Trails of a Wanderer

He calmly rode on, leaving it to his horse's discretion to go which way it pleased, firmly believing that therein consisted the very essence of adventures.

—Miguel de Cervantes (1547-1616), Don Quixote

A sharp knife bites through the papery skin of a clove of garlic, exposing the bulb's pale interior to the air. Within seconds, a pungent, penetrating odor drifts to the chef's nostrils.

Garlic bulb.

The distinctive tang of freshly chopped or crushed garlic arises from the rupture of cell membranes, which allows the huge protein molecules of an enzyme called alliinase to reach and capture tiny molecules of a chemical compound known as alliin.

The enzyme stretches and twists the trapped molecules, snapping the chemical bonds and rearranging the atoms of alliin to create the unstable compound allicin. Allicin, in turn, readily transforms itself into diallyl disulfude, which is responsible for garlic's distinctive odor.

As the odor-inducing molecules of diallyl disulfide seep out of the mashed garlic into the air, they begin to drift randomly, jostled by oxygen, nitrogen, and other molecular and atomic constituents of air and transported by wavering currents. Some soon reach the chef's nose.

The wandering molecules of diallyl disulfide travel along nasal passages to the back of the nose to reach a delicate sheet of moist, mucus-bathed tissue, where a large number of nerve cells cast their hairy, odor-sensing nets. When a receptor strand snags a molecule, it triggers a set of actions that generates an electric signal, which travels to the brain, and the chef immediately recognizes the smell of garlic.

Our capacity to smell depends on the passage of specific molecules from the source to the sensors in the nose. In contrast, we see and hear because waves of energy, whether electromagnetic radiation or vibrations of the air, carry the signals. No molecules or atoms actually make the journey from firefly and drum to eye and ear.

In the realm of smell, we deal with a statistical process—the effect of thousands upon thousands of random steps as molecules venture into the rough-and-tumble domain of incessant collisions and follow haphazard paths to the nose.

We can imagine such journeys as random walks, with molecules traveling in straight lines until they collide. With each collision, they rebound like billiard balls and start off in a new direction—not very different from the disordered steps that a blindfolded person might take if he or she were walking in an unfamiliar landscape studded with obstacles.

Random movements play a significant role in a variety of natural phenomena. Hence, the mathematics of random walks is a key element in modeling and understanding not only the jiggling of molecules but also the possible configurations of a polymer's long molecular chain, the flight paths of such foraging birds as the wandering albatross, and even the erratic fluctuations of stock market prices.

Next: Quivering Particles I