illustration (attribution, if any possible, is at the end of the article)
It tends to be considered that there are several types of kappa (P.) / kalpa (Skt.) / aeon in Buddhism, defined as multiples of one another.
The smallest kappa would be the life expectancy for humans (supposedly 'decreasing' expectancy in our day and age —the "later days of Dharma"— according to traditional Buddhism, although that's a very dubious perspective from a scientific perspective!). The longest would be either a trillion years or so, or the duration of one cycle of the Big Bounce (en.wikipedia.org/wiki/Big_Bounce).
The Buddha didn't make such distinctions though; instead, he relied on a few analogies. A kappa is longer than the time needed to fill a (16-miles)^3 cube by adding one mustard seed every 100 years, and is longer than eroding a (16-miles)^3 mountain by wiping it every 100 years with a piece of silk. Based on such definition, the 'past' that the Buddha took into consideration was rather vast: passed kappas outnumber the number of sand particles in the Ganges river, from where it begins to where it ends at the sea.
The dictionary definition seems adequate: « an indefinite and very long period of time »
In Tibetan Buddhism, one easily comes across statements such as « generating compassion has incredible power to purify many aeons of negative karma » or « if we become angry at our guru, we will destroy aeons of merit we have accumulated in the past equal in number to the moments of our anger ».
By repeating the Cundī Dhāraṇī 800,000 times, « one's deadly karma in every place, created over innumerable aeons, will be completely annihilated. » 800,000 times might seem a lot but compared to innumerable aeons, it's all relative! For the impatient, another particular mantra might also be described as « more powerful than if one makes merit by making offerings, reciting mantras, making extensive offerings everyday for aeons to the countless buddhas of the ten directions… » And another might be described as « whoever sees, hears, remembers, or touches this mantra will be purified of all negativities and gain freedom from rebirth in the lower realms. Merely seeing this mantra purifies 100 million aeons of negative karma. »
So… one good / meritorious / wholesome action might cancel many aeons of negative karma… and one bad / reprehensible / unwholesome action might cancel many aeons of positive karma…
Even if we take this in relation to 'small' aeons as short as human life expectancy, the above statements relate to very large spans of time… and they're not particularly expressed in context-dependent manner, they're not meant as humorous, these come from 'instructions'.
As instructions, they're weird though, for several reasons.
For starters, nirvāṇa is 'unconditioned' and is not attained by simply 'earning' enough merit. The schools these instructions are from all accept 'emptiness' as a core teaching, and 'merit' is therefore empty of essence: merit is defined in relation to context, and has no inherent consequence. [It is not to say that merit has no place whatsoever in Buddhism: just like opening a door helps but doesn't automatically make you cross its threshold, merit removes barriers but this doesn't make you automatically reach the other shore… yet, it's still helpful not to run into walls or closed doors!]
Moreover, our 'understanding' of karma necessarily is non-deterministic. Causality 'appears' context-dependent even to the broadest, most discerning, least biased mind. Acts unfold into consequences just like seeds unfold in plants: without water and sunlight, the seed won't grow; it will still affect the environment (maybe it'll participate in feeding an animal…) but in a very different way than if it grew into a tall tree; the seed has no inherent consequence, that might be defined independently from a context. It is important to understand that even if karma was deterministic (which isn't the case if other causal laws, or niyama, are considered in parallel), this wouldn't necessarily imply that we can make reliable predictions! Because multiple conditions influence each event, the system appears chaotic to any observer who discerns a foreground and a background, and just like stable mechanical 'laws' might lead to chaotic systems for which we cannot easily predict the evolution far ahead (en.wikipedia.org/wiki/Stability_of_the_Solar_System), karma remains largely unreadable to us as long as we cannot know, exhaustively and with infinite precision, all the ('initial') conditions of the system's evolution… i.e. it remains forever largely unreadable. When the Buddha commented on the karma of specific people, he always focused on relatively short term, BTW, at most one life ahead… even the Buddha, even considered 'omniscient'! We cannot forget the mind, and the limitations of concepts and of language, when we consider someone reading / seeing / interpreting / using causality (gplus.wallez.name/aVJ7pgjKZT6)!
Given you have no clue of how many eons you have been in this game, not even a clue about how many acts you've done one way or another in this very life, where does this leave you?
Living in fear of making the tiniest mistake? Motivating you to seize every tiniest opportunity to behave wholesomely? Maybe… but this might be seen as inappropriate tension.
Doing a lot of evils because you reassure yourself you'll be able to cancel them all with one single mantra before you die? Maybe… but this might be seen as inappropriate (lack of) tension, and as major delusional views (you don't know when you'll die, and even if you did, you cannot impose what you'll think about at that point! You cannot even control what you'll think about in a second or two!).
