Showing posts with label time. Show all posts
Showing posts with label time. Show all posts

03 March 2017

Time for a Change

Zeno was an ancient Greek famous for inventing paradoxes:
The third [paradox] is … that the flying arrow is at rest, which result follows from the assumption that time is composed of moments … . he says that if everything when it occupies an equal space is at rest, and if that which is in locomotion is always in a now, the flying arrow is therefore motionless. (Aristotle Physics, 239b.30)
In other words, if we think of an arrow flying through the air, the arrow is the same length throughout the flight. It takes up the same amount of space. At any given moment in time, the arrow is at a given location in space, taking up a given space. If we could freeze time at any random moment the arrow would appear to be stationary; it would not be moving, it would only be in one place. So if at any moment the arrow is stationary, it is stationary at every moment. Which is paradoxical. Nāgārjuna wrestles with motion and time in a similar way because moments are also built into the Buddhist understanding of time.

In a YouTube video interview, George Lakoff explains to an interviewer, in the space of approximately 3¾ minutes, that the paradox is due to the metaphorical nature of our thought and the framing of the problem. In this essay I'm going to recapitulate his argument in my own words.


So the first thing to notice is the way I write about a space of time the previous sentence. This is a metaphor. It turns out that metaphor TIME IS SPACE occurs in almost every human language. But there are two main ways of conceptualising time as space. Firstly, time is a stationary path along which we move:
  • We are approaching [the time for] lift-off
  • We're past the time for apologies
  • I'm looking forward to a future with jet packs
Or, time is a like river flowing past us:
  • Crunch time is rapidly approaching
  • The past is receding in my memory
  • Time passed without me noticing
Time is typically a one dimensional space, so it can be long or short, for example, but seldom wide, narrow, or tall. Occasionally, we may talk about a window of time, though what this comes down to is a slot marked by a beginning and end time. Here, the metaphor is not TIME IS A WINDOW but, instead, MOMENTS ARE WINDOWS. TIME FLIES, but this is a variant on the flowing time metaphor where we are fixed and time goes past us. Time may also be a container, so that events happen "in time", in the space of an hour. Again, the metaphor is, MOMENTS ARE CONTAINERS. A window can be a container, because it is framed. In this essay, I'm going to focus on the linear spatial metaphors for time.

Metaphors are linguistic structures. In the first lot of three sentences we have a human agent which acts on time (time is the patient of the verb). In the second group of three, time itself is the agent of the action. In one, time is passively acted on by us and. in the other. time is actively acting on us. And the actions in both cases are motions (go, pass, approach, recede). These are linguistic structures that help us to conceptualise and talk about of the flow of events that make up experience. However, these linguistic structures do not correspond to structures in reality. Part of the reason they do not is that the two metaphors contradict each other. Time cannot be both stationary and in motion at the same time. Maybe we could call this Lakoff's Paradox.

In English, we cannot even discuss time except in terms of the spatial metaphor - length of time, how long is a second. Length is extension in space. We have no separate word for extension in time.*
* The obvious candidate, 'endure', actually comes from a root *deru meaning "to harden"; from which, ultimately, we also get our word 'true'.
These metaphors for time describe a linear progression. But it only seems to go in one direction. We can move in any direction in space, why is the dimension of time different? This is a question that Lakoff doesn't answer, but its always useful when thinking about time, to get into this.

Time's Arrow

The answer is well-known to us now as the arrow of time, a concept developed by Sir Arthur Eddington (who was also the first to test a prediction of Einstein's theory of relativity). The basis of the arrow of time is entropy. The second law of thermodynamics says that in any closed system entropy always increases. More simplistically we can say that disorder tends to increase over time. So, comparatively, a whole egg has low entropy, a broken egg has more entropy (more disorder), and a scrambled egg has high entropy. The arrow of time means that if someone shows us a film of an egg being broken and cooked backwards we can almost always tell straight away because the film shows us things moving in ways that are not possible and events happening in an order that contradicts the arrow of time. In reality eggs never uncook themselves and reform into white and yolk.

