Isaac Newton era physics and mathematics discovered in the Hellenic world around 300-200 BC
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Unless experimental science is used to prove it, and the results are widely accepted as more valid than other views and taken up by the better engineering craftsmen, this will simply be just one more interesting idea.
We now would look on it much as we do the early atomic theory - a nice bit of philosophising that happened to be not far off the current best descriptions.
We now would look on it much as we do the early atomic theory - a nice bit of philosophising that happened to be not far off the current best descriptions.
One of the problems with this is that requires calculus, and early calculus was very sloppy which was antithetical to Greek thought.
Newton and Leibnitz both relied on infinitesimals, which don't exist. It took hundreds of years and the genius of Euler, the Bernoulli brothers, Cauchy and others to put calculus on a rigorous footing.
It's entirely possible that Archimedes had calculus- but only used it to find results which he proved more rigorously in other ways.
I suppose the best chance might be Archimedes publishes a treatise on calculus - labeling it as a quick and dirty tool to give results which then need to be proven.
Perhaps the Romans, being far more concerned with practice than theory, take it and run with it?
Newton and Leibnitz both relied on infinitesimals, which don't exist. It took hundreds of years and the genius of Euler, the Bernoulli brothers, Cauchy and others to put calculus on a rigorous footing.
It's entirely possible that Archimedes had calculus- but only used it to find results which he proved more rigorously in other ways.
I suppose the best chance might be Archimedes publishes a treatise on calculus - labeling it as a quick and dirty tool to give results which then need to be proven.
Perhaps the Romans, being far more concerned with practice than theory, take it and run with it?
I do wonder just asking how is calculus against grrek though I don't know that much about ancient Greece
By the way, one way to get a foot inside the Calculus problem was to solve the Gravity acceleration at the first place.
First, the Greeks need to somehow discover mechanical clock to accurately time seconds or in fraction of seconds. If they can done that, once Gravity acceleration constant has been properly measured (the Greco-Romans already knew linear acceleration and deceleration ) it might just need the proof about arrows being furthest launched from 45 degree angle to have rulers started to backing science up.
As I said, early calculus is logically very sloppy. Greek Geometry required great logical rigor, and Greek philosophy tried for the same.
Your best bet, as I suggested, would be to get it out their as 'a useful tool', to figure out what answers might be.
Mind you, without 0 or negative numbers or graphs or even algebra, it's going to be unnecessarily hard.
Even with calculus and the developments since the Renaissance, hydraulic engineering (how water behaves in pipes and channels) took a long time (roughly two centuries) to be developed to a robust and usable condition. Bear in mind how important this was for designing canals, getting drinking water to and around towns and cities, and for water-powered equipment (watermills) and it looks likely well into the imperial roman era before Greek calculus could be usefully applied.
Modern "atoms" aren't atoms under the Greek definition, they just happen to share a name.
I know. That's why I said "not far off".
Other philosophers postulated that thee was no limit and that things could always be cut further, so we could say that they were also not far off.
But neither they nor any other group had any way of showing they were right or of using the information. Not that this diminishes the quality of their thought experiments,but thought only is a limited path.
And they might have viewed this as the pristine case and the way things should be. And everything else as inferior.
Two diametrically opposed positions can't both be "not far off" the truth.
To borrow from Niels Bohr.
"The opposite of a correct statement is a false statement. .... A great truth is a truth whose opposite is also a great truth."
To borrow from Voltaire, "A witty phrase proves nothing."
But to get back to the subject at hand: the whole point of ancient atomism was that atoms are the smallest, most fundamental, parts of the universe. The "atoms" of modern science are neither of those things. Sure, if you squint hard enough, there are similarities between what Democritus said and what modern scientists say, but you could say the same about most ancient Greek natural philosophers.
I was attempting to use Bohr to agree with you, but the Voltaire quote is a good one, and one I wasn't previously aware of so I think it will get some use.
First of all, I think that need top be noted that the 'Isaac Newton era Physics and Mathematics' not happened in a vacuum but rather it happen thanks to the scientific buildup that made it possible. Also, that, imo, and by way of example the Greeks philosophers would need to discover and apply the concept of zero, But even so they still would need to create and develop something similar to the Hindu-Arabic numerical system.
I think the best prove of this statement is that both Newton and Leibnitz invented calculus at roughly the same time. Simply put, the world was ready for calculus.
Ahem. It did take quite a while, but since the 1960s it's been impossible to argue that infinitesimals cannot be made into a rigorous basis for calculus just as good as anything Cauchy or Weirstrauss ever did. I'm also skeptical of your "antithetical to Greek thought" comment, because frankly the Greeks were incredibly sloppy about lots of things, they just liked to pretend that they weren't.
Well, true, but that required far fancier math than existed in the 1600s, let alone classical times. I read some of that stuff back in the day. But it's really not germane to this discussion.
The invention of calculus relies heavily on the, let's say, ''Numbers Are Points on a Line'' concept or metaphor. While the Hellenic world possessed great understanding of geometry, they did not introduce numbers to that field in a way that made calculus possible. The development of calculus was a long and ardeous historical process that could not have happened 2000 years than it actually did.
Now, the history of mathematics is not deterministic. In my opinion an interesting math POD would be Cladius' (yes, the emperor) lost book on dice games. This is actually huge. Although we do not know the contents of the book, its survival could have led to a much earlier development of discrete mathematics (probability, graph theory etc.) which only happened IOTL in the 1700s.
Now, the history of mathematics is not deterministic. In my opinion an interesting math POD would be Cladius' (yes, the emperor) lost book on dice games. This is actually huge. Although we do not know the contents of the book, its survival could have led to a much earlier development of discrete mathematics (probability, graph theory etc.) which only happened IOTL in the 1700s.