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37
Informationtheoretic Limitations of Formal Systems
 JOURNAL OF THE ACM
, 1974
"... An attempt is made to apply informationtheoretic computational complexity to metamathematics. The paper studies the number of bits of instructions that must be a given to a computer for it to perform finite and infinite tasks, and also the amount of time that it takes the computer to perform these ..."
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Cited by 50 (7 self)
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An attempt is made to apply informationtheoretic computational complexity to metamathematics. The paper studies the number of bits of instructions that must be a given to a computer for it to perform finite and infinite tasks, and also the amount of time that it takes the computer to perform these tasks. This is applied to measuring the difficulty of proving a given set of theorems, in terms of the number of bits of axioms that are assumed, and the size of the proofs needed to deduce the theorems from the axioms.
Natural selection for least action
 Proc. R. Soc. A. 2008
"... The second law of thermodynamics is a powerful imperative that has acquired several expressions during the past centuries. Connections between two of its most prominent forms, i.e. the evolutionary principle by natural selection and the principle of least action, are examined. Although no fundamenta ..."
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Cited by 15 (8 self)
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The second law of thermodynamics is a powerful imperative that has acquired several expressions during the past centuries. Connections between two of its most prominent forms, i.e. the evolutionary principle by natural selection and the principle of least action, are examined. Although no fundamentally new findings are provided, it is illuminating to see how the two principles rationalizing natural motions reconcile to one law. The second law, when written as a differential equation of motion, describes evolution along the steepest descents in energy and, when it is given in its integral form, the motion is pictured to take place along the shortest paths in energy. In general, evolution is a nonEuclidian energy density landscape in flattening motion.
Projective Invariants for Affine Shapes of Point Configurations
, 1991
"... this paper also sheds some light on these stability problems. Thus, for instance, via Lemma 2, the affine constraints contribute with an explicit set of instability conditions for the relative depth, and information about the degree of instability. ..."
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Cited by 14 (3 self)
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this paper also sheds some light on these stability problems. Thus, for instance, via Lemma 2, the affine constraints contribute with an explicit set of instability conditions for the relative depth, and information about the degree of instability.
Identity, Indiscernibility, and Philosophical Claims
, 2002
"... The standard ways classical logic and mathematics deal with the concept of indiscernibility (indistinguishability), with special emphasis to the concept of indiscernibility in a structure are considered. ..."
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Cited by 4 (1 self)
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The standard ways classical logic and mathematics deal with the concept of indiscernibility (indistinguishability), with special emphasis to the concept of indiscernibility in a structure are considered.
A Discussion on Particle Number and Quantum
, 2008
"... The concept of individuality in quantum mechanics shows radical differences from the concept of individuality in classical physics, as E. Schrödinger pointed out in the early steps of the theory. Regarding this fact, some authors suggested that quantum mechanics does not possess its own language, an ..."
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Cited by 2 (2 self)
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The concept of individuality in quantum mechanics shows radical differences from the concept of individuality in classical physics, as E. Schrödinger pointed out in the early steps of the theory. Regarding this fact, some authors suggested that quantum mechanics does not possess its own language, and therefore, quantum indistinguishability Fellow of the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET) 1 is not incorporated in the theory from the beginning. Nevertheless, it is possible to represent the idea of quantum indistinguishability with a first order language using quasiset theory (Q). In this work, we show that Q cannot capture one of the most important features of quantum non individuality, which is the fact that there are quantum systems for which particle number is not well defined. An axiomatic variant of Q, in which quasicardinal is not a primitive concept (for a kind of quasisets called finite quasisets), is also given. This result encourages the searching of theories in which the quasicardinal, being a secondary concept, stands undefined for some quasisets, besides showing explicitly that in a set theory about collections of truly indistinguishable entities, the quasicardinal needs not necessarily be a primitive concept. Key words: quasisets, particle number, quasicardinality, quantum indistinguishability. 2 1
On the Brightness of the Thomson Lamp. A Prolegomenon to Quantum Recursion Theory
, 2009
"... Some physical aspects related to the limit operations of the Thomson lamp are discussed. Regardless of the formally unbounded and even infinite number of “steps” involved, the physical limit has an operational meaning in agreement with the Abel sums of infinite series. The formal analogies to accele ..."
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Some physical aspects related to the limit operations of the Thomson lamp are discussed. Regardless of the formally unbounded and even infinite number of “steps” involved, the physical limit has an operational meaning in agreement with the Abel sums of infinite series. The formal analogies to accelerated (hyper) computers and the recursion theoretic diagonal methods are discussed. As quantum information is not bound by the mutually exclusive states of classical bits, it allows a consistent representation of fixed point states of the diagonal operator. In an effort to reconstruct the selfcontradictory feature of diagonalization, a generalized diagonal method allowing no quantum fixed points is proposed.
Modeling and Analysis of Sustainable Systems
 European Research Consortium in Informatics and Mathematics
, 1999
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ACCELERATING MACHINES
, 2006
"... This paper presents an overview of accelerating machines. We begin by exploring the history of the accelerating machine model and the potential power that it provides. We look at some of the problems that could be solved with an accelerating machine, and review some of the possible implementation me ..."
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Cited by 1 (1 self)
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This paper presents an overview of accelerating machines. We begin by exploring the history of the accelerating machine model and the potential power that it provides. We look at some of the problems that could be solved with an accelerating machine, and review some of the possible implementation methods that have been presented. Finally, we expose the limitations of accelerating machines and conclude by posing some problems for further research.