Incidentally, it's frequently pointed out that living things are an exception to this rule because they sustain order against the second law. There are two responses to this assertion. Firstly, living organisms are temporary motes of complexity, and complexity varies differently than disorder. Entropy increases steadily over time, but the complexity need not. If we take the example of the universe as a whole, entropy steadily increases as times goes on, but complexity starts at a minimum, rises to a maximum at about 1010 years (about now, in fact), and then declines back to a minimum by about 10100 years. The universe will continue to expand indefinitely, but once we reach a certain point the universe is as disordered as it can get and there is no arrow of time. Secondly, life increases the entropy of the universe more rapidly than non-living systems. For every low entropy photo of sunlight that falls on the earth, living things radiate 20 high entropy photons back into space. One way of defining living things is that we are systems for efficiently converting low entropy energy into high entropy energy. So life doesn't break the second law of thermodynamics, it uses energy to create complexity, that speeds up the increase in entropy locally. 

Coming back to time, it is a narrow path or flow, and it goes one way. But why do we see time as being broken up into moments? And is it really like that?

A Moment of Your Time

We measure time relative to cyclic phenomena. There are natural cycles such as planetary orbits, annual seasonal changes, the phases of the moon, menstrual cycles, the diurnal cycle, breaths, and heartbeats. And to these we have added phenomena such as burning candles, dripping water, oscillating pendulums, vibrating piezoelectric crystals, and finally the oscillations of radiation emitted by excited caesium atoms relaxing (in "atomic" clocks). In addition to this there are firing cycles of neurons in the brain that coordinate the beating of your heart, your breathing, and other cyclic bodily events, thought these are quite variable depending on how active we are. We measure time by counting numbers of regular cyclic phenomena. A stretch of time is so many repetitions of a cycle. A "moment" in time is the time for one iteration of the shortest cyclic phenomenon.

In reality, time is not composed of moments at all. Time is a way of conceptualising the procession of events that happen as the universe evolves. These events happen at their own pace. Events are not coordinated like a symphony orchestra is coordinated by a conductor. Events are more like a marathon where everyone runs at their own pace. 

The division of time (and space) into units is arbitrary. For example, note that years, months, and days are all based on natural cyclic phenomena, but they do not match up. A year is not a whole number of months (moon cycles) or days. This is why our calendars have to be adjusted occasionally, such as adding an extra day every four years, because the year is ~365.25 days. There is no "snap to grid" feature when it comes to time. 

Aspect and the Three-Times Structure

Coming back again to linguistics, when we use language to describe events, the verbs we use contain information on aspect. Different languages note different aspects, but aspect includes such information as the beginning, persistence, or ending of an event; and event in progress, completed, or yet to begin; and whether an event is continuous, cyclic, iterative, and so on. Amateur linguist Benjamin Lee Whorf (1956) wrote some interesting essays on aspect in indigenous American languages. In English I can indicate continuing or completed actions in the past, present, or future.
  • I was running (past, incomplete )
  • I ran (past, complete)
  • I am running (present, incomplete)
  • I have run (present, complete)
  • I will run (past, incomplete)
  • I will have run (future, complete)
The structure of time into past, present, future is common to Sanskrit, and thus, I presume, to Indo-European languages in general. We can also indicate repetitive actions. So one walk is a tramp. To repeatedly walk over something is to trample it. One oscillation is a wag, many is a waggle, though in English we often express aspect through adverbs like 'constantly', 'repeatedly', 'occasionally', or 'persistently'.

In most English time metaphors, the present is where we are now, the future is what is in front of us, and the past is what is behind us. In the time-flow metaphors of some languages, the future is sneaking up from behind us and we cannot see it, while the past flows away from us in front, where we can see it. The future could be quite unnerving in such cultures!

If we are the agent, then the "present" is the moment we are in, where a "moment" is an entirely arbitrary unit of time. And we still favour traditional measures because our sense of time is geared to them. A moment is roughly a heartbeat. The idiom "in a heartbeat" means "instantaneously". But we also have idioms for moments such as "in the blink of an eye", "a finger snap", "half a tick". Of course we can measure time many orders of magnitude more precisely than this now, but anything much shorter than a heartbeat is difficult for us to imagine. Past, present, and future are features of the metaphorical structure of language, but not of time in reality, because the present is an arbitrary time.

In John Searle's language, the present is an observer-relative function. The present isn't an intrinsic feature of the universe, but occurs to us as a subjective feature of time. So, epistemically, we understand there to be this structure to time, and since we all agree on it, it is epistemically objective. But it is ontologically subjective. The present only exists in our minds, because our minds have the features they do. 

