I lean toward the hypothesis that our reality is fundamentally algorithmic, and everything within it can be described mathematically. At its core, everything follows a structured set of interactions that can be described mathematically, even if we lack the tools to fully articulate those descriptions yet. Mathematics itself arises from fundamental axioms—self-evident assumptions upon which all formal systems are built. From these axioms, we derive arithmetic, geometry, calculus, and higher mathematical structures. Physics, in turn, emerges as an abstraction of mathematics, providing a formal framework to describe the fundamental forces and behaviours of the universe. Chemistry abstracts physics, encoding complex interactions between particles and energy transformations. Biology then abstracts chemistry, manifesting as emergent complexity in molecular interactions, self-replicating systems, and evolutionary processes. Psychology and sociology can be seen as further abstractions built upon collective biological mechanisms and interactions.
This hierarchical structure suggests that even seemingly non-algorithmic phenomena—such as free will, emotion, or social behaviour—are ultimately reducible to formal descriptions and mathematical equations. We do not yet have a complete mathematical framework for consciousness, love, or decision-making, but the absence of a model does not imply that these processes are beyond mathematical formulation. The predictive processing model of consciousness already suggests that perception, thought, and behaviour arise from probabilistic computations, reinforcing the idea that even high-level abstractions follow mechanistic, algorithmic rules. The notion of something being "non-algorithmic" within an algorithmic universe is a contradiction—if reality itself is governed by structured rules, then everything within it must also adhere to those rules, even if their complexity makes them appear non-deterministic.
One may argue that quantum mechanics disproves this. Even quantum mechanics, despite its probabilistic nature, is ultimately algorithmic and follows structured mathematical rules within its own framework. The Schrödinger equation, for instance, governs the evolution of quantum wave functions in a deterministic manner, describing how quantum states evolve over time. Even when quantum mechanics appears to exhibit randomness—such as in wave function collapse or quantum superposition—it still operates within a mathematically constrained probability distribution, as dictated by Born's rule. This suggests that while individual quantum events may seem unpredictable, they are still governed by statistical regularities, meaning they are computationally structured rather than truly chaotic. The concept of quantum computation further reinforces this idea, as quantum states can be manipulated algorithmically to perform complex calculations beyond classical limits. If quantum mechanics were truly non-algorithmic, it would not be possible to encode it into a computational model at all, yet quantum computers operate precisely by leveraging these structured probabilistic rules. Thus, while quantum mechanics challenges classical determinism, it does not break the fundamental principle that reality is governed by formal, algorithmic structures—only that those structures operate at a level of abstraction beyond classical intuition.
What we call folk-psychological concepts—love, identity, morality—are placeholders for mechanistic processes we have yet to fully formalise. For example, instead of saying "I am introverted," a much more precise description would be "My brain has a lower dopamine reward in response to social uncertainty, which leads to certain behaviours categorised as introversion." These are not ineffable qualities but rather emergent properties of highly complex systems, ultimately describable in mathematical terms. The challenge is not whether they can be described algorithmically, but whether we are sophisticated enough to develop the right frameworks. The very notion of an unstructured phenomenon existing within a structured universe is incoherent. Everything is mathematical; we are simply at different stages of decoding it. Although, of course, it's theoretically possible that non-algorthmic systems can exist within an algorithmic reality, but it remains a contradiction and extremely unlikely; practically impossible within our epistemic framework, but theoretically possible.