Now, suppose Carol knows the plan and is watching all this unfold. She wants to make predictions about Bob’s picture, and doesn’t want to remember irrelevant details about Alice’s picture. Then it seems intuitively “natural” for Carol to just remember where all the green lines are (i.e. the message M), since that’s “all and only” the information relevant to Bob’s picture.
(Writing before I read the rest of the article): I believe Carol would “naturally” expect that Alice and Bob share more mutual information than she does with Bob herself (even if they weren’t “old friends”, they both “decided to undertake an art project” while she “wanted to make predictions”), thus she would weight the costs of remembering more than just the green lines against the expected prediction improvement given her time constrains, lost opportunities, … - I imagine she could complete purple lines on her own, and then remember some “diff” about the most surprising differences...
Also, not all of the green lines would be equally important, so a “natural latent” would be some short messages in “tokens of remembering”, not necessarily correspond to the mathematical abstraction encoded by the 2 tokens of English “green lines” ⇒ Carol doesn’t need to be able to draw the green lines from her memory if that memory was optimized to predict purple lines.
If the purpose was to draw the green lines, I would be happy to call that memory “green lines” (and in that, I would assume to share a prior between me and the reader that I would describe as: "to remember green lines" usually means "to remember steps how to draw similar lines on another paper" ... also, similarity could be judged by other humans ... also, not to be confused with a very different concept "to remember an array of pixel coordinates" that can also be compressed into the words "green lines", but I don't expect people will be confused about the context, so I don't have to say it now, just keep in mind if someone squirts their eyes just-so which would provoke me to clarify).
(Writing before I read the rest of the article): I believe Carol would “naturally” expect that Alice and Bob share more mutual information than she does with Bob herself (even if they weren’t “old friends”, they both “decided to undertake an art project” while she “wanted to make predictions”), thus she would weight the costs of remembering more than just the green lines against the expected prediction improvement given her time constrains, lost opportunities, … - I imagine she could complete purple lines on her own, and then remember some “diff” about the most surprising differences...
Also, not all of the green lines would be equally important, so a “natural latent” would be some short messages in “tokens of remembering”, not necessarily correspond to the mathematical abstraction encoded by the 2 tokens of English “green lines” ⇒ Carol doesn’t need to be able to draw the green lines from her memory if that memory was optimized to predict purple lines.
If the purpose was to draw the green lines, I would be happy to call that memory “green lines” (and in that, I would assume to share a prior between me and the reader that I would describe as:
"to remember green lines" usually means "to remember steps how to draw similar lines on another paper" ... also, similarity could be judged by other humans ... also, not to be confused with a very different concept "to remember an array of pixel coordinates" that can also be compressed into the words "green lines", but I don't expect people will be confused about the context, so I don't have to say it now, just keep in mind if someone squirts their eyes just-so which would provoke me to clarify).