Letters to the EditorJune 17, 2000
Two articles in the April issue of SIAM News drew unusually heavy response. Several readers wrote to express agreement with Philip Davis's dislike of the star system in mathematics (even conveyed without a mention of the $100,000 prize offered for the solution of the Goldbach conjecture!). Jim Case's identification of David Ricardo's principle of comparative advantage as a key to the events in Seattle during the WTO's December meeting also sent several readers to their keyboards. One letter on each topic appears here. Readers are encouraged to express their views more often
What Is a Productive Career in Mathematics?
To the Editor:
I appreciated Philip Davis's review ("All---Or Nothing at All") of the book by Doxiadis in the April issue of SIAM News, especially the (explicit and implied) comments about the "snobbism" of some pure mathematicians.
I first encountered such attitudes when, as a new graduate student in the math department at MIT, I was given a desk in an office with five other "pure" math students. My adviser, Eric Reissner, had given me a project to work on that, at some point, required me to find the roots of some cubic polynomials. Rather than try to learn to punch up a numerical routine, I got a book from the library that showed how to solve cubics with reasonable accuracy using nomograms. It was just what I needed, but when one of my office mates spied the book on my desk, he picked it up and in a sneering voice heard by everyone else in the room asked, "What's this?!!" It was inconceivable to him that that anyone would be the least bit interested in getting numerical answers to a problem that had been solved hundreds of years earlier.
The idea that there is only one way to do mathematics has bothered me ever since. (No doubt Bourbaki had a lot to do with this, and I remember once reading a diatribe by Bellman, who claimed that this French group had killed a generation of creative mathematicians.) Hackneyed as is sounds, I still like the metaphor of mathematics as an (infinite?) cathedral. Some work on the overall design, others work on the magnificent windows in the transepts, but still others of us may work on just a little door or a niche in the wall. Yet the overall magnificence of the structure is the sum of all its pieces.
For me, passion, motivation, satisfaction, and some minimal level of competence and talent are the prerequisites for a productive career in mathematics. Insight and simplicity are what I particularly value, even if I can achieve them only on a relatively elementary level.
Davis's informed and lively reviews are a highlight of SIAM News. This, too, in my opinion, is an important facet of the mathematical enterprise.
Jim Simmonds, Department of Civil Engineering, University of Virginia.
The Verdict in Seattle
To the Editor:
In the April issue of SIAM News, James Case takes on a hot topic ("Judgment in Seattle: A Theorem Goes on Trial"). However, he didn't state the verdict. This verdict, as I explain below, is a good example of the care that must be exercised in applying the mathematics of "soft sciences" to the real world. In this case, it takes someone with a window into the movement to understand what is going on. This is where I come in: long-time applied mathematician (at Boeing) but also long-time community and political activist who was an active participant in some of the peaceful events in Seattle during the meetings of the World Trade Organization (WTO) last December.
Case was quite right in identifying the key issue---Ricardo's principle of comparative advantage, now formulated and proved as a mathematical theorem. Among free traders, its corollary is a never-ending war against "protectionism," and the WTO is their new weapon. Let's repeat Case's verbal formulation of the theorem in terms of gross domestic product (GDP): "If two or more countries have already expanded their respective GDPs as far as possible under a given set of restraints on international trade, they can expand them still further by relaxing those restraints."
Now normally you validate the application of a theorem by examining and verifying the hypotheses. It would appear that the hypotheses of the theorem are largely satisfied for many countries today, at least those---such as the U.S.---that actively try to maximize growth. So why all the protests in Seattle? Well, let's look at the conclusion of the theorem. Its correct application to public policy requires acceptance of the idea that increasing GDP, or a similar monetary measure, is beneficial for all concerned.
But are increases in GDP always good? The "verdict" of the protesters in Seattle, and more recently in Washington, DC, against the International Monetary Fund (IMF) and the World Bank, was a resounding "No!" That is, you can criticize the application of a theorem not only by questioning the validity of the hypotheses, but also by questioning the interpretation of the conclusion. In this case the verdict of the protesters is not surprising to most citizens, the international trade in addictive drugs and guns being only the most glaring and brutal counterexamples to the "goodness" of increasing GDP. Yet faith in this overall goodness is so basic to mainstream economists and pundits that most were left clueless by the events in Seattle. Of course, this faith is also the bedrock of the WTO/IMF vision for the "world economy."
The verdict of the protesters was motivated by a wide variety of counterexamples to this goodness, especially sweatshops and associated abuses of human and labor rights, damaging environmental practices, depletion of fisheries, forests, and other resources, global air and water pollution, global mass culture, increasing inequality between rich and poor, and much more. A decade after the end of the Cold War, it has gradually dawned on many people that George Bush's proclamation of a "New World Order" is an order of globalization dominated by the power of major transnational corporations, leaving traditional democracy behind. In some ways the WTO has powers (major trade sanctions and penalties) approaching those of a global government, yet it was launched with a minimum of democratic participation and understanding, and much of global civil society feels unrepresented in its current policies and structure. The problem is that the WTO is seen as fulfilling the principle of comparative advantage too faithfully, with little distinction between good and bad increases in GDP. That is, people believe many things do need to be protected, especially human rights and the environment. In this sense, many protesters are indeed "protectionists." This is what the "Fair Trade, Not Free Trade" signs in Seattle meant.
The protesters in Seattle were actually giving our economists a hard lesson in applied mathematics: Analyze not only the validity of your hypotheses but also the interpretations of your conclusions very carefully. In this case, the lesson involves the recognition that resolving differences between good and bad increases in GDP is actually a very deep, global political issue, not something that can be done by elite technicians and negotiators behind closed doors. In Seattle, global civil society came knocking, demanding to be let in.
Personally, I see global problems demanding democratic global governance that is now lacking, and I am helping to launch a Global Peoples Assembly to that effect (the inaugural meeting was held recently in Samoa). But also the WTO/free-trade battles illustrate how the simplistic application of economic principles, often held with ideological fervor, leads to such deep conflict. Most urgent, given the current population explosion and rapid rates pollution and resource depletion, is the need of a new theory for a sustainable global political economy, based on carefully applied mathematical principles. I've seen a few hand-waving attempts, but if you know of something more substantial, let me know.
Dick Burkhart, Seattle, Washington.