Followup toHow An Algorithm Feels From Inside, Mind Projection Fallacy

Almost one year ago, in April 2007, Matthew C submitted the following suggestion for an Overcoming Bias topic:

"How and why the current reigning philosophical hegemon (reductionistic materialism) is obviously correct [...], while the reigning philosophical viewpoints of all past societies and civilizations are obviously suspect—"

I remember this, because I looked at the request and deemed it legitimate, but I knew I couldn't do that topic until I'd started on the Mind Projection Fallacy sequence, which wouldn't be for a while...

But now it's time to begin addressing this question.  And while I haven't yet come to the "materialism" issue, we can now start on "reductionism".

First, let it be said that I do indeed hold that "reductionism", according to the meaning I will give for that word, is obviously correct; and to perdition with any past civilizations that disagreed.

This seems like a strong statement, at least the first part of it.  General Relativity seems well-supported, yet who knows but that some future physicist may overturn it?

On the other hand, we are never going back to Newtonian mechanics.  The ratchet of science turns, but it does not turn in reverse.  There are cases in scientific history where a theory suffered a wound or two, and then bounced back; but when a theory takes as many arrows through the chest as Newtonian mechanics, it stays dead.

"To hell with what past civilizations thought" seems safe enough, when past civilizations believed in something that has been falsified to the trash heap of history.

And reductionism is not so much a positive hypothesis, as the absence of belief—in particular, disbelief in a form of the Mind Projection Fallacy.

I once met a fellow who claimed that he had experience as a Navy gunner, and he said, "When you fire artillery shells, you've got to compute the trajectories using Newtonian mechanics.  If you compute the trajectories using relativity, you'll get the wrong answer."

And I, and another person who was present, said flatly, "No."  I added, "You might not be able to compute the trajectories fast enough to get the answers in time—maybe that's what you mean?  But the relativistic answer will always be more accurate than the Newtonian one."

"No," he said, "I mean that relativity will give you the wrong answer, because things moving at the speed of artillery shells are governed by Newtonian mechanics, not relativity."

"If that were really true," I replied, "you could publish it in a physics journal and collect your Nobel Prize." 

Standard physics uses the same fundamental theory to describe the flight of a Boeing 747 airplane, and collisions in the Relativistic Heavy Ion Collider.  Nuclei and airplanes alike, according to our understanding, are obeying special relativity, quantum mechanics, and chromodynamics.

But we use entirely different models to understand the aerodynamics of a 747 and a collision between gold nuclei in the RHIC.  A computer modeling the aerodynamics of a 747 may not contain a single token, a single bit of RAM, that represents a quark.

So is the 747 made of something other than quarks?  No, you're just modeling it with representational elements that do not have a one-to-one correspondence with the quarks of the 747.  The map is not the territory.

Why not model the 747 with a chromodynamic representation?  Because then it would take a gazillion years to get any answers out of the model.  Also we could not store the model on all the memory on all the computers in the world, as of 2008.

As the saying goes, "The map is not the territory, but you can't fold up the territory and put it in your glove compartment."  Sometimes you need a smaller map to fit in a more cramped glove compartment—but this does not change the territory.  The scale of a map is not a fact about the territory, it's a fact about the map.

If it were possible to build and run a chromodynamic model of the 747, it would yield accurate predictions.  Better predictions than the aerodynamic model, in fact.

To build a fully accurate model of the 747, it is not necessary, in principle, for the model to contain explicit descriptions of things like airflow and lift.  There does not have to be a single token, a single bit of RAM, that corresponds to the position of the wings.  It is possible, in principle, to build an accurate model of the 747 that makes no mention of anything except elementary particle fields and fundamental forces.

"What?" cries the antireductionist.  "Are you telling me the 747 doesn't really have wings?  I can see the wings right there!"

The notion here is a subtle one.  It's not just the notion that an object can have different descriptions at different levels.

It's the notion that "having different descriptions at different levels" is itself something you say that belongs in the realm of Talking About Maps, not the realm of Talking About Territory.

It's not that the airplane itself, the laws of physics themselves, use different descriptions at different levels—as yonder artillery gunner thought.  Rather we, for our convenience, use different simplified models at different levels.

