Quantum Randomness and Value Indefiniteness

Calude, Cristian S.; Svozil, Karl

doi:10.1166/asl.2008.016

Cited by 58 publications

(54 citation statements)

References 33 publications

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“…And this may give an impression of randomness, without there actuality being any mathematical randomness embodied. This is very much in line with the research of Cris Calude and Karl Svozil on the nature of quantum randomness [11].…”

Section: Turing Invariance and The Structure Of Physicssupporting

confidence: 85%

“…Also familiar is the filling of deterministic shortcomings with a (mathematically naive) randomness underlying the predicted probabilities, which Calude and his collaborators have examined more closely in various writings (see, e.g. [10,11]) over the years. For those working with clarified notions, randomness loses its fundamentality and scientific dignity when calibrated, and made to rub shoulders with mere incomputability.…”

Section: Definability and The Collapse Of The Wave Functionmentioning

confidence: 99%

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Mathematics, Metaphysics and the Multiverse

Cooper

2012

Lecture Notes in Computer Science

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It would be nice if science answered all questions about our universe. In the past, mathematics has not just provided the language in which to frame suitable scientific answers, but was also able to give us clear indications of its own limitations. The former was able to deliver results via an ad hoc interface between theory and experiment. But to characterise the power of the scientific approach, one needs a parallel higher-order understanding of how the working scientist uses mathematics, and the development of an informative body of theory to clarify and expand this understanding. We argue that this depends on us selecting mathematical models which take account of the 'thingness' of reality, and puts the mathematics in a correspondingly rich informationtheoretic context. The task is to restore the role of embodied computation and its hierarchically arising attributes. The reward is an extension of our understanding of the power and limitations of mathematics, in the mathematical context, to that of the real world. Out of this viewpoint emerges a widely applicable framework, with not only epistemological, but also ontological consequences -one which uses Turing invariance and its putative breakdowns to confirm what we observe in the universe, to give a theoretical status to the dichotomy between quantum and relativistic domains, and which removes the need for many-worlds and related ideas. In particular, it is a view which confirms that of many quantum theorists -that it is the quantum world that is 'normal', and our classical level of reality which is strange and harder to explain. And which complements fascinating work of Cristian Calude and his collaborators on the mathematical characteristics of quantum randomness, and the relationship of 'strong determinism' to computability in nature.Academics have ever been able to build successful (and very useful) careers within the bounds of 'normal science', and to revel in a near-Laputian unworldliness. But science would not progress half so well without a leavening of the less conventional, and an occasional engagement with the real-world. Particularly appropriate to the Turing Centenary, this short piece is dedicated to Cristian Calude on his sixtieth birthday -a researcher not just of formidable expertise, but one whose innovative work on real problems related to physics and randomness has much enriched our understanding of the world around us. This relevance ?

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Section: Turing Invariance and The Structure Of Physicssupporting

confidence: 85%

Section: Definability and The Collapse Of The Wave Functionmentioning

confidence: 99%

Mathematics, Metaphysics and the Multiverse

Cooper

2012

Lecture Notes in Computer Science

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“…Most images of the real world depict objects that have some formative process, and that process can be approximately or statistically modelled to obtain compression. Even some random timeseries that occur in nature are correlated (1/f noise) or consist of intermittent events (radioactive decay) and are thus compressible, although this is not the case in general [8]. Similarly in the realm of human creations, most designs reflect some internal logic rather than being completely random.…”

Section: Are Nl Images Compressible?mentioning

confidence: 99%

Is there a universal image generator?

Calude

Lewis

2012

Applied Mathematics and Computation

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Synthetic pattern generation procedures have various applications, and a number of approaches (fractals, L-systems, etc.) have been devised. A fundamental underlying question is: will new pattern generation algorithms continue to be invented, or is there some "universal" algorithm that can generate all (and only) the perceptually distinguishable images, or even all members of a restricted class of patterns such as logos or letterforms? In fact there are many complete algorithms that can generate all possible images, but most images are random and not perceptually distinguishable. Counting arguments show that the percentage of distinguishable images that will be generated by such complete algorithms is vanishingly small. In this paper we observe that perceptually distinguishable images are compressible. Using this observation it is evident that algorithmic complexity provides an appropriate framework for discussing the question of a universal image generator. We propose a natural thesis for describing perceptually distinguishable images and argue its validity. Based on it, we show that there is no program that generates all (and only) these images. Although this is an abstract result, it may have importance for graphics and other fields that deal with compressible signals. In essence, new representations and pattern generation algorithms will continue to be developed; there is no feasible "super algorithm" that is capable of all things.

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“…Calude and physicist K. Svozil proved that "Quantum Randomness" (QR) is not Turing computable. While "true randomness" is a mathematical impossibility, the certification by value indefiniteness ensures that the quantum random bits are incomputable in the strongest sense [2,3]. Algorithmic random sequences are incomputable, but the converse implication is false.…”

Section: Introductionmentioning

confidence: 99%

The Entropy Conundrum: A Solution Proposal

Fiorini

2014

Proceedings of 1st International Electronic Conference on Entropy and Its Applications

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don't know the code used for the message you can't tell the difference between an information-rich message and a random jumble of letters. This is an entropy conundrum to solve. Even the most sophisticated instrumentation system is completely unable to reliably discriminate so called "random noise" from any combinatorially optimized encoded message, which CICT called "deterministic noise". Entropy fundamental concept crosses so many scientific and research areas, but, unfortunately, even across so many different disciplines, scientists have not yet worked out a definitive solution to the fundamental problem of the logical relationship between human experience and knowledge extraction. So, both classic concept of entropy and system random noise should be revisited deeply at theoretical and operational level. A convenient CICT solution proposal will be presented.

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Quantum Randomness and Value Indefiniteness

Abstract: As computability implies value definiteness, certain sequences of quantum outcomes cannot be computable.

Cited by 58 publications

References 33 publications

Mathematics, Metaphysics and the Multiverse

Mathematics, Metaphysics and the Multiverse

Is there a universal image generator?

The Entropy Conundrum: A Solution Proposal

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