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496
A New Kind of Science
, 2002
"... “Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical amplit ..."
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Cited by 850 (0 self)
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“Somebody says, ‘You know, you people always say that space is continuous. How do you know when you get to a small enough dimension that there really are enough points in between, that it isn’t just a lot of dots separated by little distances? ’ Or they say, ‘You know those quantum mechanical amplitudes you told me about, they’re so complicated and absurd, what makes you think those are right? Maybe they aren’t right. ’ Such remarks are obvious and are perfectly clear to anybody who is working on this problem. It does not do any good to point this out.” —Richard Feynman [1, p.161]
A topos perspective on the KochenSpecker Theorem: I. Quantum States . . .
, 1998
"... Any attempt to construct a realist interpretation of quantum theory founders on the KochenSpecker theorem, which asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined on al ..."
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Cited by 116 (20 self)
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Any attempt to construct a realist interpretation of quantum theory founders on the KochenSpecker theorem, which asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined
Constructivism and Proof Theory
, 2003
"... Introduction to the constructive point of view in the foundations of mathematics, in
particular intuitionism due to L.E.J. Brouwer, constructive recursive mathematics
due to A.A. Markov, and Bishop’s constructive mathematics. The constructive interpretation
and formalization of logic is described. F ..."
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Cited by 204 (4 self)
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. For constructive (intuitionistic)
arithmetic, Kleene’s realizability interpretation is given; this provides an example
of the possibility of a constructive mathematical practice which diverges from classical
mathematics. The crucial notion in intuitionistic analysis, choice sequence, is
briefly described and some
On Searching for Small KochenSpecker Vector Systems
"... Abstract. KochenSpecker (KS) vector systems are sets of vectors in ..."
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Cited by 8 (0 self)
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Abstract. KochenSpecker (KS) vector systems are sets of vectors in
Evasion and Prediction, the Specker Phenomenon and Gross Spaces
, 1994
"... We study the set–theoretic combinatorics underlying the following two algebraic phenomena. (1) A subgroup G ≤ Zω exhibits the Specker phenomenon iff every homomorphism G → Z maps almost all unit vectors to 0. Let se be the size of the smallest G ≤ Zω exhibiting the Specker phenomenon. (2) Given an u ..."
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Cited by 4 (0 self)
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We study the set–theoretic combinatorics underlying the following two algebraic phenomena. (1) A subgroup G ≤ Zω exhibits the Specker phenomenon iff every homomorphism G → Z maps almost all unit vectors to 0. Let se be the size of the smallest G ≤ Zω exhibiting the Specker phenomenon. (2) Given
The Specker Challenge Game for Education and Innovation in Constructive Domains
"... We have the following vision: To teach a constructive domain (e.g., domains in computer ..."
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Cited by 4 (4 self)
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We have the following vision: To teach a constructive domain (e.g., domains in computer
Nonconstructive and Deciding the Undecidable
, 2007
"... Provided by the author(s) and NUI Galway in accordance with publisher policies. Please cite the published ..."
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Provided by the author(s) and NUI Galway in accordance with publisher policies. Please cite the published
Noncontextuality, finite precision measurement and the Kochen–Specker theorem
, 2003
"... Meyer originally raised the question of whether noncontextual hidden variable models can, despite the KochenSpecker theorem, simulate the predictions of quantum mechanics to within any fixed finite experimental ..."
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Cited by 5 (0 self)
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Meyer originally raised the question of whether noncontextual hidden variable models can, despite the KochenSpecker theorem, simulate the predictions of quantum mechanics to within any fixed finite experimental
Results 1  10
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496