The world is a symphony of energy, playing out at the subatomic, human, social, and cosmic levels.
The fields, waves, particles, quarks, strings, electrons, photons, and dimensions which dance in and out of existence in the atom are like notes, tones, beats, rhythms, melodies and harmonies, all blending into an elegant and beautiful song called reality.
Jusy as we experience music on different planes of understanding, so it is with life. Our senses, minds, bodies and spirits all react to different aspects of reality in different ways.
Music resonates within the genetic structure of all life. Pitch may be encoded in our DNA.
We are all part of the orchestra of reality which plays from the subatomic to the cosmic level.
Music and mathematics are intimately related. Just as mathematics can tease out patterns of subatomic interaction, it can identify patterns of harmony.
The Music of the Spheres drives heaven and earth in a symphony of beauty, truth, justice, love and harmony.
All of art contributes to this cosmic song. Art and science give us visions of reality. Just as scientific theories emerge from the sweat of scientific research, aesthetic treasures emerge from the sweat of artistic exploration.
Language often fails both in the description and depiction of scientific and aesthetic truth. Metaphors are used to approach an understanding of the meaning of subatomic interaction and aesthetic result.
Philosophers have eternally struggled with distinctions of reality and appearance, subjective and objective, mind and body, particle and wave. Only with the advent of modern science and art can we see that all may be complementary, and at its core everything may be part of a cosmic holism.
In science we use terms like entanglement, symmetry, non locality, fuzzy and probability wave to approach an understanding of an interconnected, multi-dimensional subatomic world. Art uses words like abstract, surreal, absurd, and non-Euclidean to describe the frustration of attempting to reach an aesthetic vision of core reality.
Space, time, matter and energy are no longer the background against which reality plays, but integral parts of reality itself. Artists must revert back to their sense of childlike wonder to capture this new vision of reality.
We are all part of an interconnected web, interdependent and virtual. From Plato to Kant, Shakespeare to Sartre, philosophers have probed the mystery of reality which science is now unveiling.
Cosmic consciousness, web of nature, harmonious universe, song of the heavens, all ways of articulating the new vision.
What a wonderful world if we only let it be.
Lee
Showing posts with label plato. Show all posts
Showing posts with label plato. Show all posts
Sunday, February 8, 2009
Friday, January 30, 2009
The Math of String Theory
If there is to be a "Theory of Everything" for the forces of nature, string theory at the moment seems to have a good chance of playing a major role. Everything that happens in the physical universe may be ultimately represented in a single, elegant equation.
The mathematics of string theory gives hope to the dream of a resolution of some of the problems in the current model of particle physics. By adding dimensions to the framework, string theory provides new avenues to mathematical consistency.
Of course, if some version of string theory holds , as was the case with quantum mechanics, our world view will have to be altered dramatically. In addition to matter and energy, space and time themselves will cease to have their commonsense characteristics.
On a conceptual level, string theory uses one dimensional strings rather than zero dimensional particles in developing the formulas. The way these strings "vibrate" determines what type of particle emerges, and ultimately, what kind of universe emerges.
Just as the strings of a piano have resonant frequencies, so do the vibrating strings of subatomic reality. Whereas the strings of musical instruments produce notes, string vibrations produce particles.
The forces of nature also emerge from string vibration patterns. As a result, all matter and forces known become notes on a universal string.
Particle properties are a manifestatinof resonant pattterns of string vibrations as well.
Stretching the metaphor, there is a school of thought that this framework can be brought to bear on the more complex systems which have emerged in our universe, including life and consciousness.
While chaos theory and complexity science show new laws come into play as system compexity increases, there is a belief that those new laws may ultimately be found to be consistent with the deeper mathematics of string theory.
It takes a while to digest even the conceptual, much less the mathematical, framework of string theory. If right, it posits a multidimensional labyrinth of interconnected structures mysteriously intertwined with our notions of space and time.
In conventional physics, events occur in four dimensions. They can be undersood in the context of four factors.
In quantum mechanics, the microscopic properties of space become dissimilar to the analogous properties in classical physics. The notion of a violent quantum foam versus the smooth surface of relativity causes and results in mathematical incompatiblity between the theories.
The standard model of particle physics posits a world of pointlike objects. String/Superstring Theory unveils a cosmos emerging from a microscopic landscape of strings whose vibrations emerge as symphony of reality.
Everything in the universe emerges from vibrating strings.
When strings and their vibrations are fundamental (rather than point particles), the incompatibility of microscopic spatial structures between relaivity and quantum physics vanishes.
