What is biological complexity? How many sorts exist? Are there levels of complexity? How are they related to one another? How is complexity related to the emergence of new phenotypes? To try to get to grips with these questions, we consider the archetype of a complex biological system, Escherichia coli. We take the position that E. coli has been selected to survive adverse conditions and to grow in favourable ones and that many other complex systems undergo similar selection. We invoke (...) the concept of hyperstructures which constitute a level of organisation intermediate between macromolecules and cells. We also invoke a new concept, competitive coherence, to describe how phenotypes are created by a competition between maintaining a consistent story over time and creating a response that is coherent with respect to both internal and external conditions. We suggest how these concepts lead to parameters suitable for describing the rich form of complexity termed hypercomplexity and we propose a relationship between competitive coherence and emergence. (shrink)

The fundamental axioms of the quantum theory do not explicitly identify the algebraic structure of the linear space for which orthogonal subspaces correspond to the propositions (equivalence classes of physical questions). The projective geometry of the weakly modular orthocomplemented lattice of propositions may be imbedded in a complex Hilbert space; this is the structure which has traditionally been used. This paper reviews some work which has been devoted to generalizing the target space of this imbedding to Hilbert modules of a (...) more general type. In particular, detailed discussion is given of the simplest generalization of the complex Hilbert space, that of the quaternion Hilbert module. (shrink)

A “mental” multiplication scheme is given for the super hypercomplex numbers, which extend the 16-element Dirac algebra to 32 elements by appending the complex octonions. This extends the 5-vectors of relativity to 9-vectors. The problems with nonassociativity, for the group structures and wave equation covariance, are explored.

Wayne Martin’s Theories of Judgment marks a significant advance in the philosophical analysis of judgment. He understands that the domain of judgment is so large that it allows only a selective treatment. We can expand Martin’s insight by acknowledging that this domain is, in fact, hypercomplex and therefore unsurveyable in Wittgenstein’s sense. Martin’s treatment of judgments can, however, be extended in a number of directions. Of particular importance is it to understand the linguistic aspect of theoretical judgments, the challenges to (...) the synthetic conception of judgment constituted not only by existential, but also by impersonal and negative judgments, and the exploration of the links between the notions of judgment and truth. (shrink)

How many individuals are present where we see a pregnant individual? Within a substance ontological framework, there are exactly two possible answers to this question. The standard answer—two individuals—is typically championed by scholars endorsing the predominant Containment View of pregnancy, according to which the foetus resides in the gestating organism like in a container. The alternative answer—one individual—has recently found support in the Parthood View, according to which the foetus is a part of the gestating organism. Here I propose a (...) third answer: a pregnant individual is neither two individuals nor one individual but something in between one and two. This is because organisms are better understood as processes than as substances. With a special focus on the Parthood View, I explain why a Process View of pregnancy, according to which a pregnant individual is a bifurcating hypercomplex process, surpasses the substance ontological approaches. (shrink)

Through an exploration of theoretical physics, this paper suggests the need for regrounding natural science in phenomenological philosophy. To begin, the philosophical roots of the prevailing scientific paradigm are traced to the thinking of Plato, Descartes, and Newton. The crisis in modern science is then investigated, tracking developments in physics, science's premier discipline. Einsteinian special relativity is interpreted as a response to the threat of discontinuity implied by the Michelson-Morley experiment, a challenge to classical objectivism that Einstein sought to counteract. (...) We see that Einstein's efforts to banish discontinuity ultimately fall into the “black hole” predicted in his general theory of relativity. The unavoidable discontinuity that haunts Einstein's theory is also central to quantum mechanics. Here too the attempt has been made to manage discontinuity, only to have this strategy thwarted in the end by the intractable problem of quantum gravity. The irrepressible discontinuity manifested in the phenomena of modern physics proves to be linked to a merging of subject and object that flies in the face of Cartesian philosophy. To accommodate these radically non-classical phenomena, a new philosophical foundation is called for: phenomenology. Phenomenological philosophy is elaborated through Merleau-Ponty's concept of depth and is then brought into focus for use in theoretical physics via qualitative work with topology and hypercomplex numbers. In the final part of this paper, a detailed summary is offered of the specific application of topological phenomenology to quantum gravity that was systematically articulated in The Self-Evolving Cosmos (Rosen 2008a). (shrink)

