Theories of Consciousness

Theories of Consciousness

Key Terms

  • Consciousness
  • Neuroscience
  • Phenomenology
  • Mind and Brain
  • Hard Problem of Consciousness
  • Theory of Self
  • Theory of Consciousness
  • Atman = Brahman
  • Jivatma = Paramatma
  • Chetna
  • Universal Consciousness
  • Integrated Information Theory
  • Higher Order Theories (HOT)
  • Higher Order Thought
  • Higher Order Perception (HOP)
  • Biological Naturalism
  • Panpsychism
  • Quantum Consciousness Theory
  • Superposition
  • Entanglement
  • Wave Particle Duality
  • Orchestrated Objective Reduction Theory (Orch-OR)
  • Neural Darwinism
  • Global Workspace Theory (GWT)

Key Researchers

  • Anil Seth
  • Ned Block
  • Thomas Nagel
  • David Chalmers
  • Christof Koch
  • Patricia Churchland
  • Galen Strawson
  • John Searle
  • Swami Sarvapriyananda
  • Giulio Tononi
  • David Rosenthal
  • William Lycan
  • Roger Penrose
  • Stuart Hameroff
  • Gerald Edelman
  • Bernard Baars

Source: Mystery of the Mind: 7 Leading Theories of Consciousness Explained

Mystery of the Mind: 7 Leading Theories of Consciousness Explained

Streamlife staff writer

The nature of consciousness has mystified and intrigued humanity for centuries. As we progress in our understanding of the physical world, the question of what it means to be conscious remains one of the most complex and challenging inquiries in modern science. Despite this challenge, many leading theorists have developed compelling explanations for the phenomenon of consciousness. These theories seek to answer questions about the origins of our inner lives, the relationship between the mind and the brain, and the seemingly impenetrable problem of subjective experience. In this article, we’ll explore seven leading theories of consciousness, delving into their strengths, weaknesses, and historical roots.

Table of Contents

Integrated Information Theory: Consciousness as a Web of Information

Developed by neuroscientist Giulio Tononi in the early 2000s, Integrated Information Theory (IIT) proposes that consciousness arises from the integration of information within a system. The more interconnected and differentiated the information in a system, the higher the degree of consciousness. In other words, conscious experience is not simply a byproduct of brain activity but is fundamentally tied to the way information is structured, processed, and integrated within the brain.

IIT proposes that consciousness is quantifiable and can be measured using a mathematical value called “phi.” Phi is a measure of the degree of information integration within a system, considering both the amount of information and the complexity of its connections. According to IIT, systems with higher phi values possess a greater degree of consciousness.

A central concept in IIT is the idea of “causal power,” which refers to the ability of a system to affect its own future states. Consciousness, in this view, emerges from the causal interactions within a system, with greater causal power leading to richer conscious experiences. This approach allows IIT to provide a unified framework for understanding various aspects of consciousness, including its degrees, quality, and dynamics.

One of the most intriguing implications of IIT is its potential to extend the concept of consciousness beyond biological systems. If consciousness arises from the integration of information, then non-biological systems, such as advanced artificial intelligence, could also possess consciousness if they meet the necessary criteria.

Strengths:

  • IIT offers a quantifiable measure of consciousness called “phi,” which allows for comparisons between different systems and states.
  • The theory has provided a foundation for understanding the neural correlates of consciousness and the potential for artificial consciousness.

Weaknesses:

  • Critics argue that IIT’s reliance on a single metric oversimplifies the complexity of consciousness.
  • Some have questioned whether IIT can account for the subjective nature of conscious experience.

Higher-Order Theories: Consciousness as Self-Reflection

Higher-Order Theories (HOT) of consciousness, which originated in the 1990s with philosophers like David Rosenthal and William Lycan, propose that consciousness arises when the brain represents its own mental states. In other words, conscious experience is the result of thoughts about thoughts, or metacognition. According to HOT, unconscious mental states become conscious when they are accompanied by higher-order mental states that represent or are aware of them.

There are two main variants of HOT: Higher-Order Thought (HOT) theories, which focus on the cognitive aspect of higher-order representation, and Higher-Order Perception (HOP) theories, which emphasize the perceptual aspect. Both variants share the core idea that consciousness is a matter of self-representation, but they differ in how they conceive of the nature and role of higher-order mental states.

To further elucidate the HOT framework, it is helpful to consider an example. Imagine you are looking at a red apple. According to HOT, the perceptual experience of the red apple is an unconscious mental state. This experience becomes conscious when you have a higher-order thought that represents your experience of the apple, such as “I am perceiving a red apple.” The higher-order thought effectively “lights up” the unconscious mental state, transforming it into a conscious experience.

HOT theorists argue that this self-representational account of consciousness can explain various features of conscious experience, such as its subjective nature, introspection, and the distinction between conscious and unconscious mental states. For instance, the difference between conscious pain and unconscious pain can be understood in terms of the presence or absence of a higher-order mental state representing the pain.

Strengths:

  • HOT offers a clear distinction between conscious and unconscious mental states.
  • The theory provides a plausible explanation for introspection and self-awareness.
  • HOT is compatible with empirical findings in cognitive neuroscience, particularly the role of the prefrontal cortex in metacognition and self-representation.

Weaknesses:

  • Critics argue that HOT is circular, as it requires conscious awareness to be conscious.
  • The subjective nature of conscious experience remains unexplained within the HOT framework.
  • Some have questioned whether higher-order mental states are sufficient to account for the rich phenomenology of conscious experience.

Biological Naturalism: Consciousness as a Biological Phenomenon

Biological Naturalism, a theory proposed by the American philosopher John Searle, posits that consciousness is an emergent biological phenomenon resulting from specific neural mechanisms in the brain. Unlike some other theories of consciousness, Biological Naturalism maintains that conscious experience is a purely physical process, deeply rooted in the biological functioning of the brain.

At the core of Biological Naturalism is the idea that subjective conscious experiences, or qualia, are not separate from the physical world but are instead the product of the brain’s biological processes. This theory asserts that consciousness emerges from the complex interactions between neurons and other brain structures, forming a higher-level property of the brain’s activity, much like the properties of wetness in water molecules or the solidity of a table.

According to Searle, one of the key challenges in understanding consciousness from a biological perspective is to determine the specific neural correlates of consciousness (NCCs). NCCs are the minimal set of brain mechanisms or events responsible for producing a particular conscious experience. Identifying these correlates would help to bridge the gap between neuroscientific research and the subjective nature of conscious experience, ultimately contributing to a deeper understanding of how consciousness arises from the brain’s activity.

Strengths:

  • Biological Naturalism grounds consciousness in the physical, biological world, which aligns well with empirical scientific research and the naturalistic view of the universe.
  • The theory provides a solid foundation for investigating the neural mechanisms of consciousness, encouraging neuroscientific studies to reveal the specific brain processes that give rise to conscious experience.

Weaknesses:

  • Biological Naturalism has been criticized for not adequately addressing the “hard problem” of consciousness, which is the question of how and why specific neural processes give rise to subjective conscious experiences.
  • Some critics argue that the theory’s focus on neural correlates may not fully capture the complexity of consciousness, as it might overlook the potential contributions of other factors, such as the brain’s global neural dynamics or the interactions between different brain regions.

Panpsychism: The Universal Consciousness

Panpsychism is a philosophical theory tracing back to ancient Greece and India, which has recently been revived by contemporary philosophers like David Chalmers and Galen Strawson. Panpsychism posits that consciousness is a fundamental property of the universe, akin to mass or charge. According to this view, all physical entities, from electrons to galaxies, possess some form of consciousness or proto-consciousness, even if in a highly rudimentary form.

The core idea of panpsychism is that consciousness is not exclusive to complex biological systems, but rather is an intrinsic aspect of the fabric of reality. By attributing consciousness to all matter, panpsychism offers a unique solution to the “hard problem” of consciousness – the question of why and how certain physical processes give rise to subjective experience.

To gain a deeper understanding of panpsychism, it is important to clarify that the theory does not imply that all objects have thoughts, emotions, or self-awareness. Instead, panpsychism posits that even the most basic constituents of reality possess some form of experiential quality or “proto-consciousness.” This fundamental consciousness is thought to be combined and integrated in complex systems, such as the human brain, to give rise to the rich and varied conscious experiences we are familiar with.

One of the main challenges facing panpsychism is the so-called “combination problem.” This problem arises from the question of how individual conscious entities, such as the proto-consciousness of elementary particles, can combine to form a unified conscious experience, like the experience of a human being. Various panpsychist theorists have proposed different solutions to the combination problem, including the idea of “constitutive panpsychism,” in which higher-level conscious experiences are composed of more basic forms of consciousness.

Strengths:

  • Panpsychism offers a unique solution to the “hard problem” of consciousness by positing that subjective experience is inherent to all matter.
  • The theory provides a potential explanation for the emergence of consciousness in complex systems and avoids the difficulties associated with explaining how consciousness arises from non-conscious matter.

Weaknesses:

  • Critics argue that panpsychism is untestable and lacks empirical support.
  • The theory struggles to address the “combination problem,” which questions how individual conscious entities combine to form a unified conscious experience.
  • Some have criticized panpsychism as a form of “panprotopsychism,” arguing that attributing proto-consciousness to all matter does not necessarily explain the nature of full-fledged conscious experience.

Quantum Consciousness Theory: The Microscopic World Meets the Mind

Quantum Consciousness Theory, also known as Quantum Mind Theory, posits that the fundamental principles of quantum mechanics play a significant role in the emergence and functioning of consciousness. Developed in the late 20th century by physicists and mathematicians such as Roger Penrose and Stuart Hameroff, this theory suggests that the microtubules within the brain’s neurons are responsible for consciousness through quantum processes.

Quantum Consciousness Theory is based on the idea that microtubules, which are tiny protein structures found within neurons, can facilitate quantum computations. These quantum computations are thought to be responsible for the emergence of consciousness. According to proponents of this theory, the unique properties of quantum mechanics—such as superposition, entanglement, and wave-particle duality—allow for the generation of conscious experience in ways that classical physics cannot explain.

To delve deeper into Quantum Consciousness Theory, it’s essential to understand the concepts of quantum superposition and entanglement. Quantum superposition refers to the ability of a quantum system to exist in multiple states simultaneously until a measurement or observation is made, at which point the system collapses into one definite state. Quantum entanglement occurs when particles become interconnected in such a way that the state of one particle directly influences the state of another, even when they are separated by vast distances. Proponents of Quantum Consciousness Theory believe that these quantum phenomena can occur within the brain’s microtubules, leading to the emergence of conscious experience.

One of the most well-known models within Quantum Consciousness Theory is the Orchestrated Objective Reduction (Orch-OR) model, proposed by Roger Penrose and Stuart Hameroff. In the Orch-OR model, consciousness arises from quantum computations that occur within microtubules. These quantum computations are thought to be orchestrated by molecular structures called tubulins, which can switch between different quantum states. When a certain threshold of tubulin activity is reached, a collapse of the quantum superposition occurs, and this collapse is hypothesized to produce a moment of conscious experience.

Strengths:

  • Quantum Consciousness Theory offers an intriguing explanation for the emergence of consciousness that incorporates the exotic principles of quantum mechanics.
  • The theory has inspired interdisciplinary research, bridging the gap between neuroscience, physics, and philosophy.

Weaknesses:

  • Many scientists and philosophers remain skeptical of the role of quantum mechanics in consciousness, arguing that the brain’s warm, wet environment is not conducive to maintaining quantum states.
  • Critics also argue that Quantum Consciousness Theory does not directly address the subjective nature of conscious experience or the “hard problem” of consciousness.
  • Empirical evidence supporting the involvement of quantum processes in consciousness is limited and controversial.

Neural Darwinism: The Evolution of Consciousness

Neural Darwinism, also known as the Theory of Neuronal Group Selection, is a theory proposed by neuroscientist Gerald Edelman in the 1980s. It suggests that consciousness emerges through a process of selection among groups of neurons, akin to the principles of natural selection in biological evolution. According to Neural Darwinism, the brain’s structure and function are shaped by a competitive process in which neural circuits compete for resources and connectivity.

At the foundation of Neural Darwinism is the idea that the brain is composed of neuronal groups that are functionally interconnected. These neuronal groups, or assemblies, are constantly interacting and reconfiguring themselves based on their activity and the input they receive. Through this dynamic process, the brain’s neural networks are refined and optimized, resulting in the emergence of consciousness.

To gain a deeper understanding of Neural Darwinism, it is crucial to recognize the three main processes that drive the theory: (1) developmental selection, (2) experiential selection, and (3) reentrant signaling. Developmental selection refers to the formation of neuronal groups during development, with some groups being strengthened and others eliminated based on genetic and environmental factors. Experiential selection occurs as the brain encounters new experiences, leading to the strengthening of some neuronal groups and the weakening or elimination of others. Reentrant signaling involves the constant exchange of information between neuronal groups, which allows for the integration of information across different brain areas and the emergence of conscious experience.

Neural Darwinism posits that through these processes, the brain continually adapts and reorganizes its neural networks, giving rise to the dynamic and ever-changing nature of conscious experience. This theory emphasizes the importance of both genetic and experiential factors in shaping the structure and function of the brain and provides a compelling account of how consciousness might arise from the brain’s evolutionary processes.

Strengths:

  • Neural Darwinism offers a biologically plausible account of consciousness based on the principles of evolution and natural selection.
  • The theory provides a potential explanation for the individual variability of conscious experience, as each person’s brain develops and adapts differently based on their unique genetic and environmental influences.
  • Neural Darwinism has been supported by various empirical findings in neuroscience, such as the observation of competitive processes in neural development and plasticity.

Weaknesses:

  • Critics argue that Neural Darwinism does not directly address the subjective nature of conscious experience or the “hard problem” of consciousness.
  • Some have questioned whether the principles of natural selection can be adequately applied to neural networks and their development.

Global Workspace Theory: Consciousness as a Central Information Hub

Global Workspace Theory (GWT), proposed by psychologist Bernard Baars in the 1980s, postulates that consciousness arises from the integration and sharing of information across different brain regions. According to GWT, the brain contains a “global workspace” that functions as a central information hub, allowing various cognitive processes to communicate and cooperate with each other.

At the core of GWT is the idea that conscious experience is the result of the brain’s capacity to broadcast information to a wide array of specialized cognitive processes. In this view, consciousness is not localized to a specific brain area but is a product of the dynamic interplay between different brain regions and systems.

To better understand GWT, it is useful to consider the “theater metaphor” often used to describe the theory. In this metaphor, the global workspace is likened to a theater stage, with various cognitive processes represented as actors performing on the stage. As information is processed and integrated within the global workspace, it becomes “conscious” and is broadcast to the entire “audience” of specialized cognitive processes. This broadcast allows for the integration of information across different domains and the generation of a unified conscious experience.

GWT posits that this information integration and broadcasting process is essential for consciousness, as it enables the brain to efficiently allocate resources, make decisions, and adapt to new situations. The theory suggests that conscious experience arises when information is accessible and available to multiple cognitive processes, allowing for the flexible and adaptive behavior that characterizes conscious beings.

Strengths:

  • GWT provides a plausible account of the brain’s capacity to integrate and share information across different cognitive domains.
  • The theory has been supported by empirical evidence from neuroscience, including findings related to the role of the prefrontal cortex and other brain areas in information integration and broadcasting.
  • GWT offers a potential explanation for the functional role of consciousness in decision-making and resource allocation.

Weaknesses:

  • Critics argue that GWT does not directly address the subjective nature of conscious experience or the “hard problem” of consciousness.
  • Some have questioned whether the global workspace concept is sufficient to account for the rich phenomenology of conscious experience.

In conclusion 

The quest to understand the enigma of consciousness has been a driving force for researchers and philosophers alike for centuries. The seven leading theories presented in this article offer a glimpse into the remarkable diversity of perspectives attempting to unravel the mysteries of the conscious mind. Each theory brings its unique insights, strengths, and weaknesses to the table, and together they paint a rich, multifaceted picture of the complex phenomenon we call consciousness.

As our scientific knowledge continues to advance, it becomes increasingly clear that the path to understanding consciousness is not a one-size-fits-all endeavor. It is likely that a comprehensive understanding of this enigmatic aspect of human experience will require the integration of ideas from multiple disciplines, including neuroscience, psychology, physics, and philosophy. By exploring the intersections between these theories and fostering collaboration across fields, we may gradually unravel the secrets of the conscious mind.

In the pursuit of understanding consciousness, we are not only striving to make sense of our own experiences but also to gain insight into the very essence of what it means to be human. Ultimately, the journey to comprehend consciousness is not merely an intellectual pursuit; it has profound implications for how we perceive ourselves, our place in the world, and our connections with others. The quest to decipher the mind’s mysteries is one of the most thrilling and significant adventures of human inquiry, and it is our collective curiosity, determination, and ingenuity that will propel us forward on this exciting journey.

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Key Sources of Research

An Overview of the Leading Theories of Consciousness

Organizing and comparing the major candidate theories in the field.

Ralph Lewis, M.D., is an associate professor in the Department of Psychiatry at the University of Toronto, a psychiatrist at Sunnybrook Health Sciences Centre, and a consultant at the Odette Cancer Centre in Toronto.

Updated October 7, 2023 

https://www.psychologytoday.com/us/blog/finding-purpose/202308/an-overview-of-the-leading-theories-of-consciousness

Understanding Higher-Order Theories of Consciousness

HOTs posit a possible way for the brain to render mental states conscious

Ralph Lewis, M.D., is an associate professor in the Department of Psychiatry at the University of Toronto, a psychiatrist at Sunnybrook Health Sciences Centre, and a consultant at the Odette Cancer Centre in Toronto.

Updated October 7, 2023 

https://www.psychologytoday.com/us/blog/finding-purpose/202309/understanding-higher-order-theories-of-consciousness

Fame in the Brain—Global Workspace Theories of Consciousness

GWT is a strong but incomplete theory of consciousness.

Ralph Lewis, M.D., is an associate professor in the Department of Psychiatry at the University of Toronto, a psychiatrist at Sunnybrook Health Sciences Centre, and a consultant at the Odette Cancer Centre in Toronto.

Updated October 8, 2023 

https://www.psychologytoday.com/us/blog/finding-purpose/202310/fame-in-the-brain-global-workspace-theories-of-consciousness

An Intriguing and Controversial Theory of Consciousness: IIT

Let’s dissect the appeal and criticism of integrated information theory (IIT).

Ralph Lewis, M.D., is an associate professor in the Department of Psychiatry at the University of Toronto, a psychiatrist at Sunnybrook Health Sciences Centre, and a consultant at the Odette Cancer Centre in Toronto.

Updated October 28, 2023 |

https://www.psychologytoday.com/us/blog/finding-purpose/202310/an-intriguing-and-controversial-theory-of-consciousness-iit

Mind-Body Problem: How Consciousness Emerges from Matter

Subjective experience is built from physically encoded internal representations.

Ralph Lewis, M.D., is an associate professor in the Department of Psychiatry at the University of Toronto, a psychiatrist at Sunnybrook Health Sciences Centre, and a consultant at the Odette Cancer Centre in Toronto.

Posted January 20, 2023 

https://www.psychologytoday.com/us/blog/finding-purpose/202301/mind-body-problem-how-consciousness-emerges-from-matter

Learning May Be the Key to the Evolution of Consciousness

Capacity to learn by flexible association may define and drive consciousness.

Posted November 3, 2022 

Ralph Lewis, M.D., is an associate professor in the Department of Psychiatry at the University of Toronto, a psychiatrist at Sunnybrook Health Sciences Centre, and a consultant at the Odette Cancer Centre in Toronto.

https://www.psychologytoday.com/us/blog/finding-purpose/202211/learning-may-be-the-key-the-evolution-consciousness

Are We Ditching the Most Popular Theory of Consciousness?

Why scientists are reevaluating the most popular definition of consciousness.

Updated October 11, 2023 |

https://www.psychologytoday.com/us/blog/social-instincts/202310/are-we-ditching-the-most-popular-theory-of-consciousness

Comparing theories of consciousness: why it matters and how to do it, 

Simon Hviid Del Pin, Zuzanna Skóra, Kristian Sandberg, Morten Overgaard, Michał Wierzchoń,

Neuroscience of Consciousness, Volume 2021, Issue 2, 2021, niab019, https://doi.org/10.1093/nc/niab019

https://academic.oup.com/nc/article/2021/2/niab019/6354404

What if consciousness is not an emergent property of the brain? Observational and empirical challenges to materialistic models. 

