Denis Diderot (1713–84) criticized Hutcheson's application of uniformity amidst variety to geometrical objects and to theorems in his article on ‘Beautiful’ in the ‘Encyclopédie’.
Diderot preferred the system of Yves-Marie André (1675–1764), whose book ‘Essai sur le Beau’ was famous in its time. (I produced an open-access annotated translation in 2010; see the references in the next post.) André thought that in mathematics there was an essential geometrical beauty that was prior even to God and which had been used in the creation of the world. André saw beauty as a motivation for mathematicians from Euclid and Archimedes to Kepler and Huygens:
‘In a word, there is no academy in Europe where the love of mathematical beauty has not given in our days new conquests to the kingdom of truth.’
The attention paid to mathematical beauty in philosophical aesthetics seems to have dwindled in the 19th century with the domination in aesthetics of the philosophy of *art*, rather than of *beauty*, especially under G.W.F. Hegel's (1770–1831) influence. It revived in the first half of the 20th century in the work of philosophers like David Wight Prall (1886–1940) and Louis Arnaud Reid (1895–1986).
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“It might help to think of the universe as a rubber sheet, or perhaps not”*…
You have most likely encountered one-sided objects hundreds of times in your daily life – like the universal symbol for recycling, found printed on the backs of aluminum cans and plastic bottles.
This mathematical object is called a Mobius strip. It has fascinated environmentalists, artists, engineers, mathematicians and many others ever since its discovery in 1858 by August Möbius, a German mathematician who died 150 years ago, on Sept. 26, 1868.
Möbius discovered the one-sided strip in 1858 while serving as the chair of astronomy and higher mechanics at the University of Leipzig. (Another mathematician named Listing actually described it a few months earlier, but did not publish his work until 1861. Indeed, it had already appeared in Roman mosaics from the third century CE.)…
The discovery of the Möbius strip in the mid-19th century launched a brand new field of mathematics: topology: “The Mathematical Madness of Möbius Strips and Other One-Sided Objects.”
* Terry Pratchett, Hogfather
###
As we return from whence we came, we might wish a Joyeux Anniversaire to Denis Diderot, contributor to and the chief editor of the Encyclopédie (“All things must be examined, debated, investigated without exception and without regard for anyone’s feelings.”)– and thus towering figure in the Enlightenment; he was born on this date in 1713. Diderot was also a novelist (e.g., Jacques le fataliste et son maître [Jacques the Fatalist and his Master])… and no mean epigramist:
From fanaticism to barbarism is only one step.
We swallow greedily any lie that flatters us, but we sip only little by little at a truth we find bitter.
Man will never be free until the last king is strangled with the entrails of the last priest.
A thing is not proved just because no one has ever questioned it.
#diderot #encyclopedie #encyclopedia #history #literature #mathematics #mobiusStrip #mobius #topology
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#year1762 (1/2) : Royaume de France Ancien Régime sous Louis 15 : guerre de Sept Ans + #Diderot publie clandestinement le dernier des 17 volumes de son Encyclopédie = prône la connaissance scientifique et critique la toute-puissance de l'Église ;
-> noble François-Jean Lefebvre de La Barre 17 ans devient orphelin et ruiné par son père -> recueilli avec son frère par une tante abbesse à Abbeville Picardie (cf 1765 1766);
-> #Voltaire publie son #Dictionnaire ...
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