I feel like I understand communist theory pretty well at a basic level, and I believe in it, but I just don't see what part of it requires belief in an objective world of matter. I don't believe in matter and I'm still a communist. And it seems that in the 21st century most people believe in materialism but not communism. What part of "people should have access to the stuff they need to live" requires believing that such stuff is real? After all, there are nonmaterial industries and they still need communism. Workers in the music industry are producing something that nearly everyone can agree only exists in our heads. And they're still exploited by capital, despite musical instruments being relatively cheap these days, because capital owns the system of distribution networks and access to consumers that is the means of profitability for music. Spotify isn't material, it's a computer program. It's information. It's a thoughtform. Yet it's still a means of production that ought to be seized for the liberation of the musician worker. What does materialism have to do with any of this?
While some have remarked on the unreasonable efficacy of mathematics at representing the natural world, it is not perfect. For example, numbers are hardly useful in the field of psychiatry. Given that we are entering into an investigation pertaining strongly to the mind, I believe we should adopt at least some practices from psychiatry, including the practice of taking qualitative measurements.
Anyone who is capable of actually entertaining the narrative, you mean. No scientific proof will ever convince a flat earther that the horizon is curved, because they are incapable of entertaining the competing narrative. Likewise, my experiment ought to work on anyone, as long as they are capable of taking my narrative seriously. If they're unwilling to keep an open mind, of course they'll keep perceiving the same thing, just like the flat earther.
No we aren't. You asked about a narrative that changed the observation of the world outside of the mind. Measurement is all that matters in this realm of epistemology.
I suppose, yes, the observer does have to accept the narrative. That being said, a flat earther running an experiment to test if the world is flat does make the same observations as someone who believes the world is round, they just either contort their worldview to match or reject the observation entirely. They don't run an experiment and get different results. Such as in this clip in which a flat earther observes the exact same phenomenon as everyone else. He may choose to reject it, but the observation is the same.