It’s sheer nonsense. For one thing, the European rediscovery of ancient Greek mathematical sciences was a primary driver of the European development of infinitesimal analysis or calculus. Non-Greek mathematical innovations like decimal place-value numerals and algebra techniques also contributed, but the engagement of early modern scholars with the works of, say, Archimedes, Diophantus and Apollonius as well as Euclid was a major inspiration for the research that subsequently produced the first modern quantitative theories of ballistics, optics, materials science and mechanics in general.
Pretty much. There were decisive factors in the European context of the early modern scientific breakthroughs, but no inevitably decisive factors.
This wasn’t unique to Protestant Christianity, though. Islamic theology, for example, had been similarly engaged for quite some time. Although it might have seemed like a unique development to Europeans already steeped in self-conscious “Protestant exceptionalism”.
How did the works of the ancient Greeks lead to the development of infinitesimal analysis or calculus? Mathematicians like Democritus and Zeno essentially pointed subsequent mathematicians away from the development of calculus by declaring that seeking answers in that direction only led to paradoxes and dead ends. And while Euclid did some great work in geometry, it took mathematicians well over a thousand years to get past the proof-based model he established and explore fields like probability where you didn’t get a single definitive answer.
Along many different routes, including classical inspiration for Viete’s “zetetics” and poristics, the role of classical locus problems in the development of tangent methods by Fermat, Roberval, Descartes, ancient results on series in the infinitesimals concepts of Cavalieri, Wallis and Newton, etc.
I don’t understand why you’re focusing on the earlier Hellenic philosophers like Pythagoras, Democritus and Zeno and ignoring the contributions of the Hellenistic mathematicians whose works actually did significantly influence the work of early modern European ones.
Yes, I agree that if you’re only considering pre-third-century Greeks, their direct impact on early modern mathematics isn’t particularly substantial. But why are you ignoring the later Greeks?
So what? The infinitesimal-analysis breakthroughs and their profound consequences for early modern mathematics and physics didn’t involve probabilistic models.
I’m certainly not trying to claim that ancient Greek mathematics directly foreshadowed or facilitated all the developments of early modern science and mathematics in Europe. But it’s absurd to claim that it wasn’t a huge influence overall, especially when that claim rests mostly on making arguments about the earlier Hellenic philosophers while ignoring the far more influential post-Euclidean mathematicians.
Copernicus’ discovery that the Earth rotates around the Sun was crucial. Not just because it led to the laws of motion and gravitation — though they were important — but because when the Earth lost its centrality, religion lost its stranglehold. Columbus’ discovery of lands and people unknown to the ancients and unknown to the writers of the Bible also challenged orthodoxy and encouraged creative thought.
The Reformation of Martin Luther occurred at just the right time to encourage freedom of scientific thought.
The inventions of telescope and microscope were very important. Why weren’t these developed earlier? The basic principles were known by earlier civilizations; it is said that Emperor Nero wore lenses to correct for myopia.
The calculus was essential for the development of physics, but this wasn’t new with Newton and Leibniz. Various earlier mathematicians had developed some of it already, including Archimedes himself.
One thing we can be sure of is isolated societies tend to be backward societies. The Chinese and Japanese governments liked to limit the influence of foreigners on their societies and would limit or outright ban traders and others from their shores. This cut off the exchange of ideas that is strongly associated with trade and left them to stagnate.
Similar isolation doomed sub-Saharan Africa, not because of any political decision but because the geography of the continent prevented much collaboration. Before the invention of the railroad all the great cities of the world were built on rivers which facilitated trade and although there are many great rivers in Africa they don’t lend themselves to navigation. Whereas, for example, the Mississippi is a relatively calm river that lends itself easily to floating goods and people, the rivers of Africa, although similar in terms of water levels, are full of waterfalls and rapids that make using them for more than a few miles impossible. This isolation is evident by the thousands of languages in Africa.
Are you implying causation or just correlation? If the former, do you have evidence? It could be true, but it sounds to me like a “Just So story.”
Ditto.
I’m sure Columbus’s discovery spurred sciences related to navigation, but I don’t recall encountering the claim that they “encouraged creative thought” before. (Plenty of Europeans were already living in “lands unknown to the writers of the Bible.”)
This isn’t necessarily Protestant exceptionalism. Rather it’s two competing versions of truth attempting to prove their viewpoint. Both sides were active in promoting the sciences and for their own particular reasons. Prior to the French Revolution, the largest funder of scientific research was the Catholic Church.
Of course, the Merton thesis does postulate that Protestantism or more particularly Puritanism/Pietism and its associated ascetic tendencies promoted an even more explosive growth in scientific knowledge. They also encouraged intellectual autonomy as a buttress against the more hierarchical Catholic model and the ‘Protestant Work Ethic’ encouraged devoting oneself fully to one’s vocations which led to the rise of ‘full-time scientists’ as opposed to the Renaissance model of being a dabbler in many disciplines.
How about: “Open-mindedness about science fostered open-mindedness in religion. and vice versa. Together they formed a ‘virtuous circle.’”
I’ve never encountered the claim about Columbus’s discovery either — it’s an original septi-thought. But I think this sudden discovery “shook up” the consciousness of Europe. Note that people are often motivated by a quest for glory rather than a quest for wealth.
I picked up and re-read my copy of Singer’s Short History of Scientific Ideas to 1900 (1959). I didn’t notice any obvious support for my claims but Singer did make some interesting claims of his own. (And reinforced the idea that mass printing of books was key to the Scientific Revolution.)
Singer claims that high-quality metal-working in Germany helps explain why successful printing presses were developed there. Similarly, excellent craftsmanship led to the important inventions of telescope and microscope. Extrapolating, one wonders if there were many interesting synergies that contributed to the Revolution.
Singer also describes a trend that I will only hint at. Apparently the Arabs had translated the mathematics and science of ancient Greece but ignored Greek philosophy and literature. It was ‘Renaissance humanism’ (with some relationship to ‘Catholic scholasticism’?) that rekindled appreciation for the creativity of ancient Greece.
The text of Singer’s book is online, so I’ll let any bored Doper “take one from the team,” wade through his Chapter VI and try to discern his idea, or whether it has any merit. Here are some summary paragraphs: