Mathematical Beauty Measure
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A Mathematical Beauty Measure is a beauty measure for mathematical concepts.
- Example(s):
- applied to an elegant proof (e.g. of a Pythagorean theorem).
- …
- Counter-Example(s):
- See: Mathematician, Aesthetics, Mathematics, Information Theory, Creativity.
References
2016
- (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/Mathematical_beauty Retrieved:2016-12-25.
- Mathematical beauty describes the notion that some mathematicians may derive aesthetic pleasure from their work, and from mathematics in general. They express this pleasure by describing mathematics (or, at least, some aspect of mathematics) as beautiful. Mathematicians describe mathematics as an art form or, at a minimum, as a creative activity. Comparisons are often made with music and poetry.
Bertrand Russell expressed his sense of mathematical beauty in these words:
Paul Erdős expressed his views on the ineffability of mathematics when he said, "Why are numbers beautiful? It's like asking why is Beethoven's Ninth Symphony beautiful. If you don't see why, someone can't tell you. I know numbers are beautiful. If they aren't beautiful, nothing is".Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.
- Mathematical beauty describes the notion that some mathematicians may derive aesthetic pleasure from their work, and from mathematics in general. They express this pleasure by describing mathematics (or, at least, some aspect of mathematics) as beautiful. Mathematicians describe mathematics as an art form or, at a minimum, as a creative activity. Comparisons are often made with music and poetry.
2016
- (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/Mathematical_beauty#Beauty_and_mathematical_information_theory Retrieved:2016-12-25.
- In the 1970s, Abraham Moles and Frieder Nake analyzed links between beauty, information processing, and information theory. [1] [2] In the 1990s, Jürgen Schmidhuber formulated a mathematical theory of observer-dependent subjective beauty based on algorithmic information theory: the most beautiful objects among subjectively comparable objects have short algorithmic descriptions (i.e., Kolmogorov complexity) relative to what the observer already knows. [3] [4] [5] Schmidhuber explicitly distinguishes between beautiful and interesting. The latter corresponds to the first derivative of subjectively perceived beauty: the observer continually tries to improve the predictability and compressibility of the observations by discovering regularities such as repetitions and symmetries and fractal self-similarity. Whenever the observer's learning process (possibly a predictive artificial neural network) leads to improved data compression such that the observation sequence can be described by fewer bits than before, the temporary interestingness of the data corresponds to the compression progress, and is proportional to the observer's internal curiosity reward. [6] [7]
- ↑ A. Moles: Théorie de l'information et perception esthétique, Paris, Denoël, 1973 (Information Theory and aesthetical perception)
- ↑ F Nake (1974). Ästhetik als Informationsverarbeitung. (Aesthetics as information processing). Grundlagen und Anwendungen der Informatik im Bereich ästhetischer Produktion und Kritik. Springer, 1974, ISBN 3-211-81216-4, ISBN 978-3-211-81216-7
- ↑ J. Schmidhuber. Low-complexity art. Leonardo, Journal of the International Society for the Arts, Sciences, and Technology, 30(2):97–103, 1997. http://www.jstor.org/pss/1576418
- ↑ J. Schmidhuber. Papers on the theory of beauty and low-complexity art since 1994: http://www.idsia.ch/~juergen/beauty.html
- ↑ J. Schmidhuber. Simple Algorithmic Principles of Discovery, Subjective Beauty, Selective Attention, Curiosity & Creativity. Proc. 10th Intl. Conf. on Discovery Science (DS 2007) p. 26-38, LNAI 4755, Springer, 2007. Also in Proc. 18th Intl. Conf. on Algorithmic Learning Theory (ALT 2007) p. 32, LNAI 4754, Springer, 2007. Joint invited lecture for DS 2007 and ALT 2007, Sendai, Japan, 2007. http://arxiv.org/abs/0709.0674
- ↑ .J. Schmidhuber. Curious model-building control systems. International Joint Conference on Neural Networks, Singapore, vol 2, 1458–1463. IEEE press, 1991
- ↑ Schmidhuber's theory of beauty and curiosity in a German TV show: http://www.br-online.de/bayerisches-fernsehen/faszination-wissen/schoenheit--aesthetik-wahrnehmung-ID1212005092828.xml