Thus was Leonardo spared from being trained to accept dusty Scholasticism or the medieval dogmas that had accumulated in the centuries since the decline of classical science and original thinking. His lack of reverence for authority and his willingness to challenge received wisdom would lead him to craft an empirical approach for understanding nature that foreshadowed the scientific method developed more than a century later by Bacon and Galileo. His method was rooted in experiment, curiosity, and the ability to marvel at phenomena that the rest of us rarely pause to ponder after we’ve outgrown our wonder years.

During his early years in Florence, Leonardo lived with his father, who arranged for him to get a rudimentary education and would soon help him get a good apprenticeship and commissions. But there is one significant thing that Ser Piero did not do, which would have been easy enough for a well-connected notary: go through the legal process of having his son legitimated. This could be accomplished by the father and child appearing before a local official known as a“count palatine,” usually a dignitary who had been granted power to act on such matters, and presenting a petition as the child knelt. Piero’s decision not to do this for Leonardo is particularly surprising, since he then had no other children of his own.

In reasoning so, he showed that, as we go through life, there is a value in trying to do such tasks as designing a perpetual-motion machine: there are some problems that we will never be able to solve, and it’s useful to understand why. ... What prevents perpetual motion, Leonardo realized, is the inevitable loss of momentum in a system when it rubs against reality. Friction causes energy to be lost and prevents motion from being perpetual.

Seek knowledge for its own sake. Not all knowledge needs to be useful. Sometimes it should be pursued for pure pleasure.

Many of the workers lived and ate together in the quarters upstairs. The paintings and objects were not signed; they were not intended to be works of individual expression. Most were collaborative efforts, including many of the paintings commonly attributed to Verrocchio himself.

As Vasari explained about Leonardo’s unfinished works, he was stymied because his conceptions were “so subtle and so marvelous” that they were impossible to execute faultlessly. “It seemed to him that the hand was not able to attain to the perfection of art in carrying out the things which he imagined.” According to Lomazzo, the other early biographer, “he never finished any of the works he began because, so sublime was his idea of art, he saw faults even in the things that to others seemed miracles.”