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‘Science is universal, but the concept of science varies in different cultures’ : Staal. 1993, 1994. #195.

‘Imagine we want to transform a rectangle into a square with the same area’ : Staal 1999 and 2001a.

‘There may be links between that large unit and scientific developments in Africa, but not with Meso-American Cultures’ : Paz 1995: 91.

‘The Vedic sciences are not objects that moderns are at liberty to make up’ : Torella (ed.), 2001 treats the Vedic sciences as part of the history of Indic sciences by various authors in Section II, Part I. Flood (ed.), 2003 has a chapter on four Indian sciences in which the initial periods deal with Vedic sciences: Linguistics by Staal, Mathematics by Takao Hayashi, Calendar, Astrology and Astronomy by Michio Yano and Medicine by Dominik Wujastyk.—This was anticipated by a more adventurous list: freely after Olivelle 166–7.

‘The science of ritual is the first in which the notion of sūtra comes to the fore’ : Renou 1963. Staal. 1992. ‘Sūtra,’ in: Vatsyayan, Kapila (ed.), 1992: 303–14; Bäumer, Bettina, ‘Sūtra in the Visual Arts’: 314–21 and Tripathi, Radhavallabh, ‘Sūtradhāra,’: 321–32.

‘Other civilizations have been interested in the science of ritual … but it is unlikely that they attained the high level … we find in the Śrauta Sūtras’ : Caland 1903, 1966; Caland and Henry 1906–07; Heesterman 1957; Kashikar 1968; Gonda 1977; Einoo 1988. In Sanskrit and English: Śrautakośa. Poona: Vaidika Samsodhana MaṇḌḍala, an encyclopaedia in many volumes from 1958. # 224.

‘In the domain of śrauta, the road that led to these discoveries was paved …’ Wezler 1972.

‘But brevity … expresses the most general solution to a particular problem’ : Kiparski, Paul. 1991, ‘Economy and the Construction of the Śivasūtras,’ in: Deshpande, Madhav M. and Saroja Bhate. 1991. Pāṇinian Studies. Professor S.D. Joshi Felicitation Volume. University of Michigan: Center for South and South-east Asian Studies; and Deshpande 1997b. #277.

‘The configuration of the thousand bricks in the offering altar’ : bricks and groups of bricks have their own names: Malamoud 2004 and throughout the latter parts of Staal, CV and Itti Ravi 1983, I.

‘But the relationships may be more complex’ : A. Seidenberg in Staal, CV and Itti Ravi 1983, II: 95–126, written in 1977, studied many of these complexities, also in other publications, and influenced B.L. van der Waerden, another well-known historian of early mathematics. Seidenberg could not take into account that the term iṣṭṭ akā is not Indo-Iranian or Indo-European because I, who had mentioned it to Seidenberg, did not know it: it comes from the BMAC as we have just seen (p. 267). More recently, Seidenberg’s thesis has been discussed in Koetsier, Teun and Luc Bergmans. 2005. Mathematics and the Divine: A Historical Study. New York: Elsevier. Pp. 12–3, where the relations between Greek, Babylonian and Vedic are distorted.

‘Newton and Descartes still regarded algebra as a barbaric art’ : because it came from the Arabs.—‘Leibniz had already seen that algebraic notations were the way of the future’: Oaks, Jeffrey. 2008. ‘Medieval Arabic Algebra as an Artificial Language’ in Staal, (ed.), 2008a, discusses its earlier history.

‘My second observation is about the infinite’ : see #200–03 which discusses recursive structures and the infinite.

‘The infinite was loved throughout Indic civilization, but abhorred by the ancient Greeks, from Pythagoras onward’ : the list of ordered opposites, which is attributed to Pythagoras and includes good and bad, starts with finite and infinite. Indic numerals as an abstract notation for infinitely many numbers are discussed by Charles Burnett in Granoff, Phyllis, Michio Yano and Frits Staal (eds.), 2006. The Emergence of Artificial Languages. Proceedings of the 2002 Workshop. Journal of Indian Philosophy 34/1–2: 22: ‘the first problem (of Arab, Greek and Latin writers about mathematics) was the difficulty in conceiving that a single symbol could be used to express an infinite range of numbers.’ #200 and Whitehead in #300.