Wahbeh H, Radin D, Cannard C and Delorme A (2022)

Front. Psychol. 13:955594. doi: 10.3389/fpsyg.2022.955594

https://www.frontiersin.org/articles/10.3389/fpsyg.2022.955594/full

Explanatory profiles of models of consciousness – towards a systematic classification, 

Camilo Miguel Signorelli, Joanna Szczotka, Robert Prentner,

Neuroscience of Consciousness, Volume 2021, Issue 2, 2021, niab021, https://doi.org/10.1093/nc/niab021

Consciousness in active inference: Deep self-models, other minds, and the challenge of psychedelic-induced ego-dissolution, 

George Deane,

Neuroscience of Consciousness, Volume 2021, Issue 2, 2021, niab024, https://doi.org/10.1093/nc/niab024

https://academic.oup.com/nc/article/2021/2/niab024/6360857

Local neuronal relational structures underlying the contents of human conscious experience, 

Rafael Malach,

Neuroscience of Consciousness, Volume 2021, Issue 2, 2021, niab028, https://doi.org/10.1093/nc/niab028

https://academic.oup.com/nc/article/2021/2/niab028/6363668

Neuroscience of the yogic theory of consciousness, 

Vaibhav Tripathi, Pallavi Bharadwaj,

Neuroscience of Consciousness, Volume 2021, Issue 2, 2021, niab030, https://doi.org/10.1093/nc/niab030

https://academic.oup.com/nc/article/2021/2/niab030/6382467

A relational approach to consciousness: categories of level and contents of consciousness, 

Naotsugu Tsuchiya, Hayato Saigo,

Neuroscience of Consciousness, Volume 2021, Issue 2, 2021, niab034, https://doi.org/10.1093/nc/niab034

https://academic.oup.com/nc/article/2021/2/niab034/6397521

Time consciousness: the missing link in theories of consciousness, 

Lachlan Kent, Marc Wittmann,

Neuroscience of Consciousness, Volume 2021, Issue 2, 2021, niab011, https://doi.org/10.1093/nc/niab011

https://academic.oup.com/nc/article/2021/2/niab011/6224347

https://academic.oup.com/nc/article/2021/2/niab015/6283925

Time and time again: a multi-scale hierarchical framework for time-consciousness and timing of cognition, 

Ishan Singhal, Narayanan Srinivasan,

Neuroscience of Consciousness, Volume 2021, Issue 2, 2021, niab020, https://doi.org/10.1093/nc/niab020

https://academic.oup.com/nc/article/2021/2/niab020/6348789

Theories of Consciousness: An Introduction and Assessment / Edition 2

by William Seager

ISBN-10: 0415834090
ISBN-13: 9780415834094
Pub. Date: 02/10/2016
Publisher: Taylor & Francis

Despite recent strides in neuroscience and psychology that have deepened understanding of the brain, consciousness remains one of the greatest philosophical and scientific puzzles. The second edition of Theories of Consciousness: An Introduction and Assessment provides a fresh and up-to-date introduction to a variety of approaches to consciousness, and contributes to the current lively debate about the nature of consciousness and whether a scientific understanding of it is possible.

After an initial overview of the status and prospects of physicalism in the face of the problem of consciousness, William Seager explores key themes from Descartes – the founder of the modern problem of consciousness. He then turns to the most important theories of consciousness:

  • identity theories and the generation problem
  • higher-order thought theories of consciousness
  • self-representational theories of consciousness
  • Daniel Dennett’s theory of consciousness
  • attention-based theories of consciousness
  • representational theories of consciousness
  • conscious intentionality
  • panpsychism
  • neutral monism.

Thoroughly revised and expanded throughout, this second edition includes new chapters on animal consciousness, reflexive consciousness, combinatorial forms of panpsychism and neutral monism, as well as a significant new chapter on physicalism, emergence and consciousness.

The book’s broad scope, depth of coverage and focus on key philosophical positions and arguments make it an indispensable text for those teaching or studying philosophy of mind and psychology. It is also an excellent resource for those working in related fields such as cognitive science and the neuroscience of consciousness.

Table of Contents

Introduction  1. Consciousness & Physicalism  2. Themes from Descartes  3. Identity Theories & the Generation Problem  4. HOT Theory I: The Mentalistic Reduction of Consciousness  5. HOT Theory II: Animals, Mental Sophistication & Dispositions  6. Self-Representational Theories7. Dennett I: Qualia Eliminated  8. Dennett II: Consciousness Fictionalized  9. Consciousness & Attention10. Representational Theories of Consciousness I  11. Representational Theories of Consciousness II  12. Conscious Intentionality & the Anti-Cartesian Catastrophe  13. Consciousness, Information & Panpsychism  14. Panpsychism, Aggregation & Combinatorial Infusion  15. Monism & Models.  Index

Higher-order Theories of Consciousness: An Anthology

edited by Rocco J. Gennaro

Unifying matter, energy and consciousness, 

Mahendra Samarawickrama,

11th International Conference on Mathematical Modeling in Physical Sciences (2023).  DOI: 10.1063/5.0162815

https://phys.org/news/2023-10-energy-consciousness-physics-thorny-topic.html

Panpsychism: The Trippy Theory That Everything From Bananas to Bicycles Are Conscious

Do inanimate objects have a mental life? Probably not, but the question isn’t quite as absurd as it sounds.

By Avery Hurt

Feb 16, 2021

https://www.discovermagazine.com/mind/panpsychism-the-trippy-theory-that-everything-from-bananas-to-bicycles-are

A (Very) Brief History of Consciousness

If we understand the mechanism of subjective experience, we could choose, or not, to put it into AI.

A (Very) Brief History of Consciousness

Consciousness in Artificial Intelligence: Insights from the Science of Consciousness

https://arxiv.org/abs/2308.08708

Consciousness: The last 50 years (and the next).

Seth AK.

Brain and Neuroscience Advances. 2018;2. doi:10.1177/2398212818816019

https://journals.sagepub.com/doi/10.1177/2398212818816019

The Real Problem of Consciousness

What is it like to be you?

Posted October 21, 2021 

Anil Seth, D.Phil., a professor of cognitive and computational neuroscience at the University of Sussex, is the author of Being You.

Adapted from Being You: A New Science of Consciousness by Anil Seth with permission from Dutton, an imprint of Penguin Publishing Group, a division of Penguin Random House, LLC. Copyright © 2021 by Anil Seth.

https://www.psychologytoday.com/us/blog/consciousness-deep-dive/202110/the-real-problem-consciousness

“What Is Consciousness? Integrated Information vs. Inference” 

Cooke, James E. 2021.

Entropy 23, no. 8: 1032. https://doi.org/10.3390/e23081032

https://www.mdpi.com/1099-4300/23/8/1032

An Informal Internet Survey on the Current State of Consciousness Science. 

Michel M, Fleming SM, Lau H, Lee ALF, Martinez-Conde S, Passingham RE, Peters MAK, Rahnev D, Sergent C and Liu K (2018)

Front. Psychol. 9:2134. doi: 10.3389/fpsyg.2018.02134

https://www.frontiersin.org/articles/10.3389/fpsyg.2018.02134/full

Models of the Mind: How Physics, Engineering and Mathematics Have Shaped Our Understanding of the Brain 

by Grace Lindsay

(Bloomsbury Sigma)

https://www.bloomsbury.com/uk/models-of-the-mind-9781472966421/

The Consciousness Paradox: Consciousness, Concepts, and Higher-Order Thoughts

Rocco J. Gennaro

The MIT Press

DOI: https://doi.org/10.7551/mitpress/9780262016605.001.0001

ISBN electronic: 9780262298582

In Special Collection: CogNet

Publication date: 2011

Theories of Consciousness and the Evolutionary Origins of Consciousness

Departmental Honors in Philosophy
by Morgan R. Clouser
Lycoming College May 5, 2023

Consciousness

Theories in Neuroscience and Philosophy of Mind

Andrea Eugenio Cavanna, Andrea Nani

https://doi.org/10.1007/978-3-662-44088-9

Springer Berlin, Heidelberg

This book reviews some of the most important scientific and philosophical theories concerning the nature of mind and consciousness. Current theories on the mind-body problem and the neural correlates of consciousness are presented through a series of biographical sketches of the most influential thinkers across the fields of philosophy of mind, psychology and neuroscience. The book is divided into two parts: the first is dedicated to philosophers of mind and the second, to neuroscientists/experimental psychologists. Each part comprises twenty short chapters, with each chapter being dedicated to one author. A brief introduction is given on his or her life and most important works and influences. The most influential theory/ies developed by each author are then carefully explained and examined with the aim of scrutinizing the strengths and weaknesses of the different approaches to the nature of consciousness.



David Chalmers
Andrea Eugenio Cavanna, Andrea Nani
Pages 3-7

Paul and Patricia Churchland
Andrea Eugenio Cavanna, Andrea Nani
Pages 9-13

Tim Crane
Andrea Eugenio Cavanna, Andrea Nani
Pages 15-18

Donald Davidson
Andrea Eugenio Cavanna, Andrea Nani
Pages 19-24

Daniel Dennett
Andrea Eugenio Cavanna, Andrea Nani
Pages 25-28

René Descartes
Andrea Eugenio Cavanna, Andrea Nani
Pages 29-36

Jerry Fodor
Andrea Eugenio Cavanna, Andrea Nani
Pages 37-41

Jaegwon Kim
Andrea Eugenio Cavanna, Andrea Nani
Pages 43-47

William Lycan
Andrea Eugenio Cavanna, Andrea Nani
Pages 49-53

Colin McGinn
Andrea Eugenio Cavanna, Andrea Nani
Pages 55-59

Thomas Nagel
Andrea Eugenio Cavanna, Andrea Nani
Pages 61-65

Alva Noë
Andrea Eugenio Cavanna, Andrea Nani
Pages 67-71

Hilary Putnam
Andrea Eugenio Cavanna, Andrea Nani
Pages 73-78

David Rosenthal
Andrea Eugenio Cavanna, Andrea Nani
Pages 79-83

John Searle
Andrea Eugenio Cavanna, Andrea Nani
Pages 85-89

Bernard Baars
Andrea Eugenio Cavanna, Andrea Nani
Pages 93-97

Francis Crick and Christof Koch
Andrea Eugenio Cavanna, Andrea Nani
Pages 99-103

Theories of consciousness.

Seth, Anil & Bayne, Tim. (2022).

Nature Reviews Neuroscience. 23. 10.1038/s41583-022-00587-4.

Mystery of the Mind: 7 Leading Theories of Consciousness Explained

An Introduction to Current Theories of Consciousness

by hohenheim

https://www.lesswrong.com/posts/8FuFepryeWbSYgqyN/an-introduction-to-current-theories-of-consciousness

Challenges for theories of consciousness: seeing or knowing, the missing ingredient and how to deal with panpsychism

2018

Phil. Trans. R. Soc. B373: 2017034420170344

http://doi.org/10.1098/rstb.2017.0344

https://royalsocietypublishing.org/doi/10.1098/rstb.2017.0344

Facing upto the hard question of consciousness.

Dennett DC. 2018

Phil.Trans. R. Soc. B373: 20170342.http://dx.doi.org/10.1098/rstb.2017.0342

Why and how access consciousness can account forphenomenal consciousness.

Naccache L. 2018

Phil. Trans. R. Soc.B373: 20170357.http://dx.doi.org/10.1098/rstb.2017.0357

One Hour of Mind-Blowing Scientific Theories on Conscious Universe

Theories and measures of consciousness: An extended framework

Anil K. SethEugene IzhikevichGeorge N. Reeke, and Gerald M. Edelman edelman@nsi.edu

July 11, 2006

103 (28) 10799-10804

https://doi.org/10.1073/pnas.0604347103

https://www.pnas.org/doi/10.1073/pnas.0604347103

Comparing the major theories of consciousness.

Block, N. (2009).

In M. S. Gazzaniga, E. Bizzi, L. M. Chalupa, S. T. Grafton, T. F. Heatherton, C. Koch, J. E. LeDoux, S. J. Luck, G. R. Mangan, J. A. Movshon, H. Neville, E. A. Phelps, P. Rakic, D. L. Schacter, M. Sur, & B. A. Wandell (Eds.), The cognitive neurosciences (pp. 1111–1122). Massachusetts Institute of Technology. https://doi.org/10.7551/mitpress/8029.003.0099

https://direct.mit.edu/books/edited-volume/5453/chapter-abstract/3965030/Comparing-the-Major-Theories-of-Consciousness?redirectedFrom=fulltext

Reconciling Current Theories of Consciousness

Sébastien Maillé and Michael Lynn

Journal of Neuroscience 4 March 2020,  40 (10) 1994-1996; DOI: https://doi.org/10.1523/JNEUROSCI.2740-19.2020

https://www.jneurosci.org/content/40/10/1994

Theories of Consciousness

https://philpapers.org/browse/theories-of-consciousness

Models of consciousness

Anil Seth (2007),

Scholarpedia, 2(1):1328.

doi:10.4249/scholarpedia.1328

http://www.scholarpedia.org/article/Models_of_consciousness

The fundamental challenge of a future theory of consciousness.

Ruan Z.

Front Psychol. 2023 Jan 12;13:1029105. doi: 10.3389/fpsyg.2022.1029105. PMID: 36710768; PMCID: PMC9878380.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9878380/

Higher-Order Theories of Consciousness

Theories of consciousness.

Seth, Anil; Bayne, Tim (2022).

University of Sussex. Journal contribution. https://hdl.handle.net/10779/uos.23488103.v1

https://sussex.figshare.com/articles/journal_contribution/Theories_of_consciousness/23488103

Theory of Consciousness

https://www.sciencedirect.com/topics/psychology/theory-of-consciousness

What a Contest of Consciousness Theories Really Proved

A five-year “adversarial collaboration” of consciousness theorists led to a stagy showdown in front of an audience. It crowned no winners — but it can still claim progress.

https://www.quantamagazine.org/what-a-contest-of-consciousness-theories-really-proved-20230824/

Higher-Order Theories of Consciousness

SEP

https://plato.stanford.edu/entries/consciousness-higher/

What are the four main theories of consciousness?

By Anil Seth

https://www.newscientist.com/question/four-main-theories-consciousness/

Consciousness

SEP

https://plato.stanford.edu/entries/consciousness/

Theories of consciousness. 

Seth, A.K., Bayne, T.

Nat Rev Neurosci 23, 439–452 (2022). https://doi.org/10.1038/s41583-022-00587-4

https://www.nature.com/articles/s41583-022-00587-4#citeas

Abstract

Recent years have seen a blossoming of theories about the biological and physical basis of consciousness. Good theories guide empirical research, allowing us to interpret data, develop new experimental techniques and expand our capacity to manipulate the phenomenon of interest. Indeed, it is only when couched in terms of a theory that empirical discoveries can ultimately deliver a satisfying understanding of a phenomenon. However, in the case of consciousness, it is unclear how current theories relate to each other, or whether they can be empirically distinguished. To clarify this complicated landscape, we review four prominent theoretical approaches to consciousness: higher-order theories, global workspace theories, re-entry and predictive processing theories and integrated information theory. We describe the key characteristics of each approach by identifying which aspects of consciousness they propose to explain, what their neurobiological commitments are and what empirical data are adduced in their support. We consider how some prominent empirical debates might distinguish among these theories, and we outline three ways in which theories need to be developed to deliver a mature regimen of theory-testing in the neuroscience of consciousness. There are good reasons to think that the iterative development, testing and comparison of theories of consciousness will lead to a deeper understanding of this most profound of mysteries.

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Geometry of Human Form: Art and Science of Charles Henry

Geometry of Human Form: Art and Science of Charles Henry

Key Terms

  • Sacred Geometry
  • Sphere Packing
  • Light
  • Geometry
  • Optics
  • Pyramids
  • Vesica Piscis
  • Limestone
  • Close-packed reflective spheres
  • Golden Mean
  • Pi
  • Computer Imaging
  • Photography
  • Animation
  • Graphic Art
  • Sculpture

Meeting Prof. Charles Henry

I met Prof. Charles Henry in August of 2010. He was resident of Richmand, Virginia where I also live.

We met for lunch at one of the restaurant. He was kind to bring a CDROM with images and animations of his work for me.

We talked about Fractals and Packed Spheres.

He had a book with him on Pyramids by Christopher Dunn – The Giza Power Plant.

I kept in touch with him for next few days, We exchanged few emails.

Geometry of Human Form

Source: http://www.people.vcu.edu/~chenry/

SACRED GEOMETRY

 

New Discoveries

Linking The Great Pyramid to the Human Form

 

Copyright 1997 – 2000   CHARLES R. HENRY

All Rights Reserved

Professor, Department of Sculpture

Virginia Commonwealth University

Richmond, Virginia

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This site is best viewed on Microsoft Internet Explorer 4.0 or higher

with screen set to 1024 X 768 pixels, 24 bit …16 million colors.

Set … View/Text Size … to Meduim

Click on thumbnails to view larger images.

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For more than twenty years, I have been studying the image generating properties of reflective spheres stacked in 52 degree angle pyramids. The 52 (51.827) degree angle slope of the sides of The Great Pyramid in Cairo, Egypt embodies the Golden Mean which is the ratio that is used in Nature to generate growth patterns in space. Sacred Geometry studies such primal systems which reveal the unity of the cosmos by representing the relationships between numbers geometrically. The Vesica Piscis is one of the most fundamental geometrical forms of this ancient discipline and it reveals the relationship between the The Great Pyramid and the 2 dimensional expansion of a circle of one unit radius R as shown in Figure 1. This relationship is more completely described in The New View Over Atlantis by John Michell published by Thames and Hudson.

Figure1.gif (5952 bytes)

Figure 1         Vesica Piscis in 2 Dimensions

 

In the early 1970s, I became very interested in the three dimensional representation of this geometry and I visualized this as a three dimensional pyramid inside two intersecting spheres shown in Figure 2.

figure2.jpg (14868 bytes)

Figure 2          Vesica Piscis in 3 Dimensions

 

In an effort to visualize these 3D relationships in yet another way, I stacked reflective Christmas Tree balls in an inverted pyramid shell. I discovered that the patterns of multiple reflections created on the interior surfaces of reflective spheres stacked at this angle produce images that relate to the human form as photographed and shown in Figure 3 and Figure 4.

 

figure3.jpg (16443 bytes)Figure 3

 

figure4.jpg (27044 bytes)Figure 4

I made many pyramidal configurations of reflective spheres with different light sources and I photographed the patterns on the interior surfaces from many points of view. Another is shown here in Figure 5.

figure5.jpg (18367 bytes)Figure 5

 

 

Then in 1977, I discovered one stacking structure and viewpoint that produced a very convincing image of an archetypal human face. This structure of 10 spheres (2 5-ball pyramids) forming a cluster is shown in Figure 6.

figure6.jpg (8183 bytes)Figure 6

 

 

The face image is shown in the lower third of the pattern on one sphere inside this 10 sphere cluster and is shown in Figure 7.

figure7.jpg (34593 bytes)Figure 7   When I made this photograph, the structure was enclosed in a mirrored pyramid.

 

 

Later, I realized that the most natural structure for enclosing would be another 10 sphere, 2 pyramid structure that would totally enclose a smaller but similar cluster.  I worked out the math to find that by multiplying the inner sphere’s diameters by Pi gives the dimension for the outer sphere’s diameters as shown in Figure 8.

figure8.jpg (14227 bytes)Figure 8        One sphere is removed from the outer cluster to reveal the inner cluster. However, the inner cluster must be upside down with respect to the outer cluster to fit inside.

 

The expansion by Pi reinforced my suspicion that this 10 sphere cluster is a fundamental unit that is linked to the properties of three dimensional space.

Close-packed reflective spheres clustered in this concentric shell structure produce an optical distribution network that links the Golden Mean and Pi. The Golden Mean is expressed in the 52 degree angle pyramid structure and Pi is expressed in the ratio of the diameter to the circumference of each sphere of course; but it is also expressed in the ratio of the sizes of spheres in the 10 spheres within 10 spheres concentric shell structure that I discovered. This concentric shell structure could continue to expand with many shells and still retain the same ratio between shells. It was not until 1991 that I was able to build and photograph the images inside a ten-within-ten (2 shell) structure. I used 10 – 6″ diameter spheres and 10 – 19″ diameter hemispheres. The structure is shown here in Figure 9.

figure9.jpg (19664 bytes)Figure 9

 

 

Figure 10 and Figure 11 are photographs of the interior of the 10 spheres within 10 spheres cluster shown in Figure 9.

figure10.jpg (17924 bytes)Figure 10

figure11.jpg (13114 bytes)Figure 11

The photographs that I made from this 10-within-10 sphere structure revealed the inherent limitations of photography for this work. The final images were not what I was seeing with my eyes while directly viewing the interior of the structure. But this approach did reveal a more complete face form and I also realized that I would need at least 10 more spheres (about 60″ in diameter at $1500 each) to complete the enclosure and remove the remaining gaps in the images. Also, the lighting system was limited to the exterior and it was very difficult to control the positioning, color and brightness. So, in 1992, I purchased a computer to model these structures with ray-tracing software which enabled me to investigate more thoroughly the relationship between this cluster geometry and the archetypal images generated therein. During this tour into cyberspace, I could take a camera into the sacred chamber central to the concentric shells of reflective spheres which are simulated by a computer program (Real 3D by Realsoft Oy, Finland) that most accurately renders the effects of real-world light sources and records the patterns generated by multiple reflections on metal surfaces. With this method of investigation, I am able to more conveniently control the many variables which led to these discoveries and conclusions:

1.) At least 40 spheres (4-10 ball shells) are necessary to enclose the central area and fill in the gaps in the images.

2.) Most of the lights should be point sources placed at the points of contact between the innermost spheres of the structure; although additional symmetrically-paired, point-lights are necessary in the central area.

3.) Some of the innermost spheres are reduced in size and they can float within certain areas in the central space. Figure 12 shows typical positions and sizes.

4.) The camera position and field of view as shown in Figure 12 produces the most convincing image of the human form.

fig12.jpg (12536 bytes)Figure 12


5.) The image of this artificial anthropoid that is produced in these structures can be animated when the positions and sizes of certain spheres are modulated as shown in the three animations listed below. 

animation 1            .8 MB … estimated download time at 56k … 3.5 min.

animation 2           2.4 MB …  estimated download time at 56k … 10 min.

 

fig13.jpg (94727 bytes)

Figure 13       Human Form From Sacred Geometry

The computer image in Figure 13 was made from the camera position and field of view shown in Figure 12.

