenders of the Truth: The Battle for Science in the Sociobiology Debate and Beyond, Oxford University Press, Oxford, 2000.

[Roger] Lyndon produces elegant mathematics and thinks in terms of broad and deep ideas. . . I once asked him whether there was a common thread to the diverse work in so many different fields of mathematics, he replied that he felt the problems on which he had worked had all been combinatorial in nature.

K. I. Appel, in Contributions to Group Theory (ed. K. I. Appel, J. G. Ratcliffe and P. E. Schupp), AMS, Providence, 1984.

The miserable wasteland of multidimensional space was first brought home to me in one gruesome solo lunch hour in one of MIT's sandwich shops. "Wholewheat, rye, multigrain, sourdough or bagel? Toasted, one side or two? Both halves toasted, one side or two? Butter, polyunsaturated margarine, cream cheese or hoummus? Pastrami, salami, lox, honey cured ham or Canadian bacon? Aragula, iceberg, romaine, cress or alfalfa? Swiss, American, cheddar, mozzarella, or blue? Tomato, gherkin, cucumber, onion? Wholegrain, French, English or American mustard? Ketchup, piccalilli, tabasco, soy sauce? Here or to go?" . . . Comparative genomics and structural biochemistry say that the building blocks of living organisms are few, modular, and combinatorial. Proteins comprise a few hundred protein structural domains; nucleic acids are simpler, with a few tens of structural domains and regulatory binding sites for sequence-specific protein domains. The combinations of these elements are vastly larger than any universe we can comprehend, but a large proportion of these should work, when given familiar network architectures similar to those of existing organisms. Why waste time marking out the hyperspace of possibilities when we already know where the good stuff is?

Review by Myles Aston of Life without Genes: the History and Future of Genomes by Adrian Woolfson, in the Balliol College Annual Record 2001.

I have to admit that he was not bad at combinatorial analysis -- a branch, however, that even then I considered to be dried up.

Stanislaw Lem, His Master's Voice (1968).

Only connect!

E. M. Forster, ``Howards End'' (1910)

Logic and set theory

Reasoning and logic are to each other as health is to medicine, or - better - as conduct is to morality. Reasoning refers to a gamut of natural thought processes in the everyday world. Logic is how we ought to think if objective truth is our goal - and the everyday world is very little concerned with objective truth. Logic is the science of the justification of conclusions we have reached by natural reasoning. My point here is that, for such natural reasoning to occur, consciousness is not necessary. The very reason we need logic at all is because most reasoning is not conscious at all.

Julian Jaynes, The Origin of Consciousness in the Breakdown of the Bicameral Mind, Houghton Mifflin, New York, 1976.

Set theory has a dual role in mathematics. In pure mathematics, it is the place where questions about infinity are studied. Although this is a fascinating study of permanent interest, it does not account for the importance of set theory in applied areas. There the importance stems from the fact that set theory provides an incredibly versatile toolbox for building mathematical models of various phenomena.

Jon Barwise and Lawrence Moss, Vicious Circles: On the Mathematics of Non-Wellfounded Phenomena, CSLI, Stanford, 1996.

The Naturalist theory of possibility now to be advanced will be called a Combinatorial theory. It traces the very idea of possibility to the idea of the combinations -- all the combinations -- of given, actual elements.

--oo--

Set theory is important . . . because mathematics can be exhibited as involving nothing but set-theoretical propositions about set-theoretical entities.

--oo--

Mathematics . . . is concerned with a wider domain than that domain which it is the object of the natural sciences to describe and categorize. The natural sciences are concerned with the actual world. Mathematics is concerned with "all possible worlds".

--oo--

Philosophers have not found it easy to sort out sets . . .

D. M. Armstrong, A Combinatorial Theory of Possibility, Cambridge University Press, Cambridge, 1989.

The standard "foundation" for mathematics starts with sets and their elements. It is possible to start differently, by axiomatising not elements of sets but functions between sets. This can be done by using the language of categories and universal constructions.

--oo--

. . . in one sense a foundation is a security blanket: If you meticulously follow the rules laid down, no paradoxes or contradictions will arise. In reality there is now no guarantee of this sort of security . . .

--oo--

. . . the membership relation for sets can often be replaced by the composition operation for functions. This leads to an alternative foundation for Mathematics upon categories -- specifically, on the category of all functions. Now much of Mathematics is dynamic, in that it deals with morphisms of an object into another object of the same kind. Such morphisms (like functions) form categories, and so the approach via categories fits well with the objective of organizing and understanding Mathematics. That, in truth, should be the goal of a proper philosophy of Mathematics.

S. MacLane, Mathematics: Form and Function, Springer, New York, 1986.

"Contrariwise," continued Tweedledee, "if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic."

Lewis Carroll, Through the Looking-Glass, and what Alice found there, 1875.

If, like the truth, falsehood had only one face, we should know better where we are, for we should then take the opposite of what a liar said to be the truth. But the opposite of the truth has a hundred thousand shapes and a limitless field.

Montaigne, Essays, I, 9.

During a counterpoint class at UCLA, Schoenberg sent everybody to the blackboard. We were to solve a particular problem he had given and to turn around when finished so that he could check on the correctness of the solution. I did as directed. He said, "That's good. Now find another solution." I did. He said, "Another." Again I found one. Again he said, "Another." And so on. Finally, I said, "There are no more solutions." He said, "What is the principle underlying all of the solutions?"

John Cage, Four Statements on the Dance, from Silence: Lectures and Writings, Calder and Boyars, 1968.

In the Middle Ages the problem of infinity was of interest mainly in connection with arguments about whether the set of angels who could sit on the head of a pin was infinite or not.

N. Ya. Vilenkin, Stories about Sets, Academic Press, New York, 1968.

[Infinity] is . . . the staple of the mystic contemplation of reality - "make me one with everything" as the mystic said to the hamburger vendor

John D. Barrow, The Infinite Book, Vintage, 2005.

Inside the museums, infinity goes up on trial. Voices echo, "This is what salvation must be like, after a while."

Bob Dylan, "Visions of Johanna"

Why had not the Public Prosecutor asked him: "Defendant Rubashov, what about the infinite?" He would not have been able to answer -- and there, there lay the real source of his guilt . . . Could there be a greater?

Arthur Koestler, Darkness at Noon, quoted in Tiresias, Notes from Overground, Paladin, London, 1984.

In Geometry (which is the only science that it hath pleased God hitherto to bestow on mankind) men begin at settling the significations of their words; which . . . they call Definitions

Thomas Hobbes, Leviathan

To be is to be the value of a variable.

Willard Van Ormond Quine, "On What There Is", 1948.

To every thing there is a season, and a time to every purpose under the heaven:
A time to be born, and a time to die; a time to plant, and a time to pluck up that which is planted;
A time to kill, and a time to heal; a time to break down, and a time to build up;
A time to weep, and a time to laugh; a time to mourn, and a time to dance;
A time to cast away stones, and a time to gather stones together; a time to embrace, and a time to refrain from embracing;
A time to get, and a time to lose; a time to keep, and a time to cast away;
A time to rend, and a time to sew; a time to keep silence, and a time to speak;
A time to love, and a time to hate; a time of war, and a time of peace.

Ecclesiastes, Chapter 3

Education

The difference between principles and rules is this, that the former are persuasions and the latter are commands. There is great deal of difference between carrying 2 for such and such a reason, and carrying 2 because you must carry 2. You see boys that can cover reams of paper with figures, and do it with perfect correctness too; and at the same time, can give you not a single reason for any part of what they have done. Now this is really doing very little. The rule is soon forgotten, and then all is forgotten.

William Cobbett, From Petersfield to Kensington, Rural Rides (ed. Ian Dyck), Penguin Classics 2001. (First published 1830)

I am a profound believer that the proper, and therefore the exact study, even of so humble a subject as elementary Arithmetic is a necessary, in fact the necessary, first step towards the culture of mathematics; and although it is not given to everyone to be a mathematician any more than to be an artist, a musician, or a poet, yet just as every normal educated man or woman is rightly expected to have some fairly correct notions on art, on poetry, and on music, so some reasonable, rational and exact knowledge of numbers and their properties is to be regarded, independent of all commercial and technical applications, as an essential part of the culture that all normal educated persons should have acquired.

J. E. A. Steggall, talk to the Mathematical Association, 1914, quoted in Hilary Mason, "J. E. A. Steggall: Teaching mathematics 1880-1933", BSHM Bulletin 1 (2004), 27-38.

. . . mathematics is not best learned passively; you don't sop it up like a romance novel. You've got to go out to it, aggressive, and alert, like a chess master pursuing checkmate.

