Self-sufficient ideographies are rare because they are stifled by the issue of standardization. Similar issues arise with abstract art or drawings created by young children or great apes. We propose that mathematical indices and artificial intelligence can help us decode ideography, and if not to understand its meaning, at least to know that meaning exists.

Recent developments in artificial intelligence based on neural nets—deep learning and large language models which together I refer to as NEWAI—have resulted in startling improvements in language handling and the potential to keep up with changing human knowledge by learning from the internet. Nevertheless, examples such as ChatGPT, which is a ‘large language model’, have proved to have no moral compass: they answer queries with fabrications with the same fluency as they provide facts. I try to explain why this (...) is, basing the argument on the sociology of knowledge, particularly social studies of science, notably ‘studies of expertise and experience’ and the ‘fractal model’ of society. Learning from the internet is not the same as socialisation: NEWAI has no primary socialisation such as provides the foundations of human moral understanding. Instead, large language models are retrospectively socialised by human intervention in an attempt to align them with societally accepted ethics. Perhaps, as technology advances, large language models could come to understand speech and recognise objects sufficiently well to acquire the equivalent of primary socialisation. In the meantime, we must be vigilant about who is socialising them and be aware of the danger of their socialising us to align with them rather than vice-versa, an eventuality that would lead to the further erosion of the distinction between the true and the false giving further support to populism and fascism. (shrink)

One of the challenges facing AI governance is the need for multiple scales. Universal human rights require a global scale. If someone asks AI if education is harmful to women, the answer should be “no” regardless of their location. But economic democratization requires local control: if AI’s power over an economy is dictated by corporate giants or authoritarian states, it may degrade democracy’s social and environmental foundations. AI democratization, in other words, needs to operate across multiple scales. Nature allows the (...) multiscale flourishing of biological systems through fractal distributions. In this paper, we show that key elements of the fractal scaling found in nature can be applied to the AI democratization process. We begin by looking at fractal trees in nature and applying similar analytics to tree representations of online conversations. We first examine this application in the context of OpenAI’s “Democratic Inputs” projects for globally acceptable policies. We then look at the advantages of independent AI ownership at local micro-levels, reporting on initial outcomes for experiments with AI and related technologies in community-based systems. Finally, we offer a synthesis of the two, micro and macro, in a multifractal model. Just as nature allows multifractal systems to maximize biodiverse flourishing, we propose a combination of community-owned AI at the micro-level, and globally democratized AI policies at the macro-level, for a more egalitarian and sustainable future. (shrink)

Our likes and dislikes--our senses and sensibilities--did not fall ready-made from the sky, argues internationally acclaimed author John D. Barrow. We know we enjoy a beautiful painting or a passionate symphony, but what we don't necessarily understand is that these experiences conjure up latent instincts laid down and perpetuated over millions of years. Now, in The Artful Universe, Barrow explores the close ties between our aesthetic appreciation and the basic nature of the Universe, challenging the commonly held view that our (...) sense of beauty is entirely free and unfettered. Barrow argues that the laws of the Universe, its environments and its astronomical appearance, have imprinted themselves upon our thoughts and actions in subtle and unexpected ways. Why do we like certain types of art or music? What games and puzzles do we find challenging? Why do so many myths and legends have common elements? Who created the cornucopia of constellations in the night sky? And why? In this eclectic and entertaining survey, Barrow answers these questions and more as he explains how the landscape of the Universe has influenced the development of philosophy and mythology, and how millions of years of evolutionary history have fashioned our attraction to certain patterns of sound and color. Barrow casts the story of human creativity and thought in a fascinating light, considering such diverse topics as our instinct for language, the origins and uses of color in Nature, why we divide time into intervals as we do, the sources of our appreciation of landscape painting, and whether computer-generated fractal art is really art. Barrow reconsiders the question of whether intelligent extraterrestrial life exists, showing that the benefits (and even the likelihood) that might follow from the discovery of life on other worlds could be very different from what we might have been led to expect. Remarkably, we find that some of the properties of the Universe that are essential for the existence of any form of life play a key role in determining psychological and religious responses to the Cosmos. Drawing on a wide variety of examples, from the theological questions raised by St. Augustine and C.S. Lewis to the relationship between the pure math of Pythagoras and the music of the Beatles, The Artful Universe covers new ground and enters a wide-ranging debate about the meaning and significance of the links between art and science. It will change our view of the creation of art and the way we see the world in which we live. (shrink)

