(Nothing here is actually new, but a short explanation with pictures would have been helpful to me a while ago, so I thought I'd make an attempt.)
Let me start with a patch of territory: a set of things that exist. The number of rows is far from clear, but I'll use six candidates as a sample; and of course the diagram ought to be a tree, with many elements on each row converging to fewer on the row above, but you'll have to imagine that part.
The blue line that runs through the column is not causation, but identity. It took me a long time (and many knocks about the head from smarter people) to realize that this line is directionless. If someone labels the top Meaningful and the bottom Meaningless, or the top Important and the bottom Unimportant, we see this at once for an error; but the same labels are still errors, if applied in the opposite order. If someone labels the top Contingent and the bottom Necessary, this is another error; if the top Subjective and the bottom Objective, another; or if the top Less Real and the bottom More Real, another still. (Some errors of this type have been called "reductionism," but they aren't the thing people mean when they say "reductionism" around here.) Whatever is, is real—and equally so, wherever it appears along the blue line.
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. Suppose we grant that a mind of arbitrary power, given only the bottom row, could deduce all the others—a popular hypothesis for which we have some good evidence (though not too much). Even then: 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; if I forget this I forget what identity means, and cast myself into confusion—the same type of confusion afflicting one who says, "Science believes that morality's not real!" 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." (Until I realized this I did not understand the metaethics sequence—but that isn't the topic of this post.)
Where does that leave reductionism? Right where it was, untouched. As finite entities, we never perceive the blue line as a whole—not a single azure band of the infinite expanse in which we live. We have to divide the line into graspable segments, and therefore must explain how each segment connects to the others; we must spin the green threads of explanation, drawing a map to overlay the territory. (The diagram is simplified here as well; a green thread is not as simple as "compounds explain synapse," but an intricate dance of analysis and synthesis.) In dividing the line we introduce relation between its divisions, and in introducing relation we introduce direction; emergence is a feature of maps, not of territories. (I would not say "The mind emerges from the brain," but "The active brain is the mind, and models of the mind emerge from models of the brain.") Reductionism proper is just this: noticing that green arrows are always present, and always point up. The whole is never more, nor less, than the sum of its parts; it only seems that way, if some parts have escaped our notice.
Now let's add a few more columns; again, we'll simplify the structure so we can see it, leaving out all worlds but one.
The violet lines are causation—how things are; together with the blue of what things are, they form indigo Reality: the World That Is. (Maybe the violet lines too have no direction; this sounds like timeless physics, of which I don't feel I can wisely speak.) In any case, they extend far beyond our reach, as each effect in turn becomes a cause; once again we find ourselves dividing the lines into portions we can grasp, and to restore the continuity we once removed, we spin threads of red. These too are explanations—though of another kind than the green. Just as violet lines connect blue lines to form a complete territory, red threads connect strands of green threads to form a complete map.
There are traps to fall into here, too. If we believed that the only violet lines (or the only red threads) that counted as real or meaningful were the ones on the bottom row, we would commit another error; this error also has been called "reductionism"—small wonder that it's sometimes deployed as a term of abuse! Or—because we are fallible and the true multiply-branching structure is hard to perceive—we might draw a red arrow pointing left, and be guilty of mere illogic.
But if we can braid red and green together, our best strength is here—in threads of gold. Only a golden thread is knowledge made whole, and no golden thread is ever spun but of green and red in harmony; until I know what a thing is and how it comes to be, both, I do not understand that thing.
If you're wondering about the empty space beneath, remember that the number of rows in the true structure is far above six; I suspect it is infinite. The number of columns is far higher than shown as well, so a golden thread connects, not a single point to a single point, but a wide expanse of one row to a wide expanse of the row above it. Golden threads are far-reaching theories and models—spun of many smaller explanations.
Often, those who find their cloth too threadbare for their taste will turn to another source of material: the beige threads of supernaturalism. Beige looks a bit like gold, if not examined too closely, and these threads have one great advantage: to spin them is the easiest thing in the world. Since they're unanchored to reality, you're free to craft them in any length or shape you like, lay them with arrows pointing wherever suits you, and even cover threads of red or green or gold whose lustre seems displeasing. Some have been taught to weave with beige alone, and in years of toil wrought patterns of strange and desolate beauty; but every hour of labour made their work, not more akin to fact, but less.
In spinning green and red, and in braiding them as gold, we become scientists; in cutting loose the snarls of beige, we become naturalists; in weaving our many threads into sturdy cloth, we become rationalists. Then we join our separate cloths as one, and in such tapestries—if all goes well—we glimpse truth: the harmony of indigo and gold.
Isn't there still an asymmetry, in that all brains are made of atoms, but few atoms are part of brains, etc? Basically in some sense the higher levels are more rare and fragile than the lower levels.
That's true, and not something I thought of, since I was focused on ontological rather than statistical asymmetries. Of course, it could turn out to be a temporary condition, once Foomy starts converting its future light-cone to computronium! Also, although most of the bottom levels fail to generate interesting (knowledge-containing) structures, such structures on the higher levels might have the property that—because they squeeze the future—they tend to become present across whole swathes of Everett branches, making them in a full-multiversal sense actually less fragile.
