Indeed, people begin by assuming that since programmable computers can approximate many classes of patterns and since computers are amazing therefore everything is just an instance of this class.
Were this true, I cannot see why any system wouldn't be a model of any system; ie., alchemy would be possible.
What people forget is that "programming" in the alchemical sense requires a star.
Once you get specific about what properties and processes actually correspond to the allegdeged "complexities" you're talking about, its obvious that no programmable machine will implement them; as obvious as none will turn lead into gold.
I dont think that's where this conversation was going. I believe you got that impression from me mentioning fractals, but even so fractals are only self similar not identical.
Maybe the fractal nature of computing is not in the "are we living in a simulation?" Kind, but is in the "we can imitate what we see at a different scale with fundamental units, logic/math, and visual field". In a sense it is a universe within a universe, but that doesn't imply everything is everything. It implies there are many things at different scales that are self similar. Scale still exists and is relevant.
Were this true, I cannot see why any system wouldn't be a model of any system; ie., alchemy would be possible.
What people forget is that "programming" in the alchemical sense requires a star.
Once you get specific about what properties and processes actually correspond to the allegdeged "complexities" you're talking about, its obvious that no programmable machine will implement them; as obvious as none will turn lead into gold.