Definition
From Wikipedia:
“In philosophy, systems theory, science, and art, emergence occurs when an entity is observed to have properties its parts do not have on their own, properties or behaviors that emerge only when the parts interact in a wider whole.”
Computational and Geometric Emergence
There’s an underlying link between Stephen Wolfram’s ruleology as exemplified by his cellular automata, and Benoit Mandelbrot’s fractal patterns (initiator → generator → recursive rule).
Both start with simple patterns that, in some instances, produce unpredictable, complex forms that cannot be deduced from a top-down approach. First, let’s look at a more ordered, Sierpinsky triangle which can be derived both geometrically (for the Mandelbrotians), and computationally (for the Wolframians):
Emergence is not orderly
But it’s not all orderly like Sierpinsky. The beauty of simple computational rules or simple geometric rules is that they can result in unpredictable, complex outputs.
Extending the idea to Cybernetic Emergence
This also ties in with Valentino Braitenberg’s Vehicles and what he terms the law of Uphill Analysis and Downhill Synthesis. Braitenberg showed that with a few simple structures and circuits, emergent, unpredictable behaviour can arise from simple “vehicles”. With just a handful of features, Braitenberg’s vehicles start to resemble insects, or even tiny mammals and reptiles.
The Power of Emergence
Why is this so powerful? Well, what it means is that complex phenomena can be encoded in simple rules.
And what if we take this idea to its logical limit?
Well, there lies a promise of a simple set of rules that can explain the complex phenomenon that is the universe.
The relationship between Emergence and Deutschian Explanations
Wolfram illustrated emergence with computation.
Mandelbrot illustrated emergence with geometry.
Braitenberg illustrated emergence with cybernetics.
The whole is clearly greater than the sum in these instances. And the fact that the whole is greater than the sum also explains why different “levels” of explanation apply as David Deutsch describes depending on what perspective you take. An explanation on one level is not necessarily useful on other levels, for the very reason that the whole is greater than the sum. It does not make sense to describe human culture in the same terms as molecular physics. Because of emergence. But there is beauty in emergent rules-based systems. Somehow, they break across these Deutschian levels of explanation. Somehow, an implementation on an atomic level can result in complex phenomena on a universal level.
What are your thoughts? Comment and let me know.
Really interesting! I have been looking into this concept of the fundamental pieces forming the greater whole without coming across a lot of what you wrote about. Thanks for sharing!
Kind of back to the atomic habits paradigm again. Interesting how it is so fundamentally applicable.