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Random Interval Arithmetic is Closer to Common Sense: An Observation

By René Alt, Jean-luc Lamotte and Vladik Kreinovich

Abstract

From the commonsense viewpoint, if on a bridge whose weight we know with an accuracy of 1 ton, we place a car whose weight we know with an accuracy of 5 kg, then the accuracy with which we know the overall weight of a bridge with a car on it should still be 1 ton. This is what an engineer or a physicist would say. Alas, this is not so in traditional interval arithmetic. In this paper, we show that, in contrast to traditional interval arithmetic, the random interval arithmetic (proposed by the first two authors) actually has this important property. 1 Intuitive Property of Commonsense Arithmetic From the commonsense viewpoint, if on a bridge whose weight we know with an accuracy of 1 ton, we place a car whose weight we know with an accuracy of 5 kg, then the accuracy with which we know the overall weight of a bridge with a car on it should still be 1 ton. This is what an engineer or a physicist would say. The problem that we try to solve in this paper can be illustrated by the following joke. A museum guide tells the visitors that a dinosaur that they are looking at is 14,000,005 years old. An impressed visitor asks how scientists can be so accurate in its predictions. “I don’t know how they do it, – explains the guide – but 5 years ago, when I started working here, I was told that this dinosaur is 14,000,000 years old, so no

Year: 2011
OAI identifier: oai:CiteSeerX.psu:10.1.1.183.1978
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