How do I know what? Defining consciousness this way makes things clearer and easier to discuss, but doesn't actually explain consciousness in any way. I'm advocating a definition, not proving a fact.

You start out talking about algorithms, as you say, but then switch to talking about states of (or produced by) algorithms. A MS Word document is not the instance of MS Word that produced it. [Edit: bad example. Reworded: a snapshot of the state of a computer running MS Word is not, itself, a running instance of MS Word. That's a more precise analogy, but unfortunately more debatable. ;)]

I don't have any objection to the idea that an algorithm can give rise to (I would say "be") consciousness. I do object to the idea that numbers exist in the same sense that matter and energy exist. I am not a Platonist.