Emergence and Reductionism

My last week's post on 'Theories and Models' was actually meant to be about emergence and reductionism. While wring however, I figured it would be better to first explain what I mean with a model since my references to sex occasionally seem to confuse the one or the other reader.

Brief summary of last week's post: we want to describe the 'real world out there' by using a model that has explanatory power. The model itself captures some features of the world, it uses the framework of a theory, but should not be confused with the theory itself. I found it useful to think of this much like a function (the theory) acting on a set (some part of the real world out there) to give us a picture (the model).


The model describes some objects and the way they interact with each other (though the interaction can be trivial, or the system just static). To complete the model one usually needs initial conditions and some data as input (to determine parameters). In the following I will refer to the part of the real world out there that the model is supposed to describe as 'the system'.

To reiterate what I said last week: I don't care whether you like that use of words or not, it's just to clarify what I mean when I use them.

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I. Emergence

Today's topic is partly inspired by the book on "Complex Adaptive Systems" I just finished reading (see my review here), and partly by Lee's lecture on "The Problem of Time in Quantum Gravity and Cosmology" from April 2nd (PIRSA 08040011 and 08040013). Please don't ask me what happened in the other 13 lectures because I wasn't there.

Hmmm... I missed the first ten minutes on April 2nd. After watching the video I can now reconstruct what was written on the blackboard before I came and what the not completely wiped-off words said. I feel a bit like a time-traveler who just closed the loop. Either way, here is a brief summary of min 11:38 to 20:24. Lee explains there's three types of emergence:

1. Emergence in scale:
   In which a system described on larger scale has a property that it wouldn't have on smaller scales. As an example he mentions viscosity of fluids that isn't a property which makes sense for an atom, and the fitness of biological species that wouldn't make sense for molecules. "Atoms don't have gender but living things have gender."


2. Emergence in contingency:
   In which a system develops a property only under certain circumstances. As an example he mentions the temperature dependence of superfluidity.



3. Emergence in time:
   In which a system develops a property in time. As an example he mentions biological membranes, and that more than 3.8 billions years ago it wouldn't have made sense to speak of these.

As somebody in the audience also pointed out, these are basically different order parameters to change a system (e.g. scale, temperature, or time).

I was somewhat confused by distinguishing between these three cases, and that not only because I don't know what the plural of emergence is. (It can't be emergencies, can it?) No, because I always understood emergence vaguely as a feature the whole has but its parts don't have. Not that I ever actually thought about it very much, but that would be an order parameter like the number of constituents and and their composition - which could, or couldn't fall among point one or two.

Part of my confusion arises because in practical circumstances it isn't always clear to me which of the three cases of 'emergence' on actually has at hand. For example, take the formation of atoms in the early universe. Is this an emergence in time? Or is this an emergence in contingency? After all it's the temperature that matters I would say. Just that the temperature is related to the scale factor, which is a function of time. Also, in most experiments we change the contingent factors in time - like e.g. the cooling of the superfluid medium. So, the second and third cases seem to be very entangled. I think then I should understand emergence of a system's properties in time as it taking place without being caused by a time dependent change of environmental conditions of the system. Like e.g. the emergence of emoticons in the written language ;-) or that of the red spot on Jupiter - cases in which it 'just' takes time.

Here is a nice example for patterns that I'd say emerge in time, an oscillating chemical reaction:

[An example for a particularly pretty oscillating chemical reaction with emerging patterns. Unfortunately, the video description doesn't contain information about the chemicals used, instead it provides a very bizarre connection to migraine and 'stimulus points'. Either way, this sort of reaction is called a Belousov-Zhabotinsky-Reaction.]

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II. Strong and Weak Emergence

Okay, so after some back and forth I figured out why I was feeling somewhat uneasy with these three cases. Besides that I think - as said above - in practical circumstances distinguishing one from the other is difficult, in the second and third case I'd have said a property might be emergent in the sense that it 'arises' and becomes relevant, but was present already in the setup of the model (and if not, you should come up with a better model). E.g. Bose Einstein condensation was predicted to arise at low temperatures. Likewise, I'd say if one knows the initial conditions of a system and its evolution then one knows what will happen in time - it might turn out only later emergent properties become noticeable and important, but it's a predictable emergence. Like e.g. stars that have formed out of collapsing matter or something like this.