Robert Kanigel, The Man who Knew Infinity: A Life of The Genius Ramanujan, Scribner, New York, 1991.

Mathematics makes a nice distinction between the usually synonymous terms "elementary" and "simple", with "elementary" taken to mean that not very much mathematical knowledge is needed to read the work and "simple" to mean that not very much mathematical ability is needed to understand it. In these terms we think the content is often elementary but in places not so very simple. The reader should expect to make use of pen and paper in many places; mathematics is not a spectator sport!

Julian Havel, Gamma: Exploring Euler's Constant, Princeton University Press, Princeton, 2003.

Whoever then has the effrontery to study physics while neglecting mathematics, should know from the start that he will never make his entry through the portals of wisdom.

Thomas Bradwardine

Numbers

"Nought usually comes at the beginning," Ralph said.
"Not necessarily," said Sibyl. "It might come anywhere. Nought isn't a number at all. It's the opposite of number."
Nancy looked up from the cards. "Got you, aunt," she said. "What about ten? Nought's a number there -- it's part of ten."
"Well, if you say that any mathematical arrangement of one and nought really makes ten -- " Sibyl smiled. "Can it possibly be more than a way of representing ten?"

Charles Williams, The Greater Trumps, Victor Gollancz, London, 1932.

How many roads must a man walk down before you can call him a man?
How many seas must the white dove sail before she sleeps in the sand?
How many times must the cannonballs fly, before they're forever banned?
The answer, my friend, is blowin' in the wind
The answer is blowin' in the wind.

Bob Dylan, "Blowin' in the Wind" (1962)

What could be more general than 2, which can represent two galaxies or two pickles, or one galaxy plus one pickle (the mind doth boggle), or just 2 gently bobbing -- where? It, like God, is an "I am" and many have thought that it must be a precipitate of ultimate reality.

Alfred W. Crosby, The Measure of Reality: Quantification and Western Society, 1250-1600, Cambridge University Press, Cambridge, 1997.

I have often admired the mystical way of Pythagoras, and the secret magic of numbers.

Sir Thomas Browne, Religio Medici, I, 12.

There is divinity in odd numbers, either in nativity, chance or death.

Shakespeare, The Merry Wives of Windsor, V, 1.

"I count a lot of things that there's no need to count," Cameron said. "Just because that's the way I am. But I count all the things that need to be counted."

Richard Brautigan, The Hawkline Monster: A Gothic Western, Picador, London, 1976.

. . . mathematical knowledge . . . is, in fact, merely verbal knowledge. "3" means "2+1", and "4" means "3+1". Hence it follows (though the proof is long) that "4" means the same as "2+2". Thus mathematical knowledge ceases to be mysterious.

Bertrand Russell, History of Western Philosophy, George Allen and Unwin, London, 1961.

The man who has learned that three plus one are four doesn't have to go through a proof of that assertion with coins, or dice, or chess pieces, or pencils. He knows it, and that's that. He cannot conceive a different sum. There are mathematicians who say that three plus one is a tautology for four, a different way of saying "four" . . . If three plus one can be two, or fourteen, then reason is madness.

Jorge Luis Borges, "Blue Tigers", in Shakespeare's Memory (1983), transl. Andrew Hurley, Penguin, 1999.

"Can you do Addition?" the White Queen asked. "What's one and one and one and one and one and one and one and one and one and one?"
"I don't know," said Alice. "I lost count."
"She ca'n't do Addition," the Red Queen interrupted.

Lewis Carroll, Through the Looking-Glass, and what Alice found there, 1875.

We have learned to pass with such facility from cardinal to ordinal number that the two aspects appear to us as one. To determine the plurality of a collection, that is, its cardinal number, we do not bother anymore to find a model collection with which we can match it -- we count it. And to the fact that we have learned to identify the two aspects of number is due our progress in mathematics . . . The operations of arithmetic are based on the tacit assumption that we can always pass from any number to its successor, and this is the essence of the ordinal concept. And so matching by itself is incapable of creating an art of reckoning. Without our ability to arrange things in ordered succession little progress could have been made. Correspondence and succession, the two principles that permeate all mathematics -- nay, all realms of exact thought -- are woven into the very fabric of our number system.

Tobias Dantzig, Number: The Language of Science, Macmillan, New York, 1930.

You see, the chemists have a complicated way of counting: instead of saying "one, two, three, four, five protons", they say, "hydrogen, helium, lithium, beryllium, boron."

Richard Feynman, QED: The Strange Theory of Light and Matter, Princeton U.P., 1985.

The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic.

G. F. Leibniz, quoted by Oliver Sacks, The Man who Mistook his Wife for a Hat, Duckworth, London, 1985.

The Way begets one; one begets two; two begets three; three begets the myriad creatures.

Lao Tse, Tao Te Ching.

All of mathematics can be deduced from the sole notion of an integer; here we have a fact universally acknowledged today.

E. Borel, Contribution a l'analyse arithmetique du continu, Oeuvres 3, 1439-1485.

Although the idea that we have no bananas is unlikely to be a new one, or one that is hard to grasp, the idea that no bananas, no sheep, no children, no prospects are really all the same, in that they have the same numerosity, is a very abstract one.

Brian Butterworth, The Mathematical Brain, Macmillan, London, 1999.

Behold the One in all things; it is the second that leads you astray.

Kabir, quoted in Aldous Huxley, The Perennial Philosophy, 1944.

Huxley adds:

For example, how significant it is that in the Indo-European languages, as Darmsteter has pointed out, the root meaning "two" should connote badness. The Greek prefix dys- (as in dyspepsia) and the Latin dis- (as in dishonorable) are both derived from "duo". The cognate bis- gives a pejorative sense to such modern French words as bévue ("blunder", literally "two-sight"). Traces of that "second which leads you astray" can be found in "dubious", "doubt", and Zweifel -- for to doubt is to be double-minded. Bunyan has his Mr. Facing-both-ways, and modern American slang its "two-timers". Obscurely and unconsciously wise, our language confirms the findings of the mystics and proclaims the essential badness of division -- a word, incidentally, in which our old enemy "two"makes another decisive appearance.

In the history of the concept of number number has been adjective (three cows, three monads) and noun (three, pure and simple), and now ..., number seems to be more like a verb (to triple).

Barry Mazur, Imagining Numbers, Penguin, London, 2003.

 

Proofs

A fine collection of quotations about proof in mathematics, assembled by David Lingard, appears in the BSHM Bulletin 1 (2004), 63-66. I can't find them on the Web, but here, as a sample, are two conflicting views from Riemann and Gauss, quoted by Imre Lakatos in Proofs and Refutations:

Georg Bernhard Riemann: "If only I had the theorems! Then I should find the proofs easily enough."

Karl Friedrich Gauss: "I have had my results for a long time, but I do not yet know how to arrive at them."

A non-symbolic argument or proof can be quite rigorous when given for a particular value of the variable; the conditions for rigor are that the particular value of the variable should be typical, and that a further generalization to any value should be immediate.

R. J. Gillings, Mathematics in the Time of the Pharaohs, MIT Press, Cambridge, 1972.

A proof only becomes a proof after the social act of "accepting it as a proof".

Yu. I. Manin

I think it is said that Gauss had ten different proofs for the law of quadratic reciprocity. Any good theorem should have several proofs, the more the better. For two reasons: usually, different proofs have different strengths and weaknesses, and they generalise in different directions -- they are not just repetitions of each other.

Sir Michael Atiyah, interview in European Mathematical Society Newsletter, September 2004.

Mathematics, however, is, as it were, its own explanation; this, although it may seem hard to accept, is nevertheless true, for the recognition that a fact is so is the cause upon which we base the proof.

Girolamo Cardano, The book of my life (transl. Jean Stoner), New York Review Books, New York, 2002.

Axioms

A choice of axioms is not purely a subjective task. It is usually expected to achieve some definite aim -- some specific theorem or theorems are to be derivable from the axioms -- and to this extent the problem is exact and objective. But beyond this there are always other important desiderata of a less exact nature: the axioms should not be too numerous, their system is to be as simple and transparent as possible, and each axiom should have an immediate intuitive meaning by which its appropriateness can be judged directly.

J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, 1944.

To illustrate the strong feelings of independence which, as a part of the old traditions, are so characteristic of the English spirit, I should like to tell how Hardy and Littlewood, when they planned and began their far-reaching and intensive team work, still had some misgivings about it because they feared that it might encroach on their personal freedom, so vitally important to them. Therefore, as a safety measure, . . . they amused themselves by formulating some so-called `axioms' for their mutual collaboration. There were in all four such axioms.

