The quadratic Mandelbrot set has been referred to as the most complex and beautiful object in mat... more The quadratic Mandelbrot set has been referred to as the most complex and beautiful object in mathematics and the Riemann Zeta function takes the prize for the most complicated and enigmatic function. Here we elucidate the spectrum of Mandelbrot and Julia sets of Zeta, to unearth the geography of its chaotic and fractal diversities, combining these two extremes into one intrepid journey into the deepest abyss of complex function space. Introduction: This paper completes a discovery process I began in 2009, using computational applications I had developed, looking at the 'dark hearts' 1 -the Mandelbrot parameter planes -of a wide variety of complex functions, including the zeta function, to explore the world of complex functions as widely as possible and elucidate universal properties. This year, as I began to re-explore the parameter planes, using a more versatile second generation version of the application, I became literally sucked into the zeta abyss by an unending str...
From the beginning both mind and universe exist as paradoxical complements, each discovering its ... more From the beginning both mind and universe exist as paradoxical complements, each discovering its own nature through its complement. That is, the foundation of the mind and of the universe is the Tao. The universe is forever the Tao of Physics, as Capra noted, the paradoxical interplay of wave and particle, and as natural processes gather into the macroscopic world of experience, chaos and order, as the weather, evolution and conscious thought alike attest. For order to attempt to rule over chaos is as futile as for the particle to try to rule over the wave. Any society which attempts to rule by order alone is doomed to catastrophe as the natural process transition becomes frozen into an apocalyptic revolution collapsing the old order.
Abstract: A model,of the mind-brain relationship is developed in which novel biophysical principl... more Abstract: A model,of the mind-brain relationship is developed in which novel biophysical principles in,brain function generate a dynamic possessing attributes consistent with consciousness,and free-will. The model,invokes a fractal link between neurodynamical,chaos and quantum,uncertainty. Transactional wave,collapse allows this link to be utilized predictively by the excitable cell, in a way which bypasses and complements formal computation. The formal unpredictabilityof the model allows mind to interact upon the brain, the predictivity of consciousness in survival strategies being selected as a trait by organismic,evolution. 1 Mind and Brain, Chaos and Quantum Mechanics.
Fractal Neurodynamics and Quantum Chaos: Resolving the Mind-Brain Paradox Through Novel Biophysic... more Fractal Neurodynamics and Quantum Chaos: Resolving the Mind-Brain Paradox Through Novel Biophysics Chris King Mathematics and Statistics Department University of Auckland, New Zealand 1. Mind and brain, chaos and quantum mechanics 1.1. Paradigms in scientific discovery ...
: Twenty years ago (King 1978) I proposed the biocosmological thesis that the form of life's ... more : Twenty years ago (King 1978) I proposed the biocosmological thesis that the form of life's origin and evolution is a cosmological interactive process ultimately defined in the cosmic symmetry-breaking at the origin of the universe. Prebiotic chemists have been slow to comprehend the central role of non-linear quantum science in prebiotic and biological evolution because of a Newtonian misconception that all chemical structures are simply building blocks and life an arbitrary consequence of a series of historical accidents, rather than an expression of fundamental bifurcations 1 . However , with the passage of time, the pendulum has shifted from the green-cheese improbability of life as a random molecular accident to an awareness that central biomolecules leading to the RNA-era may be cosmologically abundant products of the clouds forming young stars. This apocalypsia unveils the non-linear quantum foundations of biocosmology as the founding science of life. Keywords : cosmolog...
Pure mathematics is often seen as an 'inverted pyramid', in which algebra and analysis st... more Pure mathematics is often seen as an 'inverted pyramid', in which algebra and analysis stand at the focal point, without which students could not possibly have a firm grounding for graduate studies. This paper examines a variety of evidence from brain studies of mathematical cognition, from mathematics in early child development, from studies of the gatherer-hunter mind, from a variety of puzzles, games and other human activities, from theories emerging from physical cosmology, and from burgeoning mathematical resources on the internet that suggest, to the contrary, that mathematics is a cultural language more akin to a maze than a focally-based hierarchy; that topology, geometry and dynamics are fundamental to the human mathematical mind; and that an exclusive focus on algebra and analysis may rather explain an increasing rift between modern mathematics and the 'real world' of the human population.