The biosemiotic complexity of acoustic communities in the primary forests of Ulu Temburong and Yasunì was investigated with continuous 24-h recordings, using the acoustic signature and multiscale approach of ecoacoustic events and their emergent fractal dimensions. The 3D recordings used for the analysis were collected in undisturbed primary equatorial forests under the scope of the project, Fragments of Extinction, which produces 3D sound portraits with the highest definition possible using current technologies – a perfect dataset on which to perform (...) a multiscale qualitative analysis. The ecoacoustic events detected by a combination of the Acoustic Complexity Indices, ACIft, ACIft evenness, and ACItf evenness, and its fractal dimension were developed according to a biosemiotics approach in which the ecofield theory states that EE functions like a species-specific carrier of meaning. EEs, extracted according to 10 levels of temporal resolution, from 1 to 360 s, confirm the hypothesis that these acoustic communities have an internal complexity that responds to a fractal structure. Yasunì was richer in EEs, with a higher coefficient of variation of hourly fractal dimension. This methodology opens up promising new perspectives in the acoustic assessment of habitat quality and monitoring landscape modification. It also confirms the great potential of the biosemiotics approach in converting acoustic frequencies into ecoacoustic events through encoding procedures that mimic potential species-specific interpretations of the sonic environment. (shrink)

In this revolutionary work, the author sets the stage for the science of the 21st Century, pursuing an unprecedented synthesis of fields previously considered unrelated. Beginning with simple classical concepts, he ends with a complex multidisciplinary theory requiring a high level of abstraction. The work progresses across the sciences in several multidisciplinary directions: Mathematical logic, fundamental physics, computer science and the theory of intelligence. Extraordinarily enough, the author breaks new ground in all these fields. In the field of fundamental (...) physics the author reaches the revolutionary conclusion that physics can be viewed and studied as logic in a fundamental sense, as compared with Einstein's view of physics as space-time geometry. This opens new, exciting prospects for the study of fundamental interactions. A formulation of logic in terms of matrix operators and logic vector spaces allows the author to tackle for the first time the intractable problem of cognition in a scientific manner. In the same way as the findings of Heisenberg and Dirac in the 1930s provided a conceptual and mathematical foundation for quantum physics, matrix operator logic supports an important breakthrough in the study of the physics of the mind, which is interpreted as a fractal of quantum mechanics. Introducing a concept of logic quantum numbers, the author concludes that the problem of logic and the intelligence code in general can be effectively formulated as eigenvalue problems similar to those of theoretical physics. With this important leap forward in the study of the mechanism of mind, the author concludes that the latter cannot be fully understood either within classical or quantum notions. A higher-order covariant theory is required to accommodate the fundamental effect of high-level intelligence. The landmark results obtained by the author will have implications and repercussions for the very foundations of science as a whole. Moreover, Stern's Matrix Logic is suitable for a broad spectrum of practical applications in contemporary technologies. (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)

Les divers lieux et aspects d'un paysage riche et changeant, mais essentiellement connexe, sont, pour le mathématicien, une métaphore de l'intelligence. Les deux conceptions contradictoires, une sorte de fractal et une belle variété, font qu'il est nécessaire de faire appel à une multiplicité de points de vue pour faire sentir la nature des mathématiques. C'est le choix qui a clairement guidé la structure novatrice des Grands courants.

