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In the Mahasatipatthana-Sutta are mentioned three kinds of sensations: pleasant sensations (dukkha vedana); unpleasant sensations (sukha vedana) and adukkhamasukha vedana.

What is the meaning of adukkhamasukha vedana? What are those sensations?

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adukkhamasukha vedana is neither painful nor pleasant feeling i.e. neutral feelings.

The definition of the 3 feelings come in MN 44 and their relationships to the 3 underlying tendencies towards greed, repulsion and ignorance:

“Pleasant feeling is pleasant when it remains and painful when it perishes.

Painful feeling is painful when it remains and pleasant when it perishes.

Neutral feeling is pleasant when there is knowledge, and painful when there is ignorance.”

“The underlying tendency for greed underlies pleasant feeling. The underlying tendency for repulsion underlies painful feeling. The underlying tendency for ignorance underlies neutral feeling.

In Contemplation of Feeling, Nyanaponika Thera explained this:

Pleasant feeling is habitually linked with enjoyment and desire; unpleasant feeling with aversion; neutral feeling with boredom and confusion, but also serving as background for wrong views.

Also in SN 36.5:

“Mendicants, there are these three feelings. What three? Pleasant, painful, and neutral feeling. Pleasant feeling should be seen as suffering. Painful feeling should be seen as a dart. Neutral feeling should be seen as impermanent. When a mendicant has seen these three feelings in this way, they’re called a mendicant who has cut off craving, untied the fetters, and by rightly comprehending conceit has made an end of suffering.

The neither-pleasant-nor-painful feelings also known as neutral feelings. For e.g. the sight of the room that you're in, may not invoke any pleasant or painful feelings. It's neutral.

For e.g. if you look at a calendar, for days of a certain month, it may not invoke any painful or pleasant feelings. It's neutral. But when you see the date of your birthday, it may invoke memories of past birthday events and those memories may be pleasant feelings.

Neutral feelings normally make us bored or dissatisfied. Cravings would lead one to seek pleasures (kama tanha) or to become something or achieve something (bhava tanha) rather than sit around all day experiencing neutral feelings that don't bring satisfaction.

No feelings at all, would also be a cause for boredom and dissatisfaction. From the same article by Nyanaponika Thera, we read the commentary of the suttas and his comment:

Comy.: "From the fourth Jhana onwards, it is the neither-painful-nor-pleasant feeling (that is present in these meditative states). But this neutral feeling, too, is called 'pleasure' (sukha), on account of its being peaceful and sublime. What arises by way of the five cords of sensual desire and by way of the eight meditative attainments is called 'pleasure as being felt' (vedayita-sukha). The state of Cessation of Perception and Feeling is a 'pleasure, not being felt' (avedayita-sukha). Hence, whether it be pleasure felt or not felt, both are assuredly 'pleasure,' in the sense of their being painfree states (niddukkhabhava-sankhatena sukhena)."

In AN 9.34, the venerable Sariputta exclaims: "Nibbana is happiness, friend; Nibbana is happiness, indeed!" The monk Udayi then asked: "How can there be happiness when there is no feeling?" The venerable Sariputta replied: "Just this is happiness, friend, that therein there is no feeling."

To the arahant, neutral feelings, no feelings and Nibbana are all pleasant.

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I think it's literally close to 'not suffering but not pleasure'

“And what is the pleasure-faculty? Any physical pleasure, physical comfort born of body-contact to be experienced as pleasure & comfort. That is called the pleasure-faculty.

“And what is the pain-faculty? Any physical pain, physical discomfort born of body-contact to be experienced as pain & discomfort. That is called the pain-faculty.

“And what is the happiness-faculty? Any mental pleasure, mental comfort born of intellect-contact to be experienced as pleasure & comfort. That is called the happiness -faculty.

“And what is the distress-faculty? Any mental pain, mental discomfort born of intellect-contact to be experienced as pain & discomfort. That is called the distress-faculty.

“And what is the equanimity-faculty? Anything, physical or mental, to be experienced as neither comfort nor discomfort. That is called the equanimity-faculty.

“With regard to this, the pleasure-faculty & happiness-faculty are to be seen as a feeling of pleasure. The pain-faculty & distress-faculty are to be seen as a feeling of pain. The equanimity-faculty is to be seen as a feeling of neither pleasure nor pain. Thus, by this exposition, the five are three; and the three, five.” https://www.dhammatalks.org/suttas/SN/SN48_38.html

"'The thirty-six states to which beings are attached should be known': thus was it said. And in reference to what was it said? Six kinds of household joy & six kinds of renunciation joy; six kinds of household distress & six kinds of renunciation distress; six kinds of household equanimity & six kinds of renunciation equanimity.

"And what are the six kinds of household joy? The joy that arises when one regards as an acquisition the acquisition of forms cognizable by the eye — agreeable, pleasing, charming, endearing, connected with worldly baits — or when one recalls the previous acquisition of such forms after they have passed, ceased, & changed: That is called household joy. (Similarly with sounds, smells, tastes, tactile sensations, & ideas.)

"And what are the six kinds of renunciation joy? The joy that arises when — experiencing the inconstancy of those very forms, their change, fading, & cessation — one sees with right discernment as it actually is that all forms, past or present, are inconstant, stressful, subject to change: That is called renunciation joy. (Similarly with sounds, smells, tastes, tactile sensations, & ideas.)

"And what are the six kinds of household distress? The distress that arises when one regards as a non-acquisition the non-acquisition of forms cognizable by the eye — agreeable, pleasing, charming, endearing, connected with worldly baits — or when one recalls the previous non-acquisition of such forms after they have passed, ceased, & changed: That is called household distress. (Similarly with sounds, smells, tastes, tactile sensations, & ideas.)

"And what are the six kinds of renunciation distress? The distress coming from the longing that arises in one who is filled with longing for the unexcelled liberations when — experiencing the inconstancy of those very forms, their change, fading, & cessation — he sees with right discernment as it actually is that all forms, past or present, are inconstant, stressful, subject to change and he is filled with this longing: 'O when will I enter & remain in the dimension that the noble ones now enter & remain in?' This is called renunciation distress. (Similarly with sounds, smells, tastes, tactile sensations, & ideas.)

"And what are the six kinds of household equanimity? The equanimity that arises when a foolish, deluded person — a run-of-the-mill, untaught person who has not conquered his limitations or the results of action [2] & who is blind to danger [3] — sees a form with the eye. Such equanimity does not go beyond the form, which is why it is called household equanimity. (Similarly with sounds, smells, tastes, tactile sensations, & ideas.)

"And what are the six kinds of renunciation equanimity? The equanimity that arises when — experiencing the inconstancy of those very forms, their change, fading, & cessation — one sees with right discernment as it actually is that all forms, past or present, are inconstant, stressful, subject to change: This equanimity goes beyond form, which is why it is called renunciation equanimity. (Similarly with sounds, smells, tastes, tactile sensations, & ideas.) https://www.accesstoinsight.org/tipitaka/mn/mn.137.than.html

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