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Shane_Patt comments on Tapestries of Gold - Less Wrong
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That's a good way of putting it, except that it would be "explains" rather than "causes." I definitely should make it more clear that—because there are actually many more columns than shown in the diagram—a golden thread connects an entire row to the entire row above it, not just one point to one point.
I wasn't clear there; please see my reply to shminux, who had the same objection.
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.
I would say: "door" is an element of the map, and could be made from "wood" or "metal," and have or not have a "handle"; but this door beside me right now is an element of the territory, and is made from wood, and does have a handle. The green arrows are map, and directional; the blue line is territory, and not directional. 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.
I tried to make what I was getting at clearer in my edit to the OP a few minutes ago.
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?
Well, what pushed me to write this post—in combination with the sequences here—was David Deutsch's books Fabric of Reality and Beginning of Infinity; I don't know that either is legally available online, I'm afraid.