"With exceptional clarity, but with no evasion of essential ideas, the author outlines the fundamental structure of mathematics."--Carl B. Boyer, Brooklyn College. This enlightening survey of mathematical concept formation holds a natural appeal to philosophically minded readers, and no formal training in mathematics is necessary to appreciate its clear exposition. Contents include examinations of arithmetic and geometry; the rigorous construction of the theory of integers; the rational numbers and their foundation in arithmetic; and the rigorous construction of elementary arithmetic. Advanced (...) topics encompass the principle of complete induction; the limit and point of accumulation; operating with sequences and differential quotient; remarkable curves; real numbers and ultrareal numbers; and complex and hypercomplex numbers. 1959 ed. 27 Figures. Index. (shrink)

Peter Sloterdijk first became known in this country for his late 1980s Critique of Cynical Reason, which confronted headlong the "enlightened false consciousness" of Habermasian critical theory. Two decades later, after spending seven years in India studying Eastern philosophy, he is now attracting renewed interest for his writings on politics and globalization and for his magnum opus Spheres, a three-volume archaeology of the human attempt to dwell within spaces, from womb to globe: Bubbles, 1998; Globes, 1999; Foam, 2004, all forthcoming (...) from Semiotext. In Neither Sun nor Death, Sloterdijk answers questions posed by German writer Hans-Jürgen Heinrichs, commenting on such issues as technological mutation, development media, communication technologies, and his own intellectual itinerary.Iconoclastic and provocative, alternatively sparkling and bombastic, a child of '68 and a libertarian, Sloterdijk is the most exciting and controversial German philosopher to appear on the world scene since Nietzsche and Heidegger. Like Nietzsche, Sloterdijk remains convinced that contemporary philosophers have to think dangerously and let themselves be "kidnapped" by contemporary "hypercomplexities"; they must forsake our present humanist and nationalist world for a wider horizon at once ecological and global.Neither Sun nor Death is the best introduction available to Sloterdijk's philosophical theory of globalization. It reveals a philosophe extraordinaire, encyclopedic and provocative, as much at ease with current French Theory as with Heidegger and Indian mystic Osho Rajneesh. (shrink)

PurposeThe purpose of this paper selected by ICIL 2019 committee in Rome is to demonstrate the current importance of the internet in the protection of democracy in developting countries.Design/methodology/approachIt is intended to make a comparison with the growing and current phenomenon of Brazilian disinformation with other contemporary phenomena related to new technologies through literature review methodology.FindingsThe Brazilian elections in 2018 represent an authentic model in a post-Cambridge Analytical phase where the myth of the sanctity of data has been broken. The (...) big influence of the algorithmic revolution on democracies in Latin America has never been more evident. The misuse of algorithms created an artificial environment that does not put us in contact with different realities; the consequences of this conjuncture have the deepest impacts, especially in countries that rely on a deficient educational system.Social implicationsBesides that, the broad use of zero-rating on the internet delivery in developing countries is also considered a factor of fake news dissemination. The information bubbles promote political polarization to the detriment of diversity – and the diversity is par excellence one of the pillars of democracy.Originality/valueThe research about the impact that the phenomenon of disinformation has on underdeveloped countries, it is essential to analyze the new role of the legislator in the elaboration of hypercomplex laws with multi-stakeholder interests that respect the essential core of digital human rights as the freedom of expression online. (shrink)

This paper aims to analyze one of the highest achievements of humankind, the classical tragedy, via the application of the heuristic paradigm proposed by Aristotle in his Physics, the fourfold determination of the concept of cause. This scientific methodology – one of the most effective viatica for a comprehensive response to the question of the nature of an object – informs the inquiry into the universal nature of tragedy, its hypercomplexity and hence its ethical and human relevance. Firstly, the (...) concept of tragedy is dissected into its four causes – material, formal, efficient and final; given that the object of research is at the same time tragedy in general and this specific tragedy , each cause is subdivided in two, a distal one and a proximal one . Then, the methodology of the four causes is applied to the formal cause alone, the tragic conflict, in an attempt to better understand tragedy’s quiddity. The results of this more specific causal determination are finally applied to the four causes of tragedy, supporting the hypothesis of a close relationship between hybris, amartia, tragic conflict and education of the phronesis. (shrink)

In this paper, we make a short history about: the neutrosophic set, neutrosophic numerical components and neutrosophic literal components, neutrosophic numbers, neutrosophic intervals, neutrosophic hypercomplex numbers of dimension n, and elementary neutrosophic algebraic structures. Afterwards, their generalizations to refined neutrosophic set, respectively refined neutrosophic numerical and literal components, then refined neutrosophic numbers and refined neutrosophic algebraic structures.

