This document discusses interpreting matter and mass in physics as a form of quantum information. It argues that the concept of mass can be seen as a quantity of quantum information, with energy and matter interpreted as amounts of quantum information involved in infinite collections. Seeing mass and energy as quantum information helps unify the concepts of concrete and abstract objects by generalizing information from finite to infinite sets. This allows information to be viewed as a universal substance that subsumes the notions of mass and energy.
Quantum information as the information of infinite seriesVasil Penchev
The quantum information introduced by quantum mechanics is equivalent to that generalization of the classical information from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The qubit, can be interpreted as that generalization of bit, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of results in time after measurement. The quantity of quantum information is the ordinal corresponding to the infinity series in question.
Both classical and quantum information [autosaved]Vasil Penchev
Information can be considered a the most fundamental, philosophical, physical and mathematical concept originating from the totality by means of physical and mathematical transcendentalism (the counterpart of philosophical transcendentalism). Classical and quantum information. particularly by their units, bit and qubit, correspond and unify the finite and infinite:
As classical information is relevant to finite series and sets, as quantum information, to infinite ones. The separable complex Hilbert space of quantum mechanics can be represented equivalently as “qubit space”) as quantum information and doubled dually or “complimentary” by Hilbert arithmetic (classical information).
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Quantum information as the information of infinite seriesVasil Penchev
The quantum information introduced by quantum mechanics is equivalent to that generalization of the classical information from finite to infinite series or collections. The quantity of information is the quantity of choices measured in the units of elementary choice. The qubit, can be interpreted as that generalization of bit, which is a choice among a continuum of alternatives. The axiom of choice is necessary for quantum information. The coherent state is transformed into a well-ordered series of results in time after measurement. The quantity of quantum information is the ordinal corresponding to the infinity series in question.
Both classical and quantum information [autosaved]Vasil Penchev
Information can be considered a the most fundamental, philosophical, physical and mathematical concept originating from the totality by means of physical and mathematical transcendentalism (the counterpart of philosophical transcendentalism). Classical and quantum information. particularly by their units, bit and qubit, correspond and unify the finite and infinite:
As classical information is relevant to finite series and sets, as quantum information, to infinite ones. The separable complex Hilbert space of quantum mechanics can be represented equivalently as “qubit space”) as quantum information and doubled dually or “complimentary” by Hilbert arithmetic (classical information).
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
A COMPREHENSIVE ANALYSIS OF QUANTUM CLUSTERING : FINDING ALL THE POTENTIAL MI...IJDKP
Quantum clustering (QC), is a data clustering algorithm based on quantum mechanics which is
accomplished by substituting each point in a given dataset with a Gaussian. The width of the Gaussian is a
σ value, a hyper-parameter which can be manually defined and manipulated to suit the application.
Numerical methods are used to find all the minima of the quantum potential as they correspond to cluster
centers. Herein, we investigate the mathematical task of expressing and finding all the roots of the
exponential polynomial corresponding to the minima of a two-dimensional quantum potential. This is an
outstanding task because normally such expressions are impossible to solve analytically. However, we
prove that if the points are all included in a square region of size σ, there is only one minimum. This bound
is not only useful in the number of solutions to look for, by numerical means, it allows to to propose a new
numerical approach “per block”. This technique decreases the number of particles by approximating some
groups of particles to weighted particles. These findings are not only useful to the quantum clustering
problem but also for the exponential polynomials encountered in quantum chemistry, Solid-state Physics
and other applications.
Em computação quântica, um algoritmo quântico é um algoritmo que funciona em um modelo realístico de computação quântica. O modelo mais utilizado é o modelo do circuito de computação quântica.
Quantum algorithm for solving linear systems of equationsXequeMateShannon
Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need to know the solution x itself, but rather an approximation of the expectation value of some operator associated with x, e.g., x'Mx for some matrix M. In this case, when A is sparse, N by N and has condition number kappa, classical algorithms can find x and estimate x'Mx in O(N sqrt(kappa)) time. Here, we exhibit a quantum algorithm for this task that runs in poly(log N, kappa) time, an exponential improvement over the best classical algorithm.
Pulse Compression Sequence (PCS) are widely used in radar to increase the range resolution. Binary sequence has the limitation that the compression ratio is small. Ternary code is suggested as an alternative. The design of ternary sequence with good Discriminating Factor (DF) and merit factor can be considered as a nonlinear multivariable optimization problem which is difficult to solve. In this paper, we proposed a new method for designing ternary sequence by using Modified Simulated Annealing Algorithm (MSAA). The general features such as global convergence and robustness of the statistical algorithm are revealed.
Sinc collocation linked with finite differences for Korteweg-de Vries Fraction...IJECEIAES
A novel numerical method is proposed for Korteweg-de Vries Fractional Equation. The fractional derivatives are described based on the Caputo sense. We construct the solution using different approach, that is based on using collocation techniques. The method combining a finite difference approach in the time-fractional direction, and the Sinc-Collocation in the space direction, where the derivatives are replaced by the necessary matrices, and a system of algebraic equations is obtained to approximate solution of the problem. The numerical results are shown to demonstrate the efficiency of the newly proposed method. Easy and economical implementation is the strength of this method.
COMPUTATIONAL PERFORMANCE OF QUANTUM PHASE ESTIMATION ALGORITHMcscpconf
A quantum computation problem is discussed in this paper. Many new features that make quantum computation superior to classical computation can be attributed to quantum coherence
effect, which depends on the phase of quantum coherent state. Quantum Fourier transform algorithm, the most commonly used algorithm, is introduced. And one of its most important
applications, phase estimation of quantum state based on quantum Fourier transform, is presented in details. The flow of phase estimation algorithm and the quantum circuit model are
shown. And the error of the output phase value, as well as the probability of measurement, is analysed. The probability distribution of the measuring result of phase value is presented and the computational efficiency is discussed.
COMPUTATIONAL PERFORMANCE OF QUANTUM PHASE ESTIMATION ALGORITHMcsitconf
A quantum computation problem is discussed in this paper. Many new features that make
quantum computation superior to classical computation can be attributed to quantum coherence
effect, which depends on the phase of quantum coherent state. Quantum Fourier transform
algorithm, the most commonly used algorithm, is introduced. And one of its most important
applications, phase estimation of quantum state based on quantum Fourier transform, is
presented in details. The flow of phase estimation algorithm and the quantum circuit model are
shown. And the error of the output phase value, as well as the probability of measurement, is
analysed. The probability distribution of the measuring result of phase value is presented and
the computational efficiency is discussed.
The mathematical and philosophical concept of vectorGeorge Mpantes
What is behind the physical phenomenon of the velocity; of the force; there is the mathematical concept of the vector. This is a new concept, since force has direction, sense, and magnitude, and we accept the physical principle that the forces exerted on a body can be added to the rule of the parallelogram. This is the first axiom of Newton. Newton essentially requires that the power is a " vectorial " size , without writing clearly , and Galileo that applies the principle of the independence of forces .
HEATED WIND PARTICLE’S BEHAVIOURAL STUDY BY THE CONTINUOUS WAVELET TRANSFORM ...cscpconf
Nowadays Continuous Wavelet Transform (CWT) as well as Fractal analysis is generally used for the Signal and Image processing application purpose. Our current work extends the field of application in case of CWT as well as Fractal analysis by applying it in case of the agitated wind particle’s behavioral study. In this current work in case of the agitated wind particle, we have mathematically showed that the wind particle’s movement exhibits the “Uncorrelated” characteristics during the convectional flow of it. It is also demonstrated here by the Continuous Wavelet Transform (CWT) as well as the Fractal analysis with matlab 7.12 version
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Development and quantification of interatomic potentials. Presented at HTCMC 9 in Toronto, Canada June 30th 2016. For further information on DFTFIT see https://github.com/costrouc/dftfit
Cocentroidal and Isogonal Structures and Their Matricinal Forms, Procedures a...inventionjournals
The vector space of all matrices of the same order on a set of real numbers with a non-negative metric defined on it satisfying certain axioms, we call it a JS metric space. This space can be regarded as the infinite union of matrices possessing a special property that there exist infinite structures having the same (virtual) point-centroid. In this paper we introduce the notion of cocentroidal matrices to a given matrix (Root Matrix) in JS metric space wherein the metric is the Euclidean metric measuring the distance between two matrices to be the distance between their centroids. We describe mathematical routines that we envisaged and then theoretically verified for its applicability in a system that is under rotational motion about a point-centroid, and various cases in physics. We have sounded the same concept by considering necessary graphs drawn on the basis of mathematical equations as an additional feature of this article. Isogonality of different cocentroidal structures is the conceptual origin of one of the main concepts, necessitating the notion of convergence in terms of determinant values of a system of cocentroidal matrices.
Sensing Method for Two-Target Detection in Time-Constrained Vector Poisson Ch...sipij
It is an experimental design problem in which there are two Poisson sources with two possible and known rates, and one counter. Through a switch, the counter can observe the sources individually or the counts can be combined so that the counter observes the sum of the two. The sensor scheduling problem is to determine an optimal proportion of the available time to be allocated toward individual and joint sensing, under a total time
constraint. Two different metrics are used for optimization: mutual information between the sources and the observed counts, and probability of detection for the associated source detection problem. Our results, which are primarily computational, indicate similar but not identical results under the two cost functions.
Is Mass at Rest One and the Same? A Philosophical Comment: on the Quantum I...Vasil Penchev
The way, in which quantum information can unify quantum mechanics (and therefore the standard
model) and general relativity, is investigated. Quantum information is defined as the generalization
of the concept of information as to the choice among infinite sets of alternatives. Relevantly, the
axiom of choice is necessary in general. The unit of quantum information, a qubit is interpreted
as a relevant elementary choice among an infinite set of alternatives generalizing that of a bit.
The invariance to the axiom of choice shared by quantum mechanics is introduced: It constitutes
quantum information as the relation of any state unorderable in principle (e.g. any coherent quantum
state before measurement) and the same state already well-ordered (e.g. the well-ordered statistical
ensemble of the measurement of the quantum system at issue). This allows of equating the classical and
quantum time correspondingly as the well-ordering of any physical quantity or quantities and their
coherent superposition. That equating is interpretable as the isomorphism of Minkowski space and
Hilbert space. Quantum information is the structure interpretable in both ways and thus underlying
their unification. Its deformation is representable correspondingly as gravitation in the deformed
pseudo-Riemannian space of general relativity and the entanglement of two or more quantum
systems. The standard model studies a single quantum system and thus privileges a single reference
frame turning out to be inertial for the generalized symmetry [U(1)]X[SU(2)]X[SU(3)] “gauging” the
standard model. As the standard model refers to a single quantum system, it is necessarily linear
and thus the corresponding privileged reference frame is necessary inertial. The Higgs mechanism
U(1) → [U(1)]X[SU(2)] confirmed enough already experimentally describes exactly the choice of the
initial position of a privileged reference frame as the corresponding breaking of the symmetry. The
standard model defines ‘mass at rest’ linearly and absolutely, but general relativity non-linearly
and relatively. The “Big Bang” hypothesis is additional interpreting that position as that of the
“Big Bang”. It serves also in order to reconcile the linear standard model in the singularity of the
“Big Bang” with the observed nonlinearity of the further expansion of the universe described very
well by general relativity. Quantum information links the standard model and general relativity in
another way by mediation of entanglement. The linearity and absoluteness of the former and the
nonlinearity and relativeness of the latter can be considered as the relation of a whole and the same
whole divided into parts entangled in general.
A COMPREHENSIVE ANALYSIS OF QUANTUM CLUSTERING : FINDING ALL THE POTENTIAL MI...IJDKP
Quantum clustering (QC), is a data clustering algorithm based on quantum mechanics which is
accomplished by substituting each point in a given dataset with a Gaussian. The width of the Gaussian is a
σ value, a hyper-parameter which can be manually defined and manipulated to suit the application.
Numerical methods are used to find all the minima of the quantum potential as they correspond to cluster
centers. Herein, we investigate the mathematical task of expressing and finding all the roots of the
exponential polynomial corresponding to the minima of a two-dimensional quantum potential. This is an
outstanding task because normally such expressions are impossible to solve analytically. However, we
prove that if the points are all included in a square region of size σ, there is only one minimum. This bound
is not only useful in the number of solutions to look for, by numerical means, it allows to to propose a new
numerical approach “per block”. This technique decreases the number of particles by approximating some
groups of particles to weighted particles. These findings are not only useful to the quantum clustering
problem but also for the exponential polynomials encountered in quantum chemistry, Solid-state Physics
and other applications.
Em computação quântica, um algoritmo quântico é um algoritmo que funciona em um modelo realístico de computação quântica. O modelo mais utilizado é o modelo do circuito de computação quântica.
Quantum algorithm for solving linear systems of equationsXequeMateShannon
Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need to know the solution x itself, but rather an approximation of the expectation value of some operator associated with x, e.g., x'Mx for some matrix M. In this case, when A is sparse, N by N and has condition number kappa, classical algorithms can find x and estimate x'Mx in O(N sqrt(kappa)) time. Here, we exhibit a quantum algorithm for this task that runs in poly(log N, kappa) time, an exponential improvement over the best classical algorithm.
Pulse Compression Sequence (PCS) are widely used in radar to increase the range resolution. Binary sequence has the limitation that the compression ratio is small. Ternary code is suggested as an alternative. The design of ternary sequence with good Discriminating Factor (DF) and merit factor can be considered as a nonlinear multivariable optimization problem which is difficult to solve. In this paper, we proposed a new method for designing ternary sequence by using Modified Simulated Annealing Algorithm (MSAA). The general features such as global convergence and robustness of the statistical algorithm are revealed.
Sinc collocation linked with finite differences for Korteweg-de Vries Fraction...IJECEIAES
A novel numerical method is proposed for Korteweg-de Vries Fractional Equation. The fractional derivatives are described based on the Caputo sense. We construct the solution using different approach, that is based on using collocation techniques. The method combining a finite difference approach in the time-fractional direction, and the Sinc-Collocation in the space direction, where the derivatives are replaced by the necessary matrices, and a system of algebraic equations is obtained to approximate solution of the problem. The numerical results are shown to demonstrate the efficiency of the newly proposed method. Easy and economical implementation is the strength of this method.
COMPUTATIONAL PERFORMANCE OF QUANTUM PHASE ESTIMATION ALGORITHMcscpconf
A quantum computation problem is discussed in this paper. Many new features that make quantum computation superior to classical computation can be attributed to quantum coherence
effect, which depends on the phase of quantum coherent state. Quantum Fourier transform algorithm, the most commonly used algorithm, is introduced. And one of its most important
applications, phase estimation of quantum state based on quantum Fourier transform, is presented in details. The flow of phase estimation algorithm and the quantum circuit model are
shown. And the error of the output phase value, as well as the probability of measurement, is analysed. The probability distribution of the measuring result of phase value is presented and the computational efficiency is discussed.
COMPUTATIONAL PERFORMANCE OF QUANTUM PHASE ESTIMATION ALGORITHMcsitconf
A quantum computation problem is discussed in this paper. Many new features that make
quantum computation superior to classical computation can be attributed to quantum coherence
effect, which depends on the phase of quantum coherent state. Quantum Fourier transform
algorithm, the most commonly used algorithm, is introduced. And one of its most important
applications, phase estimation of quantum state based on quantum Fourier transform, is
presented in details. The flow of phase estimation algorithm and the quantum circuit model are
shown. And the error of the output phase value, as well as the probability of measurement, is
analysed. The probability distribution of the measuring result of phase value is presented and
the computational efficiency is discussed.
The mathematical and philosophical concept of vectorGeorge Mpantes
What is behind the physical phenomenon of the velocity; of the force; there is the mathematical concept of the vector. This is a new concept, since force has direction, sense, and magnitude, and we accept the physical principle that the forces exerted on a body can be added to the rule of the parallelogram. This is the first axiom of Newton. Newton essentially requires that the power is a " vectorial " size , without writing clearly , and Galileo that applies the principle of the independence of forces .
HEATED WIND PARTICLE’S BEHAVIOURAL STUDY BY THE CONTINUOUS WAVELET TRANSFORM ...cscpconf
Nowadays Continuous Wavelet Transform (CWT) as well as Fractal analysis is generally used for the Signal and Image processing application purpose. Our current work extends the field of application in case of CWT as well as Fractal analysis by applying it in case of the agitated wind particle’s behavioral study. In this current work in case of the agitated wind particle, we have mathematically showed that the wind particle’s movement exhibits the “Uncorrelated” characteristics during the convectional flow of it. It is also demonstrated here by the Continuous Wavelet Transform (CWT) as well as the Fractal analysis with matlab 7.12 version
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Development and quantification of interatomic potentials. Presented at HTCMC 9 in Toronto, Canada June 30th 2016. For further information on DFTFIT see https://github.com/costrouc/dftfit
Cocentroidal and Isogonal Structures and Their Matricinal Forms, Procedures a...inventionjournals
The vector space of all matrices of the same order on a set of real numbers with a non-negative metric defined on it satisfying certain axioms, we call it a JS metric space. This space can be regarded as the infinite union of matrices possessing a special property that there exist infinite structures having the same (virtual) point-centroid. In this paper we introduce the notion of cocentroidal matrices to a given matrix (Root Matrix) in JS metric space wherein the metric is the Euclidean metric measuring the distance between two matrices to be the distance between their centroids. We describe mathematical routines that we envisaged and then theoretically verified for its applicability in a system that is under rotational motion about a point-centroid, and various cases in physics. We have sounded the same concept by considering necessary graphs drawn on the basis of mathematical equations as an additional feature of this article. Isogonality of different cocentroidal structures is the conceptual origin of one of the main concepts, necessitating the notion of convergence in terms of determinant values of a system of cocentroidal matrices.
