If Awareness is fundamental in the universe, mathematical frameworks are better suited to reveal its fundamental aspects than physical models. Awareness operates through three fundamental laws which apply at all levels of reality and is characterized by three universal powers. We explore and summarize in general terms mathematical formalisms that may take us as close as possible to conscious awareness, beginning with the primary relationships between the observer with the observed, using a Hilbert space approach. We also examine insights from category theory, and the calculus of indications or laws of forms. Mathematical frameworks as fundamental languages of our interaction with the universe should be further developed with consciousness being the driving force.
If Awareness is fundamental in the universe, mathematical frameworks are better suited to reveal its fundamental aspects than physical models. Awareness operates through three fundamental laws which apply at all levels of reality and is characterized by three universal powers. We explore and summarize in general terms mathematical formalisms that may take us as close as possible to conscious awareness, beginning with the primary relationships between the observer with the observed, using a Hilbert space approach. We also examine insights from category theory, and the calculus of indications or laws of forms. Mathematical frameworks as fundamental languages of our interaction with the universe should be further developed with consciousness being the driving force.
We develop a mathematical and philosophical framework in which conscious obser- vation is the fundamental act that brings reality into existence. Before observation, nothing exists in an actualized sense: not space, time, laws, or structures. Reality is purely a manifold of potential universes, each containing possible laws and possible observers. When a conscious observer emerges, the act of observation actualizes the unique minimal universe consistent with its existence. This is not a selection among alternatives but an ontological crystallization that transforms possibility into actuality, retroactively defining the universe’s laws, constants, structure, and history. Within this actualized universe, unobserved properties remain probabilistic un- til collapsed by observation. We formalize sensory collapse, observer priority, multi- observer shared reality, emergent time, retroactive history, and the closed feedback loop between observers and their universe. This framework unifies consciousness, existence, physics, and cosmology into a single observer-centric formalism.
We explore a mathematical formalism that ties together the observer with the observed in the view that Consciousness is primary, operating through three principles which apply at all levels, the essence of qualia of experience. The formalism is a simplified version of Hilbert space mathematics encountered in quantum mechanics. It does, however, go beyond specific interpretations of quantum mechanics and has strong philosophical foundations in Western philosophy as well as monistic systems of the East. The implications are explored and steps for the full development of this axiomatic mathematical approach to Consciousness are discussed.
We develop a complete mathematical and philosophical theory of a universe in whichconscious observation is the fundamental act that brings reality into existence. Prior toobservation, the universe exists only as pure possibility: a probability distribution overall potential laws, structures, and configurations. Upon the emergence of consciousobservers, this probability space collapses into a single, self-consistent universe whoselaws, constants, and temporal structure become fixed and retroactively defined.This framework unifies consciousness, existence, physics, and cosmology into a sin-gle observer-centric formalism. We construct a rigorous ontology of pure probability;define collapse operators tied to sensory modalities; formulate multi-observer shared re-ality; derive temporal emergence from observation; and formalize intelligence as a fixedpoint within the observer–universe mapping. We further explore multi-universe struc-tures, intersections between observer fields, and the retroactive consistency constraintsnecessary for a stable cosmos.
Humans are limited in what they know by the technical limitation of their cortical language network. A reality is a situation model. The universe is a collection of self-driven mathematical entities. If we are happy to accept randomness, it’s obviously possible that all other so-called “worlds” in the many-worlds interpretation don’t exist objectively. The so-called “physical interaction” (aka objective interaction) among any number of elementary particles is consistent with the so-called “physical law”. From the viewpoint of an imagined external observer (who is located somewhere outside of all worlds), in all worlds, every self-driven elementary particle is changing its state to match its fated state, together form a single fated self-driven state machine; the so-called “subjective reality” (aka the so-called “subjective conscious experience”) is actually the use of a mathematical model (MM) by a Turing machine (TM). The so-called “subjective reality” shouldn’t be able to alter/impact the fated world line of any elementary particle within this world. Except one objective MM which is a fitted MM of the objective reality, every other causality is not an objective MM but a Granger causality, and is an under-fitted MM of the objective reality.
In the previous chapter, we referred to dual-aspect monism frames; we observe here that whether the psycho-physically neutral reality in such frames may refer to consciousness is an open question. By consciousness, however, we mean fundamental awareness, not functional consciousness, which is conventionally meant by materialistic or physicalist frames. We will turn to the issue of fundamental consciousness in the next two chapters. In this chapter, we explore possible links between consciousness (fundamental or not) and quantum mechanics (QM), and insights for quantum-like framework (QLF) or psycho-physical reality in general. Consciousness is, by far, the most enigmatic issue to conceptualise in modern science. The mainstream direction is materialism, where consciousness is an emergent phenomenon from matter, which has been given the name the hard problem. Emergence can be of different types, for example, weak and strong (goes by other names like epistemic and ontic or metaphysical, respectively). While in the case of weak emergence, in principle, higher-level descriptions of realities can be reduced to fundamental descriptions, in the strong emergence view, higher-level descriptions of realities have their own effective dynamical laws which are irreducible.
This is a unique text that explores quantum-like modelling frameworks that connect quantum mechanics with cognitive science and consciousness studies to propose a new ontological framework that transcends traditional boundaries between physics, philosophy, and cognitive science. The book develops along two complementary paths. First, it explores quantum-like modelling, an exciting emerging field where researchers apply logical and mathematical structures from quantum mechanics and information theory to cognitive modelling and decision science. Second, it investigates the profound links between quantum science and consciousness studies, incorporating insights from advanced mathematical frameworks such as category theory. By synthesizing these two approaches, the authors propose a novel framework termed 'quantum-like reality' that moves beyond pragmatic modelling to offer deeper ontological thinking that can enrich both foundational understanding and applied research. This will be an interesting read for students and researchers working at the intersection of quantum physics, cognitive science, and consciousness studies.