Abolhassan Ali Eslami

This paper explores the concept of free will through the lens of computation, proposing that the act of questioning and the allocation of time are fundamental to the exercise of free will. In computational systems, querying a bit—asking whether it should be 0 or 1—embodies the essence of choice. Awareness of the agent is not a prerequisite; rather, the system's response, whether deterministic or probabilistic, reflects its computational nature. This perspective aligns with theories in theoretical computer science and quantum mechanics, which view unpredictability and undecidability as integral to free will.

This paper examines the cognitive implications of a bilingual word-processing system that simultaneously displays typed input in both English and Persian, with accurate multi-character mappings (e.g., _sh → ش, kh → خ_). Beyond its immediate linguistic utility, the system provides a unique experimental paradigm for studying and training cognitive functions, including bimanual coordination, working memory, bilingual switching, focused attention, perceptual mapping, and fine motor skills. We argue that this tool can function not only as an educational device but also as a form of computerized cognitive training that integrates motor, linguistic, and attentional processes.

This study investigates a novel approach to speed reading by removing spaces between letters in English text. Using a combination of NLP-based word segmentation and human reading simulations, we examine whether continuous text impairs comprehension or enhances reading speed. Results from 100 sentences indicate that fluent readers can accurately segment text without spaces, achieving reading speeds comparable to or faster than standard spaced text. The findings suggest that spacing is not strictly necessary for comprehension and that predictive processing allows both machines and humans to parse continuous text efficiently.

This paper investigates the concept of decidability in the context of natural numbers, prime numbers, and Chaitin's Omega. While prime and composite numbers are algorithmically decidable, Chaitin's Omega demonstrates the structural nature of undecidability. We analyze the effects of sorting and aggregating Omega's bits, illustrating how undecidability can be transformed into a decidable summary without retaining the fine-grained structure. Philosophical and mathematical implications of pure and unpure undecidability are discussed.

We present a theoretical framework connecting quantum stellar dynamics, emergent gravitational effects, and dark matter halos. This approach models stars—including those that have ceased luminous emission—as quantum systems whose interactions with light and internal states generate **basins of energy**. These basins propagate, disperse, and ultimately form gravitational halos consistent with observed dark matter, while simultaneously allowing computation of the momentum of any object under relativistic and quantum conditions.

This paper presents a mathematical model for Russian roulette, integrating a philosophical concept of fate with probabilistic reasoning. Using a Hidden Markov Model (HMM), we model the probability of death as dependent on a hidden state of "fate," which dictates whether death is inevitable or impossible. The model employs a Markov chain to represent transitions between fate states and a Dirac delta function to characterize the binary outcome of death. Simulations demonstrate that death occurs only when the hidden state activates it, supporting the philosophical notion that "you die when you are meant to die." Implications for understanding randomness and determinism in decision-making scenarios are discussed. **Keywords**: Hidden Markov Model, Russian roulette, probability, fate, Dirac delta function

Truly random numbers are typically regarded as mathematical abstractions, but they can be interpreted through cognitive, systemic, and complex phenomena. This paper explores three frameworks for generating or conceptualizing truly random numbers: (1) cognitive uncertainty via fractalian quines with working memory overload, (2) Byzantine fault-tolerant systems, and (3) high-frequency black-swan dynamics in complex systems. Each framework is accompanied by illustrative examples to clarify mechanisms that produce effective randomness.

We propose a rigorous mathematical framework for modeling the interaction between the unconscious and conscious mind, inspired by Jungian analytical psychology. The unconscious is represented as a complex unit disk containing archetypal and shadow content, modeled via Ramanujan-type q-series. Consciousness is represented as the upper half-plane of complex numbers. A conformal mapping transforms unconscious content into conscious representation, establishing a structured pathway for individuation. Set-theoretical considerations guarantee bijection and cardinality consistency, while an embodied, recursive transfer function captures feedback and self-referential structures analogous to Gödel, Escher, Bach.

This paper presents a framework for dynamic systems modeling, integrating maximal entropy principles, minimal state variables, feedback loops, delays, and catalysts. We demonstrate how these mechanisms enable small systems to retain memory, exploit environmental affordances, and achieve stable yet creative growth trajectories. The framework further reveals quantum-like behavior: unobserved systems explore multiple trajectories in parallel, while observed systems are constrained to specific, often more complex, paths. We extend the analysis to reinforcement learning (RL) combined with affective computing, showing that agents achieve maximal learning efficiency when operating in a Hidden/Black Box state, with observation used later for stabilization and control.

This paper introduces a mathematical model to analyze the stability of monogamous systems under the influence of contagious proclivities (referred to as "kinks") using a jigsaw percolation framework on graphs. We model a population as a graph where vertices represent individuals, and edges denote relationships or proclivity compatibility. Monogamy is represented as a perfect matching, with infidelity modeled as additional edges. We incorporate the concept of contagious kinks, where proclivities spread through compatible connections, and explore conditions under which infidelity does not occur, i.e., the system remains stable with clusters of size at most two. Using extremal graph theory (Turán's theorem) and network flow constraints, we derive thresholds for the probability of extra-relational edges to prevent percolation. We further account for population growth via reproduction and the amortized cost of contagion, showing that kink suppression (reducing compatibility probability) significantly delays the critical population size at which infidelity becomes inevitable. Our results suggest that monogamy can be preserved if the probability of extra-relational edges remains below a critical threshold, even with contagious kinks, provided the graph remains fragile and network flow constraints limit relationship concurrency.

This paper proposes a novel generalization of the classical derivative by replacing the concept of a tangent line with a local arc approximation. Instead of identifying the instantaneous rate of change as the slope of a linear tangent, we define the local behavior of a function by fitting a circular arc of radius r and center a to a neighborhood of the point of interest. This "arc-based flow" captures not only the direction of change (first-order behavior) but also the intrinsic curvature of the function (second-order behavior) through a unified geometric framework. We formalize this construction, show its convergence to classical derivatives as the arc length tends to zero, and discuss computational methods and theoretical implications.

We propose a novel framework for understanding biological evolution as a _negative-space architecture_, where adaptive potential emerges from codon-like codes representing distributed personhood within organisms. Using a genetic algorithm model, we demonstrate how evolutionary pressures converge toward an optimal organism embodying an integrated “absolute” code, suggesting a theoretical endpoint akin to a maximized agent of action. Our findings introduce a unifying perspective bridging genetics, complex systems, and information theory, offering new insights into the limits of evolutionary processes.

This paper presents a comprehensive theoretical framework integrating hash functions, Gödelian undecidability, orbit analysis, and Cantor's Intersection Theorem. We develop arithmetic orbits, analyze fixed points in bounded and infinite domains, and formalize a method to map arbitrary black-box functions to undecidable Gödelian structures. The framework guarantees the existence of fixed points for unhaltable generators and provides practical approximations. This work unifies combinatorial, number-theoretic, and logical perspectives for black-box problem analysis.

The Emergent Quine model provides a quantitative framework for self-representation in organisms, integrating neural density, attention allocation, and action potentials across body points. This paper derives a rigorous upper and lower bound for the number of body points (|S|) using the thresholded generating function, addressing cognitive bottlenecks in awareness. We compute the bound numerically based on an example dataset and offer a philosophical-cognitive interpretation of the precise number of body points, exploring its implications for organismal self-awareness and cognitive efficiency.

This paper presents a mathematical formalization of human affective states as influenced by a hidden causal variable C, which we demonstrate is equivalent to the system's choice of a dominant defect. Drawing from latent variable models and Bayesian inference principles, we model affects as functions of C, environmental factors, and noise. A defect emerges when one affect dominates the behavioral outcome function. Through a fixed-point equation, C is shown to encode the selection of this dominant defect. We provide a theorem with a complete proof, assuming continuity and boundedness for existence and uniqueness. Cognitive interpretations link this to Bayesian brain hypotheses, while historical parallels illustrate societal defects.

