Formal systems are standardly envisaged in terms of a grammar specifying well-formed formulae together with a set of axioms and rules. Derivations are ordered lists of formulae each of which is either an axiom or is generated from earlier items on the list by means of the rules of the system; the theorems of a formal system are simply those formulae for which there are derivations. Here we outline a set of alternative and explicitly visual ways of envisaging and analyzing (...) at least simple formal systems using fractal patterns of infinite depth. Progressively deeper dimensions of such a fractal can be used to map increasingly complex wffs or increasingly complex 'value spaces', with tautologies, contradictions, and various forms of contingency coded in terms of color. This and related approaches, it turns out, offer not only visually immediate and geometrically intriguing representations of formal systems as a whole but also promising formal links (1) between standard systems and classical patterns in fractal geometry, (2) between quite different kinds of value spaces in classical and infinite-valued logics, and (3) between cellular automata and logic. It is hoped that pattern analysis of this kind may open possibilities for a geometrical approach to further questions within logic and metalogic. (shrink)

The principle of Identity of Indiscernibles has been challenged with various thought experiments involving symmetric universes. In this paper, I describe a fractal universe and argue that, while it is not a symmetric universe in the classical sense, under the assumption of a relational theory of space it nonetheless contains a set of objects indiscernible by pure properties alone. I then argue that the argument against the principle from this new thought experiment resists better than those from classical symmetric (...) universes three main objections put forth against this kind of arguments. (shrink)

The paper considers a new type of objects – blinking fractals – that are not covered by traditional theories studying dynamics of self-similarity processes. It is shown that the new approach allows one to give various quantitative characteristics of the newly introduced and traditional fractals using infinite and infinitesimal numbers proposed recently. In this connection, the problem of the mathematical modelling of continuity is discussed in detail. A strong advantage of the introduced computational paradigm consists of its well-marked numerical character (...) and its own instrument – Infinity Computer – able to execute operations with infinite and infinitesimal numbers. (shrink)

Where three teacher-researchers discuss bipedal walking in humans and where the long-term dynamics of this phenomenon are interpreted in terms of complexity and predictability, two concepts that can be quantified using fractals and the mathematical tools to study them.

Benoit B. Mandelbrot, when discussing the global appeal of fractal patterns and designs, draws upon examples from across numerous world cultures. What may be missed in Mandelbrot's presentation is Immanuel Kant’s precedence in recognizing this sort of widespread beauty in art and nature, fractals avant la lettre. More importantly, the idea of the fractal may itself assist the aesthetic attitude which Kantian beauty requires. In addition, from a Kantian perspective, fractal patterns may offer a source for a (...) sense of community with humanity. I close with an excursus on the more sombre note of Kantian sublimity which fractals can also present. (shrink)

In this paper, I present what I call the symmetry conception of God within 1st order, extensional, non-well-founded set theory. The symmetry conception comes in two versions. According to the first, God is that unique being that is universally symmetrical with respect to set membership. According to the second, God is the universally symmetrical set of all sets that are universally symmetrical with respect to set membership. I present a number of theorems, most importantly that any universally symmetrical set is (...) identical to its essence, that show that the two symmetry conceptions intersect with some dominant theological conceptions of God. The theorems also show that both of the symmetry conceptions of God entail that God has a fractal like structure. (shrink)

The objective of this article is to offer an interpretation of the utopian society described in Plato's Republic from a simplified theory of fractals. Plato conceptualizes his Republic as a static society in terms of structure and its components, the people, as having a behavior that can be programmed as linear and not dynamic (LNDS). Based on this analogy, real social functioning (NLDS) is conceptualized, applying the concept of fractal and its corresponding fracton, as the force of attraction that (...) acts in social groups. Thus, social groups obey a fractal geometry, a geometry that reproduces the pyramidal shape, the apex being the crystallization of authority, power or leadership. Modern society, in analogy with Plato's Republic, is also a fractal production machine, replicating pyramid-shaped hierarchical structures and the respective fractons. Individuals are the basic unit of all these fractals. They are the building blocks of all groups at all levels of society. But replication is not self-similar due to fluctuations in cognition and behavior. (shrink)

Many biological processes and objects can be described by fractals. The paper uses a new type of objects – blinking fractals – that are not covered by traditional theories considering dynamics of self-similarity processes. It is shown that both traditional and blinking fractals can be successfully studied by a recent approach allowing one to work numerically with infinite and infinitesimal numbers. It is shown that blinking fractals can be applied for modeling complex processes of growth of biological systems including their (...) season changes. The new approach allows one to give various quantitative characteristics of the obtained blinking fractals models of biological systems. (shrink)

Survival of the fittest is an over simplification because the creature is tuned to the value in the environment. All variation is constrained and sophistication emerges as a consequence of value. -/- If we could zoom out until the entire universe appeared as an infinitesimal point, then it becomes one thing, undifferentiated, a system in search of a narrative. The system is a form of a dance, without the dancers, there is no system. The narrative unfolds as an expression in (...) a context. The meaning branches out as an increasingly rich and complex expression where the dancers enrich the environment and the environment enriches the dancers. As the deeper layers are expressed, more and more subtlety and sophistication is created and the process continues ad infinitum... Value is the measure of an enriching principle of organization. (shrink)

One conceptual question has been puzzling people for a long time: As the observable universe has been expanding, what has it been expanding into and where did it come from? In this essay I will combine the two questions above to one: What is the Total Universe? I will begin attempt to develop such a description by examining the linguistic human limitations because I believe that this language barrier between our evolved language and a description of the total universe can (...) be surmounted. The basis of this approach is the assumption that a universe would be total if it could be described without logical contradiction in infinities or zero-values. (shrink)