In lieu of an abstract, here is a brief excerpt of the content:Extra Ear:Ear on the Arm BlenderStelarc Click for larger view View full resolutionFigure 1.Blender. Teknikunst—Meat Market, Melbourne 2005. Photograph: Stelarc. Collaborator Nina Sellars stands with the Blender during an installation photograph. Text credit: K. Conden and A. Douglas. Click for larger view View full resolutionFigure 2.Blender (3D Model). Teknikunst—Meat Market, Melbourne 2005. Image: Adam Fiannaca. The installation itself stands at just over 1.6 meters high and is anthropomorphic in (...) scale and structure. Text credit: K. Conden and A. Douglas. Click for larger view View full resolutionFigure 3.Blender. Teknikunst—Meat Market, Melbourne 2005. Photograph: Stelarc. Every few minutes the Blender automatically circulates or "blends" its contents via a system of compressed air pumps and a pneumatic actuator. Text credit: K. Conden and A. Douglas.[End Page 117] Click for larger view View full resolutionFigure 4.Ear Scaffold. Los Angeles, Melbourne 2006. Photographer: Nina Sellars. The preoperative scaffolding that was surgically placed below the skin's surface of performance artist Stelarc. Text credit: R. Ferro. Click for larger view View full resolutionFigure 5.Blender (Biomaterial). Teknikunst—Meat Market, Melbourne 2005. Photograph: Cameron Jones. Both artists, Stelarc and Nina Sellars, undertook liposuction operations specifically for the purpose of this new work and have succeeded in securing the sanitized isolation and, most importantly, the legal ownership of the remnants of the procedures. Text credit: K. Conden and A. Douglas. Click for larger view View full resolutionFigure 6.Hole Hooks Forceps. As a guest at Cornell University's conference "Digital Bodies" in 2001, Stelarc spoke of his desire to implant an ear that could pick up sound. His plans become a reality in the photograph taken during surgery. Text credit: R. Ferro. Click for larger view View full resolutionFigure 7.Extra Ear: Ear on the Arm. Los Angeles, Melbourne 2006. Photographer: Nina Sellars. Stelarc's future plans are to implant Bluetooth technology into the Ear on the Arm in a subsequent surgery so that the ear will pick up sound which will be transmitted via the Internet. Text credit: R. Ferro. Click for larger view View full resolutionFigure 8.Blender (Sterile Hood). Teknikunst—Meat Market, Melbourne 2005. Photograph: Stelarc. The biomaterials are now housed within the Blender's industrial casing, on exhibition at the Meat Market Gallery B in North Melbourne until August 18. Text credit: K. Conden and A. Douglas.[End Page 118]Stelarc- Biographical NotesStelarc is an Australian artist who has performed extensively in Japan, Europe, and the USA—including new music, dance festivals, and experimental theater. He has used medical instruments, prosthetics, robotics, Virtual Reality systems, and the Internet to explore alternate, intimate, and involuntary interfaces with the body. He has performed with a THIRD HAND, a VIRTUAL ARM, a VIRTUAL BODY and a STOMACH SCULPTURE. He has acoustically and visually probed the body—having amplified brainwaves, blood-flow and muscle signals and filmed the inside of his lungs, stomach, and colon, approximately two meters of internal space. He has done twenty-five body SUSPENSIONS with insertions into the skin, in different positions and varying situations in private gallery spaces and in remote locations.For FRACTAL FLESH, as part of Telepolis in 1995, he developed a touch-screen interfaced Muscle Stimulation System, enabling remote access, actuation, and choreography of the body. Performances such as PING BODY and PARASITE (1996, 1997) probe notions of telematic scaling and the engineering of external, extended, and virtual nervous systems for the body using the Internet. In 1998 for Kampnagel, he completed EXOSKELETON—a pneumatically powered six-legged walking machine actuated by arm gestures. During 2000, he completed an EXTENDED ARM—a manipulator with eleven degrees-of-freedom that extends his arm to primate proportions and a MOTION PROSTHESIS—an intelligent, compliant servo-mechanism that enables the performance of precise, repetitive, and accelerated prompting or programming of the arms in real time. In 2002, with the collaboration of the Evolutionary and Adaptive Systems Group, COGs, University of Sussex, and TNTU, the HEXAPOD robot prototype was developed. The six-legged MUSCLE MACHINE was constructed with the assistance of The Nottingham Trent University Engineering team, using fluidic rubber muscle actuators. The PROSTHETIC... (shrink)

