Methodology – Page 35 – artdiamondblog.com

“Drawing the Best Minds into a Whirlpool of Mathematical Solipsism”

Source of book image: http://www.houghtonmifflinbooks.com/catalog/titledetail.cfm?titleNumber=689539

Physicists rightly feel uneasy about descriptions of the physical world that divide it into discrete clusters of equations and axioms, each cluster explaining one part of existence but not another. Better would be finding a Theory of Everything capable of conjoining, in a few equations, planet-pulling gravitation and the microcosmic weirdness that goes on in the quantum world of atoms and particles. Physicists would like to stitch time and space together as well.

Einstein tried and failed. In recent years, "string theory" has been the favored means of attempting to tie everything together, but it has unraveled into mathematical frippery, positing ever more intricate elaborations extending into anywhere from 10 to 26 dimensions, some arising from themselves, some hidden in ways so baroquely scrolled that you can get a migraine just thinking about thinking about them. Little wonder that, as an experimental science, string theory seems to have nowhere to go.

That is the problem that Lee Smolin identifies in "The Trouble With Physics." He laments a kind of sociological imperative drawing the best minds into a whirlpool of mathematical solipsism.

For the full review, see:

RUSSELL SEITZ. "BOOKS; Untangling the Knots in String Theory." The Wall Street Journal (Sat., December 2, 2006): P9.

The reference to the book under review, is:

Lee Smolin. The Trouble With Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next. Houghton Mifflin, 2006. (392 pages, $26)

Publishing Pretty Papers Full of Clever Mathematical Tricks

Source of book image: http://images.amazon.com/images/P/0738203491.01.LZZZZZZZ.jpg

In his elegant and thoughtful foreward, physicist, futurist, and guru Freeman Dyson writes:

(p. viii) Before I met Feynman, I had published a number of mathematical papers, full of clever tricks but totally lacking in im-(p. ix)portance. When I met Feynman, I knew at once that I had entered another world. He was not interested in publishing pretty papers. He was struggling, more intensely than I had ever seen anyone struggle, to understand the workings of nature by rebuilding physics from the bottom up.

The reference to the book, is:

Feynman, Richard P. The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman. New York: Perseus Books, 1999.

Schumpeter’s “Sarcastic Remark” on Mathematics in Economics

Erich Schneider had been a student of Schumpeter’s at the University of Bonn in the late 1920s. The following sentences are from his lectures on Schumpeter that he published in German in 1970, and that were were translated into English by W.E. Kuhn and published in that form in 1975.

(p. 41) When, after many years of separation, I saw Schumpeter again at Harvard in the fall of 1949 and heard his lectures on economic theory–which he gave at 2 p.m., as in Bonn–I found him to be exactly the same man as before. On that afternoon he talked about the nature of dynamic analysis and about the role of difference equations in the framework of such an analysis.

To the above passage, Schneider adds footnote 3:

(p. 59) He dropped the sarcastic remark: "There are economists who do not know what a difference equation is; but there are also those who know nothing else."

Schneider, Erich. Joseph A. Schumpeter: Leben Und Werk Eines Grossen Sozialokonomen (Life and Work of a Great Social Scientist). Lincoln, Neb.: University of Nebraska–Lincoln Bureau of Business Research, 1975.

Feynman: What Biology Needs is Not More Math, But to See Better at the Atomic Level

A very bright, and very mathematically competent, fellow, grants that math is not the source of all knowledge. So is economics more like physics, or more like biology?

(p. 124) We have friends in other fields–in biology, for instance. We physicists often look at them and say, "You know the reason you fellows are making so little progress?" (Actually I don’t know any field where they are making more rapid progress than they are in biology today.) "You should use more mathematics, like we do." They could answer us–but they’re so polite, so I’ll answer for them: "What you should do in order for us to make more rapid progress is to make the electron microscope 100 times better."

What are the most central and fundamental problems of biology today? They are questions like: What is the sequence of bases in the DNA? What happens when you have a mutation? How is the base order in the DNA connected to the order of amino acids in the protein? What is the structure of the RNA: is it a single-chain or double-chain, and how is it related in its order of bases to the DNA? What is (p. 125) the organization of the microsomes? How are proteins synthesized? Where does the RNA go? How does it sit? Where do the proteins sit? Where do the amino acids go in? In photosynthesis, where is the chlorophyll; how is it arranged; where are the carotenoids involved in this thing? What is the system of the conversion of light into chemical energy?