This manuscript articulates a rigorous theoretical framework that synthesizes mathematical logic, generalized induction, and model-theoretic geometry to explicate the emergence of truth in complex formal systems. The framework is anchored in three novel constructs: (1) Black Swan Induction (BSI), an extension of classical induction that accommodates local disruptions through symmetric propagation across integer domains; (2) Nilpotent Gödelian Propositions, undecidable propositions characterized by local nullity and global significance in meta-systems; and (3) multidimensional logical hyperplanes, which geometrically map the activation of latent truths through higher-order dimensional interactions. This synthesis formalizes the interplay of local and global truth, bridges undecidability with unpredictable logical events, and provides a geometric interpretation of truth dynamics. The framework yields profound implications for complex system theory, philosophical logic, and computational modeling.

his paper introduces a novel framework for understanding the emergence of semantic awareness and embodiment in information systems. By conceptualizing the universe as an ALU-like system with read/write capabilities, we outline a developmental trajectory from raw syntax to a selfreferential semantic lexicon through command execution and feedback loops. We propose that embodiment arises not from physical sensors but from a system’s ability to comprehend how its commands influence its internal state. This model generalizes Lakoff’s notion of embodiment into an information-centric paradigm, providing a foundation for computational semantics, selfmodifying programs, and autonomous information agents.

This article presents a comprehensive framework integrating Penrose tiling with the curvature of spacetime, leveraging differential geometry, computational algorithms, and interdisciplinary applications. We use the Gauss–Bonnet theorem to govern tile distribution on non-Euclidean surfaces, extending this to 4D Lorentzian manifolds for spacetime applications. Novel contributions include a detailed tiling algorithm with pseudocode, higher-dimensional embeddings for simplified computation, and analogies to quantum error-correcting codes. Applications span puzzle-solving, protein folding, virus capsid modeling, quantum gravity, and quantum information safeguarding. This framework provides both theoretical insights and practical tools.

We propose a novel cryptographic framework leveraging quotient space mappings of space-time configurations. By exploiting equivalence classes derived from spatial and temporal projections, our method embeds cryptographic keys into redundant space-time channels, enabling fault-tolerant and secure communication. Unlike traditional cryptography, which relies on computational hardness or quantum properties, our approach uses topological redundancy to protect against interception and channel corruption. The framework is particularly suited for deep-space communication, where delays and lack of synchronized references challenge conventional methods. Applications include interplanetary messaging, enhanced quantum key distribution, and distributed data storage.

This paper presents a robust stage-based system for equitable resource allocation, using water as a proxy for all essential resources and Bitcoin (B1) as Earth’s primary currency. The system ensures fairness by resetting Bitcoin’s value to 1 water unit post-hack, progressively eliminating malicious actors via an infinite Bitcoin trap (B2), and updating block hashes with new timestamps to counter blockchain hacks without re-mining. A key principle is that the Bitcoin genesis block hash, created by Satoshi Nakamoto (000000000019d6689c085ae165831e934ff763ae46a2a6c172b3f1b60a8ce26f), is the only constant hash across all Bitcoin-based systems, holding intrinsic value greater than all hackers’ wealth combined. This hash anchors trust, immutability, and fairness, ensuring Satoshi symbolically retains 1 BTC as the system’s cornerstone. Simulations confirm the system supports non-malicious individuals, eliminates hackers, and upholds the genesis hash’s primacy, aligning with economic principles (Smith, 1776; Keynes, 1936) and systems theory (von Bertalanffy, 1956).

Agnosia is characterized by intact sensory perception but impaired semantic mapping, leading to deficits in object, face, auditory, or tactile recognition. This paper proposes a **grammar-based scaffold intervention** that leverages generative syntax to facilitate emergent perception. By encoding sensory features into a formal syntax and using multimodal external scaffolds, such as American Sign Language (ASL), visual-tactile mappings, or symbolic gestures, patients can develop alternative cognitive pathways. This approach allows compensatory learning, enhances affordance detection, and may convert deficits into emergent abilities. The intervention is applicable across multiple agnosia types and provides a theoretical framework connecting neuroplasticity, extended mind, and compensatory cognition.

