Imagine a fully materialistic universe strictly following some laws, which are such that no agent from inside the universe is able to fully comprehend them...
I wonder if that is possible? For computables, it is always possible to construct a quine (standing for the agent) with arbitrary embedded contents (for the rest of the universe/laws/etc), and it wouldn’t even be that large—it only needs to hold one copy of the contents, and most data can be compressed.
All you need is a bounded universe with laws having complexity greater than can be embedded within that bound, and that premise holds.
You can even have a universe containing agents with unbounded complexity, but laws with infinite complexity describing a universe that only permits agents with finite complexity at any given time.
Multiple times have I seen an argument like this:
I wonder if that is possible? For computables, it is always possible to construct a quine (standing for the agent) with arbitrary embedded contents (for the rest of the universe/laws/etc), and it wouldn’t even be that large—it only needs to hold one copy of the contents, and most data can be compressed.
All you need is a bounded universe with laws having complexity greater than can be embedded within that bound, and that premise holds.
You can even have a universe containing agents with unbounded complexity, but laws with infinite complexity describing a universe that only permits agents with finite complexity at any given time.