 

Figure 14   is from the same camera position (shown in Figure 12) but the lens set at a very wide angle.

fig14.jpg (110837 bytes)Figure 14

 

 

Figure 15 is from the same camera position (shown in Figure 12) with the camera lens set to zoom in.

fig15.jpg (92100 bytes)Figure 15  

 

 

Figure 16   is a stereo image and it shows the interior of the cluster in 3D. Stare through the images with your eyes focused at a distant point and the two images will turn into three images and the center image will appear in 3D.

fig16.jpg (42554 bytes)Figure 16    

In 1996, I produced an animation Sacred Spaces (6 minutes) which has been screened in many national and international film festivals and it has won some awards (see resume). I have also produced Flesh Tones (5.5 Minutes) another animation completed in 1997 and I have produced many high resolution images for prints/slides (some examples are shown in Figures 13 through 36) which I have presented with the video animations at lecture presentations. These images are stills from the animations and they demonstrate the variety of image generating that is inherent in this system. I have concentrated on exhibiting the videotape documentation of my work thus far because it is the most portable presentation format that describes this research most completely.

fig17.jpg (24384 bytes)Figure 17

fig18.jpg (27816 bytes)Figure 18

fig19.jpg (34590 bytes)Figure 19

fig20.jpg (27735 bytes)Figure 20

fig21.jpg (44628 bytes)Figure 21

Conclusion

This interdisciplinary research has taken me into many related areas of study.   Geometry, Optics, Ancient History of Art and Religion, Computer Imaging, Photography, Animation, Graphic Art and of course Sculpture are the major connecting disciplines that have contributed to this work.

I feel that I have rediscovered some of what was a highly developed understanding of Mankind’s relationship to the Universe and this knowledge was utilized and documented in the geometry of ancient structures. Sacred Geometry, the study of the unity of the cosmos, demonstrates relationships between Number and Space and the Human Form. It was used in the construction of ancient glyphs and monuments thereby preserving the knowledge of these principles of Natural Law for future generations.   This construction of reflective spheres may embody the technology that produced the animated images of the deities in the temples of antiquity. The Tree of Life which is a graphic representation of the interaction between cosmic forces is shown in Figure 22. It is found in many ancient texts of the Kabbalah.

fig22.jpg (11450 bytes)Figure 22.


I realized that The Tree of Life graphic can also represent the 10 sphere cluster made with 2 5-ball pyramids as shown in Figure 23.

fig23.jpg (7127 bytes)Figure 23

The construction of this structure of clustered metal reflective spheres (offering bowls) is well within the capability of many ancient cultures and with the addition of a few glass lenses, these images could be projected onto walls or into smoke. Perhaps there is some Truth behind the smoke and mirrors of Ancient Religion … perhaps it is geometry … Sacred Geometry.

This research which is documented in four computer animations Sacred Spaces, Flesh Tones, Our Mothers and Sacred Spaces 2, in color computer prints, and in color slides has given me new insight into the motives that may have inspired the construction of The Great Pyramid.


1998 – 2000 update

The images shown in Figures 24 – 35 were made with 50 spheres and 144 point-light sources.  Each of these images was made with unique brightness, color and value settings for various groupings of lights. 

fig24.jpg (49005 bytes)Figure24

fig25.jpg (61843 bytes)Figure25

fig26.jpg (45712 bytes)Figure26

fig27.jpg (30806 bytes)Figure27

fig28h.jpg (95562 bytes)Figure28 horizontal

fig28v.jpg (34955 bytes)Figure28 vertical

fig29.jpg (59673 bytes)Figure29

fig30.jpg (42660 bytes)Figure30

fig31.jpg (53032 bytes)Figure31

fig32.jpg (36716 bytes)Figure32

InFigure32,   the camera is aimed at the sphere opposite the face shown inFigure 31.Figure 12 shows the camera position for Figure 31.  The image in Figure 32 was formed when the camera position was rotated 180 degrees around the vertical axis  shown in Figurre 12    and  zoomed in.   The face image (a child?) in Figure 32 is much smaller  than the face (mother?) in  Figure 31.  

fig33h.jpg (72697 bytes)Figure33horizontal

fig33v.jpg (81648 bytes)Figure33vertical

figure34.jpg (54241 bytes)

Figure 34

 

Figure35This is a stereo 3D image that requires shutter glasses to view and your monitor must be set to interlace mode.

 

 

fig36.jpg (170331 bytes)

Figure 36            Stereo Image for Cross-Eyed Viewing

With your monitor at arm’s length away, focus on a point 6 inches in front of your nose (put your index finger 6 inches in front of your nose and focus on it). You will see a third image in 3D between the two images on the monitor (at the tip of your finger). Shift your attention from your finger to this third/middle image which will appear in 3D.

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The cross-eyed viewing method is perhaps the most effective way to put the viewer inside the cluster to see the human image as it would exist in 3D from the cameras position as seen in Figure 12. There are many more identifiable images in this clustering geometry viewed from this position and from other camera positions and even more images with other color settings for the point lights.

fig36l.jpg (158045 bytes)Figure 36 Large

fig36zi.jpg (39939 bytes)Figure 36 Zoom-in  This is the image on the forehead of the face in Figure 36 Large.                     

fig36zob.jpg (162376 bytes)Figure 36 Wide-angle Large

fig36zod.jpg (148518 bytes)Figure 36 Very wide-angle Large

fig37.jpg (53779 bytes)

Figure 37          Rods connecting centers of nearest neighbors in 3 shells

 

 

I’m now very curious about the relationship between Sacred Geometry and Sacred Music and the Human Form. Number relates to all that science measures by virtue of the way that 3D Space is defined. Number is also used to measure Time … and, as Pythagoras observed, Music is a manifestation of Number in Time. The distribution of sounds i.e. amplitude and frequency, may well find an idealized model in the 10 within 10 sphere, space-filling, close-packing geometric system. The representation of this geometry with sticks or strings or rods as shown in Figure 37 (in which the centers of nearest neighbor spheres in three shells are joined) may represent the ideal space-filling matrix of linear oscillating elements. It may also be used to define spatially distributed, hierarchical, cellular arrays.

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The camera positions on the symmetric planes within the cluster produce a bilateral symmetry that we identify with animal and human form. Naturally, we would expect this symmetry in the idealized images of higher life forms. The multiplicity of idealized beings in this cluster of reflective spheres suggests the presence of The Company of the Gods as described in many ancient Egyptian texts. It seems that the face images occur on a vertical plane linking the centers of spheres. There seem to be faces facing faces and faces within faces throughout this reflective environment. My guess is that the sacred part of what I have discovered is a result of the way the deity put the higher life forms in three dimensions.

This cluster geometry may have other properties that would be useful for spatial organization. The nesting of 10 reflective spheres within 10 reflective spheres geometry produces a distribution system that could be used for processing of optical information between the interior to the exterior of the structure. Because of the spatial distribution of the reflective spheres in two concentric shells of ten each, optical information must be reflected and diverged in order to enter or exit the system with the exception of a few radially arrayed directions. The system becomes a more selective filter of optical information as more shells are added to the structure. This inside-to-outside transformation/translation should have many practical applications in pattern recognition tasks. For example, any point source of coherent light (laser light) anywhere outside the two-shell cluster will produce a unique light distribution pattern on the inside as viewed from the center area of the cluster. This pattern could be recorded in a holographic medium and the exterior point source could then be reconstructed using conventional holographic means.

Is Number (Geometry and Time) the link between Art, Science and Religious experience? The language of number is perhaps the most convincing form of expression between humans and between humans and the Gods. We think and imagine in visual forms. Einstein constructed his mathematics based on mental images. He said that he would first try to visualize a space/time image and then mathematize it. We use mental images to construct possible scenarios of the future so that we don’t have to live out each one in “reality”. Words and pictures and mathematical formulas are ways to document, test, realize, and communicate these visions. Although there is seldom a need to mathematize images, we sense that it would be possible. We know that we could count and number the grains of sand on the beach. The geometry of our visions is what makes them real to us and it allows us to mentally work on them and to integrate them convincingly into our life here in 3D.

I’m not quite sure how the physical human form fits into the grand scheme of things but it does seem to be a result of the space-filling, spherical, close-packing geometric system that I’ve discovered and it is indeed “Sacred Geometry” by virtue of the definition God gave to three dimensions. I don’t think this geometric system is the matrix for all life systems but I think it can serve as a model for the interactions between the various dimensional realities in which we are immersed. It may also guide us in our attempt to develop new sciences and technologies that utilize the forces that operate in the regions that we now call consider paranormal.

According to contemporary Superstring Theory as described by Dr. Michio Kaku in his many recent writings, the mathematics that most appropriately describes the forces of nature requires an expression in ten dimensions. Einstein tried to describe the forces of nature in the mathematics of 3D and Time and found that the formulas were not broad enough to include all of the forces. We can perceive 3D and Time. The other 6D in Superstrings are hidden from our normal senses due to their incredibly small size according to Dr. Kaku. Our instincts inform us that there are more than 3 Dimensions and Time in the universe and the possiblity that something else exists mathematically beyond our perceptual horizon drives my curiosities about our possible links to these worlds. The new science of parapsychology has discovered many ways that humans can perceive by means beyond the physical senses and it has found that there are some people that are more capable of extrasensory perception than others. It may well be that our only contacts with this duality of nature are through numbers and mathematics on one hand or through dreams, remote viewing, telepathy, Ouija boards and tarot cards on the other. This would certainly confirm the existence of a God with a sense of humor

 

 

 


I am interested in any information relating this technology to ancient religious traditions.  Any references that you send will certainly be appreciated and I will certainly credit any references in future publications.

A more detailed version of this research is now available on CD-ROM and it includes the 10 minute animation Sacred Spaces 2 in streaming format.

I am also making available unlimited editions of selected images on this website which will be printed in very high resolution on archival paper with archival inks.


For more specific information about the availability, formats, sizes and pricing of the prints and CD relating to this work you may contact me at:

<crhenry1@verizon.net>    

Related Material

RESUME

LINKS

 

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My Related Posts

Platonic and Archimedean Solids

The Great Chain of Being

Indira’s Pearls: Apollonian Gasket, Circle and Sphere Packing

Sapta Matrikas (Seven Mothers) and Cosmology

Chausath (64) Yogini Hindu Temples Architecture

Dasa (Ten) Maha Vidyas

On Holons and Holarchy

Fractal and Multifractal Structures in Cosmology

Fractal Geometry and Hindu Temple Architecture

Interconnected Pythagorean Triples using Central Squares Theory

Key Sources of Research

Charles Henry

VCU, Richmond, VA

http://www.people.vcu.edu/~chenry/

Cantor Sets, Sierpinski Carpets, Menger Sponges

Cantor Sets, Sierpinski Carpets, Menger Sponges

Key Terms

  • Cantor Sets
  • Sierpinski Carpets
  • Menger Sponges
  • Fractals
  • Dimension
  • Georg Cantor
  • Waclaw Sierpinski
  • Karl Menger
  • 3 Steps of Vishnu
  • Maha Maya
  • Space Time Geometry
  • Fractal Space Time
  • Cantorian Space Time
  • 9 x 9 square
  • 8 x 8 square
  • 18 and 81
  • 56 and 65 (64 + 1)
  • Chhapan Bhog
  • Chousath Kala
  • Chousath Yogini
  • Fractal Dimension
  • Noninteger Dimension
  • Euler’s Number
  • 64 Tetrahedron
  • Kal Bhairav
  • Kali
  • Geometry of Space Time
  • Truncated Icosahedron
  • Soccer Ball Geometry
  • Pentagon and Hexagon
  • 9 Planets
  • 27 Nakshatras
  • 14 Lokas
  • Hausdorff Dimension
  • Non Commutative Geometry

Cantor Sets, Sierpinski Carpets, Menger Sponges

  • The Menger Sponge is formed by removing cubes from the original cube in an iterative manner.
  • This fractal has dimension d = log 20 / log 3 = 2.7268 placing
    it a space between two and three dimensions.
  • The Sierpinski carpet has fractal dimension = log 8/ log 3 = 1.8928.
  • The fractal dimension of the ternary Cantor set is DH = ln(2)/ln(3) = 0.6309.

Source: A Short History of Fractal Dimension

Source: A Short History of Fractal Dimension

Source: A Short History of Fractal Dimension

Source: A Short History of Fractal Dimension

Source: A Short History of Fractal Dimension

Source: A Short History of Fractal Dimension

Source: Menger Universal Spaces: Introduction to Fractal Geometry and Chaos

Source: Menger Universal Spaces: Introduction to Fractal Geometry and Chaos

Source: Menger Universal Spaces: Introduction to Fractal Geometry and Chaos

Source: Fractals: The Menger Sponge

Source: THE UNIVERSALITY OF THE HYPERPOLAR IMAGES OF THE SIERPINSKI CARPET AND THE MENGER SPONGE

Source: THE UNIVERSALITY OF THE HYPERPOLAR IMAGES OF THE SIERPINSKI CARPET AND THE MENGER SPONGE

Source: THE UNIVERSALITY OF THE HYPERPOLAR IMAGES OF THE SIERPINSKI CARPET AND THE MENGER SPONGE

Source: Mathematical Impressions: The Surprising Menger Sponge Slice

Source: Mathematical Impressions: The Surprising Menger Sponge Slice

Source: Mathematical Impressions: The Surprising Menger Sponge Slice

Source: Mathematical Impressions: The Surprising Menger Sponge Slice

Source: Mathematical Impressions: The Surprising Menger Sponge Slice

Source: Mathematical Impressions: The Surprising Menger Sponge Slice

Space, Fractal Spacetime, Cantorian Spacetime in Cosmology

Prof. M. S. El Naschie has published many research papers on Fractal Spacetime, Cantorian Spacetime, Dark Energy, and structure and geometry of space.

Please see references.

Source: A Fractal Menger Sponge Space-Time Proposal to Reconcile Measurements and Theoretical Predictions of Cosmic Dark Energy

My Related Posts

Growth and Form in Nature: Power Laws and Fractals

Fractal Geometry and Hindu Temple Architecture

Indra’s Net: On Interconnectedness

Shapes and Patterns in Nature

Shape of the Universe

Cosmic Mirror Theory

Consciousness of Cosmos: A Fractal, Recursive, Holographic Universe

Geometry of Consciousness

Maha Vakyas: Great Aphorisms in Vedanta

The Great Chain of Being

Interconnected Pythagorean Triples using Central Squares Theory

Myth of Invariance: Sound, Music, and Recurrent Events and Structures

The Pillar of Celestial Fire

Key Sources for Research

Mathematical Impressions: The Surprising Menger Sponge Slice

Simons Foundation

Menger Universal Spaces

Introduction to Fractal Geometry and Chaos

Matilde Marcolli

MAT1845HS Winter 2020, University of Toronto

Click to access FractalsUToronto7.pdf

Fractals: The Menger Sponge

LCAO approximation for scaling properties of the Menger sponge fractal

Kazuaki Sakoda

Optics Express Vol. 14, Issue 23, pp. 11372-11384 (2006) • https://doi.org/10.1364/OE.14.011372

Squeezing Pi from a Menger Sponge

Ed Pegg, Wolfram Research 

https://community.wolfram.com/groups/-/m/t/822984

mrly fractals

Inspired by Carlo Mats Vincenti Mitchener
Graphics by Paul Bourke
December 2022

http://paulbourke.net/fractals/mrlymath/index.html

Marley Math: Cantor Sets, Sierpinski Carpets, Menger Sponges, And More

Carlo Mats Vincenti Mitchener

24 April 2022

Click to access mrlymath.pdf

A Fractal Menger Sponge Space-Time Proposal to Reconcile Measurements and Theoretical Predictions of Cosmic Dark Energy

Mohamed S. El Naschie

Department of Physics, University of Alexandria, Egypt

Email: Chaossf@aol.com

International Journal of Modern Nonlinear Theory and Application
Vol. 2  No. 2 (2013) , Article ID: 32969 , 15 pages

 DOI:10.4236/ijmnta.2013.22014

https://www.scirp.org/html/1-2340074_32969.htm

The Mystery of the Menger Sponge

NY Times

2011

New Classes of Regular Symmetric Fractals.

Kak, Subhash (2021):

TechRxiv. Preprint. https://doi.org/10.36227/techrxiv.14714094.v2&nbsp;

THE GENERALIZATION OF SIERPINSKI CARPET AND MENGER SPONGE IN n-DIMENSIONAL SPACE

YUN YANG

YUTING FENG and 

YANHUA YU

https://doi.org/10.1142/S0218348X17500402

Fractals

Vol. 25, No. 05, 1750040 (2017)

https://www.worldscientific.com/doi/10.1142/S0218348X17500402

Hausdorff Measures and Hausdorff Dimensions of the Invariant Sets for Iterated Function Systems of Geometric Fractals

Md. Jahurul Islam1,*, Md. Shahidul Islam1, Md. Shafiqul Islam2

1Department of Mathematics, University of Dhaka, Bangladesh
2School of Mathematics and Computational Science, University of Prince Edward Island, Canada

Mathematics and Statistics 6(3): 25-33, 2018

DOI: 10.13189/ms.2018.060301

Sound absorption by Menger sponge fractal

Tetsuji Kawabea), Takatsuna Miyazakib), Daisuke Oka, Sin’ichiro Koyanagic), and Atsushi Hinokidani

The Journal of the Acoustical Society of America 125, 2830 (2009); https://doi.org/10.1121/1.3095807

https://asa.scitation.org/doi/full/10.1121/1.3095807

Fractal Dimensions in Circular and Spiral Phenomena.

Kak, Subhash (2022):

TechRxiv. Preprint. https://doi.org/10.36227/techrxiv.21766706.v1&nbsp;

Sierpinski Carpets as Julia sets for Imaginary 3-Circle Inversions

Daniel M. Look

Williams College

Is Spacetime Fractal and Quantum Coherent in the Golden Mean?

Mae-Wan Ho , Mohamed el Naschie & Giuseppe Vitiello

Global Journal of Science Frontier Research

Volume XV Issue I Version I Year 2015

Real Analysis: The Sierpinski Carpet and its Remarkable Area Explained

Analysis on the Sierpinski Carpet

M. T. Barlow

Centre de Recherches Mathematiques

CRM Proceedings and Lecture Notes

Homeomorphisms of the Sierpinski Carpet

Karuna S. Sangam
Bard College, ks4217@bard.edu

Senior Projects Spring 2018

Bard Undergraduate Senior Projects

A SIERPINSKI CARPET LIKE FRACTAL WITHOUT STANDARD SELF-SIMILAR ENERGY

SHIPING CAO AND HUA QIU

The construction of brownian motion on the Sierpinski carpet

MARTIN T. BARLOW 

RICHARD F. BASS

Annales de l’I. H. P., section B, tome 25, no 3 (1989), p. 225-257 

Click to access AIHPB_1989__25_3_225_0.pdf

Sierpinski

https://gofiguremath.org/fractals/sierpinski/

On the Hausdorff dimension of general Cantor sets,

A. F . Beardon,

Proc. Camb. Phil. Soc, 61 (1965), 679-694.

“Sur une courbe cantorienne qui contient une image biunivoque et continue de toute courbe donne”

W. Sierpiήski,

Comptes Rendus, 162 (1916), 629-642.

THE HAUSDORFF DIMENSION OF GENERAL SIERPINSKI CARPETS

CURT McMULLEN

Nagoya Math. J. Vol. 96 (1984), 1-9

Uniqueness of Brownian motion on Sierpinski carpets. 

Richard F. Bass, Takashi Kumagai, Martin T. Barlow, Alexander Teplyaev, 

J. Eur. Math. Soc. 12 (2010), no. 3, pp. 655–701

DOI 10.4171/JEMS/211

https://ems.press/journals/jems/articles/3456

GEODESICS IN THE SIERPINSKI CARPET AND MENGER SPONGE

ETHAN BERKOVE and DEREK SMITH

Fractals

Vol. 28, No. 07, 2050120 (2020)
https://doi.org/10.1142/S0218348X20501200

https://www.worldscientific.com/doi/10.1142/S0218348X20501200

The Theory of Cantorian Spacetime and High Energy Particle Physics (An Informal Review).

El Naschie, M.S. (2009)

Chaos, Solitons & Fractals, 41, 2635-2646. 
http://dx.doi.org/10.1016/j.chaos.2008.09.059

The Ultimate Unified Physico Mathematical Theory of Nature

M.S. El Naschie

Distinguished Professor, Department of Physics, Faculty of Science, University of Alexandria, Alexandria, Egypt.

Date of publication (dd/mm/yyyy): 22/08/2022

International Journal of Innovation in Science and Mathematics

Volume 10, Issue 4, ISSN (Online): 2347–9051

Click to access IJISM_974_FINAL.pdf

Analysis on Fractal Objects

Uta Freiberg
Technische Universität Chemnitz

December 2005

Meccanica 40(4):419-436
DOI:10.1007/s11012-005-2107-0

https://www.researchgate.net/publication/226551998_Analysis_on_Fractal_Objects

Exponentially Decaying Discrete Dynamical Systems

Yogesh Joshi
CIty University of New York – Kingsborough Community College

Denis Blackmore
New Jersey Institute of Technology

April 2012

Recent Patents on Space Technology 2(1):37-48
DOI:10.2174/1877611611202010037

https://www.researchgate.net/publication/267391812_Exponentially_Decaying_Discrete_Dynamical_Systems


THE UNIVERSALITY OF THE HYPERPOLAR IMAGES OF THE SIERPINSKI CARPET AND THE MENGER SPONGE

Glaser, F. (1997, Fall).

