ar X iv : m at h . H O / 9 91 11 50 v 1 1 9 N ov 1 99 9 Machines , Logic and Quantum Physics
نویسندگان
چکیده
Though the truths of logic and pure mathematics are objective and independent of any contingent facts or laws of nature, our knowledge of these truths depends entirely on our knowledge of the laws of physics. Recent progress in the quantum theory of computation has provided practical instances of this, and forces us to abandon the classical view that computation, and hence mathematical proof, are purely logical notions independent of that of computation as a physical process. Henceforward, a proof must be regarded not as an abstract object or process but as a physical process, a species of computation, whose scope and reliability depend on our knowledge of the physics of the
منابع مشابه
ar X iv : m at h / 99 11 07 4 v 1 [ m at h . Q A ] 1 1 N ov 1 99 9 CRYSTAL GRAPHS FOR BASIC REPRESENTATIONS OF THE QUANTUM AFFINE
We give a realization of crystal graphs for basic representations of the quantum affine algebra Uq(C (1) 2) in terms of new combinatorial objects called the Young walls.
متن کاملar X iv : h ep - l at / 9 91 10 16 v 1 1 2 N ov 1 99 9 1 Future Perspectives in Lattice Field Theory ∗
I review some of the contributions which lattice simulations are likely to make during the next five years or so to the development of our understanding of particle physics. Particular emphasis is given to the evaluation of non-perturbative QCD effects in experimentally measurable amplitudes, and the corresponding extraction of fundamental parameters.
متن کاملar X iv : m at h / 99 11 10 9 v 1 [ m at h . R A ] 1 5 N ov 1 99 9 – 1 – BIRKHOFF ’ S THEOREM FOR PANSTOCHASTIC MATRICES
The panstochastic analogue of Birkhoff's Theorem on doubly-stochastic matrices is proved in the case n = 5. It is shown that this analogue fails when n > 1, n = 5.
متن کامل