If you looked at the ultimate chromodynamic model, the one that contained only elementary particle fields and fundamental forces, that model would contain all the facts about airflow and lift and wing positions—but these facts would be implicit, rather than explicit.

You, looking at the model, and thinking about the model, would be able to figure out where the wings were.  Having figured it out, there would be an explicit representation in your mind of the wing position—an explicit computational object, there in your neural RAM.  In your mind.

You might, indeed, deduce all sorts of explicit descriptions of the airplane, at various levels, and even explicit rules for how your models at different levels interacted with each other to produce combined predictions—

And the way that algorithm feels from inside, is that the airplane would seem to be made up of many levels at once, interacting with each other.

The way a belief feels from inside, is that you seem to be looking straight at reality.  When it actually seems that you're looking at a belief, as such, you are really experiencing a belief about belief.

So when your mind simultaneously believes explicit descriptions of many different levels, and believes explicit rules for transiting between levels, as part of an efficient combined model, it feels like you are seeing a system that is made of different level descriptions and their rules for interaction.

But this is just the brain trying to be efficiently compress an object that it cannot remotely begin to model on a fundamental level.  The airplane is too large.  Even a hydrogen atom would be too large.  Quark-to-quark interactions are insanely intractable.  You can't handle the truth.

But the way physics really works, as far as we can tell, is that there is only the most basic level—the elementary particle fields and fundamental forces.  You can't handle the raw truth, but reality can handle it without the slightest simplification.  (I wish I knew where Reality got its computing power.)

The laws of physics do not contain distinct additional causal entities that correspond to lift or airplane wings, the way that the mind of an engineer contains distinct additional cognitive entities that correspond to lift or airplane wings.

This, as I see it, is the thesis of reductionism.  Reductionism is not a positive belief, but rather, a disbelief that the higher levels of simplified multilevel models are out there in the territory.  Understanding this on a gut level dissolves the question of "How can you say the airplane doesn't really have wings, when I can see the wings right there?"  The critical words are really and see.

 

Part of the sequence Reductionism

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This denial that "higher level" entities actually exist causes a problem when we are supposed to identify ourselves with such an entity. Does the mind of a cognitive scientist only exist in the mind of a cognitive scientist?

The belief that there is a cognitive mind calling itself a scientist only exists in that scientist's mind. The reality is undecatillion swarms of quarks not having any beliefs, and just BEING the scientist.

Probably no one will ever see this comment, but.

"I wish I knew where reality got its computing power."

If reality had less computing power, what differences would you expect to see? You're part of the computation, after all; if everything stood still for a few million meta-years while reality laboriously computed the next step, there's no reason this should affect what you actually end up experiencing, any more than it should affect whether planets stay in their orbits or not. For all we know, our own computers are much faster (from our perspective) than the machines on which the Dark Lords of the Matrix are simulating us (from their perspective).

If reality were computed in reverse chronological order, what differences would you expect to see?

Suppose our universe was produced by specifying some particular final state, and then repeatedly computing predecessor states according to some deterministic laws of nature. Would we experience time backward? Or would we still experience it forward (the reverse of the direction of the simulation) because of some time assymetry in the physical laws or in the entropy of the initial vs final states?

Everyone always assumes that the simulation will proceed "foreward". Is that important? I honestly don't know.

You can go one step further. If folks like Barbour are correct that time is not fundamental, but rather something that emerges from causal flow, then it ought to be that our universe can be simulated in a timeless manner as well. So a model of this universe need not actually be "executed" at all---a full specification of the causal structure ought to be enough.

And once you've bought that, why should the medium for that specification matter? A mathematical paper describing the object should be just as legitimate as an "implementation" in magnetic patterns on a platter somewhere.

And if it doesn't matter what the medium is, why should it matter whether there's a medium at all? Theorems don't become true because someone proves them, so why should our universe become real because someone wrote it down?

If I understand Max Tegmark correctly, this is actually the intuition at the core of his mathematical universe hypothesis (Wikipedia, but with some good citations at the bottom), which basically says: "We perceive the universe as existing because we are in it." Dr. Tegmark says that the universe is one of many coherent mathematical structures, and in particular it's one that contains sentient beings, and those sentient beings necessarily perceive themselves and their surroundings as "real". Pretty much the only problem I have with this notion is that I have no idea how to test it. The best I can come up with is that our universe, much like our region of the universe, should turn out to be almost but not quite ideal for the development of nearly-intelligent creatures like us, but I've seen that suggested of models that don't require the MUH as well. Aside from that, I actually find it quite compelling, and I'd be a bit sad to hear that it had been falsified.

