As I’ve gotten more intentional in looking at the connections between science and religion, I’ve been reading more and more discussion about the principle of emergence. It’s taken me a while to get my head around the idea, given that in Physics we tend to focus on the simple and not the complex with the hope that by reducing everything to simple fundamental ideas, we can explain the complicated ones later on.

Emergence (as a process) speaks about properties that are “emerge” as the subject being studied becomes more complicated. The best example for my little brain that I’ve come across is the idea that pressure as a physical property is an emergent property. It’s pointless to speak of pressure if you have one or even a few molecules in a system. It’s only when you get close to a mole of stuff that pressure starts to make sense in a thermodynamic way. (Actually that’s pretty much true of all of thermodynamics, the whole field discusses what are essentially emergent properties in complicated systems.)

So essentially, emergence would imply that it’s not at all obvious (mathematically) that simple ideas can explain complicated phenomenon. (An important philosophical point, though one that seems somewhat obvious outside the context of mathematical rigor.)

When biologists try to understand how complicated systems rise out of simple ones, they invoke emergence – with the idea that the trajectory of a complicated system is inherently different than that of a simple one, and things happen in the complicated system that can’t be explained in simple ways.

The exciting news today is that a team of mathematicians centered at the University of Vermont have started to describe something that they call an autocatalytic set; essentially a group of things that automatically transform on their own without the need of an external catalytic mechanism.

The implications of what they describe are really important to the study of emergence.

“They begin by deriving some general mathematical properties of autocatalytic sets, showing that such a set can be made up of many autocatalytic subsets of different types, some of which can overlap. 

In other words, autocatalytic sets can have a rich complex structure of their own.

They go on to show how evolution can work on a single autocatalytic set, producing new subsets within it that are mutually dependent on each other.  This process sets up an environment in which newer subsets can evolve. 

‘In other words, self-sustaining, functionally closed structures can arise at a higher level (an autocatalytic set of autocatalytic sets), i.e., true emergence,’ they say.

That’s an interesting view of emergence and certainly seems a sensible approach to the problem of the origin of life. It’s not hard to imagine groups of molecules operating together like this. And indeed, biochemists have recently discovered simple autocatalytic sets that behave in exactly this way.

But what makes the approach so powerful is that the mathematics does not depend on the nature of chemistry–it is substrate independent. So the building blocks in an autocatalytic set need not be molecules at all but any units that can manipulate other units in the required way. “

More here.

The implications of this new mathematical structure are profound not just in evolution, but in economics, chaos theory, consciousness theory and all sorts of sociological fields.

To paraphrase the Vice President – this is a big big deal.