[INDOLOGY] Critical sense and the history of science

[Satyanad Kichenassamy]

Dear All,

There does not seem to be anything wrong with "encouraging an attitude of questioning and not merely accepting whatever the textbooks (or print/electronic/social media) say as infallible truth". 

On two specific issues raised in the message below, here are (very brief) indications :

(a) Newton's theory of gravitation is interesting and useful, but not correct for very basic reasons, as we now understand after the advent of the Special and General theories of Relativity.  As for the interplay between scientific theories and social conditions or ideologies, see what Aldo G. Gargani says about Newton's physics ("Le savoir sans fondements", Vrin, Paris, 2013).

(b) We have no statement of a general theorem that goes back to Pythagoras. The attribution is quite late (Vitruvius, Cicero,...), and may not refer to the full theorem. 
Cautious historians avoid referring to an alleged "Theorem of Pythagoras" or if they must, always use quotation marks, as we did. It is best to call the theorem popularly attributed to him "theorem of the square of the hypotenuse" (or, "of the diagonal (cord)" -- the Indian formulation), or Euclid I.47. There is a similar issue with what is called "Thales' theorem" in France. There are no named theorems in Euclid.

The earliest attribution extant seems to be Vitruvius' (several centuries after Pythagoras' putative time). Since the exact reference is almost never given, let alone the text, we include it. It only mentions a special case: a triangle with sides 3-4-5, and explains that the result is useful to make nice staircases):

Source : https://www.thelatinlibrary.com/vitruvius/vitruvius9.html#P.1

De Architectura, Book IX, Praefatio.

[6]  Item Pythagoras normam sine artificis fabricationibus inventam ostendit, et quam magno labore fabri normam facientes vix ad verum perducere possunt, id rationibus et methodis emendatum ex eius praeceptis explicatur. Namque si sumantur regulae tres, e quibus una sit pedes III, altera pedes IIII, tertia pedes V, eaeque regulae inter se compositae tangant alia aliam suis cacuminibus extremis schema habentes trigoni, deformabunt normam emendatam. Ad eas autem regularum singularum longitudines si singula quadrata paribus lateribus describantur, cum erit trium latus, areae habebit pedes VIIII, quod IIII, XVI quod V erit, XXV.

[7]  Ita quantum areae pedum numerum duo quadrata ex tribus pedibus longitudinis laterum et quattuor efficiunt, aeque tantum numerum reddidit unum ex quinque descriptum. Id Pythagoras cum invenisset, non dubitans a Musis se in ea inventione monitum, maximas gratias agens hostias dicitur his immolavisse. Ea autem ratio, quemadmodum in multis rebus et mensuris est utilis, etiam in aedificiis scalarum aedificationibus, uti temperatas habeant graduum librationis, est expedita.

(Vitruvius then explains why this is useful to make staircases).

See also X.6.4 for another application of the same triangle.

Best wishes,

     Satyanad Kichenassamy

On Wed, 13 Jul 2022 20:22:03 -0400
Periannan Chandrasekaran via INDOLOGY <indology at list.indology.info> wrote:

> Well, pretty soon,  someone is going to ask that with a straight face, if
> the Karanataka Govt.'s NEP proposal is implemented:
> 
> Question Pythagoras theorem and trim ‘Eurocentric’ concepts, observes the
> position paper of Karnataka’s NEP 2020
> <https://indianexpress.com/article/education/question-pythagoras-theorem-and-trim-eurocentric-concepts-observes-the-position-papers-of-karnatakas-nep-2020-8021235/>
> 
> "In the position paper of Knowledge of India, the guidelines encourage
> students to question the Pythagoras theorem and Newton’s law of gravity. It
> says, “ …encouraging an attitude of questioning and not merely accepting
> whatever the textbooks (or print/electronic/social media) say as infallible
> truth, with a clear foundation of how knowledge generation takes place and
> how fake news such as Pythagoras theorem, apple
> <https://indianexpress.com/about/apple/> falling on Newton’s head etc. are
> created and propagated.”
> 
> Regards
> Periannan Chandrasekaran
> 
> 
> On Wed, Jul 6, 2022 at 3:59 AM Dean Michael Anderson via INDOLOGY <
> indology at list.indology.info> wrote:
> 
> > How do we know the original was not written in Sanskrit long ago and only
> > later translated into Spanish?  ;-)
> >
> > Best,
> >
> > Dean
> >
> > On Wednesday, July 6, 2022 at 01:19:30 PM GMT+5:30, Richard Mahoney via
> > INDOLOGY <indology at list.indology.info> wrote:
> >
> >
> > Not something I expected to find in the paper this evening, esp.
> > after all we've been putting up with; thanks for the great news. :)
> >
> > ‘First modern novel – oldest language’: Sanskrit translation of Don
> > Quixote rescued from oblivion | Miguel de Cervantes | The Guardian
> >
> > https://www.theguardian.com/books/2022/jul/06/first-modern-novel-oldest-language-sanskrit-translation-of-don-quixote-rescued-from-oblivion
> >
> >
> > Best Richard
> >
> >
> >
> > --
> >
> > T +6433121699  M +64210640216
> > rmahoney at indica-et-buddhica.org
> > https://indica-et-buddhica.org/
> >
> > Indica et Buddhica
> > Littledene  Bay Road  Oxford  NZ
> > NZBN: 9429041761809
> >
> >
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-- 
**********************************************
Satyanad KICHENASSAMY
Professor of Mathematics
Laboratoire de Mathématiques de Reims  (CNRS, UMR9008)
Université de Reims Champagne-Ardenne
F-51687 Reims Cedex 2
France
Web: https://www.normalesup.org/~kichenassamy
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