Interestingly enough, a version of the MUH showed up in Dennis Paul Himes' (An Atheist Apology)[http://www.cookhimes.us/dennis/aaa.htm] (as part of the "contradiction of omnipotent agency" argument), written just a few years after Dr. Tegmark started writing about these ideas. Mr. Himes' essay was very influential on me as a teenager, and yet I never did hear of the "mathematical universe hypothesis" by that name until a few years ago. In past correspondence, he wrote that the argument was original to him as far as he knew, and at least one of his commenters claimed to also have developed it independently, so it may be a more intuitively plausible idea than it seems to be at first glance.

One minor quibble; how do we know there is any most basic level?

Levels are an attribute of the map. The territory only has one level. Its only level is the most basic one.

Let's consider a fractal. The Mandelbrot set can be made by taking the union of infinitely many iterations. You could think of each additional iteration as a better map. That being said, either a point is in the Mandelbrot set or it is not. The set itself only has one level.

Agreed. Why would we believe a quark is not "emergent"? Could be turtles all the way down....

Reductionism is great. The main problem is that by itself it tells us nothing new. Science depends on hypothesis generation, and reductionism says nothing about how to do that in a rational way, only how to test hypotheses rationally. For some reason the creative side of science -- and I use the word "creative" in the generative sense -- is never addressed by methodology in the same way falsifiability is:

http://emergentfool.com/2010/02/26/why-falsifiability-is-insufficient-for-scientific-reasoning/

We are at a stage of historical enlightenment where more and better reductionism is producing marginal returns. To be even less wrong, we might spend more time on the hypothesis generation side of the equation.

Really? I think of reductionism as maybe the greatest, most wildly successful abductive tool in all of history. If we can't explain some behavior or property of some object it tells us one good guess is to look to the composite parts of that thing for the answer. The only other strategy for hypothesis generation I can think of that has been comparably successful is skepticism (about evidence and testimony). "I was hallucinating." and "The guy is lying" have explained a lot of things over the years. Can anyone think of others?

Science depends on hypothesis generation, and reductionism says nothing about how to do that in a rational way, only how to test hypotheses rationally.

You may be interested in Science Doesn't Trust Your Rationality, in which Eliezer suggests that science is a way of identifying the good theories produced by a community of scientists who on their own have some capacity to produce theories, and that Bayesian rationality is a systematic way of producing good theories.

Oh, and Welcome to Less Wrong! You have identified an important point in your first few comments, and I hope that is predictor of good things to come.

But the way physics really works, as far as we can tell, is that there is only the most basic level - the elementary particle fields and fundamental forces.

To clarify (actually, to push this further): there is only one thing (the universe) - because surely breaking the thing down into parts (such as objects) which in turn lets you notice relations between parts (which in turn lets you see time, for example) -- surely all that is stuff done by modelers of reality and not by reality itself? I'm trying to say that the universe isn't pre-parsed (if that makes any sense...)

I'm surprised that this point is controversial enough that Eliezer felt the need to make a post about it, and even more surprised that he's catching heat in the comments for it. This "reductionism" is something I believe down to the bone, to the extent that I have trouble conceptualizing the world where it is false.

After talking to some non-reductionists, I've come to this idea about what it would mean for reductionism to be false:

I'm sure you're familiar with Conway's Game of Life? If not, go check it out for a bit. All the rules for the system are on the pixel level -- this is the lowest, fundamental level. Everything that happens in conway's game of life is reducible to the rules regarding individual pixels and their color (white or black), and we know this because we have access to the source code of Conway's Game, and it is in fact true that those are the only rules.

For Conways' Game to be non-reductionistic, what you'd have to find in the source code is a set of rules that override the pixel-level rules in the case of high-level objects in the game. Eg "When you see this sort of pixel configuration, override the normal rules and instead make the relevant pixels follow this high-level law where necessary."

Something like that.

