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Computational universes
 Chaos, Solitons & Fractals
, 2006
"... Suspicions that the world might be some sort of a machine or algorithm existing “in the mind ” of some symbolic number cruncher have lingered from antiquity. Although popular at times, the most radical forms of this idea never reached mainstream. Modern developments in physics and computer science h ..."
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Cited by 11 (5 self)
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Suspicions that the world might be some sort of a machine or algorithm existing “in the mind ” of some symbolic number cruncher have lingered from antiquity. Although popular at times, the most radical forms of this idea never reached mainstream. Modern developments in physics and computer science have lent support to the thesis, but empirical evidence is needed before it can begin to replace our contemporary world view.
Set Theory and Physics
 FOUNDATIONS OF PHYSICS, VOL. 25, NO. 11
, 1995
"... Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of soli ..."
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Cited by 8 (7 self)
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Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of solid threedimensional objects, (iii) in the theory of effective computability (ChurchTurhrg thesis) related to the possible "solution of supertasks," and (iv) for weak solutions. Several approaches to set theory and their advantages and disadvatages for" physical applications are discussed: Cantorian "naive" (i.e., nonaxiomatic) set theory, contructivism, and operationalism, hr the arrthor's ophrion, an attitude of "suspended attention" (a term borrowed from psychoanalysis) seems most promising for progress. Physical and set theoretical entities must be operationalized wherever possible. At the same thne, physicists shouM be open to "bizarre" or "mindboggling" new formalisms, which treed not be operationalizable or testable at the thne of their " creation, but which may successfully lead to novel fields of phenomenology and technology.
How to acknowledge hypercomputation?
, 2007
"... We discuss the question of how to operationally validate whether or not a “hypercomputer” performs better than the known discrete computational models. ..."
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Cited by 1 (0 self)
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We discuss the question of how to operationally validate whether or not a “hypercomputer” performs better than the known discrete computational models.
THE ALEPHZERO OR ZERO DICHOTOMY (New and extended version with new arguments)
, 804
"... Abstract. This paper proves the existence of a dichotomy which being formally derived from the topological successiveness of ω ∗order leads to the same absurdity of Zeno’s Dichotomy II. It also derives a contradictory result from the first Zeno’s Dichotomy. ..."
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Abstract. This paper proves the existence of a dichotomy which being formally derived from the topological successiveness of ω ∗order leads to the same absurdity of Zeno’s Dichotomy II. It also derives a contradictory result from the first Zeno’s Dichotomy.
CRITICISM OF BENACERRAF’S CRITICISM OF MODERN ELEATICS
"... Abstract. I analyze here Benacerraf’s criticism of Thomson arguments on the impossibility of ωsupertasks. Although Benacerraf’s criticism is well founded, his analysis of Thomson’s lamp is incomplete. In fact, it is possible to consider a new line of argument, which Benacerraf only incidentally ..."
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Abstract. I analyze here Benacerraf’s criticism of Thomson arguments on the impossibility of ωsupertasks. Although Benacerraf’s criticism is well founded, his analysis of Thomson’s lamp is incomplete. In fact, it is possible to consider a new line of argument, which Benacerraf only incidentally considered, based on the functioning laws of the lamp. This argument leads to a contradictory result that compromises the formal consistency of the ωordering involved in all ωsupertasks. 1.
THE ALEPH ZERO OR ZERO DICHOTOMY
"... Abstract. The Aleph Zero or Zero Dichotomy is a strong version of Zeno’s Dichotomy II which being entirely derived from the topological successiveness of the ω∗order comes to the same Zeno’s absurdity. 1. Zeno’s paradoxes and modern science Zeno’s Paradoxes have interested philosophers of all times ..."