The Cal Poly Pomona Journal of Interdisciplinary Studies, 10, 9-18.

https://scholarworks.calstate.edu/downloads/gx41mk81q?locale=es

EVALUATING THE EXACT INFINITESIMAL VALUES OF AREA OF SIERPINSKIS CARPET AND VOLUME OF MENGERS SPONGE

Yaroslav D. Sergeyev

Dipartimento di Elettronica, Informatica e Sistemistica, Universita` della Calabria, Via P. Bucci, Cubo 42-C, 87030 Rende (CS) – Italy

http://wwwinfo.deis.unical.it/∼yaro yaro@si.deis.unical.it

Chaos, Solitons & Fractals
Volume 42, Issue 5, 15 December 2009, Pages 3042-3046

https://www.sciencedirect.com/science/article/abs/pii/S0960077909003877

Dynamics of fractals in Euclidean and measure spaces

Md. Shahidul Islam and Md. Jahurul Islam 2017

 J. Phys.: Conf. Ser. 890 012058

https://iopscience.iop.org/article/10.1088/1742-6596/890/1/012058/pdf

Cantor sets

March 2010

Ferdinand Chovanec
Armed Forces Academy of General Milan Rastislav Štefánik

https://www.researchgate.net/publication/228747023_Cantor_sets

Generalizations and Properties of the Ternary Cantor Set and Explorations in Similar Sets

by Rebecca Stettin

Ashland University

May 2017

Study of Variants of Cantor Sets Using Iterated Function System

Gen. Math. Notes, Vol. 23, No. 1, July 2014, pp. 45-58

https://www.semanticscholar.org/paper/Study-of-Variants-of-Cantor-Sets-Using-Iterated-Rani-Chugh/a110f82b7bf693815b53d97ad1ae8e74eb99c7c4

Click to access 6_GMN-4682-V23N1.247122947.pdf

Volume of the hyperbolic cantor sets

Habibulla Akhadkulov & Yunping Jiang (2020) 

Dynamical Systems, 35:2, 185-196, 

DOI: 10.1080/14689367.2019.1659754

https://www.tandfonline.com/doi/full/10.1080/14689367.2019.1659754

THE GENERALIZED CAPACITY OF CANTOR SETS

A. F. BEARDON

The Quarterly Journal of Mathematics, Volume 19, Issue 1, 1968, Pages 301–304, https://doi.org/10.1093/qmath/19.1.301

https://academic.oup.com/qjmath/article-abstract/19/1/301/1570320?redirectedFrom=PDF

Box-Counting Dimension of the Cantor Set

https://users.math.yale.edu/public_html/People/frame/Fractals/FracAndDim/BoxDim/CantorBoxDim/CantorBoxDim.html

A Note on the History of the Cantor Set and Cantor Function

JULIAN F. FLERON 

SUNY at Albany

Albany, New York

Mathematics Magazine, Vol. 67, No. 2 (Apr., 1994), pp. 136-140

Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/2690689&nbsp;.

Cantor Set and Its Properties

Zhixing Guo
University of California, Santa Barbara

April 23, 2014

Click to access mathcs103_s2014_zhixing_presentation.pdf

The Cantor Set and the Cantor Function

TMA4225 – Foundations of Analysis

On the measure of arithmetic sums of Cantor sets

Boris Solomyak∗
Department of Mathematics, University of Washington, USA

Indagationes Mathematicae
Volume 8, Issue 1, 1997, Pages 133-141

https://www.sciencedirect.com/science/article/pii/S0019357797833575

Multi Dimensional Cantor Sets in Classical and Quantum Mechanics

M. S. EL NASCHIE

Chaos, Solitons & Fractals Vol. 2, No. 2. pp.211-220. 1992

An Exploration of the Cantor Set

Christopher Shaver
Rockhurst University, shaverc@hawks.rockhurst.edu

Rose-Hulman Undergraduate Mathematics Journal: Vol. 11 : Iss. 1 , Article 1.

2010

An Exact Mathematical Picture of Quantum Spacetime

Mohamed S. El Naschie

Department of Physics, University of Alexandria, Alexandria, Egypt Email: Chaossf@aol.com

Advances in Pure Mathematics, 2015, 5, 560-570

http://dx.doi.org/10.4236/apm.2015.59052

https://www.scirp.org/(S(351jmbntvnsjt1aadkposzje))/journal/paperinformation.aspx?paperid=57895

On El Naschie’s Fractal-Cantorian Space-Time and Dark Energy—A Tutorial Review

Leila Marek-Crnjac

Department of Mathematics, Technical School Center of Maribor, Maribor, Slovenia

Natural Science, 2015, 7, 581-598

http://dx.doi.org/10.4236/ns.2015.713058

https://www.scirp.org/(S(351jmbntvnsjt1aadkposzje))/journal/paperinformation.aspx?paperid=61825

High Energy Physics and Cosmology as Computation. 

El Naschie, M. (2016)

American Journal of Computational Mathematics6, 185-199.

doi: 10.4236/ajcm.2016.63020.

https://www.scirp.org/(S(351jmbntvnsjt1aadkposzje))/journal/paperinformation.aspx?paperid=67938

On the Need for Fractal Logic in High Energy Quantum Physics. 

Naschie, M. , Olsen, S. , He, J. , Nada, S. , Marek-Crnjac, L. and Helal, A. (2012)

International Journal of Modern Nonlinear Theory and Application1, 84-92.

doi: 10.4236/ijmnta.2012.13012.

https://www.scirp.org/(S(351jmbntvnsjt1aadkposzje))/journal/paperinformation.aspx?paperid=23087

Quantum Entanglement as a Consequence of a Cantorian Micro Spacetime Geometry

M. El Naschie

Journal of Quantum Information Science, Vol. 1 No. 2, 2011, pp. 50-53.

doi: 10.4236/jqis.2011.12007.

https://www.scirp.org/(S(351jmbntvnsjt1aadkposzje))/journal/paperinformation.aspx?paperid=7623

The Three Page Guide to the Most Important Results of M. S. El Naschie’s Research in E-Infinity Quantum Physics and Cosmology

M. A. Helal, L. Marek-Crnjac and J. He,

Open Journal of Microphysics, Vol. 3 No. 4, 2013, pp. 141-145.

doi: 10.4236/ojm.2013.34020.

https://www.scirp.org/(S(351jmbntvnsjt1aadkposzje))/journal/paperinformation.aspx?paperid=39841

An Exact Mathematical Picture of Quantum Spacetime. 

Naschie, M. (2015)

Advances in Pure Mathematics5, 560-570.

doi: 10.4236/apm.2015.59052.

https://www.scirp.org/(S(351jmbntvnsjt1aadkposzje))/journal/paperinformation.aspx?paperid=57895

A guide to the mathematics of E-infinity Cantorian spacetime theory


El Naschie, M. S.

Chaos, Solitons and Fractals, Volume 25, Issue 5, p. 955-964.
Pub Date: September 2005

DOI: 10.1016/j.chaos.2004.12.033

https://www.sciencedirect.com/science/article/abs/pii/S0960077905000688?via%3Dihub

Dimensional symmetry breaking, information and fractal gravity in Cantorian space.

el Naschie MS.

Biosystems. 1998 Apr;46(1-2):41-6.

doi: 10.1016/s0303-2647(97)00079-8. PMID: 9648673.

https://pubmed.ncbi.nlm.nih.gov/9648673/

Time Symmetry Breaking, Duality and Cantorian Space-Time

M. S. EL NASCHIE DAMTP, Cambridge, UK

Chaos, Solitons & Fractals Vol 7. No. 4, pp. 499 – 518, 1996

Click to access 5.Time%20Symmetry%20Breaking,%20Duality.pdf

Renormalization Approach to the Dimension of Diffusion in Cantorian Space

M. S. EL NASCHIE

Appl. Math. Lett. Vol. 8, No. 1, pp. 59-63, 1995

On the Missing Link between Cosmology and Biology 

Mohamed S. El Naschie1, Scott Olsen2, M.A. Helal3, L. Marek-Crnjac4 and S. Nada

International Journal of Innovation in Science and Mathematics

Volume 6, Issue 1, ISSN (Online): 2347–9051

Click to access MissingLinkbetweenCosmologyandBiology.pdf

Information theory and dimensionality of space. 

Kak, S.

Sci Rep 10, 20733 (2020).

https://doi.org/10.1038/s41598-020-77855-9

https://www.researchgate.net/publication/346540015_Information_theory_and_dimensionality_of_space

https://www.nature.com/articles/s41598-020-77855-9

The Ontology of Space

Subhash Kak

2021, Chapman University

https://www.academia.edu/49175956/The_Ontology_of_Space

https://www.academia.edu/49175956/The_Measure_of_Space

Our e-dimensional universe

Subhash Kak
Nov 27, 2020

https://subhashkak.medium.com/our-e-dimensional-universe-febb3a20fa64

Black holes, disk structures, and cosmological implications in e-dimensional space


Kak, Subhash ; Kafatos, Menas

Physics Essays, vol. 35, issue 4, pp. 345-355
Pub Date: December 2022

DOI: 10.4006/0836-1398-35.4.345

https://www.ingentaconnect.com/content/pe/pe/2022/00000035/00000004/art00004;jsessionid=1ngq6d7uavci8.x-ic-live-03

Asymptotic freedom and noninteger dimensionality.

Kak S.


Scientific Reports, 09 Feb 2021, 11(1):3406
DOI: 10.1038/s41598-021-83002-9 PMID: 33564046 PMCID: PMC7873067

https://europepmc.org/article/pmc/pmc7873067

On the dimensionality of spacetime

Max Tegmark†
Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA

Received 10 February 1997

Class. Quantum Grav. 14 (1997) L69–L75

The Topology and Combinatorics of Soccer Balls

Dieter Kotschick

American Scientist, Volume 94

A Short History of Fractal Dimension

DECEMBER 26, 2020 by David D. NOLTE

Box counting fractal dimension of volumetric data

Written by Paul Bourke
April-May 2014

http://paulbourke.net/fractals/cubecount/

Luminosity and Chromaticity: On Light and Color

Luminosity and Chromaticity: On Light and Color

Key Terms and Ideas

  • Luminosity and Chromaticity
  • Light and Color
  • Diwali (Festival of Light) and Holi (Festival of Colors)
  • Rama and Krishna
  • Non Dual Vedanta and Trika Philosophy
  • 1 and 3
  • Verticalism and Horizontalism
  • Vedic and Tantric
  • Flute of Krishna and Shiva Jyotir Linga
  • Bow and Arrow of Ram
  • Ram Parivar and Shiv Parivar
  • Shiv Ratri
  • Plato and Aristotle
  • Sun, Moon, Earth and Mars
  • Rods and Cones in Retina
  • Color Temperature
  • Lok and Kosh
  • Seven Chakra
  • Trishool
  • Ram, Lakshman, Sita, Hanuman
  • Achromatic and Chromatic
  • Grey scale and Color Primaries
  • Mind and Moon
  • Moon and Emotions
  • Tone Circle
  • Color Circle
  • Pythagoras
  • 3 and 7
  • 137
  • 007
  • Prism
  • Seven Colors
  • 4 + 3 = 7
  • 4 x 3 = 12
  • Pentatonic
  • Heptatonic
  • Diatonic Scale
  • Chromatic Scale

Newton’s Color Circle

Source: http://winlab.rutgers.edu/~trappe/Courses/ImageVideoS06/MollonColorScience.pdf

Color Circle in Opticks of I.Newton

Source: Reprint of Opticks by Project Gutenberg

Color Sensation

Source: Understanding color & the in-camera image processing pipeline for computer vision

Electromagnetic Spectrum

Source: Notes for the course of Color Digital Image Processing

Color Temperature

Source: Understanding color & the in-camera image processing pipeline for computer vision

Color Temperatures of the Stars

Luminosity Function

Source: Understanding color & the in-camera image processing pipeline for computer vision

CIE 1931 XYZ

Source: Understanding color & the in-camera image processing pipeline for computer vision

Luminance

Source: Human Vision and Color

Brightness, Lightness,Hue, Saturation, and Luminosity

Source: The Brightness of Colour

Brightness has been defined as the perceived intensity of a visual stimulus, irrespective of its source. Lightness, on the other hand, is defined as the apparent brightness of an object relative to the object’s reflectance. Thus increasing the intensity of light falling on an object will increase its apparent brightness but not necessarily its apparent lightness, other things being equal [1]. Saturation is a measure of the spectral ‘‘purity’’ of a colour, and thus how different it is from a neutral, achromatic stimulus. Hue is the perception of how similar a stimulus is to red, green, blue etc. Luminous efficiency, or luminosity, measures the effect that light of different wavelengths has on the human visual system. It is a function of wavelength, usually written as V(l) [2], and is typically measured by rapidly alternating a pair of stimuli falling on the same area of the retina; the subject alters the physical radiance of one stimulus until the apparent flickering is minimised. Thus luminance is a measure of the intensity of a stimulus given the sensitivity of the human visual system, and so is integrated over wavelength [3]. Luminance is thought to be used by the brain to process motion, form and texture [4].

Clearly, brightness is monotonically related to luminance in the simplest case: the more luminant the stimulus is, the brighter it appears to be. However, the Helmholtz-Kohlrausch (HK) effect shows that the brightness of a stimulus is not a simple representation of luminance, since the brightness of equally luminant stimuli changes with their relative saturation (i.e. strongly coloured stimuli appear brighter than grey stimuli), and with shifts in the spectral distribution of the stimulus (e.g. ‘blues’ and ‘reds’ appear brighter than ‘greens’ and ‘yellows’ at equiluminance) [1; 5–6].

The HK effect has been measured in a variety of psychophysical studies [7–8] and is often expressed in terms of the (variable) ratio between brightness and luminance. 

Chromaticity

Source: Human Vision and Color

Human Eye

Source: Human Vision and Color

Human Retina

Source: Human Vision and Color

Rods and Cones Photoreceptors

Source: Human Vision and Color

Color Receptors

Source: Human Vision and Color

Tristimulus Color

Source: Color/CMU

Visual Sensitivity

Source: Human Vision https://people.cs.umass.edu/~elm/Teaching/ppt/691a/CV%20UNIT%20Light/691A_UNIT_Light_1.ppt.pdf

Light and Color (Photometry and Colorimetry) I

Source: Interactive Computer Graphics/UOMichigan

Light and Color (Photometry and Colorimetry) II

Source: Interactive Computer Graphics/UOMichigan

Two Types of Light Sensitive Cells

Source: Interactive Computer Graphics/UOMichigan

Cones and Rod Sensitivity

Source: Interactive Computer Graphics/UOMichigan

Distribution of Cones in Retina

Source: DIVERSE CELL TYPES, CIRCUITS, AND MECHANISMS FOR COLOR VISION IN THE VERTEBRATE RETINA

Types of Color Stimuli

Source: Perceiving Color. https://www.ics.uci.edu/~majumder/vispercep/chap5notes.pdf

Color Perception

Source: Perceiving Color. https://www.ics.uci.edu/~majumder/vispercep/chap5notes.pdf

CIE XYZ Model

Source: Human Vision and Color

Luminance and Chromaticity Space

Source: Understanding color & the in-camera image processing pipeline for computer vision

1931 CIE Chromaticity Chart

CIE 1931 Chromaticity Diagram

Source: Human Vision and Color

Source: Notes for the course of Color Digital Image Processing

Additive Colors

Source: Human Vision and Color

Subtractive Colors

Source: Human Vision and Color

Color Mixing

Source: Human Vision and Color

Color Appearance Models
  • RGB
  • CMY
  • CIE XYZ
  • CIE xyY
  • CIE LAB
  • Hunter LAB
  • CIE LUV
  • CIE LCH
  • HSB
  • HSV
  • HSL
  • HSI
  • YIQ for NTSC TVs in USA
  • YUV for PAL TVs in EU
  • YCbCr for digital TVs
  • Munsell Color System

Color Models are device independent. For discussion of device dependent color spaces, please see my post Digital Color and Imaging.

LMS, RGB, and CIE XYZ Color Spaces

Source: Color/CMU

HSV Color Space

My Related Posts

Reflective Display Technology: Using Pigments and Structural Colors

Color Science and Technology in LCD and LED Displays

Color Science of Gem Stones

Nature’s Fantastical Palette: Color From Structure

Optics of Metallic and Pearlescent Colors

Color Change: In Biology and Smart Pigments Technology

Color and Imaging in Digital Video and Cinema

Digital Color and Imaging

On Luminescence: Fluorescence, Phosphorescence, and Bioluminescence

On Light, Vision, Appearance, Color and Imaging

Understanding Rasa: Yoga of Nine Emotions

Shapes and Patterns in Nature

Key Sources of Research

What Are The Characteristics Of Color?

https://www.pantone.com/articles/color-fundamentals/what-are-the-characteristics-of-color

Birren Color Theory

by ADMIN on MARCH 11, 2012

http://www.wonderfulcolors.org/blog/birren-color-theory/

Light, Color, Perception, and Color Space Theory

Professor Brian A. Barsky

barsky@cs.berkeley.edu

Computer Science Division
Department of Electrical Engineering and Computer Sciences University of California, Berkeley

Understanding Color Spaces and Color Space Conversion

https://www.mathworks.com/help/images/understanding-color-spaces-and-color-space-conversion.html

The Human Visual System and Color Models

Click to access Carmody_Visual&ColorModels.pdf

Defining and Communicating Color: The CIELAB System

Color Vision and Arts

http://www.webexhibits.org/colorart/index.html

PRECISE COLOR COMMUNICATION: COLOR CONTROL FROM PERCEPTION TO INSTRUMENTATION

KonicaMinolta

A short history of color theory

https://programmingdesignsystems.com/color/a-short-history-of-color-theory/index.html

Let’s Colormath

Understanding the formulas of color conversion

https://donatbalipapp.medium.com/colours-maths-90346fb5abda

A History of Human Color Vision—from Newton to Maxwell

Barry R. Masters

Optics and Photonics January 2011

https://www.osa-opn.org/home/articles/volume_22/issue_1/features/a_history_of_human_color_vision—from_newton_to_max/

The Difference Between Chroma and Saturation

Munsell Color

Charles S. Peirce’s Phenomenology: Analysis and Consciousness

By Richard Kenneth Atkins

The Evolution of Human Color Vision/ Jeremy Nathans

Jeremy Nathans Lecture on Color Vision

JEREMY NATHANS LECTURE ON COLOR VISION

JEREMY NATHANS LECTURE ON COLOR VISION

JEREMY NATHANS LECTURE ON COLOR VISION

The Genes for Color Vision

Jeremy Nathans

SCIENTIFIC AMERICAN FEBRUARY 1989

A Short History of Color Photography

Photography  |  Angie Kordic

https://www.widewalls.ch/magazine/color-photography

Blue: The History of a Color (2001)

followed by Black: The History of a Color (2009) and then Green: The History of a Color (2014), all produced by the same publisher. A fifth, devoted to yellow, should come next. 

