Asklemmy

There were democracies before industrialisation by the way, e.g. in ancient Greece.

Yeah, they called it that, but most of the population was literal slaves and like 1% of the population was actually rich and male enough to participate in the political process in any way. Same story with the Republic of Venice and all the other pre-modern republics, it was basically monarchy by council. Power actually derived from the masses is new within the last couple centuries or so. I don't think people realise this enough.

The British Empire started the same way, but suffrage fairly continuously expanded over the decades, whereas Athens had a tendency to slip back into a dictatorship for spells.

Anyway, the answer to your question is probably just population growth. We needed a critical mass of “useless” people not preoccupied with subsistence for science-y stuff to gain enough traction and spread.

That's probably part of it - science started creeping along with the invention of agriculture, although it was too slow for contemporary people to notice - but don't forget Europe wasn't the most happening place to start with and had just dealt with the black death. If it was population the Enlightenment should have long since happened in China or India. Actually, I think Roman Europe might have been more populous than early modern Europe, but I'm not sure.

Same story for wealth, and most cultural explanations.

How would Lanchester’s law apply?

It's not obviously connected, but it shifted at about the right moment in history and military matters flipping on their head could have had enough of a political impact to completely change everything like that. My working theory is something like, non-linear attrition for smaller groups favours the side that has more mass support. Before projectile weapons were dominant the French Revolution might have been crushed like every other peasant rebellion, basically.