samatha after vipassana

Can one correctly practice anapanasati when one is very used to vipassana?

The above has never practiced real vipassana if this question is asked. Brainwashing oneself via Goenka or Mahasai mental gymnastics is not vipassana.

Vipassana is not continuous mental noting. Nor is vipassana enduring pain & trying to see changing pain sensations.

Vipassana starts with directly seeing what is easily, simply, obviously & clearly seen to be impermanent & not-self.

For example, each in breath & each out breath is directly seen (without any thinking) to be impermanent; in that each breath appears, lasts, moves then disappears. Also, it is directly seen (without any thinking) the breathing or body breathes itself (rather than the sense of 'self' breathes). When it is experienced the body breathes rather than the 'self' breathes, this is seeing not-self (anatta) of the breathing & body.

This is vipassana while doing anapanasati.

Can one correctly practice vipassana when one is very used to anapanasati or any other samatha practice?

Anapanasati is not exclusively samatha. Steps 4, 8, 10 & 11 of Anapanasati are related to samatha.

Steps 3 (called experiencing all bodies), 5, 6, 7, 9, 12, 13, 14, 15 & 16 of Anapanasati are related to vipassana.

A person who is used to vipassana is supposed to turn off the habit of seeing things as they are?

Brainwashing oneself is not seeing things as they are. Truly seeing the way things are involves only direct seeing & does not involve any "thinking" or "mental noting". If one truly had the habit of seeing things as they are then one would be an Arahant.

Can vipassana be useful during anapanasati or would it be more of a distraction to onepointed consentration?

Both ideas above of 'vipassana' & 'one-pointed concentration' are wrong.

For example, developing samatha with anapanasati does not necessarily involve being "one-pointed" with a narrow focus (such as Goenka watching the nose-tip). When the mind is equanimous, non-attached, naturally awake, silent, open & clear, the breathing will calm & samatha will be felt. Vipassana will also occur.

Directly seeing the mental conditions or causes that result in samatha is also an insight of vipassana. Seeing directly interactive processes of 'cause & effect' is vipassana.

MN 149 says when the eightfold path is developed, which includes anapanasati/satipatthana as the 7th factor, the result will be samatha & vipassana occurring in tandem.

For him, having thus developed the noble eightfold path... these two qualities occur in tandem: tranquillity & insight.

MN 149

Vipassana and samatha are ultimately the same practice. You can't practice one without the other. The more you proficient you become in one, the more effective the other will be.

I think how samatha can aid in - I'd even say undergirds - vipassana practice is well established specifically in the suttas. This is basically the path that the Buddha used under the Bodhi Tree. With his mind made malleable by jhana, bright, and unblemished, he turned his attention to latent mental content and saw its impermanence, non-self, and inherent suffering. You don't necessarily have to use the fancy subjects that the Buddha used. Just experiencing the sound of water dripping from a facet can be enough vipassana to liberate a mind made bright by jhana practice. You also don't necessarily have to achieve jhana to arrive at insight, but a certain degree of calm is required in order for insight to occur (how much calm/samatha is a debatable topic which is outside the scope of this post). The important take away, of course, is that ruminating alone won't get you there. Just noting won't get you there either, not without some degree of calm. Our normal waking mind is entirely too unsteady and diffuse to observe reality in any kind of sincere and effective way. Unification is necessary. There's a reason, after all, why a vipassana retreat isn't an out patient program! Retreats help settle our minds. They are one kind of seclusion from which rapture, bliss, and other jhana factors can be born.

How vipassana can aid in samatha is a bit more tricky to explain, but I think this largely because so many people misunderstand what samatha actually is. Don't think of it as concentration practice. Think of it as a balancing act. Any talk of one pointedness refers to the one spot you've chosen for your mind to settle (e.g. the breath, the tip of your nose, a kasina, etc.). Just as you wouldn't push up on a broom stick balanced on your fingertip, you likewise shouldn't apply any force to that single point of attention. Viewed this way, vipassana in the context of samatha practice starts to make a little more sense. Just as that broom stick might start veer to the left, so too might doubt (or any of the hindrances) cause your attention to slip off that settling point. When these distractions arise, you simply note them. This is usually enough to get them to pass, at least temporarily. When they do, just let your mind settle back on its own. You might find the same distraction rising over and over again. Just keep repeating the process. It's important to be aware that if you over correct - if you really try to banish whatever is distracting you - your mind will become completely destabilized just as that broom stick would go flying if you made any exaggerated motions. As the Xin Xin Ming puts it, "when you try to stop activity to achieve passivity, your very effort fills you with activity". Just let things be in their own way. It is the nature of things to pass away.

Over the course of a sit, you'll have these little instances of vipassana literally hundreds of times. Every time you do, the mind settles a little more heavily on your balance point. After a time, that balance point begins to take on a gravity of its own. You can actually feel the weight of it. Now, when distractions do arise, your mind is pulled back to your settling point. Noting them becomes less of a necessity. Eventually, that weight reaches a critical mass. Like a black hole, you feel its energy, its enormity, but...a repulsion. If you aren't afraid (noting and passing through fear and aversion is one instance of vipassana you still have to make; the gate to jhana is made of swords), that repulsion inverts into an inescapable pull, energy becomes rapture, and 'you' disappear into the singularity of full absorption.

So a little vipassana for your samatha, a little samatha for your vipassana. You can't ignore one and hope to develop the other.

