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Archive for March 15th, 2016

The Pandit (काशीविद्यासुधानिधिः)

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The Pandit (काशीविद्यासुधानिधिः)
A Monthly Journal, of the Benares College, devoted to Sanskrit Literature

This was a journal that ran from 1866 to 1920, and some issues are available online. “The Benares College” in its title is what was the first college in the city (established 1791), later renamed the Government Sanskrit College, Varanasi, and now the Sampurnanand Sanskrit University.

There are some interesting things in there. From a cursory look, it’s mainly editions of Sanskrit works (Kavya, Mimamsa, Sankhya, Nyaya, Vedanta, Vyakarana, etc.) and translations of some, along with the occasional harsh review of a recent work (printed anonymously of course), but also contains, among other things, (partial?) translations into Sanskrit of John Locke’s An Essay Concerning Human Understanding and Bishop Berkeley’s A Treatise Concerning the Principles of Human Knowledge. Also some hilarious (and quite valid) complaints about miscommunication between English Orientalists and traditional pandits, with their different education systems and different notions of what topics are simple and what are advanced.

The journal’s motto:

श्रीमद्विजयिनीदेवीपाठशालोदयोदितः । प्राच्यप्रतीच्यवाक्पूर्वापरपक्षद्वयान्वितः ॥
अङ्करश्मिः स्फुटयतु काशीविद्यासुधानिधिः । प्राचीनार्यजनप्रज्ञाविलासकुमुदोत्करान् ॥

The metadata is terrible: there’s only an index of sorts at the end of the whole volume; each issue of the journal carries no table of contents (or if it did, they have been ripped out when binding each (June to May) year’s issues into volumes). Authorship information is scarce. Some translations have been abandoned. (I arrived at this journal looking at Volume 9 where an English translation of Kedārabhaṭṭa’s Vṛtta-ratnākara is begun, carried into three chapters (published in alternate issues), left with a “to be continued” as usual, except there’s no mention of it in succeeding issues.) Still, a lot of interesting stuff in there.

Among the British contributors/editors of the journal were Ralph T. H. Griffith (who translated the Ramayana into English verse: there are advertisements for the translation in these volumes) and James R. Ballantyne (previously encountered as the author of Iṅglaṇḍīya-bhāṣā-vyākaraṇam a book on English grammar written in Sanskrit: he seems to have also been an ardent promoter of Christianity, but also an enthusiastic worker for more dialogue between the pandits and the Western scholars), each of whom served as the principal of the college. (Later principals of the college include Ganganath Jha and Gopinath Kaviraj.) Among the Indian contributors to the journal are Vitthala Shastri, who in 1852 appears to have written a Sanskrit commentary on Francis Bacon’s _Novum Organum,_ (I think it’s this, but see also the preface of this book for context) Bapudeva Sastri, and others: probably the contributors were all faculty of the college; consider the 1853 list of faculty here (Also note the relative salaries!)

Had previously encountered a mention of this magazine in this book (post).

[Edit, added 2020-12-05: Here’s an article by Ashok Aklujkar that lists the works that were published in The Pandit.]

The issues I could find—and I searched quite thoroughly I think—are below. Preferably, someone needs to download from Google Books and re-upload to the Internet Archive, as books on Google Books have an occasional tendency to disappear (or get locked US-only).

[Edit, added 2020-12-09: Some scans by eGangotri, independent of the scanning by Google Books below, have recently been uploaded to the Internet Archive: see here.]

https://books.google.com/books?id=Z71EAAAAcAAJ 1866 Vol 1 (1 – 12)
https://books.google.com/books?id=ESgJAAAAQAAJ 1866 vol 1 (1 – 12)
https://books.google.com/books?id=Sr8IAAAAQAAJ 1866 Vol 1 (1 – 12)
https://books.google.com/books?id=JAspAAAAYAAJ 1866 vol 1-3 (1 – 36)

https://books.google.com/books?id=Y78IAAAAQAAJ 1867 Vol 2 (13 – 24)
https://books.google.com/books?id=JigJAAAAQAAJ 1867 Vol 2 (13 – 24)
https://books.google.com/books?id=cL1EAAAAcAAJ 1867 Vol 2 (13 – 24)

https://books.google.com/books?id=g78IAAAAQAAJ 1868 Vol 3 (25 – 36)
https://books.google.com/books?id=eL1EAAAAcAAJ 1868 Vol 3 (25 – 36)
https://books.google.com/books?id=OSgJAAAAQAAJ 1868 Vol 3 (25 – 36)

https://books.google.com/books?id=m78IAAAAQAAJ 1869 vol 4 (37 – 48)
https://books.google.com/books?id=WygJAAAAQAAJ 1869 Vol 4 (37 – 48)
https://books.google.com/books?id=g71EAAAAcAAJ 1869 vol 4 (37 – 48)

https://books.google.com/books?id=vr8IAAAAQAAJ 1870 vol 5 (49 – 60)
https://books.google.com/books?id=eCgJAAAAQAAJ 1870 vol 5 (49 – 60)
https://books.google.com/books?id=24dSAAAAcAAJ 1870 vol 5 (49 – 60)

https://books.google.com/books?id=0b8IAAAAQAAJ 1871 Vol 6 (61 – 72)
https://books.google.com/books?id=nigJAAAAQAAJ 1871 vol 6 (61 – 72)
https://books.google.com/books?id=5YdSAAAAcAAJ 1871 vol 6 (61 – 72)

https://books.google.com/books?id=878IAAAAQAAJ 1872 Vol 7 (73 – 84)
https://books.google.com/books?id=uCgJAAAAQAAJ 1872 Vol 7 (73 – 84)
https://books.google.com/books?id=TrZUAAAAcAAJ 1872 vol 7 (73 – 84)

https://books.google.com/books?id=6ygJAAAAQAAJ 1873 vol 8 (85 – 96)

https://books.google.com/books?id=ASkJAAAAQAAJ 1874 vol 9 (97 – 108)
https://books.google.com/books?id=KMAIAAAAQAAJ 1874 vol 9 (97 – 108)

https://books.google.com/books?id=ICkJAAAAQAAJ 1875 Vol 10 (109 – 120)
https://books.google.com/books?id=CcAIAAAAQAAJ 1875 vol 10 (109 – 120)

[New series]
https://books.google.com/books?id=jHxFAQAAIAAJ 1876 vol 1

https://books.google.com/books?id=A_lSAAAAYAAJ 1877 vol 2
https://books.google.com/books?id=M31FAQAAIAAJ 1877 vol 2
https://books.google.com/books?id=ZQspAAAAYAAJ 1877 vol 2

https://books.google.com/books?id=rgspAAAAYAAJ 1879 vol 3
https://books.google.com/books?id=w31FAQAAIAAJ 1879 vol 3

https://books.google.com/books?id=EA0pAAAAYAAJ 1882 Vol 4
https://books.google.com/books?id=Pn5FAQAAIAAJ 1882 vol 4
https://books.google.com/books?id=gzoJAAAAQAAJ 1882 vol 4

https://books.google.com/books?id=XA0pAAAAYAAJ 1883 Vol 5
https://books.google.com/books?id=jikJAAAAQAAJ 1883 Vol 5
https://books.google.com/books?id=3X5FAQAAIAAJ 1883 vol 5

https://books.google.com/books?id=zSkJAAAAQAAJ 1884 vol 6

https://books.google.com/books?id=vQ0pAAAAYAAJ 1885 vol 7
https://books.google.com/books?id=Oi8JAAAAQAAJ 1885 vol 7

https://books.google.com/books?id=FQ4pAAAAYAAJ 1886 Vol 8

https://books.google.com/books?id=JwopAAAAYAAJ 1887 vol 9

https://books.google.com/books?id=fQ4pAAAAYAAJ 1888 Vol 10

https://books.google.com/books?id=gAopAAAAYAAJ 1890 vol 12

https://books.google.com/books?id=2wopAAAAYAAJ 1891 vol 13

https://books.google.com/books?id=LwspAAAAYAAJ 1892 vol 14

https://books.google.com/books?id=pAspAAAAYAAJ 1895 Vol 17
https://books.google.com/books?id=wdc9AQAAMAAJ 1895 vol 17

https://books.google.com/books?id=BAwpAAAAYAAJ 1896 Vol 18

https://books.google.com/books?id=UwwpAAAAYAAJ 1897 vol 19

https://books.google.com/books?id=1wwpAAAAYAAJ 1898 Vol 20

https://books.google.com/books?id=1g0pAAAAYAAJ 1899 Vol 21
https://books.google.com/books?id=iBNAAQAAMAAJ 1899 Vol 21

