When two variables are correlated—say, stock prices and market sentiment—we might ask: what do they actually share? According to LessWrong, information theory offers two competing answers. One asks what each observer can independently extract from their own data. The other asks how complex an explanation needs to be to fully account for the correlation itself. These give different results, revealing that 'shared information' isn't a single fact—it's a family of answers depending on what you're trying to do. The post connects this disagreement to the natural latents framework, which tries to formalize which notion of 'latent structure' actually matters.

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