A Complex Perspective of Cake Cutting
Think of any questions one may have if they were in the scenario of wanting to cut the perfect number of slices of cake at a party. At first, you must think I am being ridiculous. There's no question, just cut the cake, right? Hold on, what about these...
How many people are attending the party?
How many people are going to eat the cake?
Are people going to eat the cake slices individually or will they share with one another?
Do people have certain preferences like no icing or no chocolate?
What if cake eaters lie about their preferences?
What if the fruit or any other treat inside the cake are not evenly spaced out?
Will people get upset about that? Are there allergies?
Will people think that the person cutting the cake is giving themself the biggest slice? Believe it or not, these are the types of questions mathematicians, economists, computer scientists, and people from so many other fields are dwelling upon. With the ultimate question being: What methods for cutting a cake guarantee that everyone who shows up at the party is happy with what they got?
Ariel Procaccia, a Harvard Computer Scientist who has attended dozens of birthday parties because of her children, focuses her work on exploring the mathematical rules for dividing stuff up. She along with other scientists have conducted experiments, models, metaphors, and created algorithms which they hope will one day help them solve the problem at hand. Why?
Well, the cake cutting question connects rigorous reasoning to questions of human preferences and real-world issues. For instance, you can think of the cake as land, time, limited resources, or really anything that is divisible. The complexity of the problem will only continue to grow as more people are added, and as the human population continues to grow. Recent studies have used a rectangular cake shape to prose questions. Many professionals attempt to understand if cake cutting is finite or infinite. Picture this: If there are a minimum and maximum number of cuts, then cake cutting is finite. But, can such a value ever be reached? If not, then it's infinite.
I get it, I get it. You must think these people are overthinking it. But, if the ability to divide something, anything divisible and make each person content is possible, then wonder its world applications and just truly how much of an impact this solution can make on society. After all, one can argue that fairness or the lack of thereof is one of, if not the most important issue in our globe today.