Incredible, Edible Foam -- and Mysterious Math Behind It

Air Date: 11/30/2010
Source:
Scientific American
Creator:
W. Wayt Gibbs, Nathan Myhrvold
Air/Publish Date:
11/30/2010
Event Date:
11/30/2010
Resource Type:
Article
Copyright:
n/a
Copyright Date:
2010
Clip Length:
-

This 2010 "Scientific American" article reports on the growing use of edible foams by innovative chefs -- and mathematicians' continuing fascination with the angles and intersections of the interlocking bubbles that make up a foam. Source: Scientific American, November 30, 2010

The Incredible, Edible Foam--and the Mysterious Mathematics behind It
Mathematicians are still struggling to understand what happens atop your morning cappuccino

By W. Wayt Gibbs and Nathan Myhrvold  November 30, 2010

If you sometimes start your morning with a frothy cappuccino and finish off the evening with a heady glass of beer, then your day opens and closes with one of the most scientifically intriguing kinds of food: the edible foam. There are deep mathematical mysteries in these interlocked bubbles, and recently they have also become one of the most fertile areas for culinary innovation.

Top-ranked chef Ferran Adrià of elBulli in Catalonia, Spain, began experimenting with culinary foams in the mid-1990s in his quest to present diners with new and unexpected culinary experiences. Adrià used unconventional foaming agents such as gelatin or lecithin rather than eggs or cream. He used whipping siphons pow­ered by pressurized nitrous oxide—much like cans of Reddi-wip but sturdier—to create eth­er­eal foams from foods as diverse as cod, foie gras, mushrooms and potatoes. That started a revolution in foams, as chefs, among them Hes­ton Blumenthal of Bray, England, New York City’s Wylie Dufresne, and Chicago’s Grant Achatz, have taken to foaming all manner of savory foods.

These dishes have an aura of mystique about them and not just for their novel texture. Although foams may look like random jumbles, the bubbles within all foams seem to self-organize to obey three universal rules first observed by Belgian physicist Joseph Plateau in 1873. These rules are simple to describe but have been remarkably hard to explain. The first rule is that whenever bubbles join, three film surfaces intersect at every edge. Not two; never four—always three. Second, each pair of intersecting films, once they have stabilized, forms an angle of exactly 120 degrees. Finally, wherever edges meet at a point, the edges always number exactly four, and the angle is always the inverse cosine of –1/3 (about 109.5 degrees).

Only a century later, in 1976, did Rutgers University mathematician Jean Taylor prove that, at least in the case of two joined bubbles, Plateau’s rules derive from the action of surface tension, which forces the bubbles to adopt the most stable configuration. Mathematicians are still attempting to nail down exactly what happens in a froth of three or more bubbles, as well as the unsolved question of what arrangement of bubble shapes in a foam will fill a container while using the least surface area (and thus the least energy). In 1887 Lord Kelvin had proposed that a honeycomb of tetra­dec­a­hedrons, each with six square and eight hexagonal faces, is the answer. But in 1994 phys­i­cists Dennis Weaire and Robert Phel­an of Trinity College in Dublin published an even better—though not neces­sar­ily optimal—solution: a foam of two kinds of cells, one made solely from 12 pentagons and the other constructed from two hexagons and 10 pentagons.

In foamy foods, bubbles that do not follow Plateau’s rules quickly pop. The same fate occurs to bubbles that are too small: surface tension raises the pressure inside them beyond the breaking point. That is one reason that liquid foams become coarser as they age—and why it is best to sip your cappuccino while it is fresh.

Close NBC Learn

FILTERING

If you are trying to view the videos from inside a school or university, your IT admin may need to enable streaming on your network. Please see the Internet Filtering section of our Technical Requirements page.

DVDs AND OTHER COPIES

Videos on this page are not available on DVD at this time due to licensing restrictions on the footage.

DOWNLOADING VIDEOS

Subscribers to NBC Learn may download videos and play them back without an internet connection. Please click here to find out more about subscribing or to sign up for a FREE trial (download not included in free trial).

Still have questions?
Click here to send us an email.

Close NBC Learn

INTERNATIONAL VISITORS

The Science of the Olympic Winter Games videos are only available to visitors inside the United States due to licensing restrictions on the Olympics footage used in the videos.

FILTERING

If you are trying to view the videos from inside a school or university, your IT admin may need to enable streaming on your network. Please see the Internet Filtering section of our Technical Requirements page.

DVDs AND OTHER COPIES

The Science of the Olympic Winter Games is not available on DVD at this time due to licensing restrictions on on Olympic footage.

DOWNLOADING VIDEOS

Subscribers to NBC Learn may download videos and play them back without an internet connection. Please click here to find out more about subscribing or to sign up for a FREE trial (download not included in free trial).

Still have questions?
Click here to send us an email.

Close NBC Learn

Choose your product

NBC Learn K-12 product site
NBC Learn Higher Ed product site

For NBC Learn in Blackboard™ please log in to your institution's Blackboard™ web site and click "Browse NBC Learn"

Close NBC Learn

If you have received a new user registration code from your institution, click your product below and use the "Register now" link to sign up for a personal account.

NBC Learn K-12 product site
NBC Learn Higher Ed product site

For further assistance, please contact our NBC Learn Support Team and we'll be happy to assist you.

Start Your Free
day
Day Trial!