What is the purpose of this post?

Taken.

Wait. "Rationality Cookie" is that a real thing? I can't find it but it sounds like a good idea to train rationality the classical way via quick rewards.

I wonder what the chances of the guy actually asking for the Machiavelli tract are relative to the chances of him being wrong about the author? When I run into a namespace collision like that, I try to be extremely clear about it precisely so that I don't run into situations like you described -- i.e. "Machiavelli's Art of War, not the one by Sun Tzu".

The belief was minor, but the story is entertaining:

A while ago a guy walked into the bookstore and asked me for a copy of The Art of War—by Machiavelli.

I've developed the habit of being polite when customers are mistaken about details, taking (and often inventing) every possible opportunity to help them save face, so I handed him a copy of Sun Tzu without comment—though you can be sure that internally I was feeling all kinds of smug at the chance to display my superior knowledge of extremely common classic books. He glanced at it and left—mortified, I imagined.

A few months later, I looked it up and discovered that Machiavelli did, in fact, write a treatise called The Art of War.

But that isn't the embarrassing part.

The embarrassing part is that, in the moment I went to check, what I was thinking was not "Hmm, I wonder if I could have been mistaken"; it was "Heh, I wonder if anyone else has made the same mistake as that idiot!" My error was corrected only incidentally—in the course of my efforts to reinforce it.

Better, then, to unlabel the blue line entirely, and when someone wants to know what ontological difference exists between the higher rows and the lower, say "Mu." ... Reductionism proper is just this: noticing that green arrows are always present, and always point up.

There's a tension here: green arrows are a property of our maps, but to the extent that our maps are accurate, they do actually reflect the territory. So sure, the green arrows are always present and always point from physically smaller to physically larger, but what are the ontological determinants of the arrow head positions, i.e, why are the rows where they are?

It often occurs in physics that from a small number of seemingly obvious and simple propositions, a great deal of far-ranging consequences can be deduced. This discussion brings up an example: the seemingly simple and obvious propositions are (i) that an element of a row is composed of a large number of components of the row immediately below; and (ii) our minds pick out rows by virtue of some kind of apparent "systematizability" or "model-ability".

From this we can deduce that there is an important ontological property which distinguishes a row from the one immediately below. It is the property of macrostate reproducibility, that is, if there is an accurate model of macrostate (i.e., upper row) quantities, then the fine details of the microstate (i.e., row immediately below) just don't matter -- we can automatically infer that almost anything that can happen at the microstate level will lead to that same description at the macrostate level.

The paradigmatic example is thermodynamics, in which all of the important information about the microstate (particle momenta and positions) is captured by a few macrostate variables (e.g., pressure, volume, temperature, chemical potential, etc.). Empirically, it is observed that knowledge of the values of only a subset of the macrostate variables suffices to predict the values of the remaining macrostate variables. We can use that empirical observation plus an accurate model of the microstates to create an accurate model of macrostates as follows: (i) create a probability distribution over the microstates by maximizing entropy subject to the constraint that the predictive subset of macrostate variables are fixed; (ii) take expectations over this probability distribution to predict the remaining macrostate variables.

The point: when someone wants to know what ontological difference exists between the higher rows and the lower, one trivial observation (upper rows are compositions of lower ones) and one mildly more subtle anthropic one (our minds distinguish rows on the basis of some kind of systematizability) provide enough information to give a much better answer than "Mu". This perspective gives a better definition of reductionism too: reductionism is the process of discovering which details of the microstate matter for accurate macrostate modeling, and which can be ignored.

Consciousness, value,meaning....

Basically anything that regularly gets dismissed as a non question...

Something I can say about the world doesn't completely determine everything else I can say about the same green strand, but something that exists in the world does completely determine what else exists along the same blue line.

That seems true. The core reductionist tenet seems to be that you don't need the thing that exists explained/observed on every level of abstraction, but rather that you could deduce everything else about the object given only the most fundamental description. This seems to imply that there is some element of direction even in the blue arrow, since one model follows from another.

It's not clear to me why it would be an error within reductionism to say that the higher levels of abstraction approximates the lower ones or something like that. Maybe I should read up on reductionism somewhere outside LW, can you recommend any specific articles that argues for directionless blue arrows?

Fair correction, I think "explanation" and "cause" got lumped together under the general file of "words that mean 'X is so because of Y' " category. Anyway, I can see the difference now and the argument makes sense the way you put it in your response to shminux.

I still think the blue arrow might be directional, though. It seems to me that in many cases things on one level could be made out of several different things on the lower level (e.g a "door" might be made out of wood or metal, it might or might not have a handle etc. but so long as your high level abstraction recognizes it as a door that doesn't matter). Given any point in the space of different things you could say about the world, it seems that granting it constrains what can be on other levels, but doesn't clearly define them (e.g of all the standard model variations you could write out equations for a subset larger than one might be used to "explain" physiology. I can't prove this to you, but it seems true.)

I might be misunderstanding what it would mean for the blue arrows to have directions in this scheme though, so if that's the case this should be easily resolved.

At one time I would have labelled the top Emergent and the bottom Fundamental, but David Deutsch convinced me that even this was a mistake. A mind of arbitrary power, given only the bottom row, could deduce all the others—granted. But finally I said to myself: could not this same mind, given only the complete row for Physiology, deduce the contents of Chemistry no less readily? The blue line has no direction

I very much like the post and think that the way of thinking and the diagrams are excellent. Furthermore, I'm not even sure you'd have to change much if you come to agree with what I say here. However, I'm not ready to agree with this statement quoted. I admit insufficient expertise in what I'm about to say, and would happily have someone explain to me I'm simply wrong, but I think that many different lower-level mathematical models can correspond to the same surface-level observations. Sean Carroll I think supports this claim in this talk (with the relevant stuff starting at 21:40 although it's a good talk all over). I think a correct example of this would be: knowing the thermodynamics of a system doesn't define all the positions and velocities of all the different particles. Lots of different lower levels could be true (but only one of them is). So the blue line sorta does have some direction, even though I agree that this 'emergence' talk is unnecessary... And now I realise I'm confused again. Hmm.