> The issue that the paper brings up is that the same physical process can be interpreted as multiple different computational processes.

I don't think this is relevant to the notion that consciousness is a form of computation.

The assertion that consciousness is a form of computation basically means that the physical process that happens in the brain/body that we recognize as consciousness can be described in terms of a computational process. A consequence of this, if it is true, is that replicating the same computation in a CPU would make the physical process that happens in the CPU just as conscious - assuming that we had identified the correct computation.

In this theory, the thing that would be conscious would be the physical CPU, just like the thing that is conscious is a physical human brain/body. The computation is just an abstract description of the common properties between the CPU and the human brain/body. It's not relevant that we could also describe the process inside the CPU as being a completely different computation - the abstract model is only required to be able to build and program the CPU.

To go back to my mechanical door analogy: we create an abstract model of the computations needed to make a computational system open a door when a person is near. We use this model to create the computational system, and we see the door opening when a person goes near the sensor. Now, we can interpret the computation happening inside the system in many other ways - but that won't change the fact that the door opens when a person is near, in any way.

I am not claiming that any of this constitutes proof that consciousness must be a computation. What I'm claiming though is that the paper, and similar arguments, are not refuting the right claims, and generally have a misunderstanding of what "computation" actually means, and its relation to physical processes.

The "hard problem" is talking about the thing that it's like to be you, to experience what is happening. I don't know about you, but I only experience one set of things happening at once, i.e. it doesn't feel like I am in two places at once or that there are two completely different versions of my life happening simultaneously.

If the physical thing that is conscious is the CPU, what are the contents of its consciousness if there are multiple interpretations of what it is computing?

Now maybe somehow there are in fact multiple consciousnesses inhabiting the CPU. I don't experience that though, so I don't have a positive reason to believe that that's true.