Equilibrium and non-equilibrium statistical mechanics with generalized fractal derivatives: A review
Modern Physics Letters A
Fractal calculus generalizes ordinary calculus, offering a way to differentiate otherwise non-dif... more Fractal calculus generalizes ordinary calculus, offering a way to differentiate otherwise non-differentiable domains and phenomena. This paper discusses the equilibrium and non-equilibrium statistical mechanics involving fractal structure, as well as fractal temperature in the partition function.
"Layman's Abstract:
This dissertation looks at how there is a texture to our temporal experien... more "Layman's Abstract:
This dissertation looks at how there is a texture to our temporal experience, how sometimes time seems to go faster, or slower, and how, on rare occasions, it seems to stop altogether. I suggest that this is a result of how time emerges from, and is mutually enfolded with timelessness. I suggest that this experience can be described with a fractal model that links our subjective experience to physical reality.
Traveling at the speed of light, photons exist outside of time. Time interacts with timelessness whenever matter interacts with light. Time emerges from timelessness at very small scales as the potential of a quantum wave function collapses into a physical manifestation. Our consciousness participates in this emergence/manifestation through quantum processes that occur at the smallest scales in our brains. Roger Penrose and Stuart Hameroff's theory of quantum consciousness link neurological quantum processes to our experience of consciousness.
As time emerges out of timelessness the boundary between the two becomes more intricate and complex. This is a fractal boundary. The "edge effect" is an example of a fractal boundary, where at the interface of two ecosystems, such as the edge between a pond and a field, the greatest biodiversity is found. Complexity is the intertwining boundary between two dualities, in this case, between time and timelessness. The fractal dimension describes the density of this intertwining. The more densely we involve ourselves in some activity, the faster time seems to go. The more shallow our involvement, the slower time seems to go. Laurent Nottale's theory of physical fractal space-time describes the process of quantum collapse while Susie Vrobel's theory of subjective fractal time describes our subjective experience of time using fractal measures.
By combining these theories I establish a link between physical fractal time and our subjective experience of fractal time describing the intertwining of time and timelessness. The infinite within the finite–this is the paradox that animates the world–eternity within a moment, the moment within eternity, and the whole body of the universe in between, chasing its tail.
Academic Abstract:
This dissertation applies Susie Vrobel and Laurent Nottale’s fractal models of time to understanding our subjective experience of time, deepening the interface of quantum mechanics and subjectivity developed by Roger Penrose and Stuart Hameroff. I first outline Penrose’s Objective Reduction (OR) version of quantum wave function collapse, and then the biological connection to microscopic brain structures and subjective states that Hameroff developed from Penrose’s theory. In the next section, I outline Nottale’s theory of scale relativity and fractal spacetime, covering his treatments of non-fractal classical time emerging from quantum, fractal, and reversible time. I then build on Vrobel’s model to identify specific properties of fractals, explore how they might model our subjective experience of time, and interface with the theories of Nottale and Penrose. At the confluence of these theories, I suggest aligning time with fractal scale. In this case, the data of the timeless present moment, like the fractal pattern, is condensed and replicated through memories, creating the fractal dimension, or temporal density, of the subjective passage of time. Thus, temporal flow unfurls from, and nests within, the timeless present. Finally, I consider the implications for the human relationship with time."
It is impossible to meditate on time and the mystery of the creative process of nature without an... more It is impossible to meditate on time and the mystery of the creative process of nature without an overwhelming emotion at the limitations of human intelligence." -Alfred North Whitehead (1964, 73) People seeking to describe time continually face the riddle of its logical inconsistency. How does the past exist in the present after all? Physics is no exception. How does the science of that quantifies motion quantify the paradox of the unmoved mover?
Through weaving together a wide variety of material, this paper outlines the intertwining of two ... more Through weaving together a wide variety of material, this paper outlines the intertwining of two states of temporal consciousness. On one hand, modern consciousness operates almost exclusively in linear time characterized by the following adjectives: unidirectional, structured, static, external, dominating, objective, logical, quantified, mathematical, and masculine. On the other hand, indigenous oral-based cultures seem to operate in a more ancient form of consciousness which I will refer to as "dreamtime" and characterize as: omnipresent, fluid, internal, co-creative, subjective, intuitive, paradoxical, qualitative, musical, and feminine. I use the term "dreamtime" to draw attention to the unique temporal experience of dreaming consciousness as well as to that of the Australian Aboriginal mythic tradition.
My ultimate goal is to understand the mystery of the human mind arising in the universe. The path... more My ultimate goal is to understand the mystery of the human mind arising in the universe. The path of exploration I have chosen for this paper follows the understanding that our relationship to time, as mediated through memory and music specifically, is an essential pivot point between cosmology and consciousness. When considering what consciousness actually is, I speculate that it hinges on our ability to project ourselves forwards and backwards in time, in other words, to plan for the future, remember the past, and make connections between temporal moments. Without these abilities, consciousness beyond immediate experience would not exist. So what is it that allows us to extend ourselves in the temporal dimension?