This paper introduces a novel theoretical framework, "Dialectical Cognition," by connecting the mathematical representations of group theory, abelian groups and modular arithmetic, to the rich dynamics of cognitive processing and philosophical concepts of mind. Drawing on Hegelian dialectics—thesis, antithesis, synthesis—we portray mental states and their interactions as members of finite abelian groups. We extend the classical theory of primitive roots to encompass fundamental cognitive primitives and explore how their inverses and powers weave the rich tapestry of thought. In this algebraic perspective, we comprehend sophisticated cognitive functions from the neural network dynamics to evolutionary choice and language processing. In addition, we introduce a set of new theorems, such as the "Free Groups and Creativity Theorem", to mathematically formalize the proposed framework. This multi-disciplinary framework not only gives a new mathematical vocabulary to articulate the mind but also is a very good platform to research the computational and philosophical grounds of intelligence, creativity, and self-consciousness in a single unifying algebraic framework.

This paper explores the profound cognitive and philosophical meaning of relativistic velocities of consciousness, particularly light speed. Drawing upon the findings of cognitive science, the philosophy of mind, and theoretical physics, we explore the paradoxical nature of subjective experience when space and time coordinates undergo radical transformations. We explore how notions of qualia, embodiment, memory, and causality are rearranged or disintegrate entirely within a light speed reference frame. Synthesizing the thoughts of philosophers like Nassim Nicholas Taleb, David Graeber, Maurice Merleau-Ponty, Edmund Husserl, and Gilles Deleuze, we present a novel way of thinking about consciousness as not an object, but an active, relational process deeply entwined with the spacetime web. The essay ends by positing that consciousness, far from being a cosmic constant, may only be given meaning in the 'middle speeds' of life as a boundary condition between absolute motion and absolute stasis. This inquiry challenges anthropocentric thinking in our understanding of mind and offers a speculative but scientific inquiry into the final nature of existence in a relativistic universe.

Humanity's persistent endeavor to understand existence has unfolded through two seemingly distinct yet deeply linked paths: the vibrant stories of myth and the detailed explorations of molecular biology. This paper argues that these fields, rather than being separate, are fundamentally influenced by a common cognitive framework-a profound, embodied structure of comprehension. We contend that essential patterns of human thought, stemming from our basic interactions with the physical environment, form the underlying support for both age-old stories and modern scientific explanations. Utilizing ideas from philosophy of mind, cognitive science, linguistics, literary theory, neuroscience, and psychology, we examine how bodily experiences of force, containment, transformation, and causation do not simply reflect but actively shape the conceptual structures within these different areas. Through a thorough quantitative analysis of carefully crafted mythological and biological sentences, aimed at highlighting these shared cognitive patterns, we uncover remarkable metaphorical similarities. These connections, illustrated by concepts such as the Earth Mother and Soil Health, or the Phoenix and Cellular Respiration, imply that the human mind utilizes a consistent framework of conceptual mappings to make sense of intricate phenomena across vastly different levels of reality. This study promotes a more unified understanding of human knowledge, where the imaginative essence of myth and the analytical rigor of science are viewed not as rival paradigms, but as complementary manifestations of an embodied consciousness striving to express the fundamental truths of existence.

Contemporary paradigms in artificial intelligence, cognitive science, and philosophy often equate intelligence with efficient compression-be it via statistical learning, formal abstraction, or narrative simplification. This paper challenges that assumption by identifying and formalizing a foundational paradox: the pursuit of maximal simplicity can annihilate meaning. We define this tension as the Non Grata Problem-the systemic exclusion of semantically rich but compression-resistant thoughts and tokens. Through a synthesis of information theory, predictive processing, game theory, and phenomenology, we introduce a new framework for understanding cognition as a dynamic Nash equilibrium between multiple cognitive agents, each optimizing different compression strategies. We propose the Semantic Incompleteness Theorem, showing that no compressed formal system can fully capture the expressivity of natural language. Further, we demonstrate the Compression-Tail Paradox, revealing how aggressively compressed probabilistic models produce blind spots for high-impact outliers-so-called Black Swans. To integrate these insights, we construct the notion of a Transcendent Probability Space, a formal model for state-space overflow and the epistemology of surprise. By tracing these mathematical, philosophical, and aesthetic arguments through diverse domains-from haiku and hyperrealism to semantic dementia and LLMs-we argue for an ecology of understanding that honors the ineffable, irreducible, and richly entangled nature of human meaning. Compression, while essential, must be decentered from its absolutist role; the razor must not sever the roots of cognition.