Landsman, Klaas · arXiv (Cornell University) · 2019
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a (Wittgensteinian) philosophical discussion of randomness in general, I argue that deterministic interpretations of quantum mechanics (like Bohmian mechanics or 't Hooft's Cellular Automaton interpretation) are strictly speaking incompatible with the Born rule. I also stress the role of outliers, i.e. measurement outcomes that are not 1-random. Although these occur with low (or even zero) probability, their very existence implies that the no-signaling principle used in proofs of randomness of outcomes of quantum-mechanical measurements (and of the safety of quantum cryptography) should be reinterpreted statistically, like the second law of thermodynamics. In appendices I discuss the Born rule and its status in both single and repeated experiments, and review the notion of 1-randomness introduced by Kolmogorov, Chaitin, Martin-Lo"f, Schnorr, and others.
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Klaas Landsman · Foundations of Physics · 2020
Abstract This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a (Wittgensteinian) philosophical discussion of randomness in general, I argue that deterministic interpretations of quantum mechanics (like Bohmian mechanics or ’t Hooft’s Cellular Automaton interpretation) are strictly speaking incompatible with the Born rule. I also stress the role of outliers, i.e. measurement outcomes that are not 1-random. Although these occur with low (or even zero) probability, their very existence implies that the no-signaling principle used in proofs of randomness of outcomes of quantum-mechanical measurements (and of the safety of quantum cryptography) should be reinterpreted statistically, like the second law of thermodynamics. In three appendices I discuss the Born rule and its status in both single and repeated experiments, review the notion of 1-randomness (or algorithmic randomness) that in various guises was investigated by Kolmogorov and others and treat Bell’s (Physics 1:195–200, 1964) Theorem and the Free Will Theorem with their implications for randomness.
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Philipp Kornreich · 2018
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2008
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Jake Neuman and Melissa Liedtke · Bulletin of Miscellaneous Information (Royal Gardens Kew)
Randomness Squared #9: Randomness Direct Download (33.7 MB) Show Notes: -Randomness -it's dang cold -The Tales of Beedle the Bard -Don't drop your iPhone! -best selling game of 2009 -and more! Jake's iPhone case: Melissa's iPod Touch case: http://www.giantbomb.com/news/nintendo-dominates-2008-console-game-sales/807/ http://itunes.apple.com/WebObjects/MZStore.woa/wa/viewAlbum?id=297301033&s=143441
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Scott Aaronson · Cambridge University Press eBooks · 2013
In the last two chapters, we talked about computational complexity up till the early 1970s. Here, we'll add a new ingredient to our already simmering stew – something that was thrown in around the mid-1970s, and that now pervades complexity to such an extent that it's hard to imagine doing anything without it. This new ingredient is randomness.
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P.M.B. (Paul) Vitányi · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 1994
These draft excerpts of the chapter ''Randomness'' in 20th Century Mathematics in preparation for the 'Matematica, Logica, lnformatica' Volume 12 of the Storia del XX Secolo, to be published by the Instituto della Enciclopedia Italiana.are dedicated to Cor Baayen.Here we present in a single essay a combination and completion of the several aspects of the problem of randomness of individual objects which of necessity occur scattered in our text [3].
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Vitányi, Paul, Apt, Krzysztof, Schrijver, Lex et al. · Data Archiving and Networked Services (DANS) · 1994
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QUICI, Fabio · IRIS Research product catalog (Sapienza University of Rome) · 2000
Le realtà delle periferie e dello spontaneismo edilizio vengono messe a confronto con diverse manifestazioni – in campo architettonico, artistico e letterario – che hanno attinto a tali fenomeni, evidenziando le diverse possibilità di assimilazione e di recupero di un linguaggio ricco di spunti
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David E. Stewart · CMS/CAIMS books in mathematics · 2022
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Deborah J. Bennett · Harvard University Press eBooks · 1999
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Bennett, Deborah J.
