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RE: Ancient Greeks and irrationals (Paul E)

🔗Manuel.Op.de.Coul@ezh.nl (Manuel Op de Coul)

3/5/1997 3:20:08 PM
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.

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