### Light Bulb Moment

#### By Ginny Olderman Sharkey ’83

It’s been a problem for a long time. Pre-med students have to take at least two math courses in addition to their chemistry and biology classes. But because there are often big gaps of time between learning a theory in math class and applying it in the lab, details can get fuzzy.

Lew Ludwig, associate professor of math and computer science, and Annabel Edwards, assistant professor of chemistry, see this as a puzzle to be solved. They’ve teamed up for a lab in Ludwig’s class, Mathematical Methods for Social and Natural Sciences, MATH-120. The goal is to show how mathematical theory is applied in the chemistry lab.

First students work with Edwards in the lab observing the diffusion of molecules. Given enough time, molecules—which are continuously vibrating in random patterns, forward, backward, sideways, and diagonally—will move themselves through gases (think of the smell of cooking bacon drifting through your home on a Sunday morning). They will also move themselves through liquids (a lump of sugar sweetens your coffee, even if you don’t stir it), and even through semi-solids (the way the cherry juice on top of your sundae stains the whipped cream). To see this in action, the students placed a clear liquid in a long, slender test tube, and topped it with red agar gel. At first the liquids seemed to remain apart, but over the course of several days, students observed the liquid slowly diffusing through the red gel. But why did the liquid need so much time to diffuse into the gel?

Here’s where Ludwig’s lessons in probability theory come in, and all he needs is a coin to demonstrate. If he flips a coin, say, 30 times and moves that coin along a number line, one spot forward for each “head flip” and one spot back for each “tail,” the coin will remain close to the “zero position” because heads and tails cancel each other out. But when Ludwig’s class used a computer to simulate 2,000 coin flips, the probability of a “heads” or “tails” streak became much more likely. Now, instead of the coin staying at the zero position, it actually moved across the number line in significant measures.

In short, Ludwig and Edwards say, those molecules in the liquid are like the coins. Given enough time, their random movements will hit “streaks,” replicating enough times to create diffusion.

A big chemistry lesson boiled down to the flip of a coin. —Ginny Olderman Sharkey ’83