The first of them said that, when one wrote to the other, . . ., it was completely indifferent whether what they wrote was right or wrong . . .

The second axiom was to the effect that, when one received a letter from the other, he was under no obligation whatsoever to read it, let alone to answer it . . .

The third axiom was to the effect that, although it did not really matter if they both thought about the same detail, still, it was preferable that they should not do so.

And, finally, the fourth, and perhaps most important axiom, stated that it was quite indifferent if one of them had not contributed the least bit to the contents of a paper under their common name . . .

I think one may safely say that seldom -- or never -- was such an important and harmonious collaboration founded on such apparently negative axioms.

From the collected works of Harald Bohr, quoted by Bela Bollobás in the foreword to Littlewood's Miscellany, Cambridge University Press, 1986.

 

[摘自帕斯卡尔思想录赏析]

 

我们从来都没有掌握住现在。我们期待未来，好像未来来得太慢，我们要加速它的进程似的；或者，我们便回想过去，好像要阻止它飞快地流逝。我们是如此的轻率，以至于只是在不属于我们的那些时间里徘徊，却根本想不到那惟一属于我们的时间；我们又是如此地虚妄，以至于梦想着那已经消失的时间，却随意地忽略了那惟一存在的时间。这是由于现在通常总是在刺痛我们。我们对现在视而不见。因为它使我们痛苦。如果它使我们快乐，我们就会遗憾于它消失得太快。我们试图用未来维系现在，而且对现在无能为力的事情，我们想要将之安排到并不能确定得时间里去。

如果每一个人都检查一下自己的思想，那么，我们会发现它们完全是被过去和未来所占据的。我们极少想到现在，而且假如我们想到的话，也只是想借助现在来安排未来。现在永远也不是我们的目的，过去和现在都是我们的手段，只有未来才是我们的目的。因此，我们从来没有真正生活过，我们只是在希望着生活。由于我们永远都在准备着能够幸福，所以，我们就必然永远也不会幸福。

麦克尔.帕金（1992年）将宏观经济理论家比作登山者。这个比喻很有用。我们已经看到，为了获得更好的经济学景观，不同的登山队（学派）是如何攀登宏观经济学之山的。但是，没有一个参赛者看到过这座山的山顶。它一直出于云遮雾罩之中。每一个队都对自己看地图的本事十分自信，都决定从不同的路线攀登这座山，都确信他们已经找到了通向顶峰的最佳路线。在攀登过程中，各登山队常常发现他们会在不同路线的交会处相遇，但在简短地交换信息之后又分手了。在除去尘霜的时候，各队还可能会偶然看见遗留在野径中的先驱者们的遗迹。有时一个队员走失了，再也找不到踪迹，或者加入了攀登速度看来较快的另一队中。有些路线后来被证明为死路，但这也是有用的信息，因为各队会明白不用去尝试那些路线。有时一个队宣称已经登上顶峰，但在云开雾散之后，随即发现，还有更高更险峻的山头需要攀登。所有登山队都一直受到雪崩即不利的经验证据的威胁，担心被它冲下山去。尽管那些留在大本营中的人努力设法与本队保持联系，这种联系也常常中断，因为在前进的道路上，往往有着料想不到的障碍，各队不得不改变路线。

在中国的民间，能工巧匠们把做工说成是“做活”，学手艺是“学活”，能工巧匠们做出来的物品“活”．以前听到这些，总觉得理所当然。现在想来，却觉得非常有道理。

　　的确，物品是“死”的，人是活的，这个“活”应该体现在头脑的灵活上．只有通过发挥想象力，才能“活”，也才能体现其活灵活现。

　　生活中的人怎样才能称之“活”呢？记得法国学者帕斯卡尔曾说:“人只不过是一根芦苇，是自然界最脆弱的东西，但他是一根能思想的芦苇。”我不知道一个失去思想或者思想已经被奴役的人和机器人有什么区别，但有一点是可以肯定的，那就是他一定不可以称之为“活”，他只是以一种类似动物的生命的形式存在而已。

　　写到这里，我自然而然的想到了自己这些年的经历．学校和家是我这些年来大部分时间的活动空间。我逐渐认识到自己好像被一种无形的东西束缚着。几乎没有想象力，像一个机器人一样，每天重复着一些类似被指定的动作。

　　值得庆幸的是，我已经意识到这个问题．我在慢慢地尝试着用自己的眼睛，去看这个未知的世界，逐渐学着从多个角度去看待问题。人是可以保持着几分固执的，但不可以偏执，因为观点和看法会随着时空的改变而发生变化，过分的偏执，可能会使自己变成自己观点和看法的奴隶。

　　如果要问我这一生最大的目标是什么，我的答案是：我可以在弥留之际问心无愧地对自己说：“我这一生，活得是个人。”

人的生命的价值在于寻找快乐－－－罗素［英］

 

二千五百年前，孙武子有言：知己知彼，百战不殆．（谋攻篇）．遗憾的是，由于后人的失误，使得孙老先生的本意没有被完全理解．“己”在“彼”之后，意在表明知己比知彼更难．所谓知彼，即通过各种调查方法搜集信息，了解对方，是要客观地看待事物；而所谓知己，即对自己的认识，在看待自己时，难免会有主观因素起作用。心中有杆称，能够称出自己几斤几两则非常人所能及啊！

　　人是什么？人应该是什么？前者是一个实证问题，后者是一个规范问题．经典科学对人的假定:人在这个宇宙中像原子一样，随机游走．我们只需要运用牛顿三大运动定律和万有引力定律就可以解释这个无比浩瀚的宇宙．所以也就有了古典经济学中对人的假定：人是理性的。即人在一定时期内，人有确定的偏好．追求效应最大化的个体之间的行为互不影响，即不存在外部性。亚当．斯密为我们勾勒出的“市场－－－无形的手”的社会蓝图是多么的美妙!美妙的像天方夜谈．

　  在现实世界中，人与人之间存在着策略行为．人是这个至今不知道从何而来的宇宙逐渐发展并形成的博弈场中的局中人．人在与自然博弈，人在与社会博弈，人在与其他个体博弈．在此过程中，人在不断地摸索中，寻求均衡解．正如海明威所言:“我们每个人都不是孤岛，但又自成一体．”一方面，我们需要依赖于其他个体所组成的群体，以寻求安全感；另一方面，我们又害怕在集体中消失，所以有了对个性的追求．

Sport and politics

Let the games begin

Jun 8th 2006
From The Economist print edition

        知识分子，一个在中国被泛化的名词。在很多望文生义的中国人看来，人是社会的一个分子，一个有知识的人就理所当然是知识分子。于是，就有了在那些曾经的“疯狂”的年代，批斗知识分子的“革命”。那么什么样的人才能称之为知识分子呢？知识分子是游离于主流社会，不与主流社会同流合污，客观地批判主流社会，为社会伸张正义、拷问社会良知的人。鲁迅、钱钟书等可以称之为知识分子，而一些御用文人被冠之于知识分子则显得牵强了。
      知识分子在客观地批判主流社会，这种“批判”具有经济学中的公共物品的属性，可以说是公共物品。为什么这么说呢？公共物品具有两个属性：一是生产非竞争性，虽然在中国有自古文人相轻之说,不过,那些文人没有几个能配得上知识分子这一称号的.一个知识分子对主流社会的批判不会影响其他知识分子,于此同时,还会刺激其他的知识分子,这就产生了正外部性.其二是消费的非排他性,知识分子对主流社会的批判,意在拷问社会的良知.作为一个普通人,在“消费”这种产品时,是不会影响其他人的消费的,而且随着消费者数量的增加,还会产生网络效应.

