Coding the Universe

Our experience hitherto justifies us in believing that nature is the realization of the simplest conceivable mathematical ideas " Einstein 2 The " Unreasonable Effectiveness of Mathematics " in Describing, Explaining and Predicting the Physical World 3 With a more or less implicit recall of Pythagorism, Leibniz once wrote that mathematics can be differentiated from music only because it a a form of conscious calculation, whereas music represents unconscious calculation. We can add that mathematics has a relationship to other sciences that is similar to music's relationship to other arts, as it is the most abstract but perhaps most effective instrument for understanding the world. From physics to biology, psychology to economics, there is no empirical science today which has not, in some way, been mathematized, and Immanuel Kant had already noted that Since in every theory of nature there can be only as much science, properly speaking, as there is a priori knowledge, it follows that the theory of nature can contain as much science, properly speaking, as mathematics that can be applied to it. 2 A few simple examples from the history of science will serve to illustrate the odd, and up until now, mysterious phenomenon on the basis of which entire parts of mathematics, which were initially invented and constructed without any applicative purpose, later proved to be highly useful in predicting, describing, and explaining new and unexpected natural phenomena, and therefore in bringing to light " areas of knowledge " which had been previously completely obscure. What renders the problem particularly difficult is that it does not seem easily resolvable by invoking one current philosophical position over another on the ontology of mathematics, given that prima facie, the applicability issue creates puzzles for all such positions. Within a constructivist philosophy of mathematics, for example, one must explain why mathematics – regarded as a creation of ours – 1 I would like to thank the audience at Copenhagen for the interesting questions raised during the discussion of a previous version of this chapter. 2 I. Kant, Metaphysische Anfangsgründe der Naturwissenschaft, Akademie Textausgabe, Bd. IV, Berlin 1968, p. 470.

Journal of Philosophical Investigations, 2024

In the Critique of Pure Reason Immanuel Kant said that cognition (objective perception) is acquired in the unity of sensibility (the receptivity of the mind to receive empirical representations of things, which yields intuitions) and the understanding (in which concepts – general representations of things – arise), and is mediated by the imagination. Here, it is shown that numbers, either pure or denominate, are cognized in the synthesis of intuition and mathematical concept, and that the phenomenal world of the cognizer is shaped accordingly. Any number can be related to any other number through a general mathematical formula conceived by the cognizer for the purpose. The judgment of the cognizer is manifest in the specifics of the mathematical relationship established between the two numbers in cognition. If the cognized number is the numerical value of a physical constant then in the (consistent) phenomenal world it will always have been of the value found in cognition, which explains why the universe seems to be fine-tuned for life. If the cognized number is the numerical value of a physical variable, then the number will be subject to change in accordance with physical laws. Symmetry is a recurrent feature of the phenomenology. A mathematical formula conceived by the cognizer may also relate, one to one, the numerical values of quantities in one set with the numerical values of quantities of different dimensionality in another set, which suggests that physical laws are human inventions and that causality is a pure concept of the understanding.

2015

Extraordinary mathematicality of physics is also shown by dimensionlessness of Planck spacetime and mass. At the same time the Planck granularity of spacetime also shows that physics can be simulated by a binary computer. So physics is informational. But mathematics is not everything in physics, consciousness cannot be solely explained by mathematics, and free will also not. The author claims also that consciousness without free will does not exist. Quantum mechanics (QM) is not complete, because foundational principle is not yet known, because consciousness and Quantum gravity (QG) are not yet explained, and because agreement between measurement and calculation is not everything. QG as dimensionless theory is the foundation of QM and not oppositely. The free will and quantum randomness are similar unexplained phenomena. Even philosophy is important in physics, because what mathematics cannot describe in physics is ontology. And, intuition affects what is mainstream physics. Simplic...

Developments in Language Theory, 1993

All science is founded on the assumption that the physical universe is ordered. Our aim is to challenge this hypothesis using arguments,from the algorithmic information theory.