Time to Get Real

Which brings us to the question of the reality of time. When the interviewer asks Lakoff about the reality of time, he says:
"There may be no such time as "time in reality". And that's what's interesting. There may be just events in reality."
Time is unlikely to exist independently of our metaphorical conception of it. This seems to be consistent with the universe that physicists describe at quantum and cosmological scales. The universe simply evolves in patterned ways. Some of those patterns persist as structures and those structures form increasingly complex layers of structure. In a sense, we could say that from this point of view that there are no entities, there are just some persistent processes, like standing waves in a river. Many physicists now think that time is not fundamental, but that it emerges as a property of the interactions of quantum fields. What his might mean in human terms, like most of quantum theory, is far from obvious or, in fact, completely obscure. It may not even be possible to disentangle our metaphorical time and what time is in reality, if it is anything. 

This insight into the metaphorical basis for how we understand time is important for deconstructing Zeno's arrow paradox. The paradox is based on reifying the notion that time can be measured in moments. It assumes that the moments we perceive in time relative to some other cyclic events are real. But they are not. In reality, the evolution of the universe is continuous and not broken down into moments. 

As we know, different layers of the universe require different descriptions. At the quantum level, events may be discrete, such as the transition of an electron from one energy state to another. This is what the quantum part of quantum theory means. At the quantum level, change can be discontinuous. But at the macro level (i.e., at the mass, length, and energy scale relevant to human experience) change is never discontinuous. It may happen very rapidly, but it is always continuous.

So, if change is continuous and we divide it up into moments, what happens is that we lose information about the continuity of the process. The same thing happens when converting music to a digital format. If the sampling rate is less than about twice the highest frequency we can hear then the loss of fidelity at the high end starts to become obvious. The average healthy person can hear sounds up to about 20 kilo-Hertz. Which is why digital music samples at roughly 48 kHz or more. But even if we sample at 96 kHz or more, we still lose information. Other factors intervene. Our equipment for turning digital signals into analogue waves in the air will not produce 100% fidelity, either, so sampling a million Hz would be pointless. The point is that dividing time into moments is a lossy process.

Time is not a series of moments, it is an unfolding of events: a marathon rather than an orchestra. So, for example, there is no such thing as "the present moment" because the idea of a moment is defined relative to some cyclical event, and we are free to choose difference reference points. Different authorities define the present moment as lasting a different number of units or fractions of seconds. A second is the length of time that it takes for a 1 meter pendulum to complete an arc. Or a second is "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom". In other words, a second is arbitrary, but if we all choose the same arbitrary measure, then we agree on how long a second is.

We now have enough information to understand the misunderstanding that creates the paradox.

Resolving the Paradox

Zeno's arrow is not stationary at any given moment. Moments are arbitrary and are arbitrarily long. If the moment is 0.001 of a second, the arrow is still moving during that time; though the amount of movement may be too small for us to see, it still moves. When the arrow is in motion, it is constantly moving. Similarly, if we observe a mountain for a year it may not perceptibly change, because mountains change on geological time scales (millions of years). A photograph of a bird on the wing may give the illusion of stillness if the exposure is short enough, but even then if one looks carefully one may find movement blur at the wingtips.

In reality, there are no moments. Moments are a structure that we subjectively impose on the flow of events. Time itself may be an emergent property of quantum systems. And events go at their own speed, with no coordinating universal clock. Time's arrow is a result of steadily increasing disorder in the universe and will disappear once entropy reaches a maximum. 

So Zeno's arrow paradox and Nāgārjuna's laborious fumbling around the subjects of time, duration, motion, and change, are difficult because they do not understand the distinction between how they conceptualise time and what time might be in reality. In other words, we once again meet the mind projection fallacy or the problem of confusing experience for reality. George Lakoff dispenses with Zeno in less than four minutes. Of course, there are many secondary questions and a lot of gaps to be filled in, but once a problem is correctly framed, things can move along more rapidly. 


George Lakoff (2016) How Does Metaphysics Reveal Reality? [Video] Closer To The Truth.

Whorf, Benjamin Lee. (1956). Language, Thought, and Reality. MIT Press.

01 May 2015

Yāmagaṇḍika: Telling the Time in Ancient India

Revision 2.0 - 3 May 2015

My Pāḷi reading group has been working through the commentary to the Kāraṇiya Metta Sutta which I translated for this blog some years ago (11 Jun 2010). In this text we come across an unusual term that has no counterpart in the suttas. In picturing some bhikkhus zealously meditating in the forest it describes them as yāmagaṇḍikaṃ koṭṭetvā. This is a curious expression and in this essay I'll attempt to elucidate what it means. The compound yāmagaṇḍika occurs only twice, both times in commentarial texts (Paramatthajotikā SnA 1.193; Papañcasūdaniyā, MNA 1.122) and these should be enough to allow us to gain some clarity. We'll see that the commentator does not see his own time in context, but wrongly assumes that his milieu reflects that of the Buddha some centuries earlier. 

The gerund koṭṭetvā must come from the verb koṭṭeti (from a rare root √kuṭ or kuṭṭ) 'to beat, crush, pound'. For example it is the action associated with a mortar (udukkhale koṭṭetvā DN ii.341) and with pounding grain (dhaññaṃ koṭṭenti Thī  117). It has other minor senses in PED, but these don't seem relevant here. The compound yāmagaṇḍika combines yāma and gaṇḍikā. We'll take these one at a time. 

According to PED gaṇḍikā derives from gaṇḍa 'a swelling; a stalk or shaft' + -ikā. The formation gaṇḍikā means 'a stalk or shaft', particularly 'the trunk of a tree' and by association 'a block of wood'. However there is a potential confusion here with ghaṇṭā 'bell' or ghaṭikā 'gong'. As we will see the CST edition of the text is quite unreliable and this means we must allow for errors. In the Digital Pāḷi Reader version of this text, we find yāmaghaṇḍikaṃ koṭṭetvā. The spelling -ghaṇḍikaṃ occurs in the Majjhima Ṭīkā  (the sub-commentary on MNA 1.121) "yāmaghaṇṭikaṃ paharati"  (MNṬ 1.196) though the Aṭṭhakāthā has -ga-. The Khuddaka Nikāya Commentary—which parallels the Suttanipata commentary—also has -gh-.

Pañjaranatha Mahākāla
with gaṇḍikā
DOP sv ghaṇṭī/ghaṇḍī, suggests a confusion with gaṇḍi and ghaṇṭā. If it does mean 'block' then it must refer to a resonant gong-like block that is 'pounded' (√koṭṭ) as a time signal. Buddhadatta's Concise Pali-English Dictionary defines gaṇḍikā as "(f.) a hollowed block of wood which is used to serve the purpose of a bell; a gong." A gaṇḍī or gaṇḍikā is the characteristic implement of a form of Mahākāla known as Pañjaranatha. In the image on the right he holds it across his body (thanks to Maitiu for pointing this out).

Yāma is complicated because it has homonyms that derive from different verbs. From √yam 'hold, hold back' + -a we get yāma 'restraint'; and from √ 'go' + -ma we get yāma 'motion, going, progress'. The latter is used figurative to mean 'a watch of the night'. We frequently read in Pāḷi of the three watches of the night (tiyāmā): paṭhamayāma, majjhimayāma, and pacchimayāma (first, middle, and last watches). The practice of dividing the night in particular in watches was common in the ancient world. The Latin name for these periods was vigilia, whence English 'vigil'. Incidentally yāma can also be a collective noun for people or things related to the God of the afterlife, Yama, in this case his name means 'twin', from √yam 'combine'.

The compound, yāmagaṇḍika, can really only be a tatpuruṣa so it must mean something like 'the block of restraint', or 'the gong of the watches'. The context is that the monks are resolute night and day, devoted to wise attention, and sitting at the foot of trees meditating. It may be that 'beating the block of restraint' is a metaphor that we no longer understand, similar to the Buddha saying to Upaka the Ājīvaka in the Ariyapariyesana Suttaāhañchaṃ amatadundubhiṃ 'I beat the drum of the deathless' (MN i.171). It's not entirely obvious what this means since drums are primarily for entertainment in our society.

