Which Number System Is “Best” for Describing Empirical Reality?
Eugene Wigner’s much-discussed notion of the “unreasonable effectiveness of mathematics” as applied to describing the physics of empirical reality is simultaneously both trivial and profound. After all, the relevant mathematics was (in the first instance) originally developed in order to be useful i...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/18/3340 |
| _version_ | 1797485177119703040 |
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| author | Matt Visser |
| author_facet | Matt Visser |
| author_sort | Matt Visser |
| collection | DOAJ |
| description | Eugene Wigner’s much-discussed notion of the “unreasonable effectiveness of mathematics” as applied to describing the physics of empirical reality is simultaneously both trivial and profound. After all, the relevant mathematics was (in the first instance) originally developed in order to be useful in describing empirical reality. On the other hand, certain aspects of the mathematical superstructure have by now taken on a life of their own, with at least <i>some</i> features of the mathematical superstructure greatly exceeding anything that can be directly probed or verified, or even justified, by empirical experiment. Specifically, I wish to raise the possibility that the real number system (with its nevertheless pragmatically very useful tools of real analysis and mathematically rigorous notions of differentiation and integration) may nevertheless constitute a “wrong turn” (a “sub-optimal” choice) when it comes to modelling empirical reality. Without making any definitive recommendation, I shall discuss several reasonably well-developed alternatives. |
| first_indexed | 2024-03-09T23:15:58Z |
| format | Article |
| id | doaj.art-c50c6eefcd474ed0866cef3467c38cee |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:15:58Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-c50c6eefcd474ed0866cef3467c38cee2023-11-23T17:37:03ZengMDPI AGMathematics2227-73902022-09-011018334010.3390/math10183340Which Number System Is “Best” for Describing Empirical Reality?Matt Visser0School of Mathematics and Statistics, Victoria University of Wellington, P.O. Box 600, Wellington 6140, New ZealandEugene Wigner’s much-discussed notion of the “unreasonable effectiveness of mathematics” as applied to describing the physics of empirical reality is simultaneously both trivial and profound. After all, the relevant mathematics was (in the first instance) originally developed in order to be useful in describing empirical reality. On the other hand, certain aspects of the mathematical superstructure have by now taken on a life of their own, with at least <i>some</i> features of the mathematical superstructure greatly exceeding anything that can be directly probed or verified, or even justified, by empirical experiment. Specifically, I wish to raise the possibility that the real number system (with its nevertheless pragmatically very useful tools of real analysis and mathematically rigorous notions of differentiation and integration) may nevertheless constitute a “wrong turn” (a “sub-optimal” choice) when it comes to modelling empirical reality. Without making any definitive recommendation, I shall discuss several reasonably well-developed alternatives.https://www.mdpi.com/2227-7390/10/18/3340mathematical physicsnumber systemsrational numbersreal numbersintegrationdifferentiation |
| spellingShingle | Matt Visser Which Number System Is “Best” for Describing Empirical Reality? Mathematics mathematical physics number systems rational numbers real numbers integration differentiation |
| title | Which Number System Is “Best” for Describing Empirical Reality? |
| title_full | Which Number System Is “Best” for Describing Empirical Reality? |
| title_fullStr | Which Number System Is “Best” for Describing Empirical Reality? |
| title_full_unstemmed | Which Number System Is “Best” for Describing Empirical Reality? |
| title_short | Which Number System Is “Best” for Describing Empirical Reality? |
| title_sort | which number system is best for describing empirical reality |
| topic | mathematical physics number systems rational numbers real numbers integration differentiation |
| url | https://www.mdpi.com/2227-7390/10/18/3340 |
| work_keys_str_mv | AT mattvisser whichnumbersystemisbestfordescribingempiricalreality |