In order to analyze the characteristics of airport flight delayed time series, based on the construction of flight delay time series, firstly, the K-means algorithm is used to cluster the time series of delayed departures. Secondly, combining with R/s analysis method of Fractal theory, Hurst index of the series is calculated, and Fractal characteristics of the series are analyzed. Then, the VAR (Vector Auto Regression) model is constructed, and Impulse Response Function (IRF) and Variance Decomposition are conducted to (...) explore the impact of the fluctuation of flight delay time series on the future delay. The results show that K-means algorithm divides the time series into five categories, and each category has significant characteristics. Hurst index values of different time series are in the interval of (0.5, 1), indicating that the time series have good fractal characteristics. Through the IRF and Variance Decomposition of VAR model, results show that the time series are significantly affected by random pulses, and the prediction changes of the series come from multiple time series fluctuations. The prediction results show that the flight delay time series is predictable. (shrink)

In this article, a new adaptive fuzzy wavelet neural network model is proposed for nonlinear function approximation problems. The AFWNN model is based on the traditional Takagi-Sugeno-Kang fuzzy system. Specifically, this model replaces the membership functions of fuzzy rules with wavelet basis functions, which are known to have time and frequency localization properties, i.e., they can approximate patterns both in the time and frequency domains. The structure of the AFWNN model is derived from that of the adaptive neuro-fuzzy inference system. (...) However, the AFWNN improves over the ANFIS by replacing Gaussian functions in the hidden layer with wavelet basis functions. The AFWNN model is trained using a gradient-based optimization algorithm. The AFWNN is then tested on three function approximation problems of time series prediction. For certain types of nonlinear time series, for instance fractal processes, the AFWNN is found to be substantially more accurate than alternative methods. (shrink)

Natural forms, often characterized by irregularity and roughness, have a unique complexity that exhibit self-similarity across different spatial scales or levels of magnification. Our visual system is remarkably efficient in the processing of natural scenes and tuned to the multi-scale, fractal-like properties they possess. The fractal-like scaling characteristics are ubiquitous in many physical and biological domains, with recent research also highlighting their importance in aesthetic perception, particularly in the visual and, to some extent, auditory modalities. Given the multitude (...) of fractal-like scaling manifestations, we explore potential commonalities in the way they might affect aesthetic preference within and across different physical and sensory domains. We use a range of visual and tactile stimuli to explore the equivalence of fractal-scaling effects on aesthetic preferences within and across visual and tactile modalities. Our results suggest that, despite some superficial differences, the underlying dimensional structure mediating the preference across the two domains is remarkably similar. The qualitative nature of this dimensional structure as well as suggestions for future research are discussed. (shrink)

One of the most common contemporary approaches for developing an ethics of artificial intelligence (AI) involves elaborating guiding principles. This essay explores the limitations of this approach, using the history of bioethics as a comparative case. The examples of bioethics and recent AI ethics suggest that principles are difficult to implement in everyday practice, fail to direct individual action, and can frequently result in a pure proceduralism. The essay encourages an additional attention to virtue, which forms the dispositions of (...) actors, directs them to valued ends, and encourages right action in particular situation to complement principles. Practices and professions like medicine or warfighting that already have rich traditions of reflection on virtue ethics will be especially fruitful fields for developing an AI ethics of virtue. (shrink)

In recent years the magnificent world of fractals has been revealed. Some of the fractal images resemble natural forms so closely that Benoit Mandelbrot's hypothesis, that the fractal geometry is the geometry of natural objects, has been accepted by scientists and non-scientists alike. The present paper critically examines Mandelbrot's hypothesis. It first analyzes the concept of a fractal. The analysis reveals that fractals are endless geometrical processes, and not geometrical forms. A comparison between fractals and irrational numbers (...) shows that the former are ontologically and epistemologically even more problematic than the latter. Therefore, it is argued, a proper understanding of the concept of fractal is inconsistent with ascribing a fractal structure to natural objects. Moreover, it is shown that, empirically, the so-called fractal images disconfirm Mandelbrot's hypothesis. It is conceded that the fractal geometry can be used as a useful rough approximation, but this fact has no bearing on the physical theory of natural forms. (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 interconnections between self and surroundings in Daoist thought have been explored in the past in a variety of contexts. This paper, however, explores the Daoist version of the relational self from the general perspective of chaos theory and, more specifically, examines the role of the self in creating emergent form and dynamism in nature and society. The fractal self and world merge through the disciplined effort of the sage until the effort becomes effortless. Both self and world are (...) transformed and become one through the emergent moment. This moment represents a new opportunity for subsequent patterns, or attractors, to emerge. We suggest that the self folds itself into the world, creating and being created by a new attractor, or pattern, in the organization of nature, which we argue is Dao. Our current investigation addresses the following aspects of chaos theory and its relation to Daoism: (1) the Daoist notion of wuwei as perfect congruence; (2) yin and yang at the edge of chaos; (3) the emergent nature of the myriad things; and (4) a Daoist warning against fractal disconnections in the world. Finally, we conclude that the self has the potential to become the world. To approach this amplified condition, the self must dedicate itself to and risk open engagement with events across the complexity of nature. Through openly engaging the world, the self is transformed, leaving the world forever changed. (shrink)