Sensing Method for Two-Target Detection in Time-Constrained Vector Poisson Ch...sipij
It is an experimental design problem in which there are two Poisson sources with two possible and known rates, and one counter. Through a switch, the counter can observe the sources individually or the counts can be combined so that the counter observes the sum of the two. The sensor scheduling problem is to determine an optimal proportion of the available time to be allocated toward individual and joint sensing, under a total time
constraint. Two different metrics are used for optimization: mutual information between the sources and the observed counts, and probability of detection for the associated source detection problem. Our results, which are primarily computational, indicate similar but not identical results under the two cost functions.
Is Mass at Rest One and the Same? A Philosophical Comment: on the Quantum I...Vasil Penchev
The way, in which quantum information can unify quantum mechanics (and therefore the standard
model) and general relativity, is investigated. Quantum information is defined as the generalization
of the concept of information as to the choice among infinite sets of alternatives. Relevantly, the
axiom of choice is necessary in general. The unit of quantum information, a qubit is interpreted
as a relevant elementary choice among an infinite set of alternatives generalizing that of a bit.
The invariance to the axiom of choice shared by quantum mechanics is introduced: It constitutes
quantum information as the relation of any state unorderable in principle (e.g. any coherent quantum
state before measurement) and the same state already well-ordered (e.g. the well-ordered statistical
ensemble of the measurement of the quantum system at issue). This allows of equating the classical and
quantum time correspondingly as the well-ordering of any physical quantity or quantities and their
coherent superposition. That equating is interpretable as the isomorphism of Minkowski space and
Hilbert space. Quantum information is the structure interpretable in both ways and thus underlying
their unification. Its deformation is representable correspondingly as gravitation in the deformed
pseudo-Riemannian space of general relativity and the entanglement of two or more quantum
systems. The standard model studies a single quantum system and thus privileges a single reference
frame turning out to be inertial for the generalized symmetry [U(1)]X[SU(2)]X[SU(3)] “gauging” the
standard model. As the standard model refers to a single quantum system, it is necessarily linear
and thus the corresponding privileged reference frame is necessary inertial. The Higgs mechanism
U(1) → [U(1)]X[SU(2)] confirmed enough already experimentally describes exactly the choice of the
initial position of a privileged reference frame as the corresponding breaking of the symmetry. The
standard model defines ‘mass at rest’ linearly and absolutely, but general relativity non-linearly
and relatively. The “Big Bang” hypothesis is additional interpreting that position as that of the
“Big Bang”. It serves also in order to reconcile the linear standard model in the singularity of the
“Big Bang” with the observed nonlinearity of the further expansion of the universe described very
well by general relativity. Quantum information links the standard model and general relativity in
another way by mediation of entanglement. The linearity and absoluteness of the former and the
nonlinearity and relativeness of the latter can be considered as the relation of a whole and the same
whole divided into parts entangled in general.
What is quantum information? Information symmetry and mechanical motionVasil Penchev
The concept of quantum information is introduced as both normed superposition of two orthogonal subspaces of the separable complex Hilbert space and invariance of Hamilton and Lagrange representation of any mechanical system. The base is the isomorphism of the standard introduction and the representation of a qubit to a 3D unit ball, in which two points are chosen.
The separable complex Hilbert space is considered as the free variable of quantum information and any point in it (a wave function describing a state of a quantum system) as its value as the bound variable.
A qubit is equivalent to the generalization of ‘bit’ from the set of two equally probable alternatives to an infinite set of alternatives. Then, that Hilbert space is considered as a generalization of Peano arithmetic where any unit is substituted by a qubit and thus the set of natural number is mappable within any qubit as the complex internal structure of the unit or a different state of it. Thus, any mathematical structure being reducible to set theory is representable as a set of wave functions and a subspace of the separable complex Hilbert space, and it can be identified as the category of all categories for any functor represents an operator transforming a set (or subspace) of the separable complex Hilbert space into another. Thus, category theory is isomorphic to the Hilbert-space representation of set theory & Peano arithmetic as above.
Given any value of quantum information, i.e. a point in the separable complex Hilbert space, it always admits two equally acceptable interpretations: the one is physical, the other is mathematical. The former is a wave function as the exhausted description of a certain state of a certain quantum system. The latter chooses a certain mathematical structure among a certain category. Thus there is no way to be distinguished a mathematical structure from a physical state for both are described exhaustedly as a value of quantum information. This statement in turn can be utilized to be defined quantum information by the identity of any mathematical structure to a physical state, and also vice versa. Further, that definition is equivalent to both standard definition as the normed superposition and invariance of Hamilton and Lagrange interpretation of mechanical motion introduced in the beginning of the paper.
Then, the concept of information symmetry can be involved as the symmetry between three elements or two pairs of elements: Lagrange representation and each counterpart of the pair of Hamilton representation. The sense and meaning of information symmetry may be visualized by a single (quantum) bit and its interpretation as both (privileged) reference frame and the symmetries of the Standard model.
MORE THAN IMPOSSIBLE: NEGATIVE AND COMPLEX PROBABILITIES AND THEIR INTERPRET...Vasil Penchev
What might mean “more than impossible”? For example, that could be what happens without any cause or that physical change which occurs without any physical force (interaction) to act. Then, the quantity of the equivalent physical force, which would cause the same effect, can serve as a measure of the complex probability.
Quantum mechanics introduces those fluctuations, the physical actions of which are commensurable with the Plank constant. They happen by themselves without any cause even in principle. Those causeless changes are both instable and extremely improbable in the world perceived by our senses immediately for the physical actions in it are much, much bigger than the Plank constant.
Universal History & the Problem of TimeVasil Penchev
The establishment of universal history requires to be understood what time is
•Time is the transformation of the future into past by the choices in the present
•History should be grounded on that understanding of historical time, which would include the present and future rather than only the past
"God’s dice" is a qubit: They need an infinite set of different symbols for all sides of them
INTRODUCTION
I A SKETCH OF THE PROOF OF THE THESIS
II GLEASON’S THEOREM (1957) AND THE THESIS
III GOD’S DIE, GLEASON’S THEOREM AND AN IDEA FOR A SHORT PROOF OF FERMAT’S LAST THEOREM
IV INTERPRETATION OF THE THESIS
V GOD’S DICE (A QUBIT) AS A LAW OF CONSERVATION AND TRANSFORMATION
VI CONCLUSION
Отвъд машината на Тюринг: квантовият компютърVasil Penchev
Книгата е посветена на възможността за компютър, чийто възможности принципно надвишават възможностите на съвременните компютри.
Машината на Тюринг е математическият модел, който ги обобщава. Квантовият компю-тър се основава на принципите на квантовата механика и теорията на квантовата ин-формация. Изследва се въпросът дали квантовият компютър е машина на Тюринг. Предпочита се нова мета-математическа интерпретация и се обсъждат взаимоотноше-нията със съществуващите. Философска и онтологическа проекция е предлаганото видоизменено, а именно „дуалистично питагорейство”.
Неразрешими твърдения ли са самите т. нар. теореми на Гьодел за непълнотата, ако те се отнесат към самите себе си? Как следва да се тълкуват явленията на сдвояване (entanglement), квантовият компютър и квантовата информация аритметически и логичес-ки?
Книгата е предназначена за научни работници в областта на физиката, математиката и философията, за докторанти и студенти, за всеки, който се интересува от този съвсем нов отрасъл на знанието.
Problem of the direct quantum-information transformation of chemical substance Vasil Penchev
The “Trigger field” from sci-fi to science
ISPC’20 - 2016
Boca Raton, FL, USA: 1-4 August 2016
International Society for the Philosophy of Chemistry:20th Annual Conference
Arthur Clark and Michael Kube–McDowell (“The Triger”, 1999) suggested the sci-fi idea about the direct transformation from a chemical substance into another by the action of a newly physical, “Trigger” field
Karl Brohier, a Nobel Prize winner, who is a dramatic persona in the novel, elaborates a new theory, re-reading and re-writing Pauling’s “The Nature of the Chemical Bond”
According to Brohier: “Information organizes and differentiates energy. It regularizes and stabilizes matter. Information propagates through matter-energy and mediates the interactions of matter-energy”
Dr Horton, his collaborator in the novel replies: “If the universe consists of energy and information, then the Trigger somehow alters the information envelope of certain substances –“
“Alters it, scrambles it, overwhelms it, destabilizes it” Brohier adds. 'And crudely, too. The units we're building now are unimaginably wasteful - like hitting a computer with ten thousand volts of lightning to change a few bytes of its programming. It was a fluke, pure serendipity, that somewhere in the smear of informational noise describing your prototype were a few coherent words in the language of resonance mechanics - the new science of matter. You stumbled on the characteristic chemical signature of certain nitrate compounds, which picked your signal out of the air like a ham radio operator finding a voice in the static.'
One can suggest that any chemical substances and changes are fundamentally representable as quantum information and its transformations
If entanglement is interpreted as a physical field, though any group above seems to be unattachable to it, it might be identified as the “Triger field”
It might cause a direct transformation of any chemical substance from a remote distance
Is this possible in principle?
John Bell and von Neumann's theorem about the absence of hidden parameters in...Vasil Penchev
Текстът разглежда статията на Бел относно теоремата на фон Нойман за отсъствие на скрити параметри в квантовата механика. Подчертани са философскито значение и тълкувание.