It's an overriding of low-level laws when they would otherwise have contradicted high-level laws.

This is a situation where a lot of confidence seems appropriate, though of course not infinite confidence. I'd put the chance that Eliezer is wrong here at below one percent.

I really have no idea what Eliezer being wrong on this would mean. Is the subject matter of this posting the nature of the territory or is it advice on the best way to construct maps?

What conceivable observations might cause you to revise that 1% probability estimate up to, say, 80%?

As I see it, reductionism is not a hypothesis about the world; it is a good heuristic to direct research.

I take the main thesis as being summed up by this sentence around the end:

Reductionism is not a positive belief, but rather, a disbelief that the higher levels of simplified multilevel models are out there in the territory.

Specific non-reductionist hypotheses, in the extremely unlikely event that any are supported by evidence, could cast doubt on reductionism. We'd need to find a specific set of circumstances under which reality appears to be computing the same entities at multiple levels simultaneously and applying different laws at each level, or we'd need to find fundamental laws that talk about non-fundamental objects. For example, if the Navy gunner were actually correct that you need to use Newtonian mechanics instead of relativity in order to get the right answer when computing artillery trajectories (given the further unlikely assumption that we couldn't find a simpler explanation for this state of affairs than "physical reductionism as a whole is wrong").

A quick Google search turns up:

But the crystal growth depends strongly on temperature (as is seen in the morphology diagram). Thus the six arms of the snow crystal each change their growth with time. And because all six arms see the same conditions at the same times, they all grow about the same way.... If you think this is hard to swallow, let me assure you that the vast majority of snow crystals are not very symmetrical.

Reductionism does have a caveat, and this is "a fact about maps" and not "a fact about the territory": the real world level can be below the algorithm. Example: a CD. A chromodynamic model would spend immense computing resources simulating the heat and location and momentum and bonds of a slew of atoms (including those in the surrounding atmosphere, or the plasticizer would boil off). In reality there are about four things that matter in a CD: you can pick it up, it fits into a standard box, it fits into a standard reader tray, and when you measure the pattern of pits they encode a particular blob of binary data. From a human utility perspective, the CD is fully replaceable with a chromodynamically dissimilar other CD that happens to have those same characteristics.

Computers are full of examples of this, where the least important level is not the fundamental level. In in some cases, each level is not just built upon lower levels, but ought to be fully independent of them. If your lisp doesn't implement the lambda calculus because of a silicon fault, an atomic model would correctly represent this, but it would be representing a mathematically unimportant bug. A correct lisp would be representable on any compute substrate, from a Mac to a cranks-and-gears Babbage engine. A model which took account of the substrate would be missing the point.

I think the point is that the model of four elements we use to describe the CD is also contained within the chromodynamic model - the four elements are a less accurate abstraction of the chromodynamic model, even if we don't recognize it as such when we used the more abstract model.

In the same way, Newtonian Mechanics is a less accurate abstraction of Special Relativity.

Therefore, no matter how precise Newtonian Mechanics is, it does not match up exactly with reality. Because it is an abstraction, it contains inaccuracies. The SR version of the same process will always be more accurate than the NM version, though the SR version is also probably not completely accurate.

A correct lisp would be representable on any compute substrate, from a Mac to a cranks-and-gears Babbage engine.

I don't think that is true. For Lisp to mean anything to any machine, it must first be compiled into the machine language of that particular machine. Because this process is fundamentally different for different types of machines, the way the same Lisp behaves on each machine will be highly dependent on its specific translation into machine language. In other words, the same Lisp code will result in slightly different behavior on a Mac than it would on a Linux machine. The difference may not be enough to take any note of, but it is still there.

This is the similar to calculating the trajectory of an artillery shell with Newtonian Mechanics vs Special Relativity. The difference between the two will be so small that it is almost unmeasurable, but there will definitely be a difference between them.

Is it fair to call the CD data a map in this case? (Perhaps that's your point.) The relationship is closer to interface-implementation than map-territory. Reductionism still stands, in that the higher abstraction is a reduction of the lower. (Whereas a map is a compression of the territory, an interface is a construction on top of it). Correct lisp should be implementation-agnostic, but it is not implementation-free.

Wockyman: It's not that they're the smallest, as such.

