I've been asked several times recently about the meaning and function of this word tadyathā - especially in the Heart Sūtra. I thought some brief comments on my Visiblemantra blog would suffice, but I found that the explanation got a bit too involved and so I moved it here. My main source is Edward Conze's Sanskrit version of the Heart Sūtra in his 1975 book Buddhist Wisdom Books, though I have consulted other Sanskrit versions especially those edited by Vaidya. There is considerable variation in the Sanskrit manuscript versions of the text. I'll use the abbreviation PP for prajñāpāramitā.
The word tadyathā is often found at the beginning of mantras and is often included in the actual chanting. There is clearly some confusion amongst Buddhists on the role of the word tadyathā as evidenced in online debates. Tadyathā is an adverbial compound consisting of tad 'that' and yathā 'as like, according to, in that way'. So tadyathā means 'like this' or 'this way'. When the mantra in the Heart Sūtra is being introduced the text says:
prajñāpāramitāyām ukto mantraḥ tadyathā: gate gate pāragate pārasaṃgate bodhi svāhā.
In the 'wisdom gone beyond' the mantra is spoken this way: gate gate pāragate pārasaṃgate bodhi svāhā. 
If we follow Conze's punctuation in Buddhist Wisdom Books (p.101) the passage is pretty confusing, because the breaks seem to come at the wrong place - and interestingly his English is in fact punctuated quite differently from his Sanskrit (cf for instance the colon after "tasmaj jñātavyam" but not after "Therefore one should know"). In Vaidya's Sanskrit editions the punctuation is minimal. A daṇḍa (i.e. the punctuation mark | )before tasmaj jñātavyam which begins the series of epithets of the mantra, and another between mantraḥ and tadyathā in both. I'm not convinced by this, and as I will show below it is more natural to take prajñāpāramitāyām ukto mantraḥ tadyathā as a single (well formed) sentence. So let us examine the grammar of this phrase:
The verb is ukta from √vac 'to speak'.  Grammatically it is a passive past-participle so means 'spoken' or 'said', and functions something like an adjective describing something. It is in the nominative singular form, uktaḥ, and sandhi dictates that the -aḥ ending changes to -o when followed by ma: hence we spell it ukto. Mantraḥ is also in the nominative case so we can deduce that ukto goes with mantraḥ, and the phrase ukto mantraḥ means 'the mantra is spoken'. Note that word order is not important in Sanskrit so it could equally be mantra uktaḥ. (in this case -aḥ followed by u > a)
Now, despite the fact that both Conze and Vaidya take tadyathā as a standalone word (separating it out with punctuation), it seems to me that tadyathā can quite naturally be seen to be an adverb modifying the verb ukto: 'spoken this way'. Separating tadyathā out seems to make for both poor Sanskrit and poor English: '...ukto mantraḥ. Tadyathā' = '...the mantra is spoken. Like this.' Sometimes a preconceived idea can blind us to the obvious, and perhaps this is what has happened in this case. So the phrase ukto mantraḥ tadyathā means 'the mantra is spoken this way'.
Prajñāpāramitāyām is actually a locative singular so I don't follow Conze's translation of it as an instrumental 'by the PP'. In Perfect Wisdom (1973: p.140) Conze aims for a more literal reading and has "In the Prajñāpāramitā has this spell been uttered".  Later in Perfect Wisdom (p.143), however, he repeats the version from Buddhist Wisdom Books 'by the PP'. The locative is used to indicate where the action of a verb takes place - in space or time. I think there are three ways to interpret this:
- In (the state of) perfect wisdom
- In the system of practice known as perfect wisdom
- In this perfection of wisdom text
Option one suggests that the mantra is spoken like this in the state of perfect wisdom, or by someone in that state. It may also refer to the point of view of perfect wisdom. Option two acknowledges that perfection of wisdom is also the name of a system of practice - we might say something like: 'in the perfection of wisdom school...' Option three allows for the possibility that the mantra is the one found in this text. Conze insists the mantra is not found in the any of the Large PP texts (Buddhist Wisdom Books: p.106). However compare Jan Nattier's note (The Heart Sūtra: p.177) of McRae and Fukui's discovery that "some or all of the mantra found in the Heart Sūtra also occurs in at least three other texts contained in the Chinese Buddhist canon".  I think Conze is opting for option one by translating Prajñāpāramitāyām as "by the perfection of wisdom" - ie he is taking Prajñāpāramitā to be the personification of perfect wisdom.