中国知识分子-----类似大熊猫的稀有的、非理性的群体。之所以说是类似大熊猫。是因为当代的中国，由于缺乏相关的保护法，知识分子群体几近灭绝。

那为什么又说是非理性的呢？因为在当代的中国，主流社会中的人是理性的，他们有确定的偏好------“声色货利”，在有“约束的条件”下追求效应最大化。与理性的主流社会相比，那些知识分子则显得很不懂“风情”了。主流社会需要的是人民民主专制，而知识分子却在大力倡导资本主义式民主与自由；主流社会需要的是冷漠和无知，而知识分子却在鼓吹道德与良知；主流社会需要的是“权贵社会主义”，而知识分子却在呼唤法治主义。

知识分子正在成为中国权贵社会主义现代化进程中的多余分子，可笑！可悲！可怜！

在一个完美的世界里，我们每个人都该有自己的“军师”，就像《教父》里的那位律师，或是德尔斐神庙的神使，他能一天 24 小时跟随我们，在我们耳边说着良言妙计。
　实际上，你现在就有了睿智的顾问供你驱使，它耐心地待在那里，等着你的召唤，你甚至可以把它揣在包里。1962 年古巴导弹危机期间，肯尼迪总统从 Barbara Tuchman的《八月炮火》(The Guns of August)一书中寻求智慧。这本书讲述了欧洲爆发第一次世界大战的经过。肯尼迪对他的兄弟说，“我不会像书中的人那么做，否则，人们这次就可以写一本名为《十月导弹》(The Missiles of October)的书了。”
    你不可能总是随身携带你想要的书。但是，你手边却可以有一份完美的阅读书目。正因为如此，《财富》调动一切资源，选出了 75 本书，这些书将激发你的思考，甚至是行动。
    这些书，并不是那种干巴巴的所谓经典商业读物。一方面，我们选出的有些书其实与商业无关。巴诺书店(Barnes & Noble)可能会把Michael Lewis的《钱与球》(Moneyball)归入体育类书籍，但该书谈到投资(和招聘)的内容，要比任何咨询师的 文章都多。另外，它也不枯燥。虽然《我在通用汽车公司的日子》(My Years at General Motors)是一部经典，但却枯燥乏味。
    不过，有些经典作品我们还是喜欢的。《股票作手回忆录》(Reminiscences of a Stock Operator) 虽然写于 1923 年，但该书仍然能够与《门口的野蛮人》(Barbarians at the Gate)摆在一起。这两本书都不是教人具体怎么做的书─总的来说，我们没有选那些有意识教导人的书，而是选了那些寓教于乐的书。而且没有比一手的信息更有价值的了。既然你可以读Warren Buffett自己写的书，为什么还要去读别人写他的书呢？
   当然，要读完书单上所有的书，大概需要 75 年吧。不过，我们可以给你提个建议: 不要只是因为你没有时间看完一本书，就不去读它。打开封面，看看介绍，直接跳到某一章。或者，留著这个书目，把它放到抽屉里。因为书中自有黄金屋，它们正等待你去发掘呢！        

1.商业兴衰
1.1《1929 年大崩盘》(The Great Crash 1929)， John Kenneth Galbraith著，1955 年出版。

1.2《非同寻常的大众幻想与群众性癫狂》(Extraordinary Popular Delusions and the Madness of Crowds)， Charles Mackay著，1841 年出版(中译本由中国金融出版社出版)。

1.3《有趣的钱财》(Funny Money)， Mark Singer著，1985 年出版。
1.4《沸腾岁月: 华尔街 60 年代牛市兴衰记》(The Go-Go Years: The Drama and Crashing Finale of Wall Street’s Bullish ’60s)， John Brooks著，1973 年出版。

 

2.企业
2.1《门口的野蛮人》(Barbarians at the Gate: The Fall of RJR Nabisco)， Bryan Burrough和John Helyar著，1990 年出版(中译本由机械工业出版社出版)。
2.2《基业长青》(Built to Last: Successful Habits of Visionary Companies)， Jim Collins)和Jerry I. Porras著，1994 年出版(中译本由中信出版社出版)。
2.3《链锯》(Chainsaw: The Notorious Career of Al Dunlap in the Era of Profit-at-any-price)， John Byrne著，1999 年出版。
2.4《谁说大象不会跳舞？》(Who Says Elephants Can’t Dance ?)， Louis V. Gerstner著，2002 年出版(中译本由中信出版社出版)。

3.决策
3.1《安那普尔那: 女人的地方》(Annapurna: A Woman’s Place)， Arlene Blum著，1980 年出版。
3.2《出类拔萃之辈》(The Best and the Brightest)， David Halberstam著，1972 年出版(中译本由新华出版社出版)。
3.3《大洋深处: 埃塞克斯捕鲸船的悲剧》(In the Heart of the Sea: The Tragedy of the Whaleship Es***)， Nathaniel Philbrick著，2000 年出版。
3.4《杀手天使》(The Killer Angels)， Michael Shaara著，1974 年出版(曾被改编为电影《葛底斯堡》，
3.5《十三天: 古巴导弹危机回忆录》(Thirteen Days: A Memoir of the Cuban Missile Crisis)， Robert F. Kennedy著，1969 年出版(中译本由上海人民出版社出版)。

4.

经济学
4.1《资本主义、社会主义和民主》(Capitalism, Socialism, and Democracy)， Joseph A. Schumpeter著，1942 年出版(中译本由商务印书馆出版)。
4.2《一切待售: 市场的好处和限度》(Everything for Sale: The Virtues and Limits of Markets)， Robert Kuttner著，1996 年出版。
4.3《就业、利息和货币通论》(The General Theory of Employment, Interest, and Money)， John Maynard Keynes著，1936 年出版(中译本由商务印书馆出版)。
4.4《流行的国际主义》(Pop Internationalism)， Paul Krugman著，1996 年出版(中译本由北京大学出版社出版)。
4.5《国富论》(The Wealth of Nations)， Adam Smith著，1776 年出版(中译本由陕西人民出版社馆出版)。

5.

道德
5.1《贼巢》(Den of Thieves)， James Stewart著，1991 年出版(中译本由国际文化出版公司出版)。
5.2《告密者》(The Informant)， Kurt Eichenwald著，2000 年出版(中译本由机械工业出版社出版)。
5.3《沉静领导》(Leading Quietly: An Unorthodox Guide to Doing the Right Thing)， Joseph L. Badaracco著，2002 年出版(中译本由机械工业出版社出版)。
5.4《房间里最精明的人》(The Smartest Guys in the Room)， Bethany McLean和Peter Elkind著，2003 年出版。
5.5《我们现在的生活方式》(The Way We Live Now)， Anthony Trollope著，1875 年出版。

6.

全球化
6.1《北京吉普: 美国企业在中国的短暂而不幸的婚姻》(Beijing Jeep: The Short, Unhappy Romance of American Business in China)， Jim Mann著，1989 年出版。
6.2《自由: 发展的目的和手段》(Development as Freedom)， Amartya Sen著，1999 年出版。
6.3《资本的神秘性: 为何资本主义在西方胜利，在其它地方却失败》(The Mystery of Capital: Why Capitalism Triumphs in the West and Fails Everywhere Else)， Hernando de Soto著，2000 年出版。
6.4《非零时代: 人类命运的逻辑》(Nonzer The Logic of Human Destiny)，Robert Wright著，2000 年出版(中译本由台北张老师出版公司出版)。
6.5《石油•金钱•权力》(The Prize: The Epic Quest for Oil, Money, and Power)， Daniel Yergin著，1991 年出版(中译本由新华出版社出版)。
6.6《工人: 工业时代考古学》(Workers: An Archaeology of the Industrial Age)， Sebastio Salgado著，1993 年出版。

7.投资

7.1《巴菲特致股东的信》(The Essays of Warren Buffett: Lessons for Corporate America)， Lawrence Cunningham编，1997 年出版(中译本由机械工业出版社出版)。
7.2《随机漫步的傻瓜－机遇在市场及人生中的隐蔽角色》(Fooled by Randomness: The Hidden Role of Change in the Markets and in Life)， Nassim Nicholas Taleb著，2001 年出版。
7.3《聪明的投资者》(The Intelligent Investor: A Book of Practical Counsel)， Benjamin Graham著，1949 年出版(中译本由江苏人民出版社出版)。
7.4《钱与球: 在不公平比赛中获胜的艺术》(Moneyball: The Art of Winning an Unfair Game)， Michael Lewis著，2003 年出版。

8.

领导力
8.1《永不退缩: 温斯顿　丘吉尔讲演精选》(Never Give in: The Best of Winston Churchill’s Speeches)， Winston S. Churchill 编，2003 年出版。“
8.2《论领导力》(On Leadership)， John Gardner著，1990 年出版。
8.3《马丁•路德•金时代的美国(1954-1963)》(Parting the Waters: America in the King Years 1954-63)， Taylor Branch著，1988 年出版。
8.4《个人历史》(Personal History)， Katharine Graham著，1997 年出版(中译本由江苏人民出版社出版)。
8.5《工商巨子》(Titan: The Life of John D. Rockfeller Sr.)， Ron Chernow著，1998 年出版(中译本由海南出版社出版)。

9.

谈判和管理
9.1《漫长的诉讼》(A Civil Action)， Jonathan Harr著，1995 年出版(中译本由译林出版社出版)。
9.2《有效的管理者》(The Effective Executive)， Peter Drucker著，1966 年出版(中译本由求是出版社出版)。
9.3《你还记得我吗？》(Remember Every Name Every Time)， Benjamin Levy著，2002 年出版。
9.4《久分必合: 戴姆勒－奔驰与克莱斯勒合并内幕》(Taken for a Ride: How Daimler-Benz Drove off with Chrysler)， Bill Vlasic和Bradley A. Stertz著，2000 年出版(中译本由华夏出版社出版)。
9.5《好女不过问: 谈判和性别鸿沟》(Women Don’t Ask: Negotiation and the Gender Divide)， Linda Babcock和Sara Laschever著，2003 年出版(中译本由台湾晨星出版公司出版)。

10.

