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The exponential growth in knowledge output and technological advancement started before the formalization of the scientific method though.

There's a variety of factors contributing to this, to name some:

- Social mobility as a result of the Black Death

- Excess agricultural output, leading to population growth and specialization

- Wealth extracted from the Americas leading to a new class of Idles

- Certain inventions, like the printing press, massively increasing knowledge retention and spread.

Even more egregiously, this is a distinctly English view - neither the French nor the Germans have such a narrow view of science and at least until the late 1800s both had a higher scientific output than the English. This narrow view of science is ok if there is a positively-connotated word to describe the process of knowledge advancement, in English I guess that would be academia, although that is too narrow still. Without engineering and mathematics, science would have started to stagnate centuries ago - or never been formalized in the first place.



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