>It is hardly a given..

Ok, fair enough. So let us also seed the simulation with all the random events from our universe. That should cover it, right?

>A mathematical description of a fire does not burn anything..

This is the self evident dogma that we have to overcome to understand this idea.

You say that a mathematical description of a fire does not burn anything. But what if both the fire as well as the thing it is burning is described by the math? Have you seen those fractal animations? In them, there would be things that appear to be a spear piercing or pushing through things around it. There both the spear (or what appears to be) and the thing it is piercing/pushing is described by the fractal. And one thing did not cause the other.

So we are turning the idea of causality on its head. In this world one thing does not cause another. But both cause and effect are described by the mathematical structure that contain them. This also connects to the earlier idea that "computable consciousnesses are self sustaining". The brain did not cause consciousness. But both the brain and consciousness are described by the math.