Perseverance or energy is a Perfected Quality, doubt is one of the ten fetters, and yet the Buddha explicitly said that "right concentration" is neither too tight nor too loose. Like a musical instrument: too tense and the string breaks, too loose and the string doesn't vibrate to emit a sound. This concentration can be seen in relation to meditation, of course —that's how it's usually interpreted— but it also applies to the eightfold path itself: too tight and one becomes obsessed, unhelpfully clings to a goal and to the 'raft', and tends to become blind to the suffering of others… Too loose and one too easily postpones the actual practice for the sake of worldly cravings.
Most teachers would suggest either to take these instructions literally, presenting their school as the 'truth' (even if they potentially understand that it's a 'conventional' truth here…), or to interpret them with a pinch of salt.
Sometimes the same teacher might suggest either, based on the specific student at hand! Literal interpretation might be recommended to negligent or nonchalant students for example, those who need of lot of pressure before they even start considering ethical dimensions in their day-to-day life. Pinch of salt might be recommended to students who are depressed and think their past condemns them to many lives in Hell and cannot find anymore the motivation to resolutely change for the better.
There's (at least) a third way.
The point lies with your not knowing your past merits and past faults, not from previous lives, not even from this life! You might be clear on a few of them, but if each act may cancel millions of previous acts, and if you admit that there's a myriad of 'small' events from this life you don't remember (clearly or at all!), then you have to admit you just plain don't know your current 'meritorious' tally.
So these instructions are directly pushing you toward a sense of humility. No matter how meritorious or unmeritorious you thought you were, if you think about it further, you have to admit that you don't actually know. And therefore your past doesn't matter much. How many years as a monk you've had, or how transgressions of precepts you've had, doesn't give you much relevant information, because you've forgotten most of the small acts that cancel millions of preceding acts.
50 years as a monastic doesn't count much if a single moment of anger toward one's teacher cancels an entire aeon of merit… but a past crime doesn't count much either if a single moment of compassion toward an 'enemy' cancels an entire aeon of inappropriate behaviour.
Once you develop this humility, you're likely to come to acknowledge that you don't know if you will be able to avoid spoiling lives of effort by a single moment of anger in the future.
You'll acknowledge that you don't know if the best behaviour now will make much of a difference in the long run.
You'll relinquish the permanency of 'merit', and realise that, just like maintaining concentration requires vigilance (so drifts are caught, and awareness is brought back to its object), maintaining merit requires vigilance and 'coming back' (gplus.wallez.name/EBDqZwQRbqV).
So, although it is framed in terms of 'merit', the instruction pushes you to see the emptiness of 'merit', and the ludicrousness of counting merit, of hoarding merit, of craving merit… the ludicrousness of using the Dharma for a personal agenda.
It's the same logic and skilful means as the apparently-paradoxical koans of some Zen traditions. The paradox can be resolved, but it takes to go 'beyond' words, beliefs, preferences, prejudices… beyond attempting to turn the Dharma into a tool to force reality to comply with your wishes. When the accounting doesn't make sense, you have to drop 'accounting' as the way to direct your life.
And if you cannot take much of the past and much of the future into consideration to define what to do now, then the instruction boils down to "do your best, here and now"! (gplus.wallez.name/Tnx1pJdhsvv).
You don't know if it'll be enough to entirely cancel a heavy past, but the instruction asserts that there's no doubt it'll improve the situation. You don't know if you will ignorantly spoil it in the future, but the instruction asserts that there's no doubt the situation will be better anyway (partly because any spoil is finite, no matter how large…). You don't know if there's any point in counting individual merit, and the instruction leads you to consider expanding your horizon beyond 'merit' and beyond yourself (gplus.wallez.name/Z38n35NGvyB)!
How do you do your best beyond 'merit'? You stop presuming that you 'know' what's meritorious or not: you pause, look at the situation at hand, and consider what the present conditions call for! You also stop presuming there's only one 'best' (gplus.wallez.name/UnoFyYsg9n2)!
Although these instructions might seem extremely deterministic and to focus on long time periods ("do <this>, it is meritorious and <so many> aeons will be covered"), they're in fact sending you back to the inadequacy of leading a life entangled in two delusions: that of 'deterministic' knowledge (including of how karma unfolds, and of a 'recipe' for enlightenment), and that of looking far back and far ahead even though you can only act / affect / influence what's happening now and you cannot know how far the ripples will go!
Like a koan, the apparent deterministic certainty is more a question than an answer, as soon as you reflect on the instruction you received and try to embody it in practical terms! And this question is: what is the most appropriate behaviour, in the present situation, while acknowledging that all sentient beings seek not to suffer?
image: "point de fuite" by Nadine FOURRÉ (Photo: Jean-Louis Dalloz) www.facebook.com/nadine.fourre/posts/1117855361560794:0