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Horgan, James S.

doi:10.1038/scientificamerican0293-22

Cited by 3 publications

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“…The proof is the same as before: the sum of the right-hand sides of (13-19) is odd, whereas the sum of the left-hand sides is necessarily even, because each answer appears twice. Apparently this conclusion rests on the impossibility of unique answers to 10 + 8 propositions: the 10 different ones in (13)(14)(15)(16)(17)(18)(19)), plus the one for the initial state (11) and the seven for orthogonal vectors (12). But in fact we can justify eqs.…”

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confidence: 99%

“…The vectors in Peres' set[7,8] can be geometrically interpreted as vectors along the 24 directions that join the center of a four-dimensional hypercube (tesseract) with the (pairwise opposite) centers of its 8 three-dimensional faces (cubes), the centers of the 24 two-dimensional intersections of them (squares), and the 16 vertices. The sets of vectors in several other BKS "state-independent" proofs have been nicknamed according to their aspect (Kochen-Specker's 117-vector set[2] is also known as the "cat's cradle"[10], Peres' 33-vector set[7,8] as the "quantum polyhedron"[11], and Penrose's 40-vector set[9,12] as the "magic dodecahedron"[13]); therefore we suggest naming Peres' 24-vector set the "quantum tesseract".…”

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Bell-Kochen-Specker theorem: A proof with 18 vectors

1996

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We present a ``state-independent'' proof of the Bell-Kochen-Specker theorem using only 18 four-dimensional vectors, which is a record for this kind of proof. This set of vectors contains subsets which allow us to develop a ``state-specific'' proof with 10 vectors (also a record) and a ``probabilistic'' proof with 7 vectors which reflects the algebraic structure of Hardy's nonlocality theorem.Comment: LaTeX, 10 page

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Bell-Kochen-Specker theorem: A proof with 18 vectors

1996

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G

Considine¹,

Considine²

1995

Van Nostrand’s Scientific Encyclopedia

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GGABBRO. Gabbro is a deep-seated and often very coarse-grained igneous rock composed of plagioclase feldspar, usually labradorite or bytownite and monoclinic pyroxene, with occasionally as accessories olivine (when it is then called olivine gabbro), biotite, magnetite, ilmenite, and hornblende. Norite is a variety of gabbro, carrying orthorhombic pyroxene, usually hypersthene instead of the monoclinic sort. Troctolite is essentially olivine and plagioclase. Quartz gabbros are known and have probably been derived from magmas somewhat oversaturated with silica. On the other hand, essexites represent gabbros whose parent magma doubtless had an insufficiency of silica resulting in the formation of nephelite. Gabbros are frequently rich in sulfides that may be of commercial value, a notable occurrence of which is at Sudbury, Canada. Here a norite carrying chalcopyrite and nickeliferous pyrrhotite forms the most important deposits of nickel known. Gold, silver and platinum are also recovered from this ore.

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Mess in Science and Wicked Problems

Schickore

2020

Perspectives on Science

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This paper discusses the claim that science is “messy.” Part I argues first, that a good portion of today’s discussions about messy science is just a portrayal of familiar features of science in new terms. In the paper, I refer to this as “messy science talk.” Second, Part I draws out rhetorical functions of messy science talk, namely the denigration of science in the popular media and the celebration of the maverick. Part II identifies one way in which it is enlightening to think about mess in current science, namely in reference to the problems that scientists need to address. It also shows that we do not need an entirely new conceptual inventory to analyze these problems. “Mess” and “wicked problems” were a theme in operations research and theories of social planning in the 1970s. These older analyses can illuminate important characteristics of today’s scientific problems. Wicked problems cut across different disciplines, engage different stakeholders (including non-scientists), are fluid, and cannot even be clearly formulated. They are urgent and need to be addressed before sufficient evidence is in.

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COBE Corroborated

Cited by 3 publications

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Bell-Kochen-Specker theorem: A proof with 18 vectors

Bell-Kochen-Specker theorem: A proof with 18 vectors

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Mess in Science and Wicked Problems

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