I don't really understand much about quantum theory but the definition of information there appears to relate to information about the entity itself rather than its relationship to and hence portrayal of something else. The picture could just be a completely abstract image without the information that it was formed by light reflected from some physical object. The information that it is a photo of a cat is not contained in the image itself.
Sure. And by extension even the highest resolution photograph of a cat is a completely inadequate representation of the
actual cat, which contains a positively unimaginably huge amount of information stored in the arrangement of its atoms and the quantum states of the particles therein. The English word for "cat" occupies all of 24 zero-one bits information when expressed in ASCII. (We could get that down to as little as 15 bits if we switch to something like Baudot.) It'd be a bit of a challenge to create a meaningful visual representation of a cat in 24 monochrome pixels, so imagine trying to explain to a being that has no idea what a "cat" is if you were only allowed to use a data of such limited resolution. (Assuming you're missing the translation table to convert "Cat" directly into something in their natural language.) On the flip side, imagine encountering some Nth dimensional being that could somehow perceive every physical dimension/state of objects in our universe simultaneously and process that symbolically as if reading them off a page; to such a being 2D photograph or even 3D hologram would almost certainly be completely inadequate to express the physical reality of these things we call "cats". (*)
(*) It's interesting to ponder how such a being would categorize "cat" symbolically based on the practically infinite differences that would exist between individual cats. We don't even understand how humans do it with just the amount of variation our crude visual perception grants us access to; somehow even very young children can, after encountering just a few different examples, generalize the concept of "cat" and apply it fairly accurately, even to crude drawings. Maybe even this:
It is 25 pixels, not 24, so I am cheating a little, and they would probably need some prompting to know they're looking for an "animal". Maybe an alien with sufficiently similar mental faculties to ours would also guess that icon is an animal, although that would no doubt depend a lot on what the fauna of their planet looks like. Making assumptions that aliens can makes such mental leaps certainly isn't a new thing:
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The image is not a photo of a cat to an observer who knows nothing about cats and indeed may not even sense the image visually as we do. My distinction was between data, which only contains facts integral to itself, and information, which relates to other things in a wider context.
Okay, but that doesn't negate my point about the amount of "information" a picture of a cat contains compared to the text representation. As I said, with just 15 bits worth of data because you and I share a common language I can transmit the word "cat" and upon reception you will know that I'm talking about "an animal of the 'feline' type". But there's a pretty huge amount of ambiguity there; I could be talking about a Persian kitten or a Bengal Tiger, and this would be very important information to know if the reason I'm telling you "cat" is I'm letting you know what awaits you on the other side of a solid steel hatch that you're about to be dropped through. At the very least you're going to require more context clues to make educated guesses about the attributes of this "cat"; does it live in a house or in a zoo? What color is this cat? What was it doing, exactly, at a given moment in time and space? What was the arrangement of its whiskers during this moment? Was it the exact moment the animal received its "cheezburger"? All of this "data" could be important "information" depending on the context.
I will grant it's more than a bit of a stretch to imagine someone being able to fill a 1,300 page book (typical print length of the Complete Works of Shakespeare) with an English description of even the most amazing photo of the most remarkable cat that ever existed without resorting to an unacceptable amount of filler and redundancy. (Although leave it up to some crazy person on the Internet to try.) But the fact that we consider most of the data we can gather with our senses about the universe "disposable" does not mean it's not
information.
... Which I guess ultimately comes around to how amazing it is that a talented writer or bard can "say so much" and invoke such a wide range of internal experiences in the reader via what is in fact a ridiculously spare, lossy, and highly compressed data stream. How we take these symbols and translate them so readily into meaning is as astounding a miracle as nature has to offer.