Either way, to come back to my rather naive sense of 'emergence' by increasing the number of constituents. If you look at a part of some larger system, specifying or examining its properties just might not be enough to understand how the whole system will behave: it can just be an incomplete description. It can be one needs further information that is the interaction with other parts of the system. As an example take one of these photographic mosaics:

Image: Artensoft.

If you'd only look at one of the smaller photos you'd have no chance of ever 'predicting' that something will 'emerge' if you zoom out.

After looking at the Wikipedia entry on Emergence I learned that this essentially is the difference between 'strong' and 'weak' emergence. In the danger of expressing my total ignorance of various words and names in that Wiki entry I've never heard before and am presently not in the mood to follow up upon, let me say that weak emergence is - at least "in principle" - already contained in a model you use to describe the system, and is thus at least "in principle" predictable, whereas strong emergence isn't.

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III. Reductionism

If you want to go back to Lee's lecture, fast forward to min 37:00, where the topic emergence and reductionism comes up again. Somebody in the audience (I believe it's Jonathan Hackett), asks (min 40:00): "Is there a phenomenon which is emergent which is not derivable and is not expected to ever be derivable from something else?" This is essentially the question whether strong emergence actually exists.

Let me paraphrase reductionism as the believe that a system can "in principle" be understood entirely by understanding its parts. Then the argument of whether or not reductionism can "in principle" explain everything is that same question: does strong emergence actually exist? Or are all emergent features 'weakly' emerging, in that they are "in principle" predictable?

Now you might have noticed a lot of "in principles" in the previous paragraphs. I'd think that most physicists believe there is no strong emergence. At least I don't believe it. As such, I do think reductionism does not discard any features. However, this believe is for practical purposes often irrelevant since the models that we use, however sophisticated, are never complete descriptions of reality anyway. Even if you had a 'theory of everything', and there was no strong emergence, it wouldn't automatically provide a useful "model for everything". If we'd find the one fundamental theory of elementary matter it wouldn't describe all of science for the same reason why specifying the properties of all atoms in a car doesn't help you to figure out why the damned thing doesn't want to start. And I doubt we'll be able to derive the 'emergence' of, say, blog memes from QCD any time soon.

[Image: xkcd]

But besides these practical limitations that we encounter when making models that still have to be useful, there is the question whether it is possible to ever figure out if a system has the potential for a 'weak emergence' of a new property. Since it's impossible to rule out something unpredictable will happen, I'd say we can never know all the 'non-relevant' factors or 'unknown unknowns' as Homer-Dixon put it in his book. For example I'd say it is possible that tomorrow the vacuum expectation value of the Higgs flips to zero and that's the end of the world as we know it. Not that I am very concerned this will actually happen, but what the bleep do we know? Anybody wants to estimate the risk this happens and sue somebody over it because we irresponsible physicists might all have completely overlooked a lot of unknown unknowns? Just asking.

I'm not actually sure what Lee is saying later about Stuart Kaufman's view since I didn't read any of Kaufman's books (got stuck in 'At Home in the Universe' somewhere around the history of the DNA or so). But I guess this argument points in the same direction: "What [Stuart] claims is that if you know all the properties that are relevant to compute the fitness function of all the species at some time, you do not know [...] enough to predict what will be the properties that will be relevant for the fitness function 100 million years later."

Thus, no matter whether there is some fundamental theory for everything or not, or whether strong emergence exists or not, we will be faced with systems in which features will unpredictably emerge. Like probably in the evolution of species on our planet, possibly in the climate, but hopefully not in the global economy.

Besides this, since it's impossible to prove that our inability to accurately make a prediction is due to the system and not due to the limitations of the human brain, the hypothesis that strong emergence doesn't exist is unfalsifiable (In other words: if you find an emergent feature you can't explain, you can't prove it can never be explained within any model). So I think I leave this domain over to philosophy.

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VI. Summary

Properties of system can emerge in various ways, they can emerge by changes in scale, under certain conditions, or in time. One can distinguish between strong and weak emergence, where weakly emergent features are in principle predictable and strongly emerging ones aren't. However, this difference is a rather philosophical one as all of our models are incomplete descriptions of the real world anyway, so there always can be a 'strong emergence' simply because the description is incomplete. Further, it is of little use to know whether a feature is in principle unpredictable or if it is in practice unpredictable. Weak emergence is not in conflict with reductionism.