News that AT&T, Verizon and BellSouth gave customer records to the National Security Agency has set off a heated debate over the intricacies of espionage law. But legal or not, this sort of spying program probably isn't worth infringing our civil liberties for -- because it's very unlikely that the type of information one can glean from it will help us win the war on terrorism.

If the program is along the lines described by USA Today -- with the security agency receiving complete lists of who called whom from each of the phone companies -- the object is probably to collect data and draw a chart, with dots or ''nodes'' representing individuals and lines between nodes if one person has called another.

Mathematicians who work with pictures like this are called graph theorists, and there is an entire academic field, social network analysis, that tries to determine information about a group from such a chart, like who the key players are or who the cell leaders might be.

But without additional data, its reach is limited: as any mathematician will admit, even when you know everyone in the graph is a terrorist, it doesn't directly portray information about the order or hierarchy of the cell. Social network researchers look instead for graph features like ''centrality'': they try to identify nodes that are connected to a lot of other nodes, like spokes around the hub of a bicycle wheel.

But this isn't as helpful as you might imagine. First, the ''central player'' -- the person with the most spokes -- might not be as important as the hub metaphor suggests. For example, Jafar Adibi, an information scientist at the University of Southern California, analyzed e-mail traffic among Enron employees before the company collapsed. He found that if you naively analyzed the resulting graph, you could conclude that one of the ''central'' players was Ken Lay's secretary.

And even if you manage to eliminate all the ''central players,'' you may well still leave enough lesser players that the cell retains a complete chain of command capable of carrying out a devastating terrorist attack.

In addition, the National Security Agency's entire spying program seems to be based on a false assumption: that you can work out who might be a terrorist based on calling patterns. While I agree that anyone calling 1-800-ALQAEDA is probably a terrorist, in less obvious situations guilt by association is not just bad law, it's bad mathematics, for two reasons.

The simplest reason is that we're all connected. Not in the Haight-Ashbury/Timothy Leary/late-period Beatles kind of way, but in the sense of the Kevin Bacon game. The sociologist Stanley Milgram made this clear in the 1960's when he took pairs of people unknown to each other, separated by a continent, and asked one of the pair to send a package to the other -- but only by passing the package to a person he knew, who could then send the package only to someone he knew, and so on. On average, it took only six mailings -- the famous six degrees of separation -- for the package to reach its intended destination.

Looked at this way, President Bush is only a few steps away from Osama bin Laden (in the 1970's he ran a company partly financed by the American representative for one of the Qaeda leader's brothers). And terrorist hermits like the Unabomber are connected to only a very few people. So much for finding the guilty by association.

A second problem with the spy agency's apparent methodology lies in the way terrorist groups operate and what scientists call the ''strength of weak ties.'' As the military scientist Robert Spulak has described it to me, you might not see your college roommate for 10 years, but if he were to call you up and ask to stay in your apartment, you'd let him. This is the principle under which sleeper cells operate: there is no communication for years. Thus for the most dangerous threats, the links between nodes that the agency is looking for simply might not exist.

If our intelligence agencies are determined to use mathematics in rooting out terrorists, they may consider a profiling technique called formal concept analysis, a branch of lattice theory. The idea, in a nutshell, is that people who share many of the same characteristics are grouped together as one node, and links between nodes in this picture -- called a ''concept lattice'' -- indicate that all the members of a certain subgroup, with certain attributes, must also have other attributes.

For formal concept analysis to be helpful, you need much more than phone records. For instance, you might group together people based on what cafes, bookstores and mosques they visit, and then find out that all the people who go to a certain cafe also attend the same mosque (but maybe not vice versa).

While researchers at Los Alamos National Laboratory have used this tool to sift through hundreds of terrorism-related reports -- and find connections that human analysts could not have found easily -- it's still dangerous to rely on the math.

This is because, as Kennedy and Lincoln assassination buffs know, two people can be a lot alike without being the same person. Even if there is only a 1 in 150 million chance that someone might share the profile of a terrorist suspect, it still means that, in a country the size of the United States, two people might share that profile. One might be a terrorist, or he might be Cat Stevens.

This isn't to say that mathematicians are useless in fighting terrorism. In September 2004 -- 10 months before the bombing of the London Underground -- Gordon Woo, a mathematician and risk-assessment consultant, gave a speech warning that London was a hotbed of jihadist radicalism. But Dr. Woo didn't anticipate violence just using math; he also used his knowledge of London neighborhoods. That's what law enforcement should have been doing then and should be doing now: using some common sense and knowledge of terrorists, not playing math games.