Yes, how a particle acts is affected by those around it. But the idea is that if you know the basic rules, then knowing those rules, plus which particles are where around it lets you predict, in principle, given sufficient computational power, stuff about how it will act. In other words, the complicated stuff that emerges arises from the more basic stuff.

Think of it this way: You know cellular automatons? Especially Conaway's Game of Life? Really simple rules, just the grid, cells that can be on and off, and basic rules for when a transition occurs based on a cell's and its neighbor's state.

Yet complicated behavior arises out of that. One would not, however, say that behavior is beyond the rules, or that reduction to those rules fails. Those complicated behaviors arise out of those simple rules.

Incidentally, if you looked through Eliezer's QM sequence, the more fundamental reduction isn't so much particles, but probably quantum amplitudes over configuration space, with particles corresponding with it being possible to "factor out" certain sets of dimensions in the configuration space.

(Reductionism does NOT mean "reduction to particles", just "reduction to simple principles that are the basic thing that give rise to everything else", not identical to, but similar to the way that comparatively simple rules of chess give rise to really complex strategies (and even more so for Go))

As for it being "just a map"... it is a map, but it's a map about something. The map may not be the territory, but there is a territory, and the fact that the map seems to tell us accurate stuff about the territory is at least a justification for suspecting that the actual underlying reality of the territory may actually resemble what the map claims it's like.

"However, reductionism is incapable of explaining the real world."

Is that the argument against Reductionism? That there are things it can't, as yet, explain? That's the same position the Intelligent Design people put forward. Your post is a big fat Semantic Stop Sign.

No, we don't understand protein folding yet. Precedent suggests that one day, we probably will, and it probably won't be down to some mystical emergent phenomenon. It'll be complicated, subtle, amazing, and fully explicable within the realms of reductionist science.

I'm surprised that this point is controversial enough that Eliezer felt the need to make a post about it, and even more surprised that he's catching heat in the comments for it. This "reductionism" is something I believe down to the bone, to the extent that I have trouble conceptualizing the world where it is false.

Seconded.

I suppose the next post is on how a non-reductionist universe would overwhelmingly violate Occam's Razor?

Ian - if minds don't create their own distinct internal maps, but simply 'latch on' to what's actually there, then how do explain the fact that maps can be wrong? In fact, how do you explain any two people holding two opposed beliefs?

Sensory perception isn't like a photograph - low-resolution but essentially representative. It's like an idiot describing a photograph to someone who's been blind all their life. This is why we get our maps wrong, and that is why it's useful to think in terms of map and territory - so that we can try and draw better ones.

But this is just the brain trying to be efficiently compress an object that it cannot remotely begin to model on a fundamental level. The airplane is too large. Even a hydrogen atom would be too large. Quark-to-quark interactions are insanely intractable. You can't handle the truth.

Less Wrongs "The Futility of Emergence" article argues against using the word "emergence", claiming that it provides no additional information. The argument went that literally everything is an emergent property, since everything can be boiled down to more fundamental components. (I would argue that it is never actually used in this broad sense, but rather to indicate cases where relatively simple circumstances, when iterated enough times, give rise to much more complex interactions in ways which are difficult to fully model.)

Isn't this article using "reductionism" in exactly the same sense as "emergence" in the broad sense? It isn't actually using "reductionism" as a curiosity stopper, though. It isn't saying "airplanes work because of quarks", and leaving it at that, which is what "The Futility of Emergence" was warning against. Still, this highlights an interesting exception to the rationalists rule against statements which are always true. In terms of Bayes theorem, a statement which excludes nothing proves nothing. But if we aren't trying to provide new insights into specific phenomena, but only to make facts about the universe more explicit, then such statements can still serve such a purpose. This only holds true if the statement is falsifiable, though. If you make some generalization such as "free will is an emergent property" or "free will can be reduced to more fundamental components", such statements can still be falsified.

I guess the takeaway message from the two articles is not to accept things like "because quarks" as answers, but also to understand that "because quarks" is in fact correct. It's the answer (or one of the answers) that you'd eventually get if you just kept asking "why" until you got to the most fundamental underlying principles. We shouldn't look for our explanations only in terms of fundamentals or only in terms of more broad terms. If we want a full understanding, we need to examine all of the layers of the onion.