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Kitchen Table Kibitzing ~ 2/11/23: Leonardo...and another genius [1]

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Date: 2023-02-11  

Mory Gharib and fellow Caltech engineers have published a new paper in the journal Leonardo, demonstrating that the Renaissance master had a clear handle on the link between gravity and acceleration, albeit four centuries before Albert Einstein demonstrated the same concept in his general theory of relativity. Gharib made the discovery while perusing some of Leonardo’s notebooks (out of 13000 pages of them, only about a third have survived), now digitized for posterity.

As reported by the intrepid Jennifer Oullette, writing for ArsTechnica:

Gharib and his collaborators described their discovery in a new paper published in the journal Leonardo, noting that, by modern calculations, Leonardo's model produced a value for the gravitational constant (G) to around 97 percent accuracy. What makes this finding even more astonishing is that Leonardo did all this without a means of accurate timekeeping and without the benefit of calculus, which Isaac Newton invented in order to develop his law of universal gravitation in the 1660s.

Most folks have at least a passing familiarity with Leonardo’s incredible notebooks, which, in addition to their voluminous anatomical studies, “contain all manner of inventions that foreshadow future technologies: flying machines, bicycles, cranes, missiles, machine guns, an “unsinkable” double-hulled ship, dredges for clearing harbors and canals, and floating footwear akin to snowshoes to enable a man to walk on water.” In this case, Gharib came across a series of small, overlapping triangles seemingly overlaid beneath a vertical and horizontal axis. At the end of the horizontal axis, Leonardo drew a water pitcher, apparently pouring out grains of sand. Gharib determined that this axis represented “directed” acceleration of the pitcher as it poured the sand, while the vertical axis represented the “natural” motion of gravity.

As Oullette reports:

From Leonardo’s many notebooks

The experiment in question involves moving a water pitcher at a fixed height along a straight line, parallel to the ground, as grains of what is most likely sand pour out. Plotting the changes in the pitcher's position moving at a constant speed, the sand falls in a vertical line, and no triangle forms. Accelerate the pitcher at a constant rate and the sand forms a straight but slanted line, forming a triangle. It was the pitcher's motion accelerating at the same rate that gravity accelerates, said Gharib, that produced the key diagram that first caught his interest: an equilateral triangle with that written phrase along the hypotenuse that translates to "equalization (equivalence) of motions."

Gharib believes he understands what Da Vinci was attempting to convey with the sketch:

"What is Leonardo trying to do?" said Gharib. "He's trying to say, 'If I could move my hand or move the jar the same way that gravity acts on particles'—in this case, sand—'if in a given time they travel the same distance, then I have mimicked the gravity just by acceleration.' He calls it the act of motion. He does it in a different direction than gravity. So that means he clearly understood that gravity is a kind of acceleration, but toward the Earth—otherwise he would not have tried to mimic it by acceleration."

Not satisfied with simply demonstrating the link between gravity and acceleration, Leonardo also sought to determine a gravitational constant, without the benefit of mathematical equations. As Gharib tells Oullette, Leonardo had “an intuitive understanding of math in its non-equation form,” and used geometry to express mathematical concepts. Although his calculation for the gravitational constant incorporated an error, “when Gharib et al. used Leonardo's "algorithm" to plot his model and fit that to our modern equations, the measurement for the gravitational constant was 97 percent accurate.”

Leonardo is, to this day, regarded by many as the world’s foremost creative genius. As Walter Isaacson, former editor of Time magazine, puts it:

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