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Abstract. The Aleph Zero or Zero Dichotomy is a strong version of Zeno’s Dichotomy II which being entirely derived from the topological successiveness of the ω∗order comes to the same Zeno’s absurdity. 1. Zeno’s paradoxes and modern science Zeno’s Paradoxes have interested philosophers of all times (see [13], [14], [79], [68], [47] or [24] for historical background), although until the middle of the XIX century they were frequently considered as mere sophisms [13], [14], [67], [68]. From that time, and particularly along the XX century, they became the unending source of new philosophical, mathematical and physical discussions. Authors as Hegel [43], James [48], Russell [67], Whitehead [81], [82] or Bergson [9], [10] focused their attention on the challenging world of Zeno’s paradoxes. At the beginning of the second half of the XX century the pioneering works of Black [11], Wisdom [83], Thomson [75], [76], and Benacerraf [8] introduced a new way of discussing the possibilities to perform an actual infinity of actions in a finite time (a performance which is involved in most of Zeno’s paradoxes). I refer to Supertask Theory [64]. In fact, infinity machines, or supermachines, are our modern Achilles substitutes. A
ON BIFURCATED SUPERTASKS AND RELATED QUESTIONS
"... Abstract. Bifurcated supertasks entail the actual infinite division of time (accelerated system of reference) as well as the existence of halfcurves of infinite length (supertask system of reference). This paper analyzes both issues from a critique perspective. It also analyzes a conflictive case ..."
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Abstract. Bifurcated supertasks entail the actual infinite division of time (accelerated system of reference) as well as the existence of halfcurves of infinite length (supertask system of reference). This paper analyzes both issues from a critique perspective. It also analyzes a conflictive case of hypercomputation performed by means of a bifurcated supertask. The results of these analyzes suggest the convenience of reviewing certain foundational aspects of infinitist theories. 1. ωOrder and ωAsymmetry At the beginning of the second half of the XX century, the discussions on the possibilities to perform infinitely many actions in a finite interval of time (a supertask according to J. F. Thomson [50]) promoted new discussions on certain classical problems related to infinity [9], [54], [50], [51], [8]. The possibilities to perform an uncountable infinitude of actions were examined, and ruled out, by P. Clark and S. Read [12]. Supertasks have also been considered from the perspective of nonstandard analysis [34], [33], [1], [31], although the possibilities to perform an hypertask along an hyperreal interval of time have not been discussed, despite that finite
EXTENDING CANTOR’S PARADOX A CRITIQUE OF INFINITY AND SELFREFERENCE
, 809
"... Abstract. This paper examines infinity and selfreference from a critique perspective. Starting from an extension of Cantor Paradox that suggests the inconsistency of the actual infinite, the paper makes a short review of the controversial history of infinity and suggests several indicators of its i ..."
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Abstract. This paper examines infinity and selfreference from a critique perspective. Starting from an extension of Cantor Paradox that suggests the inconsistency of the actual infinite, the paper makes a short review of the controversial history of infinity and suggests several indicators of its inconsistency. Semantic selfreference is also examined from the same critique perspective by comparing it with selfreferent sets. The platonic scenario of infinity and selfreference is finally criticized from a biological and neurobiological perspective. 1.
A DISTURBING SUPERTASK
, 804
"... Abstract. This paper examines the consistency of ωorder by means of a supertask that functions as a supertrap for the assumed existence of ωordered collections, which are simultaneously complete (as is required by the Actual infinity) and uncompletable (because no last element completes them). As ..."
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Abstract. This paper examines the consistency of ωorder by means of a supertask that functions as a supertrap for the assumed existence of ωordered collections, which are simultaneously complete (as is required by the Actual infinity) and uncompletable (because no last element completes them). As Cantor himself proved [2], [3], ωorder is a formal consequence of assuming the existence of denumerable sets as complete totalities. Although it is hardly recognized, to be ωordered means to be both complete and uncompletable. In fact, the Axiom of Infinity states the existence of complete denumerable totalities, the most simple of which are ωordered, i.e. with a first element and such that each element has an immediate successor. Consequently, there is not a last element that completes ωordered totalities. To be complete and uncompletable may seem a modest eccentricity in the highly eccentric infinite paradise of our days, but its simplicity is just an advantage if we are interested