办公室政治
10.1《来自纽约现场: 周六晚间直播节目野史》(Live from New York: An Uncensored History of Saturday Night Live)， Tom Shales和James Andrew Miller著，2003 年出版。
10.2《忠诚的代价》(The Price of Loyalty: George W. Bush, the White House, and the Education of Paul O’Neill)， Ron Suskind著，2004 年出版(中译本由人民文学出版社出版)。
10.3《君主论》(The Prince)， Niccol Machiavelli著，1513 年出版(中译本由陕西人民出版社出版)。
10.4《烦恼无穷》(Something Happened)， Joseph Heller著，1974 年出版。

11.

权力
11.1《小沃森自传》(Father Son & C My Life at IBM and Beyond)，Thomas Watson Jr.和Peter Petre著，1990 年出版(中译本由中信出版社出版)。
11.2《大曝光: 好莱坞与华尔街之间的斗争》(Indecent Exposure: A True Story of Hollywood and Wall Street)， David McClintick著，1982 出版。
11.3《影响力: 你为什么会说“是”？》(Influence: The Psychology of Persuasion)， Robert Cialdini著，1993 年出版(中译本由中国社会科学出版社出版)。
11.4《权力掮客: 罗伯特•摩西斯和纽约的衰败》(The Power Broker: Robert Moses and the Fall of New York)， Robert Caro著，1974 年出版。

12.

项目管理
12.1《美国钢铁: 钢铁工人和传统制造业地区的复兴》(American Steel: Hot Metal Men and the Resurrection of the Rust Belt)， Richard Preston著，1991 年出版。
12.2《价值连城的分子: 制药艰辛录》(The Billion-Dollar Molecule: One Company’s Quest for the Perfect Drug)， Barry Werth著，1994 年出版。
12.3《卡迪拉克沙漠》(Cadillac Desert: The American West and Its Disappearing Water)， Marc Reisner著，1990 年出版。
12.4《原子弹诞生记》(The Making of the Atomic Bomb)， Richard Rhodes著，1986 年出版。

13.

战略
13.1《孙子兵法》(The Art of War)，作者: 孙子(约公元前 500 年)。
13.2《黑鹰坠落: 现代战争记》(Black Hawk Down: A Story of Modern War)， Mark Bowden著，1999 年出版。
13.3《信息规则: 网络经济的策略指导》(Information Rules: A Strategic Guide to the Network Economy)， Carl Shapiro、Hal Varian著，1997 年出版(中译本由中国人民大学出版社出版)。
13.4《只有偏执狂才能生存》(Only the Paranoid Survive)， Andrew S. Grove著，1996 年出版(中译本由中信出版社出版)。这本书可以作为企业经理的特种部队培训手册。格鲁夫是英特尔(Intel)的创始人之一，也是该公司现任董事长。他向读者诚实地说明了怎样才能在最可怕的商业环境─竞争、科技或进入规则都突然间发生了变化的环境─下取得成功。
13.5《引爆流行》(The Tipping Point: How Little Things Can Make a BigDifference)， Malcolm Gladwell著，2000 年出版(中译本由中信出版社出版)。

14.

技术和创新
14.1《最后的孤独发明家》(The Last Lone Inventor: A Tale of Genius, Deceit, and the Birth of Television)， Evan I. Schwartz著，2002 年出版。
14.2《美国大众营销史话》(New and Improved: The Story of Mass Marketing in America)， Richard Tedlow著，1990 年出版
14.3《他们造就了美国》(They Made America: Two Centuries of Innovation from the Steam Engine to the Search Engine)， Harold Evans著，2004 年出版。
14.4《富甲美国》(Sam Walton: Made in America)， Sam Walton与 John Huey合著，1992 年出版(中译本由上海译文出版社出版)。
14.5《维多利亚时代的互联网》(The Victorian Internet: The Remarkable Story of the Telegraph and the 19th Century’s On-line Pioneers)， Tom  Standage著，1998 年出版

15.华尔街
15.1《与天为敌: 风险探索传奇》(Against the Gods: The Remarkable Story of Risk)， Peter L. Bernstein著，1996 年出版(中译本由清华大学出版社出版)。
15.1《华尔街之子摩根》(Morgan: American Financier)， Jean Strouse著，1999 年出版(中译本由华夏出版社出版)。
15.2《股票作手回忆录》(Reminiscences of a Stock Operator)， Edwin Lefre著，1923 年出版(中译本由海南出版社出版)。
15.3《营救华尔街》(When Genius Failed: The Rise and Fall of Long-term Capital Management)， Roger Lowenstein著，2000 年出版(中译本由上海远东出版社出版)。

15.4《客户的游艇在哪里》(Where are the Customers’ Yachts?)， Fred Schwed Jr.著，1940 年出版(中译本由海南出版社出版)。

16.工作与生活
16.1《美国生存体验实录》(Nickel and Dimed: On (Not) Getting by in America)， Barbara Ehrenreich著，2001 年出版。
16.2《成功人士战胜疲劳的秘密》(Reclaiming the Fire: How Successful People Overcome Burnout)， Steven Berglass著，2001 年出版(中译本由中信出版社出版)。
16.3《时间困扰: 工作家庭一锅粥》(The Time Bind: When Work Becomes Home and Home Becomes Work)， Arlie Russell Hochschild著，1997 年出版。
16.4《美国人谈美国》(Working: People Talk About What They Do All Day and How They Feel About What They Do)， Studs Terkel著，1974 年出版(中译本由中国对外翻译出版公司出版)。

刚刚看完央视新闻频道的《中国周刊》，一场关于小说抄袭的官司引起了我的思考，至于这场官司的原、被告是谁，在此就不必提了。

笔者在百度搜索引擎中，输入关键词“抄袭”，找到相关网页约9,050,000篇，输入“创新”，找到相关网页约24,400,000篇。在Google搜索引擎中约有7,060,000项符合抄袭的查询结果, 约有66,000,000项符合创新的查询结果。也许你会问，为什么要搜索这两个词，它们有什么关系吗？有关系，抄袭是创新的杀手。

    提到抄袭，我就会不由自主地想起强盗这个词，一般来说，人们总是想当然得认为，强盗偷取的是实物，所以行为很恶劣。而对于抄袭，一句“天下文章一大遍，看你会抄不会抄”。就说明了一个看似简单，却又十分严重的问题。人们对于抄袭的行为，态度是绥靖的，比如在《中国周刊》的节目中所说的，当被抄袭者状告抄袭者时，抄袭者所谓的“粉丝”们为其偶像鸣冤叫屈，有的甚至指责原告（被抄袭者）在炒作。事后，原告在接受记者采访时，说道，她感到很困惑。

    抄袭、学术造假，大学已经不是学术的象牙塔，其正在蜕变为名利场。而社会又怎样呢？大学的蜕变并没有什么令人惊奇之处，这只不过是适应社会发展的潮流而已，正如孙中山先生所说，社会潮流滚滚向前，顺之者昌，逆之者亡。如果大学能够长期保持出淤泥而不然，那才叫人感到奇怪呢！大学的存在，是植根于社会之中的，它就不可能不受社会的影响。

    如何打击抄袭、盗版呢？许多人想到，制定法律，通过政府强制，予以打击。颇具讽刺一位的是，中美两国领导人的每一次会晤，都会涉及到知识产权保护问题，作为回应，中国政府也在做加大力度，保护知识产权，而效果却不能让人恭维，对此笔者认为，这不只是政府的责任，更应该是社会的责任，是社会在漠视对知识产权的保护，是社会在庇护盗版、抄袭。从更深的层次来说，是这个“强盗文化”在作祟。为什么这么说呢？新制度经济学有一个论断，即外在制度（正式成文的法律、法规等）的有效实施，是需要内在制度（社会的文化、风俗、习惯等）作保障的，也就是说，外在制度是不能脱离内在制度而独立发挥效力的。接下来，我将分析一下这个“不负责任”的社会文化。

    在一个“强盗文化”的社会中，社会所崇尚的只是结果，至于过程怎样，就不重要了，正如俗话所言：不管黑猫、白猫，抓住老鼠，就是好猫。在中国的文化里，胜者为王，败者为寇，历来是不变的真理。处庙堂之高的皇帝，其实只不过是被社会所认可的山大王而已。在这种文化中，经常演绎的就是意大利学者马基雅维利在其《君王论》中所倡导的：为了达到目的，可以不则手段。