Evolution and geometry generate complexity in similar ways. Evolution drives natural selection while geometry may capture the logic of this selection and express it visually, in terms of specific generic properties representing some kind of advantage. Geometry is ideally suited for expressing the logic of evolutionary selection for symmetry, which is found in the shape curves of vein systems and other natural objects such as leaves, cell membranes, or tunnel systems built by ants. The topology and geometry of symmetry is (...) controlled by numerical parameters, which act in analogy with a biological organism’s DNA. The introductory part of this paper reviews findings from experiments illustrating the critical role of two-dimensional (2D) design parameters, affine geometry and shape symmetry for visual or tactile shape sensation and perception-based decision making in populations of experts and non-experts. It will be shown that 2D fractal symmetry, referred to herein as the “symmetry of things in a thing”, results from principles very similar to those of affine projection. Results from experiments on aesthetic and visual preference judgments in response to 2D fractal trees with varying degrees of asymmetry are presented. In a first experiment (psychophysical scaling procedure), non-expert observers had to rate (on a scale from 0 to 10) the perceived beauty of a random series of 2D fractal trees with varying degrees of fractal symmetry. In a second experiment (two-alternative forced choice procedure), they had to express their preference for one of two shapes from the series. The shape pairs were presented successively in random order. Results show that the smallest possible fractal deviation from “symmetry of things in a thing” significantly reduces the perceived attractiveness of such shapes. The potential of future studies where different levels of complexity of fractal patterns are weighed against different degrees of symmetry is pointed out in the conclusion. (shrink)

This article introduces Hegel's Eurocentric philosophy of dialectics in the 19th century and its transformation to Kelly’s planetary paradigm at the turn of the 20th-21st century. The new theory develops Hegel’s thesis—antitheses—synthesis to identity—difference—new-identity which is applicable for the entire human history, including the planetary era. The new triad generalizes Hegel’s mechanic view of nature by suggesting a dominant worldview which is featured by a series of tightening and converging dynamic fractal cycles.

This work investigates the ability of the human visual system to discriminate self-similar Gaussian random textures. The power spectra of such textures are similar to themselves when rescaled by some factor h > 1. As such, these textures provide a natural domain for testing the hypothesis that texture perception is based on a set of spatial-frequency channels characterized by filters of similar shape.

In The Divine Fractal, Studtmann (2021) introduced a novel conception of God, what he calls the symmetry conception, and showed that such a conception not only can be formalized within extensional non-well-founded set theory but also entails the Thomistic view that God is identical to her essence. In this paper, I show that Studtmann’s symmetry conception of God can be integrated into a recent approach to quantum gravity, namely causal set theory. The theory that results has two significant consequences. (...) First, God is the necessarily existing set of spacetime events. Second, the square root of the probability that a spacetime event randomly chosen from N spacetime events is uncaused is given by the following formula: ((Harmonic [N])/N)^(1/2). I conclude the paper by briefly discussing a connection between this formula and the cosmological constant. (shrink)

Entropy is ubiquitous in physics, and it plays important roles in numerous other disciplines ranging from logic and statistics to biology and economics. However, a closer look reveals a complicated picture: entropy is defined differently in different contexts, and even within the same domain different notions of entropy are at work. Some of these are defined in terms of probabilities, others are not. The aim of this chapter is to arrive at an understanding of some of the most important notions (...) of entropy and to clarify the relations between them, After setting the stage by introducing the thermodynamic entropy, we discuss notions of entropy in information theory, statistical mechanics, dynamical systems theory and fractal geometry. (shrink)

Yunkaporta’s 2019 text Sand Talk carves out a language of resistance to the McDonaldisation of Indigenous research. While historic scholarly engagement with Aboriginal culture has overemphasized content, Yunkaporta demonstrates how this has occurred to the exclusion of the processes of Indigenous knowledge transmission and creation. Yet a process view requires engagement with the how not only the what. Such knowledge transmission is discerned in daily lived relationship between land, spirit, and people; binding epistemology to participation in a specific landscape embedded (...) within a living culture. Place-making for Indigenous knowledges requires exploring how Indigenous ways of valuing, knowing and being, shaped by cultural activities on Country, offer new understandings for western metaphysics. -/- Through a close study of Yunkaporta’s Sand Talk this article explores: fractal thinking and the pattern of creation in Indigenous cosmology; the role of custodianship in respectful interaction between living systems; alternative Indigenous understandings of non-linearity, time and transience; the process-panpsychism and animism present in Indigenous perceptions of cosmos as living Country illustrated in the Dreaming and Turnaround creation event; the role of embodied-cognition, haptic- and situated- knowledge in Indigenous science; Indigenous holistic reasoning and the mind-body connection; the relational metaphysic embedded in ritual and yarning practice; the knowledge encoded in place-based totemic mythology, lore, and ritual; and Indigenous understandings of complex systems as adaptive, self-organising and patterned. This article does not offer a process reading of Indigenous thought but rather demonstrates the significant contribution to process metaphysics that may be provided by an Aboriginal Australian perspective. (shrink)

Bill D'Alessandro talks to Kenny Easwaran about fractal music, Zoom conferences, being a good referee, teaching in math and philosophy, the rationalist community and its relationship to academia, decision-theoretic pluralism, and the city of Manhattan, Kansas.

My departed point is the assessment that plurality in broadest sense characterizing any post- (for example: post-modernity, post-metaphysical, etc.) context is first of all plurality of whole. We may speak about wholes, movement of whole, and lack of any universal whole. Part do not already belongs to whole implicitly granted and common of all other parts. Now we may speak of parts in another relation: non of parts as parts of some common of all parts whole, but parts of difference (...) wholes, and at the same time without any universal whole common of all the wholes. The paper is devoted concretely to the influence of such a comprehension of whole upon some basic notion of physics (especially quantum mechanics and information, relativity) and mathematics, namely probability, set, movement,time. Their changes exert influence upon the fundamental pbilosophical concepts of being and time, knowledge and being-in-the-world. The new conception of fractal, and its meaning in philosophy points out, too. Constancy and always existing of whole is equivalent to Newton time, energy conservation law, local realism and ''hidden parameters" of any correlations, a union of sets exists always if the two sets are granted. (shrink)