Feminists have long been aware that the notion of women is problematic and using it uncritically without further qualifications leads to exclusions. In the article, I argue that the source of these problems lies in the understanding of concepts as static and clearly defined. I deploy Hegel’s idea of syllogism to define dynamic concepts, which I term ‘fractal concepts’ because of their complexity and constant development. In such structures the balance between the universal, the particular and the individual is (...) maintained and, consequently, every woman is essential for the definition of such a non-essentialist notion of women. I propose that an epistemological interpretation of the Hegelian idea of recognition can be used to describe the development of fractal concepts in the confrontation of different perspectives. It also explains the obstruction of this process by the desire for domination and control, which results in the appropriation of group identities by their privileged members. I situate the logical and political framework developed in the paper in the context of feminist controversies around the concept of woman and argue that it provides us with a comprehensive account of intersectionality as well as an explicative solution to the regress problem. (shrink)

This essay introduces this special issue on virtue ethics in relation to military AI. It describes the current situation of military AI ethics as following that of AI ethics in general, caught between consequentialism and deontology. Virtue ethics serves as an alternative that can address some of the weaknesses of these dominant forms of ethics. The essay describes how the articles in the issue exemplify the value of virtue-related approaches for these questions, before ending with thoughts for further research.

Habitat fragmentation produces isolated patches characterized by increased edge effects from an originally continuous habitat. The shapes of these patches often show a high degree of irregularity: their shapes deviate significantly from regular geometrical shapes such as rectangular and elliptical ones. In fractal theory, the geometry of patches created by a common landscape transformation process should be statistically similar, i.e. their fractal dimensions and their form factors should be equal. In this paper, we analyze 49 woodlot fragments (Pinus (...) sylvestris L.) in the Belgian Kempen region to study the direct relationship between a transformation process and the concomitant patch geometry. Although the fractal dimension of the woodlots is scattered (i.e. they are not statistically similar), the perimeter-area relation of the fragments is characterized by a single, ‘dimension-like’ exponent. This exponent suggests a certain shape homogeneity among the patches, which is confirmed by the absence of hierarchical levels associated with sharp increases of the fractal dimension at scale transitions. The interaction of different natural (soil factor, vegetation type) and anthropogenic (afforestation, urbanization) processes during patch development is assumed to have generated this feature. Comparison of the area and perimeter fractal dimension with an ecological index for habitat quality, the interior-to-edge ratio, shows that the fractal dimension is suitable for predicting interior habitat presence, which is more likely for patches with smooth perimeters and compact areas. The ratio of the area to the perimeter fractal dimension confirms this observation, with high values for high interior-to-edge ratios, characteristic for regularly shaped patches. (shrink)

One of the most classic ontological problems of philosophy is the question of why there exists something instead of nothing. In John L. Culliney and David Jones’s The Fractal Self: Science, Philoso...

In her examination of the problem of identity and its fractal character H. Arendt makes an important step towards a more profound understanding of the thinking Self. Her objective is evident - it is her effort to eliminate the negative effects of the so called identifying monism resulting in mass hysterias. Arendt argues, that the thinking Self is never identical with itself, therefore the definition of subjectivity itself should be seen from the perspective of the difference between the Self (...) and the statments about the Self. For Arendt it means opening the Self, so far shut off in his private cell of the only belief, that it is the Self, who produces the subjectivity. The fractal version of subjectivity represents an open universe of freely chosen responsibility ensuring that there is the only correspondence between the Self and the statments about the Self, namely the correspondence based on knowing the price, paid for it by every Self. And that means tolerating the differences, produced by mind as the thinking Self, differences by which we are constantly being negatively determined. Contrary to identifying monism, however, this determination is not a militant one. (shrink)