    一个“强盗文化”主导的社会中，抄袭、盗版的盛行是很容易理解的，因为只要强盗成功了，人们就不会在用强盗的标准来看待了，而会改用成功者的标准来对待。当抄袭者、盗版者取得成功时，社会的理性选择是变本加厉地抄袭、盗版，这样创新就会变成华丽的装饰品，像皇帝的新装一样。

    走技术创新之路，如果缺乏有效的知识产权保护制度，是行将不远的。

萨缪尔森幸福方程式：幸福＝效应÷欲望。效应是指商品满足人的欲望的能力，或者说，效应是指消费者在消费商品时所感受到的满足程度。效应取决于偏好，偏好是主观的 , 所以每个人的偏好是不同的，即追求的目标函数是不一样的。与此同时，为了得到一定的效应，还要付出成本（成本是指人们作出一项选择所付出的最高代价，即机会成本）。

如何才能幸福呢？笔者认为有两种途径可以达到：

一是在既定欲望的前提下，增加效应。经济学的一个假定是，人的欲望是无限，即承认人是有贪欲的，然而满足欲望的资源却是稀缺的。因此，如何配置稀缺的资源就成了经济学的一个重要的问题。经济学的解决方法很简单，即把资源通过价格机制配置给对其评价最高的人，这样就可以实现帕雷托最优配置。在不存在帕雷托改进的有效市场中，资源达到最优配置，每一个市场参与者的福利也就不存在帕雷托改进，局中人的福利也就达到了最优，因此，每一个人的幸福也就取得最高水平。

第二种方法是在既定效应的前提下，降低欲望。这是宗教所倡导的，如佛家所云：无欲则刚。在既定效应的前提下，当欲望取近于无穷小时，幸福等于无穷大，自然就会“刚”了。

幸福在哪里？唉！这么简单的问题，被搞复杂了，呵呵，这太有意思了！！！

In the long run ,we all died.--------------- John Maynard Keynes

 

      While economic theory will not necessarily make you fabulously wealthy, it does introduce you to some new ways of thinking about costs and benefits. One of the most important lessons of economics is that you should look at the marginal costs and marginal benefits of decisions and ignore past or sunk costs. We might put this as follows:

       Let bygones be bygones. Don’t look backward. Don’t cry over spilt milk or moan about yesterday’s losses. Make a hard－headed calculation of the extra costs you’ll incur by any decision based on marginal costs and marginal benefits.

        This is the   MARGINAL PRINCIPLE, which means that people will maximize their incomes or profits or satisfactions by counting only the marginal costs and marginal benefits of a decision. There are countless situations in which the marginal principle applies. We have just seen that the marginal principle of equating marginal cost and marginal revenue is the rule for profit maximization by firms. Another example is investment decisions. When deciding about whether to invest in a company or sell a house, forget about past gains or losses and decide only on the basis of marginal returns and costs. The marginal principle is one of the central lessons of economics.

       --------From ECONOMICS BY Paul A. samuelson and William D. Nordhaus P167

    

May 18th 2006 | HONGSHENG AND ANREN
From The Economist print edition

Forty years on, the government still avoids discussion of the Cultural Revolution

NB Pictures

IN THE village of Hongsheng, Li Furong feared trouble when he was summoned one day in August 1966 to a meeting. He had been denounced as a “capitalist-roader” and thought fellow peasants had gathered to attack him. Instead he found himself press-ganged into helping with the murder of octogenarian former landlords in one of the bloodiest orgies of violence in or around China's capital, Beijing, during the Cultural Revolution. Even 40 years later, the authorities are trying to suppress news of what happened in Hongsheng and nearby villages of Beijing's Daxing district.

The Communist Party's unwillingness to confront the horrors of the Cultural Revolution, which was launched on May 16th 1966 and officially ended ten years later with the death of Mao Zedong and the fall of the Gang of Four, means that for Chinese historians as well as for millions of victims that entire period is, in effect, off-limits for debate. The passage of time does not appear to be helping. Chinese scholars say the government has been even more intent on stopping public commemoration of this week's anniversary than it was a decade ago. No mention of it has appeared in the state-controlled media. A group of scholars who held a private symposium in Beijing in March to discuss the Cultural Revolution avoided using e-mail to arrange it for fear their communications would be intercepted by officials.

Partly, it is embarrassment about the scale and brutality of the violence carried out in Mao's name. In Hongsheng, Mr Li, now 75, says village officials told the meeting that former landlords and rich peasants, stripped of their holdings after the Communists took power in 1949, planned to stage a revolt. No evidence was offered. The plan was to kill the alleged plotters and their entire families that night. Mr Li, worried that as a “capitalist-roader” he too would be killed, agreed to use his well-known skills with rope to bind the victims. Two former landlords in their 80s were the first to be dealt with. Mr Li had barely finished his work before the old men were dragged away and beaten to death.

It could have been worse. Mr Li says that, had he not asked the village party chief whether he had written authority for this, other members of the landlords' families would have been murdered that night too. In some neighbouring villages there was much greater bloodshed. The youngest victim was one month old. Bodies were thrown down wells or into pits. In the commune to which Hongsheng belonged, 110 people were slaughtered within 24 hours. This was only one of 13 communes in Daxing district involved in what has become known to locals as the “8/31 [August 31st] massacre”. City officials called a halt to the violence after a couple of brave village officials travelled to the party's headquarters in central Beijing, 35 km (22 miles) away, to complain.

Even today, few in Beijing know anything about this, even though the official death toll, 324, exceeds the conservative government estimate of around 200 killed in the suppression of the Tiananmen Square protests of 1989. A brief mention of the massacre appeared in a book on the Cultural Revolution that was published in 1986 and quickly banned. A detailed government account was published only four years ago in an appendix to the “Daxing County Gazette”, a hefty and little-read tome, but was not reported in any newspaper. Of those killed, the book says, 91 were women. Nineteen entire families were eliminated.

The Daxing killings were part of what some perpetrators boasted of as a “red terror” that gripped Beijing between August and October 1966. Wang Youqin of the University of Chicago says officials have never acknowledged the extent of the bloodshed in the capital. She says that Red Guard mobs, obeying Mao's exhortation to “be violent”, killed some 2,000 Beijing residents in the space of two weeks.

One reason for the government's reticence is that, during this stage of the Cultural Revolution, many Red Guard leaders were the offspring of high-ranking officials who were subsequently purged but who became powerful again after Mao's death. Perpetrators of the violence were barred from influential positions after Deng Xiaoping took control in 1978. But Ms Wang says their family connections often protected them from punishment. The “Daxing County Gazette” says 348 people were “directly responsible” for the murders there, nearly two-thirds of them party members. Only 38 were jailed, the longest for 12 years. Pardons were granted to 246.

Officials fear that closer scrutiny of the Cultural Revolution could destabilise the country by inflaming long suppressed antagonisms. Many scholars now believe that well over 1m were killed or driven to suicide in political struggles between 1966 and 1976. The lives of almost all urban residents were profoundly disrupted. Schools and universities were closed. Educated people were forced to leave cities and work on farms. Family members turned on one another. Many of those now in their 50s belong to a “lost generation” whose education and careers were permanently blighted by the Cultural Revolution.

In 1981 the party leadership issued a long denunciation of the Cultural Revolution, as well as various other “mistakes” made by Mao, though these were portrayed as secondary to his contributions. The “Gang of Four” led by Mao's wife, Jiang Qing, who were deemed responsible for the Cultural Revolution's atrocities, were given lengthy prison terms (the last of the four died in December). Most of those persecuted were officially “rehabilitated” by the early 1980s.

There is, however, no official memorial to the victims. Appeals by some intellectuals for a museum dedicated to the events have gone unheeded. In recent months, private funds have started to remedy this. Last year, a privately run Cultural Revolution museum opened near the coastal city of Shantou in southern Guangdong province. In Anren township, near Chengdu, the capital of the south-western province of Sichuan, a wealthy real-estate developer, Fan Jianchuan, says he is preparing to open another later this month.

These ventures are still modest. The one in Shantou shows pictures of officials and other prominent figures being persecuted, but otherwise sticks to the government line. Mr Fan's will concentrate at first on porcelain artefacts from the period. His vast and lavishly designed complex, opened last year, is already home to a remarkable display of historical daring: a whole building of exhibits concerns the (positive) contribution of the Kuomintang, China's then ruling nationalist party, to the war against Japan. In Communist Party histories the Kuomintang is portrayed as having shirked the war.