In the Indian philosophical debate, the relationship between the structure of knowledge and external reality has been a persistent issue. This debate has been particularly prominent in Buddhism, as evidenced by the earliest Buddhist attestations in the Pāli canon, where reality is described as a perceptual defection. The world (loka) is perceived through cognition (citta), and the theme of designation (paññatti) is central to the analysis of the Abhidhamma. Buddhism can be viewed as navigating between nominalism and cognitive normativism, as (...) it deconstructs language, which is seen as an obfuscating element that separates the subject from the world. In this article, we explore these issues through a philosophical dialogue between Early Buddhism, Abhidhamma, and Madhyamaka, utilizing methodological tools from Western philosophical traditions, both ancient and modern. We engage in a clash between nihilism and absolutism, in search of the substantiality of entities, which, behind the emptiness of conventional designations, conceals a complex fractal network of pansematism. (shrink)

Breast cancer remains a significant health concern worldwide, necessitating the development of effective diagnostic tools. In this study, we employ a neural network-based approach to analyze the Wisconsin Breast Cancer dataset, sourced from Kaggle, comprising 570 samples and 30 features. Our proposed model features six layers (1 input, 1 hidden, 1 output), and through rigorous training and validation, we achieve a remarkable accuracy rate of 99.57% and an average error of 0.000170 as shown in the image below. Furthermore, our investigation (...) identifies the most influential features in breast cancer diagnosis, shedding light on the key determinants of malignancy. Notably, we find that factors such as fractal dimension_se, symmetry worst, compactness_worst, symmetry_se, and smoothness_se play pivotal roles in distinguishing between benign and malignant cases. This research contributes to the ongoing efforts to enhance breast cancer diagnosis, providing valuable insights into feature importance and showcasing the potential of neural networks in medical applications. Our findings have implications for improving early detection and treatment strategies, ultimately contributing to improved patient outcomes. (shrink)

If the computational theory of mind is right, then minds are realized by machines. There is an ordered complexity hierarchy of machines. Some finite machines realize finitely complex minds; some Turing machines realize potentially infinitely complex minds. There are many logically possible machines whose powers exceed the Church–Turing limit (e.g. accelerating Turing machines). Some of these supermachines realize superminds. Superminds perform cognitive supertasks. Their thoughts are formed in infinitary languages. They perceive and manipulate the infinite detail of fractal objects. (...) They have infinitely complex bodies. Transfinite games anchor their social relations. (shrink)

Our purpose in this article is to identify and suggest resolution for two core problematics of grounded theory. First, while grounded theory provides transparency to one part of the conceptualization process, where codes emerge directly from the data, it provides no such systematic or transparent way for gaining insight into the conceptual relationships between discovered codes. Producing a grounded theory depends not only on the definition of conceptual pieces, but the delineation of a relationship between at least two of those (...) pieces. Second, the conceptualization process of grounded theory is done in hierarchical fashion, where individual codes emerge from the data but then are used to generate insight into more general concepts and thematic statements. But various works on grounded theory have failed to provide any systematic way of using data specific levels of scale (the codes) to gain insight into more macro levels of scale (concepts and themes). We offer fractal concept analysis as a means of resolving both of these issues. By using a logic structure generator, fractal concept analysis delineates self-similar conceptual frameworks at various levels of abstraction, yielding a method for linking concepts together within and between levels of scale encountered in the grounded theory coding and categorization process. We conclude that this fractal analytic technique can bolster the aims of grounded theory as a formalized and systematic process for generating theory from empirical data. (shrink)

For the purposes of analytical clarity it is possible to distinguish two ways in which Nancy's ontology of sense appeals to art. First, he uses 'art' as a metaphorical operator to give features to his ontology (such as surprise and wonder); second, the practice of the contemporary arts instruct the terms of his ontological project because, in his view, this practice catches up with the fragmentation of existence and thus informs ontology about the structure of existence today. These two different (...) roles—in which 'art' is both a general category able to stage the features of sense in general and a particularly striking example of the alteration sense undergoes in our times—make available for Nancy different perspectives on the question of sense. On the one hand, the general category of 'art' allows Nancy to construct a characterology of sense around terms such as surprise and novelty; on the other, the appeal to the fractal practice of the 'contemporary arts' supports the project of giving an account of sense.This paper analyses the effects on Nancy's conception of sense of these different appeals to 'art' and the practice of 'the contemporary arts.' Are the locales from which these different perspectives on sense take shape compatible? In what ways do they inflect each other or, alternatively, undermine the perspectives of the other on the question of sense? Finally, what do these two strands tell us about what Nancy expects of 'art' and what would happen to his ontology of sense without the different appeals he makes to it? (shrink)

In the third Whitehead Psychology Nexus Studies, we have discussed (i) the dual-aspect-dual-mode proto-experience (PE)-subjective experience (SE)framework of consciousness based on neuroscience, (ii) its implication in war, suffering, peace, and happiness, (iii) the process of sublimation for optimizingthem and converting the negative aspects of seven groups of self-protective energy system (desire, anger, ego, greed, attachment, jealousy, and selfishlove)into their positive aspects from both western and eastern perspectives (Vimal, 2009b). In this article, we summarize the recent development since then as follows. (...) (1) In (Vimal, 2010), we rigorously investigated the classical and quantum matching and selection processes for precisely experiencing a specific SE in a specific neural-network. (2) In (Vimal, 2009i), we unpacked the quantum view of superposition related to the superposition-based hypothesis H1 of our framework in terms of subquantum dual-aspect primal entities (bhutatmas) and addressed the related explanatory gaps. (3) We developed alternative hypotheses of our framework, namely, the superposition-then-integration-emergence based H2, the integration-emergence based H3, the intelligent mechanism based H4, and the vacuum/Aether based H5. We concluded that our framework with H1 is the most optimal one because it has the least number of problems (Vimal, 2009j). (4) We found over 40 different but overlapping meanings attributed to the term ‘consciousness’ and suggested that authors must specify which aspect ofconsciousness they refer to when using this term to minimize confusion (Vimal, 2009f). (5) We proposed definitions of consciousness, qualia, mind, and awareness (Vimal, 2009h). (6) We investigated the necessary ingredients for access (reportable) consciousness: wakefulness, re-entry, attention, working memory and so on (Vimal, 2009g). (7) We discussed Nâgârjuna’s philosophy of dependent co-origination with respect to our PE-SE framework (Vimal, 2009a). (8) We linked dynamic systems theory and fractal catalytic theory with standard representation theory using our framework (Vimal, 2009d). (9) We introduce the PE-SE aspects of consciousness in theoretical classical and quantum physics including loop quantum gravity and string theory (Vimal, 2009k). (10) In (Vimal, 2009c), we proposed that the SE of subject or ‘self’ in self-related neural-network is tuned to the self-related SEs/PEs superposed in other innumerable entities during samadhi state via matching and selection processes. This leads to bliss, ecstasy, or exceptionally high degree of climax at samadhi state. We conclude that, so far, the dualaspect-dual-mode PE-SE framework with hypothesis H1 is the most optimal framework for explaining our conventional reality because it has the least number of problems. Keywords: Evolution of consciousness; Internal representation; Sensorimotor interaction; Dual-aspect model; Subjective experience; Protoexperiences, Explanatory gap; Mind-brain problem; Purusha; Prakriti; Eastern and Western perspectives; Yoga; Sublimation process; Whitehead; Process and Reality; Occasions of experience; Superposition; Subquantum dual-aspect primal entities (bhutatmas); Superposition-then-integration-emergence; Integration-emergence; Intelligent mechanism; Vacuum/Aether; qualia; Mind; Awareness; Nâgârjuna; Classical and quantum physics; Loop quantum gravity; String theory. (shrink)

