[Arrekin]

Seeing color(qualia) does not provide any additional information. They are just a tool your brain uses to speed up processing. Treat is as quick tagging system. It's done inside your head, we don't even know if all people tag colors in the same was(is your red, my red?). Qualia are derived information. Your senses get information, and you get some processed result. There is nothing added(beyond what your mind may add, but that's not part of the original information). You could swap red for green, green for blue and nothing changes. Imagine a wall of text, a very big one. To read it you have to carefully go line by line, focused on the content. It takes a lot of time to do. But now imagine you evolved to read such text walls. Now it's not hard, because nature developed special structures to process them, and now you have dedicated, and optimized region in the brain to handle them. You just glance at that massive text and "see" all the content, it sings to you, you understand it instantly, maybe even feel parts of it. And seeing is the same. The mass of color information hitting our eye, that for someone without innate ability to process it would look like a bunch of hard to plow through data, for us is just instant. We process multiple frames per second, detect objects, project movements. All of it without even thinking about it. Incredible. All thanks to specialised machinery in our brains. The specialized part does the heavy lifting so we can see our qualia. But it's just a tool, it does not provide additional objective information, as it's only your subjective view of the information that other parts of the brain push to you. It's processed information, enriched, but because of that, it's subjective now.

[kirkules]

Is derived information not distinct from the input? I mean, tagged information tells you about the tagging system in addition to the tagged information.

Specifically, it tells you how the tagging system interacts with the tagged information.

In this case, from a physicalist perspective, seeing red tells Mary how her specific brain (or whatever physical system explains color sight experiences) interacts with the experienceable subject "red", be it red light or whatever choice you make for the "true" subject for the sake of the thought experiment.

The ordinary discussion of the thought experiment simply assumes she can somehow already know this without experiencing it, and hand-waves away concerns about whether she could obtain that knowledge without having the experience (she is a brilliant neuroscientist, after all).

My position is that this is precisely the new information she obtains from seeing the apple.

The minimum value from a finite list of integers is derived from the list, but until you compute it (the analog of "seeing the apple"), you don't know the minimum. Even if you "know all the integers in the list" otherwise.

Edit: typo