https://books.google.com/books?id=Xg4pAAAAYAAJ 1900 Vol 22

https://books.google.com/books?id=MhApAAAAYAAJ 1901 Vol 23

https://books.google.com/books?id=4w4pAAAAYAAJ 1902 Vol 24

https://books.google.com/books?id=Tw8pAAAAYAAJ 1904 Vol 25

https://books.google.com/books?id=vw8pAAAAYAAJ 1905 Vol 27

https://books.google.com/books?id=iBApAAAAYAAJ 1907 vol 29

https://books.google.com/books?id=bQ0pAAAAYAAJ 1908 Vol 30

https://books.google.com/books?id=Bv1SAAAAYAAJ 1908 Vol 30

https://books.google.com/books?id=LNA9AQAAMAAJ 1911 Vol 33 Snippet View
https://books.google.com/books?id=ctA9AQAAMAAJ 1912 Vol 34 Snippet View
https://books.google.com/books?id=3dA9AQAAMAAJ 1913 Vol 35 Snippet View
https://books.google.com/books?id=a9E9AQAAMAAJ 1916 Vol 38 Snippet View
https://books.google.com/books?id=N9E9AQAAMAAJ 1916 Vol 37 Snippet View

Also on HathiTrust:

https://catalog.hathitrust.org/Record/008634393
c.1 v.3 1868
v. 2 (1878)
c.1 n.s v.17 1895
c.1 n.s v.21 1899
v. 30 (1908)

https://catalog.hathitrust.org/Record/009658676
ser.2 v.1 (1876-77)
ser.2 v.2 (1877-78)
ser.2 v.3 (1878-79)
ser.2 v.4 (1882)
ser.2 v.5 (1883)

https://catalog.hathitrust.org/Record/100339588
v.1-3 (1866-1869)
n.s.:v.2 (1877/1878)
n.s.:v.3 (1878/1879)
n.s.:v.4 (1882)
n.s.:v.5 (1883)
n.s.:v.7 (1885)
n.s.:v.8 (1886)
n.s.:v.9 (1887)
n.s.:v.10 (1888)
n.s.:v.12 (1890)
n.s.:v.13 (1891)
n.s.:v.14 (1892)
n.s.:v.17 (1895)
n.s.:v.18 (1896)
n.s.:v.19 (1897)
n.s.:v.20 (1898)
n.s.:v.21 (1899)
n.s.:v.22 (1900)
n.s.:v.23 (1901)
n.s.:v.24 (1902)
n.s.:v.25 (1903)
n.s.:v.27 (1905)
n.s.:v.29 (1907)
n.s.:v.30 (1908)

Written by S

Tue, 2016-03-15 at 14:18:00

Posted in sanskrit

The same in every country

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(TODO: Learn and elaborate more on their respective histories and goals.)

The formula
\frac{\pi}{4} = 1 - \frac13 + \frac15 - \frac17 + \frac19 - \frac1{11} + \dots
(reminded via this post), a special case at x=1 of
\arctan x = x - \frac{x}3 + \frac{x}5 - \frac{x}7 + \dots,

was found by Leibniz in 1673, while he was trying to find the area (“quadrature”) of a circle, and he had as prior work the ideas of Pascal on infinitesimal triangles, and that of Mercator on the area of the hyperbola y(1+x) = 1 with its infinite series for \log(1+x). This was Leibniz’s first big mathematical work, before his more general ideas on calculus.

Leibniz did not know that this series had already been discovered earlier in 1671 by the short-lived mathematician James Gregory in Scotland. Gregory too had encountered Mercator’s infinite series \log(1+x) = x - x^2/2 + x^3/3 + \dots, and was working on different goals: he was trying to invert logarithmic and trigonometric functions.

Neither of them knew that the series had already been found two centuries earlier by Mādhava (1340–1425) in India (as known through the quotations of Nīlakaṇṭha c.1500), working in a completely different mathematical culture whose goals and practices were very different. The logarithm function doesn’t seem to have been known, let alone an infinite series for it, though a calculus of finite differences for interpolation for trigonometric functions seems to have been ahead of Europe by centuries (starting all the way back with Āryabhaṭa in c. 500 and more clearly stated by Bhāskara II in 1150). Using a different approach (based on the arc of a circle) and geometric series and sums-of-powers, Mādhava (or the mathematicians of the Kerala tradition) arrived at the same formula.

[The above is based on The Discovery of the Series Formula for π by Leibniz, Gregory and Nilakantha by Ranjay Roy (1991).]

This startling universality of mathematics across different cultures is what David Mumford remarks on, in Why I am a Platonist:

As Littlewood said to Hardy, the Greek mathematicians spoke a language modern mathematicians can understand, they were not clever schoolboys but were “fellows of a different college”. They were working and thinking the same way as Hardy and Littlewood. There is nothing whatsoever that needs to be adjusted to compensate for their living in a different time and place, in a different culture, with a different language and education from us. We are all understanding the same abstract mathematical set of ideas and seeing the same relationships.

The same thought was also expressed by Mean Girls:

Written by S

Tue, 2016-03-15 at 13:53:32

Posted in history, mathematics