source file: mills2.txt Date: Wed, 5 Mar 1997 15:20:08 -0800 Subject: RE: Ancient Greeks and irrationals (Paul E) From: Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul) From: PAULE >Anyway, despite Greek geometry's perfectly adequate treatment of >irrational proportions, repugnance towards them in areas where >*number* was thought to matter was very real, and is evidenced in >many writings dealing with "mathematical" disciplines. Thank you, Jonathan, I wanted to say exactly that, but you did better by providing examples: >One fantastic >example, mentioned by Aristides Quintilianus and also found in the >Hippocratic *Endemics*, tells physicians that diseases whose symptoms >appear in "concordant" ratios (like one day for every two they are >absent) are not dangerous, while those whose symptoms appear in >irrational or continuous proportions are "deadly, and to be feared". >Heck, even Aristotle thought that pleasant colours resulted from >elementary particles of black and white mixed in simple ratios, >whereas irrational proportions gave rise to unpleasant colours (this >is somewhere in *De Sensu*). And as far as musical thinking goes, >here's Barker's translation of Adrastus: > Under irrational relations noises are irrational > and unmelodic, and should not strictly even be called > notes, but only sounds; but under relations that place > them in certain relations to one another, they are > [...] strictly and properly notes. So I think it is fair to say that the ancient Greeks were biased against even considering an irrational explanation of Aristoxenus's findings. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 6 Mar 1997 00:28 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA07217; Thu, 6 Mar 1997 00:28:12 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA07117 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id PAA11829; Wed, 5 Mar 1997 15:25:08 -0800 Date: Wed, 5 Mar 1997 15:25:08 -0800 Message-Id: <009B0D443987424B.6234@vbv40.ezh.nl> Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu