Materialism predicts that algorithms have an "inside"?
Yes. The scene from within a formal system (like algebra) has certain qualities (equations, variables, functions, etc) that are different from the scene outside (markings on paper, equals sign, BEDMAS, variable names, brackets for function application).
That's not really a materialism thing, it's a math thing.
As a further note, I'll have to say that if all the blue and if the red in my visual experience were squitched around, my hunch tells me that I'd be experiencing something different; not just in the sense of different memory associations but that the visual experience itself would be different. It would not just be that "red" is associated with hot, and that "blue" is associated with cold... The qualia of the visual experience itself would be different.
Hence the part where they are compared to other qualia. Maybe that's not enough, but imagining getting "blue" or "sdfg66df" instead of "red" (which is the evidence you are using) is of course going to return "they are different" because they don't compare equal. Even if the output of the computation ends up being the same.
That's not really a materialism thing, it's a math thing.
I'm under the impression that what you describe falls under computationalism, not materialism, but my reading on these ideas is shallow and I may be confusing some of these terms...
[Cross-posted.]
1. Defining the problem: The inverted spectrum
A. Attempted solutions to the inverted spectrum.
B. The “substitution bias” of solving the “easy problem of consciousness” instead of the “hard problem.”
2. The false intuition of direct awareness
A. Our sense that the existence of raw experience is self-evident doesn’t show that it is true.
B. Experience can’t reveal the error in the intuition that raw experience exists.
C. We can’t capture the ineffable core of raw experience with language because there’s really nothing there.
D. We believe raw experience exists without detecting it.
3. The conceptual economy of qualia nihilism pays off in philosophical progress
4. Relying on the brute force of an intuition is rationally specious.
Against these considerations, the only argument for retaining raw experience in our ontology is the sheer strength of everyone’s belief in its existence. How much weight should we attach to a strong belief whose validity we can't check? None. Beliefs ordinarily earn a presumption of truth from the absence of empirical challenge, but when empirical challenge is impossible in principle, the belief deserves no confidence.