‘A few paragraphs should be added about’ : Bharati 1965. ‘Vedic Mathematics is neither mathematics nor Vedic:’ Shukla, K.S. 1991. ‘Vedic Mathematics: The deceptive title of Swamiji’s book,’ in Issues in Vedic Mathematics (quoted by Wujastyk, D., 1998: 337 (#260), who aptly summarizes the discussion: ‘It is quite definitely the Śaṇkarācārya’s own discovery, and not Vedic.’ #104 and Jayaram websites (end of Bibliography). For reliable information on Vedic mathematics: Hayashi 2003: 360–5. Scattered remarks on the connections between Vedic and later Indic mathematics: Hayashi, Takao. 1995. The Bhakshālī Manuscript. An Ancient Indian Mathematical Treatise. Groningen: Egbert Forsten.

‘In Europe’ : Oaks, Jeffrey. 2007. ‘Medieval Arabic Algebra as An Artificial Language’, Journal of Indian Philosophy 35: 543–75.

‘The Prātiśākhyas are attached to each of the Vedic schools (śākhā)’ : Renou 1960a.—‘Scholars have long discussed whether the early Prātiśākhyas’: Thieme 1931 and especially 1935. Since the methodology of the Prātiśākhyas is similar to that of Pāṇini, the reader may refer to the latter, e.g., Staal. 1962. ‘A Method of Linguistic Description: The Order of Consonants According to Pāṇini’, Language 38: 1–10; Kiparski, Paul. 1991 in #265.—‘The Atharvaveda has two and the Sāmaveda possesses a number of compositions …: e.g., the Puṣpasūtra, ‘Flower Sūtra.’

‘Surya Kanta called the Rik-Prātiśākhyas ‘entirely free from all oversights’ : Surya Kanta. 1970. Ṛktantra. Delhi: Mejar Chand Lachman Das. ‘W.D. Whitney noted on a section of the Taittirīya Prātiśākhya, that he could not discover any case’: Whitney, W.D. 1871. ‘The Taittiriya Pratisakhya with its Commentary the Tribhāshyaratna’, Journal of the American Oriental Society 9:1–469.

‘They knew that its deeper source lies in the intention, that is the mind or heart’ : p. 67, pp. 291–2 and elsewhere: vāc manasā.

‘Modern linguistics uses distinctive features, but they would not exist’ : Jakobson in #183 and 294–5.

‘The discovery of the sound pattern of language was oral in two senses’ : the English word ‘oral’ is related to Latin os, which means ‘mouth.’

‘The most recent work on The World’s Writing Systems, a tome of almost a thousand pages’ : Daniels, Peter T. and William Bright (eds.), 1996. The World’s Writing Systems. New York and Oxford: Oxford University Press, pp. 384 ff.

‘Kepler, Tycho Brahe and were all interested in astrology though Newton’s real passion was alchemy’ : Staal. 1993, 1994. Concepts of Science in Europe and Asia. Leiden: International Institute for Asian Studies: ‘Newton’s Lesson.’—‘I shall be brief on the entire subject and rely’: mostly on Yano 2003. On Pingree: Conlon 2005.—‘The only footnote in this book should be dedicated to … 43 books and 240 articles:’ Pingree 1981, 1989, 1997 and 2001 are listed in the Bibliography.

‘Astronomy flourishes in sedentary civilizations which are able to concentrate on the skies …’ : Narasimha, Roddam. 2008. ‘Epistemology and Language in Indian Astronomy and Mathematics’ (in Staal 2008a) analyses three works of Nilakaṇṭha Somayaji (1444–1545 CE) who during his long life observed the sky daily (and performed numerous Vedic rituals as his name Somayājī indicates).

‘It explains that later Indic astronomy was very different’ : Minkowski 2002.—‘The demon myth was criticized by the astronomer Lalla’: Subbarayappa, B.V. and K.V. Sharma (eds.), 1985. Indian Astronomy: A Source-book (based primarily on Sanskrit texts). Bombay: Nehru Centre, pp. 41–5 and discussed in Staal. 1998. ‘Beyond Relativism’, in Ariel, Yoav, Shlomo Biderman and Ornan Rotem. Relativism and Beyond: Festschrift Ben-Ami Scharfstein. Brill: Leiden: 37–66: 60.