Abstract
Nobel-prize winning physicist Lev Landau liked to emphasize that logarithms are not infinity – meaning that from the physical viewpoint, logarithms of infinite values are not really infinite. Of course, from a literally mathematical viewpoint, this statement does not make sense: one can easily prove that logarithm of infinity is infinite. However, when a Nobel-prizing physicist makes a statement, you do not want to dismiss it, you want to interpret it. In this paper, we propose a possible physical explanation of this statement. Namely, in physics, nothing is really infinite: according to modern physics, even the Universe is finite in size. From this viewpoint, infinity simply means a very large value. And here lies our explanation: while, e.g., the square of a very large value is still very large, the logarithm of a very large value can be very reasonable – and for very large values from physics, logarithms are indeed very reasonable.
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Acknowledgments
This work was supported in part by the US National Science Foundation via grant HRD-1242122 (Cyber-ShARE Center of Excellence). The authors are thankful to the anonymous referees for valuable suggestions.
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Zapata, F., Kosheleva, O., Kreinovich, V. (2019). Logarithms Are Not Infinity: A Rational Physics-Related Explanation of the Mysterious Statement by Lev Landau. In: Kearfott, R., Batyrshin, I., Reformat, M., Ceberio, M., Kreinovich, V. (eds) Fuzzy Techniques: Theory and Applications. IFSA/NAFIPS 2019 2019. Advances in Intelligent Systems and Computing, vol 1000. Springer, Cham. https://doi.org/10.1007/978-3-030-21920-8_66
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DOI: https://doi.org/10.1007/978-3-030-21920-8_66
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