P. J. Davis. Fidelity in mathematical discourse: Is one and one really two? Amer. Math. Monthly 79(1972), 252-263. Home/Search Document Not in Database Summary Related Articles Check |
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Reflections on Quantum Computing - Calude, Dinneen, Svozil (2000) (1 citation) (Correct)
....of the halting qubit. Although the buildup may be very slow, there is a nonvanishing chance to obtain a solution of the halting problem in finite time. Of course, the solution is probabilistic (one can argue that all mathematical proofs or computer programs are ultimately probabilistic, see Davis [9], De Millo, Lipton, Perlis [11] but goes beyond the capability of any classical computation: 4 even the best probabilistic algorithms are not able to achieve this computational power (by a classical result [10] probabilistic algorithms are equivalent to Turing machines) Let us finally notice ....
P. J. Davis. Fidelity in mathematical discourse: Is one and one really two? Amer. Math. Monthly 79(1972), 252-263.
Counterfactual Effect, the Halting Problem, and the Busy.. - Calude, Dinneen, Svozil (1999) (Correct)
....2 . Of course, if p is pretty small, then we can run the same experiment using thehypothesisisthatP eventually halts: i =1. In this case the chance of computing the non halting probability is now better: 1 p 2 . Now that we have shown that the undecidable halting problem can be re 5 Davis [7] shows that if we tolerate one failure in a thousand of elementary instructions, and the probability of success in one such elementary instruction is 1 1 m , then we should not carry on more than m 1000 instructions. As the number of instructions executed by current computers is enormous, the ....
....p 2 # 1 2 . 3 Conclusions The computational procedures described in this paper are probabilistic (one can argue that all mathematical proofs or computer programs are ultimately 6 The only known values are B(1) 1, B(2) 4, B(3) 6, B(4) 13, and B(5) # 1915. 6 probabilistic, see Davis [7], De Millo, Lipton, Perlis [8] but go beyond the capability of any classical computation: even the best probabilistic algorithms are not able to achieve this computational power (by a classical result [11] probabilistic algorithms are equivalent to Turing machines) ....
P. J. Davis. Fidelity in mathematical discourse: Is one and one really two? Amer. Math. Monthly 79(1972), 252-263.
Understanding Mathematical Discourse - Zinn (1999) (Correct)
....proof verification. Understanding a mathematical discourse means to being able to verify the correctness of the given mathematical argument. Verifying a proof is by no means trivial and often time consuming. As DAVIS shows, only some mathematicians would volunteer to check a fifty page proof [7]. Often, only a small number of mathematicians of some sub discipline have the necessary qualification to check a proof of their domain completely for correctness. The verification process itself is error prone. It is therefore inevitable that even many published proofs are either incomplete ....
P. J. DAVIS, Fidelity in mathematical discourse: Is one and one really two?, American Mathematical Monthly, 79 (1972).
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