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Dirty Pages of Logarithm Tables, Lifetime of the Universe, and (Subjective) Probabilities on Finite and Infinite Intervals

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Reliable Computing

Abstract

In many engineering problems, we want a physical characteristic y to lie within given range Y; e.g., for all possible values of the load x from 0 to x 0, the resulting stress y of a mechanical structure should not exceed a given value y 0. If no such design is possible, then, from the purely mathematical viewpoint, all possible designs are equally bad. Intuitively, however, a design for which y ≤ y 0 for all values x ∈ [0,0.99 ⋅ x 0] is “more probable” to work well than a design for which y ≤ y 0 only for the values x ∈ [0,0.5 ⋅ x 0]. In this paper, we describe an interval computations-related formalization for this subjective notion of probability. We show that this description is in good accordance with the empirical distribution of numerical data and with the problems related to estimating the lifetime of the Universe.

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Authors and Affiliations

  1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, 88003, USA, e-mail

    Hung T. Nguyen

  2. Department of Computer Science, University of Texas at El Paso, El Paso, TX, 79968, USA, e-mail

    Vladik Kreinovich & Luc Longpré

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  1. Hung T. Nguyen
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  2. Vladik Kreinovich
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  3. Luc Longpré
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Nguyen, H.T., Kreinovich, V. & Longpré, L. Dirty Pages of Logarithm Tables, Lifetime of the Universe, and (Subjective) Probabilities on Finite and Infinite Intervals. Reliable Computing 10, 83–106 (2004). https://doi.org/10.1023/B:REOM.0000015848.19449.12

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