Kindly riddle me this. If a black hole was a closed system, then the premisses, that information inside will become lost, would be trivially true by the (2nd?)

Kindly riddle me this. If a black hole was a closed system, then the premisses, that information inside will become lost, would be trivially true by the (2nd?) law of thermodynamics. There's energy going in, so it isn't hermetically sealed. Thus, the accretion disk is part of the system. But if there's no correlated information coming out, it's closed one-way. You say there is radiation coming out, theoreticly, and I know that radiation is information. It's information in one strict sense, but not in the other--what are the different scopes; Is the radiation not observable? Are the laws of thermodynamics seemingly violated, that is, is the theory not complete (rhethoric question); Thus your remark was in effect non-constructive, as you cannot prove one unknown with another, can you? Nevermind the kind of scary question whether any system in the grand scheme of things is closed at all. BTW another comment mentioned conservation of momentum and charge. I wonder, in the focal point of an ideal lense, in theory, can the image be reconstructed? Well, by looking at the flame quite trivially, at least, albeit not in the perspective of the focal point (not easily without ambiguity, surely). Is this what Tao's one-pixel-cam is about?