CODES: The Coherence Framework Replacing Probability in Physics, Intelligence, and Reality A Unified Substrate for Intelligence, Physics, Evolution, and Cosmic Structure Author: Devin Bostick Release History Initial Release: January 29, 2025 (v1) Current Release: September 28, 2025 (v38) Affiliations: CODES Intelligence, Resonance Intelligence Core (RIC), VESSELSEED Abstract (v38) CODES (Chirality of Dynamic Emergent Systems) replaces probability with coherence as the lawful substrate of emergence. This version introduces the multiharmonic invariant PAS_m and its scalar selector PAS_h(S), proving it as the only universal, scale-free measure of coherence. Section 48 formalizes the Coherence Wager: survival requires drift reduction; drift reduction requires coherence measurement; therefore extraction must decline as governance shifts from noise to alignment. CODES/RIC instantiates this inevitability through FIELDCAST (field selector), CHORDLOCK (prime anchoring), PAS_h (multiharmonic coherence measure), TEMPOLOCK (prime-indexed time gating), and GLYPHLOCK/AURA_OUT (symbol legality and emission gate). Together these modules instantiate the only lawful mechanism for coherence-based emergence. Overview — CODES v38: Multiharmonic Closure and the Coherence Wager v34–v37 Recap v34 formalized PAS_LOCK as the canonical closure operator. v35 reframed closure as clarity, reorganizing the recursion arc from first principles to law. v36 added visual embodiments, engineering context, and §46 (Lawful Document Recursion). v37 fortified the substrate with proofs, predicates, calibration protocols, and falsifiability conditions. v38 Leap: Multiharmonic Closure (§13): PAS_s extended to PAS_m = {r_k}, with selector h(S) producing PAS_h(S). Prevents scalar blind spots (e.g. antiphase, quadrature). Proof: PAS_m is the unique invariant under N, ω scaling. Corollary: prime–chiral closure anchors persistence. The Coherence Wager (§48): Formal thesis spine: if coherence is law, drift kills; survival requires drift reduction; extraction must decline. Proves probability is not ontology but incomplete phase detection. Establishes PAS_h(S) as the universal scalar invariant binding physics, biology, cognition, and governance. Governance corollary: coherence ledger adoption is inevitable once masking capacity falls. Net Effect of v38 Universal objectivity locked: PAS_h(S) is the only lawful scalar across domains. Probability demoted: randomness reframed as missing phase. Blind spots removed: RIC and biological substrates now detect lawful coherence in multi-cluster systems. Thesis loop closed: Preface introduces the wager → §48 proves inevitability → Afterword translates it into perception. Citation Bostick, D. (2025). CODES: The Coherence Framework Replacing Probability in Physics, Intelligence, and Reality (v38). Zenodo. 10.5281/zenodo.17220582 Note on Versioning For continuity, the full change log (v25 → v38) is retained at the end of this document.

There are many good reasons to ask basic questions on the construction of reality. These questions not only concern the structure of the world we live in and how we perceive it, but also the mysteries of how our Universe was born and how it will evolve in the far future. This article aims to highlight the prominent role of information in the manifestations of matter and discusses current materialistic paradigms, versus the concept that not matter but information is primary in the evolution of our Universe. Reconciliation of these opposing views is sought in hypothesizing that matter in its various modalities intrinsically contains proto-mental (informational) aspects and/or that matter and mind are complementary aspects of a total reality. Information is treated as a multi-layered phenomenon and is differentiated in intrinsic (elementary), observed (scientific), cultural (in the sense of meaning) and nouminous (mostly non-conscious) information. Reality is pictured as a four-dimensional domain (block universe), in which all time (past, present and future) is laid-out, along with space, housing a flow of information. It is postulated that basic information for creation of the Universe was provided, either through backward causation from the far future, or has originated from a preceding version of our Universe. Individual consciousness is considered as an expression of an underlying non-local quantum field, which exhibits holographic properties. It is postulated that the human brain is interfacing this universal information field, to our individual consciousness. This universal information domain is physically identified as the zero-point-energy field, also related to a time-reversed flow of