Historic Look on Color Theory 

Steele R. Stokley

The evolution of colour in design from the 1950s to today

Francesca Valan

Journal of the International Colour Association (2012): 8, 55-60

Greek Color Theory and the Four Elements

J.L. Benson

University of Massachusetts Amherst

A SHORT HISTORY OF COLOUR PHOTOGRAPHY

https://blog.scienceandmediamuseum.org.uk/a-short-history-of-colour-photography/

History of Color System

The Origins of Modern Color Science

J D Mollon

Click to access MollonColorScience.pdf

The History of Colors

Tobias Kiefer

Click to access Assignment_History_of_Colors.PDF

Notes for the course of Color Digital Image Processing

Edoardo Provenzi

Understanding color & the in-camera image processing pipeline for computer vision

Dr. Michael S. Brown

Canada Research Chair Professor York University – Toronto

ICCV 2019 Tutorial – Seoul, Korea

Chapter 2
Basic Color Theory

Click to access t3.pdf

Color Science

CS 4620 Lecture 26

Click to access 26color.pdf

Color Image Perception, Representation and Contrast Enhancement

Yao Wang
Tandon School of Engineering, New York University

A GUIDE TO LIGHT AND COLOUR DEMONSTRATIONS

Arne Valberg, Bjørg Helene Andorsen, Kine Angelo, Barbara Szybinska Matusiak and Claudia Moscoso

Norwegian University of Science and Technology Trondheim, Norway

https://www.ntnu.edu/documents/1272527942/1272817015/2015-09-08+DEMO+web.pdf/f1695ca5-b834-4d05-a011-a185f6562e32

A Primer to Colors in Digital Design

Archit Jha

Jul 16, 2017

https://uxdesign.cc/a-primer-to-colors-in-digital-design-7d16bb33399e

Chapter 7 ADDITIVE COLOR MIXING

Click to access 07_additive-color.pdf

Computergrafik

Matthias Zwicker Universität Bern Herbst 2016

Color

Click to access ColorPerception.pdf

Introduction to Computer Vision

The Perception of Color

In: Webvision: The Organization of the Retina and Visual System [Internet]. Salt Lake City (UT): University of Utah Health Sciences Center; 1995–.2005 May 1 [updated 2007 Jul 9]

https://pubmed.ncbi.nlm.nih.gov/21413396/

Visual Pigment Gene Structure and Expression in Human Retinae 

Tomohiko Yamaguchi,  Arno G. Motulsky,  Samir S. Deeb

Human Molecular Genetics, Volume 6, Issue 7, July 1997, Pages 981–990, https://doi.org/10.1093/hmg/6.7.981

https://academic.oup.com/hmg/article/6/7/981/572151

The Difference Between Chroma and Saturation

LUMINANCE AND CHROMATICITY

https://colorusage.arc.nasa.gov/lum_and_chrom.php

Number by Colors

A Guide to Using Color to Understand Technical Data
  • Brand Fortner
  • Theodore E. Meyer

Chapter 5 Perceiving Color

The Practical Guide To Color Theory For Photographers

History of the Bauhaus

https://bauhaus.netlify.app/form_color/color/

The Digital Artist’s Complete Guide To Mastering Color Theory

byLeigh G

BASIC COLOR THEORY

Anthony Holdsworth

Molecular Genetics of Color Vision and Color Vision Defects

Maureen Neitz, PhDJay Neitz, PhD

Arch Ophthalmol. 2000;118(5):691-700. doi:10.1001/archopht.118.5.691

https://jamanetwork.com/journals/jamaophthalmology/fullarticle/413200

Color Theory: Introduction to Color Theory and the Color Wheel

https://blog.thepapermillstore.com/color-theory-introduction-color-wheel/

Color Spaces and Color Temperature

https://tigoe.github.io/LightProjects/color-spaces-color-temp.html

The Brightness of Colour

David Corney1, John-Dylan Haynes2, Geraint Rees3,4, R. Beau Lotto1*

EECS 487: Interactive Computer Graphics

Colorimetry

KonicaMinolta

Basics of Color Theory

THE BASICS OF COLOR PERCEPTION AND MEASUREMENT

Hunterlab

https://www.hunterlab.com/color-measurement-learning/glossary/

Color Matching and Color Discrimination

The Science of Color

2003

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.457.9467&rep=rep1&type=pdf

1.3 Color Temperature

https://www.mat.univie.ac.at/~kriegl/Skripten/CG/CG.html

https://www.mat.univie.ac.at/~kriegl/Skripten/CG/node10.html

Color Spaces and Color Temperature

https://tigoe.github.io/LightProjects/color-spaces-color-temp.html

Digital Camera Sensor Colorimetry

Douglas A. Kerr

Click to access Sensor_Colorimetry.pdf

Chromatic luminance, colorimetric purity, and optimal aperture‐color stimuli

DOI: 10.1002/col.20356

https://www.researchgate.net/publication/230164581_Chromatic_luminance_colorimetric_purity_and_optimal_aperture-color_stimuli

Title: A Review of RGB Color Spaces …from xyY to R’G’B’

The CIE XYZ and xyY Color Spaces

Douglas A. Kerr

Click to access CIE_XYZ.pdf

DIVERSE CELL TYPES, CIRCUITS, AND MECHANISMS FOR COLOR VISION IN THE VERTEBRATE RETINA

Wallace B. Thoreson and Dennis M. Dacey

Department of Ophthalmology and Visual Sciences, Truhlsen Eye Institute, University of Nebraska Medical Center, Omaha, Nebraska; and Department of Biological Structure, Washington National Primate Research Center, University of Washington, Seattle, Washington

Physiol Rev 99: 1527–1573, 2019 Published May 29, 2019; doi:10.1152/physrev.00027.2018

https://journals.physiology.org/doi/pdf/10.1152/physrev.00027.2018

Human Vision

Introduction to color theory

https://graphics.stanford.edu/courses/cs178-10/applets/locus.html

COLOR WHEELS

https://www2.bellevuecollege.edu/artshum/materials/art/tanzi/Winter04/111/111CLRWHLSW04.htm

Human Vision and Color

UT

Click to access 121.pdf

COLOR VISION MECHANISMS

Andrew Stockman

Department of Visual Neuroscience UCL Institute of Opthalmology London, United KIngdom

David H. Brainard

Department of Psychology University of Pennsylvania Philadelphia, Pennsylvania

Color

CMU

Click to access lecture15.pdf

What Are The Characteristics Of Color?

Pantone

https://www.pantone.com/articles/color-fundamentals/what-are-the-characteristics-of-color

A Guide to Color


Guide C-316
Revised by Jennah McKinley

https://aces.nmsu.edu/pubs/_c/C316/welcome.html

A History of Color

The Evolution of Theories of Lights and Color
  • Robert A. Crone

https://link.springer.com/book/10.1007/978-94-007-0870-9

The Brilliant History of Color in Art

Victoria Finlay

A History of Light and Colour Measurement
Science in the Shadows

Sean F Johnston

University of Glasgow, Crichton Campus, UK

Color codes: modern theories of color in philosophy, painting and architecture, literature, music and psychology

Charles Riley

Chapter 6 Colour

History of Color Systems

Knots in Yoga

Knots in Yoga

 

 

Key Terms

  • Granthies or Knots
  • Bandha or Locks
  • Chakra or Energy Centers
  • Nadis
  • Kundalini shakti
  • Tantra
  • Yoga
  • Knots
  • Triplicity
  • Tribhang
  • Trefoil Knot
  • Dhumra Linga, Bana Linga, Itara Linga
  • Brahma, Vishnu, Rudra Knots
  • Tamas, Rajas, Sattva Gunas

 

 

 

https://www.lifesloka.com/en/3-granthi-in-kundalini-yoga/

3 Granthi in Kundalini Yoga

 

In Kundalini Yoga, it is said that there are three Granthi can be responsible for preventing prana from rising up through Sushumna Nadi. This Granthi three knots prevent one’s full potential from Kundalini rising energy. These three knots are Brahma Granthi, Vishnu Granthi and Rudra Granthi. They also relate to the Prakritis three Gunas (Tamas, Rajas and Sattva).

Some yogis in yoga see Granthi as a bamboo tree, where each segment is a barrier or barrier to the increase in kundalini energy.

The chakras in the psycho-physical human body at the dormant state form complex intertwined structures, called Granthi, or knots, as they are “link” matter and spirit, enhancing the sense of ego. There are three main granthis in the human body, which make the trinity of Brahma, Vishnu, and Shiva respectively, and they are called Brahma Granthi, Vishnu Granthi and Rudra Granthi.
In any practice to achieve success in the process of Kundalini awakening it is important to open these psychic knots. However, it is quite difficult because of granthi inextricably connected with all that we are accustomed to thinking of our personality, our habits, qualities, desires.

Three granthis together constitute the unconscious complexes (samskara) woven by illusion, and the weight and rigidity of the past is strong opposition to the passage of spiritual power.

The three Granthi are :

  1. Brahma granthi. it covers the area of Mulahara and Svadhisthan chakras. Some call it the perineal knot. It relates to the Tamas Guna (Mulahara and Svadhishthana) the universal destructive power.
    In both the Jabal and the Yogashikha Upanishad state that this granthi is located in the Muladhard chakra. However, most tantric scriptures place it in the Manipura chakra.
  2. Vishnu granthi (doing and prana). It covers the area between Manipura, Anahata and Vishuddi chakras. Sometimes it is known as the navel knot. It relates to the Rajas Guna (Manipura and Anahata) – the universal power of motion and activity.
    Vishnu granthi is said to be located in the area of Anahata chakra (the heart center), which is also the seat of prana. The heart is also the major knot chakra. So, to take the Kundalini Shakti into the passage of the Sushumna through Anahata chakra is also not very easy.
  3. Rudra granthi (Jnana, true knowledge). It covers the areas of Ajna and Sahasrara chakras. It is also known as the forehead knot. Unlike the other five chakras, the Ajna chakra is not connected to the spinal cord. So, the Rudra granthi is blocking the flow of prana beyond the sixth chakra between the eyebrows, Ajna chakra, upwards toward Sahasrara. It relates to the Sattva Guna (Vishuddha and Ajna), the universal creative power.

The Brahma granthi separates the first two chakras (Mulahra and Suadhisthana chakras) from the Manipura chakra. The sympathetic chain is continuous, however, at the upper level of the splanchnic nerves, the presynaptic system changes to the post-synaptic system. So, one can say the Vishnu Granthi is between the Manipura and the Anahata chakras.

Brahma Granthi is the first major block that sadhaka need to transcend. This granthi keeps a person under the illusion of the material benefits, physical pleasures, lethargy, ignorance, and uncertainty.
Among all the most powerful is an illusion of physical pleasure. This granthi plays an important role because it is responsible for the material man’s thinking. It creates a kind of attraction in the nature of the human mind.

Brahma granthi is covered by the essence it produces. This essence is called as “Kledam”. It is colorless and smells as a lotus flower. It is like a mixture of ‘Kapha’ which covers the entrance of Sushumna and also lubricates the Nadi connected. This lubrication helps the pulses of Nadi.

This Kledam is a thick mixture and thickens when we get older if we don’t practice yoga. With the power of Yoga can penetrate this barrier and go up through Sushumna through each barrier.

In short, anatomically the Granthis exist due to either the change of systems from sympathetic to parasympathetic, the separation of Vagus nerve from the Sacral nerve, or the changes from presynaptic fibers to postsynaptic fibers.

The philosophy of Kundalini Yoga is associated with the flow of energy in the channels called Ida and Pingala, (the female and male channels of the astral body, comparable to the sensory and motor nerves of the physical body) and its criss-cross centers in the spinal canal called Sushumna Nadi called chakras.

The three major intersections in the central Sushumna Nadi are at Muladhara (pelvic region), Anahata (chest region) and Ajna chakras (between the eyebrows) are interpreted as Granthi because the exchange energies of physical and mental levels occur at these three places and named after the Trinity.

Granthi means a knotted area which prevents the free flow of energy (Prana) from rising upwards. The concept and explanations related to granthi is a vague term that deals with very internal issues of undoing it and hard to give a figurative expression in a stone medium because they are levels of awareness where the power of Maya, ignorance, and attachment to material things are especially strong.

According to ancient spiritual science, every human has a gross physical body, the subtle astral body, and mind as its counterpart which is linked to each other. Though mind resides and interacts in the physical body, it cannot be given proof for its structure nor location in the body, but the mind influences the astral body also. The energy for the physical body is through external aids, but, energy for the astral body is dependent on the calm state of mind which can be achieved by getting out of the worldly entanglements termed as granthi.

The Ida and Pingala Nadi that are like spirals of opposite poles of the central axis intertwine and unlock while passing through the seven chakras. Psychic knots of granthis are like protective blockages for the gradual change in awareness and open only with the purification of mind and balance between the two Nadi. The purpose of granthis is to block the sudden upward flow of prana, are like circuit breakers to protect the overload that may occur to the practitioner in case of a spontaneous ascension. The display of ‘granthis’ is associated with the ‘Trinity’ as the three main deities (Tri Murti).

They are visualized like psychic knots or obstacles on the path of the awakened kundalini, (The power of awareness) which is difficult to pass through for every human, as it brings about a change in personality. Each aspirant must transcend these barriers to make a clear passageway for the ascending kundalini. In tantra based sculptures, the two major components Nadi, Ida and Pingala of kundalini as are pictured in anthropomorphic form as male and female human figures and crisscross is indicated as in contact or the hand positioned in the specific region of chakra.

In sculptural representations of this topic, the figures, since it is related to mind, the core of ‘Chitta’, are usually presented in a nude form, as the bare body represents the unadorned form of mind. In symbolic representations, they are like male and female snakes coiling at three places. The psychic Knots of granthi is depicted in the symbolized form as the Shiva Linga symbol. Different temples use different motifs to convey this topic in sculptures. The two sculptural representations are:

  • Symbolic representation of granthi, through the Linga and snakes.
  • Representation of grant in the human body in a personified form.

Kundalini yoga, a classification under tantra yoga is the form of subtle energy that flows in tubular channels called Nadis towards the conductor. The conductor is nothing but the nerve energy in the physical body that is encased in the spinal canal and called Sushumna. The intersections are recognized as chakras, seven in number, where the two nadi crisscross. At every chakra, a perfect balance and harmony must be established between the two Ida, Pingala Nadi or otherwise the energy of kundalini cannot progress to higher levels in the central channel of Sushumna.

In sculptural representations of tantra yoga depictions, the mind was projected as the female deity and prana as the male deity. Some sculptures depict the two male and female figures to be in contact at three or five regions like the foot, knee, genital place (Muladhara), heart (Anahata) and the tip of the nose (that is connected to Ajna chakra). Some schools recognize the chakras to be sixteen starting from foot, knee, palm, and so on. The contact at the foot and knee is suggestive of the lower points from which the Ida and Pingala (Female and male Nadi) arise and proceed. The contact at the foot is suggestive of the initial phase of activating the Ida and Pingala Nadi.

To clear Brahma granthi is to establish in totality, clearing Vishnu granthi is perceiving the existence of universal life principle and to clear Rudra granthi is to attain a non-duality of realization of oneness and universal awareness.

granthi

Brahma Granthi

Brahma Granthi at Muladhara chakra is represented by the Dhumra Lingam. Dhum means smoky. The linga is represented smoky and ill-defined (some Lingas made of Sphatika – a crystalline form of quartz stone) as a Symbol of the physical world. It is also called Svayambhu linga- the self-created linga. It signifies the establishment of life principles in totality.

Brahma granthi functions in the base region of the Muladhara chakra at the genital area and hence a display of organs. It implies the entanglement with physical pleasures, material objects, and excessive selfishness or a sense of fear. It also implies the ensnaring power of tamas – negativity, lethargy, and ignorance. Such negative qualities act as hindrances and stop the serpent power kundalini from awakening. Once this blockage is removed from the energy instincts of the deep rootedness with worldly affairs, the realm of consciousness gets awakened and the trapped serpent power energy is released. The kundalini or primal energy is thus able to rise beyond Muladhara and Swadhisthana without bogged down by the attractions to which our consciousness is hooked. On breaking open the Brahma granthi, the practitioner feels relaxed and enjoys bliss arising from the void.

The figures related to the granthis are nude because they are related to the state of mind ‘Chitta’ and personal. Muladhara relates to, Ajna chakra as the starting and release points of prana, which is indicated in the sculptures as contact points. Muladhara has a direct link to Ajna chakra – situated in midbrain but indicated as above the nose, between the eyebrows. The subtle energy of these two Ida-Pingala currents crosses over to connect with the right and left hemispheres of the brain.

Brahma granthi is the manifest force of the energy of life and creation, depicted in sculptures as the pleasure of touch. It is known as blockage of Brahma because it holds the consciousness at the level related to physical dimensions like sensuality or procreation. Once this blockage is overcome, the consciousness of deep rootedness to worldly pleasures is released. The kundalini can rise above, crossing this knot.

Vishnu Granthi

Vishnu Granthi in Anahata chakra (between Manipura and Ajna chakra) is represented as Bana Linga. The linga is depicted red or gold-colored as a Symbol of the subtle world. Clearing Vishnu knot is to perceive the existence of universal life principles.

The contact at the chest is the second stage of awareness at Vishnu granthi – to detach from emotions related to bondage. Vishnu granthi operates in the region of the Anahata chakra in the heart region. It is associated with the bondage of emotional attachment and attachment to people and inner psychic visions. It relates to the qualities of rajas – the tendency towards passion, ambition, bondage and assertiveness, individual ego and power. Once the blockage at Vishnu granthi is removed, the practitioner feels great bliss. The sustenance energy undergoes a change from the localized centers of the physical level to the universal level which means the energies of the body become harmonious with the energies of the cosmos. The interaction between the individual personality and the cosmos begins to happen naturally & spontaneously, enhancing the quality of compassion.

The position of placement of chakra wheel as balls suggests that she is activating the Ida and Pingala in legs as well as in hand with the acupressure or chakra ball. It also gives a hint that opening out of Vishnu granthi is not a spontaneous act. It begins from the hand and leg Nadi, followed by the opening of Brahma granthi at Muladhara. In the right hand, as she is holding the ball, highlighting the thumb as the starting point of Nadi in hands. Activating the center of hands and feet is beneficial to health.

The freedom from the knotty – worldly problems and the freedom from knotty congestion in her meridians that restricts the flow of bioenergy at her mental and physical levels – are viewed as obstacles, the root cause for problems and indicated as the cloth around the breasts called ‘kanchuka’ with a knot. Philosophically, clearing the knot of kanchuka means liberation – freedom from ignorance, bondage, commitments due to obligations of bondage, power are the obstacles project as knotty problems in life. The aspirant is constantly advised to dissociate from all limitations and identify oneself with all the pervading, blissful, non-duality spirit of the Brahman.

Rudra Granthi

Rudra Granthi in Ajna chakra is called Itara or Itakhya Linga. The linga is black, well defined with a very consolidated outline. Here, in Ajna, the awareness of ‘what I am’ is more sharply defined and various capacities are being awakened. The Dhumra and Bana Linga are depicted in lotus petals and only Itara linga is well defined. It signifies a state of non-duality. Clearing of Rudra granthi promotes spiritual vision. Awareness goes at the transpersonal level with super consciousness.

The loving gaze was used as a simile in tantra based sculptures to explain the abstract concept that mind (female) and prana (male) are harmonizing and mind is coming under the control of prana, in other words, mind is one with the object concentrated upon enjoying supreme bliss and super consciousness called ‘samadhi’.

The third contact at nose tip is related to crossing the hurdle of Rudra granthi – restraining from the thoughts of pride that comes sometimes from service to others or as the knower of knowledge. The pride prevents one from uniting with all with a non-dual thought. The three granthis when crossed, open the doors of Sahasrara chakra promoting spiritual vision and super consciousness. The Ida Pingala Nadi first intersect at the base of the spine and ends at the third eye center indicated at the apex of the nose. At the third eye center, these two currents cross over to connect with the right and left hemispheres of the brain.

The nose of the two male and female figures touch to symbolize the revitalization of memory and concentration of intuitive knowledge or cognition. Physiologically, the nasal nerves of olfactory bulb travel directly to the limbic area of the brain which controls the unconscious intuition of memory and sexuality. It functions in the region of Ajna chakra governing the Ajna and Sahasrara chakras. It represents the transformation of an existing form, idea or concept into the universal aspect. It is associated with the attainment of siddhis, a psychic phenomenon but still attached to and the concept of self as the power. In a psychological perspective, though serving others is a completely satisfactory way to spend one’s life at this stage, this service could create resentment against others, and view them as lesser beings as the pride of acquiring knowledge sometimes gains an upper hand. One must surrender the sense of individual ego and transcend duality to make further spiritual progress and then complete the circle by bringing that consciousness into compassionate actions.

With awareness, yoga practitioners ascend towards the Sahasrara chakra where the final merging of the individual Soul or Atman with the universal cosmic soul takes place to achieve the realization of oneness.

Awakening of Kundalini Shakti

Rshi Patanjali said “it is very difficult to walk on this Yoga path (Kundalini) like walking in the eyes of a knife that is very sharp, wrong or slipped a little too wounded” also walked to meet Him like doing a masterpiece project, all obstacles and obstacles we must be able to overcome only with determination. , disciplined and diligent practice.

So far we leave Him to approach him is something that requires extra energy. The energy that drives the realization of the Yoga goal is Kundalini Energy. Energy is power, power, shakti, power or whatever the term all of this already exists within us and also outside ourselves. Enormous energy that lies dormant in the form of a 3.5-circle snake with his head facing down around Linga swayambhu Siwa.

If the Kundalini energy is able to be raised, this energy will push someone to reach his life goal or his Yoga goals. The increase in Kundalini’s energy will cleanse every chakra that is passed then activate the chakras and various Siddhas will be felt even though it is still only a moment. The increase in Kundalini will be very helpful, especially to increase self-awareness and the vitality of the body is also increased, for example, to help self-healing or even become a healer.

But what needs to be considered is not only the benefits that are very useful, but also how we deal with every problem caused by the rise in Kundalini. Because the increase in kundalini will clean and open the knot chakra because kundalini is only limited to energy so this energy will play just breaking down, so we need to know the knowledge and directing techniques so that nothing happens that is desired. Many spiritual aspirants have fallen ill because of Him without realizing that the cause is Kundalini (kundalini syndrome).

Everyone has this Energy hidden in our body. Kundalini energy is very large energy like nuclear energy in the body. It can be imagined how much energy is in our bodies if this energy we are able to generate. To generate Kundalini energy you need sufficient knowledge, especially regarding the Main Chakra. In addition to this knowledge, a guide who really knows about the awakening of Kundalini or a spiritual teacher is very much needed.

Kundalini is the mother who protects us, the mother of the universe is often referred to as Mrs. Durga (Hyang Nini Bagawati), Mrs. Gayatri and Mrs. Saraswati. To awaken this Sakti Energy there are various ways and with certain training.

If the awakening of Kundalini towards this negative direction will have unfavorable consequences, there are several things that are affected that can hurt the physical body, this can be really real or will change the nature, emotions, behavior, and others towards the negative.

Kundalini is more commonly interpreted as a scroll, a power is in “Kunda” which is a quadratic place or mandala (Muladhara chakra), encircling the “Linga” three half circles that are above the “Yoni” Kundalini in the form of a snake resides in the cakra Muladhara and in in Muladhara there is linga and yoni this is where Kundalini as a power of silence. Kundalini is also known by various names including Mrs. Durga, Mother at times, Mrs. Bhuta, Mother Universe, Mrs. Bagawati and so on, all Mother’s names are Himself. She is also referred to as Ibu Prana, the inner Power of the Mother or latent energy whatever the name refers to her. I offer my devotion to the Great Mother … Energy Mother …

The negative polarities will flow towards the positive polarity, and the positive polarity is in the fontanel in Sahasrara Cakra where the Supreme Lord is located. Passive Shiva who is silent but whose vibrations spread to meet nature. Single Shiva (Eka) and many (various) at the same time. Shiva who lives in Sahasrara means that the vibrations of his silence dwell in each person’s Sahasrara. He sits in his favorite siddhasana, he whose body is bright as the reflection of sunlight on a snow mountain, whose hair is neatly woven, which flows holy Ganga water, surrounded by beautiful crescent moons, wears snakes as His necklace, blue-necked, body covered with weed, His two hands lifted up to give blessings and deliver from all fears, adorned with tiger skins as His garments, who sat on a lotus of thousands of golden leaves, whose smiles emit vibrations of peace.

The awakening of the Kundalini energy flow is determined by our level of consciousness, or in other words, we process it, we are the controller.