It is very easy to answer many of these fundamental biological questions; you just look at the thing! You will see the order of bases in the chain; you will see the structure of the microsome. Unfortunately, the present microscope sees at a scale which is just a bit too crude. Make the microscope one hundred times more powerful, and many problems of biology would be made very much easier. I exaggerate, of course, but the biologists would surely be very thankful to you–and they would prefer that to the criticism that they should use more mathematics.

Source:

Feynman, Richard P. The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman. New York: Perseus Books, 1999.

“Forgotten not for lack of importance, but for lack of theoretical frame-works”

A paper by current head of the President’s Council of Economic Advisors, Ed Lazear, is significant for what it says near the end about economists forgetting facts, because the facts do not fit into current theory.

(p. 260) Human capital theory is primarily a supply-side approach that focuses on the characteristics and skills of the individual workers. It pays far less attention to the environments in which workers work. As such, the human capital framework has led researchers to focus on one class of questions, but to ignore others. Specifically, little attention has been paid to the jobs in which workers are employed.

(p. 263) The fact that some jobs and some job characteristics are more likely to lead to promotions than other jobs is not surprising. But the analysis suggests that other ways of thinking about wage determination, namely, through job selection, may have been unduly ignored in the past.

. . .

Researchers have begun to make jobs rather than individuals the unit of analysis. This change of focus can illuminate new issues and provide answers to questions that were once posed and forgotten. The questions were forgotten not for lack of importance, but for lack of theoretical frame-works. The theory is now developed and awaits confirmation in the data.

For the full paper, see:

Lazear, Edward P. "A Jobs-Based Analysis of Labor Markets." American Economic Review 85, no. 2 (May 1995): 260-265.

(Note: elipsis added.)

Does Focus on Scarcity, Blind Us to Abundance?

Chris Anderson ends chapter 8 of his stimulating The Long Tale, with a provocative jab at economists:

(p. 146) Finally, it’s worth noting that economics, for all its charms, doesn’t have the answer to everything. Many phenomena are simply left to other disciplines, from psychology to physics, or left without an academic theory at all. Abundance, like growth itself, is a force that is changing our world in ways that we experience every day, whether we have an equation to describe it or not.

The reference to Anderson’s book, is:

Anderson, Chris. The Long Tail. New York: Hyperion, 2006.

R&D Stats Better; But Still Omit a Lot of Innovation

GDPgrowthWithR&Dgraph.gif Source of graphic: online version of WSJ article cited below.

Note well Romer’s caveat below that, although we may be measuring better, we are still not measuring Schumpeterian innovations (such as the Wal-Mart innovations that are vastly increasing the efficiency of retailing).

That research and development makes an important contribution to U.S. economic growth has long been obvious. But in an important advance, the nation’s economic scorekeepers declared they can now measure that contribution and found that it is increasing.

. . .

Since the 1950s, economists have explained economic output as the result of measurable inputs. Any increase in output that can’t be explained by capital and labor is called "multifactor productivity" or "the Solow residual," after Robert Solow, the Nobel Prize-winning economist considered the father of modern growth theory.

From 1959 to 2002, this factor accounted for about 20% of U.S. growth. From 1995 to 2002, when productivity growth accelerated sharply, that grew to about 33%. Accounting for R&D would explain about one-fifth, by some measures, of the productivity mystery. It suggests companies have been investing more than the official data had previously shown — a good omen for future economic growth. "The slump in investment is not as drastic as people thought before they saw these figures," says Dale Jorgenson, professor of economics at Harvard University.

Mr. Jorgenson noted a lot of the multifactor productivity growth remains unexplained. "The great mystery of growth . . . is not eliminated."

Paul Romer, an economics professor at Stanford Business School, said the better the measurements of R&D become, the more economists and policy makers will realize other factors may be more important. "If you look at why we had rapid productivity growth in big-box retailing, there were lots of intangibles and ideas that . . . don’t get recorded as R&D."

For the full story, see:

GREG IP and MARK WHITEHOUSE. "Why Economists Track Firms’ R&D; Data on Knowledge Creation Point to an Increasing Role In Domestic Product Growth." Wall Street Journal (Fri., September 29, 2006): A2.

(Note: The slightly different online version of the title is: "Why Economists Track Firms’ R&D; Data on Knowledge Creation Point to an Increasing Role In Domestic Product Growth.")

(Note: ellipses in Jorgenson and Romer quotes, in original; ellipsis between paragraphs, added.)