There is a whole discussion around the genuine/non genuine appurtenance of the Fractal Art to the Art (Ken Keller, Tad Boniecki, Noel Huntley a.o.). Fractal Art is a new way to manipulate shapes, colors and light. It is a subclass of the visual digital art that could describe as that art form produced using a computer (PC, Mac), fractal and graphical software and output devices (monitors, plotters, printers etc.) or using fractal rules and traditional painting techniques (...) (example: Pollock) as essential tools in the creative process. It is crucial to understand that the use of a computer is not a sine qua non condition, even most of the fractal artworks were digitally realized. Fractal Art is an experimental art, engaging in a new way the relations between Creator and Work. Fractal Art has a genuine equilibrium between “pragmatic” and “theoretic”. It is rather about “discovering” than “manufacturing”, rather “evocation” than “mimesis”. The conclusion has to be: Fractal Art is a genuine art form. (shrink)

Our universe, science reveals, began in utter simplicity, then evolved into burgeoning complexity. Starting with subatomic particles, dissimilar entities formed associations—binding, bonding, growing, branching, catalyzing, cooperating—as “self” joined “other” following universal laws with names such as gravity, chemical attraction, and natural selection. Ultimately life arose in a world of dynamic organic chemistry, and complexity exploded with wondrous new potential. Fast forward to human evolution, and a tension that had existed for billions of years now played out in an unprecedented arena (...) of conscious calculation and cultural diversity. Cooperation interleaving with competition; intimacy oscillating with integrity—we dwell in a world where yin meets yang in human affairs on many levels. In The Fractal Self, John Culliney and David Jones uncover surprising intersections between science and philosophy. Connecting evidence from evolutionary science with early insights of Daoist and Buddhist thinkers, among others, they maintain that sagely behavior, envisioned in these ancient traditions, represents a pinnacle of human achievement emerging out of our evolutionary heritage. They identify an archetype, “the fractal self,” a person in any walk of life who cultivates a cooperative spirit. A fractal self is a sage in training, who joins others in common cause, leads from within, and achieves personal satisfaction in coordinating smooth performance of the group, team, or institution in which he or she is embedded. Fractal selves commonly operate with dedication and compassionate practice in the service of human society or in conserving our planet. But the competitive side of human nature is susceptible to greed and aggression. Self-aggrandizement, dictatorial power, and ego-driven enforcement of will are the goals of those following a self-serving path—individuals the authors identify as antisages. Terrorist leaders are an especially murderous breed, but aggrandizers can be found throughout business, religion, educational institutions, and governments. Humanity has reached an existential tipping point: will the horizon already in view expand with cooperative progress toward godlike emergent opportunities or contract in the thrall of corrupt oligarchs and tribal animosities? We have brought ourselves to a chaotic edge between immense promise and existential danger and are even now making our greatest choice. (shrink)

Successful applications of hierarchical complexity to the behaviors of organisms, animals and humans, and social entities evidence the scaling properties of self-similarity, thus the bounded fractal characteristics of orders of hierarchical complexity. The theory specifies an identical sequence of discrete-state transition steps required from each stage of performance to the next. It repeats at all scales. Tasks nested within the step sequence evidence self-similarity with the orders of complexity. This model introduces questions about noise categories when system tasks are (...) fully accounted for, dependent, self-similar, and measurable. Ubiquitous transition steps are inherent dynamics of evolution. (shrink)

In an extension of speculations that physical space–time is a fractal which might itself be embedded in a high-dimensional continuum, it is hypothesized to “compensate” for local variations of the fractal dimension by instead varying the metric in such as way that the intrinsic dimensionality remains an integer. Thereby, an extrinsic fractal continuum is intrinsically perceived as a classical continuum. Conversely, it is suggested that any variation of the metric from its Euclidean form can be “shifted” to (...) nontrivial fractal topology. Thereby “holes” or “gaps” in spacetime could give rise to curvature. (shrink)