Supersymmery is part of string theory. Fermions and bosons are paired, symmetric, in a supersymmetric universe, and the mathematics becomes more elegant as dimensions are added.
Fundamental properties of the universe depend on the number and structure of dimensions in which the fundamental strings vibrate.
In supersymmetry, Hamiltonians commute with supercharges and Lagrangians are transformed to produce mixed bosonic and fermionic fields. Dirac and Pauli matrices are utilized in the representation, and a supersymmetric Lagrangian emerges.
A particular class of six dimensional spaces known as Calabi-Yau spaces have the geometric struture required to meet the mathematical properties of the theory
The mathematics of string theory is important in its own right. Even if it is found that string theory doesn't fully describe our universe, the underlying mathematics has blazed new trails of understanding.
As Robert Pirsig said in Zen and the Art of Motorcycle Maintenance,"...the stream of national consciousness moves faster now, and is broader, but it seems to run less deep...Some channel deepening is called for."
There are a number of cosmic and subatomic implications of the math of string theory. These will be explored throughout my blogs.
Like a Beethoven Symphony, or Mozart Concerto, our world is a labyrinth of elements which emerges in a much more beautiful form than could be predicted from an assemblage of the parts.
The solution of a wave equation can be written in terms of a superposition, a Fourier expansion. The symmetries of the Lagrangian, the energy momentum tensor, and the Hamiltonian which governs time evolution of the worldsheet are elements of the classical analysis of strings.
The quantum extension of classical theory involves covariant quantization and Virasoro constraints. At this point there are 26 space-time dimensions.
Conformal field theory is used in peturbative string theory. A conformal transformation maps a region of the complex plane onto a more workable space.
In T-duality, open strings with Neumann boundary conditions are transformed to those with Dirichlet boundaries.
Spacetime supersymmetry involves superfields, superspaces, Grassman coordinates, and Green- Schwarz formalism.
In conclusion, string theory develops a mathematical framework by which to model the essence of all subatomoic activity. It shows that at the deepest level, reality may be interconnected and multidimensional. This has profound philosophical implcations.
This concludes our blogs on the mathematics of subatomic interactions. (whew!)
The next blogs in Mathematical Universe will deal with the mathematics of larger systems, up to and including the global economic system.
Lee
The mathematics of string theory gives hope to the dream of a resolution of some of the problems in the current model of particle physics. By adding dimensions to the framework, string theory provides new avenues to mathematical consistency.
Of course, if some version of string theory holds , as was the case with quantum mechanics, our world view will have to be altered dramatically. In addition to matter and energy, space and time themselves will cease to have their commonsense characteristics.
On a conceptual level, string theory uses one dimensional strings rather than zero dimensional particles in developing the formulas. The way these strings "vibrate" determines what type of particle emerges, and ultimately, what kind of universe emerges.
Just as the strings of a piano have resonant frequencies, so do the vibrating strings of subatomic reality. Whereas the strings of musical instruments produce notes, string vibrations produce particles.
The forces of nature also emerge from string vibration patterns. As a result, all matter and forces known become notes on a universal string.
Particle properties are a manifestatinof resonant pattterns of string vibrations as well.
Stretching the metaphor, there is a school of thought that this framework can be brought to bear on the more complex systems which have emerged in our universe, including life and consciousness.
While chaos theory and complexity science show new laws come into play as system compexity increases, there is a belief that those new laws may ultimately be found to be consistent with the deeper mathematics of string theory.
It takes a while to digest even the conceptual, much less the mathematical, framework of string theory. If right, it posits a multidimensional labyrinth of interconnected structures mysteriously intertwined with our notions of space and time.
In conventional physics, events occur in four dimensions. They can be undersood in the context of four factors.
In quantum mechanics, the microscopic properties of space become dissimilar to the analogous properties in classical physics. The notion of a violent quantum foam versus the smooth surface of relativity causes and results in mathematical incompatiblity between the theories.
The standard model of particle physics posits a world of pointlike objects. String/Superstring Theory unveils a cosmos emerging from a microscopic landscape of strings whose vibrations emerge as symphony of reality.
Everything in the universe emerges from vibrating strings.
When strings and their vibrations are fundamental (rather than point particles), the incompatibility of microscopic spatial structures between relaivity and quantum physics vanishes.
Supersymmery is part of string theory. Fermions and bosons are paired, symmetric, in a supersymmetric universe, and the mathematics becomes more elegant as dimensions are added.
