One fascinating thought is that even though we can say that something is an emergent property in physics, we can still formulate precise laws and formulas which exactly match the observations, and that can't be a coincidence. What does that tell us about reality - or mathematics?
To illustrate what an emergent property is, I think a TV set is a nice example. We see moving objects on the screen, but if we get close up, we realise that there are just a bunch of individual dots which light up and fade in a coordinated way, and they change only so many times per second and have a limited number of intensity levels so not only are the images an emergent property but also the motion. And even closer inspection reveals that the dots are made up of even smaller red, green and blue dots, and we can conclude that even the colours that we see are emergent properties. But all that doesn't mean that it's wrong to speak of images, motion and colours when we take a couple of steps back again. We are simply describing order at different levels.
Maybe that we live in a mathematical universe? Mathematics may be more than just formulations to match observations, perhaps the universe is in fact mathematical. Maybe all universes are. It makes sense because at the quantum level, everything seems to work according to mathematical relations as opposed to anything physical (maybe like a cosmic quantum computer, note the article about space-time's efficient quantum error correcting code.) It's very abstract but also wonderful in a wholistic sense.
Somewhere in those articles there should be something about the Holographic Principle and the AdS/CFT correspondence, which Juan Maldacena discovered or formulated. That was done based on a toy universe (antiDeSitter space hence the AdS part of the correspondence, obtained from string theory), a model created in which an interior space (bulk) can be created with an emergent third dimension of space from an exterior boundary where there only two dimensions of space. Gravity also emerged from this model. But in the more recent article which I also posted physicists had found a way to make the correspondence work with our kind of universe (DeSitter space), with a similar bulk/boundary (like being inside a black hole....noteworthy.....which is why I also included links about the possible solution to the black hole information paradox, which seems to be interrelated to this.) Anyway in this new DeSitter model, time becomes the emergent dimension from the boundary that only exists in the bulk and there is a strong connection between gravity and time because both are emergent and neither exists on the boundary but are only found in the bulk. The duality between gravity and time is particularly interesting because out of the 4 dimensions, time is different from all the rest and out of the 4 forces, gravity is different out of all the rest. So there seems to be a deeper connection there between the two of them. So the boundary is the timeless "outer" edge of the universe (whatever you consider "outer" to mean in this case) that contains all the information of the universe, all past, present and future, combined. I pictured it in my head as I read the description, it's like the boundary is a film reel that projects all of reality into the bulk. Every frame of the movie exists simultaneously at the boundary but we in the bulk, who are part of the movie see it as a continuously moving film.