However, I believe that here we must read yāma as 'watch of the night' and the phrase means 'beating the block or pounding the gong that marks the watches'. For confirmation we can look at the second of the two occurrences of yāmagaṇḍika at MNA 1.122 (already mentioned above):
Ajagaravihārepi kāḷadevatthero antovasse yāmagaṇḍikaṃ paharati, āciṇṇametaṃ therassa. Na ca yāmayantanāḷikaṃ payojeti, aññe bhikkhū payojenti. Atha nikkhante paṭhame yāme there muggaraṃ gahetvā ṭhitamatteyeva ekaṃ dve vāre paharanteyeva vā yāmayantaṃ patati,
We immediately strike a problem in that ajagara probably means 'python' or some other large snake and doesn't fit the context, and the spelling of the next word (with -tth-) is suspect. Consulting the Dictionary of Pāli Names we find an entry for a Thera named Kāḷadeva:
"...incumbent of Vajagaragiri-vihāra. He is mentioned as having known the exact passage of time without the help of an "hour-glass" (yāmayantanālika). MA.i.100f
This is in fact, a reference to the passage we are about to analyse. It's thus apparent that the CST (Burmese) edition is incorrect here and we must amend it to:
Vajagara[giri]vihārepi kāḷadevathero antovasse yāmagaṇḍikaṃ paharati, āciṇṇametaṃ therassa. Na ca yāmayantanāḷikaṃ payojeti, aññe bhikkhū payojenti. Atha nikkhante paṭhame yāme there muggaraṃ gahetvā ṭhitamatte yeva ekaṃ dve vāre paharante yeva ca* yāmayantaṃ patati. 
The Elder Kāḷadeva of Vajagaragiri Monastery, performs this striking of the block of the watches till the end of the rains. And he does not use a measuring device as other monks did. At the end of the first watch the Elder takes up the hammer (muggara) and strikes twice for every measure of time, just as the watch-mechanism falls. 
* The text has , but I think this must also be wrong, and have amended to ca
My translation of this passage is a little rough, but the main points are clear. For our purposes two things are important. It is entirely clear that yāma must refer to 'a watch of the night' rather than 'restraint'. Secondly we read that Kāḷadeva did not yāmayantanāḷikaṃ payojeti, that he used a hammer (muggara) to strike the block, and then yāmayantaṃ patati. And this helps to fill out what the author of the Metta Sutta commentary was thinking.

One of the problems of living a regular life is keeping time. The early forest monks had no way of telling the time apart from the sun, moon and stars. Pāḷi distinguishes day (diva) from night (ratti) and we read of monks doing things in the morning-time (pubbaṇhasamaya) or evening-time (sāyaṇhasamaya). We know that the phases of the moon—full moon (puṇṇacanda) and new moon (navacanda)—were important for organising the lives of monks. The moon takes on a magical significance for some Buddhists as a result of this. The watches of the night, however, are far more difficult to determine. How did monks, living in a forest, know when the watches began and end. Presumably the first watch started at dusk and the last ended at dawn, but what marked the other boundaries? Presumably one versed in astronomy would be able to keep track of when certain stars were due to rise and set, but the three month retreat is during the rain season when the skies are perpetually cloudy. 

The simple answer is that the first monks almost certainly did not keep accurate track of the time and that the watches were assessed subjectively. And we can point out that no references to time keeping apart from observing the sun and moon are referenced in the suttas. The texts we are dealing with here, however, are from 5th century Sri Lanka and from an environment of highly organised, large scale, urban monasteries.

If we now look at the phrase yāmayantanāḷikaṃ payojeti we can see that the DOPN glosses it is as "the help of an hour-glass". Now an hour-glass is anachronistic here, they did not exist in this time or place. But yanta does mean 'mechanism' and nāḷika 'a tube or measure'. So we know that Kāḷideva did not, as other monks did, employ (pa√yuj) a measure/tube device for the watches (yāma-yanta-nāḷika). This suggests some kind of clock, but is the idea plausible? I had a dig around in some horological books and apparently it is plausible to think that in first millennium India there were water-clocks.

Water-clocks come in two forms: a vessel with a hole that allows water to leak out slowly, and the slight more sophisticated sinking bowl, in which a bowl with a hole in it gradually sinks into a container of water. The books suggest that the sinking-bowl water-clock was common in India by medieval times and so accurate that it probably delayed the introduction of mechanical clocks. Importantly the attendant of water-clock announced the end of the time period by striking a 'gong'.  The Gujarati word  for which was ghaḍiyār. There's an outside possibility that this word is related to gaṇḍikā or ghaṭika.