Fundamental properties of the universe depend on the number and structure of dimensions in which the fundamental strings vibrate.
In supersymmetry, Hamiltonians commute with supercharges and Lagrangians are transformed to produce mixed bosonic and fermionic fields. Dirac and Pauli matrices are utilized in the representation, and a supersymmetric Lagrangian emerges.
A particular class of six dimensional spaces known as Calabi-Yau spaces have the geometric struture required to meet the mathematical properties of the theory
The mathematics of string theory is important in its own right. Even if it is found that string theory doesn't fully describe our universe, the underlying mathematics has blazed new trails of understanding.
As Robert Pirsig said in Zen and the Art of Motorcycle Maintenance,"...the stream of national consciousness moves faster now, and is broader, but it seems to run less deep...Some channel deepening is called for."
There are a number of cosmic and subatomic implications of the math of string theory. These will be explored throughout my blogs.
Like a Beethoven Symphony, or Mozart Concerto, our world is a labyrinth of elements which emerges in a much more beautiful form than could be predicted from an assemblage of the parts.
The solution of a wave equation can be written in terms of a superposition, a Fourier expansion. The symmetries of the Lagrangian, the energy momentum tensor, and the Hamiltonian which governs time evolution of the worldsheet are elements of the classical analysis of strings.
The quantum extension of classical theory involves covariant quantization and Virasoro constraints. At this point there are 26 space-time dimensions.
Conformal field theory is used in peturbative string theory. A conformal transformation maps a region of the complex plane onto a more workable space.
In T-duality, open strings with Neumann boundary conditions are transformed to those with Dirichlet boundaries.
Spacetime supersymmetry involves superfields, superspaces, Grassman coordinates, and Green- Schwarz formalism.
In conclusion, string theory develops a mathematical framework by which to model the essence of all subatomoic activity. It shows that at the deepest level, reality may be interconnected and multidimensional. This has profound philosophical implcations.
This concludes our blogs on the mathematics of subatomic interactions. (whew!)
The next blogs in Mathematical Universe will deal with the mathematics of larger systems, up to and including the global economic system.
Lee
Thursday, January 22, 2009
The Metaphysics of Harmony
As our official philosophy blog, Actuarial Universe will explore issues of ultimate reality.
There are many ways to approach ultimate reality. Many of them may be right. Some converge upon unity as the ultimate "value."
What is striking about the unity perspectives is that science and mathematics now lend support to that idea.
From Plato to Kant, Shakespeare to Locke, the idea that ultimately all is one prevails.
Now, the deepest calculations and consternations of scientists and mathematicians go there.
The Standard Model of Particle Physics gives the entities and interactions which define reality at the subatomic level. The particles and waves are virtual and probabilistic. They exist in a web of connections, called fields, and appear to be entangled.
They may emerge from dimensions beyond those our intellects and senses can perceive. When the clouds of energy within the nucleus "interact" with the electron clouds surrounding it, atoms emerge.
When the electrons of these atoms "interact "with those of other atoms, molecules emerge.
From molecules emerge the objects of chemistry and biology.
As we move up the ladder of complexity, the original elements become part of a framework which doesn't seem to reflect their origins. Only recently have scientists begun to uncover connections among complex objects which have patterns similar to those at the subatomic level.
Words like chaos, fractal, and self-organization begin to emerge from this haze of super-atomic reality.
The fact is that there is now a metaphysical scenario, supported by a partial mathematical structure, which portrays a universe in which everything is connected.
From the Big Bang to eternity, there is an underlying symmetry which connects everything at creation. The symmetry at Creation was perfect. It broke as the world cooled and structures which eventually emerged into us emerged. At the core of everything however is the primordial connection.
There are many ways to slice ultimate reality. One is the way that education has been divided. Philosophy, science, art, politics, history, economics, all part of a tapestry of human understanding.
From a scientific point of view, reality is the things we see and feel and their constituents. Nature, humanity, society, the cosmos, all part of a tapestry which scientists explore.
Reality can also be looked at as the sum of human intellectual activity. Plato's Forms, Kant's Categories, Shakespeare's Complementarities, Smith's Invisible Hand, Rousseau's General Will, Pirsig's Quality, Heisenberg's Uncertainty, Dirac's Sea, Schrodinger's Wave, Mandelbrot's Fractals, Mozart's Harmonies, a mosaic of truth and beauty.
Another perspective on ultimate reality is as the envelope of realms. There is a cosmic realm, a philosophical realm, a complex realm, an economic realm, a chaotic realm, a classical realm, a subatomic realm, a human realm, all creating a vision for our minds and bodies to experience.
