## Harvard scientists build a 3D map of brownies, scones, and other baked goods

To most people, recipes are simple sets of instructions: steps that, if followed, will yield a delicious product. To Michael Brenner, an applied mathematician at Harvard University, recipes are a largely unexplored scientific resource--a kind of collective experiment that home cooks have been running since the baking of the first primordial brownies and cookies.

In a sense, baking is an edible form of materials science--the art of combining just a handful of ingredients, like eggs and flour, to create totally different structures and textures. Think angel food cake vs. biscotti. What makes one dessert so airy and fluffy, another crisp and dense? Recipes are varied, tested, and refined over years, and the most beloved succeed in large part because they’ve hit on the right ratios.

Brenner, whose inclinations lie more in the quantitative than culinary realms, began to get seriously interested in cooking when he cotaught a class on science in the kitchen. Last summer, he teamed up with Elaine Angelino, a computer science graduate student interested in analyzing large databases. Together, they began to wonder about what fundamental principles might underlie baked goods. Could techniques more commonly used to investigate materials used to build bridges also shed light on batters? Angelino, with the help of a sous scientist, undergraduate Diana Cai, downloaded and analyzed thousands of recipes--finding out where cookies, brownies, cakes, scones, and crepes appear when they’re mapped according to the ratios of ingredients.

Drawing their inspiration from techniques used in materials science, they built a three-dimensional graph in the shape of a tetrahedron, with each triangular “face” showing the ratio of three different ingredients. A point in the middle of the triangle would have an equal proportion of all three ingredients, but as the dots move toward each corner, the ratio shifts.

As they plotted each recipe on the graph, they found that clusters formed--clouds of dots that were all cookie recipes or pancakes. And those clusters followed certain general rules. For example, on the face of the pyramid with flour, eggs, and sugar, it’s clear that loaves, clustered near the flour vertex, have a high flour-to-sugar ratio. As you move toward the sugar vertex, you get cookies and then finally brownies, which have an even larger sugar-to-flour ratio. (“That’s the whole point of brownies,” Brenner says.) Then, if you increase the ratio of eggs, you move into the realm of pancakes and crepes.

Brenner and Angelino were satisfied to find that recipe datapoints naturally separated into distinct groups. But they also found, to their surprise, lots of unexplored white space, without any recipes whatsoever. When Brenner has given talks about the recipe tetrahedron, he’ll put a star in the white space and propose, half in jest, that a new, yet undiscovered food might lurk there.

Brenner is particularly interested in the recipes on the boundary of the recipe clusters. His own favorite, the brownie recipe on the back of the Baker’s chocolate box, is on a boundary, and he wonders whether that gives it some distinct or transitional properties that appeal to him and his kids.

“The dream would be to connect the ingredient information to the things we care about at the end of the day--the words we use to describe the food: chewy, or moist, or it has some texture we like,” Angelino said.

Though the project started off as a lark, it’s provoked lots of interest among audiences ranging from other scientists to culinary professionals. Angelino recently presented the tetrahedron to a group of chefs who were involved in a class on the science of cooking, including Bill Yosses, the White House pastry chef.

“They caught on to this idea we’ve been dreaming about,” Angelino said. “Point in space to where you want to create something, and find out what recipes live there.”

Carolyn Y. Johnson can be reached at cjohnson@globe.com. Follow her on Twitter @carolynyjohnson.