Persian Water Clock.
We do know that the Achaemenid Persians possessed just such water clocks, from the records of Alexander's conquests in India by Callisthenes of Olynthus. We know that similar water-clocks were employed to mark the passage of time in monasteries in North India by the 7th century. This information comes from the records of Yijing (義淨 aka I-Tsing; ) a Chinese monk who lived 635–713 CE, and spend 25 years travelling, taking the southern sea route to India. Yijing's account (see translation by Takakusu 1896: 142-6) is widely recycled in a variety of other sources, for example Misra (1998) simply quotes Takakusu at length, while Sharfe (2002) paraphrases and the Wikipedia article on water-clocks cites Sharfe. Yijing records the use of sinking bowl water clocks in several monasteries, with each using slightly different measures and signalling conventions. The bowls were made of copper and were very expensive, generally being the gift of a king to a monastery. Such clocks were also used by the ancient Britons

Sri Lankan
water-clock bowl
So it seems at least plausible that urban monks in fifth century Sri Lanka measured the hours of the day using a water-clock and marked the increments by striking some kind of gong (probably wooden given how expensive metal was). And what our commentators have done is imagine that this is also what monks did in the Buddha's time. Thus when they tell the story of the Metta Sutta they project this technology backwards. And we know that they have done in this other ways as well. For example they projected South Indian kinship patterns familiar, to them in Sri Lanka, onto the family tree of the Buddha and his family, even though these patterns were out of place in North India (See Attwood 2012). But it is extremely unlikely that forest monks in the fifth century BC uses anything so elaborate to measure time.

One little loose end is that having struck the gong with the hammer, yeva ca yāmayantaṃ patati. Now, patati comes from √pat 'fall, fly' and it's not usually a transitive verb. Yanta being a neuter noun we can read this as 'and just as the watch-mechanism falls'. If the yāmayanta falls at the end of the time period, then this is consistent with a sinking bowl style water clock.

It is fascinating how a short phrase like this one can open a window into history. And while here we are not talking about the time of the Buddha, but of the period of the Sri Lankan commentators, it is still a glimpse of history. It reinforces the point that the commentaries reflect their own time rather than any earlier time. They are apt to project their own culture and technology backwards onto the past, making them unreliable guides to the past. Thus when we consult the Pāḷi commentaries for insights into the suttas we must be cautious in drawing historical conclusions. The commentators were no doubt sincere, but they had a vested interest in trying to establish that the past was reflected in the present because it was one way of establishing their legitimacy as bearers of the tradition. It shows how very tenuous lineage is as a guide to legitimacy or authenticity. 


Attwood, Jayarava. (2012) 'Possible Iranian Origins for Sākyas and Aspects of Buddhism.' Journal of the Oxford Centre for Buddhist Studies, 3.
Misra B.N. (1998) Nālandā: Vol. 1. Sources and Background. B.R. Publishing Corporation.
Sharfe, Harmut. (2002) Education in Ancient India. Brill 2002. 
Takakusu, J. trans. (1896) I-Tsing, A Record of the Buddhist Religion : As Practised in India and the Malay Archipelago (A.D. 671-695), Clarendon Press 1896. Reprint. New Delhi, AES, 2005.

24 May 2013


After my blog last week, a reader called Piotrek posted a comment that was very thought provoking, and as my answer grew I decided it might be better as a blog post since it touches on a number of issues.

We began discussing an article by Johannes Bronkhorst, Akālika in the Buddhist canon, in which the professor tried to show that akāliko, rather than meaning timeless means something like 'unconnected with death'. I did not find this very plausible and so Piotrek pointed me to another passage where the familiar word becomes an adjective of nijjarā instead of dhamma. In this blog I will present my assessment of Bronkhorst's article and this additional passage. 

There are some points we need to clarify for readers first. The word akālika is most familiar from the standard version a series of epithets of the Dhamma which I will call the Dhammavandana:
svākkhāto bhagavatā dhammo sandiṭṭhiko akāliko ehipassiko opaneyyiko paccattaṃ veditabbo viññūhīti.
The Dhamma of the Bhagavan is well told, evident, timeless, verifiable, progressive, and each intelligent person can see it for themselves.
The Buddhist tradition seems to be unconflicted in seeing this term as meaning 'timeless'. However some Bhikkhus have argued over what 'timeless' means. Ñāṇavīra, especially, has argued that it must mean that paṭicca-samuppāda is not a temporal sequence, but a structural one. He uses the image of a house: the foundations must be present to hold the walls up, as the walls hold up the roof. But this sequence is instantaneous (akālika) and gives rise only to mental objects. This is similar to my own view. I also use the house metaphor to show that the presence of the condition is required for the dhamma to arise. Last week I said that the use of the locative absolute syntax (with a present participle) implied this presence. However let us get back to the issue at hand. 

