[INDOLOGY] Sciences and Tantra

Matthew Kapstein mkapstei at uchicago.edu
Tue Apr 9 13:25:11 UTC 2019

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.



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…



From: Matthew Kapstein via INDOLOGY <indology at list.indology.info><mailto:indology at list.indology.info>
Reply: Matthew Kapstein <mkapstei at uchicago.edu><mailto:mkapstei at uchicago.edu>
Date: 9 April 2019 at 14:49:06
To: Paolo Eugenio Rosati <paoloe.rosati at gmail.com><mailto:paoloe.rosati at gmail.com>, Indology <indology at list.indology.info><mailto: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<http://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.



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<mailto:indology-bounces at list.indology.info>> on behalf of Paolo Eugenio Rosati via INDOLOGY <indology at list.indology.info<mailto: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 E. Rosati
PhD in Asian and African Studies
(South Asia Section)
Italian Institute of Oriental Studies
'Sapienza' University of Rome

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