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Mountain Math Software. home: consulting: videos: book: QM FAQ: contact: PDF version of this book Next: List of Figures Up: whatrh Previous: whatrh Contents. List of Figures THE PROPHECY OF THE CONDOR AND THE EAGLE From Confessions of an Economic Hit Man (page 209) by John Perkins: Nearly every culture I know prophesies that in the late 1990's we entered a period of remarkable transition. At monasteries in the Himalayas, ceremonial sites in Indonesia, and indigenous reservations in North America, from the depths of the Amazon to the peaks of the Andes, and into the ancient Mayan cities of Central America AXIOM SCHEME OF REPLACEMENT This first part says if defines uniquely as a function of then the for all there exists such that is true. The second part defines as equivalent to if and only if there exists an such that is true. is the set defined by applying the function defined by to .Since is not defined in the form of a function one has to use this somewhat convoluted definition. ESSENCE AS A PLATONIC IDEAL Essence as a Platonic ideal. Platonic philosophy attempted to capture essence in a different way. Plato thought what we see in the physical world is a dim reflection of the true ideal thing. For example circular objects are crude approximations to the ideal perfect circle. Platonic philosophy aims to understand reality in terms of the ideals MEASUREMENT IN QUANTUM MECHANICS FAQ Lucid description of existing Interpretations and their problems, accessible to general public. EINSTEIN'S INTUITION PDF version of this book Next: The dawning age of Up: Intuition Previous: Intuition as pattern recognition Contents Einstein's intuition. Einstein is universally regarded as the greatest physicist of the 20th century. He alone was responsible for relativity and was a major contributor to quantum mechanics. ATTACHMENT AND THE EGO PDF version of this book Next: The archetypal self of Up: The deeper self Previous: The deeper self Contents Attachment and the ego. We start to acquire a sense of self, probably in the womb, as we learn to distinguish me from not me. `Me' is what I feel directly and what canhurt.
MOUNTAIN MATH SOFTWARE: CONSULTING SERVICES AND MORE Mountain Math Software is a one person consulting firm specializing in image and signal processing, object oriented software engineering and parallel computing. This web site also contains information and speculation on physics, mathematics and philosophy. It includes a free draft version of a book that summarizes this material. The published version is available for purchase. DISCRETIZING THE WAVE EQUATION To fully digitize the equation we must restrict to a discrete set of values like the integers. The expression must be less than one if the difference equation is to approximate the continuous wave equation. Thus we must add an element to the equation to eliminate the possibility of non integer values. WHAT IS AND WHAT WILL BE: INTEGRATING SPIRITUALITY AND SCIENCE What is and what will be integrates science with values and meaning by making the simplest possible assumption about the connection between physical structure and conscious experience. The implications are not just philosophical. They extend to the foundations of mathematics and physics suggesting that Einstein's intuition near the end of hisCONTENTS
Mountain Math Software. home: consulting: videos: book: QM FAQ: contact: PDF version of this book Next: List of Figures Up: whatrh Previous: whatrh Contents. List of Figures THE PROPHECY OF THE CONDOR AND THE EAGLE From Confessions of an Economic Hit Man (page 209) by John Perkins: Nearly every culture I know prophesies that in the late 1990's we entered a period of remarkable transition. At monasteries in the Himalayas, ceremonial sites in Indonesia, and indigenous reservations in North America, from the depths of the Amazon to the peaks of the Andes, and into the ancient Mayan cities of Central America AXIOM SCHEME OF REPLACEMENT This first part says if defines uniquely as a function of then the for all there exists such that is true. The second part defines as equivalent to if and only if there exists an such that is true. is the set defined by applying the function defined by to .Since is not defined in the form of a function one has to use this somewhat convoluted definition. ESSENCE AS A PLATONIC IDEAL Essence as a Platonic ideal. Platonic philosophy attempted to capture essence in a different way. Plato thought what we see in the physical world is a dim reflection of the true ideal thing. For example circular objects are crude approximations to the ideal perfect circle. Platonic philosophy aims to understand reality in terms of the ideals MEASUREMENT IN QUANTUM MECHANICS FAQ Lucid description of existing Interpretations and their problems, accessible to general public. EINSTEIN'S INTUITION PDF version of this book Next: The dawning age of Up: Intuition Previous: Intuition as pattern recognition Contents Einstein's intuition. Einstein is universally regarded as the greatest physicist of the 20th century. He alone was responsible for relativity and was a major contributor to quantum mechanics. ATTACHMENT AND THE EGO PDF version of this book Next: The archetypal self of Up: The deeper self Previous: The deeper self Contents Attachment and the ego. We start to acquire a sense of self, probably in the womb, as we learn to distinguish me from not me. `Me' is what I feel directly and what canhurt.
WHAT IS MATHEMATICS ABOUT? The definition of cardinality creates problems because it depends on what infinite maps are defined in a mathematical system. Formal mathematical systems are, in effect, computer programs for enumerating theorems 1 and thus can only define a countable number of objects. Because all possible maps from integers to reals are not countable, no formal system will contain all of these maps.DIGITAL PHYSICS
Digital physics. The human eye and brain is designed to see continuous lines and other complex structures as a single entity. We do not see patterns of light. We see faces, bodies, chairs, tables. lines and circles. This helps us make sense of the complex patterns of light that strike our eyes. MEASUREMENT IN QUANTUM MECHANICS FAQ: QUANTUM MECHANICS 1. Quantum mechanics. Paul Budnik paul@mtnmath.com. Quantum mechanics is the most successful and the strangest theory in the history of physics. It is the theory that allows us to build postage stamp size computers that do billions of calculations in a second and to buildnuclear weapons.
INTUITION AS PATTERN RECOGNITION Because intuition is a generalized pattern recognition process you cannot break up the result into a series of steps or analyze the process for mistakes. The way you discipline and develop intuition is completely different then the way you develop intellect. You train a neural net by exposing it to a variety of inputs and reinforce those THE UNCERTAINTY PRINCIPLE Figure 7.3: A sine wave or pure tone A pure tone or pure sine wave extends infinitely far in both directions with no change in the size of the peaks or valleys. The frequency in cycles per second is the number of peaks that occur each second. EINSTEIN'S INTUITION PDF version of this book Next: The dawning age of Up: Intuition Previous: Intuition as pattern recognition Contents Einstein's intuition. Einstein is universally regarded as the greatest physicist of the 20th century. He alone was responsible for relativity and was a major contributor to quantum mechanics. THE REAL LINE AND CONFIGURATION SPACE PDF version of this book Next: Relativity plus quantum mechanics Up: Digital physics Previous: Quantum entanglement Contents The real line and configuration space. At the start of this chapter we observed that the continuous real line that we see is a creation of our brain andnervous system.
OBJECTIVE MATHEMATICS IN A NITE UNBOUNDED UNIVERSE statements could be logically determined by a recursively enumerable sequence2 of objective events each of which could occur within the physical universe3.Possible objective physical ATTACHMENT AND THE EGO PDF version of this book Next: The archetypal self of Up: The deeper self Previous: The deeper self Contents Attachment and the ego. We start to acquire a sense of self, probably in the womb, as we learn to distinguish me from not me. `Me' is what I feel directly and what canhurt.
A COMPUTATIONAL APPROACH TO THE ORDINAL NUMBERS 50 LimitTypeInfo descriptions through admisCodeLevel . . . . . . . . . . . . 108 51 Symbols used in limitElement Tables 52 to 55 and limitOrdTable 64 . . . 109
MOUNTAIN MATH SOFTWARE: CONSULTING SERVICES AND MORE Mountain Math Software is a one person consulting firm specializing in image and signal processing, object oriented software engineering and parallel computing. This web site also contains information and speculation on physics, mathematics and philosophy. It includes a free draft version of a book that summarizes this material. The published version is available for purchase. DISCRETIZING THE WAVE EQUATION To fully digitize the equation we must restrict to a discrete set of values like the integers. The expression must be less than one if the difference equation is to approximate the continuous wave equation. Thus we must add an element to the equation to eliminate the possibility of non integer values. WHAT IS AND WHAT WILL BE: INTEGRATING SPIRITUALITY AND SCIENCE What is and what will be integrates science with values and meaning by making the simplest possible assumption about the connection between physical structure and conscious experience. The implications are not just philosophical. They extend to the foundations of mathematics and physics suggesting that Einstein's intuition near the end of hisCONTENTS
Mountain Math Software. home: consulting: videos: book: QM FAQ: contact: PDF version of this book Next: List of Figures Up: whatrh Previous: whatrh Contents. List of Figures THE PROPHECY OF THE CONDOR AND THE EAGLE From Confessions of an Economic Hit Man (page 209) by John Perkins: Nearly every culture I know prophesies that in the late 1990's we entered a period of remarkable transition. At monasteries in the Himalayas, ceremonial sites in Indonesia, and indigenous reservations in North America, from the depths of the Amazon to the peaks of the Andes, and into the ancient Mayan cities of Central America AXIOM SCHEME OF REPLACEMENT This first part says if defines uniquely as a function of then the for all there exists such that is true. The second part defines as equivalent to if and only if there exists an such that is true. is the set defined by applying the function defined by to .Since is not defined in the form of a function one has to use this somewhat convoluted definition. ESSENCE AS A PLATONIC IDEAL Essence as a Platonic ideal. Platonic philosophy attempted to capture essence in a different way. Plato thought what we see in the physical world is a dim reflection of the true ideal thing. For example circular objects are crude approximations to the ideal perfect circle. Platonic philosophy aims to understand reality in terms of the ideals MEASUREMENT IN QUANTUM MECHANICS FAQ Lucid description of existing Interpretations and their problems, accessible to general public. EINSTEIN'S INTUITION PDF version of this book Next: The dawning age of Up: Intuition Previous: Intuition as pattern recognition Contents Einstein's intuition. Einstein is universally regarded as the greatest physicist of the 20th century. He alone was responsible for relativity and was a major contributor to quantum mechanics. ATTACHMENT AND THE EGO PDF version of this book Next: The archetypal self of Up: The deeper self Previous: The deeper self Contents Attachment and the ego. We start to acquire a sense of self, probably in the womb, as we learn to distinguish me from not me. `Me' is what I feel directly and what canhurt.
MOUNTAIN MATH SOFTWARE: CONSULTING SERVICES AND MORE Mountain Math Software is a one person consulting firm specializing in image and signal processing, object oriented software engineering and parallel computing. This web site also contains information and speculation on physics, mathematics and philosophy. It includes a free draft version of a book that summarizes this material. The published version is available for purchase. DISCRETIZING THE WAVE EQUATION To fully digitize the equation we must restrict to a discrete set of values like the integers. The expression must be less than one if the difference equation is to approximate the continuous wave equation. Thus we must add an element to the equation to eliminate the possibility of non integer values. WHAT IS AND WHAT WILL BE: INTEGRATING SPIRITUALITY AND SCIENCE What is and what will be integrates science with values and meaning by making the simplest possible assumption about the connection between physical structure and conscious experience. The implications are not just philosophical. They extend to the foundations of mathematics and physics suggesting that Einstein's intuition near the end of hisCONTENTS
Mountain Math Software. home: consulting: videos: book: QM FAQ: contact: PDF version of this book Next: List of Figures Up: whatrh Previous: whatrh Contents. List of Figures THE PROPHECY OF THE CONDOR AND THE EAGLE From Confessions of an Economic Hit Man (page 209) by John Perkins: Nearly every culture I know prophesies that in the late 1990's we entered a period of remarkable transition. At monasteries in the Himalayas, ceremonial sites in Indonesia, and indigenous reservations in North America, from the depths of the Amazon to the peaks of the Andes, and into the ancient Mayan cities of Central America AXIOM SCHEME OF REPLACEMENT This first part says if defines uniquely as a function of then the for all there exists such that is true. The second part defines as equivalent to if and only if there exists an such that is true. is the set defined by applying the function defined by to .Since is not defined in the form of a function one has to use this somewhat convoluted definition. ESSENCE AS A PLATONIC IDEAL Essence as a Platonic ideal. Platonic philosophy attempted to capture essence in a different way. Plato thought what we see in the physical world is a dim reflection of the true ideal thing. For example circular objects are crude approximations to the ideal perfect circle. Platonic philosophy aims to understand reality in terms of the ideals MEASUREMENT IN QUANTUM MECHANICS FAQ Lucid description of existing Interpretations and their problems, accessible to general public. EINSTEIN'S INTUITION PDF version of this book Next: The dawning age of Up: Intuition Previous: Intuition as pattern recognition Contents Einstein's intuition. Einstein is universally regarded as the greatest physicist of the 20th century. He alone was responsible for relativity and was a major contributor to quantum mechanics. ATTACHMENT AND THE EGO PDF version of this book Next: The archetypal self of Up: The deeper self Previous: The deeper self Contents Attachment and the ego. We start to acquire a sense of self, probably in the womb, as we learn to distinguish me from not me. `Me' is what I feel directly and what canhurt.
WHAT IS MATHEMATICS ABOUT? The definition of cardinality creates problems because it depends on what infinite maps are defined in a mathematical system. Formal mathematical systems are, in effect, computer programs for enumerating theorems 1 and thus can only define a countable number of objects. Because all possible maps from integers to reals are not countable, no formal system will contain all of these maps.DIGITAL PHYSICS
Digital physics. The human eye and brain is designed to see continuous lines and other complex structures as a single entity. We do not see patterns of light. We see faces, bodies, chairs, tables. lines and circles. This helps us make sense of the complex patterns of light that strike our eyes. MEASUREMENT IN QUANTUM MECHANICS FAQ: QUANTUM MECHANICS 1. Quantum mechanics. Paul Budnik paul@mtnmath.com. Quantum mechanics is the most successful and the strangest theory in the history of physics. It is the theory that allows us to build postage stamp size computers that do billions of calculations in a second and to buildnuclear weapons.
INTUITION AS PATTERN RECOGNITION Because intuition is a generalized pattern recognition process you cannot break up the result into a series of steps or analyze the process for mistakes. The way you discipline and develop intuition is completely different then the way you develop intellect. You train a neural net by exposing it to a variety of inputs and reinforce those THE UNCERTAINTY PRINCIPLE Figure 7.3: A sine wave or pure tone A pure tone or pure sine wave extends infinitely far in both directions with no change in the size of the peaks or valleys. The frequency in cycles per second is the number of peaks that occur each second. EINSTEIN'S INTUITION PDF version of this book Next: The dawning age of Up: Intuition Previous: Intuition as pattern recognition Contents Einstein's intuition. Einstein is universally regarded as the greatest physicist of the 20th century. He alone was responsible for relativity and was a major contributor to quantum mechanics. THE REAL LINE AND CONFIGURATION SPACE PDF version of this book Next: Relativity plus quantum mechanics Up: Digital physics Previous: Quantum entanglement Contents The real line and configuration space. At the start of this chapter we observed that the continuous real line that we see is a creation of our brain andnervous system.
OBJECTIVE MATHEMATICS IN A NITE UNBOUNDED UNIVERSE statements could be logically determined by a recursively enumerable sequence2 of objective events each of which could occur within the physical universe3.Possible objective physical ATTACHMENT AND THE EGO PDF version of this book Next: The archetypal self of Up: The deeper self Previous: The deeper self Contents Attachment and the ego. We start to acquire a sense of self, probably in the womb, as we learn to distinguish me from not me. `Me' is what I feel directly and what canhurt.
