The team’s computer models that were run using Leonardo da Vinci’s ancient notes about his thoughts on gravity.

Caltech

In 1907, Albert Einstein presented the world with a startling truth about our universe. Gravity, he realized, isn’t quite as strange and mysterious as it feels.

Rather, it’s kind of the same thing as acceleration — a force we’re very used to thinking about on the regular. He called it the equivalence principle, and soon, this eye-opening concept would blossom into the mind-bending theory of general relativity. The rest, as they say, is history.

On Monday, however, engineers with the California Institute of Technology revealed a fascinating new plot point to the story of humanity’s gravitational musings — and it has to do with none other than the renaissance genius himself, Leonardo da Vinci.

As it turns out, not only was da Vinci painting stunning masterpieces in the late 15th and early 16th century like the Last Supper and the Mona Lisa, but was also conducting gravity experiments of his own. For years, he’d been scribbling down equations and drawings about the elusive force that anchors us to Earth, written in old Italian in notebooks such as the recently released Codex Arundel.

He even did it in his signature mirrored penmanship, the researchers say, which simply refers to da Vinci’s tendency to write everything backward for secrecy.

What’s especially striking about these inscriptions is how da Vinci seems to have been on the right track.

In his notes, he’d begun decoding the strange correlation between gravity and acceleration — similar to what enamored Einstein about 400 years later. Da Vinci’s ideas about gravity preceded even Isaac Newton’s formal announcement of the universal law of gravitation in 1687 and Galileo Galilei’s law of parabolic fall, which dictates how objects falling in a gravitational field behave, brought to light in 1604.

“The fact that he was grappling with this problem in this way — in the early 1500s — demonstrates just how far ahead his thinking was,” Mory Gharib, a professor of aeronautics and medical engineering at Caltech and lead author of the paper published in the journal Leonardo, said in a statement.

## The sandy water pitcher and other stories

Here’s a quick thought experiment about how gravity and acceleration are related.

Imagine standing in a nonmoving elevator on Earth. OK, now imagine standing in an elevator in space that’s accelerating upward with a force exactly equivalent to the force of gravity (9.8 meters/second^2).

If there weren’t any windows on these elevators, how could you tell if you were in the space one or Earth one? You couldn’t.

How about this: What if you had to figure out if you were in a non-windowed elevator that wasn’t moving in space and one on Earth that was falling so you experienced weightlessness? Still nope.

Weightlessness on Earth in the presence of gravity feels just like weightlessness in space in what we’d normally consider “zero-gravity.” So, what in the world is gravity?

Well, at risk of simplification, it’s just a fancy way to think about stuff interacting while accelerating in different directions.

One way to think about this is that if a ball were rolling horizontally toward the edge of the cliff, once it reaches the end of the cliff, it won’t really be pulled down by some weird unseen force. It’s just that there wouldn’t be a cliff to hold the ball up anymore, so its trajectory, and therefore direction of acceleration, couldn’t be purely horizontal anymore either. The ball would instead be accelerating on a vertical trajectory.

And according to a press release on the recent study, da Vinci was onto that last bit.

Instead of thinking about cliffs, however, he was thinking about a water pitcher moving along a straight path parallel to the ground, dumping out either water or sand along the way.

In his notes, he specifically states that the water or sand falling out of the pitcher would start accelerating as the materials fell to the ground and that their accelerations, uninfluenced by the pitcher any longer, would be pointed downward.

The water or sand movements were graphed on diagrams that look like triangles.

“What caught my eye was when he wrote ‘Equatione di Moti’ on the hypotenuse of one of his sketched triangles — the one that was an isosceles right triangle,” Gharib said, a phrase that translates to equalization of motions, “I became interested to see what Leonardo meant by that phrase.”

Though da Vinci’s work didn’t end there.

A snippet where you can see da Vinci’s water pitcher idea drawn in his notebooks.

Caltech

His notes also suggest he started trying to mathematically describe the inner workings of the falling object over time in general, attempting to measure how downward objects increased in acceleration as seconds went by. This is related to gravitational theories put forth by Newton and Galileo, too.

To see da Vinci’s equations from the artist’s personal perspective, Gharib and fellow researchers decided to use computer models to run the pitcher experiment themselves. Da Vinci had modeled the falling object’s distance as proportional to the exponent 2 to the power of t, where t represents the time it takes for something to fall.

They wanted to see if the numbers matched up, despite da Vinci’s theoretical models not following the proportions eventually laid out for falling objects by Galilei’s law of fall. (Galilei put forth that the falling object’s distance is proportional to the square of t.)

“It’s wrong,” Chris Roh, assistant professor at Cornell University and co-author of the study, said in a statement. “But we later found out that he used this sort of wrong equation in the correct way.”

Plus, da Vinci didn’t quite have the same caliber of tools to work with as later scientists when measuring variables like time.

I can’t help but think about what he might’ve discovered if he lived today, in a world where we have technological marvels like quantum computers, ChatGPT and atomic clocks at our disposal.