Yeah, I've read through the critique (http://www.scottaaronson.com/blog/?p=3294 http://www.scottaaronson.com/blog/?p=3294) that triggered to linked blog post an

Yeah, I've read through the critique (http://www.scottaaronson.com/blog/?p=3294 http://www.scottaaronson.com/blog/?p=3294) that triggered to linked blog post and the main disagreement seems to be about this. From the critique: "In their new work, Hoel and others claim to make the amazing discovery that scientific reductionism is false—or, more precisely, that there can exist “causal information” in macroscopic systems, information relevant for predicting the systems’ future behavior, that’s not reducible to causal information about the systems’ microscopic building blocks." I think it would've helped cleared thing up if Hoel actually addressed and clarified the above quote. Instead (From the blog post): "Why does causal emergence matter? The theory does imply that universal reductionism is false when it comes to thinking about causation, and that sometimes higher scales really do have more causal influence (or information) than whatever underlies them. This is common sense in our day-to-day lives, but in the intellectual world it’s very controversial." At this point I'd really like the definition of "universal reductionism".. An illuminating example from the critique (possibly taken from Hoels paper). (Basically an example of your 1-3 steps) "For here is the argument from the Entropy paper, for the existence of macroscopic causality that’s not reducible to causality in the underlying components. Suppose I have a system with 8 possible states (called “microstates”), which I label 1 through 8. And suppose the system evolves as follows: if it starts out in states 1 through 7, then it goes to state 1. If, on the other hand, it starts in state 8, then it stays in state 8. In such a case, it seems reasonable to “coarse-grain” the system, by lumping together initial states 1 through 7 into a single “macrostate,” call it A, and letting the initial state 8 comprise a second macrostate, call it B. We now ask: how much information does knowing the system’s initial state tell you about its final state? If we’re talking about microstates, and we let the system start out in a uniform distribution over microstates 1 through 8, then 7/8 of the time the system goes to state 1. So there’s just not much information about the final state to be predicted—specifically, only 7/8×log2(8/7) + 1/8×log2(8) ≈ 0.54 bits of entropy—which, in this case, is also the mutual information between the initial and final microstates. If, on the other hand, we’re talking about macrostates, and we let the system start in a uniform distribution over macrostates A and B, then A goes to A and B goes to B. So knowing the initial macrostate gives us 1 full bit of information about the final state, which is more than the ~0.54 bits that looking at the microstate gave us! Ergo reductionism is false." From this I think we all can agree that finding out how a system with A and B as states is much simpler than figuring out the low level 9 state system. But how that somehow disproved "reductionism" is not clear. I'm not sure that this is type of compression is "controversial in the intellectual world" either? That doesn't mean the study of "Causal emergence" isn't worth studying of course.