The thing to consider is that energy is still energy, He will follow our own consciousness, follow our mindset if we think towards virtue

Purification of Karma through 3 Granthi

In each bulkhead, vertebrae are stored with positive and negative karma as long as humans life. Every action or result of mental karma will be placed according to the place that caused it.

For example karma as a result of:

  • Material things, rough emotions, supernatural powers, magic, etc. are stored at the bottom (Muladhara).
  • Desires, desires and low egos are stored in Swadistana.
  • Subtle emotions, dynamism, strength, etc. are stored in the central node of the Manipura chakra (Stomach).
  • Feelings, love, envy, sadness, happiness, will be stored in the heart’s central node (Anahata),
  • The ego is more subtle, including the highest ego that wants to reach God stored in the Wisudhi chakra.
  • Mental instability, ignorance, wisdom, weigh and decide right and wrong, good and bad, mental balance, are stored in Ajna before heading for Enlightenment (in the Sahasrara chakra), … etc … according to the causes of chakra activeness and its consequences.

The two way of Oneness and Karma Melting through this method (granthi) :

  1. From top  (Sahasrara chakra) heading down through Sushumna. The meeting was in the deepest depth of Ajna. While experiencing calm, it will release fluid from the pineal gland, producing a form of fluid / Tirta Amritha which then drips into Sushumna, penetrates and removes impurities in each segment.
    This method is considered safer, and the risk is minimal. Although safe, it does not mean without obstacles and mental obstacles that need to be overcome. The effect is cold and some even feel like ice water flowing in each segment to the lower end until it merges with the power of Kundalini (Shiva-Shakti).
  2. From bottom (Muladhara chakra) by awakening the power of Kundalini. This Kundalini fire breaks through and increases the burning of karma in each of its ascension paths until it experiences unification in Sahasrara (Shiva-Shakti).
    In every process of ascension ranging from the most subtle (the heat) to the magma fire, the perpetrator will experience many obstacles to significant changes in mental effects and the temptation to get siddhi.

Being aware of every moment of attitudes and mental changes or the like is very necessary to get to the next level, as well as efforts to unleash the power of the siddhis obtained. Giving up the siddhi that is obtained does not mean that it will disappear when the higher attainments all of the things below will also be followed and controlled (included).

Both unity from above and taking the road from the bottom produced “Amritha / Tirta Kundalini”. The effect of this will result in peace, calm, silence, towards Samadhi.

In Bali, this meaning is also poured into the song Wargasari Down the Tirta so sublime … etc. Where this is the way from above (Requesting) the union of Shiva and Durga / Shakti (Kundalini).

In Kanda pat he the power that results in the purification of Tirta seeps through the bamboo cavities, arteries and the like depending on the experience he sees,

This result is also a Tirta “wiping out” (negative melting) released through saliva (vaguely inserted in a glass of water for Tirta by some Balinese healers). While some possessed (kerauhan) he came out through a kind of mucus through the nose when possessed.

Untying the Knots That Bind Us

 

 

 

 

 

 

 

March, 2015

The Sanskrit word granthi means “knot” or “doubt” and also means “an especially difficult knot to untie.” People in India wearing a sari or dhoti cloth will form a small pouch to hold money, and close it by knotting the fabric – this tightly knotted purse is called a granthi. Granthi in spiritual practice are psychological or psychic barriers to total freedom. Granthi prevent prana from moving freely up sushumna nadi. Granthi bind the soul; they lock us to our misperception of reality (avidya) and self (asmita). They hold us to our preferences (raga and dvesha) and root us in fear of death (abhinivesha). Knowledge (jnana) is a key component to transcend fear, and together with action (karma) they give wings to our spiritual desires – the rise of Kundalini.

The hathayoga methods for untying these knots are the bandhas, or energy locks. By focusing the pranas in Sushumna Nadi the bandhas increase the potency of the rising Kundalini allowing us to transcend normal restrictions of thinking and acting.

Brahma Granthi is located at the base of the spine between Muladhara Chakraand Svadhisthana Chakra where primitive brain functioning like the “fight or flight reflexes” guarantee survival. Fear of death, anxiety about food, shelter or clothing, or general lack of grounding, all manifest as Brahma Granthi. When you experience fear in an asana like handstand or split, and the fear itself prevents success, this is Brahma Granthi. Lack of spare time can be part of this knot. When your bills and rent payment keep you at work and away from yoga, that is Brahma Granthi.

Mula (Root) Bandha is the first consolidation of Prana and Apana, piercing Brahma Granthi. Vitality, thought, breath, and speech are joined in pursuit of truth. This root lock can be applied all the time transforming every thing we do into a holy act.

Vishnu Granthi knots energy between Manipura Chakra and Anahata Chakra. This Granthi is a knot of individual ego and power. Our clinging to ego, self-cherishing and the quest for personal power can slow spiritual success. Fear of being ignored or of loosing prestige may plague our spiritual growth. This is a knot of power and manipulation, but it is also the knot of accumulation. Accumulation of power, possessions, and fame, all tie us to this level of consciousness. In order to transcend this level of consciousness we must “give up the love of power, for the power of love!” The degree of vulnerability that we show in life – the ability to put our façade aside and challenge our own status quo, unties Vishnu Granthi.

Uddiyana (Flying up) Bandha is the second consolidation of Prana, Apana, and Samana vayus.

Applied together with Mula Bandha, this lock pierces Vishnu Granthi. The individual is able to transcend individuality. The whole abdomen is drawn in and up – symbolizing the renunciation of accumulation and concentration of energy upward toward Anahata Chakra.

Rudra granthi is knotted between the Anahata and Ajña chakras. The attractiveness of heart centered action and the experience of serving others can distract the yogi who desires to “Be Love” – not just experience it. Serving others is a completely satisfactory way to spend your life, but this service could become your cross to bear, where you hold resentment against others, and view them as lesser beings. We must strive to transcend otherness and experience the “oneness of being” in the highest levels of consciousness, and then complete the circle by bringing that consciousness into our compassionate actions. When we are free from the illusion of otherness our actions emerge spontaneously from Love. Jalandhara Bandha enables this leap of consciousness.

The consummate consolidation of prana is Jalandhara Bandha (Cloud Catching Lock or Net Lock – for the network of nadis in the neck) when Prana, Apana, Samana and Udana vayu in Sushumna Nadi loosen Rudra Granthi, and the veil of separation is lifted.

Teaching Tips

  • The yoga practices reveal where we are stopped by granthi, psychological knots, and give us tools for negotiating and loosening those limitations. The granthi are pierced through asana, meditation, pranayama, samyama, virtuous acts, purification of diet, good intention, yama and niyama, mudra, and through nada techniques like chanting and mantra.
  • Practice each bandha separately.
    • Mula: This bandha can be applied while breathing and moving freely.
      The two parts of this lock are a) contraction of the interior of the perineal body on men, or the vaginal walls for women, and b) the area from the pubic bone to navel draws inward and upward slightly.
    • Uddiyana: The diaphragm moves toward the throat drawing the entire abdomen in and up. This lock is only practiced on exhale retention when breathing is not possible and movement is internalized.
    • Jalandhara: Can be applied after inhale or exhale, bringing chest to chin. The spine should stay relatively straight and the chin should rest in the cleft between the clavicle bones.
  • Teach all bandha applied simultaneously in Mahamudra. See Hathayogapradipika Chapter 3, Verses 10-13
  • Investigate the psychological barriers to freedom that are embodied in the granthi, from fear of death and anxiety about survival (Muladhara,) to the accumulation of power and prestige (Manipura,) to the “feel good” effect of helping others, rather than serving others (Anahata.)
  • Teach about the Pranamaya Kosha and it’s component vayus. Asana practice most directly affects the Pranamaya Kosha and consolidates the energy of consciousness into a force of enlightenment.

In Bhagavad Gita 7.1 there is a reference to granthi as doubt, and refuge of the Lord as freedom from that doubt. In Srimad-Bhagavatam 1.2.17-21, bhakti-yoga severs the granthi (hard knot) of material affection and enables one to come at once to the stage of asamsayam-samagram.

 

 

https://yogalinda.es/en/blog/the-bandhas-and-the-granthis/

The Bandhas and the Granthis

 

Bandhas are inner body locks that engage both the physical and the energetic body. They provide inner support during asana practice, stimulate the flow of prana and help to release the granthis, which can be understood as energy blockages or psychological knots.

By combining the action of opposing muscles, the bandhas can be activated. Their use during asana practice increases strength, stability and mental focus. Their use during pranayama intensifies its cleansing effect by directing agni or the internal fire to burn the waste matter that has settled and blocks the flow of energy.

Often referred to as locks, the bandhas help to balance two important energies within the body: the prana vayu and apana vayu. If prana is associated with drawing in that which nourishes us, apana is associated with letting go of that which is potentially toxic. Prana is connected to the inhalation and apana to the exhalation. The meeting of these two opposing energies at the base of the spine awakens the Kundalini energy.

There are three main bandhas: Jalandhara, Uddiyana and Mula bandha. Activating all three of these bandhas at the same time is referred to as Mahabandha or main lock.

The Bandhas

 

The Bandhas

Jalandhara Bandha: the throat lock. Jalandhara bandha can be applied by contracting the front muscles in the neck when tucking the chin towards the sternum. This bandha is naturally activated in some asanas like Sarvangasana (Shoulder Stand) or Halasa (Plough Pose). It is subtly activated during Ujjayi pranayama in which the glottis (the area where the vocal cords are located) is gently contracted.
This bandha focuses the mind on the fifth or throat chakra and contains the upward-flowing movement of prana past the throat. It also seals off the downward movement of “nectar” from the sahasrara or crown chakra, which is said to preserve youth and vitality.

Uddiyana Bandha: the abdominal lock. Uddiyana bandha is applied by contracting the upper abdominal muscles (just below the solar plexus). This bandha is naturally activated after each exhalation when the lungs are emptied and the diaphragm rises. During asana practice it is especially useful to apply this bandha to support the lumbar region in back bends. When used together with Mula bandha, it strengthens the abdominal muscles. While performing asanas it is not possible to fully engage this bandha as it would constrain breathing. This bandha focuses the mind on the third chakra and directs prana up towards the sixth chakra.

Mula Bandha: the root lock. Mula bandha is applied by contracting the pelvic floor and elevating the inner organs in this region like the bladder and genitals. Other groups of muscles, like the upper leg adductors (by slightly pressing the knees together), can intensify this bhanda. If engaged during asana practice it is said to “provide an extra lift, which is especially useful when jumping”. This bandha focuses the mind on the first chakra, and directs prana from the pelvic region upwards, providing energy to the whole body and stopping it from flowing downwards out of the body.

Activating the bandhas can also help to unblock the three granthisor knots that prevent prana from freely circulating within the Sushuma nadi. These knots can block the chakras and keep us tied to negative attitudes and emotions, preventing us from fully experiencing the richness of life.

The Granthi

The Granthi

 

The Bramha or Vital Granthi is associated with the first three chakras (root, sacrum and solar plexus). This granthi blocks us by feeding our attachment to physical comfort, material wealth and accumulation. It can be unblocked by activating Mula bhanda. To regulate the energy in these vital chakras and granthi, Patanjali recommends self discipline.

The Vishnu or Love Granthi is associated with the fourth and fifth chakras (heart and throat). This granthi blocks us by feeding our attachment to emotional excitement, self-centeredness and lack of receptivity to others’ needs. It can be unblocked by activating Uddyiana bandha. To boost the energy of the love chakras and granthi, Patanjali recommends devotion and commitment.

The Rudra or Light Granthi is associated with the last two chakras (third eye and crown of the head). This granthi blocks us by feeding our attachment to our opinions, prejudices, fantasies and intellectual pride. It can be unblocked by activating Jalandhara bandha. To dissolve pride and “dark” mental patterns, Patanjali recommends self-knowledge.

 

 

Please see my related posts

Knot Theory and Recursion: Louis H. Kauffman

Interconnected Pythagorean Triples using Central Squares Theory

The Great Chain of Being

Indra’s Net: On Interconnectedness

 

 

 

 

Key Sources of Resources

 

https://www.lifesloka.com/en/3-granthi-in-kundalini-yoga/

 

Untying the Knots That Bind Us

 

https://yogalinda.es/en/blog/the-bandhas-and-the-granthis/

Recursion, Incursion, and Hyper-incursion

Recursion, Incursion, and Hyper-incursion

 

How do Past and Future inform the present?

What happens in the Present is not only determined by the Past but also by the Future.  Karma and Destiny both play a role as to what is going on in your life Now.

Key Terms

  • Recursion
  • Incursion
  • Hyper Incursion
  • Discrete Processes
  • Cellular Automata
  • Fractal Machine
  • Hypersets
  • Interpenetration
  • Turing Machine
  • Symmetry
  • Non Well Founded Set Theory
  • Sets as Graphs
  • Leela
  • Predetermined Future
  • Bhagya
  • Fate
  • Destiny
  • Karma
  • Anticipation
  • Four Causes of Aristotle
  • Material Cause
  • Formal Cause
  • Efficient Cause
  • Final Cause
  • Left Computer
  • Right Computer
  • Parallel Computing
  • Fifth and the Fourth in Music Theory
  • Bicameral Brain
  • Hemispheric Division of Brain
  • One, Two, Three.  Where is the Fourth?

From GENERATION OF FRACTALS FROM INCURSIVE AUTOMATA, DIGITAL DIFFUSION AND WAVE EQUATION SYSTEMS

The recursion consists of the computation of the future value of the variable vector X(t+l) at time t+l from the values of these variables at present and/or past times, t, t-l, t-2 ….by a recursive function :

X (t+ 1) =f(X(t), X(t-1) …p..)

where p is a command parameter vector. So, the past always determines the future, the present being the separation line between the past and the future.

Starting from cellular automata, the concept of Fractal Machines was proposed in which composition rules were propagated along paths in the machine frame. The computation is based on what I called “INclusive reCURSION”, i.e. INCURSION (Dubois, 1992a- b). An incursive relation is defined by:

X(t+l) =f(…, X (t+l), X(t), X(t-1) ..p..).

which consists in the computation of the values of the vector X(t+l) at time t+l from the values X(t-i) at time t-i, i=1, 2 …. , the value X(t) at time t and the value X(t+j) at time t+j, j=l, 2, …. in function of a command vector p. This incursive relation is not trivial because future values of the variable vector at time steps t+l, t+2 …. must be known to compute them at the time step t+ 1.

In a similar way to that in which we define hyper recursion when each recursive step generates multiple solutions, I define HYPERINCURSION. Recursive computational transformations of such incursive relations are given in Dubois and Resconi (1992, 1993a-b).

I have decided to do this for three reasons. First, in relativity theory space and time are considered as a four-vector where time plays a role similar to space. If time t is replaced by space s in the above definition of incursion, we obtain

X(s+ l) =f( …, X(s+ 1), X(s), X (s-l) …p.).

and nobody is astonished: a Laplacean operator looks like this. Second, in control theory, the engineers control engineering systems by defining goals in the future to compute their present state, similarly to our haman anticipative behaviour (Dubois, 1996a-b). Third, I wanted to try to do a generalisation of the recursive and sequential Turing Machine in looking at space-time cellular automata where the order in which the computations are made is taken into account with an inclusive recursion.

We have already proposed some methods to realise the design of any discrete systems with an extension of the recursion by the concept of incursion and hyperincursion based on the Fractal Machine, a new type of Cellular Automata, where time plays a central role. In this framework, the design of the model of any discrete system is based on incursion relations where past, present and future states variables are mixed in such a way that they define an indivisible wholeness invariant. Most incursive relations can be transformed in different sets of recursive algorithms for computation. In the same way, the hyperincursion is an extension of the hyper recursion in which several different solutions can be generated at each time step. By the hyperincursion, the Fractal Machine could compute beyond the theoretical limits of the Turing Machine (Dubois and Resconi, 1993a-b). Holistic properties of the hyperincursion are related to the Golden Ratio with the Fibonacci Series and the Fractal Golden Matrix (Dubois and Resconi, 1992). An incursive method was developed for the inverse problem, the Newton- Raphson method and an application in robotics (Dubois and Resconi, 1995). Control by incursion was applied to feedback systems (Dubois and Resconi, 1994). Chaotic recursions can be synchronised by incursion (1993b). An incursive control of linear, non- linear and chaotic systems was proposed (Dubois, 1995a, Dubois and Resconi, 1994, 1995). The hyperincursive discrete Lotka-Voiterra equations have orbital stability and show the emergence of chaos (Dubois, 1992). By linearisation of this non-linear system, hyperincursive discrete harmonic oscillator equations give stable oscillations and discrete solutions (Dubois, 1995). A general theory of stability by incursion of discrete equations systems was developed with applications to the control of the numerical instabilities of the difference equations of the Lotka-Volterra differential equations as well as the control of the fractal chaos in the Pearl-Verhulst equation (Dubois and Resconi, 1995). The incursion harmonic oscillator shows eigenvalues and wave packet like in quantum mechanics. Backward and forward velocities are defined in this incursion harmonic oscillator. A connection is made between incursion and relativity as well as the electromagnetic field. The foundation of a hyperincursive discrete mechanics was proposed in relation to the quantum mechanics (Dubois and Resconi, 1993b, 1995).

This paper will present new developments and will show that the incursion and hyper-incursion could be a new tool of research and development for describing systems where the present state of such systems is also a function of their future states. The anticipatory property of incursion is an incremental final cause which could be related to the Aristotelian Final Cause.

Aristotle identified four explicit categories of causation: 1. Material cause; 2. Formal cause; 3. Efficient cause; 4. Final cause. Classically, it is considered that modem physics and mechanics only deal with efficient cause and biology with material cause. Robert Rosen (1986) gives another interpretation and asks why a certain Newtonian mechanical system is in the state (phase) Ix(t) (position), v(t) (velocity)]:

1. Aristotle’s “material cause” corresponds to the initial conditions of the system [x(0), v(0)] at time t=0.

2. The current cause at the present time is the set of constraints which convey to the system an “identity”, allowing it to go by recursion from the given initial phase to the latter phase, which corresponds to what Aristotle called formal cause.

3. What we call inputs or boundary conditions are the impressed forces by the environment, called efficient cause by Aristotle.

As pointed out by Robert Rosen, the first three of Aristotle’s causal categories are tacit in the Newtonian formalism: “the introduction of a notion of final cause into the Newtonian picture would amount to allowing a future state or future environment to affect change of state in the present, and this would be incompatible with the whole Newtonian picture. This is one of the main reasons that the concept of Aristotelian finality is considered incompatible with modern science.

In modern physics, Aristotelian ideas of causality are confused with determinism, which is quite different…. That is, determinism is merely a mathematical statement of functional dependence or linkage. As Russell points out, such mathematical relations, in themselves, carry no hint as to which of their variables are dependent and which are independent.”

The final cause could impress the present state of evolving systems, which seems a key phenomenon in biological systems so that the classical mathematical models are unable to explain many of these biological systems. An interesting analysis of the Final Causation was made by Emst von Glasersfeld (1990). The self-referential fractal machine shows that the hyperincursive field dealing with the final cause could be also very important in physical and computational systems. The concepts of incursion and hyper-incursion deal with an extension of the recursive processes for which future states can determine present states of evolving systems. Incursion is defined as invariant functional relations from which several recursive models with interacting variables can be constructed in terms of diverse physical structures (Dubois & Resconi, 1992, 1993b). Anticipation, viewed as an Aristotelian final cause, is of great importance to explain the dynamics of systems and the semantic information (Dubois, 1996a-b). Information is related to the meaning of data. It is important to note that what is usually called Information Theory is only a communication theory dealing with the communication of coded data in channels between a sender and a receptor without any reference to the semantic aspect of the messages. The meaning of the message can only be understood by the receiver if he has the same cultural reference as the sender of the message and even in this case, nobody can be sure that the receiver understands the message exactly as the sender. Because the message is only a sequential explanation of a non-communicable meaning of an idea in the mind of the sender which can be communicated to the receiver so that a certain meaning emerges in his mind. The meaning is relative or subjective in the sense that it depends on the experiential life or imagination of each of us. It is well- known that the semantic information of signs (like the coding of the signals for traffic) are the same for everybody (like having to stop at the red light at a cross roads) due to a collective agreement of their meaning in relation to actions. But the semantic information of an idea, for example, is more difficult to codify. This is perhaps the origin of creativity for which a meaning of something new emerges from a trial to find a meaning for something which has no a priori meaning or a void meaning.

Mind dynamics seems to be a parallel process and the way we express ideas by language is sequential. Is the sequential information the same as the parallel information? Let us explain this by considering the atoms or molecules in a liquid. We can calculate the average velocity of the particles from in two ways. The first way is to consider one particular particle and to measure its velocity during a certain time. One obtains its mean velocity which corresponds to the mean velocity of any particle of the liquid. The sec- ond way is to consider a certain number of particles at a given time and to measure the velocity of each of them. This mean velocity is equal to the first mean velocity. So there are two ways to obtain the same information. One by looking at one particular element along the time dimension and the other by looking at many elements at the same time. For me, explanation corresponds to the sequential measure and understanding to the parallel measure. Notice that ergodicity is only available with simple physical systems, so in general we can say that there are distortions between the sequential and the parallel view of any phenomenon. Perhaps the brain processes are based on ergodicity: the left hemisphere works in a sequential mode while the right hemisphere works in a parallel mode. The left brain explains while the right brain understands. The two brains arecomplementary and necessary.

Today computer science deals with the “left computer”. Fortunately, the informaticians have invented parallel computers which are based on complex multiplication of Turing Machines. It is now the time to reconsider the problem of looking at the “right computer”. Perhaps it will be an extension of the Fractal Machine (Dubois & Resconi, 1993a).