Whichever translation we choose it seems to me that tadyathā was not intended to be included in the mantra, though of course in many traditions it is included. This essay was sparked by someone asking about the mantra of the Medicine Buddha, as given to him by the Dalai Lama, which also has tadyathā included in the recitation. In the locus classicus for that mantra: Sūtra of the Medicine Buddha [pdf file] (Taisho XIV, 450) tadyathā is preceded namo followed by a number of epithets for the Buddha all in the dative form, then followed by the mantra: "homage to [the Medicine Buddha] like this: oṃ bhaiṣajye bhaiṣajye mahābhaiṣajya-samudgate svāhā". The grammar is quite different and suggests that this mantra is being presented as a way of paying homage to the Medicine Buddha. Here again however tadyathā forms a natural part of the introduction, but not the mantra.
Compare Frits Staal's comments on the incorporation of 'stage directions' during the recitation of Vedic mantras in Discovering the Vedas (p.115):
Stage directions should not slip into the recitation. Once I recorded a mantra recited by a priest when he gave a stick (daṇḍa) to a boy. The recitation included the final words of a rule: iti daṇḍaṃ dadhyāt, 'thus he should give the stick'.
The inclusion of tadyathā is a similar case which probably occurred amongst people who recited texts in Sanskrit without knowing the language. Interestingly from what I can tell the practice occurs in both Tibetan and in the Far Eastern lineages. The inclusion of the tadyathā, though technically an error, is actively being passed on by living, authoritative teachers such as the Dalai Lama. Sometimes convention trumps philology. Sanskrit is a difficult language to learn and we Buddhists seldom know it these days, so convention becomes our only guide. I always prefer good philology if it is available, but sometimes it is too late to correct a centuries old custom.
- I leave the manta untranslated. I think there are some problems with Conze's translation of gate as 'gone'. He gives it a (grammatically) perfect sense which is not quite right for a participle. I deal with this a bit more on the visiblemantra.org Heart Sutra Mantra page.
- Via some tortuous internal sandhi: vac + -ta > vakta [with samprasāraṇa va > u] > ukta.
- Several prominent scholars of the early to mid 20th century including Conze and Snellgrove insisted on translating mantra as 'spell'. I think this is unhelpful and Snellgrove's justification of it in Indo-Tibetan Buddhism seems disingenuous. It is one of those words with no exact equivalent in English, and though there is some cross-over under some circumstances, 'spell' gives entirely the wrong impression in most cases.
- The references are given in footnote no.52: McRae "Ch'an Commentaries" identifies T no.901, 18.785a-897b, esp p.807b20-21. See also T 18.8071b19-c9; and T 18.804c-807b.
Sanskrit texts for both versions of the Heart Sūtra can be found online at the Digital Sanskrit Buddhist Canon Website. These are copied from the texts edited by Vaidya, P.L.
- Conze, Edward. 1975. Buddhist Wisdom Books : Containing the Diamon Sūtra and the Heart Sūtra. 2nd Ed. London : George Allen & Unwin. First Ed. 1957.
- Conze, Edward. 1973. Perfect Wisdom : The Short Prajñāpāramitā Texts. Buddhist Publishing Group.
- McRae, John R. 1988. "Ch'an Commentaries on the Heart Sûtra: Preliminary Inferences on the Permutation of Chinese Buddhism". Journal of the International Association of Buddhist Studies 11, no. 2: 87-115.
- Nattier, Jan. 1992. The Heart Sūtra : a Chinese apocryphal text? Journal of the International Association of Buddhist Studies. Vol. 15 (2), p.153-223.
- Staal, Frits. 2008. Discovering the Vedas : Origins, Mantras, Rituals, Insights. Penguin.
- Vaidya, P.L. 1961. Buddhist Sanskrit Texts No. 17 Mahāyāna-sūtra-saṁgrahaḥ (part 1). Darbhanga, The Mithila Institute of Post-Graduate Studies and Research in Sanskrit Learning. [contains both versions of the Heart Sūtra]
Note 23.2.2013 I'll leave this essay to stand, but now I would translate this passage as:
prajñāpāramitāyām ukto mantraḥ tadyathā:
The mantra uttered with respect to Perfect Wisdom is like this:
Taking the locative to indicate the object towards which the mantra is spoken, and taking the sentence to have an implied copula 'is'. It's slightly odd in the sense that a mantra is not usually 'said' (ukta), we expect it to be 'muttered' (japita) or 'recited' (paṭhita) etc.