Digital companies exhibit discontinuous growth in the process of shifting from their existing core business to a newer and less familiar business. This pattern of growth often ends in failure mainly because companies invest most of their resources in maintaining the value network of their existing core business, which ultimately results in a “lock-in” effect. The fractal theory assumes that there are similarities among fractals within companies. These similarities may reduce the threats posed by the value network lock-in effect (...) and increase the chances of successful discontinuous growth. In this study, we applied fractal theory to consider the following questions: in what aspects does the successful discontinuous growth of digital companies exhibit fractal characteristics? What strategy does digital companies use to ensure these fractal characteristics? We adopted an exploratory single-case study method and chose ByteDance as the case company to analyze its successful shift from Toutiao to Douyin. Our results show that a necessary condition for the successful discontinuous growth of digital companies is that similarities exist between the existing core business and the new business and entrepreneurial bricolage is a strategy used by digital companies to ensure the existence of fractal characteristics of similarities. We discuss the theoretical contributions and practical implications of this finding. (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)

Using fractal analyses to study events allows us to capture the scale-independence of those events, that is, no matter at which level we study a phenomenon, we should get roughly the same results because events exhibit similar structure across scales. This is demonstrably true in mathematical fractals but is less assured in behavioral fractals. The current research directly tests the scale-independence hypothesis in the behavioral domain by exploring the fractal structure of aggression, a social phenomenon comprising events that (...) span temporal scales from minutes of face-to-face arguments to centuries of international armed conflicts. Using publicly available data, we examined the temporal fractal structure of four scales of aggression: wars, riots, violent crimes, and body movement during arguments. Our results lend mixed support to the scale-independence hypothesis and provide insight into the self-organization of human interactions. (shrink)

Theterm, fractal, coined by Benoit B. Mandelbrot, describes a shape or pattern within a greater pattern of which it is a scaling piece identical to the greater pattern and in which are reproduced an infinite number of parts or fragments which are also identical to it, thus, identical to the whole at all scales. In this paper, the author describes Hindu cosmology as it is replicated in the elements of the Bharata Natyam, drawing the analogy to fractal patterning.

"Fractal" is a term coined by mathematician Benoit Mandelbrot to denote the geometry of nature, which traces inherent order in chaotic shapes and processes. Fractal concepts are part of our emerging vocabulary and can be useful in identifying patterns of human behavior, culture, and history, while enhancing our understanding of the nature of consciousness. According to William J. Jackson, the more one studies fractals, the more apparent their connections to the humanities become. In the recursive patterns of religious (...) music, in temple architecture in India, in cathedral structures in Europe and America, in the imagery of religious literature depicting infinity and abundance, and in poetic descriptions of the nature of consciousness, fractal-like configurations are pervasive. Recognition of this structure, which is also found in social organizations and ritual symbolism, requires only that one develop "an eye for fractals" by studying the work of researchers and observing nature. One then begins to see that the separation of humanities and science is convenient oversimplification, not an ultimate fact. Includes a DVD of animated fractals. (shrink)

Fractal dynamics is a unique, systems-based approach of looking at and thinking about organizations. In this view, the organization is viewed as part of a pervasive organizational fractal. Many astounding properties such as fractal completion, fractal influence and fractal universality emerge in fractal space. These offer new insight into the fundamental dynamics animating all organizations. Routine management tasks such as strategy formulation, cost cutting, process redesign, product formulation, management of change and leadership development can (...) be conducted anew with powerful and innovative insights, unavailable when management is approached traditionally through a linear and sequential thinking approach. This article focuses primarily on the rationale for employing fractal dynamics, and on the search for the pervasive organizational fractal that animates all organizations. A brief example of how fractal dynamics offers insights in the case of management of change is also provided. (shrink)

In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of scales, and (ii) to a new geometric foundation of quantum mechanics and gauge field theories and their possible generalisations. In the second part, we discuss (...) some examples of application of the theory to various sciences, in particular in cases when the theoretical predictions have been validated by new or updated observational and experimental data. This includes predictions in physics and cosmology (value of the QCD coupling and of the cosmological constant), to astrophysics and gravitational structure formation (distances of extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like star cycles), to sciences of life (log-periodic law for species punctuated evolution, human development and society evolution), to Earth sciences (log-periodic deceleration of the rate of California earthquakes and of Sichuan earthquake replicas, critical law for the arctic sea ice extent) and tentative applications to systems biology. (shrink)