When we
consider mathematical patterns describing our cosmos, it is worth exploring the
question; is the cosmos mathematically open-ended - that is, does it resist
compression into a finite description? This can be a misleading question
because - assuming the cosmos is spatially finite - how can it be both open-ended and finite? But there’s a subtle yet important
thing to grasp, because 'open-ended' should not evoke a picture of the physical
cosmos stretching into the far horizons of infinity, like a cave that just
seems to get bigger and deeper the more we enter it (although analogically that
seems to be somewhat true of our observable cosmos too through a scientific
lens). No, it is a mathematical term about whether or not the cosmos has patterns that can stretch to infinity (stress; patterns,
not physical properties), and can be finitely characterisable. The
answer is, we don’t know whether or
not the cosmos has patterns that can stretch to infinity, but we do know that if
they follow rules expressible by a finite description, then the system would
count as “closed” in the algorithmic sense.
If we look at a pattern, we may try to extend it to infinity based on its observed order; if the extension is fully predictable and can be described by a finite algorithm, then in that sense the cosmos could be considered algorithmically “closed” - though this would still leave us far short of complete knowledge, of course. It is a subtle concept to grasp: that a pattern extending indefinitely can sometimes allow for a finite description.
However, there is a practical problem that likely prevents a definitive theory of such closure. When searching for patterns in the cosmos, there is no guarantee how far a pattern reliably extends before it is overtaken by another, more complex pattern. Perhaps the pattern we have inferred only applies for a limited range, then shifts according to some higher-level rule. Even if we identify this higher-level rule, it may itself be limited, replaced in turn by yet another overarching pattern. With this potential succession of pattern changes, the cosmos reveals itself as a tapestry of staggering mathematical depth and intricacy, where patterns layer upon patterns in a hierarchy of ever-expanding complexity.
But it’s even deeper than that because, given previous writings on the nature of mathematics and how the cosmos unfolds as a monument to mathematical majesty (see my side bar), the physical creation is, to all intents and purposes, effectively mathematically “open-ended,” because at best our efforts can yield only local, provisional theories, where each is but a fleeting glimpse into the infinite web of mathematical structure that underlies all of physical reality.
Let me explain it another way, for clarification. Consider that every time our "window" on the cosmic patterns increases we find that we require a new or more complex algorithm to describe the broader patterns; in effect, the pattern never stabilises into something describable by a single final, comprehensive algorithm. By the way, this is another reason why I argue in my paper on free will and determinism that determinism and indeterminism are not binary opposites, but part of a spectrum.
As our window into the cosmos gradually expands, the stock of short algorithms would eventually be exhausted, forcing algorithmic descriptions to grow ever longer and more intricate - thereby surpassing human comprehension and reaching a level of complexity that can only be accounted for by the cosmic intelligence underlying mathematics itself. And here we are talking about God - which begs the question: which kind of cosmos would the God of the Bible be most likely to create? Naturally, we can only speculate, but here’s a possible way to do so.
If God created the cosmos as “closed”, He could have created the mathematical engine with fundamental laws that are simple, consistent, and finite in description - a cosmos where patterns can, in principle, be fully captured by finite algorithms. This would be elegant and potentially intelligible - and may be tailored to God’s creative dispensation of exhibiting a cosmos with order and purpose in a background of mathematical wash.
If God created the cosmos as “open-ended”, He could have designed the cosmos to be infinitely rich, with layers of patterns that continually evolve, so that the full scope of cosmic mathematics is never exhaustively describable. This would reflect a depth of creative freedom, leaving room for unpredictability, novelty, and ongoing discovery - and may be tailored to God’s creative dispensation of exhibiting a cosmos with mystery and adventure.
In my view, neither fully satisfies - which may well be why, from our observations, God’s creation appears to deliberately combines both - exhibiting a finite set of fundamental laws (closed at a base level) that give rise to an emergent, open-ended complexity that stretches into a mystery that can only be fully captured by Omniscience Himself.