Stable adaptive strategy of Homo sapiens (SASH) is a result of the integration in the three-module fractal adaptations based on three independent processes of generation, replication, and the implementation of adaptations — genetic, socio-cultural and symbolic ones. The evolutionary landscape SASH is a topos of several evolutionary multi-dimensional vectors: 1) extraversional projective-activity behavioral intention (adaptive inversion 1), 2) mimesis (socio-cultural inheritance), 3) social (Machiavellian) intelligence, 4) the extension of inter-individual communication beyond their own social groups and their own species (...) in the rest of the world, 5) the symbolic system of communication (symbolic inheritance), 6) spiritualistic trans- formation of emotionally-shaped components of mentality, 7) the dominance of the rationalist thought mentality (enhancer of adaptive inverse 1), 8) a recursive distribution of projective-activity intentions on the man himself his genome, psyche and culture (Adaptive Inversion 2), 9) introversional reorientation of the vector of cognitive activity (adaptive inversion 3). (shrink)

An ideal constructor produces geometry from scratch, modelled through the bottom-up assembly of a graph-like lattice within a space that is defined, bootstrap-wise, by that lattice. Construction becomes the problem of assembling a homogeneous lattice in three-dimensional space; that becomes the problem of resolving geometrical frustration in quasicrystalline structure; achieved by reconceiving the lattice as a dynamical system. The resulting construction is presented as the introductory model sufficient to motivate the formal argument that it is a fundamental structure; based on (...) which, it is proposed that where mathematics’ numbers conventionally correspond to dimensionless points on the stateless number line, numbers more fundamentally correspond to an ordering of discrete objects constructed within the stateful number lattice. A second observation is that this fundamental lattice structure is helically configured with fractal character, which, as it relates to the geometry underlying spacetime, has relevance to questions in physics, particularly those involving wave-particle duality. (shrink)

Easy to understand philosophy papers in all areas. Table of contents: Three Short Philosophy Papers on Human Freedom The Paradox of Religions Institutions Different Perspectives on Religious Belief: O’Reilly v. Dawkins. v. James v. Clifford Schopenhauer on Suicide Schopenhauer’s Fractal Conception of Reality Theodore Roszak’s Views on Bicameral Consciousness Philosophy Exam Questions and Answers Locke, Aristotle and Kant on Virtue Logic Lecture for Erika Kant’s Ethics Van Cleve on Epistemic Circularity Plato’s Theory of Forms Can we trust our senses? (...) Yes we can Descartes on What He Believes Himself to Be The Role of Values in Science Modern Science Kant’s Moral Philosophy Plato’s Republic as Pol Potist Bureaucracy Schopenhauer on Human Suffering Bertrand Russell on the Value of Philosophy The Philosophical Value of Uncertainty Logic Homework: Theorems and Models Searle vs. Turing on the Imitation Game Hume, Frankfurt, and Holbach on Personal Freedom Manifesto of the University of Wisconsin, Madison Secular Society Michael’s Analysis of the Limits of Civil Protections Bentham and Mill on Different Types of Pleasure Set Theory Homework Aristotle on Virtue Nagel On the Hard Problem Wittgenstein on Language and Thought Camus and Schopenhauer on the Meaning of Life Camus’ Hero as Rebel without a Cause My Little Finger: Camus’ Absurdism Illustrated Are Late-term Abortions Ethical? Does Mathematics Assume the Truth of Platonism? The Self-defeating Nature of Utilitarianism and Consequentialism Generally What is The Good Life? Bentham and Mill regarding types of pleasures Kant’s Moral Philosophy Five Short Papers on Mind-body Dualism Tracy Latimer’s Father had the Right to Kill Her: Towards a doctrine of generalized self-defense Arguments Concerning God and Morality Goldman, Rousseau and von Hayek on the Ideal State J.S Mill on Liberty and Personal Freedom A Kantian Analysis of a Borderline Date-rape Situation Living Well as Flourishing: Aristotle’s Conception of the Good Life Three Essays on Medical Ethics: Answers to Exam Questions on Elective Amputation, Vaccination, and Informed Consent Hobbes, Marx, Rousseau, Nietzsche: Their Central Themes De Tocqueville on Egoism Mill vs. Hobbes on Liberty Exam-Essays on the Moral Systems of Mill, Bentham, and Kant Kant’s Moral System Aristotle on Virtue Plato’s Cave Allegory An Ethical Quandary Superorganisms The Tuskegee Experiment A Rawlsian Analysis Why Moore’s Proof of an External World Fails A Defense of Nagel’s Argument Against Materialism A Utilitarian Analysis of a Case of Theft The Paradox of the Self-aware Wretch: An Analysis of Pascal’s Moral Philosophy Jean-Paul Sartre: Decline and Fall of a Marxist Sell-out A One Page Proof of Plato’s Theory of Forms Plato’s Republic as Pol Potist Bureaucracy The problem of the one and the many Four Short Essays on Truth and Knowledge What is ‘the Good Life?’ The Ontological Argument Different Political Philosophies: Plato, Locke, Madison, Rousseau, Hayek, and Mill on the State What do I know with certainty? Skepticism about skepticism Neuroscience and Freewill Operant Conditioning What makes us special? Are Late-term Abortions Ethical? No Two Papers on Epistemology: Gettier and Bostrom Examination Nietzsche on Punishment God’s Foreknowledge and Moral Responsibility . (shrink)

