Did you know that when you purchase packaged fruits and vegetables, you are buying food that may contain bugs? They’re not listed on the label. You never see it mentioned on TV commercials and in newspaper advertisements. But they might be in there.
I never thought seriously about this until I received a call from Rabbi David Bistricer of the Orthodox Union asking me, as an applied mathematician, to help the OU come up with a methodology for approving fruit and vegetable products for kosher certification. You see, insects aren’t kosher. And thus for the OU to certify a product containing fruits or vegetables as kosher, they must be pretty sure that the probability of insect infestation in the product is very low.
Here’s The Problem:
A large batch of vegetables, say, a load of several thousand cabbages, is brought to a processing plant. In order to make the desired product, the vegetables are washed and then processed into the food we purchase in the store. However, if the batch of vegetables often contains insects, it must be checked before consumption. It is impractical, tedious, and very costly to check each leaf of each vegetable before deciding whether to accept or reject the whole batch. Rather, given that the vegetables all come from a single field or several fields with similar properties, can we devise a reasonable strategy for determining whether after washing one can be at least slightly greater than 90 percent certain that the whole batch of vegetables will have fewer than one bug for every ten of the vegetables. That is, how many cabbages from the batch ought to be randomly selected and tested (cut up and carefully inspected) and what criteria should be used to decide whether a batch is acceptable or must be discarded?
I must admit that at first, I was a bit queasy at the thought that for years I may have been eating bugs. The only bugs I wanted to deal with were those in my computer codes – and I wasn’t terribly fond of those bugs either. But as a kosher consumer and mathematician with the utmost respect for the OU, I was intrigued at the idea of using mathematical modeling and statistics to play a role in increasing the sanctity of the United States food supply. And despite their protein content, I figured chances of having fewer bugs is better than chances of having lots.
After consulting with statistics experts Professors Manish Bhattaharjee, Sunil Dhar and Ari Jain and graduate students Satrajit Roychoudhury and Ivan Zorych, all from our Department of Mathematical Sciences at the New Jersey Institute of Technology, and explaining to them some relevant aspects of kashrut, I started working on the problem. I found Rabbi Bistricer to be a very good listener, asking thoughtful questions and learning to understand the mathematical issues that arise when taking small samples: What can you learn and how confident can you be in your result?
After attempting several approaches and finding drawbacks in each, I implemented a simulation method that avoided those pitfalls and arrived at strategies for inspection that would enable the OU to efficiently decide which batches of vegetables to accept and which to reject. I have since learned that Rabbi Bistricer and the OU poskim have adopted my findings and implemented the recommendations in their supervision of fruit and vegetable products.
I am happy to have contributed to something that will benefit many people bug free kosher food. In addition, this can only add to the reputation of kosher food being of high quality and meeting exacting standards. Now kosher can even mean “bug free” (although I don’t know if companies will want to advertise it that way). It is quite satisfying to have one’s work adopted in the “real world.” It is not often that a mathematician in academia gets an opportunity to have his or her work influence decisions and processes in industry, especially in such a short time. I found my work for the OU to be interesting and rewarding and the people I worked with there dedicated to providing an important service to the Jewish community.