I think that the sequential way deals with the causality principle while the parallel way deals with a finality principle. There is a paradox: causality is related to the successive events in time while finality is related to a collection of events at a simultaneous time, i.e. out of time.Causality is related to recursive computations which give rise to the local generation of patterns in a synchronic way. Finality is related to incursive or hyperincursive symmetry invariance which gives rise to an indivisible wholeness, a holistic property in a diachronic way. Recursion (and Hyper recursion) is defined in the Sets Theory and Incursion (and Hyperincursion) could be defined in the new framework of the Hypersets Theory (Aczel, 1987; Barwise, Moss, 1991).

If the causality principle is rather well acknowledged, a finality principle is still controversial. It would be interesting to re-define these principles. Causality is defined for sequential events. If x(t) represents a variable at time t, a causal rule x(t+l) = f(x(t)) gives the successive states of the variable x at the successive time steps t, t+l, t+2, … from the recursive functionf(x(t)), starting with an initial state x(0) at time t=0. Defined like this, the system has no degrees of freedom: it is completely determined by the function and the initial condition. No new things can happen for such a system: the whole future is completely determined by its past. It is not an evolutionary system but a developmental system. If the system tends to a stable point, x(t+l) = x(t) and it remains in this state for ever. The variable x can represent a vector of states as a generalisation.

In the same way, I think that determinism is confused with predictability, in modern physics. The recent fractal and deterministic chaos theory (Mandeibrot, 1982; Peitgen, Jurgens, Saupe, 1992) is a step beyond classical concepts in physics. If the function is non-linear, chaotic behaviour can appear, what is called (deterministic) chaos. In this case, determinism does not give an accurate prediction of the future of the system from its initial conditions, what is called sensitivity to initial conditions. A chaotic system loses the memory of its past by finite computation. But it is important to point out that an average value, or bounds within which the variable can take its values, can be known;

it is only the precise values at the successive steps which are not predictable. The local information is unpredictable while the global symmetry is predictable. Chaos can presents a fractai geometry which shows a self-similarity of patterns at any scale.

A well-known fractal is the Sierpinski napkin. The self-similarity of pattems at any scale can be viewed as a symmetry invariance at any scale. An interesting property of such fractals is the fact that the final global pattern symmetry can be completely independent of the local pattern symmetry given as the initial condition of the process from which the fractal is built. The symmetry of the fractal structure, a final cause, can be independent of the initial conditions, a material cause. The formal cause is the local symmetry of the generator of the fractal, independently of its material elements and the efficient cause can be related to the recursive process to generate the fractal. In this particular fractal geometry, the final cause is identical to the final cause. The efficient cause is the making of the fractal and the material cause is just a substrate from which the fractal emerges but this substrate doesn’t play a role in the making.

Finally, the concepts of incursion and hyperincursion can be related to the theory of hypersets which are defined as sets containing themselves. This theory of hypersets is an alternative theory to the classical set theory which presents some problems as the in- completeness of G6del: a formal system cannot explain all about itself and some propositions cannot be demonstrated as true or false (undecidability). Fundamental entities of systems which are considered as ontological could be explain in a non-ontological way by self-referential systems.

Please see my related posts

On Anticipation: Going Beyond Forecasts and Scenarios

Autocatalysis, Autopoiesis and Relational Biology

Key sources of Research

 

Computing Anticipatory Systems with Incursion and Hyperincursion

Daniel M. DUBOIS

 

Click to access cd554835f0ae367c3d3e3fa40f3e5e5f5f11.pdf

 

 

 

Anticipation in Social Systems:

the Incursion and Communication of Meaning

Loet Leydesdorff 

Daniel M. Dubois

Click to access casys03.pdf

 

 

 

GENERATION OF FRACTALS FROM INCURSIVE AUTOMATA, DIGITAL DIFFUSION AND WAVE EQUATION SYSTEMS

Daniel M. Dubois

 

Click to access dubois.pdf

 

 

 

Non-wellfounded Set Theory

https://plato.stanford.edu/entries/nonwellfounded-set-theory/

Hypersets

  • Jon Barwise &
  • Larry Moss

https://link.springer.com/article/10.1007/BF03028340

Non-well-founded set theory

https://en.wikipedia.org/wiki/Non-well-founded_set_theory

Knot Theory and Recursion: Louis H. Kauffman

Knot Theory and Recursion: Louis H. Kauffman

 

Some knots are tied forever.

 

Key Terms

  • Louis H Kauffman
  • Heinz Von Foerster
  • George Spencer Brown
  • Francisco Varela
  • Charles Sanders Peirce
  • Recursion
  • Reflexivity
  • Knots
  • Laws of Form
  • Shape of Process
  • Trefoil Knots
  • Triplicity
  • Nonduality
  • Self Reference
  • Eigen Form
  • Form Dynamics
  • Recursive Forms
  • Knot Logic
  • Bio Logic
  • Distinctions
  • Topology
  • Topological Recursion
  • Ganth
  • Granthi – Brahma, Vishnu, Rudra
  • Chakra
  • Braids
  • Bandhu
  • Mitra
  • Vishvamitra
  • Friend
  • Relation
  • Sambandh
  • Love
  • True Love
  • Its a Knotty problem.

 

http://mathworld.wolfram.com/Knot.html

In mathematics, a knot is defined as a closed, non-self-intersecting curve that is embedded in three dimensions and cannot be untangled to produce a simple loop (i.e., the unknot). While in common usage, knots can be tied in string and rope such that one or more strands are left open on either side of the knot, the mathematical theory of knots terms an object of this type a “braid” rather than a knot. To a mathematician, an object is a knot only if its free ends are attached in some way so that the resulting structure consists of a single looped strand.

A knot can be generalized to a link, which is simply a knotted collection of one or more closed strands.

The study of knots and their properties is known as knot theory. Knot theorywas given its first impetus when Lord Kelvin proposed a theory that atoms were vortex loops, with different chemical elements consisting of different knotted configurations (Thompson 1867). P. G. Tait then cataloged possible knots by trial and error. Much progress has been made in the intervening years.

Schubert (1949) showed that every knot can be uniquely decomposed (up to the order in which the decomposition is performed) as a knot sum of a class of knots known as prime knots, which cannot themselves be further decomposed (Livingston 1993, p. 5; Adams 1994, pp. 8-9). Knots that can be so decomposed are then known as composite knots. The total number (prime plus composite) of distinct knots (treating mirror images as equivalent) having k=0, 1, … crossings are 1, 0, 0, 1, 1, 2, 5, 8, 25, … (OEIS A086825).

Klein proved that knots cannot exist in an even-dimensional space >=4. It has since been shown that a knot cannot exist in any dimension >=4. Two distinct knots cannot have the same knot complement (Gordon and Luecke 1989), but two links can! (Adams 1994, p. 261).

Knots are most commonly cataloged based on the minimum number of crossings present (the so-called link crossing number). Thistlethwaite has used Dowker notation to enumerate the number of prime knots of up to 13 crossings, and alternating knots up to 14 crossings. In this compilation, mirror images are counted as a single knot type. Hoste et al. (1998) subsequently tabulated all prime knots up to 16 crossings. Hoste and Weeks subsequently began compiling a list of 17-crossing prime knots (Hoste et al. 1998).

Another possible representation for knots uses the braid group. A knot with n+1 crossings is a member of the braid group n.

There is no general algorithm to determine if a tangled curve is a knot or if two given knots are interlocked. Haken (1961) and Hemion (1979) have given algorithms for rigorously determining if two knots are equivalent, but they are too complex to apply even in simple cases (Hoste et al. 1998).

 

LH Kauffman with Trefoil Knot in the back.

LH Kauffman

 

From Reflexivity

A Knot

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Trefoil Knot

Tricoloring

 

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From Reflexivity

This slide show has been only an introduction to certain mathematical and conceptual points of view about reflexivity.

In the worlds of scientific, political and economic action these principles come into play in the way structures rise and fall in the play of realities that are created from (almost) nothing by the participants in their desire to profit, have power or even just to have clarity and understanding. Beneath the remarkable and unpredictable structures that arise from such interplay is a lambent simplicity to which we may return, as to the source of the world.

 

From Laws of Form and the Logic of Non-Duality

This talk will trace how a mathematics of distinction arises directly from the process of discrimination and how that language, understood rightly as an opportunity to join as well as to divide, can aid in the movement between duality and non-duality that is our heritage as human beings on this planet.The purpose of this talk is to express this language and invite your participation in it and to present the possiblity that all our resources physical, scientific, logical, intellectual, empathic are our allies in the journey to transcend separation.

From Laws of Form and the Logic of Non-Duality

True Love.  It is a knotty problem.

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Wikipedia on Knot Theory

Tabela_de_nós_matemáticos_01,_crop

 

 

Please see my related posts:

Reflexivity, Recursion, and Self Reference

Jay W. Forrester and System Dynamics

Steps to an Ecology of Mind: Recursive Vision of Gregory Bateson

Second Order Cybernetics of Heinz Von Foerster

Cybernetics Group: A Brief History of American Cybernetics

Cybernetics, Autopoiesis, and Social Systems Theory

Cyber-Semiotics: Why Information is not enough

Ratio Club: A Brief History of British Cyberneticians

Autocatalysis, Autopoiesis and Relational Biology

Feedback Thought in Economics and Finance

Increasing Returns and Path Dependence in Economics

Boundaries and Distinctions

Boundaries and Relational Sociology

Boundaries and Networks

Socio-Cybernetics and Constructivist Approaches

Society as Communication: Social Systems Theory of Niklas Luhmann

Semiotics, Bio-Semiotics and Cyber Semiotics

Meta Integral Theories: Integral Theory, Critical Realism, and Complex Thought

Networks and Hierarchies

 

Key Sources of Research:

 

Home Page of Louis H. Kauffman

http://homepages.math.uic.edu/~kauffman/

Recursive Distinctioning

By Joel Isaacson and Louis H. Kauffman

 

Click to access JSP-Spr-2016-8_Kauffman-Isaacson-Final-v2.pdf

 

 

Knot Logic – Logical Connection and Topological Connection

by Louis H. Kauffman

Click to access 1508.06028.pdf

 

 

KNOTS

by Louis H. Kauffman

 

Click to access KNOTS.pdf

 

 

 

BioLogic

Louis H. Kaufman, UIC

Click to access BioL.pdf

New Invariants in the Theory of Knots

Louis H. Kaufman, UIC

https://www.researchgate.net/publication/238648076_New_Invariants_in_the_Theory_of_Knots

 

 

 

Eigenform – An Introduction

by Louis H. Kauffman

Click to access 2007_813_Kauffman.pdf

 

 

Knot Logic and Topological Quantum Computing with Majorana Fermions

Louis H. Kauffman

 

Click to access arXiv%3A1301.6214.pdf

 

 

Reflexivity

by Louis H. Kauffman

Click to access videoLKss-slides.pdf

 

 

 

Eigenforms, Discrete Processes and Quantum Processes

Louis H Kauffman 2012 J. Phys.: Conf. Ser. 361 012034

https://iopscience.iop.org/article/10.1088/1742-6596/361/1/012034/pdf

 

 

 

Eigenforms — Objects as Tokens for Eigenbehaviors

by Louis H. Kauffman

Click to access 1817.pdf

 

 

 

Reflexivity and Eigenform The Shape of Process

Louis H. Kauffman A University of

 

Click to access ReflexPublished.pdf

 

 

 

FORMAL SYSTEMS

EigenForm

Louis H. Kauffman

 

Click to access Eigen.pdf

 

 

 

EigenForm

Louis H. Kauffman UIC, Chicago

 

Click to access Eigenform.pdf

 

 

Form Dynamics

Click to access FormDynamics.pdf

 

 

Arithmetics in the Form

Click to access ArithForm.pdf

 

 

 

Self Reference and Recursive Forms

Click to access SelfRefRecurForm.pdf

Click to access Relativity.pdf

 

 

 

Laws of Form and the Logic of Non-Duality

Louis H. Kauffman, UIC

 

Click to access KauffSAND.pdf

 

 

 

Laws of Form – An Exploration in Mathematics and Foundations

by Louis H. Kauffman UIC

 

Click to access Laws.pdf

 

 

 

The Mathematics of Charles Sanders Peirce

Louis H. Kauffman1

 

Click to access Peirce.pdf

 

 

 

A Recursive Approach to the Kauffman Bracket

Abdul Rauf Nizami, Mobeen Munir, Umer Saleem, Ansa Ramzan

Division of Science and Technology, University of Education, Lahore, Pakistan

https://www.scirp.org/html/11-7402327_50601.htm

 

Law of Dependent Origination

Law of Dependent Origination

 

Linear Causality – Independent Variables – Regression Analysis

Mutual Causality – Feedbacks – Dynamic Modeling – Systems Dynamics – Non Linear Sys – Circular Causality – Reciprocity.

Connected – No Boundaries – Interconnectedness – Entanglements – Action at a distance

 

 

Key Terms

  • Codependent Origination
  • Interdependent Origination
  • Interconnectedness
  • Mutual Causality
  • Linear Causality
  • Cause and Effect
  • Joanna Macy
  • Paticca Samuppada
  • Pratitya Samutpada
  • Dependent Co-arising
  • Buddhism
  • Theravada Buddhism
  • Mahayana Buddhism
  • Indira’s Net
  • Great Chain of Being
  • Four Noble Truths
  • Twelve Nidanas
  • Eightfold Path

 

 

Screen Shot 2020-01-02 at 8.01.43 AM

 

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https://www.loudzen.com/skydancer/essays/macyonps.html

Paticca Samuppada : Dependent Co-arising

Joanna Macy, in World As Lover, World As Self , made this concept clear to me. It’s not a common idea in Western religious talk, because it makes a divine Authority unnecessary for a moral imperative. She comes to it from systems theory, where it does have a Western parallel.

From page 54, here’s a taste:

According to Western religious thought, ethical values derive from divine commandment. A supernatural source is necessary to provide moral sanction. Without the ontological security of belief in an absolute, everything seems awash, with no clear guidelines, and it’s every man for himself. This assumption is so pervasive in the West that many noted scholars judged Buddhism’s moral teachings to be weak, since they do not issue from belief in any God. It is true that the Way the Buddha taught is freed from the necessity to believe in any supernatural authority. Indeed when he was asked by what authority he spoke, he cited again and again the law of dependent co-arising; not any entity ruling our world, but the dynamics at work within our world. He cited the interdependence of all phenomena. What did he mean by that? How can radical relativity serve as a moral grounding?

Her answer to that question, a description of the vigil under the Bodhi tree, takes too much space to quote at length here, but it begins (p. 540) with…

With fascination I studied the early Buddhist texts. I read how the perception of paticca samuppada dawned on the Buddha the night of his enlightenment, and featured in his discourses. I saw how it underlay everything he taught about self, suffering, and liberation from suffering. I noted how it knocked down the dichotomies bred by hierarchical thinking, the old polarities between mind and matter, self and world, that had exasperated me as a spiritual seeker and activist, and as a woman.

…and includes, on p. 56...

Tracing thus the sources of suffering, he did not find a first cause or prime mover, but beheld instead patterns or circuits of contingency. The factors were sustained by their own interdependence.

…and on p. 58…

According to this apparently simple set of assertions, things do not produce each other or make each other happen, as in linear causality; they help each other happen by providing occasion or locus or context, and in so doing, they in turn are affected. There is a mutuality here, a reciprocal dynamic.

I left out the narrative parts and the quotations from original sources. The argument hangs together better with them, and is more interesting. When I read it I felt I’d been given a great gift: how to understand morality as implicit in the basic nature of the universe, without pinning it on divinity. Instead of being subject to a top-down authority structure, we participate in an interdependent web of being Ñ which enfolds us, dancing with the endless exchange of energy which is our dependent co-arising, our giving and receiving of the life force, of compassion and service, of the dharma.

25 November 1998

 

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Click to access Dependent+Origination-Macy.pdf

Dependent Co-Arising

Joanna Macy

When the Buddha taught, he was said to turn the Wheel of the Dharma. Indeed, his central doctrine is like a wheel, for through it he taught the dependent co-arising of all things, how they continually change and condition each other in interconnections as real as the spokes in a wheel.

I have been deeply inspired by the Buddha’s teaching of dependent co-arising. It fills me with a sense of connection and mutual responsibility with all beings. Helping me understand the non- hierarchical and self-organizing nature of life, it is the philosophic grounding of all my work.

The recognition of our essential nonseparateness from the world, beyond the shaky walls erected of our fear and greed, is a Dharma gift occurring in every generation, in countless individual lives. Yet there are historical moments when this perspective arises in a more collective fashion and when, within Buddhism as a whole (if we can even talk of “Buddhism as a whole”!), there is a fresh reappropriation of the Buddha’s central teaching. This seems to be occurring today. Along with the destructive, even suicidal nature of many of our public policies, social and intellectual developments are converging now to bring into bold relief the Buddha’s teaching of dependent co-arising–and the wheel of the Dharma turns again.

This is happening in many ways. I see it in the return to the social teachings of the Buddha, in the revitalization of the bodhisattva ideal, in the rapid spread of “engaged Buddhism,” be it among Sarvodayans in Sri Lanka, Ambedkarite Buddhists in India, or Dharma activists in Tibet, Thailand, or Southeast Asia. Western Buddhists, too, are taking Dharma practice out into the world, developing skillful means for embodying compassion as they take action to serve the homeless, restore creekbeds, or block weapons shipments. The vitality of Buddhism today is most clearly reflected in the way it is being brought to bear on social, economic, political, and environmental issues, leading people to become effective agents of change. The gate of the Dharma does not close behind us to secure us in a cloistered existence aloof from the turbulence and suffering of samsara, so much as it leads us out into a life of risk for the sake of all beings. As many Dharma brothers and sisters discover today, the world is our cloister.

Here new hands and minds, aware of the suffering caused by outmoded ways of thinking and dysfunctional power structures, help turn the wheel. Strong convergences are at play here, as Buddhist thought and practice interact with the organizing values of the Green movement, with Gandhian nonviolence, and humanistic psychology, with ecofeminism, and sustainable economics, with systems theory, deep ecology, and new paradigm science.

In his teaching of Interbeing, Vietnamese Zen master Thich Nhat Hanh captures the flavor of this turning. Not only does he model the many bodhisattva roles one life can play–scholar, activist, teacher, poet, meditator, and mediator; he opens as well through the concept and practice of Interbeing a wide gate into the Buddha’s doctrine of dependent co-arising.

Now we see that everything we do impinges on all beings. The way you are with your child is a political act, and the products you buy and your efforts to recycle are part of it too. So is meditation–just trying to stay aware is a task of tremendous importance. We are trying to be present to ourselves and each other) in a way that can save our planet. Saving life on this planet includes developing a strong, caring connection with future generations; for, in the Dharma of co-arising, we are here to sustain one another over great distances of space and time.

The Dharma wheel, as it turns now, also tells us this: that we don’t have to invent or construct our connections. They already exist. We already and indissolubly belong to each other, for this is the nature of life. So, even in our haste and hurry and occasional discouragement, we belong to each other. We can rest in that knowing, and stop and breathe, and let that breath connect us with the still center of the turning wheel.

Wikipedia on Pratitya Samutpada

Interdependence

Hua Yen school

The Huayan school taught the doctrine of the mutual containment and interpenetration of all phenomena, as expressed in Indra’s net. One thing contains all other existing things, and all existing things contain that one thing. This philosophy is based in the tradition of the great Madhyamaka scholar Nagarjuna and, more specifically, on the Avatamsaka Sutra. Regarded by D.T. Suzuki as the crowning achievement of Buddhist philosophy, the Avatamsaka Sutra elaborates in great detail on the principal of dependent origination. This sutra describes a cosmos of infinite realms upon realms, mutually containing one another.

Thich Nhat Hanh

Thich Nhat Hanh states, “Pratitya samutpada is sometimes called the teaching of cause and effect, but that can be misleading, because we usually think of cause and effect as separate entities, with cause always preceding effect, and one cause leading to one effect. According to the teaching of Interdependent Co-Arising, cause and effect co-arise (samutpada) and everything is a result of multiple causes and conditions… In the sutras, this image is given: “Three cut reeds can stand only by leaning on one another. If you take one away, the other two will fall.” In Buddhist texts, one cause is never enough to bring about an effect. A cause must, at the same time, be an effect, and every effect must also be the cause of something else. This is the basis, states Hanh, for the idea that there is no first and only cause, something that does not itself need a cause.[34]

Tibetan Buddhism

Sogyal Rinpoche states all things, when seen and understood in their true relation, are not independent but interdependent with all other things. A tree, for example, cannot be isolated from anything else. It has no independent existence, states Rinpoche.[130]

 

https://en.wikipedia.org/wiki/Joanna_Macy

Joanna Macy

Joanna Rogers Macy (born May 2, 1929), is an environmental activist, author, scholar of Buddhism, general systems theory, and deep ecology. She is the author of eight books.[1]

Contents

  • 1 Biography
  • 2 Key Influences
  • 3 Work
  • 4 Writings
  • 5 See also
  • 6 References
  • 7 External links

Biography

Macy graduated from Wellesley College in 1950 and received her Ph.D in Religious Studies in 1978 from Syracuse University, Syracuse. She studied there with Huston Smith, the influential author of The World’s Religions(previously entitled The Religions of Man). She is an international spokesperson for anti-nuclear causes, peace, justice, and environmentalism,[1]most renowned for her book Coming Back to Life: Practices to Reconnect Our Lives, Our World and the Great Turning initiative, which deals with the transformation from, as she terms it, an industrial growth society to what she considers to be a more sustainable civilization. She has created a theoretical framework for personal and social change, and a workshop methodology for its application. Her work addresses psychological and spiritual issues, Buddhist thought, and contemporary science. She was married to the late Francis Underhill Macy, the activist and Russian scholar who founded the Center for Safe Energy.[citation needed]

Key Influences

Macy first encountered Buddhism in 1965 while working with Tibetan refugees in northern India, particularly the Ven. 8th Khamtrul Rinpoche, Sister Karma Khechog Palmo, Ven. Dugu Choegyal Rinpoche, and Tokden Antrim of the Tashi Jong community. Her spiritual practice is drawn from the Theravada tradition of Nyanaponika Thera and Rev. Sivali of Sri Lanka, Munindraji of West Bengal, and Dhiravamsa of Thailand.