Static Assumptions Undermine Economic Policy Analysis

Over 50 years ago, Schumpeter emphasized that static models of capitalism miss what is most important in capitalism. Yet static analysis still dominates most policy discussions. But there is hope:

(p. A14) A bit of background: Most official analysis of tax policy is based on what economists call "static assumptions." While many microeconomic behavioral responses are included, the future path of macroeconomic variables such as the capital stock and GNP are assumed to stay the same, regardless of tax policy. This approach is not realistic, but it has been the tradition in tax analysis mainly because it is simple and convenient.

In his 2007 budget, President Bush directed the Treasury staff to develop a dynamic analysis of tax policy, and we are now reaping the fruits of those efforts. The staff uses a model that does not consider the short-run effects of tax policy on the business cycle, but instead focuses on its longer run effects on economic growth through the incentives to work, save and invest, and to allocate capital among competing uses.

For the full story, see:

ROBERT CARROLL and N. GREGORY MANKIW. "Dynamic Analysis." The Wall Street Journal (Weds., July 26, 2006): A14.

Test That Showed No Life on Mars, Now Also Shows No Life on Earth, Either

One of the Viking landers on Mars. Source of photo: http://www.msss.com/mars/pictures/viking_lander/viking_lander.html

When scientists announced Monday that the search for life on Mars 30 years ago may not have been quite the bust it has long been portrayed, it didn’t mean that the mission had missed any microorganisms, let alone advanced life forms. But it did underline the growing sense that decades of assumptions about extraterrestrial life need serious re-examination.

In 1976, scientists studying data sent back by the Viking landers were quick to dismiss life on Mars. . . .

. . .

Some three decades later, more-sophisticated instruments have shown that the Vikings couldn’t have detected organic molecules even if any were present. When scientists fed soil from the Atacama Desert of Chile and Peru, and the Dry Valleys of Antarctica, experiments like those the Vikings conducted came up empty. Yet, new techniques show the samples contained 10 to 1,500 micrograms of carbon per gram.

"If we knew this 30 years ago, our interpretation of the Viking results would have been very different," says Rafael Navarro-González of Mexico’s National Autonomous University, who led the study published in Proceedings of the National Academy of Sciences.

For the full story, see:

SHARON BEGLEY. "SCIENCE JOURNAL; Scientists Revisit Data On Mars With Minds More Open to ‘Life’." The Wall Street Journal (Fri., October 27, 2006): B1.

Omit the Footnotes?

When I was a graduate student at Chicago, Milton Friedman was rumored to have given a presentation on how to write a doctoral dissertation in which he said something like:

Take everything nonessential, and move it into footnotes. Then collect all the footnotes into an appendix. Finally, delete the appendix.

My memory is that Deirdra McCloskey, in her wonderful advice on how to write economics clearly, also advises against footnotes. I at least attribute this advice to McCloskey (and Friedman) when I pass it on to students.

But sometimes, when I write an article, a misguided referee, or editor, insists that I omit some stuff that I think is really good. When that happens, sometimes, if I feel strongly, I sneak some of that material back into the paper in footnotes. Maybe no one will ever read it, but I feel better that it is still there.

And every once in awhile, it may turn out that the footnotes are what matter most:

It was typical of Schumpeter’s love for theory that he rejected Marshall’s view that the reader could skip the footnotes and appendixes. If time were short, Schumpeter advised, read them and skip the text! (p. 7; italics in original.)

In this case, though, I suspect that Marshall was right, and Schumpeter wrong.

Source:

Samuelson, Paul. "Compete as an Economic Theorist." In Schumpeterian Economics, edited by Helmut Frisch, New York: Praeger Publishers, 1981, pp. 1-27.

Becker on Goals of Economics: Understand the World, and Improve It

Gary Becker at April 7, 2006 tribute dinner. Source of image: online press release cited below.

Gary Becker has made enormous contributions to economic theory, most notably in convincing the profession of the importance of human capital and the family. A new center has been established at the University of Chicago in Gary Becker’s honor.

Becker’s brief remarks concluded the evening. Economics will change over time, but one constant—whatever the tools or techniques—is the goal of economics, he said. “It is judged ultimately by how well it helps us understand the world, and how well we can help improve it.”

For the full story, see:

Goddu, Jenn Q. "Gift Names the Becker Center on Chicago Price Theory, Founded by Richard O. Ryan." University of Chicago News Office, 2006.