I am still at the very beginning of learning math, so maybe I am completely confused here. I do not see how there can be a difference without any difference of information content.
There can’t. But that doesn’t mean you can work back from information to medium.
It can hardly be disputed that qualia convey or encapsulate information. Yet the Mary story suggests something rather strange — that, although she has all the (physical) information about how colour works, she gains some extra information when she sees colours for the first time.
Information is something that is copied and transferred from place to place. That being the case, something is always left behing, namely the original basis (or format or medium or physical instantiation) of the information. Consider an epic poem in an oral tradition, that is then written down in manuscript, the text of which is then used in a printed book, which is then transferred to microfilm, which is then made into a CDROM. There is no way someone who has access to the CDROM could work backwards to the previous incarnations.
What is left behind is not just more information. Even if we had complete information about the original manuscript of our poem, we wouldn’t have the book itself.
There can’t. But that doesn’t mean you can work back from information to medium.
It can hardly be disputed that qualia convey or encapsulate information. Yet the Mary story suggests something rather strange — that, although she has all the (physical) information about how colour works, she gains some extra information when she sees colours for the first time.
Information is something that is copied and transferred from place to place. That being the case, something is always left behing, namely the original basis (or format or medium or physical instantiation) of the information. Consider an epic poem in an oral tradition, that is then written down in manuscript, the text of which is then used in a printed book, which is then transferred to microfilm, which is then made into a CDROM. There is no way someone who has access to the CDROM could work backwards to the previous incarnations.
What is left behind is not just more information. Even if we had complete information about the original manuscript of our poem, we wouldn’t have the book itself.