What caused the birth of agriculture and the industrial revolution?
Indeed, the most important thing in explaing these two events is to be aware of enough facts from different fields, and have sufficient doses of skepticism and common sense, that you can eliminate the many theories that are popular but obviously, if you know enough such things, wrong. For example, be aware that hunter-gatherers were experts on botany and animal behavior. It's not plausible that the simple ideas that seeds can grow into plants that you can eat later, or that you can keep an animal tied or penned up and eat it later, were not discovered and known countless times during the c. 100,000 years between when our brains became modern-sized and agriculture developed. There has to have been some major barrier to benefitting from such obvious ideas to have kept agriculture from developing far sooner. I also don't find genetics plausible as a cause of agriculture, since agriculture ended up spreading to a number of human groups that had become genetically isolated long before the dawn of agriculture. (Genetic evolution caused by agriculture is another story -- Cochran and Harpending have some ideas very much worth thinking about). Also not plausible are climate explanations -- there were many local climates hospitable to agriculture throughout those 100,000 years -- just not necessarily at Mediterranean or higher lattitudes.
That said, going back to the IR there a number of likely-to-firm differences between China and Western Europe (or Great Britain in particular):
(1) Differences in political and legal culture. What differences, specifically, it's hard to say, because there is very little about, for example, Sung or Ming dynasty commercial law that has been translated into English: far too little to compare to English law in the 18th century, for example. We know some very general things, such as that Western Europe was (and still is) a far more legalistic culture than China. Also, we know that Western Europe (contrary to Gregory Clark's claim) radically changed its property law between the 16th and 19th centuries, from a feudal model of of hierarchy of tenures and bundled political property rights to a model based on old Roman law with flattened and purely economic ownership. There ensued movements such as the enclosure movement in England and an accompanying large increase in capital investments in land. But we don't know when or to what extent similar incentives to capital investment might have been present or missing in China.
(2) China never controlled the world's oceans and merchant marine, but the British just prior and during its IR did. If this explains the IR, then to explain our explanation (i.e. why did Britain come to control the world's ocean-going trade) we have to step back and solve the even more puzzling question of how a tiny country of fishing-folk and small-time crusaders, Portugal, and not an advanced superpower like China, was the first country to take over most of the world's oceanic trade routes (later to be beaten back by other Western European countries and eventually Great Britain).
(3) China had the printing press, but in contrast to Western Europe it did not lead to a rapid growth in literacy sustained over several centuries -- perhaps because of bureaucratic central control rather than the free-enterprise printing businesses that sprung up all over Western Europe, perhaps because the much greater number of symbols did not as efficiently lend itself to printing as the Roman alphabet, or a combination of these two factors.
(The Romans were not all good -- indeed they gave our culture something quite nasty which I will blog on in the near future).
Other interesting related phenomenon to explain, (and it would be nice per Occam's Razor if it was the same general explanation, but social life is rarely that simple) is why Japan industrialized well in advance of China and Britain was a few decades ahead of the rest of Western Europe during most of the 18th and the first half of the 19th century.
Robin: "If you wanted to attribute the industrial revolution to writing, you'd have to explain why there was a strong threshold effect, so that pre-1800 writing levels had weak growth rate effects, while post-1800 writing levels had strong effects."
Besides threshold effects, there could be delay effects: for example, the the rapid growth of books and literacy after the mid-15th century in Western Europe gave rise to a slow but accelerating series of innovations (most obviously scientific and technological advances, but perhaps also innovations in business or law), which in turn gave rise to the IR.