Stay tuned.
Lee
There are many ways to approach ultimate reality. Many of them may be right. Some converge upon unity as the ultimate "value."
What is striking about the unity perspectives is that science and mathematics now lend support to that idea.
From Plato to Kant, Shakespeare to Locke, the idea that ultimately all is one prevails.
Now, the deepest calculations and consternations of scientists and mathematicians go there.
The Standard Model of Particle Physics gives the entities and interactions which define reality at the subatomic level. The particles and waves are virtual and probabilistic. They exist in a web of connections, called fields, and appear to be entangled.
They may emerge from dimensions beyond those our intellects and senses can perceive. When the clouds of energy within the nucleus "interact" with the electron clouds surrounding it, atoms emerge.
When the electrons of these atoms "interact "with those of other atoms, molecules emerge.
From molecules emerge the objects of chemistry and biology.
As we move up the ladder of complexity, the original elements become part of a framework which doesn't seem to reflect their origins. Only recently have scientists begun to uncover connections among complex objects which have patterns similar to those at the subatomic level.
Words like chaos, fractal, and self-organization begin to emerge from this haze of super-atomic reality.
The fact is that there is now a metaphysical scenario, supported by a partial mathematical structure, which portrays a universe in which everything is connected.
From the Big Bang to eternity, there is an underlying symmetry which connects everything at creation. The symmetry at Creation was perfect. It broke as the world cooled and structures which eventually emerged into us emerged. At the core of everything however is the primordial connection.
There are many ways to slice ultimate reality. One is the way that education has been divided. Philosophy, science, art, politics, history, economics, all part of a tapestry of human understanding.
From a scientific point of view, reality is the things we see and feel and their constituents. Nature, humanity, society, the cosmos, all part of a tapestry which scientists explore.
Reality can also be looked at as the sum of human intellectual activity. Plato's Forms, Kant's Categories, Shakespeare's Complementarities, Smith's Invisible Hand, Rousseau's General Will, Pirsig's Quality, Heisenberg's Uncertainty, Dirac's Sea, Schrodinger's Wave, Mandelbrot's Fractals, Mozart's Harmonies, a mosaic of truth and beauty.
Another perspective on ultimate reality is as the envelope of realms. There is a cosmic realm, a philosophical realm, a complex realm, an economic realm, a chaotic realm, a classical realm, a subatomic realm, a human realm, all creating a vision for our minds and bodies to experience.
Stay tuned.
Lee
Monday, January 19, 2009
Paradigm Actuaries and The Secret
The Secret is that the truth is not as elusive as we thought.
In a world of poverty, suspicion, ignorance, hypocrisy and irony, the deeper reality is that we are closer to an understanding of true being than ever.
Physicists "looking" into the nucleus of the atom have discovered that the fundamental "thing", the core of everything is an interconnected web of virtual energy.
The atoms which make up all nature, from trees and oceans to rocks and people, are part of a larger tapestry, a tapestry which eludes our instruments and intellects.
Plato, of course, sensed this in his Forms, as did Kant in his Categories and Hegel in his Spirit. Pirsig sensed it in his Quality as did Martin in his dream.
The difference is that, until now, there was no solid mathematical and scientific foundation for a worldview which embraces unity and harmony.
In a world of poverty, suspicion, ignorance, hypocrisy and irony, the deeper reality is that we are closer to an understanding of true being than ever.
Physicists "looking" into the nucleus of the atom have discovered that the fundamental "thing", the core of everything is an interconnected web of virtual energy.
The atoms which make up all nature, from trees and oceans to rocks and people, are part of a larger tapestry, a tapestry which eludes our instruments and intellects.
Plato, of course, sensed this in his Forms, as did Kant in his Categories and Hegel in his Spirit. Pirsig sensed it in his Quality as did Martin in his dream.
The difference is that, until now, there was no solid mathematical and scientific foundation for a worldview which embraces unity and harmony.
The metaphors of particle physics and complexity science, the waves, quarks, fields, spaces, groups, uncertainty, complementarity, exclusion, entanglement, fractals, emergence, symmetries, topologies, dimensions...all elicit a sense of connectedness, transcendence, holism...
This holism is the basis for a new metaphysics grounded in the mathematics which propels the metaphors.
Philosophy, science, politics, economics, art, and proper public policy all emerge from the idea that, at its core, reality is connected and transcendent. This idea makes all prior metaphysical speculation coherent.