In this paper, the nature and sensitivity of chaos will be illustrated. Failure to appreciate the... more In this paper, the nature and sensitivity of chaos will be illustrated. Failure to appreciate the generative nature of chaos has led to it being one of the last scientific frontiers to be discovered, over fifty years after relativity and quantum theory. Far from being the nemesis of order, or the primal ooze in which order is imposed, chaos is genesis of new form. Most complex systems arise from the mutual interaction between chaos and order, through bifurcation. The eternal religious war of light and dark is very much the battle of chaos as the dark 'force' and order as the principle of light.
The chaotic aspects of brain structure and dynamics have been discussed. The relation of chaos to... more The chaotic aspects of brain structure and dynamics have been discussed. The relation of chaos to fractal processes in the brain from the neurosystems level down to the molecule has been explored. It is found that chaos appears to play an integral, though not necessarily exclusive role in function at all levels of organization from the neurosystems to the molecular and quantum levels. An interesting consequence involving the possible interface between chaotic dynamics and quantum physics has been discussed because of its potential significance is resolving several of the most intractable conceptual problems to do with computability, the brain and the mind (Blakemore and Greenfield, 1987; Hooper and Teresi, 1987; Rose, 1973; Searle, 1979; Penrose, 1986, 1989).
This paper describes the first phase of a study that aims to identify the specific English langua... more This paper describes the first phase of a study that aims to identify the specific English language discourse features that cause problems for English as an additional language (EAL) students in advanced undergraduate mathematics. In this phase observations of ...
The conscious brain poses the most serious unsolved problem for science at the beginning of the t... more The conscious brain poses the most serious unsolved problem for science at the beginning of the third millennium. Not only is the whole basis of subjective conscious experience lacking adequate physical explanation, but the relationship between causality and ...
The conscious brain poses the most serious unsolved problem for science at the beginning of the t... more The conscious brain poses the most serious unsolved problem for science at the beginning of the third millennium. Not only is the whole basis of subjective conscious experience lacking adequate physical explanation, but the relationship between causality and ...
The quadratic Mandelbrot set has been referred to as the most complex and beautiful object in mat... more The quadratic Mandelbrot set has been referred to as the most complex and beautiful object in mathematics and the Riemann Zeta function takes the prize for the most complicated and enigmatic function. Here we elucidate the spectrum of Mandelbrot and Julia sets of Zeta, to unearth the geography of its chaotic and fractal diversities, combining these two extremes into one intrepid journey into the deepest abyss of complex function space. Introduction: This paper completes a discovery process I began in 2009, using computational applications I had developed, looking at the 'dark hearts' 1 -the Mandelbrot parameter planes -of a wide variety of complex functions, including the zeta function, to explore the world of complex functions as widely as possible and elucidate universal properties. This year, as I began to re-explore the parameter planes, using a more versatile second generation version of the application, I became literally sucked into the zeta abyss by an unending str...
From the beginning both mind and universe exist as paradoxical complements, each discovering its ... more From the beginning both mind and universe exist as paradoxical complements, each discovering its own nature through its complement. That is, the foundation of the mind and of the universe is the Tao. The universe is forever the Tao of Physics, as Capra noted, the paradoxical interplay of wave and particle, and as natural processes gather into the macroscopic world of experience, chaos and order, as the weather, evolution and conscious thought alike attest. For order to attempt to rule over chaos is as futile as for the particle to try to rule over the wave. Any society which attempts to rule by order alone is doomed to catastrophe as the natural process transition becomes frozen into an apocalyptic revolution collapsing the old order.
Abstract: A model,of the mind-brain relationship is developed in which novel biophysical principl... more Abstract: A model,of the mind-brain relationship is developed in which novel biophysical principles in,brain function generate a dynamic possessing attributes consistent with consciousness,and free-will. The model,invokes a fractal link between neurodynamical,chaos and quantum,uncertainty. Transactional wave,collapse allows this link to be utilized predictively by the excitable cell, in a way which bypasses and complements formal computation. The formal unpredictabilityof the model allows mind to interact upon the brain, the predictivity of consciousness in survival strategies being selected as a trait by organismic,evolution. 1 Mind and Brain, Chaos and Quantum Mechanics.
