also you quickly notice that all the people who originally did science were from the nobility. They had the time and money and didn't need to do any work. It was essentially all hobby work... There is an odd benefit to feudalism to have a bunch of the most well educated people laying around with free money and time.
We've found iron smelting methods in industrial use during the 11th century Song that were originally thought to be discovered be 18th century British theorists (the same sort that created the demand for industrial-revolution-level-coal-mining). Innovation doesn't come from nobility, it comes from
doing. That's why innovation happens today in China, it starts from the factory floor.
If free-time nobility was where all innovation came from why did it take until the 17-18th century for inventions to start being generated in Europe when they had nobility and feudalism since the Romans? Why were all the inventions like blast furnaces, plowshares, seed drilling, crop rotation, paper/fiat currency (and their monetary theories), gunpowder/rockets, merit-based civil service, and many more political, economic, and industrial inventions flowing from East to West rather than the other way around for almost all of human history if nobles/feudalism was what was required for inventing?
The simple reality is Europe was not a productive region until the industrial revolution. For most of written history, China (and to a lesser extent the near east) was the most productive region. European dominance was a confluence of very specific historical circumstances.
Incoming wall of text:
The Song-Jin area housed about 108 million in 1210 (the cusp of the Mongol wars) which then fell to 75 million by 1292(early Yuan), a decline of 30%. The soon after Yuan-Ming transition further caused a population decline of 23% (87 million in 1351, 67 million in 1381). Given this was happening in Chinese-style proto-total war, it meant mass migration, abandonment of many northern capital-intensive industrial sites, as well as the atomization of expertise. The result was relative technological stagnation because societies took time to recover, redevelop, and reach critical mass to start inventing again.
For the Song-Yuan-Ming transitions, pretty much only Jiangnan (modern day lower Jiangsu/Zhejiang) was left unscarred and that meant much of the focus was adapting agricultural techniques to the low-lying marshy lands of the Yellow River delta as well as the capital and labor-intensive work of draining swamps and making the land ready to farm. Markets and industrial sites were mostly situated outside of Jiangnan and destroyed by the Song-Yuan transition.
In addition, the earlier failure of the early Song in retaining the Sixteen Prefectures resulted in the lost of power by state-activists such as Wang Anshi and the increasing decentralization and power-transfer from officialdom to the emerging agricultural landlord-gentry. As the Zhu Yuangzhang (Hongwu Emperor of Ming) rose, he took care to destroy the emerging landlord-gentry & merchant class by confiscating their wealth and breaking their clans apart by forcible migrating them piecemeal into separate prefectures and towns. Some of the agricultural innovations were spread this way out of Jiangnan, as well as essays written by officials through all three dynasties, leading to the average yields per mu roughly increasing from 1 shi/mu in late Song to 1.6 shi/mu to early Ming. This was equivalent to increasing from 13 shi/worker to 16 shi/worker since the average Ming farm was half the size of those in the Song. Remember the introduction of New World crops took place in the Qing, so this was all agricultural development.
But this destruction of the landlord-gentry was quickly squandered as the later emperors were marked by a withdrawal of state industrial activities. This resulted in the worst of situations, no capital in towns to develop distributed market towns (as in the Song and early industrial Britain) and no effective use of state power to direct capital. From early Ming to late Qing, the society became increasingly feudal and increasingly stagnant (I thought feudalism is supposed to be good for innovation? lol). The Qing had about the same number of magistrates governing the prefectures from the beginning to the end despite the general population growing 5-fold over the span of the dynasty.
It took until the 16th century for market towns to start reappearing in China, this time based around the cotton and silk trade. Indeed, they were noted as though they were a new form of development at the time despite having existed 5 centuries prior in the Song! At this time though, there was no state capacity to direct capital to invest in heavy industry (capital-intensive and would result in investment into labor-saving machinery), instead they were all focused into light industry such as commercial book printing which poets complained only consisted of fluff and trashy stories. (I would like to point out that this sounds like a lot of Western economies these days - without state direction, capital flows towards the quickest buck, not the expensive but potentially transformative. Hence in their day, into light industry, in our day, into FIRE)
Meanwhile, Europe went through the Black Death which did not cause mass migration and abandonment of existing capital-intensive sites. It was also far more targeted at commoners than the nobles (the administrative class in Europe) resulting in both much higher labor costs and much greater state directive capacity. Then Pax Mongolia resulted in technological spread to Europe as well as the relative destructive of their technological competitors in China and the near east basically leveling the playing field previously built up by many centuries. This was followed up by the enormous wealth transfer from the conquest of the New World resulting in the trifecta of vast amounts of capital, insufficient labor, and effective state capacity. A perfect storm for the self-reinforcing development of labor-saving devices (industrial revolution). Even then, it was only possible because Britain had started the industrial production of iron (same as 11th century Song) through the use of coal and early steam engines were only past breakeven in profitability whilst working on pumping out water from flooded coal mines. That is, a very capital intensive machine was only barely profitable because they were financed by American silver/gold and consuming the very material they were being used to mined out (coal) - that's as free as it gets!