Math is just a tool. Used wisely, math can indeed help in warfare: consider the Battle of Britain, won in part by breaking the German codes. But use it unwisely -- as seems to be the case here -- and your approval ratings might just hit a new all-time low.

Co-author CESP senior fellow Harold A. Mooney details the dangerous impacts nitrogen-rich chemical fertilizers can have on the atmosphere and important watersheds. He asserts "the use of organic versus chemical fertilizers can play a role in reducing these adverse effects."

Organic farming has long been touted as an environmentally friendly alternative to conventional agriculture. A new study in the Proceedings of the National Academy of Sciences (PNAS) provides strong evidence to support that claim.

Writing in the March 6 online edition of PNAS, Stanford University graduate student Sasha B. Kramer and her colleagues found that fertilizing apple trees with synthetic chemicals produced more adverse environmental effects than feeding them with organic manure or alfalfa.

"The intensification of agricultural production over the past 60 years and the subsequent increase in global nitrogen inputs have resulted in substantial nitrogen pollution and ecological damage," Kramer and her colleagues write. "The primary source of nitrogen pollution comes from nitrogen-based agricultural fertilizers, whose use is forecasted to double or almost triple by 2050."

Nitrogen compounds from fertilizer can enter the atmosphere and contribute to global warming, adds Harold A. Mooney, the Paul S. Achilles Professor of Environmental Biology at Stanford and co-author of the study.

"Nitrogen compounds also enter our watersheds and have effects quite distant from the fields in which they are applied, as for example in contaminating water tables and causing biological dead zones at the mouths of major rivers," he says. "This study shows that the use of organic versus chemical fertilizers can play a role in reducing these adverse effects."

Nitrogen treatments

The PNAS study was conducted in an established apple orchard on a 4-acre site in the Yakima Valley of central Washington, one of the premiere apple-growing regions in the United States. Some trees used in the experiment had been raised with conventional synthetic fertilizers. Others were grown organically without pesticides, herbicides or artificial fertilization. A third group was raised by a method called integrated farming, which combines organic and conventional agricultural techniques.

"Conventional agriculture has made tremendous improvements in crop yield but at large costs to the environment," the authors write. "In response to environmental concerns, organic agriculture has become an increasingly popular option."

During the yearlong experiment, organically grown trees were fed either composted chicken manure or alfalfa meal, while conventionally raised plants were given calcium nitrate, a synthetic fertilizer widely used by commercial apple growers. Trees raised using the integrated system were given a blend of equal parts chicken manure and calcium nitrate.

Each tree was fertilized twice, in October and May, and given the same amount of nitrogen at both feedings no matter what the source-alfalfa, chicken manure, calcium nitrate or the manure/calcium nitrate blend.

Groundwater contamination

One goal of the PNAS experiment was to compare how much excess nitrogen leached into the soil using the four fertilizer treatments-one conventional, two organic (manure and alfalfa) and one integrated. When applied to the soil, nitrogen fertilizers release or break down into nitrates-chemical compounds that plants need to build proteins. However, excess nitrates can percolate through the soil and contaminate surface and groundwater supplies.

Besides having detrimental impacts on aquatic life, high nitrate levels in drinking water can cause serious illness in humans, particularly small children. According to the PNAS study, nearly one in 10 domestic wells in the United States sampled between 1993 and 2000 had nitrate concentrations that exceeded the Environmental Protection Agency's drinking water standards.

To measure nitrate levels during the experiment, water was collected in resin bags buried about 40 inches below the trees and then analyzed in the laboratory. The results were dramatic. "We measured nitrate leaching over an entire year and found that it was 4.4 to 5.6 times higher in the conventional treatment than in the two organic treatments, with the integrated treatment in between," says John B. Reganold, the Regents Professor of Soil Science at Washington State University and co-author of the study.

Nitrogen gas emissions

The research team also compared the amount of nitrogen gas that was released into the atmosphere by the four treatments. Air samples collected in the orchard after the fall and spring fertilizations revealed that organic and integrated soils emitted larger quantities of an environmentally benign gas called dinitrogen (N2) than soils treated with conventional synthetic fertilizer. One explanation for this disparity is that the organic and integrated soils contained active concentrations of denitrifying bacteria-naturally occurring microbes that convert excess nitrates in the soil into N2 gas. However, denitrifier microbial communities were much smaller and far less active and efficient in conventionally treated soils.