In the author’s previous contribution to this journal (Rosen 2015), a phenomenological string theory was proposed based on qualitative topology and hypercomplex numbers. The current paper takes this further by delving into the ancient Chinese origin of phenomenological string theory. First, we discover a connection between the Klein bottle, which is crucial to the theory, and the Ho-t’u, a Chinese number archetype central to Taoist cosmology. The two structures are seen to mirror each other in expressing the psychophysical (phenomenological) action (...) pattern at the heart of microphysics. But tackling the question of quantum gravity requires that a whole family of topological dimensions be brought into play. What we find in engaging with these structures is a closely related family of Taoist forebears that, in concert with their successors, provide a blueprint for cosmic evolution. Whereas conventional string theory accounts for the generation of nature’s fundamental forces via a notion of symmetry breaking that is essentially static and thus unable to explain cosmogony successfully, phenomenological/Taoist string theory entails the dialectical interplay of symmetry and asymmetry inherent in the principle of synsymmetry. This dynamic concept of cosmic change is elaborated on in the three concluding sections of the paper. Here, a detailed analysis of cosmogony is offered, first in terms of the theory of dimensional development and its Taoist (yin-yang) counterpart, then in terms of the evolution of the elemental force particles through cycles of expansion and contraction in a spiraling universe. The paper closes by considering the role of the analyst per se in the further evolution of the cosmos. (shrink)

A series of dialogues with the most exciting and controversial German philosopher writing today. Peter Sloterdijk first became known in this country for his late 1980s Critique of Cynical Reason, which confronted headlong the “enlightened false consciousness” of Habermasian critical theory. Two decades later, after spending seven years in India studying Eastern philosophy, he is now attracting renewed interest for his writings on politics and globalization and for his magnum opus Spheres, a three-volume archaeology of the human attempt to dwell (...) within spaces, from womb to globe: Bubbles, 1998; Globes, 1999; Foam, 2004, all forthcoming from Semiotext. In Neither Sun nor Death, Sloterdijk answers questions posed by German writer Hans-Jürgen Heinrichs, commenting on such issues as technological mutation, development media, communication technologies, and his own intellectual itinerary. Iconoclastic and provocative, alternatively sparkling and bombastic, a child of '68 and a libertarian, Sloterdijk is the most exciting and controversial German philosopher to appear on the world scene since Nietzsche and Heidegger. Like Nietzsche, Sloterdijk remains convinced that contemporary philosophers have to think dangerously and let themselves be “kidnapped” by contemporary “hypercomplexities”; they must forsake our present humanist and nationalist world for a wider horizon at once ecological and global. Neither Sun nor Death is the best introduction available to Sloterdijk's philosophical theory of globalization. It reveals a philosophe extraordinaire, encyclopedic and provocative, as much at ease with current French Theory as with Heidegger and Indian mystic Osho Rajneesh. (shrink)

Oswald Spengler (1880--1936) is best known for The Decline of the West, in which he propounded his pathbreaking philosophy of world history and penetrating diagnosis of the crisis of modernity. This monumental work launched a seminal attack on the idea of progress and supplanted the outmoded Eurocentric understanding of history. His provocative pessimism seems to be confirmed in retrospect by the twentieth-century horrors of economic depression, totalitarianism, genocide, the dawn of the nuclear age, and the emerging global environmental crisis. In (...) Prophet of Decline, John Farrenkopf takes advantage of the historical perspective the end of the millennium provides to reassess this visionary thinker and his challenging ideas on world history and politics and modern civilization. Farrenkopf's assessment ranges widely, placing Spengler's philosophy in its intellectual historical context and covering Spengler's ideas on democracy, capitalism, science and technology, cities, Western art, social change, and human exploitation of the environment. He also illuminates the implications of Spengler's thought for contemplating from a fresh perspective the future of the United States, the leading power of the West. Prophet of Decline is highly relevant today as many take the opportunity at the turn of the century to ponder again the direction in which humankind and our global community are moving and approach with concern the uncertain future amid globalization, hypercomplexity, and accelerating change. An interdisciplinary book about an interdisciplinary thinker, it is a substantial contribution to the literature of historical philosophy, political science, international relations, and German studies. (shrink)