But Mr Fan has no plans to display objects relating to the Cultural Revolution's factional warfare and other violence. “It's not just that I'm too cowardly and don't want trouble, but I also think it wouldn't be good for the peace of society,” he says. He may perhaps do so in 20 years.

May 18th 2006
From The Economist print edition

The riddle of technology and prosperity is explored in a fine new book

 

FIFTY years ago, Robert Solow published the first of two papers on economic growth that eventually won him a Nobel prize. Celebrated and seasoned, he was thus a natural choice to serve on an independent “commission on growth” announced last month by the World Bank. (The commission will weigh and sift what is known about growth, and what might be done to boost it.) Natural, that is, except for anyone who takes his 1956 contribution literally. For, according to the model he laid out in that article, the efforts of policymakers to raise the rate of growth per head are ultimately futile.

A government eager to force the pace of economic advance may be tempted by savings drives, tax cuts, investment subsidies or even population controls. As a result of these measures, each member of the labour force may enjoy more capital to work with. But this process of “capital-deepening”, as economists call it, eventually runs into diminishing returns. Giving a worker a second computer does not double his output.

Accumulation alone cannot yield lasting progress, Mr Solow showed. What can? Anything that allows the economy to add to its output without necessarily adding more labour and capital. Mr Solow labelled this font of wealth “technological progress” in 1956, and measured its importance in 1957. But in neither paper did he explain where it came from or how it could be accelerated. Invention, innovation and ingenuity were all “exogenous” influences, lying outside the remit of his theory. To practical men of action, Mr Solow's model was thus an impossible tease: what it illuminated did not ultimately matter; and what really mattered, it did little to illuminate.

The law of diminishing returns holds great sway over the economic imagination. But its writ has not gone unchallenged. A fascinating new book, “Knowledge and the Wealth of Nations” by David Warsh, tells the story of the rebel economics of increasing returns. A veteran observer of dismal scientists at work, first at the Boston Globe and now in an online column called Economic Principals, Mr Warsh has written the best book of its kind since Peter Bernstein's “Capital Ideas”.

Diminishing returns ensure that firms cannot grow too big, preserving competition between them. This, in turn, allows the invisible hand of the market to perform its magic. But, as Mr Warsh makes clear, the fealty economists show to this principle is as much mathematical as philosophical. The topology of diminishing returns is easy for economists to navigate: a landscape of declining gradients and single peaks, free of the treacherous craters and crevasses that might otherwise entrap them.

The hero of the second half of Mr Warsh's book is Paul Romer, of Stanford University, who took up the challenge ducked by Mr Solow. If technological progress dictates economic growth, what kind of economics governs technological advance? In a series of papers, culminating in an article in the Journal of Political Economy in 1990, Mr Romer tried to make technology “endogenous”, to explain it within the terms of his model. In doing so, he steered growth theory out of the comfortable cul-de-sac in which Mr Solow had so neatly parked it.

The escape required a three-point turn. First, Mr Romer assumed that ideas were goods—of a particular kind. Ideas, unlike things, are “non-rival”: everyone can make use of a single design, recipe or blueprint at the same time. This turn in the argument led to a second: the fabrication of ideas enjoys increasing returns to scale. Expensive to produce, they are cheap, almost costless, to reproduce. Thus the total cost of a design does not change much, whether it is used by one person or by a million.

Blessed with increasing returns, the manufacture of ideas might seem like a good business to go into. Actually, the opposite is true. If the business is free to enter, it is not worth doing so, because competition pares the price of a design down to the negligible cost of reproducing it. Unless idea factories can enjoy some measure of monopoly over their designs—by patenting them, copyrighting them, or just keeping them secret—they will not be able to cover the fixed cost of inventing them. That was the final turn in Mr Romer's new theory of growth.

As useful as poetry

How much guidance do these theories offer to policymakers, such as those sitting on the World Bank's commission? In Mr Solow's model, according to a common caricature, technology falls like “manna from heaven”, leaving the bank's commissioners with little to do but pray. Mr Romer's theory, by contrast, calls for a more worldly response: educate people, subsidise their research, import ideas from abroad, carefully gauge the protection offered to intellectual property.

But did policymakers need Mr Romer's model to reveal the importance of such things? Mr Solow has expressed doubts. Despite the caricature, he did not intend in his 1956 model to deny that innovation is often dearly bought and profit-driven. The question is whether anything useful can be said about that process at the level of the economy as a whole. That question has yet to be answered definitively. In particular, Mr Solow worries that some of the “more powerful conclusions” of the new growth theory are “unearned”, flowing as they do from powerful assumptions.

At one point in Mr Warsh's book, Mr Romer is quoted comparing the building of economic models to writing poetry. It is a triumph of form as much as content. This creative economist did not discover anything new about the world with his 1990 paper on growth. Rather, he extended the metre and rhyme-scheme of economics to capture a world—the knowledge economy—expressed until then only in the loosest kind of doggerel. That is how economics makes progress. Sadly, it does not, in and of itself, help economies make progress.

May 2006

By Diana Farrell and Susan Lund

The chief tasks of any good financial system are to attract savings and channel them to productive investments as efficiently as possible. China’s financial system does an outstanding job of mobilizing savings. But there is considerable room for improvement in its capital allocation, and its overall efficiency. Financial-system reforms could not only raise GDP by as much as 17%, or $320 billion a year, but also help spread China’s new wealth more evenly throughout the country.

China’s regulators are understandably anxious that a shift in funding toward more productive borrowers could accelerate layoffs from the less productive state-owned enterprises (SOEs), and lead to more social unrest. But such a shift will stimulate job creation in the strongest areas of China’s economy and increase tax revenues to fund social programs. Speeding the move to a fully market-based financial system will relieve, rather than exacerbate, social tensions in the long run.

Financing the Most Productive

Over the past 10 years, private companies in China—whether Chinese-owned, foreign-owned, or joint ventures—have grown faster than GDP. These companies now account for half of all output and many new jobs. The share of production from wholly state-owned enterprises, meanwhile, has shrunk to barely one-quarter of GDP. Although many SOEs have been restructured and some are highly profitable, their productivity as a group is still half that of private companies, both in aggregate and by industry.

Nevertheless, SOEs (both wholly and partially state-owned) continue to absorb most of the funding from the financial system. Private enterprises have received only 27% of loan balances. Many of them resort instead to China’s large informal lending market, which has an estimated $100 billion of assets but also higher interest rates.

As well as explaining the large volume of nonperforming loans in China’s banking system, this pattern of lending also has the effect of lowering overall productivity in the economy. As a result, China is seeing its investment efficiency decline. Whereas it required $3.30 of investment to produce $1 of GDP growth in the first half of the 1990s, each $1.00 of growth since 2001 has required $4.90 of new investment— nearly 40% more than the investment required by South Korea and Japan during their high-growth periods.

Productivity would be boosted greatly if a larger share of funding went to more productive private enterprises. Less productive SOEs would have to improve their operations to continue to attract finance, or shut down. Over the next five years, this dynamic would go a long way to closing the productivity gap between state-owned and private companies, raising GDP by as much as 13%, or $259 billion annually.

Chinese households will benefit as better capital allocation creates higher returns on savings. Chinese households save a lot by international standards—on average, roughly 25% of their disposable income. But they keep 86% of their savings in low-yielding bank deposits and savings accounts. Given the low average returns and volatility of equity and bonds over the past 10 years, opting for bank deposits has been rational.

That said, poor capital allocation by banks and the comparatively high cost of financial intermediation in China mean that returns on bank deposits are also dismal. Over the past 10 years, Chinese households’ financial assets earned just 0.5% a year after inflation. In contrast, South Korean households earned 1.8% during the same period. If real returns on their savings doubled to 1%, Chinese households would gain $10 billion annually; if returns reached the level seen in South Korea, they would gain an extra $25 billion a year. With returns at these levels, Chinese households could afford to save less and consume more.

Despite the clear benefits of better capital allocation, China’s regulators have resisted making changes, presumably in order to maintain stability and preserve jobs. But developing a market-based financial system is a more attractive way to achieve and sustain higher overall employment from both an economic and social standpoint. Although jobs will be lost from SOEs that prove unable to compete for funding on a commercial basis, the burgeoning private sector will create many new ones. Net job losses are likely to be negligible even in the short to medium term. China has already experienced this effect of liberalization in its auto industry. Restructuring has caused state-owned auto enterprises to shed many jobs, but total employment in the industry has increased.

Moreover, we estimate the increase in GDP resulting from reforms that improve capital allocation will raise government tax revenues by 16%, without any increase in tax rates. The state can use these funds to support and retrain displaced workers directly, rather than distorting the financial system to achieve social goals.