Bronkhorst points out that the two words sandiṭṭhiko and ehipassiko are known to be straight forward.  However he performs a sleight of hand here. By phrasing it this way he infers that akāliko is not so straightforward. He hints that it is somehow problematic, but to my knowledge it wasn't until now. In order for the argument to proceed he must first create the impression that there is a problem in understanding akālika.

He also proposes that sandiṭṭhiko and ehipassiko are synonyms. Firstly it's not clear why he focusses on these two and leaves out the other epithets. If the argument is proximity then we must point out that ehipassiko and opaneyyiko are similarly adjacent. The two words are not unrelated as they both come from roots meaning 'to see'. But the former means that it is 'able to to be seen', and quite frequently is applied to the visible world; while the second means 'come and see'. They are synonyms to the extent that 'visible' and 'inspect' are synonyms in English. And akālika is decidedly not from a root meaning 'to see'. It is true that Buddhist texts will sometimes string synonyms together, but this is stretching it. If we compare the epithets of the Buddha in the Buddhavandana then we see that they are very far from being synonyms.
itipi so bhagavā arahaṃ sammāsambuddho vijjācaraṇasampanno sugato lokavidū anuttaro purisadammasārathi satthā devamanussānaṃ buddho bhagavāti.
Such is the blessed Buddha, worthy, completely awakened, equipped with insight, in a happy state, with knowledge of the experiential world, unsurpassed, a tamer of men to be tamed, a teacher of gods and men, blessed.
It is only when the situation has been set up that Bronkhort can say "...the usual interpretation does not fit well". Buddhaghosa, on the contrary, hardly bothers to comment on the word, but seems in no doubt. At AA ii.256 he says "akālika means giving fruits at once." (akālikoti na kālantare phaladāyako); that is, the fruits (of a condition) arise with no time interval (kāla-antara). Also at SA i.43 and Nidd2 92 we get the short phrase "timeless simply means without time" (akāloyeva akāliko). Note that Bronkhorst carefully avoids any discussion of how the Buddhist tradition has understood this term. He goes so far as to label the Canonical commentary Cūḷaniddesa a 'late text', thus suggesting it has no relevance. Whereas generally speaking the Cūḷaniddesa is very useful for understanding obscure usage, if indeed this is an obscure usage which I dispute.

Having problematised the term to suit his purpose Bronkhorst proceeds to his ingenious reading of the Samiddhi Sutta (SN i.8-12). He tries to show that kāla must be related to the euphemistic idiom which combines kāla with a verbs deriving from √kṛ, i.e. 'to make his time', which means 'to die'. The evidence for this association in a single passage repeated in two suttas. However apart from the weaknesses already identified, lexiographers have not found a single other reference to kāla that implies kāla-kṛ. Kāla only takes on the association with death in this specific idiom when √kṛ is explicit. The word kālika is also attested in non-Buddhist Sanskrit texts in the sense of 'connected with time' (MW). 

If the author of the Dhammavandana had wanted to say "unconnected with death" he had plenty of formal and idiomatic options available to him: 'deathless' (amata) being the most blindingly obvious. What constraint was placed on the author that made him avoid the obvious in this one epithet, but not in the others? Since sensible and unproblematic translations can be made of the texts Bronkhorst submits as evidence, it looks like this was a case of a solution looking for a problem. It is not particularly plausible. And in the end how ironic would it be if one the epithets of the sandiṭṭhiko dhammo was itself asandiṭṭhiko (obscure).

Piotrek's proposition on the other hand is more interesting and more plausible even though it is not, in the final analysis, convincing. Let us work through the problem. The modified version of the Dhammavandana which includes nijjarā goes like this:
sandiṭṭhikā nijjarā akālikā ehipassikā opaneyyikā paccattaṃ veditabbā viññūhīti.
Eradication is evident, timeless, verifiable, progressive, and each intelligent person sees it for themselves.
In this version nijjarā is not described in precisely the same terms as dhamma, nijjarā does not come from the Bhagavan (bhagavatā) and lacks the quality of being well told (svākkhāto). This may reflect the difference between dhamma as verbal teaching and nijjarā as practice.

A word on what nijjarā (Skt nirjarā) means. According to the Jains, karma produces particles (dravya) which flow in (āsava) and stick to the soul (jīva), weighing it down so it stays in saṃsāra. The word nirjarā refers to the eradication (nirjarā) of these particles through austerity (tapas). Liberation (mokṣa) must be proceeded by the complete eradication (sarvanirjarā) of the particles, freeing the soul from saṃsāra

Note that because nijjarā is feminine in Pāli all the adjectives have become feminine as well (changed to the long -ā ending). Nijjarā is translated by Bodhi as "wearing away". Others translate as 'eradication, destruction, etc.'. Etymologically the word derives from nis + √jṛ 'to waste away'. Here the prefix simply seems to emphasise the nature of the action. Given the Jain reference, I settled on 'eradication'. 

This version is found in three places in the Pāli Nikāyas: AN i.220-1, AN ii.198, and most importantly at SN iv.339. In the latter passage we find a (Buddhist) description of this word. There are three kinds of nijjarā: the abandoning rāga, dosa and moha. The part of the passage that interests us is:
Rāge pahīne nevattabyābādhāya ceteti, na parabyābādhāya ceteti, na ubhayabyābādhāya ceteti.
When abandoning passion he does not intend to harm himself; does not intend to harm others; does not intend to harm both.
Note the typical way that Buddhists change doctrines when they assimilate them. Where the Jain would pursue eradication by self-torture (atta-byābādhāya) – particularly starvation and long periods of immobility – here the Buddhists have made eradication the complete opposite of what the Jains meant (to the extent we know what they meant). Just because this is a Jain term does not mean we should take the context as Jain. The context in the Pāli suttas is Buddhist. Always Buddhist. And this is why the reconstructions of early Jainism which rely so heavily on Buddhist texts are unreliable.

As in the last blog post this is a locative absolute construction: rāge pahīne 'once passion is abandoned'. The implication here is that when passion is abandoned there is the cessation of the intention to self-torture etc. The inclusion of akālika 'timeless' in the list of epithets of nijjarā suggests that there is no time lapse between abandoning passion and the cessation intention to self-torture. Which is just what we expect. There is nothing here to make us doubt that the word akālika might support Bronkhorst's  thesis.

However Piotrek's broader point was this.
"The dhamma which is described as "sandiṭṭhika akālika ehipassika" is, I think, nibbāna itself, which contrary to, for example, Jain belief is attainable in this life not only after death. So I believe that akālika has nothing to do with workings of paṭiccasamuppāda but describes nature of Buddhist goal."
It is true that later on nibbāna is described in terms which suggest timelessness. In the commentary on the Pārāyanānugīti gāthā from the Sutta-nipāta (Cūḷaniddesa 201) we find:
Nibbānaṃ niccaṃ dhuvaṃ sassataṃ avipariṇāmadhammanti asaṃhīraṃ asaṃkuppaṃ.
Nibbāna is permanent, constant, eternal, not subject to change, indomitable, unshakeable.
But it would unusual, I think, to take the Dhammavandana as referring to Nibbāna. Again, the Pāli author was free to say what he meant. This passage is in the context of praises of the three precious gifts: buddho, dhammo, sangho. It would be unusual to take dhamma here as synonymous with nibbāna and exclude the sense of paṭicca-samuppāda. After all the Śālistamba Sūtra does say:
yo pratātyasamutpādaṃ paśyati so dharmaṃ paśyati
yo dharmaṃ paśyati so buddhaṃ paśyati 
He who sees dependent arising sees the Dharma
He who sees the Dharma, sees the Buddha.
On the other hand the Dhamma as refuge often has a superlative connotation. Sangharakshita has referred to the refuges as representing a transcendental principle. So there is a sense in which the Dhamma as refuge does refer to the Dhamma in the sense of nibbāna. In this sense akālika is often read as meaning 'standing outside time', though the metaphysics of this proposition are complex to say the least. In this sense the principle of paṭicca-samuppāda is thought of as being like the law of gravity: it applies in all times and all places and thus is not time dependent. 

I'd like to thank Piotrek for his stimulating comments and hope my disagreement with him won't discourage him from continuing to contribute. As Mercier and Sperber have argued, reason really only works well when it is responding to a challenge.