A new advanced systems theory concerning the emergent nature of the Social, Consciousness, and Life based on Mathematics and Physical Analogies is presented. This meta-theory concerns the distance between the emergent levels of these phenomena and their ultra-efficacious nature. The theory is based on the distinction between Systems and Meta-systems (organized Openscape environments). We first realize that we can understand the difference between the System and the Meta-system in terms of the relationship between a ‘Whole greater than the sum of (...) the parts’ and a ‘Whole less than the sum of its parts’, i.e., a whole full of holes (like a sponge) that provide niches for systems in the environment. Once we understand this distinction and clarify the nature of the unusual organization of the Meta-system, then it is possible to understand that there is a third possibility which is a whole exactly equal to the sum of its parts that is only supervenient like perfect numbers. In fact, there are three kinds of Special System corresponding to the perfect, amicable, and sociable aliquot numbers. These are all equal to the sum of their parts but with different degrees of differing and deferring in what Jacques Derrida calls “differance”. All other numbers are either excessive (systemic) or deficient (metasystemic) in this regard. The Special Systems are based on various mathematical analogies and some physical analogies. But the most important of the mathematical analogies are the hypercomplex algebras, which include the Complex Numbers, Quaternions, and Octonions, with the Sedenions corresponding to the Emergent Meta-system. However, other analogies are the Hopf fibrations between hyperspheres of various dimensions, nonorientable surfaces, soliton solutions, etc. These Special Systems have a long history within the tradition since they can be traced back to the imaginary cities of Plato. The Emergent Meta-system is a higher order global structure that includes the System with the three Special Systems as a cycle. An example of this from our tradition is in the Monadology of Gottfried Wilhelm von Leibniz. There is a conjunctive relationship between the System schema and the Special Systems that produce the Meta-system schema cycle. The Special Systems are a meta-model for the relationship between the emergent levels of Consciousness (Dissipative Ordering based on the theory of negative entropy of Prigogine), Living (Autopoietic Symbiotic based on the theory of Maturana and Varela), and Social (Reflexive based on the theory of John O’Malley and Barry Sandywell). These different special systems are related to the various existenitals identified by Martin Heidegger in Being and Time and various temporal reference frames identified by Richard M. Pico. We also relate the special systems to morphodynamic and teleodynamic systems of Terrence Deacon in Incomplete Nature to which we add sociodynamic systems to complete the series of Special Systems. (shrink)

A series of ideas are presented about a new psychophysiology of consciousness called "The Syntergic theory." The theory postulates that the human brain is able to create a hypercomplex field of interactions that are the result of the activation of all its neuronal elements. This interaction matrix is called the "neuronal field." One of the effects of its activation is the unification of neuronal activity. It is postulated that the neuronal field produces a distortion in the basic space-time structure and (...) the reality of our percepts is the perception of this distortion. For the neuronal field to be activated a structure as complex as the brain is needed. This field is responsible for the interactions between brains produced in emphatic non-verbal communication. Consciousness is closely connected to the neuronal field. The postulates discussed are supported by the evidence from neuro an psychophysiology and new physics. (shrink)

The very existence of society depends on the ability of its members to influence formatively the beliefs, desires, and actions of their fellows. In every sphere of social life, powerful human agents (whether individuals or institutions) tend to use coercion as a favorite shortcut to achieving their aims without taking into consideration the non-violent alternatives or the negative (unintended) consequences of their actions. This propensity for coercion is manifested in the doxastic sphere by attempts to shape people’s beliefs (and doubts) (...) while ignoring the essential characteristics of these doxastic states. I argue that evidential persuasion is a better route to influence people’s beliefs than doxastic coercion. Doxastic coercion perverts the belief-forming mechanism and undermines the epistemic and moral faculties both of coercers and coercees. It succeeds sporadically and on short-term. Moreover, its pseudo doxastic effects tend to disappear once the use of force ceases. In contrast to doxastic coercion, evidential persuasion produces lasting correct beliefs in accordance with proper standards of evidence. It helps people to reach the highest possible standards of rationality and morality. Evidential persuasion is based on the principles of symmetry and reciprocity in that it asks all persuaders to use for changing the beliefs of others only those means they used in forming their own beliefs respecting the freedom of will and assuming the standard of rationality. The arguments in favor of evidential persuasion have a firm theoretical basis that includes a conceptual clarification of the essential traits of beliefs. Belief is treated as a hypercomplex system governed by Leibniz’s law of continuity and the principle of self-organization. It appears to be a mixture consisting of a personal propositional attitude and physical objects and processes. The conceptual framework also includes a typology of believers according to the standards of evidence they assume. In this context, I present a weak version of Clifford’ ethical imperative. In the section dedicated to the prerequisites for changing beliefs, I show how doxastic agents can infuse premeditated or planned changes in the flow of endogenous changes in order to shape certain beliefs in certain desired forms. The possibility of changing some beliefs in a planned manner is correlated with a feedback doxastic (macro-mechanism) that produces a reaction when it is triggered by a stimulus. In relation with the two routes to influence beliefs, a response mechanism is worth taking into consideration – a mechanism governed to a significant extent by human conscience and human will, that appears to be complex, acquired, relatively detached from visceral or autonomic information processing, and highly variable in reactions. Knowing increasingly better this doxastic mechanism, we increase our chances to use evidential persuasion as an effective (although not time-efficient) method to mold people’s beliefs. (shrink)

