Are Non-Deterministic Systems Really Non-Deterministic?

A non-deterministic system is one that is so complex that it’s future state cannot be predicted to any great degree of certainty. Weather systems, ecosystems, and economies are examples of interdependent dynamic systems that are composed of so many elements and exhibit so many emergent behaviors that it’s impossible to effectively forecast their futures. Conversely, deterministic systems are more reliable, like clockworks, where every component is known and each behaves & interacts exactly as expected. The difference between the two is in their degree of complexity and our ability to reveal the mechanisms beneath their behaviors.

This reasoning begs the question: are so-called non-deterministic systems ultimately knowable and actually deterministic? If we posit a supercomputer (or superbeing) capable of knowing every piece of a complex system and understanding the physical properties of how that system would interact, would it be possible to make exact predictions for that system? In other words, is a non-deterministic system really just a very complex deterministic system that we don’t yet know enough about? The supposition here is that emergent properties are coded by the parts.

This leads to the next question: is emergence a reversible process? Take proteins, for example. Proteins are polypeptides – linear sequences of amino acids. This initial configuration as a sequence of parts is called the primary structure, and we know the exact primary structures of many proteins. We also know a lot about the biochemistry of amino acids. Yet, a large puzzle of our times is understanding how the primary structure of proteins gives rise to their secondary & tertiary structure – the unique 3-dimensional shapes that turn polypeptide chains into functional components such as enzymes. Indeed, there are massive distributed efforts to understand how the completed 3-dimensional structure of proteins emerges from the serial coding of polypeptide chains [ See Folding At Home].

Most assume that protein folding is a behavior that is knowable, ie deterministic. The hope being that it should be possible to design novel proteins and understand why defects occur in protein folding. But does this imply that many or all seemingly-non-deterministic systems, whose utter complexity is reinforced by layers & layers of emergence upon emergence, are indeed knowable? If the emergence of 3D protein structures from serial components is not some magical event, then might the same be said for larger complex dynamic systems like weather and economies? And what does this mean for epistemology? It would seem that such talk veers back towards Newton’s Clockwork Universe, suggesting that if all the parts are known to sufficient degree, and all their behaviors & affinities known as well, then it should be possible to forecast it’s state at any time in the future. Indeed, Newton’s own very deterministic Laws of Motion scaled up to accurately model the motions of our solar system.

Of course, this begins to challenge the very notion of free will, not to mention thermodynamics and quantum mechanics which both appear to inject chaos and unpredictability into the physical world to a very deep degree. And perhaps it is these aspects of the universe that modulate complex systems into ultimately non-deterministic behaviors, like a well-spring of randomness bubbling up from the quantum plenum injected into Newton’s clockworks. The world does indeed seem highly unpredictable, especially in this day & age. As do the many unfathomable actions of us humans and our damned free will. In fact, it may just be that some things are definably unknowable in totality, as the great mystery traditions would suggest, each pole always containing the seed of it’s opposite, oscillating in some eternal dance unknowable beyond the Seven Veils.

What fate would befall the edifice of Science & Rationalism if it were truly proven that God does indeed play dice and the future is ever but a game of chance? We may reveal the secrets of protein folding and perhaps even be able to predict weather accurately beyond 3 or 4 days. But beyond that what is the boundary of knowability?

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