Food Pairs 101

What follows is a brief explanation of what our work with foodpairs is trying to do.  

Foodpairing is the theory that foodstuffs go well together if they share key chemical compounds. The ur example is Heston Blumenthal's combination of caviar and white chocolade that both contain high levels of amines. Some work has been done to turn bodies of recipes into frequency lists of foodpairs, creating an informal hierarchy of good taste. 

Here we don't buy into the theory of foodpairing, which is culturally specific anyway, but we are using its concept of a 'food pair'. Our interest is not culinary but historic: can the way cooks and cuisines combine ingredients, now and in the past, show affinities and differences. Can it illustrate larger historic explanations of how cuisines have developed.

The foodpairs for a Aloo Gobi recipe look like this:

cauliflower,chili,1
cauliflower,cumin,1
cauliflower,curcuma,1
cauliflower,garammasala,1
cauliflower,ghee,1
cauliflower,pork,1
cauliflower,salt,1
cauliflower,tomato,1
chili,cumin,1
chili,curcuma,1
chili,garammasala,1
chili,ghee,1
chili,pork,1
chili,salt,1
chili,tomato,1
cumin,curcuma,1
cumin,garammasala,1
cumin,ghee,1
cumin,pork,1
cumin,salt,1
cumin,tomato,1
curcuma,garammasala,1
curcuma,ghee,1
curcuma,pork,1
curcuma,salt,1
curcuma,tomato,1
garammasala,ghee,1
garammasala,pork,1
garammasala,salt,1
garammasala,tomato,1
ghee,pork,1
ghee,salt,1
ghee,tomato,1
pork,salt,1
pork,tomato,1
salt,tomato,1

A diagram of it looks like this, a network with all nodes connecting each other.

Here is a graph of the same aloo gobi but combined with those for a Lasagna recipe. They share an ingredient but have no foodpair in common.


When graphing foodpairs for a larger body of recipes, a cookbook, some combinations will be more common than others, this is expressed with line-width and distance as this graph of a Madhur Jaffrey cookbook shows:

It seems reasonable to suggest that different cuisines will each have a preference for certain ingredients and when they use the same ones they will combine it differently. It also seems reasonable to expect that cuisines that developed together will differ less than cuisines that didn't. This is what we want to verify.

By combining the foodpairs of the Jaffrey book with a Mexican cookbook we get the graph below. It gives some information about their commonality but without context nothing definite can be said.

To make some real sense of the ways foodpairs show affinity across the culinary scale we need a metric. The Jaccard index is a simple way to calculate similarity in data-sets. When comparing two sets that are exactly alike (comparing the foodpairs of a book with the foodpairs of its unchanged reprint) it will score 1 -> 100% similarity. If they are completely different the score is 0. 

Using the same Mexican and Indian cookbook as above we can calculate the Jaccard index as 0.11- > of the 8135 unique foodpairs the books together yield, 11% are present in both books. Without context it is a useless number but now look at the graph below that compares the foodpairs from the Jaffrey cookbook with 13 other cookbooks covering a number of styles (national cuisine and celebrity chefs). 

The Jaccard index (in whole percentages) is mapped horizontally. The vertical scale gives the total number of unique foodpairs in both books. 

That Jaffrey compares most with another Indian cookbook gives us some comfort that we are not generating random data. Jaffrey comparing least with Rene Redzepi's NOMA cookbook feels right too. The theory that Mexican and Indian food share the same middle eastern influence is hard to corroborate with this, but it could be informing that it finds more commonality with Middle Eastern food (and Greek) than with anything else.

The next graph compares the Mexican cookbook with the same books. The highest similarities found are with a book by Nigella Lawson and with a book on Hawaiian food. Notice the position of the two Chinese cookbooks in the left corner for both graphs.

Note: saying that we are comparing cuisines is obviously not true. We are comparing English language cookbooks written for an audience of English speaking home cooks, explaining them the things they expect to be explained and with ingredients that can locally purchase. Which brings us to the unanswered question what a cookbook really represents. 
In any case: the problem of meaning here is endless and this stuff will explain nothing.