Today is Shrove Tuesday (this was posted on Feb. 24th), and I will be having pancakes for dinner (yummy). Growing up in Toronto, Canada, my mom made pancakes for breakfast (teddy bear ones), my teachers made pancakes at school (in first grade I even got to pour in the flour), and my dad made pancakes for dinner on Pancake Tuesday.
It's Pancake Day to me, but depending on where you live and how you celebrate it's also called Fasnacht Day, Shrove Tuesday, and of course Mardi Gras. Why Pancakes? Eggs and fat were once forbidden during the 40 day Lenten fast, so on Shrove Tuesday, the day before Lent, British bakers would make pancakes to use up their stores of those ingredients.
So let's flip some pancakes with math on Pancake Tuesday.
You are given a stack of n pancakes, no two the same size in diameter, and asked to sort them in order of size, with the smallest on top and the largest on bottom. At each step in the sorting process, you insert a spatula anywhere you choose within the stack, and then flip over all the pancakes above the spatula. No other pancake moves are allowed. How many flips are required to get the pancakes in order?
From a mathematical point of view, the pancake problem remains unsolved: the exact number of flips needed to sort n pancakes is unknown.
So why is the pancake problem important? According to American Scientist, pancake sorting provides insights into evolutionary processes. In any evolutionary process, changes in DNA sequences (genomes) can cause a new species to split off from an existing one, thus leading to the diversity of lifeforms. Analyzing the transformation from one species to another is analogous to the problem of finding the shortest series of reversals to transform one into the other. So flip your genes like pancakes to put them order!
Don't forget to pick up pancake ingredients and some Maple Syrup (Canadian that is) for dinner tonight. Test out the pancake problem with your stack of pancakes, and let us know how you did it.
Author's Note: This article was posted to the Science Chicago blog by Heather, one of our correspondents.
Editor's Note: For more blogs from Dr. Rabiah, visit Science Chicago's website at: http://www.sciencechicagoblog.com