One key source of confusion is the Ars Technica author describing the primary science paper as saying da Vinci estimated the value of G, the universal gravitational constant. That's the one used in the expression F = G x m_1 x m_2/r^2, where F is the force due to gravity between point masses m_1 and m_2 separated by a distance r. The experiment she describes, by contrast, would instead be one to calculate g, the accleration due to gravity at the surface of the earth. da Vinci could not have estimated G, since at the least it requires Newton's equation for universal gravitation.
This does get clarified later on in the article, but it is poorly worded. The estimate of G came from the paper’s authors, using da Vinci’s models, rather than da Vinci himself.
In fact, 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.
She also says this is da Vinci anticipating Einstein, but that really seems like an overreach, and this is instead da Vinci anticipating Galileo and Newton. That's impressive enough without having to market it by invoking Einstein. And it does a disservice to Galileo, who realized gravity was a force that caused accleration that is independent of mass.
I didn’t read that reference the same way.
Finally, her description of da Vinci's error in using 2^t instead of t^2 would have been made much clearer if she just supplied the actual equation da Vinci used, with the correct one for comparison. I swear this math aversion these science writers have just leaves people more confused instead of less.
According to one of the paper authors, there wasn’t an equation per se, any mathematics as we’d understand them today seems generated by the paper’s authors translating/interpreting da Vinci’s notes.
"There was no concept of equations or math, but Leonardo had such an intuitive understanding of math in its non-equation form," Roh told Ars. "I think that's where he started using geometry to write out equations, in a way. Without any tools—no clock—he just uses this geometry as evidence for equalizing the two motions. One [motion] that he can control, one [motion] that he cannot [control] but wants to understand, and the other line to show that they're equalized at every little step. He approached it more like a computer scientist and modeled it more algorithmically."
As this article was also an interview with the paper’s authors, I have to wonder how much of the article is simply paraphrasing the interview.
There’s learning something in a book, but to be one of the first to even conceive of an idea and document it is really something that’s hard to wrap your mind around.
I think it depends on where you place the bar. The concept of taking a ship to the moon predates the German rocket program that led to the V2 and ultimately Apollo to some extent. The ability to dream about a thing tends to exceed our ability to realize that dream, sometimes by hundreds or thousands of years. That can be a lot of time for things to snowball. But I think we tend to undervalue the “standing on the shoulders of giants” aspect of how we tackle these sorts of questions/problems/etc.
I sometimes wonder how much human knowledge was lost only to be “discovered” again centuries later. Or even concurrent discoveries of principles like electric light that occurred oceans apart but at basically the same time in history, with no interaction between them.
This happens more frequently than you might think. We also have a habit of distorting our own recording of history which tends to make thinkers of the “ancient world” seem dumber than they were. Aristotle performed experiments that measured the radius of the Earth. Aristarchus pushed the idea of heliocentrism and even speculated that stars were suns, so far away that you couldn’t measure the parallax effect, arguing against geocentric thought from Aristotle, only to have his work lost. But when I was growing up, public education was teaching that Copernicus was the origin of heliocentrism, and people commonly thought the Earth was flat until Columbus “proved” otherwise. I even recall some bits about how this allowed us to move beyond the ancient greek way of thinking of the universe. Despite the fact that apparently they already had a pretty good idea what was up, even if they couldn’t probe it like we can now.
One of the most recent PBS Spacetime episodes covered the fact that early descriptions of the Weak and Strong force came out of Japan, and researchers in India were the ones seeing evidence of the meson particles that Yukawa predicted in cosmic rays. We have a tendency to focus more on folks out of Europe and the US when it comes to physics despite a lot of collaboration and concurrent work in the space. It’s also been common for multiple folks to get credit for the same work when it turns out they wrote similar/overlapping papers in physics. In the 20th century, it’s been a bit easier to find out when this happens, although it isn’t perfect.
Makes you wonder if there really is “something” out there like Collective Consciousness that we don’t understand.
I think it‘s probably a bit more boring. People are not fundamentally different today than 10,000 years ago. We‘re numerous and so ideas will bubble up multiple times in multiple places. What has changed is more that we’ve been building up knowledge through fits and starts in multiple cultures over thousands of years, but some of those ideas made it easier to record other ideas. The printing press for example. Today, if someone publishes a paper, it can be around the world in under a week for those who have means (this is unfortunately important). Not so in da Vinci’s time, let alone Aristotle’s. We’ve made it easier over time to keep hold of knowledge.
arstechnica.com
:
