منابع مشابه
What the Tortoise said to Achilles.
Practitioners and investigators often view clinical trials from very different perspectives-the former in terms of individuals and the latter in terms of groups. The following whimsical dialogue highlights the philosophical foundations of these contrasting perspectives and illustrates their potential impact on patient care and public policy. The title alludes to a piece by Lewis Carroll regardi...
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Zeno’s paradoxes of motion, which claim that moving from one point to another cannot be accomplished in finite time, seem to be of serious concern when moving towards an agreement is concerned. Parkinson’s Law of Triviality implies that such an agreement cannot be reached in finite time. By explicitly modeling dynamic processes of reaching interim agreements and using arguments similar to Zeno’...
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Mrs. Mary McCullagh reports on the progress she has been able to make in teaching her son to read, although he had been classified as ineducable. The trouble is, of course, that I'm not supposed to be doing it at all. Once your child is classified as 'in-educable', then it follows almost as the night the day that he or she will never read. Not perhaps in theory, but more often than not in pract...
متن کاملAchilles and the Tortoise Climbing Up the Arithmetical Hierarchy
In this paper we show how to construct for every set P of integers in the arithmetical hierarchy a dynamical system H with piecewise constant derivatives PCD such that deciding membership in P can be reduced to solving the reachability problem between two ratio nal points for H The ability of such apparently simple dynami cal systems whose de nition involves only rational parameters to solve hi...
متن کاملAchilles and the Tortoise Climbing up the Hyper-Arithmetical Hierarchy
In this paper, we characterize the computational power of dynamical systems with piecewise constant derivatives (PCD) considered as computational machines working on a continuous real space with a continuous real time: we prove that piecewise constant derivative systems recognize precisely the languages of the ω th (respectively: ω + 1 th ) level of the hyper-arithmetical hierarchy in dimension...
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ژورنال
عنوان ژورنال: Nature
سال: 1980
ISSN: 0028-0836,1476-4687
DOI: 10.1038/283699a0