Another reason for the effectiveness of mathematics in the natural sciences

 Unreasonable effectiveness: Consider this from a statistical perspective... if you have to, imagine multiple universes that all work differently. 

By being surprised at this "unreasonable effectiveness", you're assuming that it's highly unlikely that mathematics would be effective in predicting things about the universe, creating an "isomorphic model", in other words.

However, isn't it quite feasible that a sub-system would arise under any particular universe, say, some lifeforms, and they might have "information processing" capabilities so as to survive and propagate within that universe's rules? After all, to have some staying power within the universe's rules (particularly if one of the rules is entropy), the lifeform must "care" somewhat for its rules and global properties. This itself is the definition of what it means to actually process information -- the capability to change in response to the data, dependency, responsiveness, non-constancy. 

So it also seems feasible that these creatures might do this in some fashion, perhaps even find a way to communicate information to each other, forming an information processing mesh... and they might do this with certain patterns, protocols. Perhaps the particular instances of information-sharing pertaining to deep concepts in how to survive and replicate -- i.e. information regarding the laws and properties of how their universe work -- could be called... mathematics? In fact, this seems more than just feasible... one might say reasonable, even.

In short, mathematics is reasonably effective because mathematics arises from a smart creature's very effective attempt to understand its universe via something like simulation, to live in it better. 

If you take a meta-universe view, it seems more obvious. You can even think about different example universes like Wolfram's different cellular automata rules. Within these universes you can create self-replicating sub-systems, like the lifeforms I described above. These sub-systems can more or less simulate the laws of their own cellular automata universe under their own paradigm. Kind of like building a Minecraft server within Minecraft itself?