The emphasis of this paper is on the a-temporal landscape common to both the collective unconscio... more The emphasis of this paper is on the a-temporal landscape common to both the collective unconscious and the block universe of relativity. Part I situates two important contributors to the history of a-temporality: Mileva Maric for her unacknowledged work on relativity and Marie Louise von Franz for her understanding of the relativistic implications for the study of human consciousness through psychology and religion. Atemporality can be very difficult for our temporally bound minds to grasp. My discussion in Part II of this paper builds on the work of Maric and von Franz and offers new ways of thinking about time. I hope to help to reconcile the seemingly incompatible realms of temporality and a-temporality, and to draw attention to the discussion's parallels with its dual cultural context of masculine and feminine.
This week’s guest is philosopher Kerri Welch, whose doctoral thesis from CIIS (and current book-i... more This week’s guest is philosopher Kerri Welch, whose doctoral thesis from CIIS (and current book-in-progress) explore a fractal model of time. If you have ever wondered about time, this episode is for you. Instant classic.
We take a wild tour through the layers of the human brain and mind, examining the correlations between different brain waves and their correspondent states of consciousness – and speculate on our experience of time as an evolved response to a far more complex and awesome world than we can possibly conceive!
Twenty minutes in and we’ve already covered the fractal nature of time and we’re on to explaining what happens to the modern self and its boundaries in the torrent of novelty that awaits un in a digital age. Then we go deep for another hour and a half…
DISCUSSED:
• Fate vs Free Will in light of Chaos Theory
• The relationship between technology and our experience of time, overstimulated, interrupted
• How Jean Gebser’s structures of consciousness overlay on EEG data
• The nature of synchronicity & time vs. timelessness
• The effects of ayahuasca, illness, aging, and other time-warping events on the passage of time
• Singularities and our asymptotic approach to transcendence
• Narrative collapse, fake news, and the end of history
• Relativity, scaling laws, and city time vs. country time
• What was before TIME?
• Pet telepathy as a matter of referential framing
• The “future” causing the “past”…
• …and the physics (and psychology!) of how to feel the future.
• Schizophrenia as possibly a disorder of time perception
• Dopamine levels and the experience of duration
• Human chronobiology adapted to other planet’s days
• Integrating the rational mind with transpersonal experience
QUOTES:
“We actually can’t get precise enough to bring the level of predictability that physics once thought it could.”
“Children have to be indoctrinated into time, right? They’re not born into linear time. They’re born in a timeless space, and that’s where they live, and then they live in this hypnagogic dream time, which is all present moment. You’ll hear kids say, like, ‘I remember when you were little’ to their parents.”
“When we restrict ourselves to linear causal thinking, we are coarse-graining the present moment. We are glossing over the infinite depth of richness available within the present moment. And of course it’s paradoxical: we coarse-grain it by dividing it more finely.”
“What we’re experiencing in our culture right now is the entrainment to the fast frequencies. We’re not letting the long slow frequencies have the greatest amplitude. What does that look like? It looks like hanging out with rocks and trees and elders. And that’s the integration that we need in order to nest our super-fast frequencies within, in order to give them direction…if we can nest within the natural structures of the long, slow frequencies that surround us, it will guide these fast frequencies in healthier directions.”
“We REALLY just have to get better at holding multiple realities. AND recognizing what’s important about them.”
“The dog comes and sits by the door half an hour before the owner comes home because to the dog, the owner’s already home. Their moment is big enough that it’s happening already. But we’re so finely dividing things that we’re like, ‘It’s half an hour away! It’s an eternity!’ But for the dog that’s been sitting bored at home all day…”
“Free will comes from a future influence we can’t see. That’s one way I would interpret it.”
“The definition of human experience is, to me, the limitation of infinity, in order to have experience.”