Fractal Neurodynamics and Quantum Chaos: Resolving the Mind-Brain Paradox Through Novel Biophysic... more Fractal Neurodynamics and Quantum Chaos: Resolving the Mind-Brain Paradox Through Novel Biophysics Chris King Mathematics and Statistics Department University of Auckland, New Zealand 1. Mind and brain, chaos and quantum mechanics 1.1. Paradigms in scientific discovery ...
: Twenty years ago (King 1978) I proposed the biocosmological thesis that the form of life's ... more : Twenty years ago (King 1978) I proposed the biocosmological thesis that the form of life's origin and evolution is a cosmological interactive process ultimately defined in the cosmic symmetry-breaking at the origin of the universe. Prebiotic chemists have been slow to comprehend the central role of non-linear quantum science in prebiotic and biological evolution because of a Newtonian misconception that all chemical structures are simply building blocks and life an arbitrary consequence of a series of historical accidents, rather than an expression of fundamental bifurcations 1 . However , with the passage of time, the pendulum has shifted from the green-cheese improbability of life as a random molecular accident to an awareness that central biomolecules leading to the RNA-era may be cosmologically abundant products of the clouds forming young stars. This apocalypsia unveils the non-linear quantum foundations of biocosmology as the founding science of life. Keywords : cosmolog...
Pure mathematics is often seen as an 'inverted pyramid', in which algebra and analysis st... more Pure mathematics is often seen as an 'inverted pyramid', in which algebra and analysis stand at the focal point, without which students could not possibly have a firm grounding for graduate studies. This paper examines a variety of evidence from brain studies of mathematical cognition, from mathematics in early child development, from studies of the gatherer-hunter mind, from a variety of puzzles, games and other human activities, from theories emerging from physical cosmology, and from burgeoning mathematical resources on the internet that suggest, to the contrary, that mathematics is a cultural language more akin to a maze than a focally-based hierarchy; that topology, geometry and dynamics are fundamental to the human mathematical mind; and that an exclusive focus on algebra and analysis may rather explain an increasing rift between modern mathematics and the 'real world' of the human population.
In this paper, the nature and sensitivity of chaos will be illustrated. Failure to appreciate the... more In this paper, the nature and sensitivity of chaos will be illustrated. Failure to appreciate the generative nature of chaos has led to it being one of the last scientific frontiers to be discovered, over fifty years after relativity and quantum theory. Far from being the nemesis of order, or the primal ooze in which order is imposed, chaos is genesis of new form. Most complex systems arise from the mutual interaction between chaos and order, through bifurcation. The eternal religious war of light and dark is very much the battle of chaos as the dark 'force' and order as the principle of light.
The chaotic aspects of brain structure and dynamics have been discussed. The relation of chaos to... more The chaotic aspects of brain structure and dynamics have been discussed. The relation of chaos to fractal processes in the brain from the neurosystems level down to the molecule has been explored. It is found that chaos appears to play an integral, though not necessarily exclusive role in function at all levels of organization from the neurosystems to the molecular and quantum levels. An interesting consequence involving the possible interface between chaotic dynamics and quantum physics has been discussed because of its potential significance is resolving several of the most intractable conceptual problems to do with computability, the brain and the mind (Blakemore and Greenfield, 1987; Hooper and Teresi, 1987; Rose, 1973; Searle, 1979; Penrose, 1986, 1989).
This paper describes the first phase of a study that aims to identify the specific English langua... more This paper describes the first phase of a study that aims to identify the specific English language discourse features that cause problems for English as an additional language (EAL) students in advanced undergraduate mathematics. In this phase observations of ...
The conscious brain poses the most serious unsolved problem for science at the beginning of the t... more The conscious brain poses the most serious unsolved problem for science at the beginning of the third millennium. Not only is the whole basis of subjective conscious experience lacking adequate physical explanation, but the relationship between causality and ...
The conscious brain poses the most serious unsolved problem for science at the beginning of the t... more The conscious brain poses the most serious unsolved problem for science at the beginning of the third millennium. Not only is the whole basis of subjective conscious experience lacking adequate physical explanation, but the relationship between causality and ...
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