I expanded my comment because an important thing is to discuss whether the different levels are actually a property of the universe or just a property of our de

I expanded my comment because an important thing is to discuss whether the different levels are actually a property of the universe or just a property of our description? Is math discovered or invented. What is part of the map and what of the territory. I think people use emergence more when it's viewed and suggested as independent from our description, it really emerges on its own and we just discover and describe this. And "abstraction" is used when we view our role greater, we invented an abstraction to easier manage the complexity. So emergence is more incidental, accidental, serendipitous and unexpected, while abstraction is intentional and purposeful and designed. Now which is which and whether the distinction itself touches on something real or is just a different view of the same thing, is another great topic for discussion.