Improving Financial System Efficiency

When offering warnings that the Chinese economy is booming despite—not because of—its rudimentary financial system, many economists point out a core inefficiency of the system: political pressures continue to influence lending practices. Equally detrimental to China’s financial system, however, are inefficient operations in a banking sector that towers over the system, and the underdeveloped state of the debt and equity markets. As well as skewing the allocation of capital, these problems raise the system’s operating costs. If they could match the efficiency of systems in other emerging markets, such as South Korea, Malaysia, or Chile, we estimate that financial intermediation costs could be cut by a total of $62 billion per year, while improving capital allocation as well.

• Banking sector China’s banks have a number of operational weaknesses. They gather only sketchy information on borrowers’ credit histories and financial performance, and the coverage of independent credit rating agencies, such as Moody’s or Standard & Poor’s, is limited. Loan officers in many bank branches have rudimentary loan pricing and risk management skills, despite recent efforts to improve. To such risk-averse lenders, the scale and government ownership of even poorly performing soes can make them more attractive loan prospects than smaller private companies, because of their seemingly low risk. There may also be local political pressure to lend to what are still the largest local employers in many regions.

Poor capital allocation by banks is amplified by the dominance of the banking sector in China’s financial system. In market economies, the share of bank deposits in the financial system’s total assets typically ranges from under 20% in developed economies to about half in emerging markets. But as the graphic nearby shows, in China, banks intermediate nearly 75% of the capital in the economy. Bank deposits and savings accounts, roughly half of them from households, now total $2.6 trillion.

Banks’ inefficiencies result in higher than necessary operating costs. The main source of banks’ revenue, particularly in China where fee-based income is low, is the spread between their average borrowing and lending rates. China’s largest banks will need a total of $215 billion from the government to recapitalize their balance sheets. Around $105 billion has already been injected since the 1990s. Adding these funds to their net interest margin raises the true cost of intermediation in China’s banking sector to 4.5%, compared to 3.1% in our benchmark countries. Raising the efficiency of China’s banking operations to the benchmark would reduce their costs by $25 billion annually, given their volume of lending. More efficient banks would also be able to lend successfully to smaller, private businesses, saving these firms the premium they now pay to borrow on the informal market, worth an additional $2 billion a year.

• Payments system China is currently in the process of building a modern payments infrastructure. For wholesale payments, the China National Automatic Payment System (CNAPS) has been put in place in many cities and offers functionalities comparable to systems in more developed economies, namely gross settlement of high-value payments and net end-of-day settlement of smaller value ones. But many local banks are resisting the significant capital investment necessary to connect to the system, preferring instead to use the old “Electronic Interbank System,” which has far higher transaction costs. Most retail payments are still made in cash, since credit and debt cards are not widespread among the population, and most small retailers have not wanted to make the investment necessary to install the equipment to accept cards. Speeding the spread of electronic retail and wholesale payments would result in $20 billion of savings each year, and benefit the government by reducing tax evasion (since the gray market operates in cash). The size of this prize justifies introducing some form of incentive to retailers, consumers and banks to pay electronically.

• Debt and equity markets China’s equity and bond markets are among the smallest in the world. Equity market capitalization, excluding nontradable “legal person” shares owned by the state, is equivalent to just 17% of GDP, compared with 60% or more in other emerging markets. The corporate bond market, meanwhile, is just 1% of GDP, compared with an average of 50% in other emerging markets. It is held back by a mass of regulations that lengthen issuance time to a year or more, limit the interest rates that corporate bonds can pay, and leave the government with discretion over which companies list.

Moreover, China’s small capital markets are used almost exclusively by SOEs. Until a few years ago, state regulators selected companies for equity offerings in line with industrial policies, and still do for bond issues. Equity listing criteria have since become more independent, but here again, government regulators maintain discretion over which companies can list. So far, almost none have had a majority of private ownership at the time they initially listed shares, although some were privatized after listing.

Chinese companies need more fully developed equity and bond markets to provide competition to banks and give them a better choice of funding vehicles. In our benchmark countries, companies get roughly 60% of their debt from bond markets and 40% from bank loans. If they could match this mix of financing vehicles, Chinese companies would lower their funding costs by $14 billion annually. Efficiency improvements in China’s equity markets would reduce the costs to issuing companies by an additional $1.5 billion. Chinese households would benefit because flourishing bond and equity markets would underpin the development of more attractive financial products, such as mutual funds, pensions funds, and insurance, than bank deposits.

Priorities for Financial Reform

The current shortcomings of China’s financial system are rooted in relationships between the system’s component parts—banks, bond markets, equity markets, the payments system and institutional investors.

For instance, China needs a healthy corporate-bond market to provide funding to large companies and infrastructure projects, and to spur banks to lend more to smaller companies and consumers instead. The bond market, however, is unlikely to flourish until banks develop more accurate risk-based loan pricing and stop the flow of cheap loans to large companies. Speeding growth of domestic institutional investors is also essential, because few retail investors in any country buy corporate bonds directly. Yet all these relationships work both ways. Financial intermediaries, capital markets and banking have to evolve in tandem.

China’s four financial system regulatory bodies thus need to implement a coordinated, system-wide program of reforms. Measures to increase competition in the banking sector will be critical to prompt banks to upgrade their lending skills, management and it systems, and governance. China’s regulators have taken steps in this direction to prepare for competition from foreign banks, which will enter the local currency market in December 2006. But these banks have relatively few branches today and opening more will take time, limiting their immediate impact on competition. Regulators should therefore also allow more private domestic banks to enter the market, and relax limits on foreign ownership in banks ahead of the currently planned schedule—particularly for the smaller city and regional banks badly in need of the banking skills and technology that foreign investors bring. They should also raise the requirements for bank governance by making boards more independent and offering training programs for directors, and should strengthen financial reporting and auditing requirements to make bank performance more transparent.

In a more competitive environment, banks will likely lose their largest corporate customers to the capital markets, obliging them to turn to private companies, SMEs, and consumers instead. But to lend successfully to these segments, banks must be able to assess the credit quality of borrowers and price their risks accurately. To this end, banks need the services of independent consumer credit bureaus. To speed their development, regulators should provide incentives for lenders and utilities to report the payment histories of borrowers.

To help creditworthy SMEs to borrow, regulators should also ease the strict collateral rules on banks. Today, real estate and some forms of equipment are accepted as collateral. But unclear property rights in many parts of China deprive small businesses of needed collateral. Moreover, Chinese real-estate prices are soaring, so using this asset as the main collateral for loans may be risky. The regulators should therefore allow banks to accept more types of equipment and accounts receivable as loan collateral, and the government should consider expanding the program of loan guarantees to SMEs. Since banks have had trouble taking possession of collateral in the past, particularly when it was not a fixed asset, it is also imperative that China further develop its legal system in this regard.

The corporate bond market in China has been slow to develop largely because of inappropriate regulations. To speed its expansion, regulators should abolish preferential access to the market for policy banks to allow more private companies to issue bonds, and shorten the issue approval process to something nearer the maximum of a week it takes in most other Southeast Asian countries from the 14 months to 17 months it takes today, and abolish limits on interest rates payable on corporate bonds. They should also encourage the expansion of sophisticated corporate-rating agencies, such as Moody’s and S&P, which today have limited coverage, or build up Chinese rating agencies.

Excessive regulation is also holding back growth among institutional investors. Regulators should therefore consider relaxing restrictions on the types of investments domestic intermediaries can make, and making taxes on these investments more favorable. They should also allow domestic intermediaries to invest some portion of their assets abroad to improve the returns they can offer to households. In addition, Chinese households need education in investment and financial services planning. This could be encouraged through tax rebates or subsidies to households, and by tax incentives to private companies that offer them.

To enable more private companies and SMEs to choose equity capital as a source of finance, regulations should be changed to let more private firms that technically qualify for an IPO actually list on each of the stock exchanges, and to allow more IPOs and foreign investors on the small-cap exchange in Shenzhen. To further the joint progress of all three exchanges in China, regulators should also encourage the more strategic relationship that is developing between the Hong Kong Stock Exchange and the mainland exchanges in order to improve mainland equity market operation.

Lastly, strict capital controls prevent China’s residents today from investing in foreign financial markets or securities, where they might earn higher returns than from domestic savings vehicles. This policy also protects China’s banks and capital markets from competition that they need in order to develop. As a first step toward capital-account convertibility, regulators should gradually allow domestic intermediaries to invest some assets in Hong Kong.

Ms. Farrell is director of the McKinsey Global Institute, McKinsey’s economics think tank where Ms. Lund is a senior fellow.