Ivo Valkov

This paper investigates the phenomenon of time and articulates constraints that any robust theory must satisfy under a recovery-based criterion. Motivated by the apparent tension between static-looking fundamental descriptions, often associated with block-universe interpretations, and the dynamical character of temporal experience, the paper argues that augmenting a formalism with additional temporal structure can risk displacing rather than resolving explanatory burdens. In response, it advances a constraint on theorizing about time: a candidate time parameter counts as “real time” only insofar as it can recover, in the appropriate regime, empirically meaningful time, specifically, by providing a principled mapping to clock time. It then develops a minimal modeling strategy in three stages: 1) using hyperbolic partial differential equations together with Minkowski kinematics to encode duration, metric comparison, and causal propagation; 2) introducing a dissipative term proportional to the first time derivative to break time-reversal symmetry and yield an effective temporal orientation; and 3) representing a “moving now” via an auxiliary parameter that indexes a family of time-slices through a monotonically shifting switching time, without positing a second dynamical time variable.

The paper proposes a symmetry-based epistemological approach, grounded in Hermann Weyl’s work on group theory and based on two core claims; 1) an External Physical Reality (EPR) exists independently of observers, and 2) a Cognitive Apparatus (CA), present in sufficiently developed forms of life, constrains this reality by preserving substantial invariants. “Reality,” as it becomes accessible, is thus understood as the coupling between EPR and CA, governed by a symmetry group G (the set of patterns, drawn from group theory, that remain unchanged under lawful transformations) Mathematics, with its axiom-based formalism and rule-governed regularities, is considered as effective practice for identifying and tracking these invariants. At the same time, the paper cautions against reducing philosophical inquiry to logic alone, as it provides only the content-neutral setting underlying the richer, model-dependent body of mathematic. To test the proposed framework, the author applies it to the philosophical problem of defining notions of explanation and understanding, in both natural and mathematical language. Although natural language remains central to philosophical discourse, mathematical language is shown to exhibit a unique effectiveness in resolving essential questions.

This article develops an observer-inclusive account of time that reconciles internal (biological, cognitive) and external (physical) temporalities. Its central claim is that low-entropy memory (LEM) is a condition for an agent’s operational access to temporal continuity. By underwriting structured records and the re-identification of states across indices, LEM mediates the agent’s access to succession, duration, and direction. These procedures incur thermodynamic costs. Using Landauer’s principle, we derive a calibrated lower bound on elapsed time for a restricted class of logically irreversible memory updates under isothermal assumptions. The paper proposes a dual-perspectival account of time: objective temporal structure co-varies with the operations of memory-bearing agents who generate and exploit informational repetitions in order to measure and model it, without collapsing external reality into subjectivity. The argument is anchored in canonical results, including Kandel’s and Tonegawa’s work on memory and Prigogine’s theory of dissipative structures.