The research team also measured emissions of nitrous oxide (N2O)-a potent greenhouse gas that is 300 times more effective at heating the atmosphere than carbon dioxide gas, the leading cause of global warming. The results showed that nitrous oxide emissions were similar among the four treatments.

"We found that higher gas emissions from organic and integrated soils do not result in increased production of harmful nitrous oxide but rather enhanced emission of non-detrimental dinitrogen," Reganold says. "These results demonstrate that organic and integrated fertilization practices support more active and efficient denitrifier microbial communities, which may shift some of the potential nitrate leaching losses in the soil into harmless dinitrogen gas losses in the atmosphere."

Sustainable agriculture

Washington state produces more than half of the nation's apples. In 2004, the state crop was worth about $963 million, with organically grown apples representing between 5 and 10 percent of the total value. But the results of the PNAS study may apply to other high-value crops as well, according to the authors.

"This study is an important contribution to the debate surrounding the sustainability of organic agriculture, one of the most contentious topics in agricultural science worldwide," Reganold says. "Our findings not only score another beneficial point for organic agriculture but give credibility to the middle-ground approach of integrated farming, which uses both organic and conventional nitrogen fertilizers and other practices. It is this middle-ground approach that we may see more farmers adopting than even the rapidly growing organic approach."

Adds Mooney, "Organic farming cannot provide for all of our food needs, but it is certainly one important tool for use in our striving for sustainable agricultural systems. We need to explore and utilize all possible agricultural management techniques and technologies to reduce the very large global footprint of the needs to feed a population of over 6 billion people."

Other co-authors of the PNAS study are agroecologist Jerry D. Glover of the Land Institute in Salina, Kan., and Brendan J. M. Bohannan, associate professor of biological sciences at Stanford.

The study was funded by the U.S. Department of Agriculture, the National Science Foundation, the Land Institute and the Teresa Heinz Environmental Science and Policy Fellowship Program.

This past autumn the Freeman Spogli Institute for International Studies (FSI) in conjunction with the Woods Institute for the Environment launched a program on Food Security and the Environment (FSE) to address the deficit in academia and, on a larger scale, the global dialogue surrounding the critical issues of food security, poverty, and environmental degradation.

"Hunger is the silent killer and moral outrage of our time; however, there are few university programs in the United States designed to study and solve the problem of global food insecurity," states program director Rosamond L. Naylor. "FSE's dual affiliation with FSI and the new Stanford Institute for the Environment position it well to make significant steps in this area."

Through a focused research portfolio and an interdisciplinary team of scholars led by Naylor and CESP (Center for Environmental Science and Policy) co-director Walter P. Falcon, FSE aims to design new approaches to solve these persistent and under-prioritized problems, expand higher education on food security and the environment at Stanford, and provide direct policy outreach.

Productive food systems and their environmental consequences are at the core of the program. While many of these systems are global in character, but they are influenced significantly by differing food objectives, income level, and instruments among nations. The program thus seeks to understand the food security issues that are of paramount interest to poor countries, the food diversification challenges that are a focus of middle-income nations, and the food safety and subsidy concerns prominent in richer nations.

Chronic hunger in a time of prosperity

Although the world's supply of basic foods has doubled over the past century, roughly 850 million people (12 percent of the world's population) suffer from chronic hunger. Food insecurity deaths during the past 20 years outnumber war deaths by a factor of at least 5 to 1. Food insecurity is particularly widespread in agricultural regions where resource scarcity and environmental degradation constrain productivity and income growth.

FSE is currently assessing the impacts of climate variability on food security in Asian rice economies. This ongoing project combines the expertise of atmospheric scientists, agricultural economists, and policy analysts to understand and mitigate the adverse effects of El Niño-related climate variability on rice production and food security under current and future global warming conditions. As a consequence of Falcon and Naylor's long-standing roles as policy advisors in Indonesia, models developed through this project have already been embedded into analytical units within Indonesia's Ministry of Agriculture, the Planning Ministry, and the Ministry of Finance.

"With such forecasts in hand, the relevant government agencies are much better equipped to mitigate the negative consequences of El Niño events on incomes and food security in the Indonesian countryside," explain Falcon and Naylor.

Food diversification and intensification

With rapid income growth, urbanization, and population growth in developing economies, priorities shift from food security to the diversification of agricultural production and consumption. "Meat production is projected to double by 2020" states Harold A. Mooney, CESP senior fellow and an author of the Millennium Ecosystem Assessment. "In China alone, meat consumption has more than doubled in the past generation." As a result, land once used to provide grains for humans now provides feed for hogs and poultry.

These trends will have major consequences on the global environment-affecting the quality of the atmosphere, water, and soil due to nutrient overloads; impacting marine fisheries both locally and globally through fish meal use; and threatening human health, as, for example, through excessive use of antibiotics.

An FSE project is looking at these trends as it relates to intensive livestock production and assessing the environmental impacts to gain a better understanding of the true costs of this resource-intensive system. A product of this work recently appeared as a Policy Forum piece in the December 9, 2005, issue of Science titled "Losing the Links Between Livestock and Land".

Numerous factors have contributed to the global growth of livestock systems, lead author Naylor notes, including declining feed-grain prices, relatively inexpensive transportation costs, and trade liberalization. "But many of the true costs remain largely unaccounted for," she says. Those costs include destruction of forests and grasslands to provide farmland for corn, soybeans, and other feed crops destined not directly for humans but for livestock; utilization of large quantities of freshwater; and nitrogen losses from croplands and animal manure.

Naylor and her research team are seeking better ways to track all costs of livestock production, especially the hidden ones related to ecosystem degradation and destruction. "What is needed is a re-coupling of crop and livestock systems," Naylor says. "If not physically, then through pricing and other policy mechanisms that reflect social costs of resource use and ecological abuse."

Such policies "should not significantly compromise the improving diets of developing countries, nor should they prohibit trade," Naylor adds. Instead, they should "focus on regulatory and incentive-based tools to encourage livestock and feed producers to internalize pollution costs, minimize nutrient run-off, and pay the true price of water."

Looking ahead

The future of the program on Food Security and the Environment looks bright, busy, and expansive. While a varied portfolio of projects is in line for the upcoming year, a strong emphasis remains in the area of food security. Building on existing research at Stanford, researchers are identifying avenues for enhancing orphan crop production in the world's least developed countries-crops with little international trade and investment, but with high local value in terms of food and nutrition security. The work seeks to identify advanced genetic and genomic strategies, along with natural resource management strategies, to improve orphan crop yields and stability, enhance crop diversity, and increase rural incomes through orphan crop production.

Another priority area of research centers on the development of biofuels. Biofuels are becoming increasingly a part of the policy set for world food and agriculture. As countries such as the United States seek energy self-reliance and look for alternatives to food and feed subsidies under WTO (World Trade Organization) rules, the conversion of corn, sugar, and soybeans to ethanol and other energy sources becomes more attractive. New extraction methods are making the technology more efficient, and crude oil prices at $60 per barrel are fundamentally changing the economics of biomass energy conversion. A large switch by key export food and feed suppliers, such as the United States and Brazil, to biofuels could fundamentally alter export prices, and hence the world food and feed situation. A team of FSE researchers will assess the true costs of these conversions.

The FSE program recently received a grant through the Presidential Fund for Innovation in International Studies to initiate new interdisciplinary research activities. One such project links ongoing research at Stanford on the environmental and resource costs of industrial livestock production and trade to assess the extent and rate of Brazil's rainforest destruction for soybean production. "Tens of millions of hectares of native grassland and rainforest are currently being cleared for soybean production to supply the global industrial livestock sector," says Naylor. A significant share of Brazil's soybeans is being shipped to China, where rapid income growth is fueling tremendous increases in meat consumption."

A team of remote-sensing experts, ecologists, agronomists, and economists will be looking at the ecological effects on the landscape through biogeochemical changes and biodiversity loss, the impacts of land clearing on the regional hydrologic cycle and climate change, the economic patterns of trade, and the role of policies to achieve an appropriate balance between agricultural commodity trade, production practices, and conservation in Brazil's rainforest states.

"I'm extremely pleased to see the rapid growth of FSE and am encouraged by the recent support provided through the Presidential Fund for Innovation in International Studies," states Naylor. "It enables the program to engage faculty members from economics, political science, biology, civil and environmental engineering, earth sciences, and medicine-as well as graduate students throughout the university-in a set of collaborative research activities that could significantly improve human well-being and the quality of the environment."