Interesting corollary: one or more levels above morality, in which most moral agents are nonparticipants. I'm not sure where to go with that, so I'm going to just stroke my beard and say "Hmmm" in a wise-sounding way.
The article seems to explicitly state that the blue line mentioned is a deliberate oversimplification for explaining, in general, how to think about knowledge in a reductionist sense. The bigger issue here seems to be that you might be able to build a brain out of something that isn't atoms, rather than being able to build different things with atoms.
There is a lot less asymmetry between a brain and all the neurons which make it up. However, it is not clear that the forest-trees relationship is genuinely one of identity.
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.
No, you're absolutely right; in fact it would seem I was changing it while you were typing this comment! Please see my reply to shminux, who had the same objection.
(Definitely lesson learned here!)
Your post is an illuminating attempt to explicate some usually implicit concepts.
I sort of agree with your first diagram, that it is only human thinking that overlays a direction, or any kind of linkage, on the human-made collection of abstractions. But you lose me after that.
This is a highly contentious speculation (Deutsch, like Penrose, is fond of them), and I am not aware of any experimental evidence for it, so I refuse to grant it until I see some. Well, I suppose there is a tiny bit of it, where advances in physics let people design new chemical processes, or when understanding biology better lets us predict some behavior patterns.
I am far more comfortable with the more pedestrian definition of reductionism, where the arrows of human analysis of these abstractions point downward, and the secondary arrows of synthesis point upward, together forming "explanations", and, if we are lucky, testable predictions, when your secondary upward arrows lead to something not yet observed.
I don't understand your description of the "causation" meta-abstraction. "Meta" because it seems to connect towers of abstractions together somehow. One hint is that you describe it by "how" instead of "what", and, if I cut through your gratuitous use of pathos and evocative imagery, you seem to say that both abstraction towers and meta-abstraction connections between the abstraction towers are required for robust knowledge.
Furthermore, you seem to describe the breaks in your [what x how] mental framework as supernaturalism, which makes sense in the context, I suppose.
Hmm, I see I wasn't clear there at all. That all levels can be deduced from one level is just what Deutsch himself isn't granting—he argues against it! Rather, it (or something like it) is the explanation I usually see people give for why they label the bottom of the blue line as more "fundamental"; my intention was to point out with the next sentence that the complete-deducibility hypothesis doesn't make the blue line directional even if true, because it would allow travel along the line in both directions. I definitely need to rewrite that part. (All that being said, I do think that advances in physics letting people design new chemical processes, and that sort of thing, are strong evidence that far more is possible; I find the hypothesis more plausible than you and Deutsch do.)
It's true the directions of my green arrows are debatable; the reason I went with upward was because the simplest way I could think of to formulate what was happening was just "X explains Y"—"many compounds explain synapse." I agree that in a more zoomed-in view each green arrow would imply a complex up-and-down motion of analysis and synthesis.
Violet lines of causation connect blue lines of territory to each other, not green towers of map. Green towers are connected by red threads, which are (causal) explanation, not causation. I thought this was clear by analogy with the first two diagrams, but you're not the only one, so it looks like I should make it more explicit.
It's a fair cop! But I like it that way. ^_^
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.
I would say they aren't. There are many ways—probably an infinite number—to divide the same blue line into rows, depending on the theories and models invoked; the six in my diagrams are just an example. I don't think the row divisions we as a civilization are given to use are privileged in any particular way.
The same description, yes; but the description isn't the thing. Each microstate is identical with exactly one macrostate and vice versa, could we but perceive it in full; it does often happen that the descriptions of a large set of microstates all lead to a single description of just one macrostate, but this is only a fact about the information we've chosen to omit for our own convenience, not about the reality.
"Important" is the key word; reality never treats anything as unimportant—only we do. I think the distinction you're making is an epistemic rather than an ontological one.
Nothing I'm trying to communicate depends on the particular six rows you chose as the example. Rather, what I'm getting at is that the sheer fact of "model-ability" reflects an ontological property.
You have an idea about the way the universe operates, and it is, as far as I can tell, an incorrect idea. The heart of it is this:
The phrase "our own convenience" is the problem: that a system-composed-of-lower-level-components is convenient for us turns out, non-obviously, to be contingent on a fact about the system, not just facts about us! We as engineers (and the process of evolution by natural selection) are able to create systems which reliably do something (transmit force, store energy, process information, etc.) because it is possible to aggregate lower-level components such that the macrostate behavior of the system is robust to the overwhelming majority of the lower level degrees of freedom.
This is why you have a persistent sense of personal identity -- why the "you" that falls asleep feels the same as (and can in principle be objectively identified with) the "you" that wakes up, despite of the immense number of changes in your low-level state that take place while you're asleep. Almost all of those changes (e.g., thermal noise in your neurons, ongoing biochemical processes, some of which integrate up to physiological processes) occur in low-level degrees of freedom that just don't matter to the question of who you are. (Think of organ transplants!)