Objective. Conceptualization of the definition of space as a semantic unit of language consciousness. -/- Materials & Methods. A structural-ontological approach is used in the work, the methodology of which has been tested and applied in order to analyze the subject matter area of psychology, psycholinguistics and other social sciences, as well as in interdisciplinary studies of complex systems. Mathematical representations of space as a set of parallel series of events (Alexandrov) were used as the initial theoretical basis of the (...) structural-ontological analysis. In this case, understanding of an event was considered in the context of the definition adopted in computer science – a change in the object properties registered by the observer. -/- Results. The negative nature of space realizes itself in the subject-object structure, the components interaction of which is characterized by a change – a key property of the system under study. Observer’s registration of changes is accompanied by spatial focusing (situational concretization of the field of changes) and relating of its results with the field of potentially distinguishable changes (subjective knowledge about «changing world»). The indicated correlation performs the function of space identification in terms of recognizing its properties and their subjective significance, depending on the features of the observer`s motivational sphere. As a result, the correction of the actual affective dynamics of the observer is carried out, which structures the current perception of space according to principle of the semantic fractal. Fractalization is a formation of such a subjective perception of space, which supposes the establishment of semantic accordance between the situational field of changes, on the one hand, and the worldview, as well as the motivational characteristics of the observer, on the other. -/- Conclusions. Performed structural-ontological analysis of the system formed by the interaction of the perceptual function of the psyche and the semantic field of the language made it possible to conceptualize the space as a field of changes potentially distinguishable by the observer, structurally organized according to the principle of the semantic fractal. The compositional features of the fractalization process consist in fact that the semantic fractal of space is relevant to the product of the difference between the situational field of changes and the field of potentially distinguishable changes, adjusted by the current configuration of the observer`s value-needs hierarchy and reduced by his actual affective dynamics. (shrink)

The purpose of this paper is to open for investigation a range of phenomena familiar from dynamical systems or chaos theory which appear in a simple fuzzy logic with the introduction of self-reference. Within that logic, self-referential sentences exhibit properties of fixed point attractors, fixed point repellers, and full chaos on the [0, 1] interval. Strange attractors and fractals appear in two dimensions in the graphing of pairs of mutually referential sentences and appear in three dimensions in the graphing of (...) mutually referential triples. (shrink)

In this survey, a recent computational methodology paying a special attention to the separation of mathematical objects from numeral systems involved in their representation is described. It has been introduced with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework in all the situations requiring these notions. The methodology does not contradict Cantor’s and non-standard analysis views and is based on the Euclid’s Common Notion no. 5 “The whole is greater than the (...) part” applied to all quantities (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). The methodology uses a computational device called the Infinity Computer (patented in USA and EU) working numerically (recall that traditional theories work with infinities and infinitesimals only symbolically) with infinite and infinitesimal numbers that can be written in a positional numeral system with an infinite radix. It is argued that numeral systems involved in computations limit our capabilities to compute and lead to ambiguities in theoretical assertions, as well. The introduced methodology gives the possibility to use the same numeral system for measuring infinite sets, working with divergent series, probability, fractals, optimization problems, numerical differentiation, ODEs, etc. (recall that traditionally different numerals lemniscate; Aleph zero, etc. are used in different situations related to infinity). Numerous numerical examples and theoretical illustrations are given. The accuracy of the achieved results is continuously compared with those obtained by traditional tools used to work with infinities and infinitesimals. In particular, it is shown that the new approach allows one to observe mathematical objects involved in the Hypotheses of Continuum and the Riemann zeta function with a higher accuracy than it is done by traditional tools. It is stressed that the hardness of both problems is not related to their nature but is a consequence of the weakness of traditional numeral systems used to study them. It is shown that the introduced methodology and numeral system change our perception of the mathematical objects studied in the two problems. (shrink)

This wide ranging discourse covers many disciplines of science and the human condition in an attempt to fully understand the manifestation of time. Time's Paradigm is, at its inception, a philosophical debate between the theories of 'Presentism' and 'The Block Model', beginning with a pronounced psychological analysis of 'free will' in an environment where the past and the future already exist. It lays the foundation for the argument that time is a cyclical, contained progression, rather than a meandering voyage into (...) infinity, bringing into question the validity of a commensurate 'Big Bang'. Following, the proposal widens to encompass physics. It tackles clock rates and time dilation, acausality and the nuisance of a universal clock, and demonstrates that conscious consideration creates the present moment - time's flow - separating the solid state past and future whose reality is devoid of space. Arguments relating to Quantum Physics theory, including the Uncertainty Principle and a Superposition of States, lend credibility to key areas involving cognitive awareness. It is posited that defined points in time and space prohibit progress in linear models for progression. Thus motile paradoxes can be resolved with the absence of infinities; temporal perception, it is concluded, being the result of uncertainty. Time's Paradigm takes the bold step of asking us to consider a tangible dimension of time, representing an intimate extension of our three, known spatial dimensions. Chaos theory is briefly introduced leading to the configuration of a fractal fourth dimension of time whose assumption demands only one direction of flow. Further, it asks whether our universe is expanding or contracting. It considers the simple physics of bodies contracting in a fourth dimension of time (UC), and how that marries comfortably with standard scientific models such as Special Relativity. The rate at which matter is contracting in the universe is illustrated in a reduction factor of 1.618... coinciding with Fibonacci's Ratio and countering Time Dilation. Lastly the more complex aspects of relativistic velocities are tackled together with the conundrum of Zero Velocity and The Speed of Light being attributes of the same event in Cyclical Space-Time, and ultimately, the prospect of superluminal velocities by interaction with parallel time-zones in a multi-layered block universe. (shrink)

