Finding meaning in the impossible

Some questions may never be answered, but maybe that’s not the point

There are questions in science that have been studied for so long without anyone turning up answers that they seem to move into the realm of “unsolvable” or even “impossible.” This is the realm we explore in Scientific American ’s October issue.

When the editors first discussed this idea, a real concern became immediately apparent: Will our readers be disappointed at the very premise of an unanswerable question ? Why dive in if we can’t satisfy their, and our, curiosity with a solution?

But we soon realized that this open-endedness is part of the appeal. Often the most fascinating questions are the ones with no obvious or direct rewards. Unlike figuring out the odds that someone will have a green-eyed baby, the knotty, impossible questions sit in uncharted territory. Scientists must approach them from many different angles, some of which require new tools and experiments never before conducted. Such undirected searching is exactly what fuels serendipity.

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We probably wouldn’t have the blockbuster GLP-1 weight-loss drugs now reshaping medicine, for instance, if someone didn’t ask how Gila monsters cheat starvation—the lizards’ blood sugar never collapses even though they sometimes go months without eating. There was no obvious payoff to finding the answer and no pharmacology at the time that could explain the anomaly.

Alchemists searched for centuries for a way to turn common metals into precious ones such as gold—an impossible challenge when relying on a philosopher’s stone. Along the way, they established the field of chemistry and discovered the process of distillation that is ubiquitous today in water purification, pharmaceutical production and even fragrance making. (Physicists at the Large Hadron Collider at CERN near Geneva accidentally did turn lead into gold recently, at least for a fraction of a second.)

For more than 2,000 years mathematicians chased a problem called squaring the circle, in which they tried to craft a square with the same area as a circle, using only a compass and a straightedge. Proof that it was impossible came with the discovery of transcendental numbers, which led to theorems that opened entirely new branches of mathematics.