The square of opposition: Four colours sufficient for the “map” of logicVasil Penchev
How many “letters” does the “alphabet of nature” need?
Nature is maximally economical, so that that number would be the minimally possible one. What is the common in the following facts?
(1) The square of opposition
(2) The “letters” of DNA
(3) The number of colors enough for any geographic al map
(4) The minimal number of points, which allows of them not be always well-ordere
Началото на квантовата информация: "парадоксът" на Айнщайн-Подолски-РозенVasil Penchev
THE BEGINNING OF QUANTUM INFORMATION: THE "PARADOX" OF EINSTEIN - PODOLSKY - ROSEN
The non-paradoxical paradox ¬– The argument EPR – „The element of reality“ – A new type of physical interaction? ¬– The alleged incompleteness of quantum mechanics – The problem about the simultaneity of reality ¬– „The criterion for physical reality“ ¬– Bohr‘s answer (1935) – The fundamentality of choice and of probability – Time and energy – Bohr, Kramers, Slater‘s theory (1924) – Complementarity and the dualistic character of reality – Analogies to relativity
Непарадоксалният парадокс – Аргументът АПР – „Елементът на реалността” – Нов тип физическо взаимодействие? – Набедената непълнота на квантовата механика – Проб-лемът около едновременността на реалността – „Критерият за физическа реалност” – Отговорът на Бор (1935) – Фундаменталност на избора и на вероятността – Време и енергия – Теорията на Бор, Крамерс и Слатер (1924) – Допълнителност и дуален ха-рактер на реалността – Аналогии с теорията на относителността
Equilibrium in Nash’s mind (with references)Vasil Penchev
Capps (2009: 145)1 suggested the hypothesis that “the Nash equilibrium is descriptive of the normal brain, whereas the game theory formulated by John van Neumann, which Nash’s theory challenges, is descriptive of the schizophrenic brain”
Arguments are offered in favor of Capps’s thesis from psychiatry, game theory, set theory philosophy and theology
Language is Koto ba in Japanese: “the petals of rhapsodic silence”, according to the Questioning’s translation
The Questioning synthesizes the elucidation of the Japanese about what the Japanese word for ‘language’ means in this way
The dialog and thus text are conecntarted on that understanding of language hidden in the extraordinary definition of language which the Japanase language contains as a word for ‘language’
Quantum information as the information of infinite series Vasil Penchev
Quantum information is equivalent to that generalization of the classical information from finite to infinite series or collections
The quantity of information is the quantity of choices measured in the units of elementary choice
The qubit is that generalization of bit, which is a choice among a continuum of alternatives
The axiom of choice is necessary for quantum information: The coherent state is transformed into a well-ordered series of results in time after measurement
The quantity of quantum information is the ordinal corresponding to the infinity series in question
Quantum Information as the Substance of the WorldVasil Penchev
The concept of matter in physics can be considered as a generalized form of information, that of quantum information involved by quantum mechanics
Even more, quantum information is a generalization of classical information: So, information either classical or quantum is the universal foundation of all in the world
In particular, the ideal or abstract objects also share information (the classical one) in their common base
Quantum Computer: Quantum Model and RealityVasil Penchev
1. Can a quantum model unlike a classical model coincide with reality?
2. Is reality interpretable as a quantum computer?
3. Can physical processes be understood better and more generally as computations of quantum computer?
4. Is quantum information the real fundament of the world?
5. Does the conception of quantum computer unify physics and mathematics and thus the material and the ideal world?
6. Is quantum computer a non-Turing machine in principle?
7. Can a quantum computation be interpreted as an infinite classical computational process of a Turing machine?
8. Does quantum computer introduce the notion of “actually infinite computational process”?
Hilbert Space and pseudo-Riemannian Space: The Common Base of Quantum Informa...Vasil Penchev
Hilbert space underlying quantum mechanics and pseudo-Riemannian space underlying general relativity share a common base of quantum information. Hilbert space can be interpreted as the free variable of quantum information, and any point in it, being equivalent to a wave function (and thus, to a state of a quantum system), as a value of that variable of quantum information. In turn, pseudo-Riemannian space can be interpreted as the interaction of two or more quantities of quantum information and thus, as two or more entangled quantum systems. Consequently, one can distinguish local physical interactions describable by a single Hilbert space (or by any factorizable tensor product of such ones) and non-local physical interactions describable only by means by that Hilbert space, which cannot be factorized as any tensor product of the Hilbert spaces, by means of which one can describe the interacting quantum subsystems separately. Any interaction, which can be exhaustedly described in a single Hilbert space, such as the weak, strong, and electromagnetic one, is local in terms of quantum information. Any interaction, which cannot be described thus, is nonlocal in terms of quantum information. Any interaction, which is exhaustedly describable by pseudo-Riemannian space, such as gravity, is nonlocal in this sense. Consequently all known physical interaction can be described by a single geometrical base interpreting it in terms of quantum information.
Analogia entis as analogy universalized and formalized rigorously and mathema...Vasil Penchev
THE SECOND WORLD CONGRESS ON ANALOGY, POZNAŃ, MAY 24-26, 2017
(The Venue: Sala Lubrańskiego (Lubrański’s Hall at the Collegium Minus), Adam Mickiewicz University, Address: ul. Wieniawskiego 1) The presentation: 24 May, 15:30
The Einstein field equation in terms of the Schrödinger equationVasil Penchev
The Einstein field equation (EFE) can be directly linked to the Schrödinger equation (SE) by meditation of the quantity of quantum information and its units: qubits
•
One qubit is an “atom” both of Hilbert space and Minkovski space underlying correspondingly quantum mechanics and special relativity
•
Pseudo-Riemannian space of general relativity being “deformed” Minkowski space therefore consists of “deformed” qubits directly referring to the eventual “deformation” of Hilbert space
“No hidden variables!”: From Neumann’s to Kochen and Specker’s theorem in qua...Vasil Penchev
The talk addresses a philosophical comparison and thus interpretation of both theorems having one and the same subject:
The absence of the “other half” of variables, called “hidden” for that, to the analogical set of variables in classical mechanics:
These theorems are:
John’s von Neumann’s (1932)
Simon Kochen and Ernst Specker’s (1968)
The Emergent Entangled Informational Universe .pdfOlivierDenis15
The dream of capturing the workings of the entire universe in a single equation or a simple set of equations is still pursued. A set of five new equivalent formulations of entropy based on the introduction of the mass of the information bit in Louis de Broglie's hidden thermodynamics and on the physicality of information, is proposed, within the framework of the emergent entangled informational universe model, which is based on the principle of strong emergence, the mass-energy-information equivalence principle and the Landauer’s principle. This model can explain various process as informational quantum processes such energy, dark matter, dark energy, cosmological constant and vacuum energy. The dark energy is explained as a collective potential of all particles with their individual zero-point energy emerging from an informational field, distinct from the usual fields of matter of quantum field theory, associated with dark matter as having a finite and quantifiable mass; while resolving the black hole information paradox by calculating the entropy of the entangled Hawking radiation, and shedding light on gravitational fine-grained entropy of black holes. This model explains the collapse of the wave function by the fact that a measure informs the measurer about the system to be measured and, this model is able to invalidate the many worlds interpretation of quantum mechanics and the simulation hypothesis.
The Gödel incompleteness can be modeled on the alleged incompleteness of quantum mechanics
Then the proved and even experimentally confirmed completeness of quantum mechanics can be reversely interpreted as a strategy of completeness as to the foundation of mathematics
Infinity is equivalent to a second and independent finiteness
Two independent Peano arithmetics as well as one single Hilbert space as an unification of geometry and arithmetic are sufficient to the self-foundation of mathematics
Quantum mechanics is inseparable from the foundation of mathematics and thus from set theory particularly
Similar to Matter as Information. Quantum Information as Matter (20)
The generalization of the Periodic table. The "Periodic table" of "dark matter"Vasil Penchev
The thesis is: the “periodic table” of “dark matter” is equivalent to the standard periodic table of the visible matter being entangled. Thus, it is to consist of all possible entangled states of the atoms of chemical elements as quantum systems. In other words, an atom of any chemical element and as a quantum system, i.e. as a wave function, should be represented as a non-orthogonal in general (i.e. entangled) subspace of the separable complex Hilbert space relevant to the system to which the atom at issue is related as a true part of it. The paper follows previous publications of mine stating that “dark matter” and “dark energy” are projections of arbitrarily entangled states on the cognitive “screen” of Einstein’s “Mach’s principle” in general relativity postulating that gravitational field can be generated only by mass or energy.
Modal History versus Counterfactual History: History as IntentionVasil Penchev
The distinction of whether real or counterfactual history makes sense only post factum. However, modal history is to be defined only as ones’ intention and thus, ex-ante. Modal history is probable history, and its probability is subjective. One needs phenomenological “epoché” in relation to its reality (respectively, counterfactuality). Thus, modal history describes historical “phenomena” in Husserl’s sense and would need a specific application of phenomenological reduction, which can be called historical reduction. Modal history doubles history just as the recorded history of historiography does it. That doubling is a necessary condition of historical objectivity including one’s subjectivity: whether actors’, ex-anteor historians’ post factum. The objectivity doubled by ones’ subjectivity constitute “hermeneutical circle”.
A CLASS OF EXEMPLES DEMONSTRATING THAT “푃푃≠푁푁푁 ” IN THE “P VS NP” PROBLEMVasil Penchev
The CMI Millennium “P vs NP Problem” can be resolved e.g. if one shows at least one counterexample to the “P=NP” conjecture. A certain class of problems being such counterexamples will be formulated. This implies the rejection of the hypothesis “P=NP” for any conditions satisfying the formulation of the problem. Thus, the solution “P≠NP” of the problem in general is proved. The class of counterexamples can be interpreted as any quantum superposition of any finite set of quantum states. The Kochen-Specker theorem is involved. Any fundamentally random choice among a finite set of alternatives belong to “NP’ but not to “P”. The conjecture that the set complement of “P” to “NP” can be described by that kind of choice exhaustively is formulated.
FERMAT’S LAST THEOREM PROVED BY INDUCTION (accompanied by a philosophical com...Vasil Penchev
A proof of Fermat’s last theorem is demonstrated. It is very brief, simple, elementary, and absolutely arithmetical. The necessary premises for the proof are only: the three definitive properties of the relation of equality (identity, symmetry, and transitivity), modus tollens, axiom of induction, the proof of Fermat’s last theorem in the case of n=3 as well as the premises necessary for the formulation of the theorem itself. It involves a modification of Fermat’s approach of infinite descent. The infinite descent is linked to induction starting from n=3 by modus tollens. An inductive series of modus tollens is constructed. The proof of the series by induction is equivalent to Fermat’s last theorem. As far as Fermat had been proved the theorem for n=4, one can suggest that the proof for n≥4 was accessible to him.
An idea for an elementary arithmetical proof of Fermat’s last theorem (FLT) by induction is suggested. It would be accessible to Fermat unlike Wiles’s proof (1995), and would justify Fermat’s claim (1637) for its proof. The inspiration for a simple proof would contradict to Descartes’s dualism for appealing to merge “mind” and “body”, “words” and “things”, “terms” and “propositions”, all orders of logic. A counterfactual course of history of mathematics and philosophy may be admitted. The bifurcation happened in Descartes and Fermat’s age. FLT is exceptionally difficult to be proved in our real branch rather than in the counterfactual one.
The space-time interpretation of Poincare’s conjecture proved by G. Perelman Vasil Penchev
Background and prehistory:
The French mathematician Henri Poincaré offered a statement known as “Poincaré’s conjecture” without a proof. It states that any 4-dimensional ball is equivalent to 3-dimensional Euclidean space topologically: a continuous mapping exists so that it maps the former ball into the latter space one-to-one.
At first glance, it seems to be too paradoxical for the following mismatches: the former is 4-dimensional and as if “closed” unlike the latter, 3-dimensional and as if “open” according to common sense. So, any mapping seemed to be necessarily discrete to be able to overcome those mismatches, and being discrete impies for the conjecture to be false.
Anyway, nobody managed neither to prove nor to reject rigorously the conjecture about one century. It was included even in the Millennium Prize Problems by the Clay Mathematics Institute.
It was proved by Grigory Perelman in 2003 using the concept of information.
Physical interpretation in terms of special relativity:
One may notice that the 4-ball is almost equivalent topologically to the “imaginary domain” of Minkowski space in the following sense of “almost”: that “half” of Minkowski space is equivalent topologically to the unfolding of a 4-ball. Then, the conjecture means the topological equivalence of the physical 3-space and its model in special relativity. In turn, that topological equivalence means their equivalence as to causality physically. So, Perelman has proved the adequacy of Minkowski space as a model of the physical 3-dimensional space rigorously. Of course, all experiments confirm the same empirically, but not mathematically as he did.
An idea of another proof of the conjecture based on that physical interpretation:
Topologically seen, the problem turns out to be reformulated so: one needs a proof of the topological equivalence of a 4-ball and its unfolding by 3-balls (what the “half” of Minkowski space is, topologically).
If one adds a complementary, second unfolding to link both ends of the first unfolding, the problem would be resolved: 4-ball would be equivalent to two 3-spaces topologically. Two 3-spaces are equivalent to a single one as follows: one divides a 3-space into two parts by a certain plane (that plane does not belong to any of them). Any part is equivalent topologically to a 3-space for any open neighborhood is transformed into an open one by the mapping of each part (excluding the boundary of the plane) into the complete 3-space.
That idea is linked to the original proof of Perelman by the concept of information. It means that any bit of information interpreted physically conserves causality. In other words, the choice of any of both states of a bit (e.g. designated as “0” and “1” recorded in a cell) does not violate causality (the cell, either “0” or “1”, or both “0” and “1” are equivalent to each other topologically and to a 3-space).
FROM THE PRINCIPLE OF LEAST ACTION TO THE CONSERVATION OF QUANTUM INFORMATION...Vasil Penchev
In fact, the first law of conservation (that of mass) was found in chemistry and generalized to the conservation of energy in physics by means of Einstein’s famous “E=mc2”. Energy conservation is implied by the principle of least action from a variational viewpoint as in Emmy Noether’s theorems (1918): any chemical change in a conservative (i.e. “closed”) system can be accomplished only in the way conserving its total energy. Bohr’s innovation to found Mendeleev’s periodic table by quantum mechanics implies a certain generalization referring to
the quantum leaps as if accomplished in all possible trajectories (according to Feynman’s interpretation) and therefore generalizing the principle of least action and needing a certain generalization of energy conservation as to any quantum change.The transition from the first to the second theorem of Emmy Noether represents well the necessary generalization: its chemical meaning is the ge eralization of any chemical reaction to be accomplished as if any possible course of time rather than in the standard evenly running time (and equivalent to energy conservation according to the first theorem). The problem: If any quantum change is accomplished in al possible “variations (i.e. “violations) of energy conservation” (by different probabilities),
what (if any) is conserved? An answer: quantum information is what is conserved. Indeed, it can be particularly defined as the counterpart (e.g. in the sense of Emmy Noether’s theorems) to the physical quantity of action (e.g. as energy is the counterpart of time in them). It is valid in any course of time rather than in the evenly running one. That generalization implies a generalization of the periodic table including any continuous and smooth transformation between two chemical elements.
From the principle of least action to the conservation of quantum information...Vasil Penchev
In fact, the first law of conservation (that of mass) was found in chemistry and generalized to the conservation of energy in physics by means of Einstein’s famous “E=mc2”. Energy conservation is implied by the principle of least action from a variational viewpoint as in Emmy Noether’s theorems (1918):any chemical change in a conservative (i.e. “closed”) system can be accomplished only in the way conserving its total energy. Bohr’s innovation to found Mendeleev’s periodic table by quantum mechanics implies a certain generalization referring to the quantum leaps as if accomplished in all possible trajectories (e.g. according to Feynman’s viewpoint) and therefore generalizing the principle of least action and needing a certain generalization of energy conservation as to any quantum change.
The transition from the first to the second theorem of Emmy Noether represents well the necessary generalization: its chemical meaning is the generalization of any chemical reaction to be accomplished as if any possible course of time rather than in the standard evenly running time (and equivalent to energy conservation according to the first theorem).
The problem: If any quantum change is accomplished in all possible “variations (i.e. “violations) of energy conservation” (by different probabilities), what (if any) is conserved?
An answer: quantum information is what is conserved. Indeed it can be particularly defined as the counterpart (e.g. in the sense of Emmy Noether’s theorems) to the physical quantity of action (e.g. as energy is the counterpart of time in them). It is valid in any course of time rather than in the evenly running one. (An illustration: if observers in arbitrarily accelerated reference frames exchange light signals about the course of a single chemical reaction observed by all of them, the universal viewpoint shareаble by all is that of quantum information).
That generalization implies a generalization of the periodic table including any continuous and smooth transformation between two chemical elements necessary conserving quantum information rather than energy: thus it can be called “alchemical periodic table”.
Why anything rather than nothing? The answer of quantum mechnaicsVasil Penchev
Many researchers determine the question “Why anything
rather than nothing?” to be the most ancient and fundamental philosophical problem. It is closely related to the idea of Creation shared by religion, science, and philosophy, for example in the shape of the “Big Bang”, the doctrine of first cause or causa sui, the Creation in six days in the Bible, etc. Thus, the solution of quantum mechanics, being scientific in essence, can also be interpreted philosophically, and even religiously. This paper will only discuss the philosophical interpretation. The essence of the answer of quantum mechanics is: 1.) Creation is necessary in a rigorously mathematical sense. Thus, it does not need any hoice, free will, subject, God, etc. to appear. The world exists by virtue of mathematical necessity, e.g. as any mathematical truth such as 2+2=4; and 2.) Being is less than nothing rather than ore than nothing. Thus creation is not an increase of nothing, but the decrease of nothing: it is a deficiency in relation to nothing. Time and its “arrow” form the road from that diminishment or incompleteness to nothing.
The Square of Opposition & The Concept of Infinity: The shared information s...Vasil Penchev
The power of the square of opposition has been proved during millennia, It supplies logic by the ontological language of infinity for describing anything...
6th WORLD CONGRESS ON THE SQUARE OF OPPOSITION
http://www.square-of-opposition.org/square2018.html
Mamardashvili, an Observer of the Totality. About “Symbol and Consciousness”,...Vasil Penchev
The paper discusses a few tensions “crucifying” the works and even personality of the great Georgian philosopher Merab Mamardashvili: East and West; human being and thought, symbol and consciousness, infinity and finiteness, similarity and differences. The observer can be involved as the correlative counterpart of the totality: An observer opposed to the totality externalizes an internal part outside. Thus the phenomena of an observer and the totality turn out to converge to each other or to be one and the same. In other words, the phenomenon of an observer includes the singularity of the solipsistic Self, which (or “who”) is the same as that of the totality. Furthermore, observation can be thought as that primary and initial action underlain by the phenomenon of an observer. That action of observation consists in the externalization of the solipsistic Self outside as some external reality. It is both a zero action and the singularity of the phenomenon of action. The main conclusions are: Mamardashvili’s philosophy can be thought both as the suffering effort to be a human being again and again as well as the philosophical reflection on the genesis of thought from itself by the same effort. Thus it can be recognized as a powerful tension between signs anа symbol, between conscious structures and consciousness, between the syncretism of the East and the discursiveness of the West crucifying spiritually Georgia
Completeness: From henkin's Proposition to Quantum ComputerVasil Penchev
The paper addresses Leon Henkin's proposition as a "lighthouse",
which can elucidate a vast territory of knowledge uniformly: logic, set theory,
information theory, and quantum mechanics: Two strategies to infinity are
equally relevant for it is as universal and thus complete as open and thus incomplete.
Henkin's, Godel's, Robert Jeroslow's, and Hartley Rogers'
proposition are reformulated so that both completeness and incompleteness to
be unified and thus reduced as a joint property of infinity and of all infinite sets.
However, only Henkin's proposition equivalent to an internal position to
infinity is consistent . This can be retraced back to set theory and its axioms,
where tha t of choice is a key. Quantum mechanics is forced to introduce infinity implicitly by Hilbert space, on which is founded its formalism. One can
demonstrate that some essential properties of quantum information,
entanglement, and quantum computer originate directly from infinity once it is
involved in quantum mechanics. Thus, these phenomena can be elucidated as
both complete and incomplete, after which choice is the border between them.
A special kind of invariance to the axiom of choice shared by quantum
mechanics is discussed to be involved that border between the completeness
and incompleteness of infinity in a consistent way. The so-called paradox of
Albert Einstein, Boris Podolsky, and Nathan Rosen is interpreted entirely in
the same terms only of set theory. Quantum computer can demonstrate
especially clearly the privilege of the internal position, or "observer'' , or "user" to infinity implied by Henkin's proposition as the only consist ent ones as to infinity. An essential area of contemporary knowledge may be synthesized from a single viewpoint.
Why anything rather than nothing? The answer of quantum mechanicsVasil Penchev
The state of “nothing” is not stable
❖ The physical nothing is not a general vacuum
The being is less than nothing
❖ The creation is taking away from the nothing
Time is the destruction of symmetry
❖ The creation need not any (external) cause
The state of nothing passes spontaneously (by itself) into the state of being
❖ This represents the “creation”
The transition of nothing into being is mathematically necessary
❖ The choice (which can be interpreted philosophically as “free will”) appears necessary in mathematical reasons
❖ The choice generates asymmetry, which is the beginning of time and thus, of the physical word
❖ Information is the quantity of choices and linked to time intimately
The outlined approach allows a common philosophical viewpoint to the physical world, language and some mathematical structures therefore calling for the universe to be understood as a joint physical, linguistic and mathematical universum, in which physical motion and metaphor are one and the same rather than only similar in a sense.
Ontology as a formal one. The language of ontology as the ontology itself: th...Vasil Penchev
“Formal ontology” is introduced first to programing languages in different ways. The most relevant one as to philosophy is as a generalization of “nth-order logic” and “nth-level language” for n=0. Then, the “zero-level language” is a theoretical reflection on the naïve attitude to the world: the “things and words” coincide by themselves. That approach corresponds directly to the philosophical phenomenology of Husserl or fundamental ontology of Heidegger. Ontology as the 0-level language may be researched as a formal ontology
Both necessity and arbitrariness of the sign: informationVasil Penchev
There is a fundamental contradiction or rather tension in Sausure’d Course: between the necessity of the sign within itself and its arbitrariness within a system of signs. That tension penetrates the entire Course and generates its “plot”. It can be expressed by the quantity of information generalized to quantum information by quantum mechanics. Then the problem is how a bit to be expressed by a qubit or vice versa. The structure of the main problem of quantum mechanics is isomorphic. Thus its solution, namely the set of solutions of the Schrödinger equation, implies the solution of the above contradictionor tension.
The “cinematographic method of thought” in Bergson: Continuity by discretenes...Vasil Penchev
The success of cinematograph hides an ontological basis still in its fundamental principle for representation of motion by a linear (and thus well-ordered) series of static frames
That representation of motion by static frames is absolute for it rests on the ontological equivalence of discreteness and smoothness
The equivalence of discrete and smooth (continuous) motion underlies quantum mechanics as the principle of wave-particle duality offered by Louis de Broglie (1924)
Henry Bergson (1907) suggested the “cinematographic method of thought” for distinguishing “durée” (time by itself) from the transcendental limitation for it to be represented in human knowledge and cognition
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
3. The thesis is:
• The concept of matter in physics can be considered
as a generalized form of information, that of
quantum information involved by quantum
mechanics
• Furthermore the concept of information can unify
the concrete and abstract objects while the notion
of matter in physics demarks them
• Thus information can be seen as the universal
substance of the world and therefore, as the
relevant generalization of the notions of mass and
energy in physics referring only to the world of the
concrete objects
4. Matter and the quantity of mass
• Contemporary physics introduces the notion of
matter and quantity of mass as a form of energy
according to Einstein’s famous equation E=(mc)2
• The physical world and all entities within it (the
concrete objects) share that quantity of matter.
However, there exist abstract objects, which do not
belong to the physical world. Thus the physical
concept of mass does not refer to them
• Consequently, that quantity of mass is the
demarcation between those two worlds: that of the
concrete objects and that of the abstract ones. Any
entity should belong either to the one or to the other
5. Abstract objects and information
• All abstract objects share a common quantity,
that of information. It can be defined in
different ways, partly equivalent to each other
• It can be interpreted also as the complexity
of a given abstract object, e.g. as the length
of the shortest algorithm (or the number of
the corresponding Turing machine), by which
the object at issue can be constructed
6. Information and thermodynamic entropy
• The dimensionless physical quantity of
thermodynamic entropy shares the same or similar
mathematical formula as information
• However, it always refers to some statistical
ensembles of material (energetic) entities and thus
the demarcation between mass (energy) and
information is conserved though the concept of
information unifies both concrete and abstract
objects
• Information in both cases can be considered as a
quantity describing the degree of ordering (or
disordering, or complexity) of any collection either
of abstract or of concrete objects
7. Any physical entity and quantum
information
• The concept of quantum information
introduced by quantum mechanics allows
even more:
• Any physical entity to be interpreted as some
nonzero quantity of quantum information,
which can be seen as that generalization of
information, which is relevant to infinite
collections for the classically defined
information can refer only to finite ones
8. A hypothesis:
• The quantities of mass and energy are
interpretable as some nonzero amount of
quantum information
• Thus the demarcation between the concrete
and abstract objects can be understood as
the boundary between infinity and finiteness
in a rigorous and even mathematical sense
• This allows of diffusing concepts between
philosophy of mathematics and that of
quantum mechanics, on the one hand, and of
ontology, on the other hand
9. Mass, energy, and matter as
information
• The core is the following: the physical concept
of mass, energy and matter to be interpreted
as the notion of information in the case of
quantum information, i.e. as the information
in an infinite collection
• Furthermore, the mathematical analysis of
the relation between infinity and finiteness
can be transferred to elucidate the essence of
matter even in an ontological sense
10. Mass and energy as the complexity of
infinite sets
• Energy (and therefore mass) can be interpreted as
the change of the complexity of a relevant infinite
set in thus:
• Energy is the change of that transfinite ordinal
representing the complexity per a unit of
transfinite well-ordering
• That unit of the number of sells necessary for that
transfinite well-ordering should be a unit of time
• The change of the transfinite ordinal should be the
corresponding change of probability being due to
the change of a wave function
11. Choice in the base of information
• The notion of choice grounds that of
information: The latter can be seen as the
quantity of elementary choices in units of
choice, which are also units of information
• The generalization of information through
the boundary of infinity as quantum
information requires the axiom of choice
(Zermelo 1904) to legitimate the notion of
choice as to infinity
12. Quantum invariance: the axiom of
choice in quantum mechanics
A few theorems (Neumann 1932; Kochen, Specker
1968) deduce from the mathematical formalism of
Hilbert space that no hidden variable and thus no
well-ordering is allowed for any coherent state in
quantum mechanics. However, the latter is well-
ordered after measurement and thus needs the well-
ordering theorem equivalent to the axiom of choice
The epistemological equivalence of a quantum
system before and after measurement forces the
invariance to the axiom of choice. That invariance is
shared by the Hilbert space formalism. This fact can
be called quantum invariance
13. Choice among infinity
• One can demonstrate that quantum
mechanics involves and even develops
implicitly the concept of choice as to infinity,
on the one hand, and set theory (the so-called
paradox of Skolem, 1922, based on the axiom
of choice) does the same, on the other hand
• Thus the understanding of matter as
information elucidates how choice underlies
matter and even ontology at all
14. The concept of quantum information
• The concept of quantum information can be
introduced in different ways.:
• One of them defines it by means of Hilbert
space and thus any point in it, which is
equivalent to a wave function, i.e. to a state
of some quantum system, can be considered
as a certain value of the quantity of quantum
information
15. Quantum information as a quantity
measured in qubits
The notion of quantum bit (or ‘qubit’) underlies
that of quantum information:
• ‘Qubit’ is: 𝜶|𝟎⟩ + 𝜷|𝟏⟩ where 𝜶, 𝜷 are two
complex numbers such that 𝜶 𝟐
+ 𝜷 𝟐
= 𝟏,
and :
• |𝟎⟩, |𝟏⟩ are any two orthonormal vectors (e.g.
the orthonormal bases of any two subspaces) in
any vector space (e.g. Hilbert space, Euclidean
space, etc.)
16. A qubit as a unit ball
• A qubit is equivalently representable as a unit ball in
Euclidean space and two points, the one chosen within
the ball, and the other being the orthogonal projection
on its surface
• Consequently, the qubit links the Hilbert space of
quantum mechanics to the Minkowski space of special
relativity and even to the pseudo-Riemannian space
of general relativity (the latter by the additional
mediation of the concept of entanglement)
• The “Banach-Tarski (1924) paradox” connects the
axiom of choice and the unit-ball representation
of a qubit
17. 𝜶|𝟎⟩ defines a point of the unit ball
𝜶|𝟎⟩ and 𝜷|𝟏⟩ define a point of the unit sphere
𝜶 𝟐
+ 𝜷 𝟐
= 𝟏|𝟎⟩
|𝟏⟩
𝜶, 𝜷 are two complex numbers:
|𝟎⟩, |𝟏⟩ are two orthonormal
vectors or a basis such as two orthogonal
great circles of the unit ball
18. Hilbert space as a “tape” of qubits
Given any point in (complex) Hilbert space as a vector
𝐶1, 𝐶2, … 𝐶 𝑛, 𝐶 𝑛+1, … , one can replace any
successive couple of its components such as ( 𝐶1, 𝐶2 ,
𝐶2, 𝐶3 , … 𝐶 𝑛−1, 𝐶 𝑛 … ) with a single corresponding
qubit {𝑄1, 𝑄2, … , 𝑄 𝑛, 𝑄 𝑛+1, … } such that:
𝛼 𝑛 =
𝐶 𝑛
(+) 𝐶 𝑛
2+ 𝐶 𝑛+1
2
; 𝛽 𝑛 =
𝐶 𝑛+1
(+) 𝐶 𝑛
2+ 𝐶 𝑛+1
2
if 𝐶 𝑛, 𝐶 𝑛+1 are not both 0. However if both are 0 one
needs to add conventionally the center (𝛼 𝑛 = 0,
𝛽 𝑛 = 0) to conserve the mapping of Hilbert space
and an infinite qubit tape to be one-to-one
20. Bit vs. qubit
• Then if any bit is an elementary binary choice
between two disjunctive options usually designated
by “0” and “1”, any qubit is a choice between a
continuum of disjunctive options as many (or
“much”) as the points of the surface of the unit ball
Thus the concept of choice is the core of
computation and information. It is what can unify
the classical and quantum case, and the demarcation
between them is the bound between a finite vs.
infinite number of the alternatives of the
corresponding choice
21. A Turing machine vs. a quantum computer
• That visualization allows of highlighting the
fundamental difference between the Turing
machine (Turing 1937) and quantum computer
(Deutsch 1985, 1989; Yao 1993):
• The choice of an element of an uncountable set
necessarily requires the axiom of choice
• The axiom of choice being non-constructive is the
relevant reference frame to the concept of quantum
algorithm:
• The latter in turn involves a constructive process of
solving or computation having an infinite and even
uncountable number of steps therefor
22. Information as the number of primary
choices
• The concept of information can be interpreted as
the quantity of the number of primary choices
• Furthermore the Turing machine either classical
or quantum as a model links computation to
information directly:
• The quantity of information can be thought as
the sum of the change bit by bit or qubit by qubit,
i.e. as the change of a number written either
by two or by infinitely many digits
23. The equation
A cell of a (quantum) Turing tape = a qubit =
= a choice of (quantum) information = a “digit”
The empirical sense
of a qubit
in quantum mechanics:
a common measure
of future, present,
and past Any measured
quantum system
The “length of
now” of
the quantum
entity
The “length
of now” of
the device
is a randomly chosen point from:
Future
P
a
s
t
24. The meaning of the “length of now”:
The “length of now” of any quantum entity can be
defined as the period of the de Broglie (1925)
wave, which can be associated to that quantum
entity:
Thus the “length of now” should be reciprocal to
the energy (mass) of the quantum entity:
Then the “length of now” of the device should be a
randomly chosen point from the segment of the
“length of now” of the quantum entity therefore
including the future and the past of the apparatus
uniformly
25. From information to quantum
information
• The generalization from information to
quantum information can be interpreted as
the corresponding generalization of ‘choice’:
from the choice between two (or any finite
number of) disjunctive alternatives to
infinitely many (and even “much”) alternatives
• Thus the distinction between the classical
and quantum case can be limited within
any cell of an algorithm or (qu)bit of
information
26. About quantum information
The conception of quantum information was
introduced in the theory of quantum information
studying the phenomena of entanglement in
quantum mechanics:
The entanglement was theoretically forecast in the
famous papers of Einstein, Podolsky, and Rosen
(1935) and independently by Schrödinger (1935)
deducing it from Hilbert space, the basic
mathematical formalism of quantum mechanics
However, the former three demonstrated the
forecast phenomenon as the proof of the alleged
“incompleteness of quantum mechanics”
27. More about quantum information
• John Bell (1964) deduced a sufficient condition as
an experimentally verifiable criterion in order to
distinguish classical from quantum correlation
(entanglement)
• Aspect, Grangier, and Roger (1981, 1982)
confirmed experimentally the existence of
quantum correlations exceeding the upper limit of
all possible classical correlations
• The theory of quantum information has thrived
since the end of the last century in the areas of
quantum computer, quantum communication, and
quantum cryptography
28. Information of an infinite set as an
ordinal and as complexity
• The quantum information introduced by quantum
mechanics is equivalent to that generalization of the
classical information from finite to infinite series or
collections
Indeed information can be interpreted as the number
of choices necessary to be reached an ordering of
some item from another ordering of the same item or
from the absence of ordering. Then the quantity of
information is the quantity of choices measured in
the units of elementary choice
• The quantity of quantum information is the ordinal
corresponding to the infinity series in question
29. Two definitions of ‘ordinal’
Both definitions of ‘ordinal’ (Cantor 1897;
Neumann 1923) are applicable
The Cantor – Russell definition is admissible as
the ordinals are small: “ω” is an enough limit
The ordinal defined in Cantor – Russell (Russell,
Whitehead: any edition) generates a statistical
ensemble while that in Neumann, a well-
ordering
Both correspond one-to-one to a coherent state
as the one and same quantity of quantum
information containing in it
30. Interpretation of the two “kinds” of
ordinal in terms of quantum mechanics
The relation between the statistical ensemble and
the single and unknown well-ordering is the relation
between an ordinal defined correspondingly in
Cantor – Russell or in Neumann
The ordinal defined in Neumann should be
interpreted as a representative of ‘determinism’
for any statistical ensemble corresponding one-to-
one to an ordinal defined in Cantor – Russell
However, this representative exists only “purely” for
it is a mapping of a coherent state necessarily
requiring the axiom of choice
31. Abstract and concrete objects as sets
• The objects either abstract or concrete can be
unified as some homogenous plurality and
thus as a whole
• Furthermore that whole can be considered as
a new abstract object
• Thus the concrete and abstract objects can be
opposed as a “many” and its whole, or as a
“many” and a “much” of one and the some
quality
• That intuition addresses the concept of ‘set’
utilized in set theory
32. Abstraction and choice in set theory
• The link between abstraction and choice in
the foundation of set theory can distinguish
unambiguously the “good” principles of
abstraction from the “bad” ones
• The good abstraction is always a choice in the
sense of set theory; or in other words, that
abstraction, to which a choice does not
correspond, is a “bad abstraction” implying
contradictions
33. Abstraction as generalization and
choice: two examples
Abstraction was initially allowed to be unrestricted in
“naïve set theory” therefore admitting a lot of
paradoxes
Zermelo (1908) was who offered the relevant out way
restricting the abstraction in set theory in fact by
means of choice: a set is not only the abstraction of
its elements, but also it can be chosen from another
set
The concept of “COLAPSE” (Linnebo 2010) or Popper’s
principle of falsifiability (Popper 1935: 13) are two
possible examples more of the complement of the
generalization by the relevant choice of the abstracted
34. The axiom of choice and the axiom
scheme of specification
• The concepts of abstraction or choice in set theory
is fundamental (like that of point in geometry) and
cannot be defined rigorously otherwise than
contextually and indirectly by the axioms in set
theory
• As the axiom of choice can correspond to ‘choice’
as the axiom scheme of specification, to
‘abstraction‘
• Their intuitions are the opportunities accordingly
an element to be chosen from a set or all elements
of a set to specified by a single logical function
35. About the logical equivalence of
choice and abstraction
One can designate as the “name” or “natural name”
of a set that logical function, which is equivalent to it
according to the corresponding axiom (or axiom
scheme) of abstraction in set theory:
Then, what is the relation between the name and
the choice of one and the same set? Can a set be
chosen without having any name? Or vice versa: can
a set be named without being chosen?
One can suggest the equivalence of the name and the
choice of one and the same set for it seems intuitively
justified
36. An example by the “Gödel first
incompleteness theorem”
• Furthermore, “This set has this name” should be a
decidable proposition. However, the so-called Gödel
first incompleteness theorem, “Satz VI” (Gödel
1931: 187) implies that there are such sets and such
names, about which that proposition is not
decidable if the conditions of the validity of
the theorem are satisfied
This implies for the name of any set to be imposed
suitable restrictions, which should exclude the
application of Gödel’s theorem: One can choose as a
name any proposition out of its conditions
37. An example by the “Gödel first
incompleteness theorem”
• One believes that this can be avoided by
the restriction in the corresponding postulate in
set theory for the names to be finite or to consist of
a finite set of free variables. However, what about
the sets having no finite name, but possessing an
infinite name?
• Is there at least one set of that kind? Obviously,
yes, there is: e.g. any transcendental number
without any special designation like “π”, “e”, etc.
• One need an actual infinite set, e.g. that of its
digits, in order to construct its name.
38. An example by the “Gödel first
incompleteness theorem”
However, the restriction of name in the
corresponding axiom scheme in set theory
about abstraction should exclude it thus saving
the theory from the Gödel undecidable
propositions as names of sets
The axiom of choice would distinguish
unambiguously even between them: The
transcendental number being single can be
chosen while any set specified by some
undecidable proposition cannot be chosen
39. The definition of abstraction in
quantum mechanics
Furthermore, abstraction and choice can be defined
in terms of quantum mechanics, too:
‘Choice’ is then the relation of a coherent state (or
superposition) and a measured value of it (or an
element of the corresponding statistical ensemble)
The reverse relation (either of a single element or of
all statistical ensemble) to the coherent state can be
accordingly interpreted as that ‘abstraction’ in terms
of quantum mechanics
40. Abstraction and well-ordering in quantum
mechanics: coherence and de-coherence
Any well-ordering can be considered as an ordered
series of choices:
Thus a mapping of a coherent state into a statistical
ensemble can be interpreted in terms both of
transfinite ordinals and wave functions as the
quantity of quantum information containing in it
Furthermore, the quantity of quantum information
should be invariant both to abstraction and to choice
(as they are defined in quantum mechanics above)
after the wave functions (points in Hilbert space) and
the transfinite ordinals are mapped one-to-one into
each other
41. “Hume’s principle”
• In fact the so-called principle of Hume is suggested
by an contemporary logic, George Boolos in 1985-
1987
• Its sense seems quite simple and obvious: The
enumeration does not change the number of the
enumerated items whatever they are. The
enumeration cannot change information. Thus the
number or information should be invariant to
whether the objects are abstract or concrete
• Or in other words: Any number is the abstraction of
all sets having the same number of elements,
whatever these elements or sets are
42. “Hume’s principle” generalized in
terms of quantum mechanics
• In the quantum principle of Hume “Gs” should be
interpreted as some “many” and “Fs” as some
“much” of one and the same set or abstraction
• Indeed the axiom scheme in set theory about
abstraction can be interpreted as a scheme of
tautologies, in which each name designates a set
as a whole, i.e. as a “much”, while the collection of
elements designates as a “many” consisting of
separated individuals
• The quantum “principle of Hume” means properly
the conservation of quantum information after de-
coherence (“choice”) or coherence (“abstraction”)
43. A Turing machine vs. a quantum Turing
machine
• The quantum Turing machine processes
quantum information correspondingly qubit by
qubit serially, but in parallel within any qubit:
• The axiom of choice formalizes that parallel
processing as the choice of the result. Even the
operations on a qubit can be the same as on a
bit
• The only difference is for “write/ read”:
• It should be a value of either a binary (finite) or
an infinite set
44. A “classical” Turing machine
A quantum Turing machine
1 ... n n+1 ...
The
last
cell
A classical Turing
tape of bits:
A quantum Turing
tape of qubits:
1 ... n n+1 ...
The
/No
last
cell
The list of all
operations on a cell:
1. Write!
2. Read!
3. Next!
4. Stop!
45. Any physical process as a quantum
computation:
• Quantum computer can be equivalently
represented by a quantum Turing machine
• The quantum Turing machine is equivalent to
Hilbert space
• Quantum mechanics states that any physical state
or its change is a self-adjoint operator in Hilbert
space as any physical system can be considered as
a quantum one
• Consequently all physical process can be
interpreted as the calculation of a single
computer, and thus the universe being as it
46. A wave function as a value of quantum
information
• Any wave function can be represented as
an ordered series of qubits enumerated by the
positive integers
• Just as an ordering of bits can represent a value
of classical information, that series of qubits,
equivalent to a wave function represents a value
of quantum information
• One can think of the qubits of the series as a
special kind of digits: infinite digits
• As a binary digit can accept two values, that
infinite digit should accept infinite number of
values
47. All physical processes as informational
• Quantum mechanics is the universal doctrine
about the physical world and any physical
process can be interpreted as a quantum one
• Any quantum process is informational in
terms of a generalized kind of information:
quantum information
• Consequently, all physical processes are
informational in the above sense
48. Quantum information as
the real fundament of the world
• Indeed all physical states in the world are wave
functions and thus they are different values of
quantum information
• All physical quantities in the world are certain kind
of changes of wave functions and thus of quantum
information
• Consequently, one can certainly state that the
physical world consists only of quantum
information:
• It is the substance of the physical world, its
“matter”
49. Information as a bridge:
The conception of information and more exactly,
quantum information unifies:
• physics and mathematics
• and thus the material and the ideal world
• as well as the concrete and abstract objects:
The ground is the choice unifying
the well-ordering of past and the uncertainness of
future by the choice of present
Consequently, quantum information as the
substance of the universe is the mediator
between the totality and time and the physical
world
50. Information as a “bridge” between
the concrete and abstract
• As information is a dimensionless quantity equally
well referring both to a physical entity or to a
mathematical class, it can serve as a “bridge”
between physics and mathematics and thus
between the material and ideal world, between
the concrete and abstract objects
• In fact, quantum information being a generalized
kind of information is just what allows of the
physical and mathematical, the concrete and
abstract to be considered as two interpretations
of the underlying quantum information
51. Conclusions:
• The concept of information generalized as
quantum information generalizes also the
concept of matter in physics as well as the
corresponding quantities of matter and energy
• Furthermore, quantum information can be
interpreted as that generalization of
information, which is applicable to infinite
collections or algorithms
• Thus the fundamental properties of mass or
energy shared by all in the physical worlds turn
out to be underlain by quantum information
52. Conclusions:
• The gap between the concrete objects
(interpreted as physical ones) and the abstract
object is now bridged by the concept of
information shared by both and underlying
both kinds of objects
• The quantity of information either classical
(i.e. “finite”) or quantum (i.e. “infinite”) is
defined in both cases as the amount of
choices and measured in units of elementary
choice: correspondingly either bits or qubits
53. Conclusions:
• The case of infinite choice cannot help to involve
the axiom of choice and a series of
counterintuitive corollaries implied by it:
• One of them is the so-called paradox of Skolem
(1922): It allows of discussing the concrete and
abstract objects as complementary in the sense
of quantum mechanics as well as different
degrees of “entanglement” between them
therefore pioneering a kind of quantum
epistemology as universal
54. Conclusions:
• The physical processes can be interpreted as
informational, more exactly as quantum-
informational. Any wave function determines a
state of a quantum system and a state of a quantum
computer defined as a quantum Turing machine, in
which all bits are simply replaced by qubits infinitely
many in general
• Thus the concept of quantum information and
calculation can unify physics and mathematics
addressing some form of neo-Pythagoeranism as
the common ontological ground of the concrete
objects (studied by physics) and abstract ones
(studied by mathematics)
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