This is an essay I entered in a competition about the Bhagavad Gita. Probably written about 2,000 years ago; this writing is perhaps the greatest philosophical expression of Hinduism. I was attracted to the contest because the website included a very favourable comment about the Bhagavad Gita by Albert Einstein (see below). For a while, I actually considered it possible that I’d win the contest. But that time has passed. The winner has been announced and I can now see my (...) entry for what it is – a naïve attempt to preach science to the religionists, as well as a naïve attempt to preach religion to the scientists. -/- There’s a statement in the essay which I’m wondering about. I said, “However, the concept of possessing a soul is not automatically supported. The idea of having a reincarnating soul would be an easy way of explaining immortality thousands of years ago when people were completely unfamiliar with the scientific facts of an eternal universe, Einstein’s Unified Field, and fractal geometry.” I still think this might be correct. But “might” is the word. I’m wondering about something I later wrote – could the ghostly immaterial body described below be what we call the soul? If such a body is developed in the future to overcome present limitations, could it be referred to as a soul if it travels into the past and is absorbed into a physical body? (It might be what the Bhagavad Gita refers to as the Supersoul, and might be quantum entangled with all space and all time. And if the physical brain is receptive to this so-called entangled soul’s knowledge of everything in space and time, the presently accepted limits to acquiring knowledge would, to use the below quote of Einstein’s, be “superfluous”). The preceding agrees with Zen Buddhism's idea of intuitively getting in touch with your inner self. -/- From “Physics and Philosophy Beyond the Standard Model” (http://vixra.org/abs/1411.0585) – “In 1925, the Austrian physicist Wolfgang Pauli discovered the exclusion principle. This says two similar particles cannot have both the same position and velocity. If two electrons could have identical positions and velocities, they could all collapse into a roughly uniform, dense “soup”. Protons and neutrons would do the same, and there would be no well-defined atoms. So we need the exclusion principle. Force-carrying particles like photons and gravitons do not obey the exclusion principle so we might assume the immaterial body wouldn’t be well-defined and would collapse into a ghostly soup. But perhaps a well-defined structure can be built if the photons are first stopped. The potential for photons to possess mass by having their digital sequence altered and being converted to other particles – or the potential for programming the photons - may make this definition possible. A chrononaut whose body is defined by mass would still have a gravitational effect, and be dark matter. But if she or he would rather not be a lump of dark matter, her or his body might be defined by programming photons and gravitons; creating a body of “light matter”. The beginnings of this technology may be in [43] which speaks of one photon being “stuck” to another.” . (shrink)

Critically growing problems of fundamental science organisation and content are analysed with examples from physics and emerging interdisciplinary fields. Their origin is specified and new science structure (organisation and content) is proposed as a unified solution.

The Koch snowflake is one of the first fractals that were mathematically described. It is interesting because it has an infinite perimeter in the limit but its limit area is finite. In this paper, a recently proposed computational methodology allowing one to execute numerical computations with infinities and infinitesimals is applied to study the Koch snowflake at infinity. Numerical computations with actual infinite and infinitesimal numbers can be executed on the Infinity Computer being a new supercomputer patented in USA and (...) EU. It is revealed in the paper that at infinity the snowflake is not unique, i.e., different snowflakes can be distinguished for different infinite numbers of steps executed during the process of their generation. It is then shown that for any given infinite number n of steps it becomes possible to calculate the exact infinite number, Nn, of sides of the snowflake, the exact infinitesimal length, Ln, of each side and the exact infinite perimeter, Pn, of the Koch snowflake as the result of multiplication of the infinite Nn by the infinitesimal Ln. It is established that for different infinite n and k the infinite perimeters Pn and Pk are also different and the difference can be infinite. It is shown that the finite areas An and Ak of the snowflakes can be also calculated exactly (up to infinitesimals) for different infinite n and k and the difference An − Ak results to be infinitesimal. Finally, snowflakes constructed starting from different initial conditions are also studied and their quantitative characteristics at infinity are computed. (shrink)

The strings of physics’ string theory are the binary digits of 1 and 0 used in computers and electronics. The digits are constantly switching between their representations of the “on” and “off” states. This switching is usually referred to as a flow or current. Currents in the two 2-dimensional programs called Mobius loops are connected into a four-dimensional figure-8 Klein bottle by the infinitely-long irrational and transcendental numbers. Such an infinite connection translates - via bosons being ultimately composed of 1’s (...) and 0’s depicting pi, e, √2 etc.; and fermions being given mass by bosons interacting in matter particles’ “wave packets” – into an infinite number of 8-Kleins. Each Klein 1) is one of the universe’s subuniverses (our own is 13.7 billion years old), 2) is made flexible through its binary digits which seamlessly, or almost seamlessly, join it to surrounding subuniverses and eliminate its central hole, and 3) possesses warped time and space because its foundation is the programmed curves in its mathematical Mobius loops (along with the twists they generate [p.7]). The universe functions according to the rules of fractal geometry. So the Mobius does not exist only at the cosmic level. It also manifests at the quantum scale, giving us photons and protons etc. Space and time are no longer separate, but are an indivisible space-time. So if space and the universe are infinite, how can time not be eternal? The past and the future must both extend forever (the idea of time being finite arises from confusion of our subuniverse with the one infinite universe). -/- BITS (Binary digiTS) only suggest existence of the divine if time is linear. Although a non-supernatural God is proposed via the inverse-square law coupled with eternal quantum entanglement, Einstein taught us that time is warped. Warped time is nonlinear, making it at least possible that the BITS composing space-time and all particles originate from the computer science of humans. -/- I suspect many readers will be content with reading this abstract. While there are more details, and mathematics, in the content; my natural style of writing is to avoid jargon and maths. I also tend to get philosophical. While I personally feel that there’s a lot of precious information in the content, I realize it won’t all be to everyone’s liking. Other subjects dealt with in this article are - the “Pioneer anomaly”, refinement of gravitational physics, dark energy and dark matter, quantum phenomena like mass and electric charge and quantum spin, Kepler’s laws of planetary motion, deflection of starlight by the sun, tides, falling bodies, Earth’s orbit, ancient Greek philosophers, Newton, Kepler, Galileo, Aristotle, Parmenides, Zeno of Elea, time travel into the past as well as the future, the elimination of distances in space, humanity’s construction of this universe we live in, The Law of Conservation of Matter-Energy, and support for the science-fiction-like idea of the electronic binary digits of 1 and 0 being the building blocks of our universe. (shrink)