The Human Experience of Time with David Gilden, Brannen Temple, and Rebecca McInroy
The question of how consciousness arises within a cosmological context hinges on the issue... more The question of how consciousness arises within a cosmological context hinges on the issue of time. As Roger Penrose puts it, “One of the most striking and immediate features of conscious perception is the passage of time.” (Penrose 1994, 384) What space-time structure might facilitate our unique and variable experience of time? What mathematical model of time might encompass the diversity of our subjective experience and the insights of physics? Time, as described by physics is static, symmetrical, and made up of predictable intervals. In contrast, human subjectivity experiences time as unidirectional, flowing, and passing at different rates. The contrast of these perspectives suggests that a richer description of time is required to encompass both of these realities. Some of these differences might be reconciled through a fractal model of time, in which I suggest the progression of time carves out infinite depths within the present moment. The notion of fractal space-time was first scientifically entertained by astrophysicist Laurent Nottale. Susie Vrobel then builds a compelling interface of subjectivity and fractal time, drawing on Roger Penrose's identification of consciousness' unique ability to access, and bring back insight from, a realm of timelessness. She focuses on what the variables in fractal mathematics mean in terms of our subjective experience of time. At the confluence of these theories, I suggest aligning time with fractal scale. In this case, the data of the timeless present moment, like the fractal pattern, is condensed and replicated through memories, creating the fractal dimension, or temporal density, of the subjective passage of time. Thus, temporal flow unfurls from, and nests within, the timeless present. Finally, I consider the implications for the human relationship with time.
Pink Noise: Recalibrating Fractal Harmonics from Modern World Dis-Ease via Natural World Tuning
The ever-accelerating pace of modern life can leave one feeling perpetually off kilter. This scie... more The ever-accelerating pace of modern life can leave one feeling perpetually off kilter. This scientific look at the human relationship to time explores how to cultivate a comfortable nesting of the frequencies that make up one’s life, emphasizing entraining to the longer, slower timescales of the natural world as a fundamental container for health.
The Science of Temporal Perception
Ever wonder what neurological, biochemical, quantum, and space-time factors might play a role in ... more Ever wonder what neurological, biochemical, quantum, and space-time factors might play a role in our perception of time? In this presentation I'll explore a few possibilities touching on the roles of body temperature, entrainment, quantum superposition, and neurotransmitters in our varied experiences between time and timelessness, including those with psychedelics, wilderness, desire, and satiation.
This dissertation applies Susie Vrobel and Laurent Nottale’s fractal models of time to understand... more This dissertation applies Susie Vrobel and Laurent Nottale’s fractal models of time to understanding our subjective experience of time, deepening the interface of quantum mechanics and subjectivity developed by Roger Penrose and Stuart Hameroff. I first outline Penrose’s Objective Reduction (OR) version of quantum wave function collapse, and then the biological connection to microscopic brain structures and subjective states that Hameroff developed from Penrose’s theory. In the next section, I outline Nottale’s theory of scale relativity and fractal spacetime, covering his treatments of non-fractal classical time emerging from quantum, fractal, and reversible time. I then build on Vrobel’s model to identify specific properties of fractals, explore how they might model our subjective experience of time, and interface with the theories of Nottale and Penrose. At the confluence of these theories, I suggest aligning time with fractal scale. In this case, the data of the timeless present moment, like the fractal pattern, is condensed and replicated through memories, creating the fractal dimension, or temporal density, of the subjective passage of time. Thus, temporal flow unfurls from, and nests within, the timeless present. Finally, I consider the implications for the human relationship with time.
Anchored in the theory of quantum consciousness proposed by Roger Penrose and Stuart Hameroff, th... more Anchored in the theory of quantum consciousness proposed by Roger Penrose and Stuart Hameroff, this discussion will explore the realtionships between time, consciouness, quantum mechanics, and relativity.
A Fractal Topology of Time
Deep Transcendence: Fractal Time and the Feminine Perspective
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Papers by Kerri Welch
This dissertation looks at how there is a texture to our temporal experience, how sometimes time seems to go faster, or slower, and how, on rare occasions, it seems to stop altogether. I suggest that this is a result of how time emerges from, and is mutually enfolded with timelessness. I suggest that this experience can be described with a fractal model that links our subjective experience to physical reality.
Traveling at the speed of light, photons exist outside of time. Time interacts with timelessness whenever matter interacts with light. Time emerges from timelessness at very small scales as the potential of a quantum wave function collapses into a physical manifestation. Our consciousness participates in this emergence/manifestation through quantum processes that occur at the smallest scales in our brains. Roger Penrose and Stuart Hameroff's theory of quantum consciousness link neurological quantum processes to our experience of consciousness.
As time emerges out of timelessness the boundary between the two becomes more intricate and complex. This is a fractal boundary. The "edge effect" is an example of a fractal boundary, where at the interface of two ecosystems, such as the edge between a pond and a field, the greatest biodiversity is found. Complexity is the intertwining boundary between two dualities, in this case, between time and timelessness. The fractal dimension describes the density of this intertwining. The more densely we involve ourselves in some activity, the faster time seems to go. The more shallow our involvement, the slower time seems to go. Laurent Nottale's theory of physical fractal space-time describes the process of quantum collapse while Susie Vrobel's theory of subjective fractal time describes our subjective experience of time using fractal measures.
By combining these theories I establish a link between physical fractal time and our subjective experience of fractal time describing the intertwining of time and timelessness. The infinite within the finite–this is the paradox that animates the world–eternity within a moment, the moment within eternity, and the whole body of the universe in between, chasing its tail.