OP: Simultaneous vipassana & samatha - in this version of the question

(Yuga,naddha) Paṭipadā Sutta mention there are 4 types of practitioners:

(1) “insight preceded by calm” - samatha,pubb’angama vipassanā

(2) “calm preceded by insight” - vipassana,pubb’angama samatha

(3) “calm coupled with insight” - samatha,vipassana,yuga.naddha

(4) “a mind seized by dharma-restlessness” - dhamm’uddhacca,viggahita manasa

Practising Samatha and Vipassana together is:

(3) “calm coupled with insight” - samatha,vipassana,yuga.naddha

Regardless of which practice you start with, both Samatha and Vipassana is needed to reach the ultimate goal:

(Mūla) Samatha Vipassanā Sutta

Also, it is best one allocate time for both:

Catu Kāla Sutta 1

Also, vipassana practises (body contemplation - breath meditation, posture, movement, body parts, elements, corpse) leads to Samadhi as per Kaya,gatā,sati Sutta:

As he dwells thus diligent, exertive, resolute, his memories and thoughts of the household life are abandoned. With their abandoning, his mind steadies itself internally, settles, becomes one, attains samadhi [becomes concentrated].

In this way, bhikshus, a monk cultivates mindfulness regarding the body.

Which intern leads to the 6 super knowledges:

Kaya,gatā,sati Sutta

Edit:

OP: samatha after vipassana

This is:

(1) “insight preceded by calm” - samatha,pubb’angama vipassanā

.

OP: Can one correctly practice anapanasati when one is very used to vipassana?

Anapanasati is also a form of vipassana which takes you to the highest goal of Nibbana.

Source: Anapanasati

Can one correctly practice vipassana when one is very used to anapanasati or any other samatha practice?

If you are skilled in Vipassana it is recommended to seek a Samatha teacher and practice Samatha:

Source: (Samatha Vipassanā) Samādhi Sutta 3

(Samādhi) Bala Sutta describes how one should develop skills in Samatha:

OP: A person who is used to vipassana is supposed to turn off the habit of seeing things as they are?

No, not necessarily:

Even this first dhyana is (mentally) constructed [mind-made], intentionally formed.

What is constructed and intentionally formed is impermanent, subject to ending.

If he is steady therein, he attains the destruction of the mental influxes.

Similarly in other Jhanas as given in Aṭṭhaka,nāgara Sutta

Here one sees the true nature of things while doing Samatha/Samadhi.

Also, Saṅkhitta Dhamma Sutta discusses the teachings in concise form, mentions the practice of mindfulness with Jhana ultimately resulting in full enlightenment:

When, bhikshu, this samadhi has been cultivated, well cultivated by you, then you should train yourself thus:

“I will dwell exertive, clearly aware, mindful,

observing [contemplating] [body | feeling | mind | dhamma] the in the [body | feeling | mind | dhamma],

removing covetousness and displeasure [discontent] in regard to the world.”

Thus, bhikshu, you should train yourself.

When, bhikshu, this samadhi has been cultivated, well cultivated by you, then, you, bhikshu,

THE 1 ST DHYANA:

should cultivate this samadhi with initial application, with sustained application;

should cultivate this samadhi without initial application, with only sustained application;

THE 2 ND DHYANA:

should cultivate this samadhi without initial application, without sustained application;

should cultivate this samadhi with zest;

THE 3RD DHYANA:

should cultivate this samadhi zest-free;

should cultivate this samadhi attended by comfort;

THE 4 TH DHYANA:

should cultivate this samadhi attended by equanimity.

Saṅkhitta Dhamma Sutta

OP: Can vipassana be useful during anapanasati or would it be more of a distraction to onepointed consentration?

Each triad corresponds to a Satipattana, which is Vipassana.

The last triad of Anapanasathis is explicitly to see things as they are which is vipassana:

Source: Ānâpāna,sati Sutta

Essentially one is doing Vipassana when one is doing Anapanasati.

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The need of Samadhi in tandem is evident from the following Suttas.

Also, a meditation how can attain and also have a theoretical understanding of Samadhi is the foremost meditator:

Samādhi Samāpatti Sutta. Similar one who understands Samadhi can remain in Samadhi is the foremost:

Samādhi Mūlaka Ṭhiti Sutta

Similarly, one who understands and skilful in emerging from Samadhi is the foremost meditator. - Samādhi Mūlaka Vuṭṭhāna Sutta

Similarly, one who understands samadhi and is fitfor Samadhi is the foremost meditator. - Samādhi Mūlaka Kallita Sutta

Similarly, one who is understands samadhi and is skilled in the concentration object is the foremost meditator. - Samādhi Mūlaka Ārammaṇa Sutta

Similarly, one who understands and resorts to samadhi is the foremost meditator. - Samādhi Mūlaka Go,cara Sutta

Similarly, one who understands and has resolution in samadhi is the foremost meditator. - Samādhi Mūlaka Abhinīhāra Sutta

Similarly, one who understands and care about samadhi is the foremost meditator. - Samādhi Mūlaka Sakkacca,kārī Sutta

Similarly, one understands and is committed to samadhi is the foremost meditator. - Samādhi Mūlaka Sātacca,kārī Sutta

Similarly, one who understands and is skilled in what is suitable regarding samadhi is the foremost meditator. - Samādhi Mūlaka Sappāya,kārī Sutta

Following skills:

Himavanta Sutta. Also Vasa Suttā which includes theoretical knowledge.

And the following masteries are useful: