Math Is Hard, Floating Concrete

In the best seller “A Brief History of Time,” famed physicist Stephen Hawking notes that he purposely included only one mathematical equation in the book’s pages: E = mc². The scientist did this, he says, because someone once warned him that for each equation he added to his text, book sales would fall 50%.

According to a new study in the Proceedings of the National Academy of Sciences, the advice Hawking received might not have been too far off (DOI: 10.1073/pnas.1205259109).

Tim W. Fawcett and Andrew D. Higginson, biologists at the University of Bristol, in England, surveyed the citation rates and math content of about 650 journal articles on ecology and evolution from 1998. The researchers discovered that citations of an article dropped by a whopping 28% for every additional equation included in the paper’s main text.

Although Hawking’s musings weren’t the inspiration for this investigation, Fawcett tells Newscripts, they “nicely illustrate the kind of dilemma people face when trying to write about scientific ideas grounded in mathematical theory.” He adds, “Many of our colleagues in biology frequently say they find heavily mathematical papers tough to read or even avoid them altogether.”

On the basis of their findings, Fawcett and Higginson suggest moving equations to a paper’s appendix—a place, they found, where equation density has no effect on citation rate. But if the math is vital to a paper’s findings and must stay in the main text, the pair suggests adding more explanatory sentences to steer readers carefully through the formulas. “It’s a case of ‘use more words,’ not ‘use fewer equations,’ ” Fawcett contends.

The Newscripts gang hopes that the civil engineers who participated in last month’s National Concrete Canoe Competition (NCCC) didn’t shy away from equations when designing their seafaring vessels. After all, concrete canoes require a calculated balance of properties to prevent them from sinking, well, like concrete.

The contest, launched in 1989, helps engineering students go beyond the classroom and solve real-world problems, says Lacey N. Williamson, chair of the NCCC committee. “It’s also a team-building and management opportunity.”

The budding civil engineers who compete in NCCC spend the better part of a year planning and testing the materials for their canoes, casting the vessels, and then decorating them. During the competition, Williamson says, teams are ranked on the basis of a technical paper, an oral presentation, the canoe’s aesthetics, and the vessel’s performance in a series of five races.

This year’s overall winner of NCCC, which was held on June 14–16 in Reno, Nev., was a team from California Polytechnic State University, San Luis Obispo. Decorated to honor California’s gold rush and aptly named Prospector, the winning vessel weighed 170 lb.

“Historically, that’s on the lighter end of concrete canoes,” says Erik Bjornstrom, a fourth-year student and the Cal Poly team’s project manager. “Teams have been getting pretty light with their canoes in the past few years.”

Credit for the trend in decreasing weight goes to advances in materials, Williamson says. Typical concrete is a stew of cement; aggregates such as crushed stone; and admixtures, which are chemicals that can alter the air and water content of the final product. Instead of stone aggregates, many teams, including Cal Poly’s, are now using lightweight glass beads to give their canoes extra buoyancy.

Bjornstrom estimates that the Cal Poly team put some 5,000 hours of effort into the Prospector this year. “NCCC can be a lot of work,” he says, “but it’s also quite a bit of fun.”