Safe Haven

Nature's Admonition

THE SWISS FAMILY BERNOULLI

The city of Basel is perched at the northern corner of Switzerland along the Rhine where the river forms a crossroads with France and Germany today, as it races through steep gorges toward the North Sea. In the seventeenth century, this geographic position made it the commercial hub of central Europe. Basel was among the Free Cities, having gained its recognized independence from the Holy Roman Empire in 1648. Likewise, it became a banking and cultural capital, a place for free thinkers, and even came to be thought of as a safe haven from the political turbulence of Europe.

The Swiss family Bernoulli was among the most prominent in Basel. While the family business was mostly spice trading, they spawned two mathematician brothers, Jacob and Johann, starting a dynasty. In time, the brothers formed a renowned competitive and belligerent mathematical relationship, certainly to the benefit of each other's careers, if not their sanity.

Among the problems they tackled together was the Brachistochrone problem, whereby a marble is rolled down a ramp, and the objective was to find the optimal shape of the ramp to achieve the quickest descent of the marble. Johann demonstrated that a very particular curved ramp won the day—a counterintuitive design because this roundabout route required the marble to travel a farther distance than the straight‐shot ...