This perspective begins with mathematical realism: the conviction that mathematical truths and entities, like the number $\pi$ or the set of natural numbers, exist objectively and independently of the human mind. They are not invented; they are discovered. The physical world is a partial instantiation of this underlying mathematical reality, meaning the lawfulness we observe in the cosmos reflects a deep, pre-existing structure.
Our access to this transcendent realm of mathematics is through rational intuition, a faculty disciplined and verified by the rigor of proof. This access is both incomplete and fallible, always open to correction. Kurt Gödel’s incompleteness theorems are central here: they prove that any sufficiently complex formal system will contain true statements that cannot be proven within that system’s own axioms. This has a profound implication: either human understanding is not entirely mechanizable and can “see” truths beyond its current formalisms, or some mathematical truths are absolutely unknowable.
When inquiry is blocked by such independent questions, progress demands the search for new axioms. These are not arbitrary rules but foundational principles chosen for their intrinsic clarity (how well they capture the essence of a mathematical concept) and their extrinsic fruitfulness (their power to solve problems, unify disparate results, and generate a rich theory).
Two key consequences follow from this stance:
The Hawking-Hertog “top-down” model of cosmology provides a physical counterpart to this mathematical view. It rethinks the universe’s origin not as a single, determined classical history unfolding from a Big Bang, but as an initial quantum state representing a superposition of countless possible histories.
From this vast quantum potential, classical regularities emerge through evolution. Processes like decoherence, influenced by the universe’s boundary conditions, effectively “select” certain histories to become the stable, classical reality we experience. This suggests that even the fundamental laws and parameters of physics may not be eternally fixed but could have stabilized into their current forms as the universe expanded, cooled, and formed complex structures.
Crucially, this model incorporates observership as a fundamental physical principle. We are not detached onlookers but participants inside the system. Therefore, all physical predictions are inherently conditional. They are relative to our specific place in the universe, the way we “coarse-grain” reality (i.e., ignore fine-grained details to see larger patterns), the instruments we use, and the very fact of our own existence as complex, information-processing beings. Our presence filters the possible histories we can perceive.
These two perspectives fit together seamlessly. The immense set of all possible cosmic histories and their emergent regularities, as described by quantum cosmology, can itself be understood as a vast and intricate mathematical object. The universe doesn’t just follow mathematical rules; it is a mathematical structure being realized.
Observership, then, is the process of our alignment with that object. Our scientific instruments are designed to expose its invariants (like symmetries and conservation laws), while our theories, models, and proofs serve to articulate its structure. We are mapping this mathematical reality from the inside out.
In practice, this alignment works through a form of Bayesian conditioning. We begin with the boundless space of all mathematical and physical possibilities. Then, we update our knowledge by conditioning on our actual observations and, most importantly, on our own existence as observers. This allows us to move from the set of all possibilities to the specific subset compatible with our experiential situation.
Mathematics is the foundational ground of possibility, physics is its dynamic realization, and observership is our conditional access to that reality.
This framework suggests a specific approach to scientific inquiry: