Results for 'Infinite Computation'

999 found
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  1. A New Applied Approach for Executing Computations with Infinite and Infinitesimal Quantities.Yaroslav D. Sergeyev - 2008 - Informatica 19 (4):567-596.
    A new computational methodology for executing calculations with infinite and infinitesimal quantities is described in this paper. It is based on the principle ‘The part is less than the whole’ introduced by Ancient Greeks and applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). It is shown that it becomes possible to write down finite, infinite, and infinitesimal numbers by a finite number of symbols as particular cases of (...)
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  2. A Quantum Computer in a 'Chinese Room'.Vasil Penchev - 2020 - Mechanical Engineering eJournal (Elsevier: SSRN) 3 (155):1-8.
    Pattern recognition is represented as the limit, to which an infinite Turing process converges. A Turing machine, in which the bits are substituted with qubits, is introduced. That quantum Turing machine can recognize two complementary patterns in any data. That ability of universal pattern recognition is interpreted as an intellect featuring any quantum computer. The property is valid only within a quantum computer: To utilize it, the observer should be sited inside it. Being outside it, the observer would obtain (...)
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  3. Infinitely Complex Machines.Eric Steinhart - 2007 - In Intelligent Computing Everywhere. Springer. pp. 25-43.
    Infinite machines (IMs) can do supertasks. A supertask is an infinite series of operations done in some finite time. Whether or not our universe contains any IMs, they are worthy of study as upper bounds on finite machines. We introduce IMs and describe some of their physical and psychological aspects. An accelerating Turing machine (an ATM) is a Turing machine that performs every next operation twice as fast. It can carry out infinitely many operations in finite time. Many (...)
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  4. Computers Aren’T Syntax All the Way Down or Content All the Way Up.Cem Bozşahin - 2018 - Minds and Machines 28 (3):543-567.
    This paper argues that the idea of a computer is unique. Calculators and analog computers are not different ideas about computers, and nature does not compute by itself. Computers, once clearly defined in all their terms and mechanisms, rather than enumerated by behavioral examples, can be more than instrumental tools in science, and more than source of analogies and taxonomies in philosophy. They can help us understand semantic content and its relation to form. This can be achieved because they have (...)
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  5. Quantum Computer: Quantum Model and Reality.Vasil Penchev - 2020 - Epistemology eJournal (Elsevier: SSRN) 13 (17):1-7.
    Any computer can create a model of reality. The hypothesis that quantum computer can generate such a model designated as quantum, which coincides with the modeled reality, is discussed. Its reasons are the theorems about the absence of “hidden variables” in quantum mechanics. The quantum modeling requires the axiom of choice. The following conclusions are deduced from the hypothesis. A quantum model unlike a classical model can coincide with reality. Reality can be interpreted as a quantum computer. The physical processes (...)
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  6. Natural Argument by a Quantum Computer.Vasil Penchev - 2020 - Computing Methodology eJournal (Elsevier: SSRN) 3 (30):1-8.
    Natural argument is represented as the limit, to which an infinite Turing process converges. A Turing machine, in which the bits are substituted with qubits, is introduced. That quantum Turing machine can recognize two complementary natural arguments in any data. That ability of natural argument is interpreted as an intellect featuring any quantum computer. The property is valid only within a quantum computer: To utilize it, the observer should be sited inside it. Being outside it, the observer would obtain (...)
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  7.  91
    The Infinite Regress of Optimization.Philippe Mongin - 1991 - Behavioral and Brain Sciences 14 (2):229-230.
    A comment on Paul Schoemaker's target article in Behavioral and Brain Sciences, 14 (1991), p. 205-215, "The Quest for Optimality: A Positive Heuristic of Science?" (https://doi.org/10.1017/S0140525X00066140). This comment argues that the optimizing model of decision leads to an infinite regress, once internal costs of decision (i.e., information and computation costs) are duly taken into account.
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  8. Almost Ideal: Computational Epistemology and the Limits of Rationality for Finite Reasoners.Danilo Fraga Dantas - 2016 - Dissertation, University of California, Davis
    The notion of an ideal reasoner has several uses in epistemology. Often, ideal reasoners are used as a parameter of (maximum) rationality for finite reasoners (e.g. humans). However, the notion of an ideal reasoner is normally construed in such a high degree of idealization (e.g. infinite/unbounded memory) that this use is unadvised. In this dissertation, I investigate the conditions under which an ideal reasoner may be used as a parameter of rationality for finite reasoners. In addition, I present and (...)
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  9. Many-Valued Logics. A Mathematical and Computational Introduction.Luis M. Augusto - 2020 - London: College Publications.
    2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, and (...)
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  10.  49
    Halting Problem Undecidability and Infinitely Nested Simulation (V2).P. Olcott - manuscript
    The halting theorem counter-examples present infinitely nested simulation (non-halting) behavior to every simulating halt decider. Whenever the pure simulation of the input to simulating halt decider H(x,y) never stops running unless H aborts its simulation H correctly aborts this simulation and returns 0 for not halting.
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  11. UN SEMPLICE MODO PER TRATTARE LE GRANDEZZE INFINITE ED INFINITESIME.Yaroslav Sergeyev - 2015 - la Matematica Nella Società E Nella Cultura: Rivista Dell’Unione Matematica Italiana, Serie I 8:111-147.
    A new computational methodology allowing one to work in a new way with infinities and infinitesimals is presented in this paper. The new approach, among other things, gives the possibility to calculate the number of elements of certain infinite sets, avoids indeterminate forms and various kinds of divergences. This methodology has been used by the author as a starting point in developing a new kind of computer – the Infinity Computer – able to execute computations and to store in (...)
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  12.  24
    Halting Problem Undecidability and Infinitely Nested Simulation (V5).P. Olcott - manuscript
    This is an explanation of a key new insight into the halting problem provided in the language of software engineering. Technical computer science terms are explained using software engineering terms. -/- To fully understand this paper a software engineer must be an expert in the C programming language, the x86 programming language, exactly how C translates into x86 and what an x86 process emulator is. No knowledge of the halting problem is required.
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  13. Philosophy of Probability: Foundations, Epistemology, and Computation.Sylvia Wenmackers - 2011 - Dissertation, University of Groningen
    This dissertation is a contribution to formal and computational philosophy. -/- In the first part, we show that by exploiting the parallels between large, yet finite lotteries on the one hand and countably infinite lotteries on the other, we gain insights in the foundations of probability theory as well as in epistemology. Case 1: Infinite lotteries. We discuss how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. The solution boils down (...)
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  14.  50
    Numerical Point of View on Calculus for Functions Assuming Finite, Infinite, and Infinitesimal Values Over Finite, Infinite, and Infinitesimal Domains.Yaroslav Sergeyev - 2009 - Nonlinear Analysis Series A 71 (12):e1688-e1707.
    The goal of this paper consists of developing a new (more physical and numerical in comparison with standard and non-standard analysis approaches) point of view on Calculus with functions assuming infinite and infinitesimal values. It uses recently introduced infinite and infinitesimal numbers being in accordance with the principle ‘The part is less than the whole’ observed in the physical world around us. These numbers have a strong practical advantage with respect to traditional approaches: they are representable at a (...)
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  15.  14
    Halting Problem Undecidability and Infinitely Nested Simulation (V4).P. Olcott - manuscript
    A Simulating Halt Decider (SHD) computes the mapping from its input to its own accept or reject state based on whether or not the input simulated by a UTM would reach its final state in a finite number of simulated steps. -/- A halt decider (because it is a decider) must report on the behavior specified by its finite string input. This is its actual behavior when it is simulated by the UTM contained within its simulating halt decider while this (...)
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  16. Higher Order Numerical Differentiation on the Infinity Computer.Yaroslav Sergeyev - 2011 - Optimization Letters 5 (4):575-585.
    There exist many applications where it is necessary to approximate numerically derivatives of a function which is given by a computer procedure. In particular, all the fields of optimization have a special interest in such a kind of information. In this paper, a new way to do this is presented for a new kind of a computer - the Infinity Computer - able to work numerically with finite, infinite, and infinitesimal number. It is proved that the Infinity Computer is (...)
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  17. Blinking Fractals and Their Quantitative Analysis Using Infinite and Infinitesimal Numbers.Yaroslav Sergeyev - 2007 - Chaos, Solitons and Fractals 33 (1):50-75.
    The paper considers a new type of objects – blinking fractals – that are not covered by traditional theories studying dynamics of self-similarity processes. It is shown that the new approach allows one to give various quantitative characteristics of the newly introduced and traditional fractals using infinite and infinitesimal numbers proposed recently. In this connection, the problem of the mathematical modelling of continuity is discussed in detail. A strong advantage of the introduced computational paradigm consists of its well-marked numerical (...)
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  18.  43
    Lagrange Lecture: Methodology of Numerical Computations with Infinities and Infinitesimals.Yaroslav Sergeyev - 2010 - Rendiconti Del Seminario Matematico dell'Università E Del Politecnico di Torino 68 (2):95–113.
    A recently developed computational methodology for executing numerical calculations with infinities and infinitesimals is described in this paper. The approach developed has a pronounced applied character and is based on the principle “The part is less than the whole” introduced by the ancient Greeks. This principle is applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). The point of view on infinities and infinitesimals (and in general, on Mathematics) presented in (...)
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  19. The Exact (Up to Infinitesimals) Infinite Perimeter of the Koch Snowflake and its Finite Area.Yaroslav Sergeyev - 2016 - Communications in Nonlinear Science and Numerical Simulation 31 (1-3):21–29.
    The Koch snowflake is one of the first fractals that were mathematically described. It is interesting because it has an infinite perimeter in the limit but its limit area is finite. In this paper, a recently proposed computational methodology allowing one to execute numerical computations with infinities and infinitesimals is applied to study the Koch snowflake at infinity. Numerical computations with actual infinite and infinitesimal numbers can be executed on the Infinity Computer being a new supercomputer patented in (...)
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  20. Representation and Reality by Language: How to Make a Home Quantum Computer?Vasil Penchev - 2020 - Philosophy of Science eJournal (Elsevier: SSRN) 13 (34):1-14.
    A set theory model of reality, representation and language based on the relation of completeness and incompleteness is explored. The problem of completeness of mathematics is linked to its counterpart in quantum mechanics. That model includes two Peano arithmetics or Turing machines independent of each other. The complex Hilbert space underlying quantum mechanics as the base of its mathematical formalism is interpreted as a generalization of Peano arithmetic: It is a doubled infinite set of doubled Peano arithmetics having a (...)
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  21.  59
    The Completeness: From Henkin's Proposition to Quantum Computer.Vasil Penchev - 2018 - Логико-Философские Штудии 16 (1-2):134-135.
    The paper addresses Leon Hen.kin'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 t hus 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 (...)
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  22.  58
    Observability of Turing Machines: A Refinement of the Theory of Computation.Yaroslav Sergeyev & Alfredo Garro - 2010 - Informatica 21 (3):425–454.
    The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the relativity of mathematical languages used to describe the Turing machines. A deep investigation is performed on the interrelations between mechanical computations and their mathematical descriptions emerging when a human (the researcher) starts to describe a Turing machine (the object of the study) by (...)
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  23. Solving Ordinary Differential Equations by Working with Infinitesimals Numerically on the Infinity Computer.Yaroslav Sergeyev - 2013 - Applied Mathematics and Computation 219 (22):10668–10681.
    There exists a huge number of numerical methods that iteratively construct approximations to the solution y(x) of an ordinary differential equation (ODE) y′(x) = f(x,y) starting from an initial value y_0=y(x_0) and using a finite approximation step h that influences the accuracy of the obtained approximation. In this paper, a new framework for solving ODEs is presented for a new kind of a computer – the Infinity Computer (it has been patented and its working prototype exists). The new computer is (...)
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  24. Interpretation of Percolation in Terms of Infinity Computations.Yaroslav Sergeyev, Dmitri Iudin & Masaschi Hayakawa - 2012 - Applied Mathematics and Computation 218 (16):8099-8111.
    In this paper, a number of traditional models related to the percolation theory has been considered by means of new computational methodology that does not use Cantor’s ideas and describes infinite and infinitesimal numbers in accordance with the principle ‘The part is less than the whole’. It gives a possibility to work with finite, infinite, and infinitesimal quantities numerically by using a new kind of a compute - the Infinity Computer – introduced recently in [18]. The new approach (...)
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  25.  39
    Numerical Methods for Solving Initial Value Problems on the Infinity Computer.Yaroslav Sergeyev, Marat Mukhametzhanov, Francesca Mazzia, Felice Iavernaro & Pierluigi Amodio - 2016 - International Journal of Unconventional Computing 12 (1):3-23.
    New algorithms for the numerical solution of Ordinary Differential Equations (ODEs) with initial condition are proposed. They are designed for work on a new kind of a supercomputer – the Infinity Computer, – that is able to deal numerically with finite, infinite and infinitesimal numbers. Due to this fact, the Infinity Computer allows one to calculate the exact derivatives of functions using infinitesimal values of the stepsize. As a consequence, the new methods described in this paper are able to (...)
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  26.  65
    Review of The Art of the Infinite by R. Kaplan, E. Kaplan 324p(2003).Michael Starks - 2016 - In Suicidal Utopian Delusions in the 21st Century: Philosophy, Human Nature and the Collapse of Civilization-- Articles and Reviews 2006-2017 2nd Edition Feb 2018. Michael Starks. pp. 619.
    This book tries to present math to the millions and does a pretty good job. It is simple and sometimes witty but often the literary allusions intrude and the text bogs down in pages of relentless math--lovely if you like it and horrid if you don´t. If you already know alot of math you will still probably find the discussions of general math, geometry, projective geometry, and infinite series to be a nice refresher. If you don´t know any and (...)
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  27. Supermachines and Superminds.Eric Steinhart - 2003 - Minds and Machines 13 (1):155-186.
    If the computational theory of mind is right, then minds are realized by machines. There is an ordered complexity hierarchy of machines. Some finite machines realize finitely complex minds; some Turing machines realize potentially infinitely complex minds. There are many logically possible machines whose powers exceed the Church–Turing limit (e.g. accelerating Turing machines). Some of these supermachines realize superminds. Superminds perform cognitive supertasks. Their thoughts are formed in infinitary languages. They perceive and manipulate the infinite detail of fractal objects. (...)
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  28. Отвъд машината на Тюринг: квантовият компютър.Vasil Penchev - 2014 - Sofia: BAS: ISSK (IPS).
    Quantum computer is considered as a generalization of Turing machine. The bits are substituted by qubits. In turn, a "qubit" is the generalization of "bit" referring to infinite sets or series. It extends the consept of calculation from finite processes and algorithms to infinite ones, impossible as to any Turing machines (such as our computers). However, the concept of quantum computer mets all paradoxes of infinity such as Gödel's incompletness theorems (1931), etc. A philosophical reflection on how quantum (...)
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  29. The Physics of God and the Quantum Gravity Theory of Everything.James Redford - manuscript
    Analysis is given of the Omega Point cosmology, an extensively peer-reviewed proof (i.e., mathematical theorem) published in leading physics journals by professor of physics and mathematics Frank J. Tipler, which demonstrates that in order for the known laws of physics to be mutually consistent, the universe must diverge to infinite computational power as it collapses into a final cosmological singularity, termed the Omega Point. The theorem is an intrinsic component of the Feynman-DeWitt-Weinberg quantum gravity/Standard Model Theory of Everything (TOE) (...)
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  30. On the Possibilities of Hypercomputing Supertasks.Vincent C. Müller - 2011 - Minds and Machines 21 (1):83-96.
    This paper investigates the view that digital hypercomputing is a good reason for rejection or re-interpretation of the Church-Turing thesis. After suggestion that such re-interpretation is historically problematic and often involves attack on a straw man (the ‘maximality thesis’), it discusses proposals for digital hypercomputing with Zeno-machines , i.e. computing machines that compute an infinite number of computing steps in finite time, thus performing supertasks. It argues that effective computing with Zeno-machines falls into a dilemma: either they are specified (...)
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  31.  49
    Квантовият компютър: квантовите ординали и типовете алгоритмична неразрешимост.Vasil Penchev - 2005 - Philosophical Alternatives 14 (6):59-71.
    A definition of quantum computer is supposed: as a countable set of Turing machines on the ground of: quantum parallelism, reversibility, entanglement. Qubit is the set of all the i–th binary location cells transforming in parallel by unitary matrices. The Church thesis is suggested in the form relevat to quantum computer. The notion of the non–finite (but not infinite) potency of a set is introduced .
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  32. El infinito y el continuo en el sistema numérico.Eduardo Dib - 1995 - Dissertation, Universidad Nacional de Rio Cuarto
    This monography provides an overview of the conceptual developments that leads from the traditional views of infinite (and their paradoxes) to the contemporary view in which those old paradoxes are solved but new problems arise. Also a particular insight in the problem of continuity is given, followed by applications in theory of computability.
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  33. Statements and Open Problems on Decidable Sets X⊆N That Contain Informal Notions and Refer to the Current Knowledge on X.Apoloniusz Tyszka - manuscript
    Let f(1)=2, f(2)=4, and let f(n+1)=f(n)! for every integer n≥2. Edmund Landau's conjecture states that the set P(n^2+1) of primes of the form n^2+1 is infinite. Landau's conjecture implies the following unproven statement Φ: card(P(n^2+1))<ω ⇒ P(n^2+1)⊆[2,f(7)]. Let B denote the system of equations: {x_j!=x_k: i,k∈{1,...,9}}∪{x_i⋅x_j=x_k: i,j,k∈{1,...,9}}. The system of equations {x_1!=x_1, x_1 \cdot x_1=x_2, x_2!=x_3, x_3!=x_4, x_4!=x_5, x_5!=x_6, x_6!=x_7, x_7!=x_8, x_8!=x_9} has exactly two solutions in positive integers x_1,...,x_9, namely (1,...,1) and (f(1),...,f(9)). No known system S⊆B with a (...)
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  34. Logically Possible Machines.Eric Steinhart - 2002 - Minds and Machines 12 (2):259-280.
    I use modal logic and transfinite set-theory to define metaphysical foundations for a general theory of computation. A possible universe is a certain kind of situation; a situation is a set of facts. An algorithm is a certain kind of inductively defined property. A machine is a series of situations that instantiates an algorithm in a certain way. There are finite as well as transfinite algorithms and machines of any degree of complexity (e.g., Turing and super-Turing machines and more). (...)
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  35. Single-Tape and Multi-Tape Turing Machines Through the Lens of the Grossone Methodology.Yaroslav Sergeyev & Alfredo Garro - 2013 - Journal of Supercomputing 65 (2):645-663.
    The paper investigates how the mathematical languages used to describe and to observe automatic computations influence the accuracy of the obtained results. In particular, we focus our attention on Single and Multi-tape Turing machines which are described and observed through the lens of a new mathematical language which is strongly based on three methodological ideas borrowed from Physics and applied to Mathematics, namely: the distinction between the object (we speak here about a mathematical object) of an observation and the instrument (...)
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  36. Numerical Infinities Applied for Studying Riemann Series Theorem and Ramanujan Summation.Yaroslav Sergeyev - 2018 - In AIP Conference Proceedings 1978. AIP. pp. 020004.
    A computational methodology called Grossone Infinity Computing introduced with the intention to allow one to work with infinities and infinitesimals numerically has been applied recently to a number of problems in numerical mathematics (optimization, numerical differentiation, numerical algorithms for solving ODEs, etc.). The possibility to use a specially developed computational device called the Infinity Computer (patented in USA and EU) for working with infinite and infinitesimal numbers numerically gives an additional advantage to this approach in comparison with traditional methodologies (...)
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  37. It Was the 15th of December.James Bardis - 2016 - Jpeg Cover-Dubai2016 ISSN: 2189-1036 – The IAFOR International Conference on Education – Dubai – 2016 Official Conference Proceedings:87-93.
    A reflection on the merits of an a priori poeto-epistemology in relation to tacitly held assumptions about the a fortiori validity of computational logic to transcend the limits of contradiction and infinite regression and establish a valid ontology.
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  38. Absolutely No Free Lunches!Gordon Belot - forthcoming - Theoretical Computer Science.
    This paper is concerned with learners who aim to learn patterns in infinite binary sequences: shown longer and longer initial segments of a binary sequence, they either attempt to predict whether the next bit will be a 0 or will be a 1 or they issue forecast probabilities for these events. Several variants of this problem are considered. In each case, a no-free-lunch result of the following form is established: the problem of learning is a formidably difficult one, in (...)
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  39.  24
    Natural Recursion Doesn’T Work That Way: Automata in Planning and Syntax.Cem Bozsahin - 2016 - In Vincent Müller (ed.), Fundamental Issues of Artificial Intelligence. Wil, Switzerland: Springer. pp. 95-112.
    Natural recursion in syntax is recursion by linguistic value, which is not syntactic in nature but semantic. Syntax-specific recursion is not recursion by name as the term is understood in theoretical computer science. Recursion by name is probably not natural because of its infinite typeability. Natural recursion, or recursion by value, is not species-specific. Human recursion is not syntax-specific. The values on which it operates are most likely domain-specific, including those for syntax. Syntax seems to require no more (and (...)
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  40. THE CYBERPHYSICS OF TOMORROW'S WORLD.Rodney Bartlett - 2016 - Dissertation,
    This article would appeal to people interested in new ideas in sciences like physics, astronomy and mathematics that are not presented in a formal manner. -/- Biologists would also find the paragraphs about evolution interesting. I was afraid they'd think my ideas were a bit "out there". But I sent a short email about them last year to a London biologist who wrote an article for the journal Nature. She replied that it was "very interesting". -/- The world is fascinated (...)
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  41. Unification of Science - Einstein's Missing Steps in E=Mc2 and His Missing Link to Quantum Gravity.Rodney Bartlett - 2018 - Beau Bassin, Mauritius: Lambert Academic Publishing.
    A Monograph Dealing With Unification In Relation To Dark Energy, Dark Matter, Cosmic Expansion, E=mc2, Quantum Gravity, "Imaginary" Computers, Creation Of The Infinite And Eternal Universe Using Electronic BITS + PI + "Imaginary" Time, Earthly Education, Science-Religion Union, The Human Condition, Superconductivity, Planetary Fields, How Gravitation Can Boost Health, Space-Time Propulsion From The Emdrive To The Brouwer Fixed-Point Theorem, "Light Matter", Etc. These Effects Were Originally Discussed In Several Short Internet Articles. Table Of Contents Introduction Superconductivity And Planetary Magnetic (...)
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  42. An Evolutionary Argument for a Self-Explanatory, Benevolent Metaphysics.Ward Blondé - 2015 - Symposion: Theoretical and Applied Inquiries in Philosophy and Social Sciences 2 (2):143-166.
    In this paper, a metaphysics is proposed that includes everything that can be represented by a well-founded multiset. It is shown that this metaphysics, apart from being self-explanatory, is also benevolent. Paradoxically, it turns out that the probability that we were born in another life than our own is zero. More insights are gained by inducing properties from a metaphysics that is not self-explanatory. In particular, digital metaphysics is analyzed, which claims that only computable things exist. First of all, it (...)
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  43. Approximating Propositional Calculi by Finite-Valued Logics.Matthias Baaz & Richard Zach - 1994 - In 24th International Symposium on Multiple-valued Logic, 1994. Proceedings. Los Alamitos: IEEE Press. pp. 257–263.
    The problem of approximating a propositional calculus is to find many-valued logics which are sound for the calculus (i.e., all theorems of the calculus are tautologies) with as few tautologies as possible. This has potential applications for representing (computationally complex) logics used in AI by (computationally easy) many-valued logics. It is investigated how far this method can be carried using (1) one or (2) an infinite sequence of many-valued logics. It is shown that the optimal candidate matrices for (1) (...)
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  44. Numerical Infinities and Infinitesimals: Methodology, Applications, and Repercussions on Two Hilbert Problems.Yaroslav Sergeyev - 2017 - EMS Surveys in Mathematical Sciences 4 (2):219–320.
    In this survey, a recent computational methodology paying a special attention to the separation of mathematical objects from numeral systems involved in their representation is described. It has been introduced with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework in all the situations requiring these notions. The methodology does not contradict Cantor’s and non-standard analysis views and is based on the Euclid’s Common Notion no. 5 “The whole is greater than the (...)
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  45. The Olympic Medals Ranks, Lexicographic Ordering and Numerical Infinities.Yaroslav Sergeyev - 2015 - The Mathematical Intelligencer 37 (2):4-8.
    Several ways used to rank countries with respect to medals won during Olympic Games are discussed. In particular, it is shown that the unofficial rank used by the Olympic Committee is the only rank that does not allow one to use a numerical counter for ranking – this rank uses the lexicographic ordering to rank countries: one gold medal is more precious than any number of silver medals and one silver medal is more precious than any number of bronze medals. (...)
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  46. The Significance of Evidence-Based Reasoning in Mathematics, Mathematics Education, Philosophy, and the Natural Sciences.Bhupinder Singh Anand - 2020 - Mumbai: DBA Publishing (First Edition).
    In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. (...)
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  47.  67
    Some Paradoxes of Infinity Revisited.Yaroslav Sergeyev - 2022 - Mediterranian Journal of Mathematics 19:143.
    In this article, some classical paradoxes of infinity such as Galileo’s paradox, Hilbert’s paradox of the Grand Hotel, Thomson’s lamp paradox, and the rectangle paradox of Torricelli are considered. In addition, three paradoxes regarding divergent series and a new paradox dealing with multiplication of elements of an infinite set are also described. It is shown that the surprising counting system of an Amazonian tribe, Pirah ̃a, working with only three numerals (one, two, many) can help us to change our (...)
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  48.  23
    Thoughts on Artificial Intelligence and the Origin of Life Resulting From General Relativity, with Neo-Darwinist Reference to Human Evolution and Mathematical Reference to Cosmology.Rodney Bartlett - manuscript
    When this article was first planned, writing was going to be exclusively about two things - the origin of life and human evolution. But it turned out to be out of the question for the author to restrict himself to these biological and anthropological topics. A proper understanding of them required answering questions like “What is the nature of the universe – the home of life – and how did it originate?”, “How can time travel be removed from fantasy and (...)
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  49. The Research of the V-I Characteristics of a Solar Panel Using a Computerized Measuring Bench “EPH 2 Advanced Photovoltaics Trainer”.Mirzayev Uchqun & Tulakov Jahongir - 2019 - International Journal of Academic and Applied Research (IJAAR) 3 (4):16-24.
    Abstract: At present, much attention is paid to the use of solar energy. Solar energy, in addition to traditional energy, is ecologically clean while changing. The rarity and the rising cost of fuel is one of the main problems of the scientific technique, which is the acquisition of infinite resources of solar energy. Further research and experiments on the use of solar energy, as well as the use of solar power plants in a number of countries, shows that solar (...)
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  50. From Analysis to Synthesis: Conceiving a Transformative Metaphysics for the Twenty-First Century.Mikhail Epstein - 2020 - In Russian Philosophy in the Twenty-First Century. An Anthology. Leiden, Boston: Brill, Rodopi. pp. 74–100.
    The article aims to substantiate the philosophy of synthesis, which is built on the basis of analysis, but gives it a constructive direction. The turning point from analysis to synthesis is the problematization of the elements identified in the analysis, their criticism, replacement, or rearrangement, leading to the construction of alternative concepts and propositions that expand the field of the thinkable and innovate the categorical apparatus of philosophy. This article provides examples of philosophical synthesis at different levels: alternative terms and (...)
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