Academic Abstract:
This dissertation applies Susie Vrobel and Laurent Nottale’s fractal models of time to understanding our subjective experience of time, deepening the interface of quantum mechanics and subjectivity developed by Roger Penrose and Stuart Hameroff. I first outline Penrose’s Objective Reduction (OR) version of quantum wave function collapse, and then the biological connection to microscopic brain structures and subjective states that Hameroff developed from Penrose’s theory. In the next section, I outline Nottale’s theory of scale relativity and fractal spacetime, covering his treatments of non-fractal classical time emerging from quantum, fractal, and reversible time. I then build on Vrobel’s model to identify specific properties of fractals, explore how they might model our subjective experience of time, and interface with the theories of Nottale and Penrose. At the confluence of these theories, I suggest aligning time with fractal scale. In this case, the data of the timeless present moment, like the fractal pattern, is condensed and replicated through memories, creating the fractal dimension, or temporal density, of the subjective passage of time. Thus, temporal flow unfurls from, and nests within, the timeless present. Finally, I consider the implications for the human relationship with time."
Talks by Kerri Welch
We take a wild tour through the layers of the human brain and mind, examining the correlations between different brain waves and their correspondent states of consciousness – and speculate on our experience of time as an evolved response to a far more complex and awesome world than we can possibly conceive!
Twenty minutes in and we’ve already covered the fractal nature of time and we’re on to explaining what happens to the modern self and its boundaries in the torrent of novelty that awaits un in a digital age. Then we go deep for another hour and a half…
DISCUSSED:
• Fate vs Free Will in light of Chaos Theory
• The relationship between technology and our experience of time, overstimulated, interrupted
• How Jean Gebser’s structures of consciousness overlay on EEG data
• The nature of synchronicity & time vs. timelessness
• The effects of ayahuasca, illness, aging, and other time-warping events on the passage of time
• Singularities and our asymptotic approach to transcendence
• Narrative collapse, fake news, and the end of history
• Relativity, scaling laws, and city time vs. country time
• What was before TIME?
• Pet telepathy as a matter of referential framing
• The “future” causing the “past”…
• …and the physics (and psychology!) of how to feel the future.
• Schizophrenia as possibly a disorder of time perception
• Dopamine levels and the experience of duration
• Human chronobiology adapted to other planet’s days
• Integrating the rational mind with transpersonal experience
QUOTES:
“We actually can’t get precise enough to bring the level of predictability that physics once thought it could.”
“Children have to be indoctrinated into time, right? They’re not born into linear time. They’re born in a timeless space, and that’s where they live, and then they live in this hypnagogic dream time, which is all present moment. You’ll hear kids say, like, ‘I remember when you were little’ to their parents.”
“When we restrict ourselves to linear causal thinking, we are coarse-graining the present moment. We are glossing over the infinite depth of richness available within the present moment. And of course it’s paradoxical: we coarse-grain it by dividing it more finely.”
“What we’re experiencing in our culture right now is the entrainment to the fast frequencies. We’re not letting the long slow frequencies have the greatest amplitude. What does that look like? It looks like hanging out with rocks and trees and elders. And that’s the integration that we need in order to nest our super-fast frequencies within, in order to give them direction…if we can nest within the natural structures of the long, slow frequencies that surround us, it will guide these fast frequencies in healthier directions.”
“We REALLY just have to get better at holding multiple realities. AND recognizing what’s important about them.”
“The dog comes and sits by the door half an hour before the owner comes home because to the dog, the owner’s already home. Their moment is big enough that it’s happening already. But we’re so finely dividing things that we’re like, ‘It’s half an hour away! It’s an eternity!’ But for the dog that’s been sitting bored at home all day…”
“Free will comes from a future influence we can’t see. That’s one way I would interpret it.”
“The definition of human experience is, to me, the limitation of infinity, in order to have experience.”
Some of these differences might be reconciled through a fractal model of time, in which I suggest the progression of time carves out infinite depths within the present moment. The notion of fractal space-time was first scientifically entertained by astrophysicist Laurent Nottale. Susie Vrobel then builds a compelling interface of subjectivity and fractal time, drawing on Roger Penrose's identification of consciousness' unique ability to access, and bring back insight from, a realm of timelessness. She focuses on what the variables in fractal mathematics mean in terms of our subjective experience of time. At the confluence of these theories, I suggest aligning time with fractal scale. In this case, the data of the timeless present moment, like the fractal pattern, is condensed and replicated through memories, creating the fractal dimension, or temporal density, of the subjective passage of time. Thus, temporal flow unfurls from, and nests within, the timeless present. Finally, I consider the implications for the human relationship with time.