This is one of the best popular cosmology books ever written and Guth is now (2016) a top physics Professor at MIT. He tells the extremely complex story of inflation and related areas of particle physics in such an absorbing style that it reads like a detective novel-in fact, it is a detective novel-how he and others found out how the universe started! The interweaving of his personal story and that of many colleagues along with their photos and many wonderfully (...) clear diagrams allows just the right amount of relaxation from the intensity of the physics. In places the style reminds one of Watson´s famous book ``The Double Helix``. He tells how his work on magnetic monopoles and spontaneous symmetry breaking led to the discovery of the inflationary theory of the very early universe (ca. 10 to minus 35 seconds!). -/- Along the way you will learn many gems that should stay with you a long time such as: the observed universe(e.g., everything the Hubble telescope etc. can see out to ca. 15 billion light years when the universe began) is likely just a vanishingly tiny part of the entire inhomogeneous universe which is about 10 to the 23rd times larger; the big bang probably took place simultaneously and homogeneously in our observed universe; there probably have been and will continue to be an infinite number of big bangs in an infinite number of universes for an infinite time; when a bang happens, everything(space, time, all the elements) from the previous universe are destroyed; the stretching of space can happen at speeds much greater than the speed of light; our entire observed universe lies in a single bubble out of an endless number so there may be trillions of trillions just in our own entire(pocket) universe(and there may be an endless number of such); none of these infinite number of universes interact-i.e., we can never find out anything about the others; each universe started with its own big bang and will eventually collapse to create a new big bang; all this implies that the whole universe is fractal in nature and thus infinitely regresses to ever more universes(which can lead one to thinking of it as a giant hologram); disagreements between the endless(hundreds at least) variations of inflation are sometimes due to lack of awareness that different definitions of time are being used; some theories suggest that there was a first big bang but we can never find out what happened before it; nevertheless it appears increasingly plausible that there was no beginning but rather an eternal cycle of the destruction and creation, each being the beginning of spacetime for that universe; to start a universe you need about 25g of matter in a 10 to minus 26cm diameter sphere with a false vacuum and a singularity(white hole). -/- He deliberately spends little time on the endless variants of inflation such as chaotic, expanded and supernatural inflation or on dark matter´, supersymmetry and string theory, though they were well known at the time as you can find by reading other books such as Michio Kaku´s `Hyperspace` (see my review) and countless others. Of course much has happened since this book appeared but it still serves as an excellent background volume so cheap now it’s free for the cost of mailing. -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

The cosmological constant problem arises because the magnitude of vacuum energy density predicted by the Quantum Field Theory is about 120 orders of magnitude larger then the value implied by cosmological observations of accelerating cosmic expansion. We pointed out that the fractal nature of the quantum space-time with negative Hausdorff-Colombeau dimensions can resolve this tension. The canonical Quantum Field Theory is widely believed to break down at some fundamental high-energy cutoff ∗ Λ and therefore the quantum fluctuations in the (...) vacuum can be treated classically seriously only up to this high-energy cutoff. In this paper we argue that the Quantum Field Theory in fractal space-time with negative Hausdorff-Colombeau dimensions gives high-energy cutoff on natural way. We argue that there exists hidden physical mechanism which cancels divergences in canonical QED4 ,QCD4 , Higher-Derivative-Quantum gravity, etc. In fact we argue that corresponding supermassive Pauli-Villars ghost fields really exist. It means that there exists the ghost-driven acceleration of the universe hidden in cosmological constant. In order to obtain the desired physical result we apply the canonical Pauli-Villars regularization up to ∗ Λ . This would fit in the observed value of the dark energy needed to explain the accelerated expansion of the universe if we choose highly symmetric masses distribution between standard matter and ghost matter below the scale ∗ Λ , i.e. , ( ) ( ) . . eff eff s m g m , , , f μ f μ μ mc μ μ μ c ∗  − = ≤ < Λ The small value of the cosmological constant is explained by tiny violation of the symmetry between standard matter and ghost matter. Dark matter nature is also explained using a common origin of the dark energy and dark matter phenomena. (shrink)

In the light of the results obtained during the last two decades in analysis of signals by time series, it has become evident that the tools of non linear dynamics have their elective role of application in biological, and, in particular, in neuro-physiological and psycho-physiological studies. The basic concept in non linear analysis of experimental time series is that one of recurrence whose conceptual counterpart is represented from variedness and variability that are the foundations of complexity in dynamic processes. Thus, (...) the recurrence plots and the Recurrence Quantification Analysis (RQA) are discussed. It is shown that RQA represents the most general and correct methodology in investigation of experimental time series. By it we arrive to inspect the inner structure of the time series connected to the signals under investigation. Linked to RQA we prospect also the method CZF, recently introduced by us. It is able to account for a true estimation of variability of signals in time as well as in frequency domain. And, consequently, it may be used in conjunction with classical Fourier analysis, accounting however that it is inappropriate in analysis of non linear and non stationary experimental time series. The use of CZF method in fractal analysis is also considered in addition to standard index as Hurst exponent. A large field of possible applications in neurological as well as in psycho-physiological studies is given. Also, there are given examples of other and (possibly linked) applications as example the analysis of beat-to-beat fluctuations of human heartbeat intervals that is sovereign in psycho-physiological studies. We give applications on some different planes to evidence the particular sensitivity of such methods. We reach the objective to show that the previously exposed methods are also able to predict in advance the advent of ventricular tachycardia and/or of ventricular fibrillation. The RQA analysis gives good results. The CZF method gives the most excellent results showing that it is able to give very significant indexes of prediction. We also apply such methods in investigation of state anxiety, and proposing in detail a quantum like model of such phenomenological status of the mind. (shrink)