A COMPUTATIONAL APPROACH TO THE ORDINAL NUMBERS 50 LimitTypeInfo descriptions through admisCodeLevel . . . . . . . . . . . . 108 51 Symbols used in limitElement Tables 52 to 55 and limitOrdTable 64 . . . 109
MOUNTAIN MATH SOFTWARE: CONSULTING SERVICES AND MORE Mountain Math Software is a one person consulting firm specializing in image and signal processing, object oriented software engineering and parallel computing. This web site also contains information and speculation on physics, mathematics and philosophy. It includes a free draft version of a book that summarizes this material. The published version is available for purchase. DISCRETIZING THE WAVE EQUATION To fully digitize the equation we must restrict to a discrete set of values like the integers. The expression must be less than one if the difference equation is to approximate the continuous wave equation. Thus we must add an element to the equation to eliminate the possibility of non integer values. WHAT IS AND WHAT WILL BE: INTEGRATING SPIRITUALITY AND SCIENCE Videos. A five minute video poem, The Erotic Universe, touches on one of the fundamental themes of this book. A twenty minute video poem, Surviving the Singularity, develops the fundamental themes of this book in the light of Ray Kurzweil's The Singularity is Near. A thirty minute video, Mathematical Infinity and Human Destiny (), gives an overview of the major technical and philosophicalCONTENTS
Mountain Math Software. home: consulting: videos: book: QM FAQ: contact: PDF version of this book Next: List of Figures Up: whatrh Previous: whatrh Contents. List of Figures THE PROPHECY OF THE CONDOR AND THE EAGLE From Confessions of an Economic Hit Man (page 209) by John Perkins: Nearly every culture I know prophesies that in the late 1990's we entered a period of remarkable transition. At monasteries in the Himalayas, ceremonial sites in Indonesia, and indigenous reservations in North America, from the depths of the Amazon to the peaks of the Andes, and into the ancient Mayan cities of Central America AXIOM SCHEME OF REPLACEMENT This first part says if defines uniquely as a function of then the for all there exists such that is true. The second part defines as equivalent to if and only if there exists an such that is true. is the set defined by applying the function defined by to .Since is not defined in the form of a function one has to use this somewhat convoluted definition. ESSENCE AS A PLATONIC IDEAL PDF version of this book Next: Gödel and unfathomable complexity Up: Structure and essence Previous: Essence and chemistry Contents Essence as a Platonic ideal. Platonic philosophy attempted to capture essence in a different way. Plato thought what we see in the physical world is a dim reflection of the true ideal thing. For example circular objects are crude approximations to the idealTHE TOTALITY AXIOM
PDF version of this article Next: Creative mathematics and Gödel Up: rvhtm Previous: Immediate experience The Totality Axiom. Michael Tye has argued that the explanatory gap is a cognitive illusion.The consciousness we experience is what it means for certain physical structures in us to exist. MEASUREMENT IN QUANTUM MECHANICS FAQ Lucid description of existing Interpretations and their problems, accessible to general public. ATTACHMENT AND THE EGO PDF version of this book Next: The archetypal self of Up: The deeper self Previous: The deeper self Contents Attachment and the ego. We start to acquire a sense of self, probably in the womb, as we learn to distinguish me from not me. `Me' is what I feel directly and what canhurt.
MOUNTAIN MATH SOFTWARE: CONSULTING SERVICES AND MORE Mountain Math Software is a one person consulting firm specializing in image and signal processing, object oriented software engineering and parallel computing. This web site also contains information and speculation on physics, mathematics and philosophy. It includes a free draft version of a book that summarizes this material. The published version is available for purchase. DISCRETIZING THE WAVE EQUATION To fully digitize the equation we must restrict to a discrete set of values like the integers. The expression must be less than one if the difference equation is to approximate the continuous wave equation. Thus we must add an element to the equation to eliminate the possibility of non integer values. WHAT IS AND WHAT WILL BE: INTEGRATING SPIRITUALITY AND SCIENCE Videos. A five minute video poem, The Erotic Universe, touches on one of the fundamental themes of this book. A twenty minute video poem, Surviving the Singularity, develops the fundamental themes of this book in the light of Ray Kurzweil's The Singularity is Near. A thirty minute video, Mathematical Infinity and Human Destiny (), gives an overview of the major technical and philosophicalCONTENTS
Mountain Math Software. home: consulting: videos: book: QM FAQ: contact: PDF version of this book Next: List of Figures Up: whatrh Previous: whatrh Contents. List of Figures THE PROPHECY OF THE CONDOR AND THE EAGLE From Confessions of an Economic Hit Man (page 209) by John Perkins: Nearly every culture I know prophesies that in the late 1990's we entered a period of remarkable transition. At monasteries in the Himalayas, ceremonial sites in Indonesia, and indigenous reservations in North America, from the depths of the Amazon to the peaks of the Andes, and into the ancient Mayan cities of Central America AXIOM SCHEME OF REPLACEMENT This first part says if defines uniquely as a function of then the for all there exists such that is true. The second part defines as equivalent to if and only if there exists an such that is true. is the set defined by applying the function defined by to .Since is not defined in the form of a function one has to use this somewhat convoluted definition. ESSENCE AS A PLATONIC IDEAL PDF version of this book Next: Gödel and unfathomable complexity Up: Structure and essence Previous: Essence and chemistry Contents Essence as a Platonic ideal. Platonic philosophy attempted to capture essence in a different way. Plato thought what we see in the physical world is a dim reflection of the true ideal thing. For example circular objects are crude approximations to the idealTHE TOTALITY AXIOM
PDF version of this article Next: Creative mathematics and Gödel Up: rvhtm Previous: Immediate experience The Totality Axiom. Michael Tye has argued that the explanatory gap is a cognitive illusion.The consciousness we experience is what it means for certain physical structures in us to exist. MEASUREMENT IN QUANTUM MECHANICS FAQ Lucid description of existing Interpretations and their problems, accessible to general public. ATTACHMENT AND THE EGO PDF version of this book Next: The archetypal self of Up: The deeper self Previous: The deeper self Contents Attachment and the ego. We start to acquire a sense of self, probably in the womb, as we learn to distinguish me from not me. `Me' is what I feel directly and what canhurt.
WHAT IS MATHEMATICS ABOUT? The definition of cardinality creates problems because it depends on what infinite maps are defined in a mathematical system. Formal mathematical systems are, in effect, computer programs for enumerating theorems 1 and thus can only define a countable number of objects. Because all possible maps from integers to reals are not countable, no formal system will contain all of these maps.DIGITAL PHYSICS
PDF version of this book Next: Time and distance scales Up: whatrh Previous: A philosophy of mathematical Contents Digital physics. The human eye and brain is designed to see continuous lines and other complex structures as a single entity. MEASUREMENT IN QUANTUM MECHANICS FAQ: QUANTUM MECHANICS 1. Quantum mechanics. Paul Budnik paul@mtnmath.com. Quantum mechanics is the most successful and the strangest theory in the history of physics. It is the theory that allows us to build postage stamp size computers that do billions of calculations in a second and to buildnuclear weapons.
ESSENCE AND CHEMISTRY PDF version of this book Next: Essence as a Platonic Up: Structure and essence Previous: Structure and essence Contents Essence and chemistry. Chemistry defies this sort of analysis. Salt is made out of sodium, a highly reactive metal, and chlorine, a highly reactive gas. THE REAL LINE AND CONFIGURATION SPACE PDF version of this book Next: Relativity plus quantum mechanics Up: Digital physics Previous: Quantum entanglement Contents The real line and configuration space. At the start of this chapter we observed that the continuous real line that we see is a creation of our brain andnervous system.
THE UNCERTAINTY PRINCIPLE Figure 7.3: A sine wave or pure tone A pure tone or pure sine wave extends infinitely far in both directions with no change in the size of the peaks or valleys. The frequency in cycles per second is the number of peaks that occur each second. INTUITION AS PATTERN RECOGNITION Intuitive insights suddenly appear as ideas or feelings. The solution to a problem leaps into your mind. You have a strong anxiety about taking some action but cannot understand why. EINSTEIN'S INTUITION PDF version of this book Next: The dawning age of Up: Intuition Previous: Intuition as pattern recognition Contents Einstein's intuition. Einstein is universally regarded as the greatest physicist of the 20th century. He alone was responsible for relativity and was a major contributor to quantum mechanics. SCHRÖDINGER'S CAT FOR A 6TH GRADER Schrödinger's cat for a 6th grader The following is my response to a 6th grade student's questions about Schrödinger's cat. It involves a limited discussion of some of the issues in quantum mechanics, which led to Schrödinger's famous cat. ATTACHMENT AND THE EGO PDF version of this book Next: The archetypal self of Up: The deeper self Previous: The deeper self Contents Attachment and the ego. We start to acquire a sense of self, probably in the womb, as we learn to distinguish me from not me. `Me' is what I feel directly and what canhurt.
MOUNTAIN MATH SOFTWARE: CONSULTING SERVICES AND MORE Mountain Math Software is a one person consulting firm specializing in image and signal processing, object oriented software engineering and parallel computing. This web site also contains information and speculation on physics, mathematics and philosophy. It includes a free draft version of a book that summarizes this material. The published version is available for purchase. DISCRETIZING THE WAVE EQUATION To fully digitize the equation we must restrict to a discrete set of values like the integers. The expression must be less than one if the difference equation is to approximate the continuous wave equation. Thus we must add an element to the equation to eliminate the possibility of non integer values. WHAT IS AND WHAT WILL BE: INTEGRATING SPIRITUALITY AND SCIENCE What is and what will be integrates science with values and meaning by making the simplest possible assumption about the connection between physical structure and conscious experience. The implications are not just philosophical. They extend to the foundations of mathematics and physics suggesting that Einstein's intuition near the end of hisCONTENTS
Mountain Math Software. home: consulting: videos: book: QM FAQ: contact: PDF version of this book Next: List of Figures Up: whatrh Previous: whatrh Contents. List of Figures MEASUREMENT IN QUANTUM MECHANICS FAQ 1. Quantum mechanics. Paul Budnik paul@mtnmath.com. Quantum mechanics is the most successful and the strangest theory in the history of physics. It is the theory that allows us to build postage stamp size computers that do billions of calculations in a second and to buildnuclear weapons.
THE REAL LINE AND CONFIGURATION SPACE PDF version of this book Next: Relativity plus quantum mechanics Up: Digital physics Previous: Quantum entanglement Contents The real line and configuration space. At the start of this chapter we observed that the continuous real line that we see is a creation of our brain andnervous system.
ESSENCE AS A PLATONIC IDEAL Essence as a Platonic ideal. Platonic philosophy attempted to capture essence in a different way. Plato thought what we see in the physical world is a dim reflection of the true ideal thing. For example circular objects are crude approximations to the ideal perfect circle. Platonic philosophy aims to understand reality in terms of the ideals AN OVERVIEW OF THE ORDINAL CALCULATOR The calculator does addition, multiplication and exponentiation on ordinal notations. For a recursive limit ordinal notation, , it can list an initial segment of an in nite sequence MEASUREMENT IN QUANTUM MECHANICS FAQ Lucid description of existing Interpretations and their problems, accessible to general public. AXIOM SCHEME OF REPLACEMENT This first part says if defines uniquely as a function of then the for all there exists such that is true. The second part defines as equivalent to if and only if there exists an such that is true. is the set defined by applying the function defined by to .Since is not defined in the form of a function one has to use this somewhat convoluted definition. MOUNTAIN MATH SOFTWARE: CONSULTING SERVICES AND MORE Mountain Math Software is a one person consulting firm specializing in image and signal processing, object oriented software engineering and parallel computing. This web site also contains information and speculation on physics, mathematics and philosophy. It includes a free draft version of a book that summarizes this material. The published version is available for purchase. DISCRETIZING THE WAVE EQUATION To fully digitize the equation we must restrict to a discrete set of values like the integers. The expression must be less than one if the difference equation is to approximate the continuous wave equation. Thus we must add an element to the equation to eliminate the possibility of non integer values. WHAT IS AND WHAT WILL BE: INTEGRATING SPIRITUALITY AND SCIENCE What is and what will be integrates science with values and meaning by making the simplest possible assumption about the connection between physical structure and conscious experience. The implications are not just philosophical. They extend to the foundations of mathematics and physics suggesting that Einstein's intuition near the end of hisCONTENTS
Mountain Math Software. home: consulting: videos: book: QM FAQ: contact: PDF version of this book Next: List of Figures Up: whatrh Previous: whatrh Contents. List of Figures MEASUREMENT IN QUANTUM MECHANICS FAQ 1. Quantum mechanics. Paul Budnik paul@mtnmath.com. Quantum mechanics is the most successful and the strangest theory in the history of physics. It is the theory that allows us to build postage stamp size computers that do billions of calculations in a second and to buildnuclear weapons.
THE REAL LINE AND CONFIGURATION SPACE PDF version of this book Next: Relativity plus quantum mechanics Up: Digital physics Previous: Quantum entanglement Contents The real line and configuration space. At the start of this chapter we observed that the continuous real line that we see is a creation of our brain andnervous system.
ESSENCE AS A PLATONIC IDEAL Essence as a Platonic ideal. Platonic philosophy attempted to capture essence in a different way. Plato thought what we see in the physical world is a dim reflection of the true ideal thing. For example circular objects are crude approximations to the ideal perfect circle. Platonic philosophy aims to understand reality in terms of the ideals AN OVERVIEW OF THE ORDINAL CALCULATOR The calculator does addition, multiplication and exponentiation on ordinal notations. For a recursive limit ordinal notation, , it can list an initial segment of an in nite sequence MEASUREMENT IN QUANTUM MECHANICS FAQ Lucid description of existing Interpretations and their problems, accessible to general public. AXIOM SCHEME OF REPLACEMENT This first part says if defines uniquely as a function of then the for all there exists such that is true. The second part defines as equivalent to if and only if there exists an such that is true. is the set defined by applying the function defined by to .Since is not defined in the form of a function one has to use this somewhat convoluted definition.PAUL BUDNIK, PH.D.
555 Cresci Road, Los Gatos, CA 95033-8512. paul@mtnmath.com · 408.353.3824. Image and Signal Processing. Parallel Computing. Led major projects in image and signal processing. Creative solutions for difficult problems with quality management through project structure and tools that create transparency.DIGITAL PHYSICS
Digital physics. The human eye and brain is designed to see continuous lines and other complex structures as a single entity. We do not see patterns of light. We see faces, bodies, chairs, tables. lines and circles. This helps us make sense of the complex patterns of light that strike our eyes. THE PROPHECY OF THE CONDOR AND THE EAGLE From Confessions of an Economic Hit Man (page 209) by John Perkins: Nearly every culture I know prophesies that in the late 1990's we entered a period of remarkable transition. At monasteries in the Himalayas, ceremonial sites in Indonesia, and indigenous reservations in North America, from the depths of the Amazon to the peaks of the Andes, and into the ancient Mayan cities of Central America OVERVIEW - MTNMATH.COM PDF version of this book Next: Structure Up: whatrh Previous: From the empty set Contents Overview. The journey of this book begins with the distinction between structure and essence. The former is the world of mathematics, science and technology and the latter is the domain of conscious experience. THE REAL LINE AND CONFIGURATION SPACE PDF version of this book Next: Relativity plus quantum mechanics Up: Digital physics Previous: Quantum entanglement Contents The real line and configuration space. At the start of this chapter we observed that the continuous real line that we see is a creation of our brain andnervous system.
WHAT IS AND WHAT WILL BE: INTEGRATING SPIRITUALITY AND What is and what will be integrates spirituality and science by making the simplest possible assumptions about the relationship between conscious experience and physical structure. These assumptions have their roots in mathematical and scientific understanding and have implications for those disciplines. INTUITION AS PATTERN RECOGNITION Because intuition is a generalized pattern recognition process you cannot break up the result into a series of steps or analyze the process for mistakes. The way you discipline and develop intuition is completely different then the way you develop intellect. You train a neural net by exposing it to a variety of inputs and reinforce those MEASUREMENT IN QUANTUM MECHANICS FAQ: THE COPENHAGEN 4. The Copenhagen interpretation. Paul Budnik paul@mtnmath.com. This is the oldest of the interpretations. It is based on Bohr's notion of `complementarity'. Bohr felt that the classical and quantum mechanical models were two complementary ways of dealing with physics both of which were necessary. Bohr felt that an experimental observation collapsed or ruptured (his term) the wave ATTACHMENT AND THE EGO PDF version of this book Next: The archetypal self of Up: The deeper self Previous: The deeper self Contents Attachment and the ego. We start to acquire a sense of self, probably in the womb, as we learn to distinguish me from not me. `Me' is what I feel directly and what canhurt.
EINSTEIN'S INTUITION PDF version of this book Next: The dawning age of Up: Intuition Previous: Intuition as pattern recognition Contents Einstein's intuition. Einstein is universally regarded as the greatest physicist of the 20th century. He alone was responsible for relativity and was a major contributor to quantum mechanics. MOUNTAIN MATH SOFTWARE: CONSULTING SERVICES AND MORE Mountain Math Software is a one person consulting firm specializing in image and signal processing, object oriented software engineering and parallel computing. This web site also contains information and speculation on physics, mathematics and philosophy. It includes a free draft version of a book that summarizes this material. The published version is available for purchase. DISCRETIZING THE WAVE EQUATION To fully digitize the equation we must restrict to a discrete set of values like the integers. The expression must be less than one if the difference equation is to approximate the continuous wave equation. Thus we must add an element to the equation to eliminate the possibility of non integer values. WHAT IS AND WHAT WILL BE: INTEGRATING SPIRITUALITY AND SCIENCE What is and what will be integrates science with values and meaning by making the simplest possible assumption about the connection between physical structure and conscious experience. The implications are not just philosophical. They extend to the foundations of mathematics and physics suggesting that Einstein's intuition near the end of hisCONTENTS
Mountain Math Software. home: consulting: videos: book: QM FAQ: contact: PDF version of this book Next: List of Figures Up: whatrh Previous: whatrh Contents. List of Figures MEASUREMENT IN QUANTUM MECHANICS FAQ 1. Quantum mechanics. Paul Budnik paul@mtnmath.com. Quantum mechanics is the most successful and the strangest theory in the history of physics. It is the theory that allows us to build postage stamp size computers that do billions of calculations in a second and to buildnuclear weapons.
THE REAL LINE AND CONFIGURATION SPACE PDF version of this book Next: Relativity plus quantum mechanics Up: Digital physics Previous: Quantum entanglement Contents The real line and configuration space. At the start of this chapter we observed that the continuous real line that we see is a creation of our brain andnervous system.
ESSENCE AS A PLATONIC IDEAL Essence as a Platonic ideal. Platonic philosophy attempted to capture essence in a different way. Plato thought what we see in the physical world is a dim reflection of the true ideal thing. For example circular objects are crude approximations to the ideal perfect circle. Platonic philosophy aims to understand reality in terms of the ideals AN OVERVIEW OF THE ORDINAL CALCULATOR The calculator does addition, multiplication and exponentiation on ordinal notations. For a recursive limit ordinal notation, , it can list an initial segment of an in nite sequence MEASUREMENT IN QUANTUM MECHANICS FAQ Lucid description of existing Interpretations and their problems, accessible to general public. AXIOM SCHEME OF REPLACEMENT This first part says if defines uniquely as a function of then the for all there exists such that is true. The second part defines as equivalent to if and only if there exists an such that is true. is the set defined by applying the function defined by to .Since is not defined in the form of a function one has to use this somewhat convoluted definition. MOUNTAIN MATH SOFTWARE: CONSULTING SERVICES AND MORE Mountain Math Software is a one person consulting firm specializing in image and signal processing, object oriented software engineering and parallel computing. This web site also contains information and speculation on physics, mathematics and philosophy. It includes a free draft version of a book that summarizes this material. The published version is available for purchase. DISCRETIZING THE WAVE EQUATION To fully digitize the equation we must restrict to a discrete set of values like the integers. The expression must be less than one if the difference equation is to approximate the continuous wave equation. Thus we must add an element to the equation to eliminate the possibility of non integer values. WHAT IS AND WHAT WILL BE: INTEGRATING SPIRITUALITY AND SCIENCE What is and what will be integrates science with values and meaning by making the simplest possible assumption about the connection between physical structure and conscious experience. The implications are not just philosophical. They extend to the foundations of mathematics and physics suggesting that Einstein's intuition near the end of hisCONTENTS
Mountain Math Software. home: consulting: videos: book: QM FAQ: contact: PDF version of this book Next: List of Figures Up: whatrh Previous: whatrh Contents. List of Figures MEASUREMENT IN QUANTUM MECHANICS FAQ 1. Quantum mechanics. Paul Budnik paul@mtnmath.com. Quantum mechanics is the most successful and the strangest theory in the history of physics. It is the theory that allows us to build postage stamp size computers that do billions of calculations in a second and to buildnuclear weapons.
THE REAL LINE AND CONFIGURATION SPACE PDF version of this book Next: Relativity plus quantum mechanics Up: Digital physics Previous: Quantum entanglement Contents The real line and configuration space. At the start of this chapter we observed that the continuous real line that we see is a creation of our brain andnervous system.
ESSENCE AS A PLATONIC IDEAL Essence as a Platonic ideal. Platonic philosophy attempted to capture essence in a different way. Plato thought what we see in the physical world is a dim reflection of the true ideal thing. For example circular objects are crude approximations to the ideal perfect circle. Platonic philosophy aims to understand reality in terms of the ideals AN OVERVIEW OF THE ORDINAL CALCULATOR The calculator does addition, multiplication and exponentiation on ordinal notations. For a recursive limit ordinal notation, , it can list an initial segment of an in nite sequence MEASUREMENT IN QUANTUM MECHANICS FAQ Lucid description of existing Interpretations and their problems, accessible to general public. AXIOM SCHEME OF REPLACEMENT This first part says if defines uniquely as a function of then the for all there exists such that is true. The second part defines as equivalent to if and only if there exists an such that is true. is the set defined by applying the function defined by to .Since is not defined in the form of a function one has to use this somewhat convoluted definition.PAUL BUDNIK, PH.D.
555 Cresci Road, Los Gatos, CA 95033-8512. paul@mtnmath.com · 408.353.3824. Image and Signal Processing. Parallel Computing. Led major projects in image and signal processing. Creative solutions for difficult problems with quality management through project structure and tools that create transparency.DIGITAL PHYSICS
Digital physics. The human eye and brain is designed to see continuous lines and other complex structures as a single entity. We do not see patterns of light. We see faces, bodies, chairs, tables. lines and circles. This helps us make sense of the complex patterns of light that strike our eyes. THE PROPHECY OF THE CONDOR AND THE EAGLE From Confessions of an Economic Hit Man (page 209) by John Perkins: Nearly every culture I know prophesies that in the late 1990's we entered a period of remarkable transition. At monasteries in the Himalayas, ceremonial sites in Indonesia, and indigenous reservations in North America, from the depths of the Amazon to the peaks of the Andes, and into the ancient Mayan cities of Central America OVERVIEW - MTNMATH.COM PDF version of this book Next: Structure Up: whatrh Previous: From the empty set Contents Overview. The journey of this book begins with the distinction between structure and essence. The former is the world of mathematics, science and technology and the latter is the domain of conscious experience. THE REAL LINE AND CONFIGURATION SPACE PDF version of this book Next: Relativity plus quantum mechanics Up: Digital physics Previous: Quantum entanglement Contents The real line and configuration space. At the start of this chapter we observed that the continuous real line that we see is a creation of our brain andnervous system.
WHAT IS AND WHAT WILL BE: INTEGRATING SPIRITUALITY AND What is and what will be integrates spirituality and science by making the simplest possible assumptions about the relationship between conscious experience and physical structure. These assumptions have their roots in mathematical and scientific understanding and have implications for those disciplines. INTUITION AS PATTERN RECOGNITION Because intuition is a generalized pattern recognition process you cannot break up the result into a series of steps or analyze the process for mistakes. The way you discipline and develop intuition is completely different then the way you develop intellect. You train a neural net by exposing it to a variety of inputs and reinforce those MEASUREMENT IN QUANTUM MECHANICS FAQ: THE COPENHAGEN 4. The Copenhagen interpretation. Paul Budnik paul@mtnmath.com. This is the oldest of the interpretations. It is based on Bohr's notion of `complementarity'. Bohr felt that the classical and quantum mechanical models were two complementary ways of dealing with physics both of which were necessary. Bohr felt that an experimental observation collapsed or ruptured (his term) the wave ATTACHMENT AND THE EGO PDF version of this book Next: The archetypal self of Up: The deeper self Previous: The deeper self Contents Attachment and the ego. We start to acquire a sense of self, probably in the womb, as we learn to distinguish me from not me. `Me' is what I feel directly and what canhurt.
EINSTEIN'S INTUITION PDF version of this book Next: The dawning age of Up: Intuition Previous: Intuition as pattern recognition Contents Einstein's intuition. Einstein is universally regarded as the greatest physicist of the 20th century. He alone was responsible for relativity and was a major contributor to quantum mechanics.home
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* Consulting services * Physics * Mathematics * Philosophy * Economics * Videos * Speculation * Book * GPL free software *About
Welcome to Mountain Math Software * Mountain Math Software is a one person consulting firm specializing in image and signal processing, object oriented software engineering and parallel computing. This web site also contains information and speculation on physics, mathematics and philosophy. It includes a free draft version of a book that summarizes this material. The published version is available for purchase.Physics
* Bell's inequality in a regular discrete topology * _The Trouble with Physics_ and mathematics * Measurement in quantum mechanics FAQ * Schrödinger's cat for a 6th grader* Digital physics
* Emergent properties of discretized wave equations * Physics facts and speculation * Einstein on the future of quantum mechanics * Views of contemporary physicists* Bell's Inequality
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* Developing a more complete theoryMathematics
* Objective mathematics in a finite unbounded universe * Mathematical incompleteness and objectively guided intrinsic values * Incompleteness versus a Platonic multiverse * An overview of the ordinal calculatory * Relating mathematical questions to physical reality * Generalizing Kleene's O * Foundations of Mathematics (FOM) postings * Formalizing objective mathematics * 'Recursive notations' for countable admissible level ordinals Ordinal arithmetic calculator and research tool * What is Mathematics About? * A philosophy of mathematical truth * Mathematical infinityPhilosophy
* Mathematical incompleteness and objectively guided intrinsicvalues
* Incompleteness versus a Platonic multiverse * Diversity and the Limits of Reason * Justifying and Exploring Realistic Monism * _The Singularity is Near_ --- Are we ready?* Enough
* The Prophecy of the Condor and the EagleEconomics
* Excessive income inequality destroys economic growth * Inequality of wealth and income in the Great Depression * Long term solutions to disruptive income inequality * The BananaRepublic Computer
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* Mathematical Infinity and Human Destiny Video---transcript
* Surviving the Singularity a video poem about the implications of Ray Kurzweil's _The Singularity is Near_ * The Erotic Universe, a video poem about the erotic creative force that has given birth to us.Speculation
* Are we made of aliens? MOUNTAIN MATH SOFTWAREhome
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