Is it a network?

A common idealization borrowed from engineering and computing is the idea of the "network". A network may seem like very basic system geometry, after all, it's just a 'graph' in discrete mathematics. But the idea of a network is also rather problematic, and seems to have led many scientists down the wrong road for centuries. 

We need to take a closer look at our use of the idea of 'network', in every circumstance. In the same way that 'objects' and 'properties' are mental constructs, networks are too. All these ideas are of course innate, and generally useful, but when we're involved in the natural sciences, and asking questions about complex systems, we need to regularly check our epistemology. Is it a network? 

If something was a network, how would it compare to something that was not a network? Would we be able to build a meter to tell them apart? If it's a mental construct, what are its characteristics and limits?

The complexity of biological and cognitive objects of interest cause us to get lost in our own innate toolset. Post-Galilean physics has been the study of the simplest possible problem. Complexity was the enemy. The basic method was to simplify models, ask basic questions, and reduce experimental interests and influences. Really complex problems were thrown over the transom, to the chemists and the biologists, who for centuries barely even considered themselves scientists, because they were stuck, unable to put aside all these many interesting questions, which the physicists could ignore in their pursuit of foundation issues.

When dealing with the natural science of complex 'systems', we often feel we have nothing important to say unless we fall back on these highly-structured intellectual instincts. And so we have our questionable science --  'learning networks', and 'objects' and zoological-typological 'categories', and selective pressures upon 'bags of qualities' -- scientific  dead-ends whose weaknesses we've been uncovering slowly in various post-positivist enlightenments.

Let's get back to 'network' for a moment. Whether or not 'network' is a useful idea in any given research situation is of course up to the investigators. We see things that are human products which seem to have this 'network geometry': paths, roads, train systems, computer networks, etc. In the physicists' world, it's not that simple. There are many forces and gradients with varying character and various mutual influences. But nothing that could be called a 'network', except by popularizers. In the chemist's world, this becomes harder to resist, because everything under investigation is, on one level, a 'network' of elements. But in any other way, these high-energy mashes of dense mutual influences don't seem anything like the discrete signaling networks that people create. You could use them to create a network. You could use graph theory to give you approximations. But it's a mistake to consider that anything at the chemical 'level' actually is a network.

In biology, with its even more complex investigations, it gets harder to resist our tendency to put phenomena into the 'network' category. There are so many complex results that need to be integrated with one another, that it's sometimes easiest to just imagine networks of influences. These network-diagrams can look massively complex, so much so that it doesn't look like we've made any scientific progress, that is, we're not much enlightened by the result.

But, again, the diagrams are maps. The object of biological inquiry is the territory. We're doing ourselves a disservice to mistake our tools for the object of our investigations. The 'network' is a perception, a tool. It may or may not be helpful. But there should be no 'network theory' of biological systems, or the more complex ecological systems. Exploratory network diagrams, like a finite-element analysis, are at best a kind of limited simulation tool. There's no actual 'network' there, in any external sense.

Which brings us to the biggest misconception of at least the past century, and perhaps the last three centuries. That the human brain, even the animal nervous system, is a 'network'.

There's very little evidence for it. Again, these systems are so complex and difficult to understand that we immediately fall back on any intelligible characterization. And the characterization that is ready and waiting in our mind, is the network.

It's interesting how the innate concept of 'network' is integrally related to that of 'object'. Certainly we try to turn things into 'objects' as part of our instinct. But when we investigate the world, even casually, using this idea of 'objects', we immediately find 'objects within objects', 'objects relating to objects', 'objects influenced by objects' … and adding the concept of 'signaling', we get 'objects signaling objects'. That's a 'network'.

Really, I'm making a very old argument here: the more complex a system, the more we fall back on 'natural ideas' which will probably distract us from discovering what is really going on outside our percepts and concepts.

I'll still make use of networks in my simulations. But like anyone who has tried to simulate reality on a digital machine, I know there are much harder problems than 'graph theory' ahead of us. But to even approach these problems, we need to be aware of the 'network bias' in the human mind.

It's probable that calling the nervous system a 'network' is completely meaningless.

What do I mean by that? If I could tell a didactic Socratic story … 

… let's say some alien intelligences, who study our cognition, were to look at a clock, and speculate upon how we would look at a clock today. 

They might imagine that each of the clock's parts were what we call 'objects', and that the tight interrelations among the parts are what we would call a 'network'. 

Hearing this speculation, we might beg to differ with them: "no, the parts are not similar enough to be a 'network' ". 

They would point out, "interesting … your concept of a network is quite specific … the network 'nodes' need to share some specific, unspoken 'quality' for you to accept them as 'nodes' in a 'network'."

Our alien friends decide to add something: "You do understand that you are like this clock? Your brain, at the very least. The 'connected' 'parts' in your brain do not have these qualities that, if you were to see them, would qualify as a 'network' to you. And yet, you assume they do. Whether the nervous system or the brain is a network should be a scientific question about the natural world, but since 'network' is a mysteriously defined word in your mind, there is no way to even ask that question. And yet, even though humans know almost nothing about their minds, they say 'yes, a nervous system is a network, and so is the brain … just look at those neurons and dendrites and synapses'. They say this confidently, even though there's no evidence that this is the appropriate way to view these structures, and no evidence that they behave as 'nodes' do in the human perception of human-constructed networks."

The moral of the tale … if it's in the real world, and it's not something that a person constructed and called a 'network' ... then it's not likely to be a 'network', despite the efforts of your imagination, or the structure of your simulation.