Foundations of Physics, 2005

As an approach to a Theory of Everything a framework for developing a coherent theory of mathematics and physics together is described. The main characteristic of such a theory is discussed: the theory must be valid and and sufficiently strong, and it must maximally describe its own validity and sufficient strength. The mathematical logical definition of validity is used, and sufficient strength is seen to be a necessary and useful concept. The requirement of maximal description of its own validity and sufficient strength may be useful to reject candidate coherent theories for which the description is less than maximal. Other aspects of a coherent theory discussed include universal applicability, the relation to the anthropic principle, and possible uniqueness. It is suggested that the basic properties of the physical and mathematical universes are entwined with and emerge with a coherent theory. Support for this includes the indirect reality status of properties of very small or very large far away systems compared to moderate sized nearby systems. Discussion of the necessary physical nature of language includes physical models of language and a proof that the meaning content of expressions of any axiomatizable theory seems to be independent of the algorithmic complexity of the theory. Gödel maps seem to be less useful for a coherent theory than for purely mathematical theories because all symbols and words of any language must have representations as states of physical systems already in the domain of a coherent theory.

The central motivating idea behind the development of this work is the concept of prespace, a hypothetical structure that is postulated by some physicists to underlie the fabric of space or space-time. I consider how such a structure could relate to space and space-time, and the rest of reality as we know it, and the implications of the existence of this structure for quantum theory. Understanding how this structure could relate to space and to the rest of reality requires, I believe, that we consider how space itself relates to reality, and how other so-called "spaces" used in physics relate to reality. In chapter 2, I compare space and space-time to other spaces used in physics, such as configuration space, phase space and Hilbert space. I support what is known as the "property view" of space, opposing both the traditional views of space and space-time, substantivalism and relationism. I argue that all these spaces are property spaces. After examining the relationships of these spaces to causality, I argue that configuration space has, due to its role in quantum mechanics, a special status in the microscopic world similar to the status of position space in the macroscopic world. In chapter 3, prespace itself is considered. One way of approaching this structure is through the comparison of the prespace structure with a computational system, in particular to a cellular automaton, in which space or space-time and all other physical quantities are broken down into discrete units. I suggest that one way open for a prespace metaphysics can be found if physics is made fully discrete in this way. I suggest as a heuristic principle that the physical laws of our world are such that the computational cost of implementing those laws on an arbitrary computational system is minimized, adapting a heuristic principle of this type proposed by Feynman. In chapter 4, some of the ideas of the previous chapters are applied in an examination of the physics and metaphysics of quantum theory. I first discuss the "measurement problem" of quantum mechanics: this problem and its proposed solution are the primary subjects of chapter 4. It turns out that considering how quantum theory could be made fully discrete leads naturally to a suggestion of how standard linear quantum mechanics could be modified to give rise to a solution to the measurement problem. The computational heuristic principle reinforces the same solution. I call the modified quantum mechanics Critical Complexity Quantum Mechanics (CCQM). I compare CCQM with some of the other proposed solutions to the measurement problem, in particular the spontaneous localization model of Ghirardi, Rimini and Weber. Finally, in chapters 5 and 6, I argue that the measure of complexity of quantum mechanical states I introduce in CCQM also provides a new definition of entropy for quantum mechanics, and suggests a solution to the problem of providing an objective foundation for statistical mechanics, thermodynamics, and the arrow of time.

arXiv: Quantum Physics, 1997

The central motivating idea behind the development of this work is the concept of prespace, a hypothetical structure that is postulated by some physicists to underlie the fabric of space or space-time. I consider how such a structure could relate to space and space-time, and the rest of reality as we know it, and the implications of the existence of this structure for quantum theory. Understanding how this structure could relate to space and to the rest of reality requires, I believe, that we consider how space itself relates to reality, and how other so-called “spaces” used in physics relate to reality. In the first chapter I compare space and space-time to other spaces used in physics, such as configuration space, phase space and Hilbert space. I support what is known as the “property view” of space, opposing both the traditional views of space and space-time, substantivalism and relationism. I argue that all these spaces are property spaces. After examining the relationships of t...

2020