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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 9 (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.
Science At the Crossroad Between Randomness and Determinism
, 2000
"... Time and again, man's understanding of Nature is at the crossroad between total worldcomprehension and total randomness. It is suggested that not only are the preferences influenced by the theories and models of today, but also by the very personal subjective inclinations of the people involved ..."
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Cited by 2 (2 self)
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Time and again, man's understanding of Nature is at the crossroad between total worldcomprehension and total randomness. It is suggested that not only are the preferences influenced by the theories and models of today, but also by the very personal subjective inclinations of the people involved. The second part deals with the principle of selfconsistency and its consequences for totally deterministic systems.
Conventions in Relativity Theory and Quantum Mechanics
, 2002
"... ons. They lie at the very foundations of our world conceptions. Conventions serve as a sort of "scaffolding" from which we construct our scientific worldview. Yet, they are so simple and almost selfevident that they are hardly mentioned and go unreflected. To the author, this unreflectedness and ..."
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Cited by 1 (1 self)
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ons. They lie at the very foundations of our world conceptions. Conventions serve as a sort of "scaffolding" from which we construct our scientific worldview. Yet, they are so simple and almost selfevident that they are hardly mentioned and go unreflected. To the author, this unreflectedness and unawareness of conventionality appears to be the biggest problem related to conventions, especially if they are mistakenly considered as physical "facts" which are empirically testable. This confusion between assumption and observational, operational fact seems to be one of the biggest impediments for progressive research programs, in particular if they suggest postulates which are based on conventions different from the existing ones. In what follows we shall mainly review and discuss conventions in the two dominating theories of the 20th century: quantum mechanics and relativity theory. 2. CONVENTIONALITY OF THE CONSTANCY OF THE CHARACTERISTIC SPEED Sup
Undecidability Everywhere?
, 1996
"... We discuss the question of if and how undecidability might be translatable into physics, in particular with respect to prediction and description, as well as to complementarity games. 1 1 Physics after the incompleteness theorems There is incompleteness in mathematics [22, 63, 65, 13, 9, 12, 51 ..."
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Cited by 1 (0 self)
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We discuss the question of if and how undecidability might be translatable into physics, in particular with respect to prediction and description, as well as to complementarity games. 1 1 Physics after the incompleteness theorems There is incompleteness in mathematics [22, 63, 65, 13, 9, 12, 51]. That means that there does not exist any reasonable (consistent) finite formal system from which all mathematical truth is derivable. And there exists a "huge" number [11] of mathematical assertions (e.g., the continuum hypothesis, the axiom of choice) which are independent of any particular formal system. That is, they as well as their negations are compatible with the formal system. Can such formal incompleteness be translated into physics or the natural sciences in general? Is there some question about the nature of things which is provable unknowable for rational thought? Is it conceivable that the natural phenomena, even if they occur deterministically, do not allow their complete d...
ONETOONE
"... Reversible computation is a great metaphor for the foundations of physics. General discussion A reversible computation is a computation which can be reversed completely. That is, after insertion of the input into a reversible computer, the reversible computer generates some output (if ever). In such ..."
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Reversible computation is a great metaphor for the foundations of physics. General discussion A reversible computation is a computation which can be reversed completely. That is, after insertion of the input into a reversible computer, the reversible computer generates some output (if ever). In such a case one may run the entire computation backward by inserting the output as new input, thereby obtaining the input one started with. The computation can flow back and forth an arbitrary number of times. The implicit time symmetry spoils the very notion of “result, ” since what is a valuable output is purely determined by the subjective meaning the observer associates with it and is devoid of any syntactic relevance. In more formal terms, reversible computation can be characterized by onetoone operations, by a reversible, bijective evolution of the computer states onto themselves [Lan61, Ben73, FT82, Ben82, Lan94, LR90]. If only a finite number of such states are involved, this amounts to their permutation. In such a scheme, not a single bit gets lost, and any piece of information (including the trash) remains in the computer forever. That may be good