The following is a basic run-through of the fundaments of an Indo-European act of piety. Ostensibly, it is explication of how Vedic ritual processes work – but as Witzel (excellently) points out, it is also very much how our current-day Hindu ritual understandings work as well. I say that it presents an “Indo-European act of piety” formulation not only because of these things – but because in reading it, if you know a few things about the religious customs of the more western (i.e. European) Indo-Europeans you shall immediately start to see the similarities: that, as we have always and ever maintained, even though some of the words might be different, or surface-level manifestations unique … the essence of the thing is fundamentally the same (Samrajya, we might say!) at its core! I have also, as is my custom added a few points of annotation to Witzel’s own remarks to clarify several things or to explicate in a slightly different manner something of particular importance. 

“Another important aspect of the form of ritual is that it originally (in the RigVeda) had the form of guest worship. This feature has been well known ever since Paul Thieme’s (1971) study. Such relationships of a host with a guest are governed by a set of  rules based on mutual acceptance and trust; ‘trust, belief’ is called sraddha in Sanskrit. It is not surprising, then, that this term is central in the relation between humans and between humans and either gods or ancestors. Vedic rituals work only if this relationship of  trust exists (KathU 1.2; RV 10.151). In the post-RigVedic period the meaning is further narrowed to ‘trust in the efficacy of the ritual’ (Kohler 1972). The main ritual of ancestor worship, sraddha, is but a derivative of the term: ‘that which is related to trust,’ for without the trust of the ancestors in their descendants’ faithfulness in carrying out these rites they would go hungry in the next world, just as the gods would without Vedic sacrifice. Among humans, the term for guest friendship, aryaman, is derived, rather artificially, from arya, ‘hospitable’, (and ari, ‘stranger’), the etymology of the self-designation of Iranian and Vedic Hindus, the Aryas. The concept of hospitality, thus, was crucial for the self-image of Vedic Hindus, and they wanted to treat their gods in the same fashion. [ C.A.R.: I’d disagree somewhat with the (folk) etymology advanced here – insofar as it’s right in a more general sense. ‘Arya’ effectively means somebody who knows and performs the proper customs, the proper ways, and is therefore able to participate in the life of his or her community as part of same. It is not hard to see how the specific adherency to Sacred Hospitality, something quite integral to the ancient Indo-European way of life [c.f both the Greek notions of Xenia – as well as Odin’s appearance in the Grimnismal, for example; showing, along with Shiva’s appearance as the Vratya at the Gates, that this element is so important that the Sky Father Himself turns up to test its commitment amidst His Peoples], would be quite intrinsic to this more generalized concept of righteous conduct and propriety that is connoted by ‘Arya’, ‘Aryan’. [-C.A.R.] ]

In short, the Vedic gods are ceremoniously invited (avahana) to the offering ground (vedi), seated on the grass strewn around the fires (barhis), feasted with a meal (havis) of food and drink, which is accompanied by poems, some of which are sung (stotra), lauding them and their great deeds (mantra, sastra). The gods are then sent off – until next time. The parting gift, however, is given to the priest (as dakshina), not to the departing guests. [ C.A.R.: actually, this is not quite accurate – the notion is that the Priest here is representing the God(s), and so therefore, yes, yes the Dakshina [‘righteous conduct’ – from same root as European ‘Dexter’] is indeed being given to the departing Guests … and it is also intriguing to consider the ‘Guest’/’Geist’ coterminity in the relevant Germanic linguistics … which we have done elsewhere [-C.A.R.] ]

This might sound like a description of a modern puja; the basic structure, in fact, is the same, and it is even sometimes recognized as a structure of guest friendship by modern Hindus (Ostor 1982). Though a puja can comprise 16 or 36, in Bhaktapur even 60 (639), sets of actions, its most basic structure still is: first, avahana (‘driving here,’ or even akarsana, ‘drawing close,’ in Tantra); second, worship with food (stotra/stuti), and the giving of a gift; and third, visarjana, the ‘sending away’ ceremony. The return gift of the gods, the ucchista/prasada, is applied by the performer of the puja, be it a private person or a priest, in the form of a tilaka on the forehead of the worshipper. In accordance with one possible etymology of the word puja (Mayrhofer 1953-80), the unstudied history of this act seems to go back to a smearing of the blood of the victim (Witzel n.d.a.), [C.A.R.: While speculative – Witzel would appear to be on some rather solid ground here; one of my colleagues has alerted me to a Sri Ramakrishna commentary that appears to substantiate the supposition being made – at least, in terms of a relatively recent Tilaka practice which is thusly congealed in the blood of the sacrificial offering. [-C.A.R.] ] Interestingly, the very word is not, as has often been supposed, a post-Vedic loan or innovation; it is attested in the RigVeda (Witzel 1980b), though in an unclear context. 

The guest or the god is supposed to return the favour by a counter-invitation (to heaven) or by a more substantial return gift (rain, for example, or children). Even then, the cycle of giving and taking is kept in progress, as the exact amount of gift and counter-gift is difficult to measure and evaluate. Humans give, the gods give back, to a degree, and the humans have to give again. The Stone Age mentality (Sahlins 1972) of do ut des (‘I give, so that you might give’) applies to the Veda (dehi me, dadami te, ‘give me, I give you’; TS 1.8. 4.1, VS 3.50) and modern puja as well.”

From ‘Macrocosm, Mesocosm, and Microcosm: The persistent nature of ‘Hindu’ beliefs and symbolic forms’ by Michael Witzel