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A New Computational Approach to Infinity for Modelling Physical Phenomena

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Frontiers of Fundamental Physics and Physics Education Research

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 145))

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Abstract

A new computational methodology for computations with infinite and infinitesimal quantities is described. It is based on the principle ‘The part is less than the whole’ introduced by Ancient Greeks and observed in the physical world. It is applied to all sets and processes (finite and infinite) and all numbers (finite, infinite, and infinitesimal). It is shown that it becomes possible to work with all of them in a unique framework (different from non-standard analysis) allowing one to easily manage mathematical situations that traditionally create difficulties (divergences of various kind, indeterminate forms, etc.) and to construct mathematical models of physical phenomena of a new type.

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Notes

  1. 1.

    This is true also for the modern non-standard analysis [1] that re-writes the standard one in terms of infinitesimals and realizes the program of Leibniz. For instance, one of the basic concepts in the non-standard analysis is monad, the notion taken from Physics that, however, is not used in Physics for a long time.

  2. 2.

    We remind that a numeral is a symbol or group of symbols that represents a number. The difference between numerals and numbers is the same as the difference between words and the things they refer to. A number is a concept that a numeral expresses. The same number can be represented by different numerals written in different numeral systems. For example, the symbols ‘4’, ‘four’, and ‘IV’ are different numerals, but they all represent the same number. Rules used in different numeral systems to execute arithmetical operation can be also different.

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Author information

Authors and Affiliations

  1. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

  2. N.I. Lobatchevsky State University, Nizhni Novgorod, Russia

    Yaroslav D. Sergeyev

  3. Institute of High Performance Computing and Networking of the National Research Council of Italy, Roma, Italy

    Yaroslav D. Sergeyev

Authors
  1. Yaroslav D. Sergeyev
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Editor information

Editors and Affiliations

  1. Birla Science Centre, Hyderabad, India

    Burra G. Sidharth

  2. DCFA - Section ofMathematics and Physics, University of Udine, Udine, Italy

    Marisa Michelini

  3. DCFA - Section of Mathematics and Physic, University of Udine, Udine, Italy

    Lorenzo Santi

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Sergeyev, Y.D. (2014). A New Computational Approach to Infinity for Modelling Physical Phenomena. In: Sidharth, B., Michelini, M., Santi, L. (eds) Frontiers of Fundamental Physics and Physics Education Research. Springer Proceedings in Physics, vol 145. Springer, Cham. https://doi.org/10.1007/978-3-319-00297-2_35

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