Science

A Doodle Reveals da Vinci’s Early Deconstruction of Gravity


When Leonardo da Vinci wasn’t painting a masterpiece or dreaming up flying machines, he was pondering the mysteries of gravity. The Renaissance thinker considered himself as much a man of science as an artist and spent untold hours exploring how the “attraction of one object to another” could affect such things as the flight of birds and the fall of water.

Now, scientists have discovered that Leonardo did detailed experiments that sought to illuminate the nature of gravity a century before Galileo and some two centuries ahead of Newton’s making its investigation an exact science. The scientists’ study of his gravitational ideas and experimentation was published earlier this month in the journal “Leonardo.”

“Nothing could stop him,” Morteza Gharib, an author of the paper and a professor of aeronautics at California Institute of Technology, said in an interview. “He was far ahead in his thinking. It could not wait for the future.”

Z. Jane Wang, a professor of physics at Cornell University who has studied some of da Vinci’s pioneering analyses but was not involved in the current paper, said the new study revealed a man determined to find an iron law of nature that would shed light on the overall dynamics of falling objects.

“It’s not enough” to call the polymath an artist, Dr. Wang said. More accurately, she added, he was “a quintessential” man of the Renaissance, which gloried in the revival of not only art and literature but also science and explorations of nature.

Leonardo has long been famous for his technical ingenuity and versatility, for his sketches of flying machines and fighting vehicles. He also made advances in geology, optics, anatomy, engineering and hydrodynamics, the arm of science that explores the behavior of fluids.

Walter Isaacson, in his biography of da Vinci, reports that as a close observer of nature, he gave much attention to how birds shift their center of gravity as they twist, turn and maneuver in the wind. He also said that Leonardo realized that gravitational attraction kept the seas from falling off the earth.

What caught Dr. Gharib’s eye is what he calls “a mysterious triangle” near the top of Page 143. Its strangeness lay in how Leonardo’s sketch showed an adjoining pitcher and, pouring from its spout, a series of circles that formed the triangle’s hypotenuse. Dr. Gharib used a computer program to flip the triangle and the adjacent areas of backward writing.

Suddenly, the static image seemed to come to life. “I could see motion,” Dr. Gharib recalled. “I could see him pouring stuff out.” It was a eureka moment that unveiled Leonardo’s precocious experiment.

The effects of gravity are typically seen as causing something to fall straight down — be it a dropped ball or Newton’s apocryphal apple. In gazing at Leonardo’s drawing, Dr. Gharib realized that he had managed to split the effects of gravity into two parts that revealed an aspect of nature normally kept hidden.

The first effect was the natural downward pull. The second was added when the holder of the pitcher moved it along a straight path parallel to the ground, pouring out sand or something else along the way. In the drawing, Leonardo noted where the movement of the pitcher had begun, labeling it with the capital letter A. Then, to show the falling material, he added a series of vertical lines going down from the triangle’s top line, the series getting longer as the pitcher moved farther and farther from its starting point. Their growing lengths defined the hypotenuse.

The setup turned gravity’s hidden nature into visible increments. The pitcher experiment, Dr. Gharib said, revealed that gravity was a constant force that resulted in a steady acceleration — a steady gain in speed. Leonardo illustrated the gain as the pitcher’s contents falling lower and lower over time. He succeeded in deconstructing gravity.

The researchers say Leonardo wrote in the codex that he witnessed fast-moving clouds from which pellets of hail had fallen, which they believe inspired the experiment.

Dr. Gharib said “the fascinating part” of Leonardo’s feat was that it let him estimate a constant of nature, the gravitational constant, represented today in physics by the letter G. The constant quantifies the exact strength of gravity’s pull and thus how quickly it can accelerate an object.

Despite the crudeness of his experimental setup 500 years ago, da Vinci, Dr. Gharib said, was able to calculate the gravitational constant to an accuracy within 10 percent of the modern value.

“It’s mind boggling,” Dr. Gharib said. “That’s the beauty of what Leonardo does.”

The researchers say that Galileo and Newton could better address the gravitational question because they had better tools of mathematics and better ways of measuring time precisely as objects fell.



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