On the Informational Requirements of Indian Cooking

This short note is inspired by Prof. S. K. Mitter’s comments on the informational requirements of Indian cooking, made in response to Prof. D. Shah’s “Salt Lemma” on September 20. It casts cooking as a problem of controlling a dynamical system; the system may be stable or unstable (depending on the cook and the food being cooked). It discusses a scenario where there is a local actuator/observer and a distant controller, connected through a communication link. The communication link is modeled after a parallel channel that has recently been deployed in India, connecting Lucknow to rural villages. Comments on the Indian notion of jūt.hāpana and its inducement of noisy observations are also made. The Problem of Cooking Cooking typically involves a cook following a recipe to transform ingredients into food. Following a systems theoretic approach, the ingredients are the system inputs, the cooked food is the system output, the recipe is the system input-output map (often specified in an inexact way), and the cook is an actuator/observer/controller. Often when cooking, the recipe is not implemented exactly, and the system is perturbed. When such a perturbation occurs, the cook must use some control strategy to return the system to its intended trajectory. The perturbation usually does not cause the system to become unstable, however it is definitely possible. The ability to deal with perturbations is the sign of an expert cook. Some recipes are more prone to instability than others. As an example from Indian cooking, systems that involve turmeric as an input are quite prone to instability. Too little turmeric results in food that is insipid, whereas too much turmeric results in food that is overly bitter. Cooking at a Distance Consider a situation where one wants to recreate food from a proximate point at a distant point, assuming that there is no knowledge of cooking at this distant point. We will denote the proximate point as mother, and the distant point as son. Clearly, one must transmit the system input-output map, as specified by the recipe, from the mother to the son. Furthermore, the son must be able to implement the mother’s control strategy. Often, however, this control strategy is not specifiable in a form that allows it to be communicated from the mother to the son. If however, there is a communication link with sufficient reliability and low latency, the mother’s controller can directly control the system through the son’s actuator. There is an interesting question regarding the channel requirements for such a cooking at a distance problem. Communication of the recipe apparently does not have particular latency requirements but may have large capacity requirements, whereas communication of the observations from the son to the mother and the control signals from the mother to the son apparently have small capacity requirements but significant latency requirements. Thus it appears that there are two qualitatively different information streams that are involved in the mother–son communication procedure, in a fashion similar to the anytime information theory results on exponentially unstable stochastic processes shown by Sahai and Mitter [1].