Yeah, I can see how that would happen -- we don't have a good jargon for distinguishing the kind of "importance" I'm trying to communicate. The key point is that systems do exist in which the robustly determined upper-level degrees of freedom in one sub-system are coupled essentially only to the robustly determined upper-level degrees of freedom of another subsystem. In such a setup, the uncontrolled low-level degrees of freedom of the subsystems have no (okay, negligible) physical influence on one another. This is a fact about the system, not a fact about humans. (It does require counterfactual reasoning to discern this fact, which might confuse the issue.)
Here's an example of a system in which one set of subsystem microstate detail is irrelevant to a second set of subsystem microstate detail. A thermally well-isolated piston contains a gas at a certain pressure, temperature, and volume. When a force is exerted on the head of the piston, the microstate of the gas changes in a way that depends only on the magnitude of the force, and not on (essentially) any of the microstate detail about how that force came to be exerted.
I really like the imagery in your explanation, but I am not entirely clear on what the golden threads symbolize here. Would it be fair to say that the golden threads are the explanations of how a law or model on a lower level of abstraction causes the observations on a higher level?
Also, I don't really think you could deduce the entire structure of the blue line given by any one point as you seem to imply.
If you are given the physics of a universe, there might be several possible types of physiology, and for every such physiology there might be several different types of neural circuitry. Similarly you could say that there are still some degrees of freedom left over when some arbitrary psychology is given; it might be possible to have human-like cognition within the framework of purely newtonian physics, or we might be able to have a mind with the same morality but vastly different circuitry.
Of course you gain information about the entire blue line when you are given a single point, but it does not seem sufficient for crafting a complete model to know a lot about, say, the moral values of humans or the mental states of earthworms.
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.
Adopting naturalism leaves a lot of questions unanswered; likewise adopting reductionism. One issue you haven't touched on is whether there is always a reductive relation between causal relations on different levels, or whether there can be independent laws at difference levels.
Yes, it absolutely does; but then supernaturalism, even if granted, fails to actually answer them. It's the difference between saying "Here are Maxwell's Equations, which tells the angels where to push the electrons" or just, "Here are Maxwell's Equations." (Of course, the other option—having only the angels and not Maxwell's laws—is obsolete; it would make an electronic device a miracle, and each other electronic device a separate and additional miracle.)
I would say that the history of science is a history of what seemed like contingent equalities turning out to have been necessary identities all along; that is the character of the Law, as far as we have grasped it.
Scientists have argued .for independent higher level laws.
You have tried to argue that supernaturalism fails to answer any question by extrapolation from one example, where naturalism does well. The supernaturalist could likewise cherry-pick examples.
Examples where supernaturalism is methodologically successful? I would love to hear some!
(Not being sarcastic here; I really would.)
Basically anything that regularly gets dismissed as a non question...
Hmm, I don't know that we mean the same thing by "methodological."
When has someone succeeded in producing any effect or predicting any event, specifically by invoking supernatural knowledge?
To which the supernaturalism replies: when did natural knowledge tell you what the meaning and purpose of your life is? Same problem as before, IOW.
I don't know how I got into this. I only claimed that naturalist and reductionism don't answer all questions. That doesn't mean something else does.
Overall, I liked this post. Here's the primary exception:
The compression could easily be lossy. Most higher level concepts are relational in some way- to use an example from image processing, we could build cats out of noses out of edges out of pixels. If we have an idea of how a cat acts on the level of catness, that does not necessarily give us all we need to figure out the components of a cat, or how those components appear visually, or what the basics of the visual field are. If we know pixels, it is easy to come up with edges; if we know edges, it may not be clear if there are pixels or if the underlying image is continuous, for example. More mathematically, if I know the difference of two variables, that does not imply that I can determine what those original variables were.
And typically, when a human makes these sorts of maps, they do so in a reductive (i.e. lossy) way. I mean that in the sense that a molecule is a single element in the chemistry map, but many elements in the physics map; a hand is a handful of elements in the physiology map, but a staggeringly massive number of elements in the chemistry map.
If you were given the complete story of some hunter-gatherer tribe on the moral level- what they did, what they thought about each other, what values they held, and so on- do you think that from just this account a superintelligence could determine the fundamental nature of the particles in their universe? That just seems information-theoretically implausible.
Anyway, I thought the diagram was cool. I could have done without the mystical language.
Ok, I didn't understand the post. Like you are saying that the blue lines don't have any direktion, and then you go on to paint (directed) arrows over it.. Is this by mistake? Did you want to make the green arrows double directed or something like that? I suppose that not only does the blue line not have a direction, it also doesn't have an order? E.g. could you have written from top to bottom "Psychology Physiology Chemistry Morality Physics Neuroscience"? It's clearly no accident that you wrote those "sets of things that exist" in that familiar order, but is there any way to justifiy that order if the blue line represents identity? Is it simply meaningless convention?
But I like how the beige threads look like vandalism. Tells me what I should think about supernaturalism. Would be even more impressive if you used the MS Paint spray-can tool.