From the ancients' first readings of the innards of birds to your neighbor's last bout with the state lottery, humankind has put itself into the hands of chance. Today life itself may be at stake when probability comes into play-in the chance of a false negative in a medical test, in the reliability of DNA findings as legal evidence, or in the likelihood of passing on a deadly congenital disease-yet as few people as ever understand the odds. This book is aimed at the trouble with trying to learn about probability. A story of the misconceptions and difficulties civilization overcame in progressing toward probabilistic thinking, Randomness is also a skillful account of what makes the science of probability so daunting in our own day. To acquire a (correct) intuition of chance is not easy to begin with, and moving from an intuitive sense to a formal notion of probability presents further problems. Author Deborah Bennett traces the path this process takes in an individual trying to come to grips with concepts of uncertainty and fairness, and also charts the parallel path by which societies have developed ideas about chance. Why, from ancient to modern times, have people resorted to chance in making decisions? Is a decision made by random choice "fair"? What role has gambling played in our understanding of chance? Why do some individuals and societies refuse to accept randomness at all? If understanding randomness is so important to probabilistic thinking, why do the experts disagree about what it really is? And why are our intuitions about chance almost always dead wrong? Anyone who has puzzled over a probability conundrum is struck by the paradoxes and counterintuitive results that occur at a relatively simple level. Why this should be, and how it has been the case through the ages, for bumblers and brilliant mathematicians alike, is the entertaining and enlightening lesson of Randomness
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Paul Vitányi · 2007
Here we present in a single essay a combination and completion of the several aspects of the problem of randomness of individual objects which of necessity occur scattered in our text [10]. The reader can consult different arrangements of parts of the material in [7, 20]. Contents 1 Introduction 2 1.1 Occam's Razor Revisited : : : : : : : : : : : : : : : : : : : : : : : 3 1.2 Lacuna of Classical Probability Theory : : : : : : : : : : : : : : : 4 1.3 Lacuna of Information Theory : : : : : : : : : : : : : : : : : : : : 4 2 Randomness as Unpredictability 6 2.1 Von Mises' Collectives : : : : : : : : : : : : : : : : : : : : : : : : 8 2.2 Wald-Church Place Selection : : : : : : : : : : : : : : : : : : : : 11 3 Randomness as Incompressibility 12 3.1 Kolmogorov Complexity : : : : : : : : : : : : : : : : : : : : : : : 14 3.2 Complexity Oscillations : : : : : : : : : : : : : : : : : : : : : : : 16 3.3 Relation with Unpredictability : : : : : : : : : : : : : : : : : : : 19 3.4 Kolmogorov-Lo...
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Vitányi, P.M.B. (Paul) · CWI's Institutional Repository (Centrum Wiskunde & Informatica) · 1995
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Thomas, Nicola, Donnelly, Kelsie, Orsini, Francesca · Lancaster EPrints (Lancaster University) · 2021
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Vitányi, Paul · Data Archiving and Networked Services (DANS) · 1995
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Vitányi, P.M.B. (Paul) · CWI's Institutional Repository (Centrum Wiskunde & Informatica) · 1994
These draft excerpts of the chapter "Randomness" in 20th CentunJ Mathematics in preparation for the 'Matematica, Logica, lnformatica' Volume 12 of the Storia del XX Secolo, to be published by the Instituto delta Enciclopedia Italiana, are dedicated to Cor Baayen.Here we present in a single essay a combination and completion of the several aspects of the problem of randomness of individual objects which of necessity occur scattered in our text [3}.
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P.M.B. Vitanyi · UvA-DARE (University of Amsterdam) · 1994
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V. Griffith, E. K. P. Chong, R. G. James et al. · 2014
SFI Working Papers contain accounts of scienti5ic work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peer-‐reviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for papers by our external faculty, papers must be based on work done at SFI, inspired by an invited visit to or collaboration at SFI, or funded by an SFI grant. ©NOTICE: This working paper is included by permission of the contributing author(s) as a means to ensure timely distribution of the scholarly and technical work on a non-‐commercial basis. Copyright and all rights therein are maintained by the author(s). It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may be reposted only with the explicit permission of the copyright holder. www.santafe.edu SANTA FE INSTITUTEIntersection Information based on Common
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Henry E. Kyburg · PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association · 1972
Mr. Coffa's admirable and lucid exposition of the history of mathematical randomness, leaves, to my mind, nothing to be desired. I am not sure whether, or how, its end result is of use to the theoretically minded statistician, but it is certainly interesting enough in its own right to need no excuse. I tend also to agree wholeheartedly with Mr. Coffa's treatment of physical randomness, or at least with his conclusion. I can easily imagine that he will not have succeeded in convincing those who are sure that epistemology is built into physics - say in quantum mechanics - but he has certainly given even these people some food for thought. I can even swallow the peroration of his last paragraph whole, and agree that one might hope and expect that physics can make its claims without a reference to knowledge or to randomness.
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