This used to be called "Non-Reduction and Nonapples" but thanks to a comment by Slider I've realized this put the emphasis in the wrong place.

Selling nonapples is a great piece about how critiquing a certain technique, or process, or system can often sneak into proposing a non-existent alternative. This new system, as it is overly general, fails to address the problems that the first exists to solve.

I think reductionism vs non-reductionism is sometimes a similar debate, but sometimes not. First let's distinguish between philosophical reductionism, and practical reductionism.

• Philosophical reductionism is (sort of) the belief that complex systems act the way they do because of the simpler actions of simpler systems that make them up. I think that this is pretty solidly true in our universe, and I won't discuss it further.
• Practical reductionism is the belief that the best and most effective way to study complex systems is to study their components individually, then build up to a larger model of the whole system.

(As an aside I actually think a lot of the reductionism vs non-reductionism debate suffers from a motte-and-bailey issue around this)

Microbiological Ecosystems

An example of practical reductionism is the study of microbiological ecosystems: there are lots and lots of different microbes in any given area (such as the sea, the soil, your intestines) which all require different nutrients and produce different sorts of waste. Some photosynthesize, some turn atmospheric nitrogen into a form which is bioavailable, and some break down carbon-containing material. Clearly if we knew everything about every type of microbe present we could understand the ecosystem. Unfortunately, unlike in macroscopic ecosystems, it's difficult to study a single microbe's behaviour while it is inside the ecosystem. They're just too small! So the standard technique is to get a pure culture, containing just one sort of microbe, and study the behaviour of that culture.

Unfortunately, this often doesn't work very well. Microbes in culture can behave differently from how they normally behave in general systems. Lots of microbes are either impossible to form a pure culture of, or require some incredibly specific nutrient only produced by another microbe, that we don't know the identity of. This means the standard "practical reductionist" technique is doomed to failure.

Here people often like to say things like "Reductionism has failed! We need to study whole systems instead of just trying to understand pieces of them!"

I think this kind of fails to capture the benefits of practical reductionism. Practical reductionism solves the problem of "How do we go about studying complex systems?". The answer here is "Break them down into simpler components and study those individually!". Without reductionism, we are left without an obvious solution.

I have avoided using the word "holism" yet. To continue with microbiology, there are a whole set of "holistic" techniques for studying microbiological ecosystems. One example is to mix up all the bacteria and sequence all their genomes at once. This tells you what all of them are doing, as if they were one big organism. In particular it tells you (in theory) all the metabolic pathways that are going on, but doesn't tell you which microbes are doing which metabolism.

This is a way to gain understanding of the system without using the standard "reductionist" techniques, so non-reductionism isn't a nonapple in this case!

Protein-Metal Binding

Another case: the group I am working in was studying how a particular protein binds to a particular metal complex. As part of this, one of the members of the group studied the binding of this metal complex to every single amino acid individually. Turns out that two of the three parts of the protein that bind the metal, will actually not bind the metal when they're not part of the protein! This was mildly interesting but not particularly surprising, as the group already knew that two of the binding parts are bad at binding. Worse than this, very little was learnt from studying the one that did bind!

I'm sure part of the reason for this was that this person was only an undergraduate, and needed something to do which wasn't too difficult, and the overall research wasn't impacted negatively, but I think it speaks to a certain bias.

The bias goes like:

The protein-metal interaction is made up of amino acid-metal interactions, therefore studying amino acid-metal interactions will help us understand the protein-metal interaction.

Comparing the Two Cases

In the microbiology case: we can study systems with reductionist, or holistic methods. Unfortunately, the two methods don't give us the same sort of information, and we can't bridge the gap between the two, even though we care about both.

In the protein case: we can study systems more easily with a reductionist method than a holistic method. Unfortunately, the two methods don't give us the same sort of information, and we can't bridge the gap between the two, and we care about the holistic system much more than the reduced systems.

I think this brings us to a conclusion about bias in studying complex systems:

Studying simple things is easier than studying complex ones. But just because complex systems are built up of simpler parts, that doesn't mean that studying the simpler parts is the best way to understand the complex system.

And it is particularly tempting to study smaller systems if possible! A simple system is very legible, we can understand it fully. Looking at it feels like progress on the bigger problem. A complex system is illegible, we might not make progress for months or days, and our models might not be good at reflecting underlying reality. People who like to understand things can easily be repulsed by this. 

This mostly refers to complex systems which already exist in the world. Particularly biological ones. Toy models are very useful for systems we can't study directly (like decision theories and AI). I just think that lots of work is being wasted on studying over-reduced parts of bigger systems.

I suspect the antidote is the question: 

What's the best thing that could come out of this? What results of this investigation would bring me to a greater understanding, and how likely do I think these are?

If you ask this about all your investigations, it should help to clarify why a certain object is being studied. If the answer is just that it seems like something that you ought study, you might be reducing more than is helpful.