Exploring the Science of Cooking: Mathematica's Role in Modernist Cuisine

Nathan Myhrvold, Author of Modernist Cuisine and former CTO, Microsoft

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The Mathematica Edge
  • Does everything, from equation solving to producing graphics for publication, in one piece of software
  • Creates any kind of compelling graphic for the best visual understanding of concepts and presentation of results
  • Solves differential equations for heat transfer and other phenomena to perfect new techniques
"I wind up using Mathematica for lots of things people might not use it for. It's my first choice for doing a lot of things that require a certain amount of mathematics and a certain amount of programming."

Challenge

Much of the science behind cooking isn't well known to chefs, according to longtime Mathematica user Nathan Myhrvold, CEO of Intellectual Ventures, former CTO of Microsoft, founder of Microsoft Research, and trained chef. To change that, he wanted to include answers to questions about heat transfer, the growth and death of pathogens, and other technical subjects in Modernist Cuisine, the six-volume cookbook he co-authored with chefs Chris Young and Maxime Bilet. The book's 2,438 pages delve into the science and technology of cooking. It was the James Beard Foundation's 2012 Cookbook of the Year.

Solution

Myhrvold developed the cookbook by drawing on decades of Mathematica experience he gained working in physics research and computer science.

Myhrvold wrote thousands of lines of Mathematica code for the Modernist Cuisine, including modeling heat transfer during grilling, using an ice bath, and other cooking methods. The variety of capabilities meant he could solve differential equations and produce unique graphics to visualize the results in one piece of software. "No package that I'm aware of has the breadth of things that Mathematica does," Myhrvold said.

An Example: Ice Baths

"People's intuition as to how heat conduction works is not always correct," Myhrvold said. One surprise that Mathematica helped him discover was that using an ice bath doesn't stop food from cooking any faster than taking it off the stove does. His team ran simulations of what happens when hot food is put into an ice bath. "It turns out there's almost no variation in the actual temperature between putting it in an ice bath and leaving it on the counter," he said.

"The fundamental reason the ice bath doesn't stop it is simple to explain. When heat is conducted through a solid, the rate at which it moves depends on the properties of the solid, thermal conductivity, and also thermal diffusivity that is a property of the food.... There's a speed limit on how fast heat moves. When I'm cooking something, I'm applying excess heat to the outside to make the inside get hotter. Heat is flowing into the food at a characteristic speed."

"...If I now plunge it in ice water I start drawing heat out of the food, and that will of course make it cooler. However, imagine a little bit of heat I added just before putting it in the ice bath. That heat is heading to the center of the food... now there's heat moving in the other direction from the food out. But that bit of heat that I launched toward the center, it will keep moving at the same speed, and the heat that's being sucked out by the ice water, that travels at the same speed. So it can never overtake the other heat. So the maximum temperature that is experienced in the center of the food will be identical, or very, very close to identical, regardless of whether I dump it in the ice bath or not."

Benefits

Mathematica gave Myhrvold the information he needed and allowed him to present it visually so that others can use what he's learned. "Having the ability to create great compelling graphics and really interesting scientific and effectively engineering results... adds something to the cookbook," he said.


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