Key formative influences to her teaching in the field of the connection to living systems theory have been Ervin Laszlo who introduced her to systems theory through his writings (especially Introduction to Systems Philosophy and Systems, Structure and Experience), and who worked with her as advisor on her doctoral dissertation (later adapted as Mutual Causality) and on a project for the Club of Rome. Gregory Bateson, through his Steps to an Ecology of Mindand in a summer seminar, also shaped her thought, as did the writings of Ludwig von Bertalanffy, Arthur Koestler, and Hazel Henderson. She was influenced in the studies of biological systems by Tyrone Cashman, and economic systems by Kenneth Boulding. Donella Meadows provided insights on the planetary consequences of runaway systems, and Elisabet Sahtourisprovided further information about self-organizing systems in evolutionary perspective.

Work

Macy travels giving lectures, workshops, and trainings internationally. Her work, originally called “Despair and Empowerment Work” was acknowledged as being part of the deep ecology tradition after she encountered the work of Arne Naess and John Seed [2], but as a result of disillusion with academic disputes in the field, she now calls it “the Work that Reconnects”. Widowed by the death of her husband, Francis Underhill Macy, in January 2009, she lives in Berkeley, California, near her children and grandchildren. She serves as adjunct professor to three graduate schools in the San Francisco Bay Area: the Starr King School for the Ministry, the University of Creation Spirituality, and the California Institute of Integral Studies.[cit

Writings

See also

  • David Korten, a collaborator with Macy on the Great Turning Initiative

References

External links

 

 

Please see my related posts:

Indra’s Net: On Interconnectedness

On Synchronicity

Key Sources of Research:

 

Dependent Origination: The Twelve Links Explained

 

Dependent Origination: The Twelve Links Explained

 

 

 

The Co-arising of Self and Object, World, and Society:

Buddhist and Scientific Approaches

William S. Waldron

Middlebury College

Click to access waldron_co-arising_of_mind_and_world0.pdf

 

 

 

Dependent Origination and the Buddhist Theory of Relativity

By Kottegoda S. Warnasuriya

Click to access 134f4e6d2088df76fb7cf033299efb3cf27a1058.pdf

 

 

 

Lama Tsongkhapa’s In Praise of Dependent Origination

 

Click to access The-Full-Commentary-In-Praise-of-Dependent-Origination-Final.pdf

 

 

 

The Significance of Dependent Origination in Theravada Buddhism

Nyanatiloka Mahāthera

Click to access wh140.pdf

Click to access the_significance_of_dependent_origination__nyantiloka_mahathera.pdf

 

 

 

Nagarjuna’s Seventy Stanzas: A Buddhist Psychology ofEmptiness

David Ross Komito

Translation and commentary on the Seventy Stanzas on Emptiness by Venerable Geshe Sonam Rinchen, Venerable Tenzin Dorjee, and David Ross Komito.

 

Click to access nagarjuna_seventy-stanzas.pdf

 

 

 

Chapter XXIV

Examination of the Four Noble Truths

 

Click to access nagarjuna_middleway24.pdf

 

 

 

From Grasping to Emptiness – Excursions into the Thought-world of the Pāli Discourses (2)

Click to access from-grasping.pdf

 

The Doctrine of Dependent Origination as Basis for a Paradigm of Human-Nature Relationship of Responsibility and Accountability

https://www.researchgate.net/publication/321076086_The_Doctrine_of_Dependent_Origination_as_Basis_for_a_Paradigm_of_Human-Nature_Relationship_of_Responsibility_and_Accountability

 Joanna Macy, Buddhism and Power for Social Change

Caiti Schroering

 

https://digitalcommons.denison.edu/cgi/viewcontent.cgi?article=1065&context=religion

 

Paticca Samuppada : Dependent Co-arising

 

https://www.loudzen.com/skydancer/essays/macyonps.html

Wikipedia on Pratitya Samutpada

 

https://en.wikipedia.org/wiki/Pratītyasamutpāda

Mutual Causality in Buddhism and General Systems Theory
The Dharma of Natural Systems

By Joanna Macy

https://www.sunypress.edu/p-1176-mutual-causality-in-buddhism-an.aspx

 

 

 

Dependent Co-Arising

Joanna Macy

 

Click to access Dependent+Origination-Macy.pdf

 

 

 

A brief history of Interdependence.

 

Click to access 10McMahan.pdf

 

 

 

Beyond Nature\Nurture Buddhism and Biology on Interdependence

W.S. Waldron. Middlebury College

 

Click to access waldron_beyondnaturenuture0.pdf

 

 

 

 World as Lover, World as Self

Courage for Global Justice and Ecological Renewal

By Joanna Macy · 2007

 

Toward a Buddhist Systems Methodology 1: Comparisons between Buddhism and Systems Theory

Systemic Practice and Action Research

 

Considering Causality

Click to access 52247.pdf

 

Indira’s Net

 

On Synchronicity

On Synchronicity

There are invisible ties between us.

 

Click to access Synchronicity2010.pdf

Causality has to do with events that happen in sequence, a cause producing an effect, whereas synchronicity has to do with events that happen together.

Synchronicism is the prejudice of the East, causality is the modern prejudice of the West.  – Carl Jung, 1929

 

 

Key Terms

  • Synchronicity
  • Serendipity
  • Interconnected Universe
  • Quantum Entanglements
  • Fractal Universe
  • Recursive Universe
  • Platonic Solids
  • Carl G Jung
  • Events in Sequence
  • Events in Parallel
  • Space Structure
  • Ether
  • Geometry of space
  • Complex Numbers
  • Shri Yantra Geometry
  • Mind and Matter
  • Brain and Mind
  • Parapsychology
  • Occult
  • Esoteric

 

https://coincider.com/about-coincidences/history/ 

History

The history of coincidence studies can be told through the stories of thefour people who coined words for the types of coincidences they noticed in their lives. The most famous is Carl Jung and synchronicity, but he was not the first.

Serendipity: Horace Walpole (1717-1797)

Horace_Walpole_by_John_Giles_Eccardt

Horace Walpole, a member of the British House of Commons in the 18th century, recognized in himself a talent for finding what he needed just when he needed it.A gift in the form of a portrait of a Grand Duchess whom Walpole had long admired arrived from his distant cousin in Florence, Italy. Walpole needed a coat of arms to decorate the new picture frame and just happened to find it an old book. On January 28, 1754, Walpole, thrilled with this coincidence, wrote to his cousin Horace, giving a name to his ability to find things unexpectedly—serendipity.

He got the name from a fairy tale called “The Travels and Adventures of Three Princes of Sarendip.” Sarendip (or Serendib) is an ancient name for the island nation Sri Lanka off India’s southern coast. The king of the fable recognized that education requires more than learning from books, so he sent his sons out of the country to broaden their experience. Throughout the story, the clever princes carefully observed their surroundings, and then used their observations in ways that saved them from danger and death.

For Walpole, serendipity meant finding something by informed observation (sagacity as he called it) and by accident. The main ingredients of serendipity include luck, chance, active searching, and informed observation.

Seriality: Paul Kammerer (1880-1926)

PaulKammerer

Biologist Paul Kammerer spent hours sitting on benches in various public parks in Vienna noting repetitions among the people who passed by. He classified them by sex, age, dress, whether they carried umbrellas or parcels, and by many other details. He did the same during the long train rides from his home to his office in Vienna. Kammerer was not particularly interested in meaning—only repeated sequences of numbers, names, words, and letters. Two examples can illustrate his thinking: His wife was in a waiting room reading about a painter named Schwalbach when a patient named Mrs. Schwalbach was called into the consultation room.A second example involved his friend Prince Rohan. On the train his wife was reading a novel with a character “Mrs. Rohan.” She then saw a man get on the train who looked like Prince Rohan. Later that night the Prince himself unexpectedly dropped by their house for a visit.

He defined “seriality” as “a recurrence of the same or similar things or events in time and space” which, “are not connected by the same acting cause.”  To him these repetitions were simply natural phenomena.

Kammerer thought these similarities were part of the structure of natural law, and in his 1919 book Das Gesetz Der Serie outlined what he thought these laws to be along with a broad set of classifications of their types and qualities.

Synchronicity: Carl Jung (1875-1961)

Psychologist Carl G. Jung

Carl Jung grew up in Swiss family that, on his mother’s side, embraced the paranormal. His personal experiences included apparitions (the disembodied figure of another person) and poltergeists (troublesome ghosts), spiritualistic communications (communication with people after their deaths), and materializations (creation of matter from unknown sources). His experiences also included telepathic, clairvoyant, and precognitive dreams, prophetic visions, psychokinetic events, and out-of-body and near-death experiences.

He invented the word synchronicity from the Greek syn—with, together—andchronos—time. Synchronicity means moving-together-in-time. Its fundamental characteristic is the surprise that occurs when a thought in the mind is mirrored by an external event to which it has no apparent causal connection. He also used the word synchronicity to refer to “an acausal connecting principle” that he placed on equal status with causation.

He included many strange events under the synchronicity umbrella including telepathy, precognition, and clairvoyance, along with poltergeists, apparitions, divination (e.g. the I Ching), and astrology. The definition of synchronicity has been stretched in many different directions.

Simulpathity: Bernard Beitman (1942–) Founder of Coincidence Studies

BernardBeitman

The term “simulpathity” defines a specific subclass of meaningful coincidences: the simultaneous experience at a distance by one person of another person’s distress. The experience occurs without the two people being together in the same place and sometimes without conscious awareness of its source. One person is in pain and another person feels distress for no apparent reason. Sometimes the distress is very similar to the other person’s pain. Often, the two people share a strong emotional bond. The largest number of simulpathity reports comes from twins, although reports involving mothers and their children are also prominent.

Simulpathity suggests that the individuals are more closely bonded than current scientific thought holds possible.

Simulpathity — from the Latin simul (simultaneous) and the Greek pathos (suffering) — differs from “sympathy.” The sympathetic person is aware of the suffering of the other but does not usually feel it. In the experience of simulpathity, one person suffers along with the other person and can experiences some form of that suffering. Only later is the simultaneity of the distress recognized, although some twins know just why they are feeling pain—the other twin is now feeling it.

Please see my related posts:

Interconnected Pythagorean Triples using Central Squares Theory

Indra’s Net: On Interconnectedness

The Great Chain of Being

On Holons and Holarchy

Mind, Consciousness and Quantum Entanglement

Geometry of Consciousness

Systems View of Life: A Synthesis by Fritjof Capra

Consciousness of Cosmos: A Fractal, Recursive, Holographic Universe

Myth of Invariance: Sound, Music, and Recurrent Events and Structures

Shape of the Universe

Reflexivity, Recursion, and Self Reference

Key Sources of Research

 

Synchronicity: Nature and Psyche in an Interconnected Universe

·
Joseph Cambray

https://www.researchgate.net/publication/26905461_Synchronicity_Nature_and_Psyche_in_an_Interconnected_Universe

 

 

Synchronicity and Healing

BERNARD D. BEITMAN, ELIF CELEBI, AND STEPHANIE L. COLEMAN

 

Click to access 18-Beitman-Chap18.pdf

 

 

 

SYNCHRONICITY
An Acausal Connecting Principle

CG Jung

https://archive.org/details/223463118SYNCHRONICITYAnAcausalConnectingPrincipleJung

 

 

 

CHANGING VIEWS OF SYNCHRONICITY-
FROM CARL JUNG TO ROBERT PERRY

Christopher Jargodzki

 

Click to access Synchronicity2010.pdf

Synchronicity, Mind, and Matter

Wlodzislaw Duch

 

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.79.8651&rep=rep1&type=pdf

 

 

 

Synchronicity: did Jung have it right?

Kurt Forrer

 

Click to access bb26804cdc465b355e2f2e09c574d50dc4bb.pdf

 

 

 

C.G. Jung’s Synchronicity and Quantum Entanglement:  Schrodinger’s Cat ‘Wanders’ Between Chromosomes

 

Click to access Limar.Synchronicity.pdf

Synchronicity: The Bridge Between Matter and Mind

F. David Peat
Bantam Books (1987)

Emotions Over Time: Synchronicity and Development of Subjective, Physiological, and Facial Affective Reactions to Music

C. G. Jung’s Psychology of Religion and Synchronicity

By Robert Aziz

Jung on Synchronicity and the Paranormal

By Carl Gustav Jung

 

 

Synchronicity and Emergence

JOSEPH CAMBRAY

Click to access Cambray.pdf

Jung, synchronicity, & human destiny: Noncausal dimensions of human experience.

Synchronicity: Science, Myth, and the Trickster

Allan Combs
Marlowe & Co. (1996)

Synchronicity, Science and Soul-Making: Understanding Jungian Synchronicity …

By Victor Mansfield

Synchronicity: Nature and Psyche in an Interconnected Universe

By Joseph Cambray

Rituals | Recursion | Mantras | Meaning : Language and Recursion

Rituals | Recursion | Mantras | Meaning : Language and Recursion

 

Key Terms

  • Rituals
  • Recursion
  • Mantras
  • Japa
  • Puja
  • Prayer
  • Psychological Development
  • Meaning
  • Meditation
  • Yoga
  • Vedas
  • Tantra
  • Hindu Vedic Rituals
  • Hindu Tantric Rituals
  • Language and Recursion
  • Speech
  • Communication
  • Organizing principle
  • Cognitive science
  • Linguistics
  • Panini
  • Pingala
  • Sanskrit
  • Act of walking and Talking
  • Take a walk
  • Vedic Meters
  • Gayatri Mantra
  • Grammer
  • Panini’s Asthadhyayi
  • Univarsal Grammer
  • Noam Chomsky
  • Frits Staal
  • Subhash Kak
  • Word and World
  • Structure of a Mantra
  • Structure of a Ritual
  • Prose and Poetry
  • Gadya and Padya
  • Fractals
  • Holarchy
  • Holons

Why Language and Thought Resemble Russian Dolls

Michael Corballis is a professor emeritus at the University of Auckland, who has written extensively on the evolution of language and the origins of thought.

 

Michael Corballis is a professor emeritus at the University of Auckland, who has written extensively on the evolution of language and the origins of thought. In his 2011 book The Recursive Mind, he wrote about how the structure of human language allows for recursion—in which ideas are nested within each other: “He thinks that I think that he thinks.” Recursion allows the construction of sentences of of theoretically unlimited complexity

The main argument of The Recursive Mind is that recursion applies to thought processes and actions that are not limited to language itself, but characterize other aspects of human thought, such as our ability to imagine ourselves in the past or future. I queried Corballis on some of these ideas. An edited transcript follows:

You wrote a book in the last few years called The Recursive Mind. What is recursion and why is it important?

Recursion can refer to a procedure that references itself or similar procedures, or to a structure that contains an embedded structure of the same type. It is important because it allows one to build entities of theoretically unlimited complexity by progressively embedding structures within structures.

Some scholars think that language may be built on the use of recursive building blocks. Isn’t that a fundamental tenet of the modern linguistics pioneered by Noam Chomsky.

Yes, Chomsky’s view of language is that it is recursive, and this gives language its potential for infinite complexity—or what he has also called “discrete infinity.” In recent formulations, this is achieved through an “unbounded Merge,” in which elements are merged, and the merged elements can then themselves be merged—a process that can be repeated without bounds. To Chomsky, though, language is essentially internal thought, a mental monologue, known as I-language, and not a means of communication. The structure of language is therefore a by-product of internal thought. This implies a common structure, called “universal grammar,” that underlies all languages. But there is growing doubt as to whether such a structure exists.

Wasn’t one of the flaws of Chomsky’s work that he thought that the recursion as found in internal self-talk was not linked in any way to natural selection and evolution

Yes, I think so. In Chomsky‘s view, the recursive principle emerged in a single step—a “great leap forward”—at some particular point in human evolution, probably within the time span of our own species. This is contrary to Darwinian evolution, which postulates that change occurs in small, incremental steps, implying that something as complex as language could not have occurred in a single step. Chomsky also argues that language could not have evolved through natural selection because the elements of language are fundamentally symbolic, with no direct reference to the external world, and could not have been “selected” by natural events.

I think these are flawed arguments. The idea of a single step is based in part on evidence of a sudden appearance of symbolic thought in the archeological record, but one can just as easily make a case for a gradual rise. Apes and dogs can fairly easily learn to respond meaningfully to spoken words, suggesting that they, like humans, have innate, mental concepts, to which words are easily attached. Even in humans, the apparently abstract nature of language might well have arisen from more iconic or even pantomimimed representations used as forms of communication that have become “conventionalized” through the generations, sustained through culture rather than biological endowment

I would argue instead that recursive thought may have origins in our ape-like forebears over 6 million years ago, but gained increasing complexity during the Pleistocene, dating from over 2 million years ago, largely as an adaptation toward increasing social complexity. Language depended on this broader recursive capacity, but also owed its earlier origins to manual gesture, perhaps developing a more complex structure through pantomime, with the iconic structure eventually replaced by vocal gestures (speech) or the more arbitrary signs of signed languages.

Hasn’t more recent work extended the idea of recursion? Isn’t it thought that recursive behaviors may actually precede language—and may have led to the emergence of language?

To some extent Chomsky’s view can be seen as consistent with this, since recursion applies to what he calls I-language, which is the language of thought rather than of communication. Communicative language can then regarded as a means of externalizing thought so that we can share our thoughts with others. It may have emerged after the “great leap forward” that gave us I-language, although Chomsky does not, as far as I know, suggest that thought and communicative language arose in sequence.

My own view is that recursive thoughts preceded language in broader ways. So-called theory of mind (“I know what you’re thinking”) or mental time travel (mentally reliving what I did yesterday, or foreseeing what I will do tomorrow) involve the embedding of thoughts within thoughts, and otherwise seem quite independent of what we understand as language. Navigation may be another example, as we embed maps within maps (my office in my house in my city in my country in the world). As I understand it, I-language is based on the structuring of internal symbols, whereas the extended examples I have given are more spatial or iconic than abstract, and therefore have a more direct relation with the external world. It is entirely plausible that they could have emerged through natural selection, which rescues language evolution from the “miracle” of a sudden great leap forward.

Since writing the book, I have moved further from the Chomskyan notion that language is uniquely human to finding the basis of mental time travel even in the ability of rats to “replay” and perhaps “preplay” trajectories in spatial environments. The aim of researchers should be to develop an account of the evolution of thought and language through natural selection, and not through some miraculous event within the past 100,000 years. .

Why are the origins of human language, considered to be one of the hardest problems in science?

The reason is that grammatical language, with its recursive structure, is considered unlike any other form of animal communication, and is restricted to our own species. Part of the difficulty is that we have no historical evidence to go on, since we are the only remaining species among the 20 or so hominins that split from the line leading to the great apes, and even the great apes closest to us do not appear to have grammatical language.

My sense is that we now have enough information from fossil evidence, primate communication, ancient DNA, and the structure of human cognition to begin to construct plausible Darwinian scenarios of how language might have evolved over the past 6 million or so years, and perhaps even earlier, without having to postulate a one-off miracle within the past 100,000.

From Art and Cosmology in India

 

General equivalences

The view that the arts belong to the domain of the sacred and that there is a connection between them is given most clearly in a famous passage in the Vishnudharmottara Purana in which the sage Markandeya instructs the king Vajra in the art of sculpture, teaching that to learn it one must first learn painting, dance, and music:

Vajra: How should I make the forms of gods so that the image may always manifest the deity?

Markandeya: He who does not know the canon of painting (citrasutram) can never know the canon of image-making (pratima lakshanam).

Vajra: Explain to me the canon of painting as one who knows the canon of painting knows the canon of image-making.

Markandeya: It is very difficult to know the canon of painting without the canon of dance (nritta shastra), for in both the world is to be represented.

Vajra: Explain to me the canon of dance and then you will speak about the canon of painting, for one who knows the practice of the canon of dance knows painting.

Markandeya: Dance is difficult to understand by one who is not acquainted with instrumental music (atodya).

Vajra: Speak about instrumental music and then you will speak about the canon of dance, because when the instrumental music is properly understood, one understands dance.

Markandeya: Without vocal music (gita) it is not possible to know instrumental music.

Vajra: Explain to me the canon of vocal music, because he, who knows the canon of vocal music, is the best of men who knows everything.

Markandeya: Vocal music is to be understood as subject to recitation that may be done in two ways, prose (gadya) and verse (padya). Verse is in many meters.

Please see my related posts

Sounds True: Speech, Language, and Communication

Reflexivity, Recursion, and Self Reference

Society as Communication: Social Systems Theory of Niklas Luhmann

Consciousness of Cosmos: A Fractal, Recursive, Holographic Universe

On Holons and Holarchy

Indra’s Net: On Interconnectedness

The Great Chain of Being

 

Key Sources of Research

God in the Fractals: Recursiveness as a Key to Religious Behavior

in Method & Theory in the Study of Religion

 

https://www.researchgate.net/publication/266226046_God_in_the_Fractals_Recursiveness_as_a_Key_to_Religious_Behavior

Eternal Recursion, the Emergence of Metaconsciousness, and the Imperative for Closure