Some of the terminology is confusing: e.g. saṅkhārā, nāmarūpa, bhava. The confusion is only added to in the process of translation. Some of the explanations are confusing as well, but my focus here is on the canonical presentation. I should say upfront that although the idea that the 12 nidānas occur over three lifetimes is traditional, that idea is not explicit in any sutta. So I don't think this was the idea the Buddha had in mind, and I don't think we can use it to explain the scheme, though I will make some nods in that direction.
I think it's fair to say that saṅkhārā is the most confusing term in Buddhism. It literally means 'making together, or completing'. (Note the relationship to the name Sanskrit (saṃskṛta) which is often said to mean 'perfected' or 'polished'.) The most literal English translation would be confection: con = sam; khāra is from √kṛ 'to make or do', which is not cognate but coincides very closely to the Latin facere  and therefore to words such as affect, confect, defect, effect, faculty (etc there are many more examples). Saṅkhāra has several distinct senses but in this context is variously rendered "volitional tendencies, volitional formations (or just formations), mental dispositions, determinations". The idea that saṅkhāra is about volition or will I take to be related to the texts that explain it as cetanā, e.g. at S iii.60 saṅkhāra is explained as six kinds of cetanā: rūpasañcetanā, sadda-, gandha-, rasa-, phoṭṭabba- and dhammasañcetanā. Bhikkhu Bodhi renders them as 'volition regarding forms, -sounds, -odours, -tastes, -tactile objects, and -mental phenomena'. I'm still none the wiser - what is "volition regarding forms"? As I have often said: cetanā is how the Buddha defines kamma, but in this context it doesn't help.
Things get more complex when the texts say that saṅkhārā conditions viññāṇa - (typically translated as consciousness). The relationship is sometimes described as causal so formations (or whatever) cause consciousness, but the Pāli terminology suggests a conditional, rather than a causal relationship.  So volition precedes consciousness and is a (the?) condition for it to exist, and similarly when there is no volition there is no consciousness. The question then is how do volitions precede consciousness, in order to be a condition for it to arise? Are volitions not a product of consciousness rather than the other way around?
The situation gets substantially worse with nāmarūpa. Although the tradition is fairly unanimous that it means "mind and body" scholars are by no means agreed what the word means in a Buddhist context (or why it means that). Like saṅkhāra it is an old Vedic term and Joanna Jurewicz (a Sanskritist specialising in the Vedas) has used the Vedic origins of the names for the nidānas as a cipher to show that the Buddha intended them as a parody of the Vedas. However my friend Dhīvan examined this claim from the Buddhist point of view in his M.Phil thesis, and didn't find a great deal of evidence to support Jurewicz's conjecture. Let us leave aside the confusion amongst scholars and focus on the idea that nāma-rūpa means 'body and mind'. There are two conclusions from this. Firstly that body comes into being some time after consciousness has been operating - so volition precedes consciousness and body, and consciousness precedes body - this is somewhat counter-intuitive (backwards even). It gets worse if we follow some traditions and take form to be objects of consciousness - now consciousness is a condition for existence more generally (a variation on the strong Anthropic Principle?). Secondly we now effectively have the sequence: mind conditions mind, which conditions mind. Which is meaningless.
Having given rise to the body in this unusual fashion the sequence settles down and becomes conceptually easier - the senses are the condition for contact (phassa the meeting of sense organ and sense object) which is the condition for sensations (vedanā), which are the conditions desire (taṇha - literally 'thirst') which is the condition for grasping (upādāna). Grasping gives rise to being or becoming (bhava - although as previously stated we already 'are' by this time). I've discussed in the past that upādāna could mean 'fuel' and I would argue that desire fuelling the fire of becoming, makes marginally more sense than grasping as a condition for becoming. But what is bhava, what is becoming or being? Bhava means 'being' in quite a similar range of senses to the English word. It's an action noun from √bhū which is cognate with 'be'.
Perhaps at this point the early Buddhists realised that this is a bit circular - we've already come into being (in body and mind - mind three times even!), and now the nidānas are telling us about how being is conditioned. This short circuits the nidāna chain. But it leaves two links unaccounted for: birth (jati), old age and death (jarāmaraṇa). Sometimes all the various kinds of suffering are added onto jarāmaraṇa - especially the wonderfully miserable compound sokaparidevadukkhadomanassupāyāsā. The move from becoming to birth is fine, except that we already have both mind and body, etc. The death, which does follow naturally from birth, but then where do we go? In Indian thinking we go to birth. The traditional circle suggests that death is a condition for ignorance. But again this makes no sense, and in any case we do not find the Pāli phrase anywhere in the canon: jarāmaraṇapaccaya avijjā. Old age and death are not in fact a condition for anything!
One major problem with the idea that the nidānas occur over three lifetimes is that if each link can only cease by the ceasing of the previous one, then we need to tackle ignorance (avijjā) in a past life in order to be liberated in this or a future life. This necessity for retro-active action is probably the greatest flaw in that in approach and seems to be an insurmountable problem.
Far from being a straight forward chain or circle the nidāna sequence is like a game of snakes and ladders (one proceeds up, down, sideways, and often retraces one's steps). I've realised that in fact it does not make sense to me on it's own terms. I've always found the received explanations quite pleasing and even useful - and I've been hearing about it for more than 15 years. But when I look closely it's not quite that the emperor has no clothes, it's more like he got dressed in the wrong order and used a mix of styles. It's disconcerting to get this far and realise that I can't make head nor tale of the Buddha's most important teaching on its own terms!
One of the ways scholars have understood the nidāna chain is to chop it up: it is "clearly" made of at least two, if not three shorter sequences mashed together. I was not initially very happy with this approach, but it's grown on me. I can more or less make sense of the chain from the six senses up to becoming. I think we can hive off birth and death as explanatory of what is meant by becoming - becoming is the cycle of birth and death (and therefore only makes sense in the context of rebirth). In which case, contra the three lifetimes model, the last two links go nowhere, they just cycle from birth to death. The most worrisome part are the links from ignorance to name and form. My inclination is just to say they don't make sense, but I think it's important to say that they don't make sense to me. However we hardly need them because the process we are interested in does not require them. I think ignorance as a problem comes in later after we have contact, but as a cause it probably conditions all the other links directly.
Eviatar Shulman points out that at some points there really are ontological implications to the nidānas (if for instance viññāṇa gives rise to nāmarūpa (and rūpa is either 'the body' or 'forms'); or taṇha/upādāna give rise to bhava 'being': this is ontology), but I notice that the terms which appear to have ontological implications are also the ones involving most confusion and ambiguity. I'd like to focus on this in a future post.
So I can make sense of the teaching, but I have to do what other Buddhists have done and chop it about, make stuff up, and bluff to a certain extent. Which is hardly intellectually satisfying. It's all rather embarrassing.
- Shulman, Eviatar. 'Early Meanings of Dependent-Origination,' Journal of Indian Philosophy, 36(2) 2008: 297-317. http://www.springerlink.com/content/7656238535363p05/
- A direct Sanskrit cognate to facere would be √dhā present dadhati, though the sense has drifted away from 'do' towards 'put'.
- Contrarily as Krishna Del Toso makes clear in his blog post on cause/condition in early Buddhism the distinction between the two types of relationship (hetu vs paccaya) only solidified in later texts. In favour of my statement the imasmiṃ idaṃ hoti formula, which almost always appears in conjunction with the 12 nidana paṭicca-samuppāda formula and appears to be a comment on how the links are connected, implies a conditional rather than causal relationship; as does the word paṭicca itself.