[Jensson]

> they also would have been invented a 3. time if necessary

Not sure what you mean? Romans would have had great use of Newtonian physics, they made a ton of machines, but they didn't manage to invent the math/physics to do those calculations at the time. What do you suggest would replace this for making calculations for machines?

[lukan]

Well, they have been invented 2 times, roughly at the same time largely independent from each other. But it needed a general high level of math. The romans lacked many of the more sophisticated math tools I think.

[Jensson]

No they weren't invented two times, Newtons physics equations were invented one time, then Leibniz reconstructed calculus after reading Newtons work on physics. Leibniz almost surely wouldn't have invented calculus without having read Newtons work on motion, so they aren't comparable.

The only thing that event proves is that inventing calculus if you have the the formulas of motion is easy, both Newton and Leibniz did that, but it was Newton who invented the formulas of motion that was required to invent calculus.

So I think Newtons equations of motions was a requirement for the industrial revolution, that is a key that unlocks the ability to understand machines on a whole new level.

Also Newtons motion equations are simply just

F = ma

They don't require a lot of mathematical pre work etc. But, nobody solved that properly for a really long time, and that is the basis for classical physics so basically every single thing we did during the industrial revolution. It was the key to modern engineering where we use math to calculate machine properties. I don't think it is just random chance that the industrial revolution happened just a few decades after classical physics was invented.

It is such a ridiculous coincidence otherwise, that the formulas and concepts that are the foundation to all of engineering was invented just before engineering took off for real.

[bluGill]

Was it the case that nobody solve the problem, or was it solved many times but since there was no value in the solution at the time we don't remember those solutions? Or maybe it was the industrial revolution getting underway finally made it worth studying at all.

[lukan]

I recently learned, that the pythagorans were more of a cult (who liked secrecy?). I totally can believe that some ancient math nerds solved lots of things already, but with the people around them not understanding. One war could have been enough, to eradicate lots of (semi) isolated thinkers.

[bluGill]

Every book had to be copied by hand so if it wasn't seen as useful the paper rotted in a few hundred years.

[lukan]

My physic courses have been a while, but I would argue with "F = ma" alone, you won't get far, when you want to build high pressure machines and model them before. You do need calculus for that. And quite a bit more I would think.

[Jensson]

F = ma leads to calculus was my point, and that is the starting point if you want to think about pressure etc. Once you have F = ma the rest of physics happened pretty fast, getting to F = ma took millennia, getting from there to exploring most of classical physics took a century.

I got a degree in engineering physics, I have a fairly good idea what kind of physics and math is used for machines and structures. Without the concept of force that Newton invented basically all useful calculations are beyond you, so all machines before then were made via rules of thumb as the math wasn't useful. But when you have the concept of force many of the easy things like how to calculate structural integrity or treating pressure as a field of force isn't that far away.

Then you can start designing machines where you know the components will hold without testing, since you have done the calculations. That is what enables complex machines with many parts.