In Sutta 18, verse 8 is footnoted with a (very) long footnote (229) in which Bhikkhu Bodhi says that the interpretation of verse 8 hinges on the meanings of Papańca and Papańca-sanna-sankha. I agree with BB's translation of Papańca as "mental proliferation". It is quite amazing to watch as the mind takes the simplest thought, jumps on it, and runs off in all directions. Just as the ear hears without any effort (and in fact it takes a lot of effort to make the ear not hear), the mind proliferates effortlessly, and it takes a lot of effort and/or training to hold this tendency in check. It's the unbidden "going" of the mind to so many different subsequent thoughts that is important, rather than the diverse places it goes. Therefore I much prefer BB's "conceptual proliferation" to Bhikkhu Nanamoli's "diversification".
As BB says, Papańca-sanna-sankha is more difficult. I know so very little Pali and that knowledge is useless here. All I have to rely on is other peoples' scholarship and my own experience. That said, I would translate Papańca-sanna-sankha as "perceptual concepts [arisen from] proliferation", which is one of BB's alternate suggestions in footnote 229. The proliferation in and of itself it fascinating to watch, but it would be nothing more than relatively harmless static except that we believe all this stuff! There is a great story that illustrates this:
Verse 8 of Sutta 18 can therefore be understood as follows: There exists in the mind the very strong tendency for thoughts to proliferate. These thoughts lead to various concepts. The concepts that we take delight in, we hang onto, we believe them to be true. By hanging onto erroneous concepts we wind up with lust, aversion, views, doubt, conceit, desire for being and ignorance. These (unwholesome) states of mind lead to taking up of weapons, quarrels, brawls, disputes, recrimination, malice and false speech. By recognizing these concepts for what they are, that they have arisen purely from the mind's tendency to proliferate, we don't take them to be the truth and we don't become mired in the unwholesome states.
Maha Kaccana's explanation of Buddha's teaching in verses 16 - 18 is an explanation of how Papańca works and how concepts dependent on Papańca arise. Any sensory input will do to trigger a burst of Papańca. The sensory input generates feeling which generates perception which generates thinking. And thinking is Papańca - that's how our minds have evolved. And Papańca leads to Papańca-sanna-sankha. In verse 18, Maha Kaccana suggests that the best way to shut off Papańca is to be secluded from the senses. If there is no sensory input, the train never leaves the station. And being secluded from the senses is how the (Jhana) meditation instructions always begin.
Sutta 19 addresses dealing with Papańca in a slightly different way than Maha Kaccana suggests. Here the Buddha recommends noting which thoughts lead to trouble and which thoughts don't. He points out that the types of thoughts that most frequently proliferate are the types that we most frequently think and ponder upon. By directing our minds towards wholesome thoughts, we are much more peaceful and much more able to meditate (which, of course, will lead to our enlightenment; but also has the effect of slowing down our rate of Papańca).
Sutta 20 provides instructions for how to direct the thoughts in wholesome directions. By becoming masters of the directions in which our thoughts proliferate, we can achieve freedom. The Buddha recognizes that the mind's tendency towards Papańca is unavoidable, and instead of fighting the inevitable, he teaches us how to ride (and tame) the tiger.
Sutta 131 is also a teaching on how to direct the mind so that the thoughts that proliferate are less likely to be unwholesome. The teaching here is to keep the thoughts in the present moment. The specific instructions are again about not taking delight in the proliferating thoughts about past and future. The way to keep from being mislead about the present is to not mistake body, feelings, perceptions, mental formations or consciousness for a self. It is quite interesting to note in Sutta 133 that Maha Kaccana's teaching about the present moment closely parallels his teaching in Sutta 18.
I strongly agree with Maha Kaccana that meditation is the best antidote for Papańca. I mentioned above that stopping this proliferation requires as much effort as stopping the ear from hearing, or it requires sufficient training. The meditation practice provides this training. The main purpose of the calming of the mind is to slow the tendency towards mental proliferation. The technique described in the Anapanasati Sutta (118) is effective; even more effective is Jhana practice (in my opinion). Once the mind is not running off in every direction, it can much more easily see things as they are. It can see the three characteristics of all phenomena, it can see things from a non-egocentric perspective.
It is interesting to note that the Tibetans describe the "natural state of the mind" (rigpa) as having three marks - no artifact, no effort and no distraction. This is quite a contrast to the rampantly proliferating mind we have been discussing. The normal mind seems to effortlessly generate all these artificial, distracting thoughts. I think the apparent contradiction is resolved in that "natural state of the mind" is not a good translation of rigpa. Rigpa seems to be much more the state of mind that the Buddha and Maha Kaccana are advocating that arises out of the mediation practice. It's a state of effortlessness, with nothing artificial, where the thoughts that arise do not run off in all directions. It is a state where Papańca has been tamed, a state very conducive to seeing things as they are.
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/ Revised 16 July 12