It also gives us a path to a brighter future.
Yes we can.
Lee
Sunday, January 18, 2009
Hunter, Matt & Lee
In the current issue of Rolling Stone, Matt Taibbi says to a clueless "W " who doesn't understand why people don't appreciate his service...
"OK, here it is.You're the child of two emotionally abscent aristocrats who denied you any kind of love and affection..
You grew up resentful and lacking completely in any natural gifts or curiosity...You were aided in (this) quest by a bunch of narrow-minded lackeys...who...manipulated your obvious Oedipal resentments...
...you're about to spend the rest of eternity pondering your now-official legacy as the worst and most pigheaded leader in the history of Western democracy, a man who almost single-handedly sank the mightiest nation on earth by turning the Presidency into a $50 trillion therapy session that ended in two disastrous wars, a financial crisis...and a legacy of corruption on a scale not seen since the Borgias..."
Of course, Matt is gentle when put beside Hunter Thompson who, in Generation of Swine said about poppa Bush..."It is difficult for an ordinary voter to come to grips with the notion that a truly evil man, a truthless monster with the brains of a king rat and the soul of a cockroach, is about to be sworn in as President of the United States..."
Now, since the point of my blogs is that there is hope in America to restore the dream of our Founding Fathers, I don't want to dwell too much on the dark side.
In a world of Platonic Forms, dancing waves of inter-connected energy, and fields of harmonic resonance, there is much about which to be hopeful.
A true leader is to be sworn in tomorrow. He will be in a position to transform the country not just economically but spiritually. The values of life, liberty and true happiness can be combined with courage, integrity, compassion, truth, justice, beauty and wisdom to create a tapestry of hope not seen since 1968.
The American spirit as manifest in the lives of Washington, Jefferson, Lincoln, Martin, Bobby and now Barack has never been more healthy. We can overcome the obstacles which have arisen in recent years.
Yes we can.
Lee
"OK, here it is.You're the child of two emotionally abscent aristocrats who denied you any kind of love and affection..
You grew up resentful and lacking completely in any natural gifts or curiosity...You were aided in (this) quest by a bunch of narrow-minded lackeys...who...manipulated your obvious Oedipal resentments...
...you're about to spend the rest of eternity pondering your now-official legacy as the worst and most pigheaded leader in the history of Western democracy, a man who almost single-handedly sank the mightiest nation on earth by turning the Presidency into a $50 trillion therapy session that ended in two disastrous wars, a financial crisis...and a legacy of corruption on a scale not seen since the Borgias..."
Of course, Matt is gentle when put beside Hunter Thompson who, in Generation of Swine said about poppa Bush..."It is difficult for an ordinary voter to come to grips with the notion that a truly evil man, a truthless monster with the brains of a king rat and the soul of a cockroach, is about to be sworn in as President of the United States..."
Now, since the point of my blogs is that there is hope in America to restore the dream of our Founding Fathers, I don't want to dwell too much on the dark side.
In a world of Platonic Forms, dancing waves of inter-connected energy, and fields of harmonic resonance, there is much about which to be hopeful.
A true leader is to be sworn in tomorrow. He will be in a position to transform the country not just economically but spiritually. The values of life, liberty and true happiness can be combined with courage, integrity, compassion, truth, justice, beauty and wisdom to create a tapestry of hope not seen since 1968.
The American spirit as manifest in the lives of Washington, Jefferson, Lincoln, Martin, Bobby and now Barack has never been more healthy. We can overcome the obstacles which have arisen in recent years.
Yes we can.
Lee
Wednesday, January 14, 2009
Actuarial Universe
This entry in each of my blogs will outline the blog structure.
The blogs are:
Name; Content; Address
Huffingtonpost; General; huffingtonposta.blogspot.com
Art of Hardball; Politics; slatea.blogspot.com
Quantum Universe; Science; rollingstonea.blogspot.com
Mathematical Universe; Math; paradigmactuaries.blogspot.com
Actuarial Universe; Philosophy; dailybeasta.blogspot.com
My website is paradigmactuaries.com
Lee
The blogs are:
Name; Content; Address
Huffingtonpost; General; huffingtonposta.blogspot.com
Art of Hardball; Politics; slatea.blogspot.com
Quantum Universe; Science; rollingstonea.blogspot.com
Mathematical Universe; Math; paradigmactuaries.blogspot.com
Actuarial Universe; Philosophy; dailybeasta.blogspot.com
My website is paradigmactuaries.com
Lee
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