[INDOLOGY] Sciences and Tantra

Tue Apr 9 13:43:30 UTC 2019

Dear Matthew,

Alsdorf’s article is indeed on combinatorics in the metrical literature,
not in mathematics…
as for combinatorics in music there is notably in French

Patte, François. 2012. “Rythmes et Algorithmes.” In *Astronomy and
Mathematics in Ancient India - Astronomie et Mathématiques de l’Inde
Ancienne Actes de La Journée d’études Organisée Le 24 Avril 2009 à
l’Université Libre de Bruxelles*, edited by Jean-Michel Delire, 159–174.
Peeters.

and recently
Petrocchi Alessandra. 2018. “Music Theory, Mathematics, and Patterns of
Innovation in the Saṅgītaratnākara.” *Asiatische Studien - Études
Asiatiques* 72 (2): 395. https://doi.org/10.1515/asia-2016-0003.

best

Agathe

From: Matthew Kapstein <mkapstei at uchicago.edu> <mkapstei at uchicago.edu>
Reply: Matthew Kapstein <mkapstei at uchicago.edu> <mkapstei at uchicago.edu>
Date: 9 April 2019 at 15:25:13
To: Agathe Keller <kelleragathe600 at gmail.com>
<kelleragathe600 at gmail.com>, Paolo
Eugenio Rosati <paoloe.rosati at gmail.com> <paoloe.rosati at gmail.com>, Indology
<indology at list.indology.info> <indology at list.indology.info>
Subject:  Re: [INDOLOGY] Sciences and Tantra

Thank you Agathe,

I wasn't intending to refer to Indian mathematics broadly, but just to the
application outside of mathematics per se. Besides poetic metrics and
"tantric geometry", I imagine that the musicological literature offers some
other examples, but i do not know them off hand.

best,

Matthew

Matthew Kapstein
Directeur d'études,
Ecole Pratique des Hautes Etudes

Numata Visiting Professor of Buddhist Studies,
The University of Chicago
------------------------------
*From:* Agathe Keller <kelleragathe600 at gmail.com>
*Sent:* Tuesday, April 9, 2019 8:19:23 AM
*To:* Paolo Eugenio Rosati; Matthew Kapstein; Indology
*Subject:* Re: [INDOLOGY] Sciences and Tantra

Dear Matthew,

On the topic of combinatorics (including Pascal triangle), Piṅgala and his
commentators  there is a classical article by Ludwig Alsdorf

 Die Pratyayas. Ein Beitrag zur indischen Mathematik". Zeitschrift fur
Indologie und Iranistik, 9 (1933), pp. 97-157; reprinted in: Albrecht
Wezler (ed.), Ludwig Alsdorf: Kleine Schriften, Wiesbaden, 1974, pp.
600-660.

This paper was translated into English by  Sarma, S. R. 1991. “The
Pratyayas: Indian Contributions to Combinatorics.” Indian Journal of
History of Science 26: 17–61.

although much still needs to be investigated, there are quite a number of
publications on this topic  actually…

best

Agathe

From: Matthew Kapstein via INDOLOGY <indology at list.indology.info>
<indology at list.indology.info>
Reply: Matthew Kapstein <mkapstei at uchicago.edu> <mkapstei at uchicago.edu>
Date: 9 April 2019 at 14:49:06
To: Paolo Eugenio Rosati <paoloe.rosati at gmail.com> <paoloe.rosati at gmail.com>,
Indology <indology at list.indology.info> <indology at list.indology.info>
Subject:  Re: [INDOLOGY] Sciences and Tantra

Dear Paolo,

Although it is not quite on tantra, there is a highly interesting article
in modern Sanskrit on the relationship between Sanskrit analysis of poetic
metre and Pascal's triangle. I do not have the full reference available in
my present location, but it may be found in the introduction to the late
Michael Hahn's edition of the ChandoratnAkara, which may be available on
his academia page, if that is still accessible.

In Buddhist tantra, quite a lot has been written on the mathematics of the
KAlacakratantra. The late Edward Henning's webpage kalacakra.org has some
useful material on this, as does Henning's book, KAlacakra and the Tibetan
Calendar.

There is also quite a lot on this in German, by Dieter Schuh, but
exclusively concerned with the Tibetan legacy of the Indian sources and not
with the Indian materials themselves.

best,

Matthew

Matthew Kapstein
Directeur d'études,
Ecole Pratique des Hautes Etudes

Numata Visiting Professor of Buddhist Studies,
The University of Chicago
------------------------------
*From:* INDOLOGY <indology-bounces at list.indology.info> on behalf of Paolo
Eugenio Rosati via INDOLOGY <indology at list.indology.info>
*Sent:* Tuesday, April 9, 2019 4:47:07 AM
*To:* Indology
*Subject:* [INDOLOGY] Sciences and Tantra

Dear indologists,

Can anyone points me out any study on Tantra in connection to sciences,
mathematics and more specifically geometry?

With the best wishes,
Paolo

--
*Paolo E. Rosati*
*PhD in Asian and African Studies*
(South Asia Section)
*Italian Institute of Oriental Studies*
'Sapienza' University of Rome

*https://uniroma1.academia.edu/PaoloRosati/
<https://uniroma1.academia.edu/PaoloRosati/>*
paoloe.rosati at uniroma1.it
paoloe.rosati at gmail.com
Skype: paoloe.rosati
Mobile: (+39) 338 73 83 472

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Agathe Keller

tel : +33 1 57 27 68 87

Université Paris 7 Laboratoire SPHERE UMR 7219
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Agathe Keller

tel : +33 1 57 27 68 87

Université Paris 7 Laboratoire SPHERE UMR 7219
Bâtiment Condorcet
Parcels: 3è étage bureau 387A
Office: 6th floor 688 A
 10 rue A.Domont et L.Duquet
75013 PARIS

Postal Address :
Université Paris 7 - CNRS
Laboratoire SPHERE UMR 7219
Equipe Sphere
Case 7093
5 rue Thomas Mann
75205 PARIS CEDEX 13
France

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