Years ago, I traveled to Amboise, to the Château du Clos Lucé in France's Loire Valley, where Leonardo da Vinci, the Renaissance polymath, artist, architect, engineer, anatomist, and designer of flying machines, spent his final years. In 1516, he accepted King Francis I's invitation to settle there and work on a variety of projects. Leonardo died in 1519 at age 67, in the very room where I stood, gazing at the bed in which he passed. The room opened onto gardens and grounds filled with towering trees. I stood there, looking up into their expansive canopy. Leonardo's curiosity about the natural world was boundless. Among the many subjects in his notebooks were his observations on tree growth, which continue to intrigue scientists and artists to this day. "All the branches of a tree at every stage of its height when put together are equal in thickness to the trunk.…