why did it take thousands of years for the West to surpass India/China?

For a long time, China was a highly stable country with robust and fairly well-designed institutions. It's well-provided with natural resources, with silk perhaps being one of the most important. China was able to develop many technologies before the rest of the world.

Some of China's core regions are extremely productive agriculturally, particularly for growing rice. Rice itself can produce more calories per acre than most other grains. The Chinese developed a sophisticated agricultural system, and invested a large amount into capital, such as terraces, to improve productivity.

The earliest Angus Madison Project estimate for Chinese GDP/head is $600 in 1820. Compare that to England/GB/UK, where the estimates go (erratically) back to 0AD, and are never lower than $600. So China was not particularly productive per head, but it was able to support a very large population so its total GDP was very large. IIRC, China's population around 1700 was c.1/4 of the world's.

I assume it had something to do with the industrial revolution in the West

You're correct - the main reason is that Europe and North America experience agricultural and industrial revolutions. These increased productivity per head and increased population.

In the UK, the population roughly doubled during the 19th century, while GDP/head doubled. Even peripheral European countries saw significant increases in GDP and population.

why didn't China form their own industrial revolution?

The whole "what caused the industrial revolution/why didn't it happen elsewhere?" question is one that economic historians have been arguing about for a long time. I can't give you a definite answer, but I'll give you some common arguments.

• The industrial revolution, and to a lesser extent the agricultural revolution, required the build-up of capital. Large investments in land, mines, factories, railways, etc. were required. Europe (especially the UK) was already wealthier per head than China, with a significant middle class. The fairly rapid pace of the agricultural revolution meant production ran ahead of population growth, allowing a build-up of wealth for investment.

• The influx of goods and bullion from the New World helped the build up of capital in Europe (particularly Britain, which accumulated much Spanish wealth). Huge quantities of silver also ameliorated the persistent European trade deficit with China. European naval and military technology took control of the spice trade, for a further improvement in Europe's trade balance with the world.

• In China, by contrast, agricultural techniques had already reached a high level, and population had grown in proportion. Much of the population lived barely at subsistence level. So there were limited opportunities for growth or the extraction of further surpluses. China is said to have been caught in what's called an "involution" trap, where even though agricultural productivity was high (per acre), extra labour and capital inputs were pushed into eking out marginal gains in the fields or household, rather than being free for revolutionary economic changes.

• China also had a different economic problem to Western Europe. It had a surplus of cheap labour (later exported to the US) but needed more food. European were more likely to have an adequate amount of food, and to be trying to reduce labour inputs. (Ireland may be the exception that proves the rule here.)

• Military and economic competition between European states encouraged technological development and increases in productivity, and gave states a role in this. For example, in the Napoleonic wars, building and maintaining the Royal Navy took some of the era's most advanced technology (eg. rope manufacturing). The UK is a good example of a country where war could stimulate industrial and economic growth, without the biggest downside to a war - the destruction of capital, organisations, etc. that tends to happen during an invasion.

• By contrast, the main military threats for China for a long time were land-based and nomadic. This limited incentives to improve naval technology or firearms (there's at least one recent thread on here about why gunpowder technology in China didn't develop further).

• European states also tended to have more open and flexible political and social systems than China. China's systems were stable, but ill-suited to change. In particular, they were more inward-looking and anti-trade. It's easy to see a kind of institutional sclerosis here, with old, established institutions becoming ineffective and unable to adapt to change.

• By the mid-19th century, the threat to China from Europe was more clear. However by this time they had solidified their economic, political and military advantages. A couple of other factors are also important. It's hard to say how much opium use hit China's economy itself. It was a serious problem generally to be the focus of much political attention and, of course, to be one of the factors behind the Opium Wars. What we can say is that it finally reversed the balance of trade, so that silver began flowing out of China to Europe. Second, the Taiping rebellion was devastating for some of China's core regions, lasting 14 years and leading to the deaths of tens of millions of people.

In terms of sources, this is largely drawn from a degree-level module I did on the economic development of China and Japan. I should have a reading list on this subject somewhere if anyone wants suggestions.

This is a common source of debate amongst people studying late imperial China. One source you might want to read about is the "high level equilibrum trap" theory.

In essence, it states that China didn't industrialize precisely because it was quite efficient in its usage of existing manpower for supply and demand, meaning they never had a need for technological innovation to compensate for shortfall. (e.g. why invent a car when you have around and can hire 4 people to carry you in a sedan chair?)

The lack of existential threats to the central state also reoriented the direction of technological innovation. Meaning, there was no need for an "arms race" with other competing nations to drive production, and Chinese goals were focused on internal social stability. If you think about it, there is nothing quite as socially disturbing as industrialization, the dislocation of large bodies of artisans and farmers with more efficient machinery.

I only say this because people shouldn't think of industrialization as teleological (everyone should've industrialized, and those that didn't are bad and should feel bad). They should view it as among the choices a state had at its disposal among a myriad of counteracting priorities.

That industrialization allowed a small corner of the world to conquer and monopolize the rest of it, should not be a justification for its rightness or wrongness. It's just a testament to its efficiency for the purpose of conquest and production.

When I saw this graphic, the only question I wonder about is not why does it start to collapse in 1820 but rather, why does it not start to do so much earlier, given the industrial revolution.

but why didn't China form their own industrial revolution?

You seam to have a false view about what industrial revolution is and how it happens. You can just make a industrial revolution happen when some emporer or king says "Well, I want a industrial economy".

In all of human history, something like the industrial revolution has happend only once, while the 'why' is still debated I think most people agree that its not as simple as 'X caused Y'. We know about some things that need to be in place to make a economy that is capable of supporting such economy growth. You need a lot of farm surplus, you need property rights, you need a contract enforment system (can be private or public), you need a system of banking for investment and many more. People are still debating the 'root cause' but I think all agree that these are some of the things that need to be in place.

So the country that has a industrial revolution needs to look a lot diffrent then china did back then. A rich emporer might put in place a large modern gun production but its quite impossible for them to copy the west. Later of course ruissa tried a new way (socialism) and they did manage do have a industrialisation of the economy but the nature of that is very diffrent then what had happend in england.

You can look at what happend to japan as a example for what it takes to go down that road.

Also, why did it take thousands of years for the West to surpass India/China?

If you look at the map england or west europe they are tiny compared to china. So your question should be the other way around "Why did they ever manage to overtake china?". Your quesiton makes it sound as if it was always clear that it would happen, and it was just a question of how long it would take, but that is not the case, history does not work like that. If you had looked at a map in 1000 or even 1500 most people would not bet on england or france take over huge parts of the world.

On the question that might be more intresting, "Was a avg. person living in china better of then living in europe?". Maybe a small amount, but its hard to agree on something like this. Depending on what your intrested in you should look more at GDP per person, GDP is rarly usful (exept in miltary matters).

Another phenomena, why is India lagging China's growth?

This is a harder question and I dont feel I can answer this, at least not in the scope of a reddit comment without preparing for it. I would suggest you start to learn economics and then start to get into history of economics (and history of economic thougth) to takle these kinds of questions. There are a number of diffrent economic theorys on growth and lots of study specially around the idea of 'devloping nations'.