The aim of this article is to depict as accurately as possible the ideological conflict between liberal democracy and an insidious present-day version of communism, namely cultural socialism. Obviously, it is not easy to describe the essential relationships between two complex phenomena that evolve nonlinearly within a hypercomplex environment. The ideological systems of liberal democracy and cultural socialism involve both objective and subjective facts, material and immaterial components, neutral and emotion-laden aspects, deliberate and unintentional behaviors, linear and nonlinear effects, and (...) planner-dependent and observer-dependent events. They affect each other and also fall under the influence of different non-political factors that characterize the Euro-Atlantic societies. In order to cope with the complexity of this research object we adopt the methodological dualism and a praxeological approach. The system of discursive liberal democracy can be seen – from a praxeological perspective – as a spontaneous order generated and maintained by three classes of attractors: the attractors of democracy (inclusion, political equality, high level of political participation, and majority rule), the attractors of liberalism (rule-governed political agency and the right to reasonable self-determination), and the attractors of public rationality (publicness, objectivity, verifiability, and revisability). Liberal democracy subsists in any society only if a sufficient number of its members reproduce the corresponding attractors in their political (and non-political) conduct. It is important to note that it is much easier to reproduce the attractors of democracy than the attractors of liberalism and rationality. Maybe because of that the socialists strive to undermine the system of liberal democracy by perverting – in the first instance – the standards of (public) rationality. One of the most important ingredient of cultural socialism is so-called "political correctness", by means of which people are prevented from expressing genuinely and politely certain beliefs or doubts in the public sphere even if they profess the standards of objectivity, verifiability, and revisability. Under the pressure of political correctness the attractors of public rationality tend to wither, the liberal dimension of the political system disappears too, and democracy becomes a sheer tyranny. Choosing a form of political organization is not a scientific, but a socio-political matter. It is not the job of social scientists to recommend or impose political goals in general and a specific political system in particular. However, inasmuch as some goals are set, social scientists can indicate the most appropriate means of meeting them. If the Euro-Atlantic societies still value liberal democracy and want to preserve it, it is important to teach them how to reproduce its attractors and to counteract the pernicious effects of cultural socialism. (shrink)

The strength and defects of wave mechanics as a theory of chemistry are critically examined. Without the secondary assumption of wave–particle duality, the seminal equation describes matter waves and leaves the concept of point particles undefined. To bring the formalism into line with the theory of special relativity, it is shown to require reformulation in hypercomplex algebra that imparts a new meaning to electron spin as a holistic spinor, eliminating serious current misconceptions in the process. Reformulation in the curved space–time (...) of general relativity requires the recognition of nonlinear effects that invalidate the practice of linear combination of atomic orbitals, ubiquitous in quantum chemistry, and redefines the electron as a nondispersive wave packet, or soliton. (shrink)

The operator structures for the constants of the motion of the relativistic hydrogen atom are examined. ThoughJ 3 andJ · J are constants of the motion,J is not. Its replacement, $\tilde {\rm K}$ , is shown to emerge rather naturally in transforming the equation to spherical coordinates. The separation of variables is presented in hypercomplex number form. This leads to some interesting suggestions regarding the matter/antimatter operator for the Dirac equation.

A survey is presented of the essential principles for formulating relativistic wave equations in curved spacetime. The approach is relatively simple and avoids much of the philosophical debate about covariance principles, which is also indicated. Hypercomplex numbers provide a natural language for covariance symmetry and the two important kinds of covariant derivative.

Wayne Martin 's Theories of Judgment marks a significant advance in the philosophical analysis of judgment. He understands that the domain of judgment is so large that it allows only a selective treatment. We can expand Martin 's insight by acknowledging that this domain is, in fact, hypercomplex and therefore unsurveyable in Wittgenstein's sense. Martin 's treatment of judgments can, however, be extended in a number of directions. Of particular importance is it to understand the linguistic aspect of theoretical judgments, (...) the challenges to the synthetic conception of judgment constituted not only by existential, but also by impersonal and negative judgments, and the exploration of the links between the notions of judgment and truth. (shrink)