The cosmological constant problem arises because the magnitude of vacuum energy density predicted by quantum eld theory is about 120 orders of magnitude larger than the value implied by cosmological observations of accelerating cosmic expansion. We pointed out that the fractal nature of the quantum space-time with negative Hausdor - Colombeau dimensions can resolve this tension. The canonical Quantum Field Theory is widely believed to break down at some fundamental high-energy cuto  and therefore the quantum uctuations in the (...) vacuum can be treated classically seriously only up to this high-energy cuto . In this paper we argue that Quantum Field Theory in fractal space-time with negative Hausdor -Colombeau dimensions gives high-energy cuto on natural way. We argue that there exists hidden physical mechanism which cancel divergences in canonical QED4;QCD4; Higher-Derivative - Quantum-Gravity, etc. In fact we argue that corresponding supermassive Pauli-Villars ghost elds really exists. It means that there exists the ghost-driven acceleration of the univers hidden in cosmological constant. In order to obtain desired physical result we apply the canonical Pauli-Villars regularization up to : This would t in the observed value of the dark energy needed to explain the accelerated expansion of the universe if we choose highly symmetric masses distribution between standard matter and ghost matter below that scale ;i.e., fs:m () . (shrink)

The purpose of this article is to present an evidence-supported curriculum covering the fundamentals of logic, reasoning, and argumentation skills to address the emphasized basic knowledge, skills, and abilities required to be scientifically literate, which will prepare the public to understand and engage with science meaningfully. An analytic-synthetic approach toward understanding the notion of public is taken using a theoretical biomimetics framework that identifies naturally occurring objects or phenomena that descriptively captures the essence of a construct to facilitate creative problem-solving. (...) In the present case, the problem being solved is how to reconcile what is meant by public, how it ought to be interpreted, determining the diverse levels of confidence in science that exist, and various understandings of science all with one another. The results demonstrate there is an inherent denotative-connotative inconsistency in the traditional notion of public that can be explicated through the concept of a fractal allowing for comprehension of the relationship between public confidence in, and understanding of, science. (shrink)

This paper develops a new structural psychology, and therein proposes a specific model for the scientific study of consciousness. The presented model uses Earth's geologic history of mass-extinction & recovery (evolutionary dynamics) in determining humanity’s adaptive response (conscious and non-conscious traits). It argues humanity adaptively mirrors Earth’s basic evolutionary dynamics, in a “mythologizing of natural adversity” as foundation for all human knowledge – a process that continues well into the modern era. The intellectual lineage used to develop this model includes: (...) • Evolutionary biology offers a context for this study – answering Chalmers’ “hard question,” • Paleoanthropology defines the circumstance of human emergence from Gaia, • Environmental forces on neurophysiology derive an ambiguous but instructive narrative logic (mythic sensibility), • Psychology tracks humanity’s shift from animal-self to modern creative-self, using work of Hegel > Freud > Jung > Rank > Joseph Campbell > Arnold Mindell as a new structural psychology, • Fractal geometry offers a holographic design for modeling consciousness, • Memetics presents a tool for measuring conscious traits, in a variation of the Hall-Tonna values inventory, • Finally, Structured Opportunistic Thinking, a hybrid of NTL’s T-group, and Pierce’s Power Equity Group Theory, suggests a developmental methodology. This work presents a “general hypothesizing model” of human consciousness, in attempting a science of consciousness. (shrink)

This article theorizes the relationship between three fundamental categories for bell hooks' formulations regarding cultural critique and subjectivity - keeping in mind that hooks' thought establishes a fractal system - oppositionality, affectability and radical black subjectivity. From this, we establish the main objective of this text: to think with hooks about the importance of the positionality of the body (subject) in the construction of knowledge and of itself, from its capacity to be affected (affectability) and to affect people, as (...) being primordial stages of the fertile context for the emergence of radical black subjectivity. For this analysis, this article will address the following questions: 1) the construction and role of radical black subjectivity in bell hooks; 2) the recovery of the body and affectability in the production of knowledge; and 3) the centrality of the oppositional gaze and the potency of imagination in the displacement of binaries towards new consciousnesses and new worlds. (shrink)

Commensurate with our work on dark consciousness, we present a small extension of our previous formalism to model the mixed-frequency states as time crystals. We then posit shared intelligence as an Everettian phone, which is a looking-glass p-adic periodicity in time.

Protein α-helices provide an ordered biological environment that is conducive to soliton-assisted energy transport. The nonlinear interaction between amide I excitons and phonon deformations induced in the hydrogen-bonded lattice of peptide groups leads to self-trapping of the amide I energy, thereby creating a localized quasiparticle (soliton) that persists at zero temperature. The presence of thermal noise, however, could destabilize the protein soliton and dissipate its energy within a finite lifetime. In this work, we have computationally solved the system of stochastic (...) differential equations that govern the quantum dynamics of protein solitons at physiological temperature, T=310 K, for either a single isolated α-helix spine of hydrogen bonded peptide groups or the full protein α-helix comprised of three parallel α-helix spines. The simulated stochastic dynamics revealed that although the thermal noise is detrimental for the single isolated α-helix spine, the cooperative action of three amide I exciton quanta in the full protein α-helix ensures soliton lifetime of over 30 ps, during which the amide I energy could be transported along the entire extent of an 18-nm-long α-helix. Thus, macromolecular protein complexes, which are built up of protein α-helices could harness soliton-assisted energy transport at physiological temperature. Because the hydrolysis of a single adenosine triphosphate molecule is able to initiate three amide I exciton quanta, it is feasible that multiquantal protein solitons subserve a variety of specialized physiological functions in living systems. (shrink)

Very often traditional approaches studying dynamics of self-similarity processes are not able to give their quantitative characteristics at infinity and, as a consequence, use limits to overcome this difficulty. For example, it is well know that the limit area of Sierpinski’s carpet and volume of Menger’s sponge are equal to zero. It is shown in this paper that recently introduced infinite and infinitesimal numbers allow us to use exact expressions instead of limits and to calculate exact infinitesimal values of areas (...) and volumes at various points at infinity even if the chosen moment of the observation is infinitely faraway on the time axis from the starting point. It is interesting that traditional results that can be obtained without the usage of infinite and infinitesimal numbers can be produced just as finite approximations of the new ones. (shrink)